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Research on fault detection and identification methods of nonlinear dynamic process based on ICA

  • Chao Xie , Rui Zhang and Jyoti Bhola EMAIL logo
Published/Copyright: April 27, 2022
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Nonlinear Engineering
From the journal Nonlinear Engineering Volume 11 Issue 1

Abstract

In the present study, nonlinear dynamic process data are mapped into the kernel state space by kernel gauge variable analysis method to obtain decorrelated state data. The time-lapse covariance matrix of the state data is weighted and summed to obtain the time-lapse structure matrix of the state data, and then supervised kernel independent component analysis (SKICA) is established, the independent component feature data is extracted from the status data and the monitoring statistics are constructed to detect the process faults. The data show that kernel independent component analysis (ICA) method (KICA) method can detect slow fault faster than the ICA method, except that the statistical detection ability of F3 and FS is reduced, and the KICA method can significantly improve the detection performance of other faults and statistics. By analyzing the detection results of SKICA method, it is obvious that in the detection process of all five kinds of slow faults, the fault detection capability of SKICA is better than that of ICA and KICA. The results of continuous stirred reactor simulation system show that, compared with the basic linear process, the slow fault detection has a good monitoring performance, it can detect the small deviation in the process sensitively and give alarm information to the slow fault in time, to improve the fault detection rate.

Keywords: independent component analysis; fault detection; nonlinear dynamics

1 Introduction

With the extensive application of advanced computer measurement and control technology in the modern industrial process, production equipment is developing toward large-scale, integrated, and intelligent direction [1]. On the one hand, large-scale complex industrial systems can effectively improve the production efficiency and fully meet the market demand for products; on the other hand, the system has a large number of components that are prone to failure. If the small failure of a single component is not eliminated in time, it may cause a chain reaction, resulting in abnormal shutdown, or even catastrophic accidents, especially in the oil and petrochemical industry, due to its special working environment and strict operation requirements, any failure may cause irreparable losses. For example, in 2010, BP’s Deepwater Horizon oil rig in the Gulf of Mexico exploded and caught fire after failing to stop the blowout, causing serious human casualties, environmental damage, and economic losses. Domestic Shengli oil field suffers great economic loss due to pipeline leakage every year. More and more problems of production, safety, and economic benefits require timely and accurate fault detection and diagnosis to ensure safe and efficient operation of industrial systems [2,3]. The complexity of the production process data often exhibit strong nonlinear and dynamic at the same time. Therefore, SKICA method can better meet the needs of the process monitoring but cannot guarantee the accuracy of the extracted principal component which can reflect the dynamic characteristics of the process data [4,5,6] (Figure 1).

Figure 1 Fault detection process.
Figure 1

Fault detection process.

2 Literature review

In view of the nonlinear and dynamic characteristics of industrial processes, Ni et al. proposed a fault detection method, SKICA, based on nuclear state space independent element analysis [7]. Shang et al. found that compared with the traditional fault detection method based on dynamic kernel principal component analysis (PCA), this method can detect the occurrence of faults more sensitively and improve the fault detection rate [8]. In recent years, fault detection and diagnosis of data-driven processes has become a hot topic in academia and industry. Cai and Tian, proposed that statistical analysis is a data-driven method with many studies and wide attention from researchers [9]. Shi et al. believed that the reason was that actual industrial process variables were usually closely correlated. Multivariate statistical analysis, such as PCA, partial least squares (PLS), independent meta-analysis (ICA), etc., could consider the statistical correlation information between process variables and extract characteristic variables for fault detection and diagnosis [10]. It is worth noting that Dou et al. study is different from PCA, PLS, and other multivariate statistical analysis methods that only consider zero-time-delay second-order information to extract Gaussian features [11]. Du et al. believed that ICA could extract non-Gaussian features by considering high-order information, or simultaneously extract Gaussian and non-Gaussian features by considering second-order time information [12]. According to Shokry et al., as characteristic variables of industrial processes tend to follow non-Gaussian distribution, or some follow Gaussian distribution, some follow non-Gaussian distribution, ICA can extract process features more essentially than other multivariate statistical analysis methods [13]. In many cases, Rui suggests that the collected industrial process data may have complex characteristics, such as outliers, measurement noise, or nonlinear structure, etc., but the current ICA method is not fully considered and cannot obtain effective and reliable feature extraction results [14].

