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Mathematical Modeling and Numerical Simulation in Engineering
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Mathematical Modeling and Numerical Simulation in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 22286

Special Issue Editor

Prof. Dr. Miaojuan Peng

E-Mail Website
Guest Editor
School of Mechanics and Engineering Science, Shanghai University, Shanghai 200044, China
Interests: mathematical model; numerical method; numerical simulation; finite element method; meshless method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Because of the complexity of engineering problems, it is important to present the mathematical model and the corresponding numerical methods. Now partial differential equation with the corresponding boundary and initial conditions is the basic model for engineering problems. Finite element method, boundary element method and meshless method are several kinds of major numerical methods for simulating engineering problems. Various numerical methods are presented for solving the problems in different engineering fields, and the corresponding computational efficiency, accuracy and convergence are studied as well. The applications of the mathematical models and numerical methods in complicated engineering problems also should be studied.

In this Special Issue, we particularly take an interest in manuscripts that report relevance of mathematical models and numerical computation for complicated engineering and social problems. The special issue will become an international forum for researchers to summarize the most recent developments of mathematical models and numerical simulations for engineering problems within the last five years, especially for the mathematical model of new problems. Moreover, the manuscripts on the mathematical theories of mathematical model and numerical computation for complicated science, engineering or social problems are welcome. We also concern the development of the corresponding aspects based on data analysis, including the corresponding theory, numerical method and the applications.

Prof. Dr. Miaojuan Peng
Guest Editor

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical model
  • numerical method
  • numerical simulation
  • engineering problem
  • social problem

Published Papers (14 papers)

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Research

24 pages, 9284 KiB  
Article
A Novel Imputation Model for Missing Concrete Dam Monitoring Data
by Xinran Cui, Hao Gu, Chongshi Gu, Wenhan Cao and Jiayi Wang
Mathematics 2023, 11(9), 2178; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092178 - 05 May 2023
Cited by 1 | Viewed by 1187
Abstract
To ensure the safety of concrete dams, a large number of monitoring instruments are embedded in the bodies and foundations of the dams. However, monitoring data are often missing due to failure of monitoring equipment, human error and other factors that cause difficulties [...] Read more.
To ensure the safety of concrete dams, a large number of monitoring instruments are embedded in the bodies and foundations of the dams. However, monitoring data are often missing due to failure of monitoring equipment, human error and other factors that cause difficulties in diagnosis of dam safety and failure to precisely predict their deformation. In this paper, a new method for imputing missing deformation data is proposed. First, since the traditional deformation increment speed distance index of the deformation similarity index does not take into account the fact that there is little change in deformations occurring in two consecutive days, the denominator of the index tends to be equal to zero. In this paper, an improved index for solving this problem is proposed. A combined weighting method for calculating the deformation similarity comprehensive index and the k-means clustering method is then proposed and used to classify deformation monitoring points. Subsequently, a panel data model that imputes different types of missing data is established. The method proposed in this paper can impute missing concrete dam deformation data more accurately; therefore, it can effectively solve the missing deformation monitoring data problem. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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16 pages, 7314 KiB  
Article
Deterioration Model for Reinforced Concrete Bridge Girders Based on Survival Analysis
by Li Li, Yu Lu and Miaojuan Peng
Mathematics 2022, 10(23), 4436; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234436 - 24 Nov 2022
Viewed by 1402
Abstract
The prediction of bridge service performance is essential for bridge maintenance, operation, and decision making. As a key component of the superstructure, the performance of the main girders is critical to the structural safety of the bridge. This study makes full use of [...] Read more.
