Volume 12, Issue 1

In this study, a numerical approach is presented to solve the linear and nonlinear hyperbolic Volterra integrodifferential equations (HVIDEs). The regularization of a Legendre-collocation spectral method is applied for solving HVIDE of the second kind, with the time and space variables on the basis of Legendre-Gauss-Lobatto and Legendre-Gauss (LG) interpolation points, respectively. Concerning bounded domains, the provided HVIDE relation is transformed into three corresponding relations. Hence, a Legendre-collocation spectral approach is applied for solving this equation, and finally, ill-posed linear and nonlinear systems of algebraic equations are obtained; therefore different regularization methods are used to solve them. For an unbounded domain, a suitable mapping to convert the problem on a bounded domain is used and then apply the same proposed method for the bounded domain. For the two cases, the numerical results confirm the exponential convergence rate. The findings of this study are unprecedented for the regularization of the spectral method for the hyperbolic integrodifferential equation. The result in this work seems to be the first successful for the regularization of spectral method for the hyperbolic integrodifferential equation.

In this article, we study the generalized q q -deformed sinh-Gordon equation analytically using the new general form of Kudryashov’s approach and numerically using the finite difference method. We develop a general form of the Kudryashov method that contains more than one constant that is used to give more explanations for the solutions that are obtained. The numerical results are also presented using the finite difference approach. We also provide numerous figures to demonstrate the various solitons propagation patterns. The proposed equation has opened up new options for describing physical systems that have lost their symmetry. The equation under study has not been studied extensively, so we completed the lesson that started a short time ago on it.

This work tackles the problem of attitude control of a space-based synthetic aperture radar with a deployable reflector antenna, representing a lightly damped uncertain vibratory system with highly nonlinear dynamics. A control strategy based on two identifiable in-orbit vector parameters is proposed to make the robust controller less conservative. The first parameter is used in the feedforward loop to achieve a trade-off between the energy efficiency of maneuvers and the amplitudes of the oscillatory response. The feedback loop utilizes the second parameter to accurately handle the controller-structure interactions by adaptive notch filters. The notch filters are included in the augmented plant at the design stage to guarantee closed-loop robustness against disturbances, unmodeled dynamics, and parametric uncertainty. The system’s robustness and specified requirements are confirmed by formal criteria and numerical simulations using a realistic model of the flexible spacecraft.

Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering. The aim of current study is to apply the well-known optimal homotopy asymptotic method (OHAM) on a specific and famous model of these equations. It is illustrated that auxiliary functions and the number of Taylor series terms affect the accuracy of the solution. Hence, at first a solution has been found with an acceptable error by OHAM. Then, it has been continued to attain a better solution by Multistep optimal homotopy asymptotic method. All these processes had improved the precision of the solution. Auxiliary polynomials of two, three, and four degrees and different numbers of Taylor series term have been investigated to solve a nonlinear system derived by two biological species ‎living together. Ultimately, appropriate results with auxiliary polynomials of degree four and Taylor series with six terms have been obtained precisely. In addition, the error values decrease significantly compared to the other cases.

In this article, we consider the flow of a Burgers’ fluid of transient electro-osmotic type in a small tube with a circular cross-section. Analytical results are found for the transient velocity and, electric potential profile by solving the Navier–Stokes and the linearized Poisson–Boltzmann equations. Moreover, these equations are solved with the help of the integral transform method. We consider cases in which the velocity of the fluid changes with time and those in which the velocity of the fluid does not change with time. Furthermore, special results for classical fluids such as Newtonian, second grade, Maxwell, and Oldroyd-B fluids are obtained as the particular cases of the outcomes of this work and that these results actually strengthen the results of the solution. This study of the nonlinear problem of Burgers’ fluid in a specified physical model will help us to understand the behavior of blood clotting and the block of any kind of problem in which this type of fluid is used. The solution of the complex velocity profile of Burgers’ fluid will help us in the future to solve the problems in which this transient electro-osmotic type of small tube is involved. At the end, numerical results are shown graphically that can help us to understand the complex behavior of the Burgers’ fluid, and also the analysis of the Burgers’ fluid shows dissimilarity with other fluids that are considered in this work.

Artificial intelligence has been applied to many fields successfully and saved many human and material resources. The intelligent examination system is a typical application case, which makes teachers can not only master the study situation of every candidate at any time but also design further study plans with the help of the examination system. A self-optimization examination system is shown in this paper, which is carried out by an improved particle swarm optimization. The intelligent examination system can surmount two difficulties shown in the construction of the traditional examining system, one is the setting of the attributes of the examination questions, and another is the maintenance of the database of the examination questions. The experiment shows that the novel method can not only optimize the attributes of the questions in the examination database intelligently but also maintain the examination database effectively through massive training.

The improvement in thermal performance of fluid and the control of energy loss are equitably significant. Therefore, the purpose of this study is to analyze entropy generation, stagnation point flow, and thermal characteristics of non-Newtonian third-grade modified hybrid nanofluid generated by a stretchable/shrinkable Riga plate in a porous medium with varying flow viscosity. In this analysis, a modification of hybrid nanofluid is considered by using pure water as a base fluid and three various nanomaterials (aluminium oxide, copper, and nickel) as nanoparticles in the characterization of heat transfer. Furthermore, the contribution of heat source/sink and viscous dissipation are accounted for in the model. The suited transformations are enforced to remodel the governing mathematical equations to produce ordinary differential equations that are conveniently tackled via spectral quasilinearization method (SQLM) along with the overlapping grid idea to yield numerical solutions. The preference of this approach over others has been justified through discussion of error bound theorems, residual and solution errors, computational time, and conditioning of matrices. The physical significance of disparate governing parameters on flow variables, velocity gradient, thermal rate, and entropy generation are scrutinized through graphs and tables. Crucial findings of the study include that temperature of the modified hybrid nanofluid enhances quickly (better thermal conductor) than temperature of single nanofluid, hybrid nanofluid, and conventional third-grade fluid for higher Biot number, variable viscosity, and heat source parameters. Mass suction enhances fluid flow and physical quantities of interest, but suppresses the fluid temperature. An increase in variable fluid viscosity, modified Hartmann number, and third-grade parameters enhances the wall drag coefficient while lowering the rate of heat transfer, and the opposite is true for porous media. More entropy is generated in the system by high variable fluid viscosity, suction, viscous dissipation, modified Hartman number, and non-Newtonian parameters. Owing to high velocity and temperature associated with modified hybrid nanoparticles, modified hybrid technology is recommended in enhancing the physical attributes of the fluid with minimal cost effects. In engineering and industrial point of view, this study can contribute significantly in thermal improvement of the working fluid.

Due to the influence of crystal vibration, clock offset, and clock skew, time synchronization error will be caused. This study introduces several algorithms to reduce or eliminate the influence of time synchronization error on positioning results, including iterative time-of-arrival algorithm, linear position line algorithm, classical CHAN algorithm, quadratic programming algorithm, and an improved algorithm for quadratic programming problem using weighted least squares algorithm. They are applied to two-dimensional (2D) single target, 2D multi-target, three-dimensional, and various positioning scenarios considering the influence of clock skew and clock offset for the simulation test, which overcomes the defect that the previous algorithm simulation test has few application scenarios. The results show that the iterative time-of-arrival algorithm has smaller root mean square error, higher positioning accuracy, and stable positioning results, and the algorithm has universal applicability to each positioning scene with time synchronization error.

A top drive is an essential mechanical device in oil field drilling since it provides the necessary torque for the drilling operations. Manufacturers in the oil and gas industry typically perform in-housing testing and classify the Safe Working Load of top drives. Testing a top drive requires a unique test stand, thus making testing top drives from other manufacturers a difficult challenge. A fixture adapter can be designed using geometric constraints and intuition to make testing apparatus semi-universal, yet they are often bulky and heavy, posing more significant safety concerns. This study aims to first numerically assess the existing fixture adapter and then structurally optimize it for enhancing its structural integrity and efficiency under various severe working environments. Therefore, finite element analysis (FEA) was performed on the existing fixture adapter, and compliance minimization topology optimization was employed. Four load and boundary conditions were used from the three most frequent operation scenarios for the fixture adapters: (i) drilling standby, (ii) staging area, (iii) drilling make-up, and (iv) break-up. The FEA results indicated that no safety factor was compromised with a 50% and 60% mass retention constraint via topology optimization compared to the original fixture adapter. The optimized fixture adapter was also tested under compression using printed 3D prototypes to validate the finite analysis and topology optimization processes.

Nonlinear adaptive sliding mode control (NASMC) has the capability to adequately control a system whose parameters are unknown to the controller designer. Conventional model-based controllers require a mathematical dynamic model of the system with known parameters. These system parameters are normally determined by extensive system identification experiments, which are expensive and time-consuming to perform. A NASMC approach that does not require known system parameters is proposed. Using NASMC, a controller designer can skip the expensive and time-consuming system parameter identification and fast-forward to the control implementation. In addition, once a controller is derived for a quadcopter using NASMC, the same controller will work on any quadcopter with the same equations of motion but different dynamic parameters. The formulation of the NASMC is presented for general second-order and fourth-order systems. Then, as an implementation example, the application of the general NASMC approach is demonstrated by applying it to a quadcopter unmanned aerial vehicle in simulation.

Via modified quartic hyperbolic B-spline DQM, Burgers’ equation is numerically approximated in the current study. Ten numerical instances are discussed, and the findings are compared with those already in existence and with exact results. Error norms are assessed, and findings are shown in tabular as well as graphical formats, to validate the resilience and applicability portion of established numerical system. Matrix stability analysis approach is used to discuss proposed scheme’s stability. The current plan is robust, precise, and simple to put into action.