Therefore, combined with the characteristics of industrial process data, targeted algorithm research is carried out around SKICA method in ICA theory, and a set of process fault detection and diagnosis methods based on SKICA are established to enrich and develop ICA theory; it is of great theoretical significance and application value to meet the requirements of fault detection and diagnosis under complex industrial process data [15,16].

3 Methods

3.1 Nonlinear ICA method: Kernel ICA (KICA)

The basic idea of ICA is to conduct blind source separation of multichannel observation signals to obtain mutually independent source signals, which is essentially a linear transformation method [7]. To establish the nonlinear ICA model, the observed data x is mapped to the linear space through the nonlinear transformation, and the data y of the linear relationship is obtained, and then linear ICA analysis was applied to extract the independent elements to establish the overall nonlinear ICA model [17]. For the thousand observation vectors, assuming nonlinear mapping, little φ ( ⋅ ) maps the data to a high-dimensional linear space F:y = ϕ(x), where y is regarded as the normalized data. In ICA method, y needs to be automatized first, that is, to find the automatized transformation matrix Q to make z = Qy satisfy Eq. (1).

(1) E ∣ z z T ∣ = 1 .

The calculation of the automatized transformation matrix Q is shown in Eq. (2).

(2) Q = Λ − 1 / 2 U T .

Type Λ = diag( λ 1 , λ 2 , … ) , U = [ u 1 , u 2 , … ] , λ i , u i is the eigenvalue and eigenvector of the covariance matrix R y , as shown in Eq. (3).

(3) R y = E ∣ y y T ∣ = U Λ U T .

As the nonlinear mapping function φ ( ⋅ ) is often unknown, the covariance matrix on the left side of Eq. (3) cannot be obtained directly; hence, Λ, U cannot be calculated. Kernel function technology is used to solve the nonlinear mapping problem, let X, Y, respectively, represent the observation matrix composed of n observation samples of x and y, then the covariance matrix of Y is shown in Eq. (4).

(4) R y = 1 n − 1 Y Y T = 1 n − 1 φ ( X ) φ ( X ) T .

The eigenvalue decomposition of R y is performed, as shown in Eq. (5).

(5) R y u i = λ i u i .

The eigenvector u i is in the span of φ ( x i ) ( j = 1 , … , n ) , so Eq. (6) holds.

(6) u i = φ ( x ) u i = ∑ j = 1 n u i j φ ( x j ) .

Eqs. (4) and (6) are substituted into Eq. (5) and then multiplied both sides by φ ( x ) T , as shown in Eq. (7).

(7) 1 n − 1 φ ( x ) T φ ( X ) φ ( x ) T φ ( X ) u i = λ φ ( x ) T φ ( X ) u i .

Therefore, the kernel function is defined by applying the kernel function technique to Eq. (7) k ( x i , x j ) = 〈 φ ( x i ) , φ ( x j ) 〉 , the meaning of kernel function is to calculate the innermost product of the nonlinear transformation with the kernel function of the vector in the original space [18]. The existing literature provides a variety of kernels for selection, using polynomial kernels, for the observation data matrix X, there are φ ( x ) T φ ( x ) = K , among them [ K ] i j = k ( x i , x j ) . Therefore, Eq. (7) becomes the eigenvalue decomposition process described by the kernel function matrix, as shown in Eq. (8).

(8) 1 n − 1 K 2 u i = λ K u i .

To ensure that the original feature vector is the standard vector, namely u i T u i = 1 , the following processing is required, as shown in Eq. (9).

(9) u i = 1 ( n − 1 ) λ i u i .

In combination with the definition of albino transformation matrix, Q, in Eqs. (2) and (10) can be obtained.

(10) Q = Λ − 1 / 2 U T = Λ − 1 / 2 ( φ ( x ) V ) T .

Then, the data expression after whitening processing is shown in Eq. (11).

(11) z = Λ − 1 / 2 V T φ ( x ) T φ ( x ) = Λ − 1 / 2 V T K x .