The prediction of bridge service performance is essential for bridge maintenance, operation, and decision making. As a key component of the superstructure, the performance of the main girders is critical to the structural safety of the bridge. This study makes full use of the inspection records from the Bridge Management System (BMS) in Shanghai and performs pre-processing work on a large amount of data. Recent advances in survival analysis were utilized to investigate the inspection records of over 40,000 reinforced concrete bridge main girders over a 14-year period. Survival analysis methods based on the Weibull distribution were used to predict the service performance of the main girders, and, in addition, a COX proportional hazards model was used to analyze the effect of different covariates on the survival of the main girders. The results show that the deterioration rate of main girders increases with age, with an average life of 87 years for main girders in Shanghai. The grade of the road on which the bridge is located and the position of the main girder in the bridge superstructure have a significant impact on the probability of survival of the main girder. It can be concluded that more attention should be paid to the inspection and maintenance of side girders on branch roads to reduce the pressure on bridge management in the future. Furthermore, the analysis in this study found that the deterioration rate of the main girders is faster than the deterioration rate of the whole bridge and superstructure, and, therefore, more attention and necessary preventive maintenance measures should be taken in the maintenance and management of the main girders. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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16 pages, 5480 KiB  
Article
Data Reconstruction-Based Two-Step Non-Intrusive Reduced-Order Modeling Using Fourier Transform and Interpolations
by Jonggeon Lee, Euiyoung Kim and Jaehun Lee
Mathematics 2022, 10(20), 3738; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203738 - 11 Oct 2022
Cited by 1 | Viewed by 1084
Abstract
This study presents a data reconstruction-based two-step non-intrusive reduced-order modeling (ROM) based on discrete Fourier transformation (DFT) and proper orthogonal decomposition-radial basis function (POD-RBF) interpolation. To efficiently approximate a system for various parametric inputs, two offline and one online stage are proposed. The [...] Read more.
This study presents a data reconstruction-based two-step non-intrusive reduced-order modeling (ROM) based on discrete Fourier transformation (DFT) and proper orthogonal decomposition-radial basis function (POD-RBF) interpolation. To efficiently approximate a system for various parametric inputs, two offline and one online stage are proposed. The first offline stage adjusts and reconstructs sampled data using a scaling factor. During the adjusting procedure, the fast Fourier transform operation is used to transform a domain between the time and frequency, and the POD-RBF interpolation method efficiently generates adjusted data. The second offline stage constructs multiple ROMs in the frequency domain for interpolation with respect to the parameter. Finally, in the online stage, the solution field depending on the changes in input parameters, is approximated using the POD-RBF interpolation and the inverse Fourier transformation. The accuracy and efficiency of the proposed method are verified using the 2-D unsteady incompressible Newtonian fluid problems and are compared to the OpenFOAM software program showing remarkable efficiencies in computing approximated solutions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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32 pages, 16329 KiB  
Article
Stability Evaluation of Medium Soft Soil Pile Slope Based on Limit Equilibrium Method and Finite Element Method
by Xiaoyan Du and Jinfei Chai
Mathematics 2022, 10(19), 3709; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193709 - 10 Oct 2022
Cited by 1 | Viewed by 1262
Abstract
The stability of an open-pit slope is an extremely important factor related to the safe production of an open-pit mine. It is the first safety technical problem encountered and should be solved in the process of mine design and production. By the means [...] Read more.