To investigate the influence of high temperatures on the bond performance of recycled concrete and steel bar, this article considers the influence of different concrete types (ordinary concrete and recycled concrete) and different temperatures (20, 100, 150, 200, 250, and 300°C) on the concrete compressive strength and the bond performance of concrete and steel bar. On this basis, the calculation formula of bond strength and bond slip between concrete and steel bar after the high temperature is established. The test results show that the concrete compressive strength presents a downward trend with the increase in temperature; the compressive strength loss of recycled concrete is higher than that of ordinary concrete; when the temperature reached 300°C, the compressive strength loss of ordinary concrete is 24.4%, while that of recycled concrete is 41.6%. The bond strength of pull-out specimens decreases with the increase of temperature, while the bond slip increases with the increase of temperature; the bond strength between recycled concrete and steel bar is lower than that between ordinary concrete and steel bar, while the bond slip between recycled concrete and steel bar is higher than that between ordinary concrete and steel bar. This article can provide a theoretical basis for the application of recycled concrete in high-temperature environment.

Recently, the deformable derivative and its properties have been introduced. In this work, we have investigated the concept of deformable Laplace transform (DLT) in more detail. Furthermore, some classical properties of the DLT are also included. The Heaviside expansion formula and convolution theorem for deformable inverse Laplace transform are also discussed. Furthermore, some illustrative numerical examples are also discussed to validate the applicability of the proposed DLT and finally conclude the theory.

Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.

Via UAH tension B-spline DQM in the present research, numerical approximation of coupled Schrödinger equations in one and two dimensions is fetched. In the present research, a novel regime is generated as a fusion of a UAH tension B-spline of fourth-order and DQM to fetch the requisite weighting coefficients. To ensure the adaptability and effectiveness of the proposed regime, different numerical examples are elaborated. Present results are matched with previous results, and the elastic property is also validated for solitons. The fetched ordinary differential equations system is handled via the SSP-RK43 regime. The stability of the present method is verified via the matrix method. The robustness of the proposed regime is affirmed via error norms. The fetched results are acceptable and validated. Elasticity property via wave interaction is also covered in the present research. The present study also focuses on one very important property of physics, like elasticity, which is rarely discussed in the literature. The developed numerical regime will undoubtedly be useful in addressing various fractional partial differential equations of complex nature as well.

In this article, the bond performance between recycled concrete and corroded steel bars is analyzed by the nonlinear numerical simulation. The result shows that the maximum bond strength between recycled concrete and steel bar decreases with the increase in steel bar corrosion rate; when the recycled concrete strength is large, the simulated maximum bond strength is in good agreement with the experimental maximum bond strength; when the recycled concrete strength is small, the simulated maximum bond strength is in relatively poor agreement with the experimental maximum bond strength, but there is still an error within the allowable range; the slip between recycled concrete and steel bar increases with the increase in steel bar corrosion rate; when the steel bar corrosion rate exceeded 5%, the bond strength decreases more rapidly; the maximum bond strength increases with the increase in specimen sizes under the same steel bar corrosion rate; the maximum bond strength decreases with the increase in steel bar diameter under the same steel bar corrosion rate.

In the present study, 1D, 2D, and 3D fractional hyperbolic telegraph equations in Caputo sense have been solved using an iterative method using Sawi transform. These equations serve as a model for signal analysis of electrical impulse transmission and propagation. Along with a table of Sawi transform of some popular functions, some helpful results on Sawi transform are provided. To demonstrate the effectiveness of the suggested method, five examples in 1D, one example in 2D, and one example in 3D are solved using the proposed scheme. Error analysis comparing approximate and exact solutions using graphs and tables has been provided. The proposed scheme is robust, effective, and easy to implement and can be implemented on variety of fractional partial differential equations to obtain precise series approximations.

The application of nanoparticles in the base fluids strongly influences the presentation of cooling as well as heating techniques. The nanoparticles improve thermal conductivity by fluctuating the heat characteristics in the base fluid. The expertise of nanoparticles in increasing heat transference has captivated several investigators to more evaluate the working fluid. This study disputes the investigation of convection flow for magnetohydrodynamics second-grade nanofluid with an infinite upright heated flat plate. The fractional model is obtained through Fourier law by exploiting Prabhakar fractional approach along with graphene oxide ( GO ) ({\rm{GO}}) and molybdenum disulfide ( Mo S 2 ) ({\rm{Mo}}{{\rm{S}}}_{2}) nanoparticles and engine oil is considered as the base fluid. The equations are solved analytically via the Laplace approach. The temperature and momentum profiles show the dual behavior of the fractional parameters ( α , β , γ ) (\alpha ,\beta ,\gamma ) at different times. The velocity increases as Grashof number {\rm{Grashof\; number}} increases and declines for greater values of magnetic parameter and Prandtl number. In the comparison of different numerical methods, the curves are overlapped, signifying that our attained results are authentic. The numerical investigation of governed profiles comparison shows that our obtained results in percentages of 0.2 0.2 ≤ temperature ≤ 4.36 4.36 and velocity 0.48 ≤ 7.53 0.48\le 7.53 are better than those of Basit et al. The development in temperature and momentum profile, due to engine oil–GO is more progressive, than engine oil–MoS 2 .

In this article, the sensitivity coefficients of dynamic characteristic damage identification of blades with different sizes were investigated. The results show that the first third-order vibration modes of the blade before and after damage are consistent, and the wind turbine blade size has no significant effect on the vibration mode; with the increase of the blade size, the first-, third- and fourth-order natural frequency sensitivity coefficients decrease gradually, while the second-, fifth- and sixth-order natural frequency sensitivity coefficients increase gradually; as the blade size increases, the third-order displacement mode sensitivity coefficient of the blade gradually increases, which indicates that the displacement modes identification effect is better with the increase of the blade size. With the increase of the blade size, the first- and third-order strain modal sensitivity coefficients increase gradually, which indicates that when using first- and third-order strain modes for damage identification, the larger the blade size, the better the identification effect; with the increase of the blade size, the second-order strain modal sensitivity coefficient decreases gradually, which indicates that when using second-order strain mode for damage identification, the larger the blade size, the worse the identification effect. This research could provide a theoretical basis for the application of the dynamic characteristic damage identification method in the damage identification of wind turbine blades of different sizes.

A mathematical model is presented to analyze the double diffusive transport of hybrid nanofluids in microchannel. The hybrid nanofluids flow is driven by the cilia beating and electroosmosis in the presence of radiation effects and activation energy. Cu–CuO/blood hybrid nanofluids are considered for this analysis. Phase difference in the beatings of mimetic cilia arrays emerge symmetry breaking pump walls to control the fluid stream. Analytical solutions for the governing equations are derived under the assumptions of Debye–Hückel linearization, lubrication, and Rosseland approximation. Dimensional analysis has also been considered for applying the suitable approximations. Entropy analysis is also performed to examine the heat transfer irreversibility and Bejan number. Moreover, trapping phenomena are discussed based on the contour plots of the stream function. From the results, it is noted that an escalation in fluid velocity occurs with the rise in slippage effects near the wall surface. Entropy inside the pump can be eased with the provision of activation energy input or by the consideration of the radiated fluid in the presence of electroosmosis. The results of the present study can be applicable to develop the emerging thermofluidic systems which can further be utilized for the heat and mass transfer at micro level.

In the present research study, time-fractional hyperbolic telegraph equations are solved iteratively using natural transform in one, two, and three dimensions. The fractional derivative is considered in the Caputo sense. These equations serve as a model for the wave theory process of signal processing and transmission of electric impulses. To evaluate the validity and effectiveness of the suggested strategy, a graphical comparison of approximated and exact findings is performed. Convergence analysis of the approximations utilising L ∞ {L}_{\infty } has been done using tables. The suggested approach may successfully and without errors solve a wide variety of ordinary differential equations, partial differential equations (PDEs), fractional PDEs, and fractional hyperbolic telegraph equations. Graphical abstract

In this article, analytical solutions of couple stress fluid flow modeled with a power law fractional differential operator are discussed. Stokes’ second problem for an incompressible couple stress fluid is studied for an horizontal plate of infinite length. The governing equations of the flow problem are expressed in terms of a partial differential operator and then converted into a non-dimensional model by using dimensional analysis. Then the integer order problem was formulated in terms of the non-integer order of three types of fractional derivatives and then solved with the help of the Laplace transform method. The obtained solutions are complex and expressed in terms of series. In order to check the memory index of the solutions obtained with three different fractional operators, we have plotted some graphs. It is found that the constant proportional operator provides us a better choice about the memory and maximum enhancement achieved in the comparison of Caputo and Caputo–Fabrizio. Furthermore, in order to check the accuracy of the present results, we have compared the obtained solutions with the existing literature and found a good agreement between them.

In this study, the Caputo-type fractional time-derivative is simulated by inserting a proportional time-delay into the field function of the perturbed-KdV equation. Two effective methods have been adapted to obtain analytical solutions for this model. Then, independently, the effect of the fractional derivative and the proportional delay on the topological shape of the pKdV propagation was extrapolated. The significant conclusions of the current article reveal that the fractional derivative plays the same role as the presence of a proportional delay in the time coordinate if it is assigned as a substitute for it. With this, from a practical mathematical point of view, we have provided one of the geometric explanations of the fractional derivative. Finally, via the obtained approximate solution, we studied the impact of the perturbed coefficient on propagating the waves of the proposed KdV model.

This article deals with the problem of finding a pricing formula for weather derivatives based on temperature dynamics through an uncertain differential equation. Weather-related derivatives are being employed more frequently in alternative risk portfolios with multiple asset classes. We first propose an uncertain process that uses data from the past to describe how the temperature has changed. Despite this, pricing these assets is difficult since it necessitates an incomplete market framework. The volatility is described by a truncated Fourier series, and we provide a novel technique for calculating this constant using Monte Carlo simulations. With this approach, the risk is assumed to have a fixed market price.

Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations and subject to axial loads. The elastic layer connecting the beams are modelled as a three-parameter nonlinear Winkler–Pasternak layer with the Winkler layer having linear and nonlinear components and Pasternak layer having only a linear component. Variational principles are derived for the forced and freely vibrating double beam system using a semi-inverse approach. Hamilton’s principle for the system is given and the Rayleigh quotients are derived for the vibration frequency of the freely vibrating system and for the buckling load. Natural and geometric variationally consistent boundary conditions are derived which leads to a set of coupled boundary conditions due to the presence of Pasternak layer connecting the beams.

In this research article, a nonlinear time–space fractional order (4+1)-dim Fokas wave equation that is crucial for examining the corporal marvels of waves on and inside the surface of water is examined. For this purpose, a well-known analytical method is utilized, namely, the Sardar sub-equation (SSE) method along with a truncated M-fractional derivative. As a result, many new families of solitary wave solutions, such as kink-type solitons, singular and periodic solitons, dark and bright solitons, are established. By using the SSE method, the outcomes are portrayed in 3-dim, 2-dim, and contour plots for distinct parametric values. The attained hyperbolic and trigonometric function-type results demonstrate the capability of recognizing the exact solutions of the other nonlinear evolution equations through the executed technique.

To reduce the hazards of collapse accidents in the construction process and to ensure that the lives, health, and property of construction workers are protected, this study used the theory of safety system engineering to identify the hazards of collapse accidents, analyze the hazards, predict the consequences, evaluate the systemic risks, and evaluate the effects and improve them. At the same time, the risk factors of collapse were evaluated qualitatively and quantitatively by using the analysis methods of fault tree analysis (FTA) and the analytic hierarchy process (AHP). Finally, according to the evaluation results, the main factors causing collapse accidents were found; this provided a reliable and practical basis for the prevention of collapse accidents. Then, according to the decisive factors, corresponding measures were taken in advance to achieve the aim of preventing and controlling collapse accidents. The results show that equipment maintenance, material inspection, and construction site safety management play an important role in preventing collapse accidents.

In this study, a new structure for the septic B-spline collocation algorithm in n -dimensional is presented as a continuation of generating B-spline functions in n -dimensional to solve mathematical models in n -dimensional. The septic B-spline collocation algorithm is displayed in three forms: one dimensional, two dimensional, and three dimensional. In various domains, these constructs are essential for solving mathematical models. The effectiveness and correctness of the suggested method are demonstrated using a few two- and three-dimensional test problems. The proposed new structure provides better results than other methods because it deals with a larger number of points than the field. To create comparisons, we use different numerical approaches accessible in the literature.

In this study, the gray box method has been used to model traffic accidents for the first time. This work examines the problem of estimating and identifying a single-input single-output state-space system. In this way, the state-space model was used, which has both a black box section (experimental data) and the parameters have been estimated by acquiring prior knowledge (white box). First, the state-space of the desired system is formed, and the algorithm for estimating the parameters and their convergence and the state vector estimation algorithm are written. In comparison, the system changes from nonlinear to linear. The parameters and prior knowledge are entered from the system. Finally, by implementing the presented method on the data related to the factors affecting accidents in Qazvin (Iran), the accuracy of the presented materials is investigated. The error output shows that initially, the error increased slightly, but then it shows a downward trend, and with the increase in the data, the error tends to zero (0.658). The results also show good fit and optimal accuracy of the model in less processing time.

In this article, the inverse time problem is investigated. Regarding the ill-posed linear problem, utilize the quasi-reversibility method first. This problem has been regularized and after that provides an iterative regularizing strategy for noisy input data that are based on homotopy. For the regularizing solution, the error analysis is proved when we employ noisy measurement data as our initial guess. Finally, numerical implementations are presented.

The significance of different types of periodic solutions in nonlinear equations is vital across various practical applications. Our objective in this study was to uncover novel forms of periodic solutions for the modified regularized long wave equation. This particular model holds great importance in the realm of physics as it characterizes the propagation of weak nonlinearity and space-time dispersion waves, encompassing phenomena like nonlinear transverse waves in shallow water, ion-acoustic waves in plasma, and phonon waves in nonlinear crystals. By employing the methodology of modified rational sine-cosine and sinh–cosh functions, we successfully derived new kink-periodic and convex–concave-periodic solutions. To showcase the superiority of our proposed approach, we conducted a comparative analysis with the alternative Kudryashov-expansion technique. Furthermore, we visually depicted the diverse recovery solutions through 2D and 3D plots to enhance the understanding of our findings.

In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The L ∞ {L}_{\infty } and L 2 {L}_{2} norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm.

On September 22, 2022, a spacecraft, designed by the Double Asteroid Redirection Test (DART) team, successfully attempted to deflect the orbit of the asteroid Dimorphos, which together with Didymos, constitutes a binary system of near-Earth asteroids orbiting around the Sun. The effect of the impact of the spacecraft was to shorten the orbit of Dimorphos of about 33 min with respect to the original one. In this communication, a simple nonlinear circuit emulator based on a mathematical model allowing the emulation of the DART mission behavior is presented. The modeling is approached referring to the Kepler problem that leads to a highly nonlinear dynamical model. The problem is approached numerically, by using appropriate integration algorithms for both the two-body and three-body formulations of the problem, and experimentally, by means of an analog/digital electronic circuit emulator of the system that allows us to realize faster and qualitative more efficient experiments.

Damages on railway sleepers due to heavy impact loads induced by the movement of trains can be reduced by improving their impact resistance. Fibre-reinforced/pre-treated crumb rubber concrete sleepers (RCSs) have the potential to display significant impact resistance to withstand a high-magnitude impact load. The ideal proportions of pre-treated crumb rubber, steel fibres, and polypropylene fibres (PFs) can be identified based on the minimum cost-to-impact energy ratio after conducting a drop weight impact test on prisms. The numerical model developed to assess the behaviour of ballasted tracks has been validated using both simulation results and field measurements. Numerical studies have been conducted on ballasted rail tracks with steel and PF-reinforced/pre-treated RCSs using LS-DYNA software. Dynamic strain rate-dependent material parameters are introduced in the numerical simulations. The nonlinear effect of higher train speeds on dynamic track responses has been highlighted in this article. Although the static load-carrying capacity and modulus of elasticity of rubber concrete are low, their dynamic performance controls the track displacements from exceeding permissible limits. The outcome of this study will provide new insights into the effects of railway concrete sleepers incorporated with reinforced fibres and pre-treated crumb rubber on railway track performance in order to ensure safety and reliability before it is put into services.

Vector giant wave cluster solutions of (2+1)-dimensional coupled partially nonlocal nonlinear Schrödinger equation are found by means of a coupled relation with the Darboux method. These vector optical field components display different excitation governance behaviors. The effective distance in the coupled relation has a maximum. Comparing this maximum with the excited values at the location of the giant wave peaks in the cluster, the excitation governance of giant wave cluster is achieved.

This article discusses the bifurcation analysis and control of a valve-controlled hydraulic cylinder system. The dynamic system of the valve-controlled hydraulic cylinder is established. Normal form theory and Hopf bifurcation theory are used to analyse the bifurcation characteristic at equilibria of the system. Then, a dynamic-state feedback control method is proposed. A nonlinear controller is set for the system to control the bifurcation with the method. By adjusting the control parameters, the delay of model bifurcation and the stability of the system can be changed. Numerical analysis verifies the correctness of bifurcation control.

The power grid (referred to as PG for convenience) structure is becoming increasingly complex. Aiming at the problem that it is difficult for traditional PG monitoring methods to accurately detect PG faults, an intelligent PG fault monitoring system is constructed using Internet of Things (IoT) and geographic information system (GIS) to improve the effectiveness of fault monitoring. The sensor equipment is used to collect the current information in the circuit, and the change of induced current is used to judge the cause of the fault, and the fault information is transmitted to the monitoring center through communication technology. The staff can directly locate the geographical location of the fault in the visual interface. One hundred overhead lines of Xianyang Power Supply Company are selected for analysis, and the performance of the traditional PG monitoring method and intelligent PG fault monitoring system is compared. The average fault detection accuracy of the traditional PG monitoring method and the system proposed in this article is 72.0 and 94.8%, respectively. The average fault location accuracy of the traditional PG monitoring method and this system is 80.8 and 96.5%, respectively. The intelligent monitoring system of PG fault based on IoT and GIS has high accuracy in PG fault detection and fault location, which can improve the effectiveness of fault monitoring.

In this work, the generalized scale-invariant analog of the Korteweg–de Vries equation is studied. For the first time, the tanh–coth methodology is used to find traveling wave solutions for this nonlinear equation. The considered generalized equation is a connection between the well-known Korteweg–de Vries (KdV) equation and the recently investigated scale-invariant of the dependent variable (SIdV) equation. The obtained results show many families of solutions for the model, indicating that this equation also shares bell-shaped solutions with KdV and SIdV, as previously documented by other researchers. Finally, by executing the symbolic computation, we demonstrate that the used technique is a valuable and effective mathematical tool that can be used to solve problems that arise in the cross-disciplinary nonlinear sciences.

Foreign object detection is one of the most critical issues in electric vehicle wireless charging systems. This article proposes a foreign object detection scheme with an induced coil in the charging system. The proposed method uses a multifunctional tunneling resistance sensor matrix to detect the presence of a foreign metal object between the coils. An asymmetrical induction coil design scheme is proposed to eliminate the blind area. The suggested method utilizes size-modulated c-shaped coil units to remove invisible zones that result from the magnetic field’s axial uniformity. The induced voltage in the transmission coil is measured using ANSYS/MAXWELL software. The experimental results show that the suggested method has a number of benefits over regular even-sensing coils, including higher uniformity in the induced current, position-dependent detection sensitivity, and detection accuracy. It provides a feasible and affordable way to get around the drawbacks of the traditional detecting coil.

This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.

