基于混合耗散不等式约束优化的故障检测新方法

A New Fault Detection Method Based on Mixed Dissipativity Inequality Constrained Optimization

摘要: 本文基于混合耗散不等式约束优化提出了一种面向离散时间脉冲系统的分布式故障检测方法，充分考虑了系统单元间的相互作用特性。首先针对脉冲作用下的故障检测观测器设计，确保其满足故障混合敏感性和干扰混合鲁棒性要求。通过引入混合矢量耗散性概念，系统地处理脉冲效应、故障混合敏感性和干扰混合鲁棒性条件，确保脉冲误差动态相对于混合供给率是混合矢量耗散的。接着，推导出保证脉冲估计误差动态矢量耗散的充分条件。最后，通过求解混合耗散不等式约束的优化问题离线获得观测器参数，并实现在线故障检测。在数值仿真中，通过与现有方法的比较，验证了本文提出方法的有效性和优越性。

Abstract: This paper presents a novel distributed fault detection approach for discrete-time impulse systems, leveraging an optimization framework constrained by a mixed dissipativity inequality. The interaction characteristics between system units are considered. First, the research emphasizes the design of a fault detection observer that operates under impulse actions, ensuring compliance with fault mixed sensitivity and disturbance mixed robustness requirements. By introducing the concept of mixed vector dissipativity, the proposed approach systematically addresses the effects of impulse actions, fault sensitivity conditions, and disturbance robustness conditions, ensuring that the impulse error dynamics are mixed vector dissipativity with respect to the mixed supply rate. Then, sufficient conditions are derived to guarantee the dynamic vector dissipativity of the impulse estimation error. Finally, the parameters of the fault detection observer are obtained offline by solving the optimization problem constrained by mixed dissipativity inequalities, and online fault detection is realized. In numerical simulation, the effectiveness and superiority of the proposed method are verified by comparing with existing method.