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Intermittent Fault Detection for Nonlinear Stochastic Systems

Yichun Niu*, Li Sheng*, Ming Gao*, Donghua Zhou**

• College of Control Science and Engineering, China University of Petroleum (East China), Qingdao, 266580, China. Corresponding author: Li Sheng. (email: shengli@upc.edu.cn).

** College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China.

Abstract: In this paper, the problem of intermittent fault detection is investigated for nonlinear stochastic systems. The moving horizon estimation with dynamic weight matrices is proposed, where the weight matrices are adjusted by an unreliability index of prior estimate to avoid the smearing effects of intermittent faults. Based on the particle swarm optimization algorithm, the nonlinear optimization problem is solved and the approximate estimate is derived. Finally, the feasibility and effectiveness of the proposed algorithm are validated by a numerical example.

Keywords: Intermittent fault detection, Nonlinear stochastic systems, Moving horizon estimation, Dynamic weight matrices, Particle swarm optimization.

1. INTRODUCTION

For the sake of strengthening the reliability and safety of industrial processes, during the past several decades, tremendous effort has been devoted to the study of fault diagnosis techniques and a large number of research results have been effectively applied in various fields, such as chemical processes, aerospace systems, power systems and so on, see Fazai et al. (2019); Mandal et al. (2019); Shen et al. (2019). Nevertheless, it should be pointed out that most existing literature has concentrated on permanent faults, while little attention has been paid on another kind of common faults, intermittent faults (IFs). Different from permanent faults, a IF usually recurs by the same reason and lasts within a limited period of time. Since the appearing and disappearing times of IFs are nonde-terministic, the system can recover without fault-tolerant operations (Rashid et al. (2015)). Nonetheless, if IFs are not treated properly and promptly, the destructiveness of IFs may become larger over time and finally lead to major accidents (Correcher et al. (2012)). In fact, in power systems, mechanical equipment, electrical industries and many other engineering applications with electronics, the occurrence frequency of IFs is much larger than permanent faults. Therefore, it is an urgent need to develop the fault diagnosis methods for IFs.

Generally speaking, the objective of fault diagnosis consists of fault detection, isolation and estimation, which respectively study the time, location and size of faults. It should be noted that the IF detection is more difficult than the permanent fault, since its aim is to detect all appearing

and disappearing times of IFs. Especially for the detection of disappearing times, the residual is affected by previous IFs and then remains above the threshold for an uncertain period of time, which is the so-called smearing effects of IFs. Up to now, there have been some research results on the IF detection based on qualitative or quantitative analysis methods, see Constantinescu (2008); Correcher et al. (2012); Kim (2009); Yan et al. (2018, 2016). For example, in Yan et al. (2018) and Yan et al. (2016), the intermittent actuator and sensor fault detection problems for linear stochastic systems have been investigated, respectively.

On the other hand, it is well known that nonlinearity pervasively exists in almost all dynamic systems. In order to solve the fault detection for nonlinear systems, fruitful methods have been proposed by a variety of communities. These methods include, but are not limited to, the extended Kalman filter (EKF) method (Wang et al. (2019)), particle filter (PF) method (Daroogheh et al. (2018); Yin and Zhu (2015)), strong tracking filter (STF) method (Qin et al. (2016)). However, after a thorough literature search, it has been revealed that, for IFs in nonlinear systems, the corresponding research results on the fault detection are still in the blank.

In order to fill the research gap of existing literature, this paper studies the IF detection for nonlinear systems with stochastic noises. The main contributions are listed as follows.

1. This paper represents the first of few attempts to investigate the IF detection problem for nonlinear systems.
2. By means of the moving horizon estimation with dynamic weight matrices (MHEDWM), the smearing effects of IFs are properly suppressed.

The rest of this paper is organized as follows. Section 2 gives the problem description about the IF detection for nonlinear systems and analyzes the deficiencies of existing methods for detecting IFs. Section 3 proposes the MHED-

• This work is supported by National Natural Science Foundation of China (Nos. 61773400, 61751307), Key Research and Development Program of Shandong Province (No. 2019GGX101046), Fundamental Research Funds for the Central Universities of China (No. 19CX02044A), and Research Fund for the Taishan Scholar Project of Shandong Province of China.