After whitening in Eq. (11), the data x in the original nonlinear space is mapped to the data z in the linear space; furthermore, the linear ICA algorithm is used to estimate the nonlinear independent element variable, s, by optimizing the unmixing matrix B [19], as shown in Eq. (12).

(12) s = B T z

The above nonlinear ICA method uses kernel function in the analysis engineering, so this method is called KICA [20]. When using KICA to detect whether there is a fault in the industrial process, d nonlinear independent element s d should be extracted from the original data, and the reconstruction error e based on d independent elements, s d, be calculated, and e based on the construction of appropriate monitoring measurement can effectively monitor the changes in the process, as shown in Eqs. (13) and (14).

(13) s d = B d T z ,

(14) e = Λ − 1 / 2 ( z − B d s d ) .

3.2 SKICA method

Because many faults in the industrial production process are slow type faults, the process changes caused by faults are slow, reflected in the change of nonlinear independent element sd and reconstruction error e is also slow; therefore, even the nonlinear ICA method can only detect the fault after a long time [21].

Accumulation and cumulative sum (CUSUM) control charts are an effective means to detect micro shifts in the process, its theoretical basis is the sequential probability ratio test in the principle of sequential analysis, which determines whether the production process is in the state of statistical control by the cumulative results of previous observations [22,23]. As the process information is accumulated and the amount of information used increases, the CUSUM control chart can improve the detection sensitivity of small process deviation [24]. Based on the idea of accumulation and control chart, for the nonlinear independent element and reconstruction error in Eqs. (13) and (14), we define new cumulates and descriptors, as shown in Eqs. (15) and (16).

(15) s ¯ d ( k ) = s d ( i ) , k < h s ¯ d ( k ) = ∑ i = k − h + 1 k s d ( i ) , k = h , … , N ,

(16) e ¯ ( k ) = e ( i ) , k < h e ¯ ( k ) = ∑ i = k − h + 1 k e ( i ) , k = h , … , N .

In the formula, h is the width of the sliding window.

Therefore, a new nonlinear ICA method, SKICA, is established [15]. This method first performs nonlinear processing based on ICA and then applies a sliding window to the nonlinear independent elements for cumulative sum [25]. Two monitoring statistics can be established based on SKICA model: I 2 and squared prediction error (SPE) statistics, where I 2 monitors the data changes in the independent meta-space, SPE monitors data changes in the error space, and the confidence limits of the two statistics are obtained by kernel density estimation. When SKICA is used for online monitoring, if any statistic exceeds the confidence limit (threshold), a fault occurs in the system, as shown in Eqs. (17) and (18).

(17) I 2 = s ¯ d s ¯ d T

(18) SPE = e ¯ e ¯ T

4 Results and analysis

Considering a typical industrial process continuous stirred reactor (CSTR) system as the simulation research object, to compare the effectiveness of the algorithm, first, five typical industrial process changes are simulated (as shown in Table 1), in which failures F1, F2, and F3 describe the slow change of process T. Faults F4 and F5 describe the slow change of process parameters, record the process variables during the simulation, collect the data of 500 samples for each fault, and apply faults at the 201th sampling moment in each sampling process. ICA, KICA, and SKICA were used to detect faults, respectively, and their fault detection thresholds all adopted 95% confidence limits of statistics [26]. In the detection process, to facilitate the comparison of methods, if eight consecutive samples exceed the detection threshold, the time is defined as the time of fault detection.

Table 1

Five kinds of slow type faults

The fault Fault description
F1 The feed concentration increased gradually at the rate of 5 × 10−4 (mol/L)/min
F2 The feed temperature changes gradually at a rate of 0.15 K/min
F3 The inlet temperature of cooling water increased gradually at a rate of 0.05 K/min
F4 Catalyst failure: catalyst activity gradually decreases
F5 Heat transfer fault: the heat transfer capacity gradually decreases

Considering fault F1 as an example, the I 2 statistics and SPE statistics of ICA method detected the fault at the 303rd and 344th sampling time, respectively (see Figure 2), whereas the corresponding fault detection time of KICA method is 284 and 284 sampling times, respectively (see Figure 3). It can be seen that KICA method can detect fault F1 faster than the linear ICA method. SKICA method is a further improvement than KICA method for calculating the cumulative and statistics of nonlinear independent elements, the SKICA method’s cad, corpse, and SPE statistics detect the fault at 248 and 227 times, respectively (see Figure 4), which are closer to the true time when the fault occurred. Similarly, fault 2 describes the gradual change in feed temperature. Fault 3 shows the increase in the inlet temperature of cooling water. Fault 4 depicts the catalyst failure problem in which catalytic activity decreases, and the F5 is the heat transfer issue in the system.

