Prognostics based on the generalized diffusion process with parameters updated by a sequential Bayesian method

Hong Pei

doi:10.1007/s11432-020-2980-9

Prognostics based on the generalized diffusion process with parameters updated by a sequential Bayesian method

2022-05-26

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DOI：10.1007/s11432-020-2980-9

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The realistic degradation process for the engineering equipment is generally stochastic and complicated owing to the uncertain operational condition and multiple functional loading, exhibiting the absolute nonlinear distinction. Such a nonlinear degradation process is widely modeled as a generalized diffusion process. When utilizing the generalized diffusion process-based model, certain model parameters are considered as the random variables to characterize the unit-to-unit discrepancies. Hence, the estimation of these kinds of parameters usually resorts to the Bayesian method. However, owing to the complex pattern of the model parameters in the generalized diffusion process, computing the Bayesian updated parameters requires plenty of repeated calculation and integration operations once the new degradation monitoring information is available. This will inevitably lower the computing efficiency and real-time performance. Toward this end, this paper presents an adaptive prognostic method based on the generalized diffusion process to determine the remaining useful life (RUL) of degraded equipment. First, a generalized diffusion process-based degradation modeling framework is constructed to describe the health performance of stochastic degraded equipment under complex conditions. Then, we utilize the maximum likelihood estimation (MLE) method to estimate the initial model parameters by analyzing the historical degradation information. Furthermore, a sequential Bayesian method is proposed to recursively update the stochastic model parameters in the generalized diffusion process for particular equipment in service. Unlike the existing studies utilizing the Bayesian method, the primary contrast in the presented method lies in that there is no need to implement the calculation process with complicated integration repeatedly utilizing the whole degradation information obtained before the current time. Particularly, the current measured information is incorporated into the estimates of the stochastic parameters in the previous time to determine the corresponding posterior estimates at the current time. This can avoid repeated calculation and raise the efficiency to a certain extent. Thereafter, the RUL distribution is updated adaptively by incorporating the acquired posterior estimates. Finally, we provide two practical case studies associated with the gyroscope and 2017-T4 aluminum alloy to demonstrate the efficiency and advantage of the proposed sequential Bayesian method. The experimental results exhibit that the proposed method can increase the RUL prediction accuracy compared with the existing methods in the literature.

Keywords:

generalized diffusion process

stochastic model parameters

remaining useful life

maximum likelihood estimation

sequential Bayesian methods

Prognostics based on the generalized diffusion process with parameters updated by a sequential Bayesian method

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