Abstract
Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime’s closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.
Highlights
With the rapid development of technology, prognostics and health management (PHM)technique has gained increasing attention and been applied to industrial systems, military devices, aerospace equipment, and so on [1,2]
The contributions of the paper can be summarized as follows: (1) We propose a two-phase degradation model with the fixed jump at the change point governed by the Wiener process, and attain the analytical form of the lifetime under the concept of first passage time (FPT) with a predefined changing time and fixed parameters
(3) We further provide a model identification method based on the Expectation Maximization (EM) algorithm and Bayesian rule
Summary
With the rapid development of technology, prognostics and health management (PHM). technique has gained increasing attention and been applied to industrial systems, military devices, aerospace equipment, and so on [1,2]. Kong et al [26] utilized a two-phase Wiener process model with an abrupt fixed jump to model the bearing’s degradation, and further proposed a method of lifetime estimation. The contributions of the paper can be summarized as follows: (1) We propose a two-phase degradation model with the fixed jump at the change point governed by the Wiener process, and attain the analytical form of the lifetime under the concept of FPT with a predefined changing time and fixed parameters.
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