|
|
Pure Mathematics 2025
基于耗散阈值的数据驱动故障检测新方法
|
Abstract:
本文基于耗散阈值提出了一种面向线性系统的数据驱动故障检测方法。首先，通过引入线性系统中的耗散不等式概念，并采用二次差分形式(QdF)的供给率和存储函数，可以将耗散性条件转化为关于输入和输出数据轨迹的二次函数，与传统耗散性相比，可以捕捉更加详细的动态特征。接着，通过求解线性矩阵不等式约束的优化问题获得关于供给率和存储函数的系数矩阵。最后，通过设定基于耗散率的评估函数及其故障检测阈值，实现在线检验系统中的输入输出数据轨迹，并实时检测故障的发生。在实验案例中，通过引入热交换器故障检测的案例研究，验证了本文提出方法的有效性。
This paper presents a novel data-driven fault detection method for linear systems based on the dissipative threshold. First, by introducing the concept of the dissipative inequality in linear systems and adopting the supply rate and storage function in the quadratic difference form (QdF), the dissipativity conditions can be transformed into quadratic functions of the input and output data trajectories. Compared with traditional dissipativity, this approach can capture more detailed dynamic features. Subsequently, the coefficient matrices of the supply rate and storage function are obtained by solving an optimization problem with linear matrix inequality constraints. Finally, an evaluation function based on the dissipation rate and its fault detection threshold are set to online inspect the input/output data trajectories of the system and detect the occurrence of faults in real time. In the experimental case, the effectiveness of the proposed method is verified through a case study of fault detection in a heat exchanger.
| [1] | Isermann, R. and Ballé, P. (1997) Trends in the Application of Model-Based Fault Detection and Diagnosis of Technical Processes. Control Engineering Practice, 5, 709-719. https://doi.org/10.1016/s0967-0661(97)00053-1 |
| [2] | Frank, P.M. and Ding, X. (1997) Survey of Robust Residual Generation and Evaluation Methods in Observer-Based Fault Detection Systems. Journal of Process Control, 7, 403-424. https://doi.org/10.1016/s0959-1524(97)00016-4 |
| [3] | Patton, R.J. and Chen, J. (1991) A Review of Parity Space Approaches to Fault Diagnosis. IFAC Proceedings Volumes, 24, 65-81. https://doi.org/10.1016/s1474-6670(17)51124-6 |
| [4] | Frank, P.M. (1990) Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge-Based Redundancy. Automatica, 26, 459-474. https://doi.org/10.1016/0005-1098(90)90018-d |
| [5] | Kresta, J.V., Macgregor, J.F. and Marlin, T.E. (1991) Multivariate Statistical Monitoring of Process Operating Performance. The Canadian Journal of Chemical Engineering, 69, 35-47. https://doi.org/10.1002/cjce.5450690105 |
| [6] | Venkatasubramanian, V. and Chan, K. (1989) A Neural Network Methodology for Process Fault Diagnosis. AIChE Journal, 35, 1993-2002. https://doi.org/10.1002/aic.690351210 |
| [7] | Vapnik V. (2006) Estimation of Dependences Based on Empirical Data. Springer. |
| [8] | Willems, J.C. (1972) Dissipative Dynamical Systems Part I: General Theory. Archive for Rational Mechanics and Analysis, 45, 321-351. https://doi.org/10.1007/bf00276493 |
| [9] | Lei, Q., Wang, R. and Bao, J. (2018) Fault Diagnosis Based on Dissipativity Property. Computers & Chemical Engineering, 108, 360-371. https://doi.org/10.1016/j.compchemeng.2017.09.024 |
| [10] | Li, W., Yan, Y. and Bao, J. (2023) Data-Based Fault Diagnosis via Dissipativity-Shaping. IEEE Control Systems Letters, 7, 484-489. https://doi.org/10.1109/lcsys.2022.3193978 |
| [11] | Rosa, T.E., de Paula Carvalho, L., Gleizer, G.A. and Jayawardhana, B. (2024) Fault Detection for LTI Systems Using Data-Driven Dissipativity Analysis. Mechatronics, 97, Article 103111. https://doi.org/10.1016/j.mechatronics.2023.103111 |
| [12] | Willems, J.C. and Trentelman, H.L. (1998) On Quadratic Differential Forms. SIAM Journal on Control and Optimization, 36, 1703-1749. https://doi.org/10.1137/s0363012996303062 |
| [13] | Kojima, C. and Takaba, K. (2006) A Generalized Lyapunov Stability Theorem for Discrete-Time Systems Based on Quadratic Difference Forms. Transactions of the Society of Instrument and Control Engineers, 42, 493-502. https://doi.org/10.9746/sicetr1965.42.493 |
| [14] | Willems, J.C., Rapisarda, P., Markovsky, I. and De Moor, B.L.M. (2005) A Note on Persistency of Excitation. Systems & Control Letters, 54, 325-329. https://doi.org/10.1016/j.sysconle.2004.09.003 |
| [15] | Chen, J. and Patton, R.J. (2012) Robust Model-Based Fault Diagnosis for Dynamic Systems. Springer Science & Business Media. |
| [16] | Isermann, R. (2011) Fault-Diagnosis Applications: Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault-Tolerant Systems. Springer Science & Business Media. |
| [17] | Grant, M. and Boyd, S. (2014) CVX: Matlab Software for Disciplined Convex Programming. Version 2.1. https://cvxr.com/cvx |
| [18] | 俞立. 鲁棒控制-线性矩阵不等式[M]. 北京: 清华大学出版社, 2002. |
