Volume 13, Issue 1

Due to the particularity and complexity of sedimentary environments, the wave impedance differences between different reflection interfaces in underground media may vary greatly. Therefore, an encoder–decoder neural network is proposed to enhance erroneous seismic weak reflection signals. The convolutional neural network (CNN) has the problem of difficulty in parallel computing, resulting in slow network training and computational efficiency. Considering that attention has an innate global self-attention mechanism, can compensate for long-term dependency deficiencies, and has the ability to perform parallel computing, which greatly compensates for the shortcomings of CNNs and recurrent neural networks, a seismic impedance inversion method based on convolutional attention networks is proposed. To improve the ability to extract noise, residual structure and convolutional attention module (CBAM) were introduced. The residual structure utilizes residual jump to weaken network degradation and reduce the difficulty of feature mapping. The CBAM uses a mixed attention weight of channel and space, which can enhance features with high correlation and suppress features with low correlation. In the decoder, in order to improve the dimension recovery ability of feature fusion, bilinear interpolation is selected for upsampling. The application results of the model and actual data indicate that this method can effectively enhance the weak reflection signals caused by the formation itself and improve the reservoir identification ability of seismic data.

This research focuses on implementing a robust passivity-based nonlinear control method for bilateral/teleoperation systems. The key challenge is addressing communication pathways between the master and slave, control delays, and load disturbances, which can lead to instability and reduced transparency. To tackle these issues, the proposed controller incorporates a second-order super-twisting sliding-mode observer to counteract communication and control delays. A sliding mode assist disturbance observer compensates for load torque variations. The approach aims to ensure stability and transparency by handling time-varying delays. The system model comprises two interconnected direct-drive motors, simulating robotic configurations without a physical robot. The nonlinear controller framework simplifies the complex bilateral control problem, significantly improving stability and transparency performance. Computer simulations with step and sinusoidal inputs demonstrate the effectiveness of the approach, providing a satisfactory level of accuracy and transparency between estimated and actual slave positions, even with varying delays and load variations. The research contributes to control engineering by offering a robust method to enhance bilateral system performance, ensuring stable and transparent communication between the master and slave, particularly suitable for real-time internet-based bilateral control systems.

The integration of artificial intelligence (AI) into computational fluid dynamics (CFD) has significantly expanded the scope of fluid modeling, allowing enhanced analysis capabilities and improved simulation performance. While Eulerian methods already benefit extensively from AI, notably in reliable weather prediction, the application of AI to Lagrangian methods remains less consolidated. Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh-less numerical method for CFD with well-established advantages for the simulation of highly dynamic free-surface flows. Here, we explore an application of AI to SPH simulations, utilizing an artificial neural network (ANN) to estimate hydrodynamic forces between particle pairs, learning from SPH-simulated results. A model of this nature, which emulates the mathematical representation of physics, is termed an emulator . We examine the physical significance of the emulator, presenting its applications in benchmark tests, assessing its faithfulness to traditional SPH simulations, and highlighting its ability to generalize and simulate test cases with varying levels of complexity beyond its training data.

In this article, asymmetrical novel system with two exponential functions, which can show hyperchaotic behavior, has been proposed. Although new system possesses only one unstable equilibrium. The dynamical behaviors of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Furthermore, the synchronization of the proposed system are also presented by an adaptive synchronization approach of two identical hyperchaotic systems. An application to image encryption has been obtained.

Seismic vulnerability assessments are conventionally conducted by using sophisticated nonlinear analytical models, leading to aggressive computational demands. Previous attempts were made to reduce computational efforts for establishing vulnerability assessment of structures; however, the area of super tall and tubular structures still faces considerable lack. Advent of efficient machine learning (ML) has enabled engineering practitioners to automate the processes for fragility analysis; however, its application for high-rise tubular structures is not yet exploited, and most implementations are limited to basic ML. In this work, an attempt was made to reduce computational demand for the fragility assessment process for tubular structures by employing genetic algorithms (GAs) for nonlinear structural modeling, and development of artificial neural network (ANN) using deep learning for fragility development. Consequently, a simple lumped parameter model had been developed using open-source code of ZEUS-NL, containing parameters selected by GA to acutely account for convoluted interactive behavior of structural systems and dynamic demands. Subsequently, incremental dynamic analysis (IDA) was performed on the optimized model. A new framework has been established to develop and train ANN architecture by amalgamating Weka’s capability of data preprocessing with deep learning. The established ANN model resulted in correlation coefficient of 0.9972 and R 2 of 0.95, demonstrating adequate performance.

The significance of nanofluid research in nanotechnology, pharmaceutical, drug delivery, food preparation, and chemotherapy employing single- and two-phase nanofluid models has drawn the attention of researchers. The Tiwari–Das model does not capture the diffusion and random movement of nanoparticles (NPs) when they are injected into complex functional fluids. In order to fix the peculiar behavior of NPs, more complex models like the Buongiorno model are coupled with the single-phase model. To examine the heat-mass transfer attributes of nanofluids, a single- and two-phase mixture model is coupled for the first time. The effect of hybrid NPs on the hemodynamic properties of the blood flow through a stretched surface with interface slip in the neighborhood of the stagnation point is examined. Due to their significance in medicinal uses and nominal toxicity, blood is loaded with zinc–iron ( ZnO − F e 2 O 3 ) {\rm{ZnO}}\left-{\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) NPs. However, blood is speculated to have the hematocrit viscosity of the Powell–Eyring fluid. The single-phase model predicts an improvement in heat transport due to an increased volumetric friction of NPs, while the two-phase models provide closer estimates of heat-mass transfer due to Brownian and thermophoretic phenomena. Entropy evaluation predicts the details of irreversibility. The mathematical structures are effectively solved with a Runge–Kutta fourth-order algorithm along with a shooting mechanism. The Eyring–Powell parameters decrease the drag coefficient and mass/thermal transport rate. A higher estimation of the slip, material, and magnetic parameters decreases the flow behavior. The Bejan number increases with the diffusion parameter and decreases as the magnetic and Brinkman numbers increase. The effect of iron oxide ( F e 2 O 3 ) \left({\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) is observed to be dominant.

This article proposes a nonlinear deterministic mathematical model that encapsulates the dynamics of the prevailing degree of corruption in a population. The objectives are attained by exploring the dynamics of the corruption model under fractional-order derivative in the Caputo sense. The outcomes of the research are facilitated by stratifying the population into five compartments: susceptible class, exposed class, corrupted class, recovered class, and honest class. The developed model is validated by proving pivotal delicacies such as positivity, invariant region, basic reproduction number, and stability analysis. The Ulam–Hyers stability technique is used to prove the stable solution. The Adam–Bashforth numerical scheme is employed to estimate the numerical solution. Moreover, the research environment is further enriched by studying each compartment with respect to a wide range of relevant parametric settings. The realizations of this study indicate that susceptible individuals remain subject to being influenced by corrupt individuals. In addition, it is observed that the population of exposed individuals, recovered individuals, and honest individuals asymptotically approach toward the corruption equilibrium point, whereas the magnitudes of susceptible individuals and corrupted individuals decrease asymptotically to the corruption equilibrium state. The compartment dynamics are witnessed to be sensitive for various fractional-orders indicating the utility of the fractional approach. The findings of this study support the fundamental understanding of conceptualizing corruption in accordance with the viral transmission of infectious disease.

In this article, we present a novel extended exponential kernel Laplace-type integral transform. The Laplace, natural, and Sumudu transforms are all included in the suggested transform. The existence theorem, Parseval-type identity, inversion formula, and other fundamental aspects of the new integral transform are examined in this article. Integral identities define the connections between the new transforms and the established transforms. In order to solve specific initial-boundary value problems, the new transforms are used.

