基于耗散阈值的数据驱动故障检测新方法
A New Data-Driven Fault Detection Method Based on Dissipative Threshold
DOI: 10.12677/pm.2025.153075, PDF,   
作者: 李思睿, 宋 健：上海理工大学理学院，上海
关键词: 故障检测；数据驱动；耗散阈值；Fault Detection； Data-Driven； Dissipative Threshold
摘要: 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。
Abstract: 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.
文章引用：李思睿, 宋健. 基于耗散阈值的数据驱动故障检测新方法[J]. 理论数学, 2025, 15(3): 46-55. https://doi.org/10.12677/pm.2025.153075

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