The stability of an open-pit slope is an extremely important factor related to the safe production of an open-pit mine. It is the first safety technical problem encountered and should be solved in the process of mine design and production. By the means of an engineering geology and hydrogeological investigation of the waste dump area of the Nayuan open-pit coal mine and numerical simulation research, this paper analyzes and studies the slope stability of the stope and waste dump of the Nayuan open-pit coal mine in detail and puts forward measures such as slope prevention and automatic monitoring to achieve the goal of protecting the slope of the stope and waste dump and the surrounding environment. The main research results are as follows: (1) The geotechnical physical and mechanical indexes of stope and waste dump are collected and analyzed, and the geotechnical mechanical indexes in this report were determined, which basically meet the requirements of slope stability analysis. (2) The limit equilibrium method and finite element method were used to analyze and evaluate the current slope stability of the Nayuan open-pit coal mine. It was concluded that the foundation of the waste dump is basically stable, and the potential landslide modes of the slope are arc-shaped sliding surface and arc-shaped straight-line sliding surface. The numerical simulation and checking results showed that the current stope and waste dump slope are stable. (3) According to the analysis and evaluation results of slope stability, feasible slope prevention measures are put forward. The research results are of great significance to the safety of important facilities in open-pit mines and provide a basis for the design and safety implementation of open-pit slope engineering. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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18 pages, 572 KiB  
Article
Research on the Mathematical Model for Optimal Allocation of Human Resources in the Operation and Maintenance Units of a Heavy Haul Railway
by Linfang Shen, Kuoyu Liu, Jinfei Chai, Weibin Ma, Xiaoxiong Guo, Yao Li, Peng Zhao and Boying Liu
Mathematics 2022, 10(19), 3707; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193707 - 10 Oct 2022
Cited by 1 | Viewed by 1439
Abstract
According to the existing personnel structure, quantity, development strategy, and market demand of the Shuohuang Railway Company’s operation and maintenance project, the demand quantity of various employees of the company for the past three years is predicted, and a human resource optimization model [...] Read more.
According to the existing personnel structure, quantity, development strategy, and market demand of the Shuohuang Railway Company’s operation and maintenance project, the demand quantity of various employees of the company for the past three years is predicted, and a human resource optimization model based on existing human resources and future plans is established. Then, the optimal solutions of the two mathematical models were calculated and analyzed using LINGO software. Finally, combined with the actual situation, the optimal allocation of human resources for the operation and maintenance project of KY company was obtained. The following conclusions are obtained. (1) For the optimal allocation model of existing human resources, the maximum net profit of the optimal staffing model is CNY 3258000. (2) The human resources allocation cost of the minimum dismissal model is CNY 81000. (3) The human resources allocation cost of the lowest cost model is CNY 15500. The research results can effectively guide the human resource management of the operation and maintenance project of the Shuohuang Railway Company, and have important theoretical and practical significance for further analysis of human resources model and its optimal allocation method. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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23 pages, 2364 KiB  
Article
Analyzing the Passenger Flow of Urban Rail Transit Stations by Using Entropy Weight-Grey Correlation Model: A Case Study of Shanghai in China
by Pei Yin, Jing Cheng and Miaojuan Peng
Mathematics 2022, 10(19), 3506; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193506 - 26 Sep 2022
Cited by 6 | Viewed by 1628
Abstract
In this paper, the factors influencing the passenger flow of rail transit stations in Shanghai of China are studied by using the entropy weight-grey correlation model. The model assumptions and the corresponding variables are proposed, including traffic accessibility, built environment, regional characteristics of [...] Read more.
In this paper, the factors influencing the passenger flow of rail transit stations in Shanghai of China are studied by using the entropy weight-grey correlation model. The model assumptions and the corresponding variables are proposed, including traffic accessibility, built environment, regional characteristics of the district to which the rail transit station belongs, conditions of the station and spatial location, which affect the passenger flow of rail transit stations. Based on the assumptions and the variables, the entropy weight-grey correlation model for analyzing the passenger flow of urban rail transit stations is presented. By collecting the data of passenger flow of rail transit stations and corresponding influencing factors in Shanghai, the results of the entropy weight-grey correlation model are obtained. It is shown that the influencing factors, such as the distances from the rail transit station to the adjacent third-class hospital and the adjacent large commercial plazas, district committees, parking areas and the transaction price of important plots, and the gross output value of the tertiary industry, have significant impacts on the passenger flow of a subway station. Finally, some suggestions are proposed for the local governments to formulate improved policies for rail transit development. The conclusions can provide a reference for the development of rail transit in other large cities and countries. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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22 pages, 3997 KiB  
Article
An Automatic Extraction Method of Rebar Processing Information Based on Digital Image
by Zhaoxi Ma, Qin Zhao, Yiyun Zhu, Tianyou Cang and Xinhong Hei
Mathematics 2022, 10(16), 2974; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162974 - 17 Aug 2022
Cited by 1 | Viewed by 1861
Abstract
Reinforced steel is one of the most important building materials in civil engineering and improving the intelligence of steel reinforcement engineering can greatly promote the intelligent development of the construction industry. This research addressed the problems of the slow speed and poor accuracy [...] Read more.