One of the efficient and reliable methods for resolving fractional order linear as well as non-linear differential equations is the Laplace transform with residual power series method. This approach is used in the current research to obtain the numerical solutions of the two-dimensional fractional differential equations, namely, the temporal fractional order diffusion equation and the fractional biological population equation. The unknown coefficients of the series solutions to these equations are determined using the proposed approach. The difference between exact and analytical-numerical solutions is presented for these equations in the form of errors. The advantage of the suggested method over alternative approaches is that it requires less computation to solve these two-dimensional differential equations of time-fractional order.

The fractional-order controllers (FOCs) have recently had a significant impact on control applications. However, they still need further research for feedback systems with hard nonlinearities, such as dead zones. The above compelling evidence motivates the design of a new robust FOC to avoid limit cycles caused by dead zones in the control loops. The proposed FOC consists of the cascade of two shifted in frequency, fractional-order lead networks. They provide high-value and sufficiently flat phase leads in sufficiently large frequency intervals. In this way, the linear part of the control loop can be easily shaped to achieve avoidance of limit cycles. The article applies classical concepts, such as the Nyquist plot and describing function method, to derive guidelines for designing the free parameters of the FOC. Moreover, a realization algorithm and a parameter setting procedure make the new FOC easily implementable in engineering practice.

Fractional diffusion partial differential equation (PDE) models are used to describe anomalous transport phenomena in fractal porous media, where traditional diffusion models may not be applicable due to the presence of long-range dependencies and non-local behaviors. This study presents an efficient hybrid meshless method to the compute numerical solution of a two-dimensional multiterm time-fractional convection-diffusion equation. The proposed meshless method employs multiquadric-cubic radial basis functions for the spatial derivatives, and the Liouville-Caputo derivative technique is used for the time derivative portion of the model equation. The accuracy of the method is evaluated using error norms, and a comparison is made with the exact solution. The numerical results demonstrate that the suggested approach achieves better accuracy and computationally efficient performance.

Considering the continuous threat of terrorist attacks on vital structures, it is imperative to enhance their resilience to blast impacts. Current analytical approaches are costly and complex, necessitating a more streamlined method to evaluate structures under such threats. This research addresses this by introducing a machine learning (ML) model that predicts the highly nonlinear behaviour of reinforced concrete (RC) slabs under blast loadings. A database with 936 samples, including both experimental and numerical data, was carefully created for this study. The investigation scrutinized eight ML algorithms, refined them to four based on their performance, and optimized them using grid search, genetic algorithm, and particle swarm optimization (PSO). The gradient boosting-PSO hybrid model emerged to be superior, with a remarkable 91% accuracy in predicting maximum deflection. Further, a comprehensive influence analysis was conducted using the SHapley Additive exPlanations (SHAP) method to understand the contributions of various input parameters, pinpointing scaled distance and panel thickness as critical factors. This study, besides offering a rich database, also serves as an educational tool, shedding light on hyperparameter optimization techniques and SHAP analysis. The research promises a robust and interpretable ML model poised to significantly influence the practical engineering domain in improving the structural design of RC slabs facing blast impacts.

Recently, fractals and fractional calculus have received much attention from researchers of various fields of science and engineering. Because the said area has been found applicable in modeling various real-world processes and phenomena. Hybrid differential equations (HDEs) play significant roles in mathematical modeling of various processes because the aforesaid equations incorporate different dynamical systems as specific cases. For instance, it is possible to model and describe non-homogeneous physical phenomena on using the said equations. Therefore, this research work is concerned with studying a class of nonlinear hybrid fractal–fractional differential equations. We develop the existence result for the qualitative study using a hybrid fixed point theorem. For the mentioned goal, a fixed point theory for the product of two operators is applied to deduce appropriate conditions for the existence of exactly one solution. Additionally, the stability result based on Ulam–Hyers is also deduced. The said stability results play an important role in numerical investigations. In addition, a numerical method based on Euler procedure is utilized to approximate the solution of the proposed problems. Various computational test problems are given to demonstrate the results. Also, using various fractal–fractional order values, several graphical presentations are given for the examples. The concerned analysis will help in investigating many real-world problems modeled using HDEs with fractal–fractional orders in the near future.

The two-dimensional conformal time-fractional generalized q q -deformed sinh-Gordon equation has been used to model a variety of physical systems, including soliton propagation in asymmetric media, nonlinear waves in optical fibers, quantum field theory, and condensed matter physics. The equation is able to capture the complex dynamics of these systems and has been shown to be a powerful tool for studying them. This article discusses the two-dimensional conformal time-fractional generalized q q -deformed sinh-Gordon equation both analytically and numerically using Kudryashov’s approach and the finite difference method. In addition, the stability analysis and local truncation error of the equation are discussed. A number of illustrations are also included to show the various solitons propagation patterns. The proposed equation has opened up new possibilities for modeling asymmetric physical systems.

In this study, the influence of concentrated damage on the stability of beams under static loads is investigated according to a co-rotational-based large displacement approach. Well-known benchmark beam-like structures have been considered under different loading conditions and damage scenarios. The concentrated damage has been modelled by means of a cross section reduction of a beam element, following a strategy already adopted in the literature. The results have been expressed in terms of buckling loads and post-buckling responses for different damage scenarios associated with a concentrated damage characterized by different positions, intensities, and extensions.

This article develops approximate numerical solutions through the generalized method of lines for the time-independent, incompressible Navier–Stokes system in fluid mechanics. More specifically, we highlight the main objective of this article is the development of new approximate procedures for solving numerically the equation systems originated from a domain discretization related to a finite differences scheme. We recall that for such a method, the domain of the partial differential equation in question is discretized in lines (or more generally in curves), and the concerning solutions are written on these lines as functions of the boundary conditions and the domain boundary shape. Finally, it is worth emphasizing that in this text, we have presented softwares and results for a concerning approximate proximal approach, as well as results based on the original conception of the generalized method of lines.

In spite of the enormous applications of heating combustible materials due to exothermic chemical reactions, scientists and engineers still face a problem with these materials’ tendency to self-ignition, which can result in significant property damage if serious precautions are not taken. Therefore, the thermal decomposition of combustible viscoelastic material in a cylindrical channel is investigated in this study. With a third-order constitutive model considered for viscoelastic flow behavior, momentum and energy-balanced governing equations are provided. The chemical reaction of the material is assumed exothermic and thus follows Arrhenius’s kinetics. A numerical solution is provided for the boundary value problem via the bivariate spectral collocation method, and the impact of kinetics parameters on the combustible viscoelastic material is investigated. Our findings show that self-ignition is delayed with higher values of activation energy parameter ( ε \varepsilon ) and third-order parameter ( γ \gamma ), as well as lower values of magnetic field parameter ( M M ), current density parameter ( δ \delta ), and electrical conductivity exponent ( m m ).

This study aims to propose novel Zernike wavelets and a new method based on the operational matrices for solving nonlinear fractional differential equations. First, non-orthogonal Zernike wavelets are introduced using the Zernike polynomials. Then, a new technique based on combining these wavelets with the block pulse functions is presented to derive the operational matrix of fractional integration and to solve nonlinear fractional differential equations. Moreover, an error analysis is conducted by providing required theorems. Besides, the proposed method is employed to solve a nonlinear fractional competition model of breast cancer. Finally, a parametric study is performed to consider the effect of fractional order on the population of healthy, cancer stem, tumour, and immune cells, as well as the excess estrogen.

In this work, we explore the generalized discrete wave equation, which utilizes a specific irregular space interval. The introduction of this irregular space interval is motivated by its connection to the q -addition, a mathematical operation that arises in the nonextensive entropy theory. By taking the continuous limit, we obtain the wave equation with q -deformation, which captures the effects of the q -addition. To solve the generalized q -deformed wave equation, we investigate three different methods: the separation method, the reduced differential transform method, and the finite difference method. These methods offer distinct approaches for finding solutions to the equation. By comparing the results obtained from each method, we can evaluate their effectiveness and identify their respective strengths and limitations in solving the generalized q -deformed wave equation. The solutions obtained from this newly defined equation have potential applications in modeling physical systems with violated symmetries. The inclusion of the q -deformation allows for a more comprehensive description of such systems, which may exhibit nonextensive behavior or possess irregularities in their spatial intervals. By incorporating these features into the wave equation, we can improve our understanding and modeling capabilities of complex physical phenomena.