A nonlinear Boussinesq equation under fractal fractional Caputo’s derivative is studied. The general series solution is calculated using the double Laplace transform with decomposition. The convergence and stability analyses of the model are investigated under Caputo’s fractal fractional derivative. For the numerical illustrations of the obtained solution, specific examples along with suitable initial conditions are considered. The single solitary wave solutions under fractal fractional derivative are attained by considering small values of time ( t ) \left(t) . The wave propagation has a symmetrical form. The solitary wave’s amplitude diminishes over time, and its extended tail expands over a long distance. It is observed that the fractal fractional derivatives are an extremely constructive tool for studying nonlinear systems. An error analysis is also carried out for compactness.

With the improvement of the accuracy of experimental devices and measuring instruments, cavitation experiments such as cross-media vehicles and propellers have been carried out in small pools. However, the water quality in the laboratory and the engineering application waters differs, especially the concentration of the gas nuclei that cause cavitation, resulting in experimental results that differ from prototype experimental results, and the scale effect occurs. In order to reduce the influence of the scale effect, according to the conditions of cavitation, gas nuclei can be mixed with water before the experiment is formally implemented. Aeration behavior will affect the size and concentration of gas nuclei (gas nuclei spectrum) in water. In order to obtain better experimental results, it is necessary to clarify the variation of the gas nuclei spectrum in small-scale experimental pools before and after aeration, so as to master aeration technology. Through research, it is found that the artificial aeration method can effectively change the gas nuclei spectrum in water and increase the concentration of gas nuclei. By using the underwater acoustic measurement method, the change in the gas nuclei spectrum can be captured sensitively. The gas nuclei spectrum in water after aeration is in good agreement with the mathematical model of gas nuclei spectrum under non-artificial intervention, which shows that the distribution of gas nuclei in water under artificial aeration is similar to that under non-artificial intervention, which is conducive to the occurrence of cavitation. At the same time, it shows that the combination of experiment and numerical method can reduce the measuring state and the measurement cost and improve the measurement efficiency.

It is well known that viral infections have a high impact on public health in multiple ways, including disease burden, outbreaks and pandemic, economic consequences, emergency response, strain on healthcare systems, psychological and social effects, and the importance of vaccination. Mathematical models of viral infections help policymakers and researchers to understand how diseases can spread, predict the potential impact of interventions, and make informed decisions to control and manage outbreaks. In this work, we formulate a mathematical model for the transmission dynamics of COVID-19 in the framework of a fractional derivative. For the analysis of the recommended model, the fundamental concepts and results are presented. For the validity of the model, we have proven that the solutions of the recommended model are positive and bounded. The qualitative and quantitative analyses of the proposed dynamics have been carried out in this research work. To ensure the existence and uniqueness of the proposed COVID-19 dynamics, we employ fixed-point theorems such as Schaefer and Banach. In addition to this, we establish stability results for the system of COVID-19 infection through mathematical skills. To assess the influence of input parameters on the proposed dynamics of the infection, we analyzed the solution pathways using the Laplace Adomian decomposition approach. Moreover, we performed different simulations to conceptualize the role of input parameters on the dynamics of the infection. These simulations provide visualizations of key factors and aid public health officials in implementing effective measures to control the spread of the virus.

This article develops duality principles, a related convex dual formulation and primal dual formulations suitable for the local and global optimization of non convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg–Landau type equation. Other applications include primal dual variational formulations for a Burger’s type equation and a Navier–Stokes system. We emphasize the novelty here is that the first dual variational formulation developed is convex for a primal formulation which is originally non-convex. Finally, we also highlight the primal dual variational formulations presented have a large region of convexity around any of their critical points.

In order to solve the problem of accumulation of glass waste seriously affecting people’s life safety, it is of great significance to study the crushing mechanism of glass waste. At present, no scholars have studied and analyzed the waste glass head, especially the single-axis compression test. In this study, a three-dimensional waste glass is established by discrete element software, and the single-axis compression characteristics of waste glass at different loading rates are analyzed by using Hertz contact model provided by the software. The results show that the loading rate is influenced by the equilibrium iteration rate and stress loading step length. The study also analyzes the pressure plate extruding waste glass in different positions. Finally, the stress–strain strength of five groups of waste glass under the action of uniaxial compression is analyzed, and the stress strength is between 0.3 and 0.56 MPa. This study provides a theoretical basis for further study of the breakage characteristics of waste glass under composite loading.

This research presents the spatial Durbin method, which may be used to analyze the relationship between economic educational attainment and economic development in China. The method accounts for regional dependence and variety when calculating the impact of economic education on a province economic development. A pedagogical economic strategy has also taken into account how varied the education model is while implementing it. The study’s conclusions, which were based on data from Chinese provinces, showed that China’s distribution of postgraduates (PGs) was geographically autocorrelated and unstable. This work contributes to existing in two ways. It quantifies the influence of postgraduate education on technical innovation in a big, quickly rising economy. The research assesses direct and indirect impacts to comprehend postgraduate education. Overall, PG education has a big impact on technological innovation. Three geographical weighting matrices were utilized in the research study to assess spatial overflow, and it was shown that PG education in nearby provinces greatly boosted innovation. The spatial overflow effect of the economic matrix (EM) was stronger than that of the matrix adjacent to it. In both the EM and the economic-geographical matrix, the spatial overflow impact of postsecondary education was bigger than its direct influence. This research contributes to an improved considerate of the characteristics and goals of PG training in a rapidly changing market.

In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross-rational propagation, and interaction between lump periodic and kink wave was examined. Some M-shaped solution, M-shaped interaction with periodic and kink, M-shaped interaction with rogue and kink, M-shaped rational solution, M-shaped rational solution with one kink, M-shaped rational solution with two kink, solutions for lump soliton waves, lump one kink waves, lump two kink waves, periodic-cross lump wave propagation, periodic wave propagation, rogue wave propagation, and multiwave propagation were also acquired. Likewise, our solution was also graphically presented, and also their stability was checked.

Mathematical models for infectious diseases can help researchers, public health officials, and policymakers to predict the course of an outbreak. We formulate an epidemic model for the transmission dynamics of Zika infection with carriers to understand the intricate progression route of the infection. In our study, we focused on the visualization of the transmission patterns of the Zika with asymptomatic carriers, using fractional calculus. For the validity of the model, we have shown that the solutions of the system are positive and bounded. Moreover, we conduct a qualitative analysis and examine the dynamical behavior of Zika dynamics. The existence and uniqueness of the solution of the system have been proved through analytic skills. We establish the necessary conditions to ensure the stability of the recommended system based on the Ulam–Hyers stability concept (UHS). Our research emphasizes the most critical factors, specifically the mosquito biting rate and the existence of asymptomatic carriers, in increasing the complexity of virus control efforts. Furthermore, we predict that the asymptomatic fraction has the ability to spread the infection to non-infected regions. Furthermore, treatment due to medication, the fractional parameter or memory index, and vaccination can serve as effective control measures in combating this viral infection.

In this work, an application of two noded beam finite element methodology, which is demonstrated in the previous research work for vibration analysis of beam with a flexible joint problem, has been further extended here to investigate the buckling behaviour of free–free beam subjected to an in-plane compressive load. Joint is modelled as rotational spring, where the rotational spring stiffness governs the behaviour of the flexible joint. Variation of first five non-dimensional buckling loads of free–free beam with reference to the joint location as well as joint stiffness parameters are briefly presented. It is understood that looseness of the joint can significantly influence the buckling behaviour of free–free beam and plays an important role in accurately determining the buckling behaviour of jointed beams subjected to an in-plane compressive loads.

To ensure the safe functioning of lifting equipment, a data mining-based optimization study of a crane failure predictive control system is provided. To diagnose lifting machinery faults, the system employs decision tree categorization. Using association rules, a correlation study of hoisting machinery defect and failure was performed. When the minimal confidence and support degree are entered, a total of 244 instances of 18 frequent itemset A9 (safety protection device) may be obtained, indicating that lifting machinery does not perform well in this category. A6 (main parts) and A9 appeared a total of 98 times, with support and confidence of 29.4 and 35.6, respectively, indicating that the main parts can detect that the safety protection device is also having problems. A7 (electrical control system) and A9 appeared a total of 67 times, with support and confidence of 20.1 and 27.3, respectively, indicating that the electrical control system can detect that the safety protection device is also having problems; the correlation between them was also quite large. The system’s feasibility and efficacy shows that it has some application value.

To explore the extraction of computer image scene and target information, a nonlinear method based on big data technology is proposed. The method can decompose the computer image into a plurality of components when the SAR computer image is processed such as target extraction and computer image compression, which represent different captured image features, respectively. Selecting the most suitable processing method according to the characteristics of different components can greatly improve the performance. Using nonlinear diffusion method, the computer image is decomposed into structural components representing large-scale structural information and texture components representing small-scale detailed information, and the automatic threshold estimation in the diffusion process is studied. The LAIDA criterion is introduced into the automatic threshold solution of nonlinear diffusion-based computer image decomposition to test and evaluate the diffusion process of various diffusion parameter forms. The results show that the experimental outcome of the diffusion decomposition based on automatic threshold estimation is very close on each index, which shows that using automatic threshold estimation, no matter what diffusion index is used, very close results can be obtained. Specifically, for each algorithm, the parameter estimation threshold l for outliers plays an obvious role. The third is the degree of initiative of the estimation process. The larger the L , the larger the outlier, which will lead to a greater extent of the diffusion process, resulting in a continuous decrease in the structural similarity index and compositional correlation. It is proved that the algorithm has strong global search ability, can effectively avoid premature convergence, has fast convergence speed, and good long stability. It can be widely used for optimization of various multimodal functions.