Reinforced steel is one of the most important building materials in civil engineering and improving the intelligence of steel reinforcement engineering can greatly promote the intelligent development of the construction industry. This research addressed the problems of the slow speed and poor accuracy of manually extracting rebar processing information, which leads to a low degree of rebar processing intelligence. Firstly, based on digital image processing technology, image preprocessing methods such as binarization and grayscale were used to eliminate redundant information in a detail drawing of a rebar. An image segmentation method based on pixel statistics was proposed to store the geometric and non-geometric information of the detail drawing of the rebar separately. Next, the bending angle was extracted by line thinning and corner detection, and the bending direction of the steel bar was determined based on the mathematical characteristics of the vector product. Finally, the non-geometric information was extracted by combining the morphological algorithm and the Optical Character Recognition (OCR) engine. According to the characteristics of the information sequence, an information mapping method was proposed to realize the integration of geometric and non-geometric information. The applicability and accuracy of this method for extracting the steel bar’s information were tested by experiments, and it was shown that the method also provides a theoretical basis for realizing the intelligentization and informatization of steel bar processing. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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20 pages, 4646 KiB  
Article
Analysis of the Complex Network of the Urban Function under the Lockdown of COVID-19: Evidence from Shenzhen in China
by Jing Cheng and Pei Yin
Mathematics 2022, 10(14), 2412; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142412 - 11 Jul 2022
Cited by 8 | Viewed by 1356
Abstract
In this paper, the complex network of the urban functions in Shenzhen of China under the lockdown of the corona virus disease 2019 (COVID-19) is studied. The location quotient is used to obtain the dominant urban functions of the districts in Shenzhen before [...] Read more.
In this paper, the complex network of the urban functions in Shenzhen of China under the lockdown of the corona virus disease 2019 (COVID-19) is studied. The location quotient is used to obtain the dominant urban functions of the districts in Shenzhen before and under the lockdown of COVID-19. By using the conditional probability, the interdependencies between the urban functions are proposed to obtain the complex networks of urban functions and their clusters. The relationships between the urban functions, and the overall and cluster characteristics of the urban functions before and under the lockdown of COVID-19 are analyzed based on the complex networks. The mean degree and mean weighted degree of the primary categories of the urban functions are obtained to discuss the classification characteristics of the urban functions before and under the lockdown of COVID-19. Then, the differences and changes of the urban functions before and under the lockdown of COVID-19 are compared, and the corresponding policy implications under the lockdown of COVID-19 are presented. The results show that under the lockdown of COVID-19, the correlation of the urban functions is stronger than that before the lockdown; the common urban functions are more useful and essential, and finance, fine food and medical treatment are important; public service and government departments have the most positive relationship with other urban functions, and finance service has the highest spatial agglomeration distribution trend; and the cluster characteristics of urban functions are more related to people’s livelihood, and the urban functions show incomplete and cannot be operated for long term. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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10 pages, 2329 KiB  
Article
A Novel Inverse Time–Frequency Domain Approach to Identify Random Forces
by You Jia, Ruikai Li, Yanhong Fan and Haijie Huang
Mathematics 2022, 10(13), 2331; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132331 - 03 Jul 2022
Viewed by 1065
Abstract
In order to ensure the reliability and safety of complex engineering structures and allow their redesign and evaluation, the estimation of dynamic loads applied on them is vital. In this paper, a novel time–frequency domain approach is proposed to identify random forces based [...] Read more.
