Degradation analysis with nonlinear exponential‐dispersion process: Bayesian offline and online perspectives

Abstract

Exponential‐dispersion (ED) process has been recently introduced and demonstrated as a promising degradation model, which can include classical Wiener, gamma, and inverse Gaussian (IG) processes as special cases. However, most related studies are based on offline and point estimation methods, which limit their capability for uncertainty quantification and online update inference. In this paper, nonlinear ED process models equipped with Bayesian offline and online inference methods are presented. Tweedie ED process models are studied for degradation analysis with accelerated factors and unit‐to‐unit variability. Bayesian offline method based on NO‐U‐Turn sampler (NUTS) algorithm and Bayesian online method based on particle filter are developed, respectively. The offline method is presented to enhance the ED process based degradation analysis with uncertainty quantification. The online method is developed for the applications with limited storage and computing resources, for which degradation observations are analyzed on‐the‐fly with improved efficiency. Effectiveness and characteristics of the proposed methods are demonstrated through a simulation study and two case studies.

Log‐location‐scale increment degradation model: A Bayesian perspective

“…where Φ(⋅) is the cumulative distribution function associated with 𝜙(⋅). Hence for each unit, we can plot the empirical quartiles 𝑦 (1) , … , 𝑦 (15) (the ordered observarions) versus Φ −1 ( 𝑗−0.5…”

Direct position updating‐based trying‐mutation particle swarm optimization algorithm and its application on reliability optimization

“…Usually, the classical linear decreasing inertia weight is conducive to balancing the population ability of exploitation and exploration in the early or later iterations. 31,32 On the contrary, the increasing inertia weight, fully considering the population dispersion and aggregation in the early or later iterations, can ensure the population has a higher probability for leaving the local optimal area in the later iteration, so the increasing inertia weight is more conducive to solving the plate shaped or valley shaped unipolar optimization problems. 33,34 Furthermore, considering the characteristics of decreasing inertia weight and increasing inertia weight comprehensively, in formula (2), a nonlinear increasing inertia weight is proposed and calculated as follows: 𝜔 = (𝜔 min − 𝜔 max ) ⋅ sin…”

Performance reliability degradation analysis and lifetime prediction based on generalized normal grey cloud Bayesian Wiener process

“…Guo et al 20 proposed a Bayesian information fusion method based on multi-source degradation information to improve the accuracy of degradation model parameter estimation. Ding et al 21 proposed a nonlinear exponential diffusion (ED) process model using Bayesian offline and online inference methods, which enhanced the degradation analysis and uncertainty quantification based on the ED process and improved the efficiency of real-time analysis of the degradation process. Hence, compared with moment estimation and maximum likelihood estimation, Bayesian-based parameter estimation methods require less sample information, are less computationally expensive, and are more suitable for dynamic assessment of reliability of performance degradation processes and real-time prediction of RUL.…”

“…proposed a Bayesian information fusion method based on multi‐source degradation information to improve the accuracy of degradation model parameter estimation. Ding et al 21 . proposed a nonlinear exponential diffusion (ED) process model using Bayesian offline and online inference methods, which enhanced the degradation analysis and uncertainty quantification based on the ED process and improved the efficiency of real‐time analysis of the degradation process.…”