A Stochastic Minimax Estimation Framework for Predictive Maintenance Of Industrial Equipment

Abstract

Reliable estimates of equipment degradation in industrial systems are highly important for predicting their behavior under uncertain conditions. However, most existing methods have good prediction capabilities but are not provided with an adequate mathematical framework for the minimization of worst-case degradation estimation error and robustness of the process. In this research, a minimax estimation framework for the assessment of industrial equipment degradation is developed in the form of a risk optimization model. The proposed framework involves stochastic modeling of degradation, its uncertain observation, formulation of the estimation error, and minimax optimization to yield a reliable estimator of the equipment health condition. Mathematical properties of the new estimator are studied in terms of its existence, uniqueness, stability, and convergence. A stochastic optimization algorithm is formulated to solve the estimation problem with uncertain degradation parameters. Numerical experiments are performed based on various stochastic models of equipment degradation, while the proposed estimation method is compared with the conventional approaches, such as Kalman filtering, Bayesian estimation, and maximum likelihood estimation. It is shown that the proposed estimator can provide a better accuracy of estimation, lower worst-case risk, stable behavior, and robustness to stochastic uncertainties.