On the design of Optimal Health Indicators for early fault detection and their statistical thresholds

Abstract

This research presents a method for developing optimal health indicators for early fault detection in machine condition monitoring. The devised health indicators are optimal in the Neyman–Pearson sense, as they maximize the probability of detection while maintaining a constant false alarm rate. They are generated through a generalized likelihood ratio test that involves the probability density functions representing the healthy and faulty states. The essence of the approach lies in establishing a framework that defines optimal health indicators as functions of the partial derivatives of the healthy probability density function and a modulation function, representing the distortion of the probability density function in the faulty state. Specific modulation functions lead to the recovery of several traditional health indicators, including kurtosis, skewness, the crest factor, the clearance factor, the smoothness factor, the shape factor, the impulse factor, ℓp/ℓq-norms, the negentropy, among others. New health indicators are also derived. As the proposed optimal health indicators asymptotically follow a chi-squared distribution, they come with a statistical threshold. The study comprehensively outlines the methodology, with its performance assessed through simulated and experimental signals. The results reveal that the early transition from healthy to faulty can be well detected via the established optimal health indicators and their thresholds.