The most important and core technology of the Internet of things (IoT) is still the internet, and it also includes many other technical fields and is applied to many fields. The various processes of IoT data are the guarantee that the IoT can meet the management and management requirements in a certain application field, so that each application field can better meet the requirements of people’s lives. In order to study the nonlinear analysis and processing of software development data under the IoT monitoring system, this work uses QT software and socket programming to build the detection, control, and transmission module of the system, and uses multiple processes to classify and process the data. The user interface technology is used to display the data in real time. The system can control the type of transmitted data through interface operation. The classified transmission of data is realized, and the transmission speed is guaranteed to be about 50 MB/s. The experimental results show that after the functional design of each module is completed, the whole system is finally tested to determine whether the system can meet the requirements of data transmission, control, and processing. Since these data are simulated data, video playback is used to simulate the occurrence of a real accident. When an abnormal situation occurs, the whole system starts to work. If an accident occurs, a signal is sent after the accident. The system not only ensures the intellectualization of control, but also ensures the rapidity of data transmission.

In order to study the nonlinear remote monitoring system of the manipulator based on the network communication technology, a research method of the nonlinear remote monitoring system of the manipulator based on the network communication technology is proposed. In this article, in the Visual C++ environment, the transmission control protocol/internet protocol technology is used to build a remote monitoring system for the robotic arm, and it mainly realizes the function of the robotic arm running according to the trajectory in the remote. When storing video, you need to specify the ID of the video source, i.e. , the synchronization source in the real-time transport protocol data packet header identifies the robot, which can monitor more clearly. The remote monitoring technology is widely used in the modern automation industry, which not only further extends the human space activity ability, but also removes the human from the dangerous and complex working environment. Therefore, the remote monitoring technology has broad application prospects.

In order to study the bridge deflection monitoring and prediction system based on network communication, first, the development status of the bridge deflection monitoring system, overall demand of the system, hardware composition of the system, realization of the system software, and the timely processing and analysis of monitoring data are discussed. Then, the dynamic prediction of the change trend of the external load and the decay information of the structural resistance contained in the deflection monitoring data is carried out, and the prediction function of the external effect of the structure is established at the same time. Finally, a rapid monitoring system specially designed to deal with accidental bridge disasters was developed, and it was installed and applied in the engineering experiment of Chongqing Gaojia Garden Bridge. The deflection data analysis of Gaojia Huayuan Bridge was carried out, and suggestions for the operation and maintenance of the bridge were put forward, and the safety status assessment of the bridge was realized. The results show that the system has strong practicability, real-time monitoring and accuracy. It provides a convenient and accurate way for bridge managers to supervise bridges and formulate specific bridge maintenance plans in a timely manner. During the radio frequency modulation of communication data, harmonic oscillations occur due to the nonlinear characteristics of oscillating data, so it is difficult to improve the wireless ability to modulate and demodulate transmitted data in communications. The traditional method uses neural network fuzzy control distribution estimation harmonic balance algorithm and nonlinear rolling. The performance of dynamic predictive control is poor in quality, harmonic balance, and stability control. An improved harmonic-based communication network is proposed to balance the stability control model of nonlinear communication system, construct nonlinear communication system model, and extract signal and channel characteristics of the communication system. The channel model is designed and the communication network control method is adopted to improve the control algorithm. The simulation results show that the proposed algorithm can be used to improve the stability of nonlinear communication system, reduce the bit error rate, overcome the interference of coherent component in sidelobe, and autocorrelated the impulse response of receiver. The stability of the cumulative output is good, which can overcome the communication error caused by the harmonic oscillation due to the nonlinear characteristics of the oscillating data, and improve the communication quality.

Recently, it has become a popular strategy in multi-label image recognition to predict those labels that co-occur in a picture. Previous work has concentrated on capturing label correlation but has neglected to correctly fuse picture features and label embeddings, which has a substantial influence on the model’s convergence efficiency and restricts future multi-label image recognition accuracy improvement. In order to better classify labeled training samples of corresponding categories in the field of image classification, a cross-modal multi-label image classification modeling and recognition method based on nonlinear is proposed. Multi-label classification models based on deep convolutional neural networks are constructed respectively. The visual classification model uses natural images and simple biomedical images with single labels to achieve heterogeneous transfer learning and homogeneous transfer learning, capturing the general features of the general field and the proprietary features of the biomedical field, while the text classification model uses the description text of simple biomedical images to achieve homogeneous transfer learning. The experimental results show that the multi-label classification model combining the two modes can obtain a hamming loss similar to the best performance of the evaluation task, and the macro average F 1 value increases from 0.20 to 0.488, which is about 52.5% higher. The cross-modal multi-label image classification algorithm can better alleviate the problem of overfitting in most classes and has better cross-modal retrieval performance. In addition, the effectiveness and rationality of the two cross-modal mapping techniques are verified.

To improve data mining and data clustering performance to improve the efficiency of the cloud computing platform, the author proposes a bionic optimized clustering data extraction algorithm based on cloud computing platform. According to the Gaussian distribution function graph, the degree of aggregation of the categories and the distribution of data points of the same category can be judged more intuitively. The cloud computing platform has the characteristics of large amount of data and high dimension. In the process of solving the distance between all sample points and the center point, after each center point update, the optimization function needs to be re-executed, the author mainly uses clustering evaluation methods such as PBM-index and DB-index. The simulation data object is the Iris dataset in UCI, and N = 500 samples are selected for simulation. The experiment result shows that when P is not greater than 15, the PBM value changes very little, and when P = 20, the PBM performance of all the four clustering algorithms decreased significantly. When the sample size is increased from 50,000 to 100,000, the DB performance of this algorithm does not change much, and the DB value tends to be stable. In terms of clustering operation time, the K -means algorithm has obvious advantages, the DBSCAN algorithm is the most time-consuming, and the operation time of wolf pack clustering and Mean-shift is in the middle. In the actual application process, the number of samples for each training can be dynamically adjusted according to the actual needs, in order to improve the applicability of the wolf pack clustering algorithm in specific application scenarios. Flattening in cloud computing for data clusters, this algorithm is compared with the common clustering algorithm in PBM. DB also shows better performance.

In order to study the optimization of information acquisition security of broadband carrier communication and solve the problem of low baud rate of data acquisition in traditional communication operation data acquisition systems, this article reconstructs the required arrangement of communication operation data signals in the acquisition path by taking broadband carrier communication in the station area as an example through the linear equation method of genetic algorithm. The baud rate of the designed acquisition system is significantly higher than that of the control group, and the acquisition accuracy is 100% by using phase shift key modulation and high carrier frequency. It can solve the problem of low baud rate of data acquisition in traditional communication operation data acquisition systems and improve the security of information acquisition. The security (loss, anti-interference) of broadband carrier communication information collection based on the improved legacy algorithm is better than that of the traditional genetic algorithm, indicating that the security of broadband carrier communication information collection based on the improved legacy algorithm does not increase with the number of iterations and decrease.

Radio telemetry is being used in India to capture the location and movements of radio-collared wild animals. Radio telemetry data analysis has changed the scenario for wildlife conservation. It has provided many models and solutions for natural habitat utilization, genetic diversity, and even implementing green corridors for the species. Insights drawn from the data collected through radio telemetry from radio-collared animals have provided impactful information to understand the wild animal’s ecology. In the past few years, India has remarkably improved the population of tigers using telemetry studies and other conservation methods. In this study, a review of the telemetry studies conducted for tigers in India in the past decade has been presented. This study summarizes the telemetry studies of tigers in India and discusses how telemetry has enhanced the knowledge of ecologists and scientists to understand tiger ecology. This study also discusses the challenges and issues of conducting telemetry studies on tigers in India. Finally, the authors address the gaps in understanding the tiger’s ecology based on these studies and outline how radio telemetry can address these issues to better understand and conserve tigers.

In order to improve the accuracy of collected data and avoid table lookup, the adaptive weighted fusion algorithm is improved. According to the characteristics of the median and the mean value in the normal distribution, a new method of preprocessing to remove outliers is proposed to improve the accuracy of the final fusion result. The algorithm is used to calculate the temperature data to be processed in a greenhouse. The results showed that the fusion result after average processing was X ˆ \hat{X} = 15.77°C. The standard deviation is σ \sigma = 0.1194°C. After the treatment of the Grabbs criterion, the fusion result is X ˆ \hat{X} = 15.73°C and the standard deviation is σ \sigma = 0.1110°C. The fusion result of the improved algorithm is X ˆ \hat{X} = 15.74°C. The standard deviation is σ \sigma = 0.0959°C. Advantages of various preprocessing algorithms: improved algorithm > Grubbs method > no preprocessing. From the processing results of group A1 data, it can be seen that the improved algorithm can effectively suppress the ipsilateral shielding effect. Compared with the traditional Grubbs method to eliminate outliers and other algorithms, the improved algorithm can make the standard deviation of the fusion result smaller, and the fusion result can better represent the overall distribution, and there is no need to look up the table.

A three-dimensional simulation model of the electromechanical control system was built using the fuzzy control proportional–integral–derivative (PID) adjustment algorithm after an automatic electromechanical control system based on programmable logic controller (PLC) technology was optimized to achieve the practical use of electromechanical program control. First, the hardware of the electromechanical control system is discussed and designed. The findings demonstrate the viability of the mechanical and electrical integration PLC program optimization solution based on three-dimensional (3D) model. The system has a higher control and management efficiency, which is 30% greater than that of the conventional system. The mechatronic manufacturing system’s continuous operation efficiency enhancement can significantly lower the investment costs and boost the financial gains of industrial organizations. Traditional systems have a control and management efficiency of around 30%, but automatic electromechanical control systems based on PLC technology and created using 3D models have a control and management efficiency between 60 and 70%.

In order to effectively upgrade the training quality of the athlete, the study of the three-dimensional optical steps of sports, a three-dimensional optical action amplitude tracing process based on improved reverse kinematics is discussed. The method passes through a pinhole camera, the model calibrate the camera imaging plane, the positioning mark appears in the marker point in the apart neighboring single-sequence action amplitude and then the five-point perspective imaging of the same line is captured on the same straight line by the camera on different positions and postures. The matching method’s accuracy and superiority are demonstrated through experimental evaluation and compared with other similar measures. This characteristic is distinguished by the left and right image frames of the same camera. The translational movement is altered in 10–80 mm/s and the rotational movement is adjusted in 10–300 mm/s. During the confirmation, the spinning of the operational target, the longitudinal movement and the spatial location of the rotation point Measurement, the calculation variability of the stereoscopic visual moving calculation system, is given, and the method of tracking the method is high, which lay the foundation for the promotion of the training quality of the athlete. The experimental findings from simulation demonstrate that the implemented approach has great searching accuracy, establishing a solid platform for further improving the quality of athletes’ training.