Figure 2 Fault F1 detection results based on ICA method.
Figure 2

Fault F1 detection results based on ICA method.

Figure 3 Fault F1 detection results based on KICA method.
Figure 3

Fault F1 detection results based on KICA method.

Figure 4 Detection results of fault F1 based on SKICA method.
Figure 4

Detection results of fault F1 based on SKICA method.

The comparison of the detection time of five faults is shown in Table 2.

Table 2

Fault detection time comparison of the three methods

The fault types ICA KICA SKICA
I 2 SPE I 2 SPE I 2 SPE
F1 303 344 284 284 248 227
F2 277 324 277 277 252 227
F3 374 408 411 392 311 289
F4 412 462 394 394 319 280
F5 340 / 431 318 316 302

“/” in the table indicates that the statistics cannot detect faults.

In general, KICA method can detect slowly varying faults faster than ICA method, except that the statistical detection ability of F3 and FS is reduced; the KICA method can improve the detection performance of other faults and statistics significantly. According to the analysis of the detection results of SKICA method in Table 2, it is obvious that SKICA is superior to ICA and KICA method in the detection process of all five kinds of slow faults. Either the traditional fault detection method based on kernel fast ICA or the proposed fault detection method based on kernel timing structure ICA, their focus is on how to effectively estimate independent element characteristics from nonlinear process data; however, how to make full use of the estimated independent element features to further improve the fault detection performance is not considered. First, in the off-line modeling stage, the ICA algorithm of kernel timing structure is used to estimate the independent element sample data from the process data of normal working conditions, Gaussian mixture model is introduced to estimate the probability density function of each independent element. Based on this, the probability of sample data of independent element under normal working conditions is calculated, and then the corresponding probability threshold of each independent element is determined. Then, during the online fault detection, the kernel time-sequence structure SKICA algorithm is used to estimate the independent element sample data from the current measurement data, and according to the independent element probability density function obtained during the offline modeling, the probability of the current independent element sample data is calculated, and it is compared with the probability threshold corresponding to the independent element to determine the correlation degree between the current independent element sample data and the fault, a large weight is assigned to the sample data of independent elements with a large correlation with the fault, whereas a small weight is assigned to the sample data of independent elements with a small or unrelated correlation with the fault; therefore, at different sampling times, features of independent elements that are highly correlated with faults can be highlighted, whereas features of independent elements that are less or unrelated to faults can be suppressed to achieve the purpose of improving fault detection performance.

5 Conclusions

The SKICA method was proposed, a typical industrial process CSTR system was considered as the simulation research object, the KICA method and SKICA method were compared and studied, the results of CSTR simulation system show that compared with the basic linear process, the slow type fault detection has good monitoring performance and can detect the small deviation in the process of sensitive, warning information can be given to slow type faults in time, it can be clearly seen that in the detection process of all five kinds of slow type faults, the fault detection capability of SKICA is better than that of ICA and KICA. Although fault detection and diagnosis based on ICA theory has attracted extensive attention of many researchers and engineers in the field of industrial process monitoring; however, due to the complexity of industrial process production equipment, the diversity of operating conditions, and the variability of uncertain factors, the collected process data usually has very complex characteristics. As a result, combined with the characteristics of industrial process data, targeted algorithm research is carried out around the SKICA method in ICA theory, and a set of process fault detection and diagnosis methods based on SKICA is established, enriching, and developing ICA theory, and it is of great theoretical and application value to meet the requirements of fault detection and diagnosis under complex industrial process data.

