Overall fault diagnosability evaluation for dynamic systems: A quantitative–qualitative approach

doi:10.1016/j.automatica.2022.110591

Automatica

Volume 146, December 2022, 110591

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Abstract

The issue of overall fault diagnosability evaluation is addressed to provide a standard for system design from the fault diagnosis perspective. An overall fault diagnosability measure is first defined statistically by combining quantitative and qualitative evaluation results. On this basis, a randomized algorithm-based method is developed for estimating this quantitative–qualitative measure with a preset accuracy. Then, a tractable method for computing the lower bound of the measure is created, which provides a way to assess fault diagnosis performance without a large computational burden. Finally, a spacecraft attitude control system is used to verify the effectiveness of the proposed methods.

Section snippets

KLD-based diagnosability analysis methods

Consider a dynamic system modeled by the following linear discrete time-invariant model: $x (k + 1) = A x (k) + B_{u} u (k) + B_{f} f (k) + B_{w} w (k),$ $y (k) = C x (k) + D_{u} u (k) + D_{f} f (k) + D_{v} v (k),$ where $x (k) \in R^{l_{x}}$ , $u (k) \in R^{l_{u}}$ , $f (k) \in R^{l_{f}}$ and $y (k) \in R^{l_{y}}$ are the state, input, and output vectors at time instant $k$ , respectively; $w (k) \in R^{l_{w}}$ and $v (k) \in R^{l_{v}}$ are the process and measurement noise vectors, respectively; and $A$ , $B_{u}$ , $B_{f}$ , $B_{w}$ , $C$ , $D_{u}$ , $D_{f}$ and $D_{v}$ are known system parameter matrices with appropriate dimensions.

Assumption 1

$w$ and $v$ are independent and identically

Overall measure of fault diagnosability

To analyze the overall fault diagnosis performance of dynamic systems from the FDI perspective, a new fault diagnosability measure that simultaneously focuses on different faults is studied in this section. To this end, the following assumption is first given.

Assumption 2

Each fault $f_{i}$ has known lower and upper bounds $f_{i}^{l}$ and $f_{i}^{u}$ , respectively, i.e., $f_{i}^{l} \leq f_{(i)} (η) \leq f_{i}^{u}, η = k - n + 1, \dots, k$ .

Under Assumption 2, let $F_{n, i}^{b} = {f_{n, i} | f_{n, i} = {[f_{(i)} (k - n + 1) \dots f_{(i)} (k)]}^{T}, f_{i}^{l} \leq f_{(i)} (η) \leq f_{i}^{u}, η = k - n + 1, \dots, k}$ denote all possible fault time

RA-based overall fault diagnosability evaluation

Due to the existence of random vectors $f_{n, i}$ ( $i = 1, \dots, l_{f}$ ), analytically calculating the proposed measure (7), which includes distributions with quadratic forms $K_{i, j} (f_{n, i}) = \frac{1}{2} f_{n, i}^{T} F_{i}^{T} S_{[H F_{j}]}^{T} S_{[H F_{j}]} F_{i} f_{n, i}$ , is difficult. Hence, a new method needs to be proposed to estimate the developed measure with high accuracy.

According to the metrics’ characteristics, an intuitive and feasible idea for determining the solutions of Eq. (7) is to directly estimate $O_{i, j} (K_{i, j}^{t h})$ via the use of sufficient i.i.d. random

Lower bound of the fault diagnosability measure

Through the use of Theorem 1 proposed in Section 3, an overall fault diagnosability evaluation with acceptable estimation accuracy can be performed. Notably, if the required accuracy of the measure estimation results is (extremely) high, a heavy computational burden is required due to the need for a considerable number of generated samples and many computed measures for the successful application of Theorem 1. However, in some cases, it may be not necessary to obtain (very) exact measures. For

Verification

To demonstrate the effectiveness of the proposed measure and the corresponding fault diagnosability evaluation methods, a spacecraft attitude control system proposed in Zhong, Liu, Zhou, Li, and Xue (2019) is considered with slight modifications.

Let the sampling time $T_{s} = 0.1 s$ and the acceptable diagnosis time limit $t_{a} = 1.5 s$ ; $f_{i}^{l} = - 1$ and $f_{i}^{u} = 1$ with $i = 1, 2, 3$ denote momentum wheel faults, and $f_{i}^{l} = - 0.1$ and $f_{i}^{u} = 0.1$ with $i = 4, \dots, 9$ denote star sensor faults; the fault diagnosability threshold is set as $K_{i, j}^{t}$

Conclusion

This study contributes to general overall fault diagnosability research for dynamic systems subject to diverse faults, process noise, and measurement noise. According to the results, we can achieve a more comprehensive and in-depth understanding of the fault diagnosis performance of a given system, which is helpful for further optimizing the system configuration (for instance, striking a balance between diagnosis performance and diagnostic cost by optimizing the placement of sensors).

Future

Acknowledgments

This work was supported in part by the National Key Research and Development Program of China under grant no. 2021YFB1715000; in part by the National Natural Science Foundation of China undergrant nos. 62022013 and 62103450; in part by the Guangdong Basic and Applied Basic Research Foundation under grant no. 2020A1515110311; and in part by the Shanghai Aerospace Science and Technology Innovation Foundation of China Aerospace Science Corporation under Grant SAST2020-066.

