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Mathematics
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Modeling and Optimization of Complex Engineering Systems under Uncertainties
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Modeling and Optimization of Complex Engineering Systems under Uncertainties

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 25 July 2025 | Viewed by 14733

Special Issue Editors

Dr. Debiao Meng

E-Mail Website
Guest Editor
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Interests: uncertainty-based design and optimization; reliability analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Shui Yu

E-Mail Website
Guest Editor
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China
Interests: time-dependent reliability-based robust design optimization

Special Issue Information

Dear Colleagues,

In engineering problems, complex systems usually consist of many subsystems. The coupled disciplines represented by these subsystems are interrelated. Additionally, multi-source mixed uncertainties are accompanied by the transmission and accumulation of coupled information in complex systems. Therefore, the modeling and design processes of complex systems in engineering problems are often time-consuming and inefficient. Moreover, the reliability and safety of system performance cannot be completely guaranteed.

To tackle the above challenges, the development of advanced modeling technology and a design optimization algorithm of complex engineering systems considering mixed uncertainties is necessary. On the one hand, the continuing development of engineering systems makes it difficult for existing modeling methods to efficiently address all new problems. On the other hand, because of the limited time and cost, designers have to select an appropriate method among various design and optimization methods to solve their problems. Consequently, newer uncertainty-based design and optimization methods should be developed to provide greater options for engineering designers.

The aim of this Special Issue is to establish an academic forum between experts and scholars and come to an agreement regarding the current state of this research field; draw a roadmap of where research is headed, highlight issues, and discuss their possible solutions; and provide the data, models and tools necessary for performing complex system modeling and a multidisciplinary design optimization algorithm considering mixed uncertainties. Potential topics include, but are not limited to:

  • System modeling;
  • Multidisciplinary design optimization;
  • System reliability and risk assessment;
  • Structural safety;
  • Interval and fuzzy mathematics;
  • Structural analysis;
  • Optimization problem and computational methods;
  • Information fusion;
  • Fault diagnosis;
  • Probabilistic physics of failure;
  • Uncertainty-based design optimization;
  • Uncertainty quantification and propagation;
  • Performance degradation modeling and analysis.

Dr. Debiao Meng
Dr. Shui Yu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • Complex systems
  • Reliability
  • Control
  • Advanced modeling technology
  • Design optimization
  • Uncertainty-based design and optimization
  • Reliability-based design and optimization
  • Optimization methods
  • Uncertainty quantification and propagation
  • Multidisciplinary design optimization
  • Risk assessment
  • Fault diagnosis
  • Physics of failure
  • Reliability hazard analysis
  • Fuzzy reliability Analysis
  • Uncertainty in engineering

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Published Papers (7 papers)