  1. Funding information: The authors state no funding involved.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

References

[1] Song X, Wang M, Song S, Ning Z. Space-sampling-based fault detection for nonlinear spatiotemporal dynamic systems with Markovian switching channel. Inf Sci. 2020;520(5):400–15.10.1016/j.ins.2020.02.032Search in Google Scholar

[2] Odiowei PP, Cao Y. State-space independent component analysis for nonlinear dynamic process monitoring. Chemom Intell Lab Syst. 2010;103(1):59–65.10.1016/j.chemolab.2010.05.014Search in Google Scholar

[3] Chen L, Jagota V, Kumar A. Research on optimization of scientific research performance management based on BP neural network. Int J Syst Assur Eng Manag. 2021. 10.1007/s13198-021-01263-z.Search in Google Scholar

[4] Zhang Y. Fault detection and diagnosis of nonlinear processes using improved kernel independent component analysis (KICA) and support vector machine (SVM). Ind Eng Chem Res. 2008;47(18):6961–71.10.1021/ie071496xSearch in Google Scholar

[5] Jagota V, Sethi AP, Kumar K. Finite element method: an overview. Walailak J Sci Technol. 2013;10(1):1–8.Search in Google Scholar

[6] Kouadri A, Hajji M, Harkat MF, Abodayeh K, Mansouri M, Nounou H, et al. Hidden Markov model based principal component analysis for intelligent fault diagnosis of wind energy converter systems. Renew Energy. 2020;150:598–606.10.1016/j.renene.2020.01.010Search in Google Scholar

[7] Ni Z, Tian X, Cai L, Deng X. Process fault detection based on dynamic kernel slow feature analysis. Comput Electr Eng. 2015;41:9–17.10.1016/j.compeleceng.2014.11.003Search in Google Scholar

[8] Shang J, Chen M, Zhang H. Fault detection based on augmented kernel Mahalanobis distance for nonlinear dynamic processes. Comput Chem Eng. 2018;109:311–21.10.1016/j.compchemeng.2017.11.010Search in Google Scholar

[9] Cai L, Tian X. A new fault detection method for non-Gaussian process based on robust independent component analysis. Process Saf Environ Prot. 2014;92(6):645–58.10.1016/j.psep.2013.11.003Search in Google Scholar

[10] Shi H, Guo J, Bai X, Guo L, Sun J. Research on a nonlinear dynamic incipient fault detection method for rolling bearings. Appl Sci (Basel). 2020;10(7):2443.10.3390/app10072443Search in Google Scholar

[11] Dou C, Zheng L, Wang W, Shabaz M. Evaluation of urban environmental and economic coordination based on discrete mathematical model. Math Probl Eng. 2021;2021. 10.1155/2021/1566538.Search in Google Scholar

[12] Du Y, Duever TA, Budman H. Generalized polynomial chaos-based fault detection and classification for nonlinear dynamic processes. Ind Eng Chem Res. 2016;55(7):2069–82.10.1021/acs.iecr.5b04694Search in Google Scholar

[13] Shokry A, Ardakani MH, Escudero G, Graells M, Espuna A. Dynamic kriging based fault detection and diagnosis approach for nonlinear noisy dynamic processes. Comput Aided Chem Eng. 2017;106:758–76. 10.1016/j.compchemeng.2017.03.016.Search in Google Scholar

[14] Rui LS. Based on LabNIEW environment auto fault detection research of virtual test system. Appl Mech Mater. 2015;727–728:855–8.10.4028/www.scientific.net/AMM.727-728.855Search in Google Scholar

[15] Rakhra M, Singh R, Lohani TK, Shabaz M. Metaheuristic and machine learning-based smart engine for renting and sharing of agriculture equipment. Math Probl Eng. 2021;2021. 10.1155/2021/5561065.Search in Google Scholar

[16] Sun L, Li Y, Jia H, Ying Y. Research on fault detection method for air handling unit system. IFAC-PapersOnLine. 2019;52(3):79–84.10.1016/j.ifacol.2019.06.014Search in Google Scholar

[17] Jagota V, Sharma RK. Interpreting H13 steel wear behavior for austenitizing temperature, tempering time and temperature. J Braz Soc Mech Sci Eng. 2018;40:219.10.1007/s40430-018-1140-6Search in Google Scholar

[18] Ma H, Hu Y, Shi H. Fault detection and identification based on the neighborhood standardized local outlier factor method. Ind Eng Chem Res. 2013;52(6):2389–402.10.1021/ie302042cSearch in Google Scholar

