New Shapeness Property and Its Convex Optimization Model for Interpretable Machine Degradation Modeling

Abstract

Performance degradation modeling is promising to construct an advanced health index (HI). Currently, domain knowledge including monotonicity, trendabilty, and identifiability has been widely recognized as desirable properties to evaluate the suitability of an HI. Nevertheless, a quantitative criterion to evaluate the suitability of the curvature of an HI is still lacked, which can be used to describe different machine degradation rates. In this article, a new property of an HI named “shapeness” is proposed and it expects that an HI would have a monotonic degradation rate when the HI has a monotonic curve. Subsequently, a mathematical quantitative formulation and optimization model of the shapeness is put forward to be integrated with other desirable properties, which can formulate a composite optimization degradation model. Here, the main variables of the proposed optimization degradation model are weights that are used to fuse spectra lines of vibration signals so that the sum of weighted spectra lines can be used to form a generalized HI. Besides, it is proved that the proposed optimization model is a convex optimization problem so that a global optimal solution is uniquely guaranteed. Two run-to-failure case studies are conducted and some comparisons with state-of-the-art models show that the proposed HI has better performance.