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Research

24 pages, 6543 KiB  
Article
Optimization of Analog Circuit Parameters Using Bidirectional Long Short-Term Memory Coupled with an Enhanced Whale Optimization Algorithm
by Hengfei Yang, Shiyuan Yang, Debiao Meng, Chenghao Hu, Chaosheng Wu, Bo Yang, Peng Nie, Yuan Si and Xiaoyan Su
Mathematics 2025, 13(1), 121; https://doi.org/10.3390/math13010121 - 31 Dec 2024
Cited by 1 | Viewed by 805
Abstract
The development of surrogate models based on limited data is crucial in enhancing the speed of structural analysis and design optimization. Surrogate models are highly effective in alleviating the challenges between design variables and performance evaluation. Bidirectional Long Short-Term Memory (BiLSTM) is an [...] Read more.
The development of surrogate models based on limited data is crucial in enhancing the speed of structural analysis and design optimization. Surrogate models are highly effective in alleviating the challenges between design variables and performance evaluation. Bidirectional Long Short-Term Memory (BiLSTM) is an advanced recurrent neural network that exhibits significant advantages in processing sequential data. However, the training of BiLSTM involves the adjustment of multiple hyperparameters (such as the number of layers, the number of hidden units, and the learning rate), which complicates the training process of the model. To enhance the efficiency and accuracy of neural network model development, this study proposes an Improved Whale Optimization Algorithm-assisted BiLSTM establishment strategy (IWOA-BiLSTM). The new algorithm enhances the initial population design and population position update process of the original Whale Optimization Algorithm (WOA), thereby improving both the global search capability and local exploitation ability of the algorithm. The IWOA is employed during the training process of BiLSTM to search for optimal hyperparameters, which reduces model training time and enhances the robustness and accuracy of the model. Finally, the effectiveness of the model is tested through a parameter optimization problem of a specific analog circuit. Experimental results indicate that, compared to traditional neural network models, IWOA-BiLSTM demonstrates higher accuracy and effectiveness in the optimal parameter design of analog circuit engineering problems. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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23 pages, 4949 KiB  
Article
Artificial Bee Colony Algorithm to Optimize the Safety Distance of Workers in Construction Projects
by Eric Forcael, Ibzan Carriel, Alexander Opazo-Vega, Francisco Moreno, Francisco Orozco, Rubén Romo and Duzgun Agdas
Mathematics 2024, 12(13), 2087; https://doi.org/10.3390/math12132087 - 3 Jul 2024
Cited by 3 | Viewed by 2117
Abstract
This paper presents the results of a simulation model regarding the productivity and safety working space for construction workers through the floors of a building using swarm intelligence (SI), a field of artificial intelligence (AI), and specifically using artificial bee colony (ABC) optimization. [...] Read more.
This paper presents the results of a simulation model regarding the productivity and safety working space for construction workers through the floors of a building using swarm intelligence (SI), a field of artificial intelligence (AI), and specifically using artificial bee colony (ABC) optimization. After designing the algorithm used to build the simulation model, the simulation was used in an actual building project by comparing the travel times of workers conventionally transporting material with another group working on routes optimized by the algorithm. Thus, the proposed algorithm provides routes combining shorter travel times and correct distances between workers when transporting materials in a construction site, handling the interference between crews. After validating the algorithm on-site, no statistically significant differences were found between the travel times of workers and the times delivered by the algorithm. Additionally, the travel times using the routes obtained through the algorithm were significantly lower than those made by workers who moved freely without a predefined route. In summary, the algorithm proposed may help construction practitioners maintain safe movements that respond to hazard contexts imposed by any restriction that demands a safety distance. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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26 pages, 2814 KiB  
Article
A Coupled Simulated Annealing and Particle Swarm Optimization Reliability-Based Design Optimization Strategy under Hybrid Uncertainties
by Shiyuan Yang, Hongtao Wang, Yihe Xu, Yongqiang Guo, Lidong Pan, Jiaming Zhang, Xinkai Guo, Debiao Meng and Jiapeng Wang
Mathematics 2023, 11(23), 4790; https://doi.org/10.3390/math11234790 - 27 Nov 2023
Cited by 20 | Viewed by 2241
Abstract
As engineering systems become increasingly complex, reliability-based design optimization (RBDO) has been extensively studied in recent years and has made great progress. In order to achieve better optimization results, the mathematical model used needs to consider a large number of uncertain factors. Especially [...] Read more.
As engineering systems become increasingly complex, reliability-based design optimization (RBDO) has been extensively studied in recent years and has made great progress. In order to achieve better optimization results, the mathematical model used needs to consider a large number of uncertain factors. Especially when considering mixed uncertainty factors, the contradiction between the large computational cost and the efficiency of the optimization algorithm becomes increasingly fierce. How to quickly find the optimal most probable point (MPP) will be an important research direction of RBDO. To solve this problem, this paper constructs a new RBDO method framework by combining an improved particle swarm algorithm (PSO) with excellent global optimization capabilities and a decoupling strategy using a simulated annealing algorithm (SA). This study improves the efficiency of the RBDO solution by quickly solving MPP points and decoupling optimization strategies. At the same time, the accuracy of RBDO results is ensured by enhancing global optimization capabilities. Finally, this article illustrates the superiority and feasibility of this method through three calculation examples. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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24 pages, 25404 KiB  
Article
Residual Strength Modeling and Reliability Analysis of Wind Turbine Gear under Different Random Loadings
by Jianxiong Gao, Yuanyuan Liu, Yiping Yuan and Fei Heng
Mathematics 2023, 11(18), 4013; https://doi.org/10.3390/math11184013 - 21 Sep 2023
Cited by 6 | Viewed by 1876
Abstract
A novel method is proposed to investigate the pattern of variation in the residual strength and reliability of wind turbine gear. First, the interaction between loads and the effect of the loading sequence is considered based on the fatigue damage accumulation theory, and [...] Read more.