[19] Yao Q, Shabaz M, Lohani TK, Wasim Bhatt M, Panesar GS, Singh RK. 3D modelling and visualization for vision-based vibration signal processing and measurement. J Intell Syst. 2021;30(1):541–53.10.1515/jisys-2020-0123Search in Google Scholar

[20] Zhirabok A, Shumsky A, Solyanik S, Suvorov A. Fault detection in nonlinear systems via linear methods. Int J Appl Math Comput Sci. 2017;27(2):261–72.10.1515/amcs-2017-0019Search in Google Scholar

[21] Kazemi H, Yazdizadeh A. Fault detection and isolation of gas turbine engine using inversion-based and optimal state observers. Eur J Control. 2020;56:206–17.10.1016/j.ejcon.2020.01.002Search in Google Scholar

[22] Fan J, Wang Y. Fault detection and diagnosis of non-linear non-Gaussian dynamic processes using kernel dynamic independent component analysis. Inf Sci. 2014;259:369–79.10.1016/j.ins.2013.06.021Search in Google Scholar

[23] Yasoda K, Ponmagal RS, Bhuvaneshwari KS, Venkatachalam K. Automatic detection and classification of EEG artifacts using fuzzy kernel SVM and wavelet ICA (WICA). Soft Comput. 2020;24(21):16011–9.10.1007/s00500-020-04920-wSearch in Google Scholar

[24] Du Y, Budman H, Duever TA. Comparison of stochastic fault detection and classification algorithms for nonlinear chemical processes. Comput Chem Eng. 2017;106:57–70. 10.1016/j.compchemeng.2017.05.016.Search in Google Scholar

[25] Huang J, Yan X. Dynamic process fault detection and diagnosis based on dynamic principal component analysis, dynamic independent component analysis and Bayesian inference. Chemom Intell Lab Syst. 2015;148:115–27.10.1016/j.chemolab.2015.09.010Search in Google Scholar

[26] Han H, Yang Y, Li L, Ding SX. Performance-based fault detection and fault-tolerant control for nonlinear systems with t-s fuzzy implementation. IEEE Trans Cybern. 2021;51(2):801–14.10.1109/TCYB.2019.2951534Search in Google Scholar PubMed

Received: 2021-09-15
Revised: 2021-12-07
Accepted: 2021-12-12
Published Online: 2022-04-27