Improving corrosion resistance in alloys made of stainless steel is an important innovation on the petroleum trade. The effect of heat treatments (HT) and cold working on the corrosion behaviour, surface hardness, and microstructure of 316 stainless steel was investigated experimentally. The corrosion environment is seawater and crude oil. The corrosion rates (CRs) were obtained using the mean loss of weight approach, which was then optimised using the Taguchi method. The specimens used in this study are made of 316 stainless steel rod, which is first annealed to obtain the qualities of the raw material before being put through a tensile test to assess the mechanical characteristics of the metal. After cold working, the hardness test, the corrosion test utilising the lost weight method, and the microstructure test are all carried out. By performing these tests, the metal show excellent mechanical properties such as yield stress, tensile stress, and hardness; in the corrosion test, the raw metal show higher resistance in both seawater and crude oil, while in cold working and HT with cold working, samples show higher corrosion The HT samples had the lowest corrosion resistance as the cold working percentage increased. In this work, the input parameters such as ultimate corrosion media, HT and cold work (CW) are optimised utilising a multiple objective optimisation approach that uses weighted grey relational analysis. Two objectives, that are CR and Hardness (H), are simultaneously optimised. We suggested a quantitative approach to establish the weight factors of various responses for grey relational analysis called weighted grey relational analysis. The optimum input parameters were determined using weighted grey relational analysis, and the outcomes showed that HT is the most relevant parameter. Cold working has been observed in association with stress-related twinning and austenite phase deformation, resulting in fast grain splitting and the production of a microstructure that resembles a ribbon composed of austenite and ferrite.

The KdV–mKdV equation is investigated in this study. This equation is a useful tool to model many nonlinear phenomena in the fields of fluid dynamics, quantum mechanics, and soliton wave theory. The exact soliton solutions of the KdV–mKdV equation are extracted using three distinct exact methods, namely, the generalized projective Riccati equation method, the modified auxiliary equation method, and the generalized unified method. Many novel soliton solutions, including kink, periodic, bright, dark, and singular dark–bright soliton solutions, are obtained. Rational functions, exponential functions, trigonometric functions, and hyperbolic functions are contained in the acquired nontrivial exact solutions. The graphical simulation of some obtained solutions is depicted using 3D plots, 2D contour plots, density plots, and 2D line plots. For the first time, the KdV–mKdV equation is investigated using the proposed three exact methods, and many novel solutions, such as dark, bright, and dark–bright singular soliton solutions, are determined, which have never been reported in the literature.

This study outlines the development of a three-dimensional model for the crankshaft-bearing and a multi-body dynamics model for a four-stroke marine diesel engine. The models are constructed through a simulation approach that integrates the finite element method and multi-body dynamics method. Additionally, the Greenwood/Tripp asperity contact theory and average flow model are incorporated. The investigation also delves into the dynamic coupling between the crankshaft-bearing multi-body system and the mixed lubrication effects, accounting for lubricating oil as a thermo-electrohydrodynamic model and the journal as an elastomer. The study meticulously examines the lubrication characteristics of main bearings in marine diesel engines during normal operational conditions and scrutinizes the impact of various parameters on crankshaft-bearings. The study concludes by offering recommendations and technical support for innovative optimization design and model enhancement of diesel engine crankshaft-bearings.

This article aims to examine the pricing of debt and equity in the context of credit risk structural models, where the value of a company’s assets is influenced by mixed fractional Brownian motion. Three distinct scenarios are analyzed, including when the assets are trade-able, fixed, and subject to partial recovery of debt. The study culminates with the evaluation of debt pricing under the barrier model, where a bankruptcy threshold is established for the company’s asset value.

Accurate extraction of abnormal communication signal features in the network is the basis to ensure the completion of network communication. Therefore, a method of feature extraction of abnormal communication signal in network based on nonlinear technology is proposed. In this method, wavelet transform is adopted to decompose the abnormal network communication signals in the high- and low-frequency bands. According to the distribution characteristics of noise and signal in the frequency band, the corresponding parameters are selected for phase space reconstruction and nonlinear dimension reduction of local tangent space mainstream shape recognition algorithm, and the decomposition coefficients of wavelet packet after noise reduction are reconstructed to realize the nonlinear noise reduction of abnormal signal; the denoised abnormal communication signal in network is mapped to the high-dimensional feature space. The principal component is analyzed in accordance with the nonlinear function in the mapped feature space, and the nonlinear function is solved by self-organizing neural network to output the principal component extraction result. According to test results, this method has a significant signal noise reduction effect, results are more than 92% for different abnormal communication signals, and the features of abnormal signals are accurately extracted.

This article presents a new binocular vision method for accurate deformation measurements of flexible membrane structures. Using enhanced marker points on the membrane, the method identifies areas for displacement measurements, filtering out unwanted image features with scale-invariant feature transform and threshold correlation. It integrates Canny edge recognition and quadratic weighted averaging for precise positioning of measurement points. By comparing reference images and utilizing the principle of minimum distance between matching points, the method achieves fast matching and determines the three-dimensional coordinates of marker points, enhancing measurement efficiency and robustness. This approach has been empirically tested on membrane structures, providing new insights. The results highlight that our novel algorithm can achieve high-precision measurements down to millimeters, and its accuracy increases with the actual displacement of the membrane structure. Notably, this groundbreaking measurement method remains unaffected by the form of the membrane surface, addressing a long-standing challenge in the field.

Positivity analysis for a fractional difference operator including an exponential formula in its kernel has been examined. A composition of two fractional difference operators of order ( ν , μ ) \left(\nu ,\mu ) in the sense of Liouville–Caputo type operators has been analysed in cases when ν ≠ μ \nu \ne \mu and ν = μ \nu =\mu . Due to the kernel of the fractional difference operator being convergent, there has been a restriction in the domain of the solution. Incidentally, a negative lower bounded condition has been carried out through analysing the positivity results. For a better understanding, an increasing function has been considered as a test for the main results.

In this article, the modified extended direct algebraic method is implemented to investigate the strain wave model that governs the wave propagation in micro-structured solids. The proposed method provides many new exact traveling wave solutions with certain free parameters. Exact solutions are extremely important in interpreting the inner structures of the natural phenomena. Solitary and other wave solutions are provided for this model, such as bright solitary solutions, dark solitary solutions, singular solitary solutions, singular-dark combo solitary solutions. Also, periodic solutions and Jacobi elliptic function solutions are presented. To show the physical characteristics of the raised solutions, the graphical illustration of some solutions is presented.

Exploring nonlinear equations and systems with predetermined coefficient values constrains the depth of understanding of the dynamics inherent in various applications and phenomena represented by such equations. On the contrary, exploration of nonlinear models with free coefficients offers avenues for improved development and ongoing refinement. In light of this, this study aimed to reassess the Wu–Zhang (WZ) system and Sawada–Kotera (SK) model by introducing arbitrary coefficients. Our goal is to identify the constraints necessary to ensure the existence of soliton solutions. Through the application of two distinct approaches, namely, the sine–cosine function method and tanh–coth expansion method, we systematically examine the conditions that facilitate the emergence of solitons within the WZ system and SK model. The insights gained from this analysis are supported by the presentation of 2D and 3D plots, providing a visual depiction of the propagation characteristics exhibited by the obtained solutions. The findings of the current work on conditions for the existence of soliton solutions for both generalized Wu–Zhang and generalized Sawada–Kotera models are novel and presented here for the first time.

In this study, wavelet method has been proposed to solve fractal-fractional differential equations (FFDEs) with power law kernel (FFDPL) and exponential decay kernel (FFDED). The proposed method is based on scale 3 Haar wavelets with collocation method, and fractional integral operational matrices for derivatives of Caputo and Caputo–Fabrizio sense are derived to solve FFDPL and FFDED. The applicability of the proposed method is shown by solving some numerical examples, and the obtained results are compared with available solutions in the literature. The solutions are presented in the graphical and tabular forms also.