A novel method is proposed to investigate the pattern of variation in the residual strength and reliability of wind turbine gear. First, the interaction between loads and the effect of the loading sequence is considered based on the fatigue damage accumulation theory, and a residual strength degradation model with few parameters is established. Experimental data from two materials are used to verify the predictive performance of the proposed model. Secondly, the modeling and simulation of the wind turbine gear is conducted to analyze the types of fatigue failures and obtain their fatigue life curves. Due to the randomness of the load on the gear, the rain flow counting method and the Goodman method are employed. Thirdly, considering the seasonal variation of load, the decreasing trend of gear fatigue strength under multistage random load is calculated. Finally, the dynamic failure rate and reliability of gear fatigue failure under multistage random loads are analyzed. The results demonstrate that the randomness of residual strength increases with increasing service time. The seasonality of load causes fluctuations in the reliability of gear, providing a new idea for evaluating the reliability of the wind turbine gear. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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13 pages, 1768 KiB  
Article
A New Loss Function for Simultaneous Object Localization and Classification
by Ander Sanchez-Chica, Beñat Ugartemendia-Telleria, Ekaitz Zulueta, Unai Fernandez-Gamiz and Javier Maria Gomez-Hidalgo
Mathematics 2023, 11(5), 1205; https://doi.org/10.3390/math11051205 - 1 Mar 2023
Viewed by 2315
Abstract
Robots play a pivotal role in the manufacturing industry. This has led to the development of computer vision. Since AlexNet won ILSVRC, convolutional neural networks (CNNs) have achieved state-of-the-art status in this area. In this work, a novel method is proposed to simultaneously [...] Read more.
Robots play a pivotal role in the manufacturing industry. This has led to the development of computer vision. Since AlexNet won ILSVRC, convolutional neural networks (CNNs) have achieved state-of-the-art status in this area. In this work, a novel method is proposed to simultaneously detect and predict the localization of objects using a custom loop method and a CNN, performing two of the most important tasks in computer vision with a single method. Two different loss functions are proposed to evaluate the method and compare the results. The obtained results show that the network is able to perform both tasks accurately, classifying images correctly and locating objects precisely. Regarding the loss functions, when the target classification values are computed, the network performs better in the localization task. Following this work, improvements are expected to be made in the localization task of networks by refining the training processes of the networks and loss functions. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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20 pages, 7387 KiB  
Article
Investigation of Warning Thresholds for the Deformation of GINA Gasket of Immersed Tunnel Based on a Material-to-Mechanical Analysis
by Hao Ding, Jingsong Huang, Xinghong Jiang, Yu Yan, Shouji Du, Juntao Chen and Qing Ai
Mathematics 2023, 11(4), 1010; https://doi.org/10.3390/math11041010 - 16 Feb 2023
Cited by 3 | Viewed by 2418
Abstract
As the first waterproof component of the immersed tunnel, it is very important to ensure the remaining compression of the GINA gasket to resist external water intrusion. This paper proposed a method for determining warning thresholds for the remaining compression of the GINA [...] Read more.
As the first waterproof component of the immersed tunnel, it is very important to ensure the remaining compression of the GINA gasket to resist external water intrusion. This paper proposed a method for determining warning thresholds for the remaining compression of the GINA gasket based on a material-to-mechanical analysis. In terms of material analysis, two factors that affect the GINA gasket are investigated: rubber hardness and cross-sectional shape, and they are adopted as the basis for subsequent mechanical analysis. In terms of mechanical analysis, uneven settlement during the operation period is considered to be the major cause of joint deformation, which is further divided into four modes: bending, shear, expansion, and torsion, with the computation model of the GINA gasket established to obtain the warning threshold. After that, a graded early warning method is adopted, and corresponding thresholds are given after an investigation of previous studies, which are validated by a three-dimensional finite element analysis. The deformation monitoring data between the E28 and E29 elements of the Hong Kong–Zhuhai–Macao Bridge Immersed Tunnel are used to verify the proposed method. The results show that the GINA gasket of the Hong Kong–Zhuhai–Macao Bridge Immersed Tunnel is currently in a safe state, and its deformation is much lower than the minimum warning level. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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24 pages, 54197 KiB  
Article
A Robust Learning Methodology for Uncertainty-Aware Scientific Machine Learning Models
by Erbet Almeida Costa, Carine de Menezes Rebello, Márcio Fontana, Leizer Schnitman and Idelfonso Bessa dos Reis Nogueira
Mathematics 2023, 11(1), 74; https://doi.org/10.3390/math11010074 - 25 Dec 2022
Cited by 6 | Viewed by 1600
Abstract
Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. [...] Read more.
Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. Hence, this work proposes a comprehensive methodology for uncertainty evaluation of the SciML that also considers several possible sources of uncertainties involved in the identification process. The uncertainties considered in the proposed method are the absence of a theory, causal models, sensitivity to data corruption or imperfection, and computational effort. Therefore, it is possible to provide an overall strategy for uncertainty-aware models in the SciML field. The methodology is validated through a case study developing a soft sensor for a polymerization reactor. The first step is to build the nonlinear model parameter probability distribution (PDF) by Bayesian inference. The second step is to obtain the machine learning model uncertainty by Monte Carlo simulations. In the first step, a PDF with 30,000 samples is built. In the second step, the uncertainty of the machine learning model is evaluated by sampling 10,000 values through Monte Carlo simulation. The results demonstrate that the identified soft sensors are robust to uncertainties, corroborating the consistency of the proposed approach. Full article
(This article belongs to the Special Issue Modeling and Optimization of Complex Engineering Systems under Uncertainties)
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