© 2022 Chao Xie et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2022-0003
Keywords for this article
independent component analysis; fault detection; nonlinear dynamics
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  12. Solution of two-dimensional fractional diffusion equation by a novel hybrid D(TQ) method
  13. Investigation of three-dimensional hybrid nanofluid flow affected by nonuniform MHD over exponential stretching/shrinking plate
  14. Solution for a rotational pendulum system by the Rach–Adomian–Meyers decomposition method
  15. Study on the technical parameters model of the functional components of cone crushers
  16. Using Krasnoselskii's theorem to investigate the Cauchy and neutral fractional q-integro-differential equation via numerical technique
  17. Smear character recognition method of side-end power meter based on PCA image enhancement
  18. Significance of adding titanium dioxide nanoparticles to an existing distilled water conveying aluminum oxide and zinc oxide nanoparticles: Scrutinization of chemical reactive ternary-hybrid nanofluid due to bioconvection on a convectively heated surface
  19. An analytical approach for Shehu transform on fractional coupled 1D, 2D and 3D Burgers’ equations
  20. Exploration of the dynamics of hyperbolic tangent fluid through a tapered asymmetric porous channel
  21. Bond behavior of recycled coarse aggregate concrete with rebar after freeze–thaw cycles: Finite element nonlinear analysis
  22. Edge detection using nonlinear structure tensor
  23. Synchronizing a synchronverter to an unbalanced power grid using sequence component decomposition
  24. Distinguishability criteria of conformable hybrid linear systems
  25. A new computational investigation to the new exact solutions of (3 + 1)-dimensional WKdV equations via two novel procedures arising in shallow water magnetohydrodynamics
  26. A passive verses active exposure of mathematical smoking model: A role for optimal and dynamical control
  27. A new analytical method to simulate the mutual impact of space-time memory indices embedded in (1 + 2)-physical models
  28. Exploration of peristaltic pumping of Casson fluid flow through a porous peripheral layer in a channel
  29. Investigation of optimized ELM using Invasive Weed-optimization and Cuckoo-Search optimization
  30. Analytical analysis for non-homogeneous two-layer functionally graded material
  31. Investigation of critical load of structures using modified energy method in nonlinear-geometry solid mechanics problems
  32. Thermal and multi-boiling analysis of a rectangular porous fin: A spectral approach
  33. The path planning of collision avoidance for an unmanned ship navigating in waterways based on an artificial neural network
  34. Shear bond and compressive strength of clay stabilised with lime/cement jet grouting and deep mixing: A case of Norvik, Nynäshamn
  35. Communication
  36. Results for the heat transfer of a fin with exponential-law temperature-dependent thermal conductivity and power-law temperature-dependent heat transfer coefficients
  37. Special Issue: Recent trends and emergence of technology in nonlinear engineering and its applications - Part I
  38. Research on fault detection and identification methods of nonlinear dynamic process based on ICA
  39. Multi-objective optimization design of steel structure building energy consumption simulation based on genetic algorithm
  40. Study on modal parameter identification of engineering structures based on nonlinear characteristics
  41. On-line monitoring of steel ball stamping by mechatronics cold heading equipment based on PVDF polymer sensing material
  42. Vibration signal acquisition and computer simulation detection of mechanical equipment failure
  43. Development of a CPU-GPU heterogeneous platform based on a nonlinear parallel algorithm
  44. A GA-BP neural network for nonlinear time-series forecasting and its application in cigarette sales forecast
  45. Analysis of radiation effects of semiconductor devices based on numerical simulation Fermi–Dirac
  46. Design of motion-assisted training control system based on nonlinear mechanics
  47. Nonlinear discrete system model of tobacco supply chain information
  48. Performance degradation detection method of aeroengine fuel metering device
  49. Research on contour feature extraction method of multiple sports images based on nonlinear mechanics
  50. Design and implementation of Internet-of-Things software monitoring and early warning system based on nonlinear technology
  51. Application of nonlinear adaptive technology in GPS positioning trajectory of ship navigation
  52. Real-time control of laboratory information system based on nonlinear programming
  53. Software engineering defect detection and classification system based on artificial intelligence
  54. Vibration signal collection and analysis of mechanical equipment failure based on computer simulation detection
  55. Fractal analysis of retinal vasculature in relation with retinal diseases – an machine learning approach
  56. Application of programmable logic control in the nonlinear machine automation control using numerical control technology
  57. Application of nonlinear recursion equation in network security risk detection
  58. Study on mechanical maintenance method of ballasted track of high-speed railway based on nonlinear discrete element theory
  59. Optimal control and nonlinear numerical simulation analysis of tunnel rock deformation parameters
  60. Nonlinear reliability of urban rail transit network connectivity based on computer aided design and topology
  61. Optimization of target acquisition and sorting for object-finding multi-manipulator based on open MV vision
  62. Nonlinear numerical simulation of dynamic response of pile site and pile foundation under earthquake
  63. Research on stability of hydraulic system based on nonlinear PID control
  64. Design and simulation of vehicle vibration test based on virtual reality technology
  65. Nonlinear parameter optimization method for high-resolution monitoring of marine environment
  66. Mobile app for COVID-19 patient education – Development process using the analysis, design, development, implementation, and evaluation models
  67. Internet of Things-based smart vehicles design of bio-inspired algorithms using artificial intelligence charging system
  68. Construction vibration risk assessment of engineering projects based on nonlinear feature algorithm
  69. Application of third-order nonlinear optical materials in complex crystalline chemical reactions of borates
  70. Evaluation of LoRa nodes for long-range communication
  71. Secret information security system in computer network based on Bayesian classification and nonlinear algorithm
  72. Experimental and simulation research on the difference in motion technology levels based on nonlinear characteristics
  73. Research on computer 3D image encryption processing based on the nonlinear algorithm
  74. Outage probability for a multiuser NOMA-based network using energy harvesting relays
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