加速通用趨勢更新過程下的貝氏分析及其在鋰電池資料之應用;Bayesian Analysis of Accelerated Generic Trend Renewal Processes with an Application to Lithium-ion Battery Data

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/98048

Title:	加速通用趨勢更新過程下的貝氏分析及其在鋰電池資料之應用;Bayesian Analysis of Accelerated Generic Trend Renewal Processes with an Application to Lithium-ion Battery Data
Authors:	李霽軒;Li, Chi-Hsuan
Contributors:	統計研究所
Keywords:	通用趨勢更新過程;階層貝氏;貝氏適合度檢定;失效時間分布;性能終止時間;generic trend renewal process;hierarchical Bayesian;Bayesian goodness of fit;failure time distributions;end of performance
Date:	2025-08-26
Issue Date:	2025-10-17 12:17:39 (UTC+8)
Publisher:	國立中央大學
Abstract:	針對經由充放電過程可重複使用但性能遞減的鋰電池衰變資料，通常可利用與時間相關的趨勢函數經變數變換轉換為衰變增量為獨立同分布的更新過程 (renewal process)，即趨勢更新過程 (trend renewal process) 來配適。囿於參數的不可辨別性，傳統趨勢更新過程限制更新分布之期望值為一，卻因此使模型中之參數失去原有的共軛 (conjugate) 結構，導致難以建構隨機效應模型描述具個別差異性的資料。為保留更新分布參數的共軛性，通用趨勢更新過程 (generic trend renewal process) 以趨勢函數參數之限制取代期望值為一的假設，俾能更具彈性地發展隨機效應模型。本文將通用趨勢更新過程推廣至加速通用趨勢更新過程 (accelerate trend renewal process; AGTRP)，在參數與加速應力呈對數線性關係下，分別考慮伽瑪、韋伯與逆高斯更新分布之 AGTRP 模型，利用參數之共軛性質，建立貝氏 AGTRP 模型，用以分析不同放電電流下的電池電容量比資料；在隨機效應模型中以階層貝氏 (hierarchical Bayes) 方法，引入隱藏變數捕捉電池間的個別差異。依據偏差訊息準則 (deviance information criterion; DIC) 以及對數邊際概似 (log marginal likelihood; LML) 值兩種常用的貝氏選模準則作為綜合依據，並由後驗預測 p-值 (posterior predictive p-value) 確認模型與資料之適切性。最後，根據加速資料配適之最適 AGTRP 模型，外插至正常應力水準下推估可修復產品的使用壽命。應用於電池充放電資料實例分析中，亦將 AGTRP 模型下所得電池的壽命指標與正常放電電流下衰變資料所得結果進行比較，經兩樣本 Kolmogorov-Smirnov 貝氏檢定，顯示兩組資料所得之預測壽命分布並無顯著不同，驗證由加速模型外插至正常應力水準下之壽命推論的合理性。;For the cyclic degradation data of lithium-ion batteries, which can be repeatedly charged and discharged but exhibit gradual performance decline, the trend renewal process (TRP) is commonly adopted. In this approach, time-dependent trend functions transform correlated data into independent and identically distributed increments that follow a renewal process. However, due to the issue of parameters identifiability, TRP models assume the expectation of the renewal distribution to be one. Such restriction destroys the conjugate structure of the parameters. The generic trend renewal process (GTRP), making the restriction on the trend-function parameter instead of expectation, preserves conjugacy and thus provides greater flexibility for modeling random effects. Based on this framework, this study develops Bayesian accelerated generic trend renewal processes (AGTRP) with gamma, Weibull, and inverse Gaussian renewal distributions respectively, by assuming a log-linear relationship between the parameters and the accelerated stress variable. Leveraging the conjugate structure, random-effects AGTRP models are further constructed by introducing latent variables within a hierarchical Bayesian model to capture unit-to-unit heterogeneity. Model performance is assessed using the deviance information criterion (DIC) and log marginal likelihood (LML), while posterior predictive p-value evaluates the corresponding model adequacy. The selected AGTRP model is extrapolated to draw the predictive life inference under normal use condition. A Bayesian two-sample Kolmogorov-Smirnov test comparing the extrapolated distribution with normal-stress experimental data shows insignificant differences between the resulting life distributions in the all data analysis, supporting the validity of AGTRP for extrapolative lifetime prediction.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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