In this article, the authors propose a method to identify the bridge damage using a backpropagation (BP) neural network. It uses bridge vibration response to solve the accuracy of bridge damage. A particle swarm optimization algorithm based on chaotic mutation is adopted to perform chaotic mutation operations and make the group jump out of the local optimum. CPSO (particle swarm optimization algorithm based on chaotic variation) algorithm can make up for the BP neural network model, easy to fall into the shortcomings of local optima, so the author will combine the two algorithms and discuss the environmental data of the bridge. Establishing a finite element model of the bridge through actual analysis, through data comparison, comparing the frequencies of the intact stages with the frequencies of the damaged stages, and verifying the neural network with random samples, for the degree of bridge damage, we get the root mean square error m s e mse and the correlation coefficient r . The result shows that the root mean square error m s e = 0.003196 mse=0.003196 , and the correlation coefficient r = 0.9654 r=0.9654 . There are only a few individual points; it seems that the relative error is relatively large. The rest of the fit is basically the same; it can meet the factors of vibration through the environment and perform damage identification for the structural damage monitoring of the bridge. Using the BP neural network model optimized by chaotic particle swarms, combined with the modal analysis of environmental vibration, it can be used in the monitoring of the health structure of the bridge, plays a certain recognition effect, and provides a new technical idea.

A tube bundle heat exchanger is a typical heat exchange equipment that exchanges heat between two fluids with different temperatures. Through this equipment, one fluid can be cooled down and another fluid can be heated up to meet their respective needs. The equipment is widely used in chemical, petroleum, pharmaceutical, energy, and other industrial sectors, and is one of the indispensable and important equipments in chemical production. To improve the heat transfer performance and service life of the heat exchanger, a numerical analysis of the vibration response of the elastic tube bundle in the heat exchanger based on fluid–structure coupling analysis is proposed. Using the weak coupling method of fluid–structure coupling, the vibration response of multiple rows of elastic tube bundles induced by shell side fluid in a heat exchanger with different tube row spacing and different tube row numbers is studied numerically, and the effects of shell side fluid and tube side fluid on the vibration response of elastic tube bundles are compared and analyzed. The results show that the maximum relative error of monitoring point amplitude is 43.36% when H = 40 mm and 10.17% when H = 70 mm. For connection IV, the maximum relative error of monitoring point amplitude is 31.71% when H = 40 mm and 24.08% when H = 70 mm. This is because when H is small, the interaction between rows of tube bundles is strong, so the amplitude changes violently with the number of the tube bundle. The step-by-step calculation strategy of rough calculation and actuarial calculation proposed in this article can greatly reduce the calculation time and improve the calculation efficiency.

In order to explore the establishment of a nonlinear network security situational awareness model based on random forest in the context of big data, a multi-level network security knowledge system evaluation model based on random forest is proposed. This article proposes a multi-level CSSA analysis system and then uses random memory algorithm to create a CSSA evaluation model. Also, it proposes a CSSA multi-level analysis framework and then uses random forest algorithm to build a CSSA evaluation model. A random vector distribution of the same values is used for all forest trees. In this article, the interval [0,1] is used to quantitatively describe the weight of the security level. The training sample ratio of test samples is 110:40, in order to predict the security of the network, the prediction of knowledge is closer to the true value, and the complexity of multi-level security is predicted. Use unusual forests. The tree returns the most recommended part, which is a more realistic assessment of network security. The experimental results show that considering the network security situation, the prediction performance of this method is closer to the actual value, and the performance is better than the other two methods. Therefore, perception of multi-level security situations can be effectively predicted using random access memory. It is proved that random forest is faster and more efficient in network security.

In order to better realize the secret-related information monitoring system, an algorithm based on a nonlinear network is proposed and is combined with the traditional algorithm. This article mainly analyzes the theory of nonlinear networks, designs and trains new network parameters according to their own needs, and combines the nonlinear network as a feature extractor with the existing intrusion detection and wandering detection algorithms, which greatly improves the recognition ability of traditional algorithms. The main feature of a nonlinear network is that it can extract the positional features of objects from the network while also extracting object features, that is, positioning and classification are realized in the same network. As a feature extractor, this network can not only have a higher recognition rate than background difference, hog, and other algorithms but also have a greater ability to extract position information than other convolutional neural networks. The successful application of nonlinear production network systems in TV stations at all levels has greatly improved the editing and production capability and efficiency of TV programs. How to ensure the safe, reliable, stable, orderly, and efficient operation of nonlinear production network systems requires vendors and TVS Taiwan technical staff to jointly conduct in-depth research and summarize their findings. In this article, from the perspective of TV users, information components in nonlinear production network systems are analyzed, including class, title management mode, storage space management, material management, security management, and workflow management in nonlinear systems. Make some analysis, discussion, and summaries of network system and operation management problems. The experimental results show that the nonlinear algorithm in this article has a significant advantage over the original tracking algorithm; that is, most tracking algorithms do not have the ability of category recognition during the initial tracking process, which means that these tracking algorithms cannot accurately know what they are tracking. Because the nonlinear network has the ability to output categories, whether it is initial tracking or tracking loss recovery, nonlinearity has fundamentally better advantages than other tracking algorithms. Therefore, it can be predicted that there is a strong recognition ability in the later monitoring and wandering detection. It has been proved that the nonlinear algorithm can be effectively applied to the secret information monitoring system.

The present article proposes a new-integral transform-based variational iteration technique (NTVIT) to study the behavior of higher-order nonlinear time-fractional delayed differential equations. The NTVIT is a hybrid technique that is developed via the concept of variational theory with the use of the properties of a new integral transform. The stability and convergence of NTVIT are analyzed via Banach’s fixed point theory. The effectiveness and validity of NTVIT solutions are demonstrated via the evaluation of error norms: relative/absolute errors for some test suitable delayed problems of different fractional order. The numerical experiments confirms that NTVIT is capable of producing highly accurate behaviors as compared to some existing techniques.

In this work, an exhaustive study on post effect processing of three-dimensional (3D) image is carried to solve the problem of nonlinear digital watermarking algorithm. First, through the feature space decomposition method of the host image, the embedded watermark is constructed with the full row or column rank of the matrix, and then the public key is constructed by using the existence of the unitary matrix of the full row rank and column rank matrix, so that the algorithm can embed and extract the watermark in an asymmetric way. Watermark extraction correlation coefficient ( ρ ) value is 1. When the deformation amplitude of the model is slight and the noise intensity is σ = 0.0001, the watermark can be extracted successfully, and the watermark extraction correlation coefficient ( ρ ) is 0.92. In addition, the security of the algorithm is analyzed from many angles, the theoretical analysis is given, and verified by the experimental results. The proposed 3D watermarking methods are used to examine the information capacity of various 3D meshes. The 3D watermarking methods’ resistance to noise perturbation and object cropping is also investigated.

This article attempts to effectively reduce the impact of active noise pollution on human life, and to make up for the traditional passive noise control technique. In low-frequency noise control, there are some shortcomings. The making of active noise control (ANC) technique, in low-frequency noise reduction, can achieve very good results. This article proposes a versatile dynamic noise control framework based on computer simulation and modeling. The research is mainly focused on the principle and application of versatile dynamic noise control framework. To accomplish this, a research method combining theoretical analysis, software simulation, and hardware realization is adopted. The derivation process of the adaptive algorithm (LMS algorithm, filter-XLMS algorithm, etc. ) is introduced in detail, and the influencing factors of algorithm performance, a variable step size normalization algorithm based on relative error is proposed. Perform simulation calculations on various algorithms in MATLAB, analyze parameters such as step factor, filter order, etc. , and the degree of influence on the algorithm’s convergence speed and steady-state performance. Common command set software is used, the path adaptive identification is realized, and the program design of the versatile dynamic noise control framework is used. After completion of software and hardware debugging on the experimental platform of generalized comfort, the experimental equipment layout is completed. Using the additive random noise method, the adaptive offline modeling of the first path of the versatile dynamic noise control framework is realized. Finally, utilizing the experimental platform of generalized comfort, the adaptive ANC experiment of the single-channel filtered least mean square algorithm is conducted, then the experimental data are analyzed, and at last, the actual application effect of the versatile dynamic noise control framework is verified.

A fully fledged face recognition system consists of face detection, face alignment, and face recognition. Facial recognition has been challenging due to various unconstrained factors such as pose variation, illumination, aging, partial occlusion, low resolution, etc . The traditional approaches to face recognition have some limitations in an unconstrained environment. Therefore, the task of face recognition is improved using various deep learning architectures. Though the contemporary deep learning techniques for face recognition systems improved overall efficiency, a resilient and efficacious system is still required. Therefore, we proposed a hybrid ensemble convolutional neural network (HE-CNN) framework using ensemble transfer learning from the modified pre-trained models for face recognition. The concept of progressive training is used for training the model that significantly enhanced the recognition accuracy. The proposed modifications in the classification layers and training process generated best-in-class results and improved the recognition accuracy. Further, the suggested model is evaluated using a self-created criminal dataset to demonstrate the use of facial recognition in real-time. The suggested HE-CNN model obtained an accuracy of 99.35, 91.58, and 95% on labeled faces in the wild (LFW), cross pose LFW, and self-created datasets, respectively.

