An important initial step in fault detection for complex industrial systems
is gaining an understanding of their health condition. Subsequently, continuous
monitoring of this health condition becomes crucial to observe its evolution,
track changes over time, and isolate faults. As faults are typically rare
occurrences, it is essential to perform this monitoring in an unsupervised
manner. Various approaches have been proposed not only to detect faults in an
unsupervised manner but also to distinguish between different potential fault
types. In this study, we perform a comprehensive comparison between two
residual-based approaches: autoencoders, and the input-output models that
establish a mapping between operating conditions and sensor readings. We
explore the sensor-wise residuals and aggregated residuals for the entire
system in both methods. The performance evaluation focuses on three tasks:
health indicator construction, fault detection, and health indicator
interpretation. To perform the comparison, we utilize the Commercial Modular
Aero-Propulsion System Simulation (C-MAPSS) dynamical model, specifically a
subset of the turbofan engine dataset containing three different fault types.
All models are trained exclusively on healthy data. Fault detection is achieved
by applying a threshold that is determined based on the healthy condition. The
detection results reveal that both models are capable of detecting faults with
an average delay of around 20 cycles and maintain a low false positive rate.
While the fault detection performance is similar for both models, the
input-output model provides better interpretability regarding potential fault
types and the possible faulty components.

无监督的健康状况监测在复杂工业系统的故障检测中起着重要作用。本研究通过对自编码器和输入 - 输出模型进行综合比较，探索了这两种基于残差的方法在健康指标构建、故障检测和健康指标解释方面的性能。结果显示，输入 - 输出模型在潜在故障类型和可能故障部件的解释方面具有更好的可解释性。

残差方法在故障检测上的比较

A Comparison of Residual-based Methods on Fault Detection

We develop a new method which extends Dynamic Mode Decomposition (DMD) to
incorporate the effect of control to extract low-order models from
high-dimensional, complex systems. DMD finds spatial-temporal coherent modes,
connects local-linear analysis to nonlinear operator theory, and provides an
equation-free architecture which is compatible with compressive sensing. In
actuated systems, DMD is incapable of producing an input-output model;
moreover, the dynamics and the modes will be corrupted by external forcing. Our
new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all
of the advantages of DMD and provides the additional innovation of being able
to disambiguate between the underlying dynamics and the effects of actuation,
resulting in accurate input-output models. The method is data-driven in that it
does not require knowledge of the underlying governing equations, only
snapshots of state and actuation data from historical, experimental, or
black-box simulations. We demonstrate the method on high-dimensional dynamical
systems, including a model with relevance to the analysis of infectious disease
data with mass vaccination (actuation).

本研究提出了一种名为 DMDc 的新方法，在保留传统动态模式分解 (DMD) 的优点的同时，能够将外部驱动信号与模型本身动力学有机结合，实现了准确提取复杂系统的低阶模型。该方法不需要系统方程的知识，只需要使用实验或历史快照数据即可。我们将该方法应用于具有广泛应用前景、复杂度高的多个实际案例。