References (21)

ÅslundJan et al.
Asymptotic behavior of a fault diagnosis performance measure for linear systems
Automatica
(2019)
AlikhaniHamid et al.
Event-triggered robust fault diagnosis and control of linear roesser systems: A unified framework
Automatica
(2021)
CuiYiqian et al.
System-level operational diagnosability analysis in quasi real-time fault diagnosis: The probabilistic approach
Journal of Process Control
(2014)
ErikssonDaniel et al.
A method for quantitative fault diagnosability analysis of stochastic linear descriptor models
Automatica
(2013)
KościelnyJan M. et al.
Actuator fault distinguishability study for the DAMADICS benchmark problem
Control Engineering Practice
(2006)
LiLinlin et al.
Gap metric techniques and their application to fault detection performance analysis and fault isolation schemes
Automatica
(2020)
SharifiReza et al.
Isolability of faults in sensor fault diagnosis
Mechanical Systems and Signal Processing
(2011)
WangDayi et al.
A review of the diagnosability of control systems with applications to spacecraft
Annual Reviews in Control
(2020)
YongSze Zheng et al.
A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems
Automatica
(2016)
ZhaoYinghong et al.
Detection of intermittent faults based on an optimally weighted moving average T2 control chart with stationary observations
Automatica
(2021)

There are more references available in the full text version of this article.

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Fangzhou Fu received the B.Eng. degree in automation from the Harbin Institute of Technology, Harbin, China, in 2013, the M.E. degree in control science and engineering from the Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China, in 2015, and the Ph.D. degree in control science and engineering from the Beijing Institute of Control Engineering, China Academy of Space Technology, Beijing, China, in 2019. From 2017 to 2018, he was a Joint Training Ph.D. Student with the Institute for Automatic Control and Complex Systems (AKS), the University of Duisburg–Essen, Duisburg, Germany. From 2019 to 2021, he joined the School of Aeronautics and Astronautic, Sun Yat-sen University, Shenzhen, as a Postdoctoral Research Fellow, where he is currently an Associate Research Fellow. His research interests include fault diagnosis and tolerant control, fault diagnosability evaluation, and design for satellite control systems.

Dayi Wang received the B.Eng., M.E., and Ph.D. degrees from the Harbin Institute of Technology, Harbin, China, in 1995, 1997, and 2000, respectively. From 2003 to 2016, he was a Professor with the Beijing Institute of Control Engineering, China Academy of Space Technology, Beijing, China.

He is currently a Professor with the Beijing Institute of Spacecraft System Engineering, China Academy of Space Technology, Beijing. He has published three monographs and over 100 papers. He conducted innovative research in the field of spacecraft autonomous navigation, control, and fault diagnosis, solved a series of key technical issues, and made great contributions to the success of key flight tests such as the Change-1 and the Change-3 soft-landing probes. His research interests include autonomous guidance, navigation and control, fault diagnosis, and tolerant control for space crafts. He was a recipient of the National Science Fund for Distinguished Young Scholars in 2015. He is an Executive Editor of the journal Aerospace Control and Application.

Wenbo Li received the Ph.D. degree from the Harbin Institute of Technology, Harbin, China, in 2012. He is currently a Senior Engineer with the Beijing Institute of Control Engineering, China Academy of Space Technology, Beijing, China. His research interests include fault diagnosis and tolerant control, fault diagnosability evaluation, and design for satellite control systems.

Dong Zhao received the B.S. degree in automation and the Ph.D. degree in control science and engineering from Beijing University of Chemical Technology, Beijing, China in 2011 and 2016, respectively. From March 2017 to September 2018, he worked as a postdoctoral research fellow with the Institute for Automatic Control and Complex Systems (AKS), University of Duisburg–Essen, Germany. Since October 2018, he joined KIOS Research and Innovation center of Excellence at the University of Cyprus as a postdoctoral research fellow. His research interests are fault diagnosis, fault-tolerant control, cyber–physical systems, nonlinear system control, and adaptive control.

Zhigang Wu received the B.S. and Ph.D. degrees from the Harbin Institute of Technology, Harbin, China, in 1993 and 1998, respectively. He is currently the Dean and a Professor with the School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou, China. He is also a Professor with State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China. He is the author of four books and more than 100 articles. His current research interests include spacecraft dynamics and control, robot system, numerical methods for optimal control, and robust control. Prof. Wu is a Senior Member of AIAA.

^☆: The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Angelo Alessandri under the direction of Editor Thomas Parisini.

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Brief paperOverall fault diagnosability evaluation for dynamic systems: A quantitative–qualitative approach☆

Abstract

Section snippets

KLD-based diagnosability analysis methods

Overall measure of fault diagnosability

RA-based overall fault diagnosability evaluation

Lower bound of the fault diagnosability measure

Verification

Conclusion

Acknowledgments

Automatica

Automatica

Journal of Process Control

Automatica

Control Engineering Practice

Automatica

Mechanical Systems and Signal Processing

Annual Reviews in Control

Automatica

Automatica

Brief paper
Overall fault diagnosability evaluation for dynamic systems: A quantitative–qualitative approach☆