In order to accurately and easily calculate the settlement of the foundation, a high-speed roadbed based on a nonlinear algorithm is proposed to broaden the uneven and uniform reduction numerical analysis. The basic loading test results of the foundation loading test results in a series of sand-bearing test results made by gear suppressive elastic Mohr–COMB were verified using general finite element procedure ABAQUS. The results show that for most original slopes of 1:1.5 highways, according to the above research results and relevant specifications, the high-wig ratio of the steps should be controlled in 1:1.2 to 1:1.5. That is, when the width is controlled in a range of about 1.2 m, the height of the step is held at 0.8–1.0 m. The larger the role of filling the top surface, the more obvious is the role of the geogrid to reduce the settlement of the road embankment. Under the conditions of the same subgraduation, the reinforced road embankment of the geotechnical grille, the settling effect that occurs in the load activity is also more obvious. This method offers a better design and construction technique for expanding the project, investigates the control of differential settlements caused by excavation step size and geogrid size, and seeks more complete, scientific programmes. It has the potential to drastically reduce the project’s investigation effort, shorten the survey cycle, and provide incalculable economic and social benefits. Therefore, the research results of this paper have improved the reliability of existing ground settlement analysis.

The typical power transformer diagnosis approach is imprecise and unstable. A support vector machine classification algorithm is proposed, by designing an algorithm program that can improve the accuracy and speed of energy transformer diagnosis, the vibration signals of the surface twisting in different states are extracted by wavelet packet energy spectrum signal processing method, it is verified that the curve similarity between the vibration simulation model and the measured data is greater than 0.98, proving the simulation model’s validity. The calculation technique of online short circuit inductance is developed from the equivalent transformer model, and the variation error of simulation results is less than 0.05% when compared to the real transformer characteristics. The suggested state diagnostic technique successfully compensates for the drawbacks of the reactance method, which is incapable of detecting and judging the slightly loose or faulty winding. The method’s accuracy and superiority, as well as the practicability of the state diagnosis system, are demonstrated.

In every network, traffic anomaly detection system is an essential field of study. In the communication system, there are various protocols and intrusions. It is still a testing area to find high precision to boost the correct distribution ratio. Many authors have worked on various algorithms such as simple classification, K -Means, Genetic Algorithm, and Support Vector Machine approaches, and they presented the efficiency and accuracy of these algorithms. In this article, we have proposed a feature extraction technique known as “ k -means clustering,” which has its roots in signal processing and is employed to divide a set of n observations into k clusters, each of which has its origin from the observation with the closest mean. K -Means method is applied in this study to investigate the stream and its implementation and applications using Python and the dataset on the KDDcup99. The effectiveness of the outcome indicates the planned work’s efficiency in relation to other widely available alternatives. Apart from the applied method, a web-based framework is designed, which can inspect an actual network traffic packet for identifying network attacks. Instead of using a static file for testing the network attack, a web page-based solution uses database to collect and test the information. Real-time packet inspection is provided in the proposed work for identifying new attacks.

In this study, we show a new way for a small unmanned aerial vehicle (UAV) to move around on its own in the plantations of the tree using a single camera only. To avoid running into trees, a control plan was put into place. The detection model looks at the image heights of the trees it finds to figure out how far away they are from the UAV. It then looks at the widths of the image between the trees without any obstacles to finding the largest space. The purpose of this research is to investigate how virtual reality (VR) may improve student engagement and outcomes in the classroom. The emotional consequences of virtual reality on learning, such as motivation and enjoyment, are also explored, making this fascinating research. To investigate virtual reality’s potential as a creative and immersive tool for boosting educational experiences, the study adopts a controlled experimental method. This study’s most significant contributions are the empirical evidence it provides for the efficacy of virtual reality in education, the illumination of the impact VR has on various aspects of learning, and the recommendations it offers to educators on how to make the most of VR in the classroom.

Multimedia and mobile learning are effective teaching tools because of their many useful characteristics. Transmission of educational material to students is facilitated by technology in both multimedia and mobile learning environments. A more interesting and engaging learning experience may be achieved by combining text, graphics, music, video, and animation. Media-rich classrooms are often referred to as “multimedia learning.” In contrast, students who use mobile learning may access their courses from any place with an internet connection and a mobile device such as a smartphone or a tablet. Whenever this involves commonplace technological needs, its cellular gadget and notably its clever telephone take the cake. Smartphone gadgets have a very wide range of potential applications and uses. Some ethical considerations are preventing media from reinforcing stereotypes or prejudice in the communities where they are utilized. Student information are gathered and used in a way that protects their privacy, with materials required for students to engage in mobile learning, and respecting intellectual property and copyright regulations while using multimedia language-learning tools. This importance of learning cannot be overstated but when such results come, mobile devices have increasingly been used in schools. This question of whether mobile devices have an impact on education remains open. Because of such “mobile gaining knowledge,” along with an overall phrase describing researching where different devices could be utilized in combination to enhance schooling, mobile devices had become more popular. Because today’s kids utilize their mobile devices frequently, studies on their effect on word learning are immediately required. This pilot research seeks to understand why school learners think via smartphone-based L2 exercises. In particular, this study collects data about several plenty applications using cell phones in linguistic research. Two hundred and ninety-four college children from one top Turkish institution participated in this research. This project uses some hybrid reporting models and relies on description analysis over its methodology. Their results show that users place one high value on obtaining ready accessibility to materials while studying some foreign language. Respondents not only remarked about their cellphone’s portability but also proposed new applications for enhancing their learning in other countries.

Since the beginning of the digital music era, the number of available digital music resources has skyrocketed. The genre of music is a significant classification to use when elaborating music; the role of music tags in locating and categorizing electronic music services is essential. To categorize such a large music archive manually would be prohibitively expensive and time-consuming, rendering it obsolete. This study’s main contributions to knowledge are the following: This article will break down the music into many MIDI (music played on a digital musical instrument) movements, playing way close by analysis movement, character extraction from passages, and character sequencing from movement so that you may get a clearer picture of what you are hearing. The procedure includes the following steps: extracting the note character matrix, extracting the subject and segmentation grouping based on the note character matrix, researching and extracting beneficial characteristics based on the theme of the segments, and composing the feature sequence. It is challenging for the sorter to acquire spatial and contextual knowledge about music using traditional classification techniques due to its shallow structure. This study uses the unique pattern of input MIDI segments, which are used to probe the relationship between recurrent neural networks and attention. The approach for music classification is verified when paired with the testing precision of the same-length segment categorization; thus, gathering MIDI tracks 1920 along with genre tags from the network to construct statistics sets and perform music classification analysis.

Global Software Development (GSD) is a contemporary approach to software development that offers numerous advantages, including enhanced cost-effectiveness and timely delivery. It enables access to a vast pool of skilled developers and facilitates the exchange of best practices and innovative ideas within the software industry. However, effective project management plays a vital role in ensuring successful product development. Organizations that achieve project success consistently adhere to well-defined project management methodologies, resulting in desired outcomes within predefined time frames and allocated resources. The success rate of software projects significantly increases with diligent software management efforts. Nevertheless, the distributed nature of GSD presents significant challenges related to collaboration, information dissemination, and process control, which ultimately impede effective development and compromise software quality. In this study, we identify various challenges associated with the GSD process and propose strategies to overcome obstacles to effective project management. Additionally, we introduce a comprehensive framework designed to enhance managerial activities in GSD.

In modern industrial production, many advanced manufacturing technologies are constantly developing with the progress of social sciences. Welding, as an indispensable manufacturing technology in industrial production, has received close attention from various industries. High frequency welding technology is needed in fields such as mechanical manufacturing, machine making in the food industry, and intelligent robot model making. High frequency welding is an important technical means in the production process of welded pipes, and the level of welding temperature has a significant impact on the quality of welded pipe welds. This article studied the shortcomings of traditional high-frequency welding, analyzed the application method of nonlinear finite element method in high-frequency welding, and analyzed the dynamic process of welding and its influencing factors. The finite element method formula is used to stabilize the value of three-dimensional (3D) temperature field. This work studied the temperature distribution of welded pipe welding, welded pipe materials, inside and outside of welded pipe, and temperature changes under different voltages. The experimental results showed that the error value between the simulation results of the 3D temperature field of high-frequency welding and the measured experimental results was about 4.3542°C, which was basically similar, indicating the effectiveness of the 3D temperature field simulation experiment. With the development of science and technology, high-frequency welding technology would continue to improve, and the quality of welded pipe welds would become better and better with the progress of technology. The improvement in quality promotes the development and progress of industry, and maintains the quality of machine manufacturing. The simulation experiment method of 3D temperature field has shortened the experimental time and reduced the experimental cost, providing a new reference for other temperature related experiments.

In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 10 7 mm 3 , and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 ∘ , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.

In order to efficiently and accurately diagnose train electrical faults, we propose a fault diagnosis method for electrical equipment based on virtual simulation technology. First, Creo software was used to build a subway train model. Then, 3DMAX software was used to make animation and demonstrate the working principle and action process of the train electrical system. Finally, using Unity 3D software, a human–computer interaction mechanism was established, achieving presence and realism. This system realizes the functions of knowledge learning, student assessment, principal display, and troubleshooting of the electrical system of subway trains and is compared with the method of manual diagnosis. Experimental results show that in the designed fault diagnosis system, the detection time for various types of faults is shorter than 30 s, whereas the diagnosis time of the manual diagnosis method is 30–52 s. It shows that the electrical equipment fault diagnosis system based on virtual simulation has the advantages such as short fault diagnosis time and high efficiency. In addition, the highest diagnostic accuracy of the manual diagnosis method is 75.48%, which is far lower than the accuracy of the diagnostic system. Conclusion: It is proved that the designed fault diagnosis system has the advantages such as short detection time and high accuracy and can meet the safety requirements of industrial production.