With an emphasis on the combined degradation of railway track geometry and components, a new numerical-analytical method is proposed for predicting the track geometrical vertical levelling loss (VLL). In contrast to previous studies, this research unprecedentedly considers the influence of initial track irregularities (ITI) on VLL under cyclic loadings, elastic-plastic behaviour, and different operational dynamic conditions. The non-linear numerical models are simulated using an explicit finite element package known as LS-Dyna, and their results are validated by full-scale experimental and field measurement data. The outcomes are iteratively regressed by an analytical logarithmic function that cumulates permanent settlements, which innovatively extends the effect of ITI on VLL in a long-term behaviour. For a typical heavy-haul railway operating under 30 tons axle load and 60 km/h train velocity, the result indicates that the set of ITI with the highest standard deviation (SD) of vertical profile (VP) degrades faster (37% on average) than that with the lowest SD. Additionally, our new findings reveal that the worst scenario is related to a train running at 60 km/h and carrying a load of 20 tons/axle in an uneven track whose SD of VP evolves from 3.23 mm at N = 0 (ITI) to 7.20 mm, whereas the best one corresponds to a train at 60 km/h and 30 ton axle load in an uneven track whose SD of VP downgrades from 0.48 to 1.50 mm, both at 3 M cycles (or 60 million gross tons). These findings indicate the importance of considering the ITI for predicting track geometrical VLL under cyclic loadings. Therefore, based on this research, an acceptable condition (thresholds) of ITI can be redefined for a minimum effect on VLL, which can support the development of practical maintenance guidelines to extend the railway track service life.

This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

In this study, an efficient calculation method of matrix exponential function and vector product is proposed to reduce the calculation error. This method is based on the flexible exponential integral scheme; using B-series theory and two-color tree theory, the numerical series expression is obtained, and the exponential integral of the matrix exponential function is solved. By constructing a specific numerical integration scheme and analyzing its convergence under the theoretical framework of analytic semigroups, the convergence analysis of numerical schemes is studied and perfected. The numerical results show that the proposed method of matrix exponential function and vector product has a small error, which shows obvious advantages in reducing the calculation error.

Scheduling scientific workflows is essential for edge data centers operations. Fault tolerance is a crucial focus in workflow scheduling (WS) research. This study proposed fault-tolerant WS in edge data centers using Task Prioritization Adaptive Particle Swarm Optimization (TPAPSO). The aim is to minimize the Makespan, execution costs, and overcoming failures at all workflow processing stages, including when virtual machines are insufficient or tasks fail. The approach proposes three components: initial heuristic list, scheduling tasks with TPAPSO, and implementing performance monitoring with fault tolerance (PMWFT). TPAPSO-PMWFT is simulated using CloudSim 4.0. The experiments indicate that the suggested approach shows superior results compared to existing methods.

This article presents a non-linear mathematical model that captures the dynamics of drinking prevalence within a population. The model is analyzed under an optimal control framework, dividing the total population into four compartments: susceptible, heavy drinker, drinker in treatment, and recovered classes. The model’s validity is affirmed through considerations of positivity, boundedness, reproduction number, stability, and sensitivity analysis. Stability theory is employed to explore both local and global stabilities. Sensitivity analysis identifies parameters with a significant impact on the reproduction number ( R 0 {R}_{0} ), with maximum sensitivity observed in parameters related to drinking transmission and transitions from heavy drinking to treatment stages. These parameters exhibit sensitivity indices of ( 0.538 , 1 ) \left(0.538,1) , indicating that a 10% increase in these parameters would result in a ( 5.38 , 1 ) \left(5.38,1) increase in the threshold quantity. The study introduces an optimal control strategy that involves awareness campaigns and treatment as control variables. These controls aim to minimize the number of heavy drinkers while maximizing the number of recovered individuals. Pontryagin’s maximum principle is used to solve optimal control problems. Additionally, the research explores various parametric settings for each compartment, enriching the study environment. The effectiveness of the proposed control scheme is evaluated through rigorous numerical simulations, highlighting its competitive edge. The results, validated using MATLAB simulations, are detailed throughout the article.

Every institution in China has undergone reform and piloting based on its unique situation to enhance the quality of instruction as a result of the ongoing advancement of the times and the educational idea in the information age. The effectiveness of education is increased by hybrid teaching, which combines offline and online approaches. It empowered educators and motivates learners to take responsibility for their learning. Classes in physical education (PE) that place a strong emphasis on training and technical performance are especially well-suited for hybrid instruction. This mode improves teaching abilities and supports the long-term growth of education. As a result, we offer an online and offline technique for assessing the quality of PE instruction that is relied on mobile edge computing (MEC). With the use of the target, index, weight, and standard assessments, this study builds a quality evaluation index (QEI) approach for PE that combines online and offline techniques. Assessing the corresponding significance of every index, factor, and cluster analysis compresses index elements. The weights of the QEIs for integrated instruction are determined using MEC. The efficacy of combined PE is assessed using the fuzzy logic-based comprehensive assessment methodology. According to the analytical model, this strategy increases teaching quality while reducing costs and mistakes and improves assessment effectiveness. The experimental results proved that the proposed model has provided an accuracy of 95.98%.

The pursuit of solitary wave solutions to complex nonlinear partial differential equations is gaining significance across various disciplines of nonlinear science. This study seeks to uncover the solutions to the perturbed nonlinear Schrödinger equation using a robust and efficient analytical method, namely, the generalized exponential rational function technique. This equation is a fundamental tool used in various fields, including fluid mechanics, nonlinear optics, plasma physics, and optical communication systems, and has numerous practical applications across multiple disciplines. The employed method in this study stands out from existing approaches by being more comprehensive and straightforward. It offers a broader range of symbolic structures, surpassing the capabilities of some previously known methods. By applying this method to the perturbed nonlinear Schrödinger equation, we obtain a variety of exact solutions that significantly expand the existing literature and provide a fresh understanding of the model’s properties. Through numerical simulations, we demonstrate the dynamic characteristics of the system, including bifurcation and chaos analysis, and validate our findings by adjusting parameter settings to match expected behaviors.

This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo equation. The proposed solution is expressed as a double sum of basis functions that are chosen to be the convolved Fibonacci polynomials that generalize the well-known Fibonacci polynomials. In order to be able to apply the proposed collocation method, the operational matrices of derivatives of the convolved Fibonacci polynomials are introduced. The convergence and error analysis of the double expansion are carefully investigated in detail. Some new identities and inequalities regarding the convolved Fibonacci polynomials are introduced for such a study. Some numerical results, along with some comparisons, are provided. The presented results show that our proposed algorithm is efficient and accurate.

This article aims to study double-diffusive magneto-convective flow of electrically conducting and Newtonian fluid in the presence of throughflow and concentration modulation. Here, two infinite horizontal plates have been considered with heated from below and cooled and salted from above. The flow is also influenced by the induced magnetic field for which a constant magnetic field is applied in the perpendicular direction to the plates and vertically upward direction. A weakly nonlinear analysis is used to obtain the expression of heat and mass transport rate using Ginzburg–Landau equation. The influence of various physical parameters on Nusselt and Sherwood numbers is presented by graphs. From the numerical outcome, it is found that Péclet, Chandrasekhar, and magnetic Prandtl numbers enhance the mass and heat transport rate, while Lewis number increases only the rate of mass transport. The major result of this study is that the onset of convection postpones in the presence of throughflow and magnetic field.