In order to ensure the reliability and safety of complex engineering structures and allow their redesign and evaluation, the estimation of dynamic loads applied on them is vital. In this paper, a novel time–frequency domain approach is proposed to identify random forces based on the weighted regularization algorithm. Firstly, the Newmark’s algorithm was applied to obtain structural dynamic responses, then a weighed regularization algorithm was used to identify the random forces exerted on the engineering structure. The weighting matrix was used to control the identified error of the random forces. A spatial frame model was built to illustrate the practicality of the proposed approach. The experimental results demonstrated that the proposed method is more effective than other methods for random forces identification. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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19 pages, 2069 KiB  
Article
A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels
by Gonzalo García-Ros, Juan Francisco Sánchez-Pérez, Julio Valenzuela, Manuel Conesa and Manuel Cánovas
Mathematics 2022, 10(13), 2301; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132301 - 01 Jul 2022
Cited by 1 | Viewed by 1046
Abstract
In this work, the network simulation method is presented as a tool for the numerical resolution of the electroosmotic and pressure-driven flow problem in microchannels with rectangular and cylindrical geometries. Based on the Brinkman equation for steady flow and constant porosity, the network [...] Read more.
In this work, the network simulation method is presented as a tool for the numerical resolution of the electroosmotic and pressure-driven flow problem in microchannels with rectangular and cylindrical geometries. Based on the Brinkman equation for steady flow and constant porosity, the network model is designed using spatial discretization. An equivalent electrical circuit is obtained by establishing an analogy between the physical variable fluid velocity and electric potential. The network model is solved quickly and easily employing an electrical circuit resolution code, providing solutions for the velocity profile in the channel cross-section and the total circulating flow. After simulating two practical cases, the suitability of the grid is discussed, relating the relative errors made in the variables of interest with the number of cells used. Finally, two other applications, one for rectangular geometries and the other for cylindrical channels, show the effects the main parameters controlling the flow in these types of channels have on velocities and total flow: the zeta potential of the soil pores, applied potential and pressure gradients, and the boundary condition modified by the zeta potential in the walls of the channel. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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21 pages, 4487 KiB  
Article
A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems
by Zhijuan Meng, Xiaofei Chi and Lidong Ma
Mathematics 2022, 10(13), 2244; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132244 - 27 Jun 2022
Cited by 2 | Viewed by 1045
Abstract
A hybrid interpolating meshless (HIM) method is established for dealing with three-dimensional (3D) advection–diffusion equations. To improve computational efficiency, a 3D equation is changed into correlative two-dimensional (2D) equations. The improved interpolating moving least-squares (IIMLS) method is applied in 2D subdomains to obtain [...] Read more.
A hybrid interpolating meshless (HIM) method is established for dealing with three-dimensional (3D) advection–diffusion equations. To improve computational efficiency, a 3D equation is changed into correlative two-dimensional (2D) equations. The improved interpolating moving least-squares (IIMLS) method is applied in 2D subdomains to obtain the required approximation function with interpolation property. The finite difference method (FDM) is utilized in time domain and the splitting direction. Setting diagonal elements to one in the coefficient matrix is chosen to directly impose Dirichlet boundary conditions. Using the HIM method, difficulties created by the singularity of the weight functions, such as truncation error and calculation inconvenience, are overcome. To prove the advantages of the new method, some advection–diffusion equations are selected and solved by HIM, dimension splitting element-free Galerkin (DSEFG), and improved element-free Galerkin (IEFG) methods. Comparing and analyzing the calculation results of the three methods, it can be shown that the HIM method effectively improves computation speed and precision. In addition, the effectiveness of the HIM method in the nonlinear problem is verified by solving a 3D Richards’ equation. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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35 pages, 61535 KiB  
Article
DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations
by Ying Li, Longxiang Xu and Shihui Ying
Mathematics 2022, 10(12), 1976; https://0-doi-org.brum.beds.ac.uk/10.3390/math10121976 - 08 Jun 2022
Cited by 8 | Viewed by 2818
Abstract
In this paper, we propose a deep wavelet neural network (DWNN) model to approximate the natural phenomena that are described by some classical PDEs. Concretely, we introduce wavelets to deep architecture to obtain a fine feature description and extraction. That is, we constructs [...] Read more.
