AI 中文总结
针对自编码器故障检测方法可解释性不足的问题，本文基于Koopman算子理论提出双自编码器方法，通过假设检验框架检测非线性随机机械系统的参数故障，在仿真与真实基准上表现出良好性能。
AI 中文摘要
自编码器通常用于非线性动力系统的无监督数据驱动故障检测，尽管其应用广泛且性能常优于传统方法，但多数应用依赖于从标称训练数据中学习到的特征对测量数据进行启发式重构，缺乏对潜在非线性动力学的明确洞察。这种可解释性的缺失限制了基于自编码器的故障检测方法向更高层次故障诊断（如故障定位与量化）的扩展，且在很大程度上局限了其应用导向研究。为解决该局限，本文提出一种用于非线性随机机械系统参数故障检测的策略。利用Koopman算子理论开发输出数据的数学表示，该理论促使将输出数据嵌入流形并通过两阶段自编码器对其进行近似。故障检测在假设检验框架内构建，其中对新数据进行测试以判断其是否与标称观测所确定的流形邻域一致。通过对具有两类非线性的玩具机械系统进行蒙特卡洛仿真验证了所提方法，并将其应用于两个知名真实基准，与标准自编码器相比，该方法提供了良好的故障检测性能。
英文摘要
Autoencoders are commonly used for unsupervised data-driven fault detection in nonlinear dynamical systems. Despite their widespread success and often favorable performance compared with traditional approaches, most applications rely on heuristic reconstruction of measured data using features learned from nominal training data, without explicit insight into the underlying nonlinear dynamics. This lack of interpretability limits the extension of autoencoder-based fault detection methods to higher levels of fault diagnosis, e.g., fault localization and quantification, and confines their use largely to application-oriented studies. To address this limitation, we propose a strategy for detecting parametric faults in nonlinear stochastic mechanical systems. A mathematical representation of the output data is developed using Koopman operator theory, which motivates their embedding on a manifold and its subsequent approximation with a two-stage autoencoder. Fault detection is formulated within a hypothesis-testing framework, in which new data are tested for consistency with a neighborhood of the manifold identified from nominal observations. The proposed method is validated through Monte Carlo simulations of a toy mechanical system with two types of nonlinearity and applied to two well-known real benchmarks, where it provides favorable fault-detection performance compared with standard autoencoders.