In this article, two main assumptions commonly used in the reported literature are relaxed. First, instead of a continuous time controller, a discrete time controller is proposed. Second, the controller uses the flapping frequency as opposed to flapping force/moments as the control input commonly assumed by other research groups. A discrete time controller is more suitable for implementation and deployment to most real flapping wing micro aerial vehicles (FWMAVs), in which a computer controls a sampled system and the flapping wings are driven by servomotors. A robust reaching law based on the discrete sliding mode control method is proposed to stabilize the vertical altitude of a simulated FWMAV. The continuous time model of the FWMAV is converted to a discrete time model, and the discrete time sliding mode controller is developed for the new form of the model. Using the variable sampling time, the robust discrete sliding mode controller developed in this article is able to control a simulated FWMAV to successfully stabilize its position in spite of a 16% difference in model parameters, as well as a 0.7 m/s wind gust. The controller was able to withstand the wind gust with negligible deviation from its desired position. These simulation results further show an input frequency range similar to that of the experimentally derived model previously reported in the literature.

We propose high-order computational schemes for solving nonlinear fractional integro-differential equations (FIDEs) that are commonly used to model systems with memory or long-term behavior. From the known structure of the smooth solution, we show that the solutions of such FIDEs are equivalent to those of Volterra integral equations (VIEs). The fractional integral appearing in the integral form of the resulting VIE is then split into a history term and a local term. Subsequently, we develop an efficient strategy that utilizes a combination of a kernel compression scheme and an integral deferred correction (IDC) scheme to obtain a high-order solution. The kernel compression scheme reduces the costs in approximating the history term, while the IDC scheme approximates VIEs on short intervals to obtain the local information. Error analysis demonstrates high-order accuracy of the proposed schemes, and numerical examples illustrate their effectiveness, particularly for nonlinear FIDEs. The results suggest that the proposed scheme provides accurate solutions even for large time steps, making it a valuable tool for researchers and engineers working on systems with memory or long-term behavior.

In this study, the fractional variational iteration method using He’s polynomials is employed for constructing semi-analytical solutions of the fractional-in-time generalized nonlinear Schrödinger equation involving Jumarie’s modified Riemann–Liouville derivative. As a result, we obtain the solutions of the original problems in the forms of convergent series that are calculated easily. Our calculation results indicate that the method is quite efficient and convenient for these problems.

In this study, novel numerical methods are presented for solving nonlinear Fisher equations. These equations have a wide range of applications in various scientific and engineering fields, particularly in the biomedical sciences for determining the size of brain tumors. The challenges posed by the nonlinearity of the equations are effectively addressed through the development of numerical techniques. The nonlinearity is tackled using a combination of the method of lines and backward differentiation formulas of varied orders. This method is unconditionally stable, and its accuracy is evaluated using error norms. The methods are successfully validated against test problems with known solutions, demonstrating their superiority through comparative analyses with existing methodologies in the literature.

This article depicts the heat and mass transport of the double-diffusive convective flow of Walter-B viscoelastic fluid in highly permeable porous media with an internal heat source. We used weakly nonlinear analysis to quantify the nature of heat and mass transport using the Ginzburg–Landau equation. The Ginzburg–Landau equation has been derived in terms of the amplitude of the stream function. The effect of physical parameters has been examined on Nusselt and Sherwood numbers, which has represented graphically. According to the boundary condition, we have discussed the four scenarios based on the phase angles. Our study has demonstrated that internal heat plays a significant role in heat transfer processes. Furthermore, the elastic parameter leads to a transient augmentation in the heat and mass transfer rate. The main output of the current study is that the highest transport was found when both the modulations were put in out-phase condition (Scenario 1).

This research offers an advanced investigation into the examination of squeezed flow and heat mass transfer mechanisms of non-Newtonian Carreau dissipative nanofluids across a sensor surface. This analysis takes into consideration both variable thermal conductivity and variable viscosity aspects. It is widely accepted that the phenomenon of viscous dissipation has a significant impact on both the temperature distribution and heat transfer characteristics within nanofluids. Hence, it is being considered here. The governing equations of the problem are formulated using the Carreau model for the non-Newtonian fluid for the nanofluid. The thermal conductivity of the sensor surface is assumed to vary linearly with the temperature. The resulting nonlinear ordinary differential equations are solved numerically using the shooting method. The effects of various parameters such as suction parameter and magnetic parameter on the flow, the solutal characteristics, and thermal characteristics are analyzed. The results show that the slip parameter, the magnetic parameter, and the suction parameter have a significant effect on the flow and thermal fields. The heat transfer rate is improved by the squeezed flow index parameter and the Weissenberg number, but reduced by the power law index parameter and the Eckert number. Ultimately, the precision and reliability of the proposed approach are confirmed by benchmarking our data against previous findings. Understanding how variable viscosity impacts flow characteristics, heat transfer efficiency, and the performance of heat exchangers and cooling systems optimizes the design of nanofluids for efficient thermal systems in practical applications.

The nonlinear Schrödinger equation, held in high regard in the realms of plasma physics, fluid mechanics, and nonlinear optics, reverberates deeply within the field of ocean engineering, imparting profound insights across a plethora of phenomena. This article endeavours to establish a connection between the equation’s theoretical framework and its practical applications in ocean engineering, presenting a range of solutions tailored to grasp the intricacies of water wave propagation. By employing three methodologies, namely, the simplest equation method, the ratio technique, and the modified extended tanh-function method, we delineate various wave typologies, encompassing solitons and periodic manifestations. Enhanced by visual representations, our findings have the potential to deepen the comprehension of wave dynamics, with promising implications for the advancement of ocean engineering technologies and the refinement of marine architectural design.

Fibre-reinforced foamed urethane (FFU) composite sleepers and bearers are safety-critical components installed in complex railway switches and crossings. Not only does they need to provide vertical track support, the composite sleepers and bearers must also endure longitudinal and lateral actions stemming from complex wheel and rail interactions. In reality, the railway bearers at crossing noses are susceptible to coupling torsional-flexural loading. The complex non-linear behaviours have never been investigated numerically nor experimentally. It is thus necessary to comprehend torsional-flexural behaviours of FFU composite sleepers and bearers through finite element and experimental approaches. 3D finite element modelling of FFU composite beams have been established to predict the non-linear coupling behaviours. Three specimens of FFU beams have been prepared for robust experiments under each load case. Our studies exhibit excellent agreement between numerical and experimental results. The ductile failure behaviours (post yield point) have been observed from the experiments. Considerable effects of load eccentricity on the flexure–torsion behaviours of the composite members can also be noted. In addition, the load-eccentricity curves have been identified to portray the non-linear behaviour of the railway components under coupling flexural and torsional loadings. The new insights considering their load–displacement relationships, modes of failure and damage, flexural and torsional interactions are the precursors for railway engineers to design and adopt FFU composite sleepers and bearers in practice where complex wheel/rail interface generally causes coupling torsional and vertical loading conditions.

The nonlinear fractional Klein–Fock–Gordon (KFG) equation represents an advanced theoretical physics and applied mathematical tool that provides a more extraordinary framework for studying fields with complex and non-standard behaviors. Here, we aim to delve into the new wave profiles of this fractional KGF equation. Initially, this system is successfully converted into an ordinary differential equation (ODE) with the help of wave conversion, and the ODE is solved through the unified and unified solver techniques for the first time. In addition, the 3D and 2D plots of these solutions are drawn using a mathematical software package for different parameters with different values. Therefore, some unique waveforms can be found in these solutions. Moreover, stability and multistability analyses are prepared and shown graphically to confirm the converging limitations of appropriate parameters. This work will be practiced more effectively in future research on nonlinear partial differential models.

This study utilises mathematical modelling and computations to analyse the magnetohydrodynamic (MHD) effects on non-Newtonian Eyring–Powell fluid flow in an inclined non-uniform channel under long-wavelength, low Reynolds number conditions. The governing equations are solved by applying slip boundary conditions to determine the velocity, temperature, concentration, and streamline profiles. The key findings show that the magnetic parameter dampens the flow rate. The relationship between the variable viscosity, velocity, and temperature is nonlinear. The wall rigidity parameter and axial velocity are directly proportional until a threshold. Increasing inclination angles distorts streamlines. The magnetic field alters concentration contours and thermal transport. MATLAB parametric analysis explores MHD effects. This study enhances the understanding of inclined channel fluid dynamics, offering insights into variable viscosity, magnetic fields, wall properties, and impacts of inclination angles on non-Newtonian flow characteristics. This knowledge can optimise industrial MHD conduit/channel transport applications.