In this paper, we propose a deep wavelet neural network (DWNN) model to approximate the natural phenomena that are described by some classical PDEs. Concretely, we introduce wavelets to deep architecture to obtain a fine feature description and extraction. That is, we constructs a wavelet expansion layer based on a family of vanishing momentum wavelets. Second, the Gaussian error function is considered as the activation function owing to its fast convergence rate and zero-centered output. Third, we design the cost function by considering the residual of governing equation, the initial/boundary conditions and an adjustable residual term of observations. The last term is added to deal with the shock wave problems and interface problems, which is conducive to rectify the model. Finally, a variety of numerical experiments are carried out to demonstrate the effectiveness of the proposed approach. The numerical results validate that our proposed method is more accurate than the state-of-the-art approach. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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20 pages, 6025 KiB  
Article
Symmetric Diffeomorphic Image Registration with Multi-Label Segmentation Masks
by Chenwei Cai, Lvda Wang and Shihui Ying
Mathematics 2022, 10(11), 1946; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111946 - 06 Jun 2022
Cited by 2 | Viewed by 1558
Abstract
Image registration aims to align two images through a spatial transformation. It plays a significant role in brain imaging analysis. In this research, we propose a symmetric diffeomorphic image registration model based on multi-label segmentation masks to solve the problems in brain MRI [...] Read more.
Image registration aims to align two images through a spatial transformation. It plays a significant role in brain imaging analysis. In this research, we propose a symmetric diffeomorphic image registration model based on multi-label segmentation masks to solve the problems in brain MRI registration. We first introduce the similarity metric of the multi-label masks to the energy function, which improves the alignment of the brain region boundaries and the robustness to the noise. Next, we establish the model on the diffeomorphism group through the relaxation method and the inverse consistent constraint. The algorithm is designed through the local linearization and least-squares method. We then give spatially adaptive parameters to coordinate the descent of the energy function in different regions. The results show that our approach, compared with the mainstream methods, has better accuracy and noise resistance, and the transformations are more smooth and more reasonable. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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14 pages, 375 KiB  
Article
Robust Fault-Tolerant Control for Stochastic Port-Hamiltonian Systems against Actuator Faults
by Song Xu, Wei Wang and Sheng-Yuan Chen
Mathematics 2022, 10(9), 1477; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091477 - 28 Apr 2022
Cited by 1 | Viewed by 1051
Abstract
Exploiting the stochastic Hamiltonian structure, this paper investigates the robust fault-tolerant control (FTC) for stochastic port-Hamiltonian systems (SPHSs) with actuator faults. First, an energy-based robust FT controller is developed for SPHSs against the loss of actuator effectiveness. Then, an alternative condition, as well [...] Read more.
Exploiting the stochastic Hamiltonian structure, this paper investigates the robust fault-tolerant control (FTC) for stochastic port-Hamiltonian systems (SPHSs) with actuator faults. First, an energy-based robust FT controller is developed for SPHSs against the loss of actuator effectiveness. Then, an alternative condition, as well as its corresponding controller are given to extend the application of the proposed controller. Unlike the existing FT controllers, they are continuous, and there is no need to solve the Lyapunov function and Hamilton–Jacobi–Isaacs (HJI) inequalities associated with the nominal systems. Finally, an energy-based robust adaptive FT controller is presented for the faulty SPHSs to deal with parameter perturbations, and an alternative condition with its corresponding controller is also given. Both the adaptive controllers preserve the main stochastic Hamiltonian structure of the faulty systems. Compared to the existing adaptive controller, simulations on synchronous generators show the effectiveness of the proposed methods. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering)
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