Mathematical Analysis Advances in System Fault Analysis, Prediction and Control (Close)

Deadline for manuscript submissions: 31 December 2025

Special Issue Editors

Prof. Tiejun Cui Website E-Mail: ctj.159@163.com
Guest Editor
Shenyang Ligong University, China
Interests: system safety and system engineering; industrial safety intelligence

Special Issue Information

Dear colleagues,

The processes underlying system fault are complex, and ensuring system safety is a fundamental challenge in industrial manufacturing. A highly effective approach to understanding these fault processes is through mathematical analysis and modeling. In recent years, the development of technologies such as artificial intelligence and big data has given rise to novel mathematical methods and models in the field of system fault research, thereby introducing novel concepts and solutions to the industry. Consequently, this special issue is devoted to the examination of safety production processes in diverse industrial systems and the presentation of mathematical models pertaining to system fault analysis, prediction, and control. In order to establish a connection between theoretical concepts and practical applications, it is imperative to incorporate examples that demonstrate the application of these concepts in real-world settings. These practical cases assist in verifying the efficacy of mathematical models in real-world scenarios and offer valuable references for engineers and technicians to solve practical problems. Consequently, this special issue has been convened to serve as a forum for scholars to disseminate their findings and observations.

The objective of this endeavor is two fold: first, to compile the most recent research results and experiences of various scholars in order to promote the in-depth development of mathematical analysis in system fault-related fields; and second, to contribute to the improvement of system safety in various industrial applications.

The primary topics are as follows (not limited to those listed):
- Intelligent control and dynamic evolution of system fault
- Data-driven fault process control and system reliability
- Intelligent description and analysis of system fault processes
- System fault prediction and intervention
- Data-driven emergency system operation and dynamic optimization

Special Note: In this context, the term "system" encompasses various types of industrial systems, including those related to natural disasters, production systems, and abstract systems like public safety.

Keywords:

system fault
mathematical models
intelligent methods
prediction
analysis
control

Guest Editor

Prof. Tiejun Cui

Published Papers

Open Access

Article

Article ID: 3307

Research on safety sustainability of LNG tanks based on multi-attribute decision-making-FCEM coupled modeling
by Dehong Zhou, Peihe Zhang, Jingyi Zang, Shiyu Peng

Advances in Differential Equations and Control Processes, Vol.32, No.4, 2025;

Against the backdrop of the “dual carbon goals”, China has been advancing its “coal-to-gas transition” strategy, during which LNG leakage incidents have occurred frequently. Addressing the challenge of assessing the interrelated risks of multiple factors, this study constructs an ANP-CRITIC-FCEM coupled model, establishing a micro-level risk identification system from five dimensions: “environment, equipment, process, personnel, and materials”. Considering the conflicts and mutual influences between different risk factors, the model integrates game theory to couple subjective and objective weights and combines fuzzy comprehensive evaluation to quantify safety and sustainable development capabilities. The study indicates that the safety and sustainable development capability level of a certain factory’s LNG storage tank area is Grade IV, with equipment factors dominating as the primary risk source, with a comprehensive weight of 0.5205. Among these, pipeline C22 and safety accessory C23 have a significant impact on the tank’s sustainable development capability; This model improves the accuracy of traditional AHP-FCEM identification, fully considers the influence and conflicts between various factors, visualizes the influence sensitivity between factors, and identifies process factors (25.36% weight) such as pressure regulation process (40.28% sub-weight), personnel “three violations” behavior (69.01% sub-weight), and methane concentration (64.35% sub-weight) constitute secondary key risks. Based on this, targeted improvement strategies are proposed, including equipment-level corrosion monitoring, process-level intelligent pressure regulation, and management-level behavioral analysis and early warning, providing a data-driven framework for the coordinated advancement of LNG storage tank safety management and dual carbon goals. Through comparative analysis, this model is found to be relatively accurate and effective.

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Open Access

Article

Article ID: 3444

Partial differential analytical expression for the failure rate change of electrical components under multi-fault coupling
by Tiejun Cui, Pengpeng Wei, Shasha Li

Advances in Differential Equations and Control Processes, Vol.32, No.3, 2025;

With the trend of high integration and complex working conditions of electronic equipment, multi-fault coupling failures have become a key threat to operational reliability. To study the influence mechanism of multi-factor-induced multi-fault modes on the failure of electrical components and consider the time-dependent effect of component operation, an analytical expression in the form of a partial differential equation for the component failure rate is established. The time-dependent of failure rate, multi-fault coupling terms, and coupling coefficients in the expression are further determined. The research shows that constructing the partial differential expression for failure rate should consider electromigration, corrosion, hot carrier, and dielectric breakdown faults and their influencing factors. By introducing multi-fault coupling terms, the impacts of parameters such as temperature, current density, etc. on various fault modes and component failure rates are reflected. Electromigration-corrosion, heat-carrier-dielectric breakdown accelerate the occurrence of faults, and the analytical and approximate formulas for coupling coefficients are provided. Case analysis obtains the failure rates of each fault, the component failure rate, and two coupling coefficients; and it is found that the failure rate changes significantly at 100s, serving as a critical life point. This study provides a method for analyzing the failure rate of electrical components under multi-factor influences over time.

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Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

Numerical solution of a 3D mathematical model for the progression of tumor angiogenic factor in a tissue

In this work, the movement of tumor angiogenic factor in a three-dimensional tissue is obtained by the Method of Lines. This method transforms a partial differential equation into a system of ordinary differential equations together with the initial and boundary conditions. The more the number of lines is increased, the more the accuracy of the method increases. This method results in very accurate numerical solutions for linear and non-linear problems in contrast with other existing methods. We present Matlab-generated figures, which are the movement of tumor angiogenic factor in porous medium and explain the biological importance of this progression. The computer codes are also provided.

Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.