In this article, we are interested in the standard finite element approximation method of linear additive Schwarz iterations for a class of semi-linear elliptic problems, for two subdomains, in the context of non-matching grids. More precisely, by means of a uniform convergence result from the study by Lui and a fundamental lemma consisting of estimating, at each iteration, the gap between the continuous and the finite element Schwarz iterates, we prove that the discrete Schwarz sequences converge, in the maximum norm, to the true solution. Moreover, we also give numerical results to support the theoretical findings.

This article presents the application of the Faedo–Galerkin compactness method to establish the local well-posedness of the Newell–Whitehead–Segel equation. By analyzing a finite-dimensional approximate problem, the existence and uniqueness of a local solution were demonstrated. A priori estimates were derived, enabling the transition to the limit and the recovery of the original problem’s local solution. The study further proves the uniqueness and continuous dependence of the solution on initial data. Additionally, under certain conditions, it is shown that the energy norm of the solution decays exponentially over time, and the L 2 {L}^{2} -norm of the time derivative of the solution approaches zero asymptotically.

This study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u ″ ″ + q u = f u^{\prime\prime} ^{\prime\prime} +qu=f . The equation entails two distinct boundary conditions: pinned–pinned conditions on u u and u ′ u^{\prime} , and clamped–clamped conditions on u u and u ″ {u}^{^{\prime\prime} } . To satisfy these boundary conditions, we have built two sets of basis functions. The explicit forms of all spectral matrices were reported. The nonhomogeneous boundary conditions were easily handled using perfect transformations, ensuring the numerical solution’s accuracy. Detailed analysis of the method’s convergence was studied. Some numerical examples were presented, accompanied by comparisons with other existing methods in the literature.

We investigate a class of third-order nonlinear integro-differential equations (IDEs) with parallel computing of intelligent Internet of Things and wireless networks for numerical solutions. A numerical scheme based on the Haar wavelet has been established to compute the approximate solution for the problem under our consideration. By utilizing the mentioned tool, we discretize the involved derivatives and integrals. In this way, a sophisticated scheme is derived. Formulations for maximum root mean square and absolute errors have been given. Also, the convergent method has been discussed. In engineering, such as structural dynamics and control systems, third-order IDEs can improve modelling precision and solution effectiveness. Various examples have been testified by the aforementioned method. Additionally, by using different Gauss and collocation points (CPs), the aforementioned error terms were recorded. The convergence rate using distinct numbers of CPs has also been calculated, which is nearly equal to 2.

Hepatitis B, a liver disease caused by the hepatitis B virus (HBV), poses a significant public health burden. The virus spreads through the exchange of bodily fluids between infected and susceptible individuals. Hepatitis B is a complex health challenge for individuals. In this research, we propose a nonlinear HBV mathematical model comprising seven compartments: susceptible, latent, acutely infected, chronically infected, carrier, recovered, and vaccinated individuals. Our model investigates the dynamics of HBV transmission and the impact of vaccination on disease control. Using the next-generation matrix approach, we derive the basic reproduction number R 0 {R}_{0} and determine the disease-free equilibrium points. We establish the global and local stability of the model using the Lyapunov function. The model is numerically solved using the higher-order Galerkin time discretization technique, and a comprehensive sensitivity analysis is carried out to investigate the impact of all physical parameters involved in the proposed nonlinear HBV mathematical model. A comparison was made of the accuracy and dependability with the findings produced using the Runge–Kutta fourth-order (RK4) approach. The findings highlight the critical need for vaccination, particularly among the exposed class, to facilitate rapid recovery and mitigate the spread of HBV. The results of this study provide valuable insights for public health policymakers and inform strategies for hepatitis B control and elimination.

A practical examination of the traditional robotic arm (RA) in operation revealed a significant limitation in its ability to control the position of motion. This underscores the urgent need to enhance the current RA’s position control capabilities. Therefore, this study proposes the use of nonlinear differential equations (NDEs) to establish a mathematical model and the design of NDE-based RA motion control algorithms in conjunction with a central pattern generator neural network. A comparison of the control effects showed that the proposed method was highly fitted to the target trajectory. The joint node (JN) motion tracking trajectories of the three RAs were similar, up to 90–85% to the target trajectories of the JNs. In addition, the control of the motion position was similar up to 95–98% to the target motion position trajectories. The motion control algorithm based on NDEs was effective in improving the average execution time of the Pareto optimal frontier of the RA by 58.29%. The joint velocity and angle changes of the three types of RAs under the NDE control algorithm exhibited a high degree of similarity to the fluctuations observed in the expected and predicted curves. These observations contribute to an understanding of the effectiveness of the system observer in observing the joint angle changes. This indicates that the motion control based on NDEs can effectively enhance the tracking effectiveness of the JN positions of the RA, improve the control ability of the RA motion, and increase the joint stability of the RA.

Shallow water waves represent a significant and extensively employed wave type in coastal regions. The unconventional bidirectional transmission of extended waves across shallow water is elucidated through nonlinear fractional partial differential equations, specifically the space–time fractional-coupled Whitham–Broer–Kaup equation. The application of two distinct analytical methods, namely, the generalized logistic equation approach and unified approach, is employed to construct various solutions such as bright solitons, singular solitary waves, kink solitons, and dark solitons for the proposed equation. The physical behavior of calculated results is graphically represented through density, two- and three-dimensional plots. The obtained solutions could have significant implications across a range of fields including plasma physics, biology, quantum computing, fluid dynamics, optics, communication technology, hydrodynamics, environmental sciences, and ocean engineering. Furthermore, the qualitative assessment of the unperturbed planar system is conducted through the utilization of bifurcation theory. Subsequently, the model undergoes the introduction of an outward force with the aim of inducing disruption, resulting in the emergence of a perturbed dynamical system. The detection of chaotic trajectory in the perturbed system is accomplished through the utilization of a variety of tools designed for chaos detection. The execution of the Runge–Kutta method is employed to assess the sensitivity of the examined model. The results obtained serve to underscore the effectiveness and applicability of the proposed methodologies for the assessment of soliton structures within a broad spectrum of nonlinear models.

This study presents a space–time variable-order fractional carbon nanotube (CNT) mathematical model. Fractional differential equations successfully describe the model and its physical and biological properties. The mathematical model simulates the mixed free convection flow of a nanofluid in porous space using single- and multi-walled CNTs. The heat transfer characteristics of the base fluid (human blood) are studied. The numerical solutions for the temperature and velocity fields were derived from the modified Atangana–Baleanu–Caputo derivative, and the model was very effective. The higher compact finite difference method is used to study the numerical technique. Stabilization is construed as a technique related to John Neumann’s stabilization analysis. Additionally, the truncation error was studied, and various graphs were used to present numerical results. The results in the tables and the numerical figures emphasize that the schemes attained from applying the submitted numerical methods are completely compatible with the exact solution.

The synchronization of chaotic systems has garnered considerable attention across various fields, including neuroscience and physics. Particularly in these domains, synchronizing physical systems such as laser models is crucial for secure and rapid information transmission. Consequently, numerous studies investigate the synchronizability of different laser networks by establishing logical network frameworks. In this study, we employed a minimal universal laser (MUL) model designed to capture the essential dynamics of an actual laser model within just three dimensions. Within the network model of MUL systems, we introduced the linear diffusive function of neighboring nodes’ fast variables into the feedback term of the lasers, with models arranged in a global network structure. Our examination of synchronization within the constructed MUL network utilized master stability functions and the time-averaged synchronization error index. The findings suggest that while the network fails to achieve complete synchrony, it exhibits various synchronization phenomena, including cluster synchronization, chimera states, extreme events, and multistability. These results shed light on the complex dynamics underlying the synchronization of chaotic systems in networked environments, offering insights relevant to numerous applications across diverse fields.

