A Variable Projection-Based Algorithm for Fault Detection and Diagnosis

Effective fault detection and diagnosis (FDD) is crucial in modern industry applications, but developing accurate and interpretable FDD models for complex processes remains a challenge. In this article, we propose a novel approach that partitions measurements into a principal component and a residual subspace, formulating the FDD model-building problem as a separable nonlinear optimization problem. To improve model interpretability, we incorporate sparse regularizers to derive sparse loadings. Taking advantage of the special separable structure presented in such problems, we present an efficient variable projection-based algorithm that significantly reduces the dimension of the parameters by solving a least-squares problem with an orthonormal constraint. This results in a reduced problem that only contains loading parameters. We further establish a significant theorem, which is essential for computing the gradient of the reduced objective function and addressing the coupling between different parts of the parameters, leading to improved identification performance of the proposed algorithm. Numerical results on synthetic and real-world datasets demonstrate that our algorithm achieves faster convergence speed and better evaluation metrics.