Explainable Fault Diagnosis Using Invertible Neural Networks—A Left Manifold-Based Solution

The series includes two parts, articulating the two novel avenues of research on intelligent fault diagnosis (FD) for nonlinear feedback control systems. In Part I of the series, we design a novel FD paradigm by elaborating an invertible neural network (INN) for feedback control systems. With the aid of a left manifold, the core idea behind the INN-based FD scheme is as follows: 1) formulation of residual generator used for FD as a projection of system data onto the null space that has the same dimension as system outputs; 2) in a topological space, elaboration of a homeomorphism that delivers an invertible relationship between system outputs and residual signals when the system input is given; and 3) skillful introduction of both the master and slave objective functions to achieve system/parameter identification with information loseless property. Comparing with the existing FD approaches, the three superior strengths of the proposed FD scheme deserving mentation are as follows: 1) it specializes in nonlinear feedback control systems; 2) it can effectively avoid the overfitting problem when approximating or learning nonlinear system dynamics; and 3) control theory guides the whole design, ensuring the interpretability of the learning process. Finally, two studies on nonlinear systems demonstrate the feasibility of the invertible left manifold (ILM)-based FD strategy. Part I would contribute to the future development of machine learning (ML)-based system identification and explainable FD approaches, and also benefits the right manifold-based FD designs in Part II.