A forward start option is an exotic option with delayed activation and reduced premium that allows investors to avail market opportunities in the future. Moreover, mean-reversion explores the investment strategies. This study examines the pricing of forward start options based on the uncertain mean-reverting stock model by applying Liu’s uncertain finance. Call and put options pricing formulas are derived. The study depicts that the pricing patterns in uncertain environments are consistent with the common characteristics of financial markets.

In response to the shortcomings of insufficient efficiency in calculating geometric nonlinear features and high environmental impact in the current construction, this study explores the control of nonlinear geometric structures based on an updated Lagrangian model function in the construction. In this method, the change in the geometric nonlinear stiffness is analyzed using generalized stiffness parameters and a displacement increment method, and the iteration step size and loading/unloading directions are adjusted in the iteration process to achieve the convergence of the solution. In the simulation experiment, the proposed method took 126 s to calculate the incremental iteration steps 700 times in a conventional environment, which is 28.8% more efficient than the cross-sectional method. In the simulated disaster environment, the model took 1,615 s to calculate the ultimate load of 84 contact elements, which is 43.1% more efficient than the section method and 62.6% more efficient than the discrete analysis method. Experimental results showed that the displacement judgment calculation efficiency of the method proposed in this study is higher than that of other models under different loading and unloading conditions and even in geological disaster states. This method had high environmental adaptability in solving nonlinear building structures and could improve the efficiency of solving general nonlinear building results.

The study aspires to adopt back propagation fuzzy neural networks to solve fuzzy quadratic programming problems. The main motivation behind proposing a back propagation neural network is that it can easily adjust and fine-tune the weights of the network from the error rate obtained at the previous layer. The error rate customarily called the loss function is the dissimilarity between the desired and predicted outputs. The chain and power rules of the derivative allow back propagation and successively update the weights of the network to perform efficiently. Thus, the gradient of the loss function is calculated by iterating backward layer by layer but one at a time to reduce the difference between the desired and the predicted outputs. The research flow is such that first of all the quadratic programming problem is formulated in a fuzzy environment. The problem with fuzzy quadratic programming is formulated as a lower, central, and upper model. The formulated models are then solved with backpropagation fuzzy neural networks. The proposed method is then implemented in the capital market to identify the optimal portfolio for potential investors in the Pakistan Stock Exchange. Six leading stocks traded on the stock exchange from Jan 2016 to Oct 2020 were taken into consideration. At all three levels (lower, central, and upper), the results of identifying the best investment portfolio for investors are consistent. The proposed three models identify the investors to invest in ATHL, MCB and ARPL, whereas, the remaining three IGIHL, INIL and POL are not desirable for investment. In all three cases, the convergence is obtained at 475 iterations which is faster than the previously conducted studies. Moreover, another advantage of the proposed technique is that it brings an improvement of 28.77% in the objective function of mean variance optimization MVO model.

This study commences by delving into B-spline curves, their essential properties, and their practical implementations in the real world. It also examines the role of knot vectors, control points, and de Boor’s algorithm in creating an elegant and seamless curve. Beginning with an overview of B-spline curve theory, we delve into the necessary properties that make these curves unique. We explore their local control, smoothness, and versatility, making them well-suited for a wide range of applications. Furthermore, we examine some basic applications of B-spline curves, from designing elegant automotive curves to animating lifelike characters in the entertainment industry, making a significant impact. Utilizing the de Boor algorithm, we intricately shape the contours of everyday essentials by applying a series of control points in combination with a B-spline curve. In addition, we offer valuable insights into the diverse applications of B-spline curves in computer graphics, toy design, the electronics industry, architecture, manufacturing, and various engineering sectors. We highlight their practical utility in manipulating the shape and behavior of the curve, serving as a bridge between theory and application.

This article presents an online speed estimation method for cooling fans in resource-limited embedded systems, considering modeling uncertainties and measurement noise. In the current thriving information technology era, monitoring the state of cooling fans is crucial, particularly for high-performance artificial intelligence server cabinets. Accurate fan speed estimation can be used not only to detect fan abnormalities but also for speed control-related applications. Several challenges arise in developing speed estimation algorithms, including state-dependent measurement noise variance, errors in nonlinear fan dynamic modeling, and uncertainties in parameter estimation. To address these issues, this study employs the unscented Kalman filter (UKF) algorithm, incorporating state-dependent noise modeling and mathematical modeling of parameter uncertainties. An UKF-based parameter update mechanism is developed to compensate for model uncertainties and estimation errors, improving the speed estimation accuracy. Simulation results indicate that the root-mean-square errors are reduced from 1.3393 with the traditional UKF to 0.7485 with the parameter update mechanism. Experimental verifications further validate the effectiveness of the proposed methods and strategies in addressing the challenges associated with speed estimation in cooling fans under uncertainties and noise interference.

As an important measure of traffic demand management, ride sharing can effectively increase the number of passengers from private car and bicycle, reduce vehicle travel rates, and thus alleviate traffic congestion and air pollution. With the rapid development of the internet of vehicles technology, the systematic study of private car sharing behavior and key technologies of sharing systems, and the construction of a road network spatiotemporal resource dynamic optimization theory and method guided by sharing priority in the internet of vehicles environment is a research work with great theoretical and practical values. This study investigates the ride sharing behavior and the influencing factors, such as education background, occupation, time and cost, and so on, based on internet of vehicles. Meanwhile, a Game-theory-based model was proposed and the local stability at equilibrium point was quantitatively studied. Private car sharing travel is influenced by various factors such as policies, technology, and system efficiency. Only by coordinating the operation of multiple factors can its effectiveness be fully utilized, and traffic congestion can be truly alleviated.

In this article, a review focusing on the frost resistance of recycled coarse aggregate concrete (RAC) and the bond performance of RAC with rebar under freeze–thaw environment is carried out. The results show that there are still some controversies about the advantages and disadvantages of the frost resistance of RAC, and many influencing factors have not been considered. The mass of the RAC pullout specimens shows a trend of first increasing and then decreasing after freeze‒thaw cycles. The failure modes of the RAC pullout specimens after freeze‒thaw cycles include pullout failure, pullout-splitting failure, splitting failure, and rebar yielding failure. The bond performance of RAC with rebar shows a degradation trend after freeze‒thaw cycles, mainly in the decrease in bond strength and the increase in bond slip. The bond performance of RAC specimens is inferior to that of natural aggregate concrete specimens after freeze‒thaw cycles. The bond strength prediction models and the bond–slip constitutive relation prediction models of RAC with rebar after freeze‒thaw cycles have been summarized to ensure that engineers can better understand their applicability. The bond stress distribution between the RAC and rebar in the anchoring area is not uniform and constantly changes with the number of freeze‒thaw cycles. The degradation mechanism of the bond performance of RAC with rebar after freeze‒thaw cycles is analyzed.

Motion planning and controller design are challenging tasks for highly coupled and nonlinear dynamical systems such as autonomous vehicles and robotic applications. Nonlinear model predictive control (NMPC) is an emerging technique in which sampling-based methods are used to synthesize the control and trajectories for complex systems. In this study, we have developed the sampling-based motion planning algorithm with NMPC through Bayesian estimation to solve the online nonlinear constrained optimization problem. In the literature, different filtration techniques have been applied to extract knowledge of states in the presence of noise. Due to the detrimental effects of linearization, the Kalman filter with NMPC only achieves modest effectiveness. Moving horizon estimation (MHE), on the other hand, frequently relies on simplifying assumptions and lacks an effective recursive construction. Additionally, it adds another optimization challenge to the regulation problem that has to be solved online. To address this problem, particle filtering is implemented for Bayesian filtering in nonlinear and highly coupled dynamical systems. It is a sequential Monte Carlo method that involves representing the posterior distribution of the state of the system using a set of weighted particles that are propagated through time using a recursive algorithm. For nonlinear and strongly coupled dynamical systems, the novel sampling-based NMPC technique is effective and simple to use. The efficiency of the suggested method has been assessed using simulated studies.