In order to solve the coordinated operation of voltage and frequency of microgrids and achieve effective distribution of output power, we propose the application of fractional-order nonlinear equations in coordination. This method designs a distributed impulse coordinated control strategy, to achieve the coordinated operation of the system. The distributed coordinated control structure and mathematical model are established, and the distributed two-level coordinated control strategy of the microgrid system is adopted. Aiming at the secondary control problem of microgrids, a distributed coordinated control protocol is designed. The results showed that after adding the distributed second-level coordination control of frequency at 3 s, the output active power of the four distributed power sources in the microgrid model is maintained to an evenly divided state after about 1 s. The output voltage and frequency utilizing the microgrid’s decentralized power supply quickly reach the ideal reference value, within the allowable error range, the output of the system can achieve coordinated control, and the active power can be distributed proportionally.

The reliability and effectiveness of a high-speed train’s operation depend heavily on the traction drive system. The purpose of this project was to construct an electromechanical connection model for a bullet train. The model contains the gear-to-gear connection, the differential output of the transmission, which circuits similar to those found in motors, and indirect power management. The purpose of this research is to investigate how modern railroad systems have implemented locomotive driving safety assistance technologies in order to get a deeper understanding of the effects that technological progress has on train operators. The purpose of this study is to learn how technological developments have altered the job of train operators. We will investigate the feasibility, compatibility, and potential consequences of introducing innovative technologies into established workflows. We will look at how well it works with current technologies, too. The current investigation has the authority to look at these issues. The ultimate goal of this project is to improve railway operations by providing essential insights for guaranteeing a balance between technological progress and human skill. The ultimate purpose of the project is to enhance the efficiency and security of railway operations. This may be achieved by strengthening the effectiveness and security of railway operations. In addition, the high-speed train model is simulated numerically to maintain that steady rate of travel, and grip, while slowing. The study determined that the stator current is the result of the interaction between the fundamental frequency and the higher harmonics of the rotational frequency. Furthermore, both frequencies can be detected even when traveling at a constant speed. Despite this, unless the rotation frequency is increased, they are often not visible. During traction, the root-mean-square (RMS) values of the rotor and stator currents are lower than that during braking. There is a significant rise in current when the wheels and brakes are first applied. The RMS value of the current lowers dramatically as grip and braking improve. As a result, it is essential to carefully consider how the change may influence the reliability of the system.

Background Computer networks are involved in many fields such as business, education, marketing, government, and tourism in several forms. Technologies related to security protection and improvement of information integrity are used and developed for computer networks intruded on by unauthorized people and help save their confidentiality. Methods To improve the risk identification of computer networks, this manuscript combined a fuzzy hierarchical reasoning model with the scientific inversion parallel programming method to study the risk of computer networks. Moreover, this article defined and analyzed a d -order neighborhood message propagation algorithm. A d -order neighborhood parallel message propagation algorithm using the Gaussian graph model was proposed. Results The risk of the computer network was analyzed using the proposed method resulting in better protection effectiveness. Conclusion The simulations showed that the proposed algorithm could effectively detect risks and improve the security of the computer network.

To improve the accuracy effect of the iterative hard threshold, an improved iterative hard threshold (IHT) method is proposed. The specific contents of this method include the principle of an IHT algorithm based on compression sensing (nonlinear optimization), weighted least squares improvement, the establishment of an IHT algorithm model based on weighted least squares improvement, and the experimental research of traditional algorithms and improved algorithms on one-dimensional signal reconstruction. The results show that the improved IRLSIHT algorithm takes 8.37, 29.63, and 30.86 s when the sampling rate is 0.2, 0.5, and 0.8, respectively, and the signal-to-noise ratio is 20.11, 27.47, and 31.82 dB, respectively. Compared with the traditional IHT algorithm, it takes a long time, which is a deficiency, but the signal-to-noise ratio is the largest, and the improved algorithm improves the accuracy. It has been proven that combining the method proposed in this article with automatic control can significantly save time and increase industrial output.

Bounded rationality, asymmetric information, and R&D spillovers are widely existed in monopoly markets, and they have been researched separately by a large number of literatures; however, there are few works that discussed both R&D spillovers and asymmetric information in oligopolistic games with bounded rational firms. Considering that R&D spillovers only flow from the R&D leader to the R&D follower, a duopoly Cournot game with heterogeneous expectations and asymmetric information is presented. In our model, a firm with private information of his marginal cost is designed, and the coefficient of R&D spillovers is introduced. Interesting findings show the following: (i) In a static duopoly Cournot game with perfect rationality, the equilibrium output of firm 1 with private information is negatively related to R&D spillovers and the probability of high marginal cost, while firm 2’s equilibrium output is positively correlated with them. (ii) In a dynamic duopoly Cournot game with asymmetric information and heterogeneous expectations, if firms adopt adaptive expectation and naïve expectation respectively, the Nash equilibrium is always globally asymptotically stable; if they use adaptive expectation and gradient dynamical expectation respectively, the Nash equilibrium tends to be locally asymptotically stable under certain conditions. Furthermore, the bigger the probability of high marginal cost or R&D spillovers are, the more volatile the monopoly market is, while higher technology innovation efficiency (TIE) of firm 1 is conducive to the stability of the product market. Our study would have theoretical and practical significance to the technological innovation activities of homogeneous products in oligopoly markets.

In order to further improve the prediction accuracy, the network packet loss rate (PLR) prediction mathematical model based on the Internet of Things (IoTs) was proposed. First, the network data transmission module was established, and the network PLR prediction process was developed based on IoTs; second, the prediction framework of PLR was designed to obtain more accurate prior information. The relationship between PLR and user experience quality QoE is univariate and nonlinear. The mapping between PLR and user experience quality QoE is established using univariate nonlinear regression analysis; finally, a mathematical model of network PLR prediction is constructed to further improve the prediction accuracy. Experimental results show that the delays of network nodes are all within 5 s, which can ensure the real-time nature of data transmission. When the total number of packets and the number of lost packets are the same, the PLR predicted by the mathematical model designed by the authors is consistent with the actual PLR. Conclusion: The prediction effect of the model is better and has higher promotion value.

In order to realize the automatic detection system of electric sensor, a method based on sensor and nonlinear machine vision is proposed. Aiming at complex scenes and dynamic changes in target recognition and detection in large-scale industrial field, a target recognition and detection system based on the fusion of vision sensor and nonlinear machine vision is proposed. The system introduces nonlinear features and uses deep neural network to realize multi-scale analysis and recognition of image data on the basis of traditional machine vision. The system uses C++ language development and has a good user interface. The photoelectric sensor weld image is collected by machine vision technology, the target area of the image is detected by Gaussian model, the feature points of the target area are extracted by combining Hessian matrix, the extracted feature points are input into the quantum gate neural network model, and the recognition results are obtained. The simulation results show that the author’s method has the highest value among the three test indicators, with the highest accuracy rate of 97%, the highest recall rate of 98%, and the highest F 1 value of 94. The time consumed by the author’s method for automatic identification of photoelectric sensor welding is within 6 s, the time spent on the film wall recognition method for automatic identification of photoelectric sensor welding is within 20 s, and the time spent by the feature extraction and identification method for automatic identification of photoelectric sensor weld is within 22 s. It has been proven that the method based on the fusion of sensors and nonlinear machine vision can achieve an automatic recognition and detection system for electrical sensor welds. The object detection and recognition method proposed in this article can be applied to dynamic changes and complex scenes in various complex backgrounds and has a good application prospect. The system proposed in this article has some limitations, such as the algorithm in the calculation accuracy, real-time, and other aspects that have room for improvement.

To solve the problem of calculating the probability of ship collision in ship bridge collision risk assessment, the impact parameters of ship collision are obtained based on the automatic identification system (AIS) data to solve the problem that the existing methods do not consider the actual navigable ship information in a specific bridge navigation area. Based on AIS data, the dynamics of sailing ships are analyzed, parameters such as ship position, speed, and yaw angle, are obtained, ship traffic flow is analyzed, and the geometric probability in the actual ship traffic flow specification model is modified. The results before and after correction were compared and analyzed. The results show that the maximum transverse displacement of the anti-collision device is about 1.5 s under all working conditions, indicating that the collision force drops continuously from this moment to 0 in the collision force time history. In the process of collision, the anti-collision device absorbs part of the collision energy through its own deformation. Under the premise of a certain initial kinetic energy, the deformation caused by the collision energy absorption after fortification will be reduced. The anti-collision device has local permanent deformation under the impact of 5,000 t ship, but no damage and failure, and will not cause water entry and subsidence. It proves that the constructed fishery ship collision risk assessment model and the developed fishery ship safety management and evaluation system are reliable and the prediction results are credible, which can provide scientific methods for the safety management and evaluation of fishery vessels. For the bridge area with complicated ship navigation conditions, it is necessary to use the actual navigable ship information obtained based on AIS data to estimate the distribution of ships in the bridge area to improve the accuracy of the calculation results.

In order to achieve facial object detection and tracking in video, a method based on nonlinear sequence Monte Carlo filtering technology is proposed. The algorithm is simple, effective, and easy to operate, which can solve the problems of scale change and occlusion in the process of online learning tracking, so as to ensure the smooth implementation of learning effect evaluation. Experimental methods should be added to the article summary section. The results show that the algorithm in this study outperforms the basic KCF in terms of evaluation accuracy and success rate, as well as outperforms other tracker algorithms in benchmark, achieving scores of 0.837 and 0.705, respectively. In terms of overlapping accuracy, the reason why this study’s algorithm is higher than KCF is that this study determines the tracking status of the current target by calculating the primary side regulated (PSR) value when the target is obscured or lost, which does not make the tracking error to accumulate. The tracking algorithm in this study is not ranked first in the two attributes of motion blur and low resolution, but the rankings of all other nine attributes belong to the first. Compared with the KCF algorithm, the accuracy plots for the three attributes of scale change, occlusion, and leaving the field of view are improved by 10.26, 13.48, and 13.04%, respectively. Thus, it is proved that the method based on nonlinear sequence Monte Carlo filtering technology can achieve video facial object detection and tracking.

In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.