The anti-control of Hopf bifurcation is a method used for bifurcation control. It can be used to realize the occurrence or delay of bifurcation at the specified position to meet the needs of engineering applications. In this study, a 4D chaotic system is studied, and a dynamic state feedback control method is proposed to realize the anti-control of Hopf bifurcation for the system. By adjusting the control parameters of the controller, the system Hopf bifurcation can be generated or delayed at the specified position to realize the anti-control of Hopf bifurcation. This control method avoids complicated calculation processes and has remarkable control effects. Through numerical simulation analysis, the correctness of this control method is verified.

Traditional position and image-based visual servoing techniques often pose challenges in terms of target loss and actuator saturation. These challenges arise due to the requirement of calculating inverse Jacobians to determine robot motions and the susceptibility of these methods to image noise. To address the aforementioned challenges, this article presents a nonrecursive augmented dynamics control (NRADC) that establishes a direct correlation between variations in image pixels and the thrust and torque commands of a multirotor. By incorporating pixel variations into the dynamics of the multirotor, this approach enables the utilization of state constraints to address the issue of target loss. In addition, the correlation between image pixels and control commands allows for the integration of image noise with system uncertainties. Consequently, a single controller can be designed to simultaneously handle both aspects while considering input constraints, effectively addressing the problem of actuator saturation. Notably, unlike conventional control approaches that handle input and state constraints, the proposed NRADC approach is nonrecursive, making it well suited for implementation on systems with limited on-board computational resources, such as multirotors. The effectiveness of the proposed method is demonstrated through experimental validations, including a performance comparison with a nonrecursive controller from recent literature.

Multi-manipulator systems face challenges in coordinating their movement in complex environments. To enhance the collaborative control stability of multi-manipulator systems in intelligent manufacturing, this study utilizes event-triggered (ET) mechanisms to reduce the signal transmission burden and frequency, and combines adaptive strategy to solve interference factors in complex environments. In addition, the study combines adaptive strategy with neural network structure using adaptive neural network control methods, and adopts ET mechanism to design auxiliary variables. Then, the neural network approximates the nonlinear uncertain model of the system online to cope with external disturbances and improve the robustness. From the results, the maximum fitting error of the multi-manipulator system based on ET and adaptive strategy was 0.59%, which was 2.05 and 3.99% lower than the errors of the other two advanced control systems, respectively. In summary, the research on multi-manipulator systems in intelligent manufacturing on the basis of ET and adaptive strategy effectively improved its control stability in intelligent manufacturing.

The strong support for the rural revitalization strategy has gradually made greenhouse monitoring systems an important component of modern agriculture and the planting industry in China. To efficiently and intelligently monitor and regulate the greenhouse environment, a greenhouse monitoring system based on narrowband Internet of Things and a cloud service framework was proposed. The experiment introduced particle swarm optimization and genetic algorithms to improve the parameter optimization of this system, ultimately achieving intelligent regulation of the greenhouse environment. When the system iterated to the 49th and 78th iterations on the training and testing sets, respectively, the constructed method had the optimal fitness value, with values as high as 97.58 and 96.27. Comparing the packet loss rates, the communication success rate of the monitoring system was over 99% when the constructed method was running. Upon comparing the relative errors, under the operation of the constructed method, the average relative measurement errors of particulate matter, hydrogen sulfide, and ammonia were ±2.58 μg/m 3 , ±0.216 × 10 −6 , and ±0.175 × 10 −6 , respectively, all within a reasonable range. In addition, the constructed method was closer to the actual control values for temperature, humidity, light, and carbon dioxide. In summary, the greenhouse monitoring system constructed by this method has lower energy consumption and can reduce manual intervention, providing new ideas for achieving precision agriculture and sustainable development.

Epidemiological models feature reliable and valuable insights into the prevention and transmission of life-threatening illnesses. In this study, a novel SIR mathematical model for COVID-19 is formulated and examined. The newly developed model has been thoroughly explored through theoretical analysis and computational methods, specifically the continuous Galerkin–Petrov (cGP) scheme. The next-generation matrix approach was used to calculate the reproduction number ( R 0 ) ({R}_{0}) . Both disease-free equilibrium (DFE) ( E 0 ) ({E}^{0}) and the endemic equilibrium ( E ⁎ ) ({E}^{\ast }) points are derived for the proposed model. The stability analysis of the equilibrium points reveals that ( E 0 ) ({E}^{0}) is locally asymptotically stable when R 0 < 1 {R}_{0}\lt 1 , while E ⁎ {E}^{\ast } is globally asymptotically stable when R 0 > 1 {R}_{0}\gt 1 . We have examined the model’s local stability (LS) and global stability (GS) for endemic equilibrium   \text{&#x00A0;} and DFE based on the number ( R 0 ) ({R}_{0}) . To ascertain the dominance of the parameters, we examined the sensitivity of the number ( R 0 ) ({R}_{0}) to parameters and computed sensitivity indices. Additionally, using the fourth-order Runge–Kutta (RK4) and Runge–Kutta–Fehlberg (RK45) techniques implemented in MATLAB, we determined the numerical solutions. Furthermore, the model was solved using the continuous cGP time discretization technique. We implemented a variety of schemes like cGP(2), RK4, and RK45 for the COVID-19 model and presented the numerical and graphical solutions of the model. Furthermore, we compared the results obtained using the above-mentioned schemes and observed that all results overlap with each other. The significant properties of several physical parameters under consideration were discussed. In the end, the computational analysis shows a clear image of the rise and fall in the spread of this disease over time in a specific location.

Multi-sensor management and control technology generally constructs a reasonable objective function to solve the optimal control command set to control a limited number of sensors to obtain higher quality measurement information, thus obtaining better target tracking performance. In the process of multi-sensor information fusion, there is not only the problem of information redundancy but also obvious time delay. A sensor fusion algorithm combined with global optimization algorithm is innovatively proposed. According to the key frames saved in the previous steps, feature points in local maps, sensor information, and loop information, a global optimization algorithm based on graph optimization model is constructed to optimize the position and pose of intelligent hardware system and the position of spatial feature points. Moreover, this work studies and experiments on multi-sensor fusion simultaneous localization and mapping (SLAM) comprehensively and systematically, and the experimental results show that the algorithm proposed in this work is superior to common open-source SLAM algorithm in positioning accuracy and mapping effect under special circumstances. Therefore, the method proposed in this work can be applied to intelligent driving of vehicles, vision-assisted movement of robots and intelligent control of unmanned aerial vehicles, thus effectively improving the hardware control accuracy of intelligent systems.

Smart grids utilize advanced communication, information, and control technologies to build a more friendly power supply system. However, the development of technology leads to the increasing complexity of smart meter (SM) data in the power grid, and analyzing SM data becomes difficult. Therefore, in order to realize the effective analysis and forecasting of users’ electricity consumption behavior, an SM data analysis technique integrating the Internet of Things and artificial intelligence is proposed, which contains three major techniques: meter reading systems, load clustering, and load forecasting, and at last the technique is validated. Finally, the technology is validated. The experimental results showed that the average value of the Davis-Balding index for the proposed method combining recursive graphs and convolutional autoencoders was 1.87, which was significantly lower than the average value of 2.35 for other methods. The average value of the Dunn index was 0.086, which was higher than the 0.065 for the comparison method. In the load forecasting model, the model that employs multi-task learning and a gated cycle unit demonstrates superior performance across all comparison schemes, with the lowest average absolute percentage error of 12.90%. This is significantly lower than the comparison model’s 15.35%, which highlights the enhanced efficacy of the proposed model. The study realizes the effective analysis and prediction of consumers’ electricity consumption behavior and provides new ideas and solutions for the optimization and management of smart grids.