本計畫將探討關於可回充式鋰電池衰變試驗資料之貝氏可靠度分析。近年因高科技產品快速發展，伴隨鋰電池長時間使用之需求與評估更顯重要。鋰電池衰變資料來自於鋰電池充放電時電池之電壓、電流和電容之變化；在重複充放電中觀測資料具有週期性，且其使用狀況逐時遞減，使得週期間之資料呈現遞減趨勢的負相關性。工程上傳統關於鋰電池壽命的評估多著重於以建構狀態空間之濾波器為主軸，有其限制，使壽命評估之精確性上有很大的改善空間，因此應用統計模配適鋰電池衰變試驗資料的統計方法逐漸受到重視。Wang et al. (2019) 提出以趨勢更新過程 (Trend Renewal Process) 來描述鋰電池加速衰變試驗資料，將觀測資料做一趨勢轉換函數的累積，使其間隔時間符合獨立同分布的更新過程, 為可靠度研究提供一個新的統計模型。然而因鋰電池衰變試驗需時甚長且相對應成本亦高，試驗中受測電池個數極為有限，此時結合來自資料以外的其他先驗資訊的貝氏統計方法應是最為可行的分析方式。本三年期子計畫即將探討關於鋰電池衰變試驗資料之貝氏可靠度推論及其相關問題。 本子計畫第一年，擬由 Wang et al. (2019)之趨勢更新過程出發，考慮資料不同更新時間分布及不同轉換趨勢下之配適狀況。藉由貝氏方法調整未知參數之先驗分布的超參數來預測各電池最終使用狀況及壽命評估。另外，因為資料之週期性，或可以更具彈性的隨機過程分析各週期內之資料，再整合各週期間遞減的關聯性，得一模型予以評估其最終使用狀況。故本計畫的第二年，將考慮以較寬廣的隨機過程，分別分析各週期內之資料，再以經驗貝氏的方法予以整合，以發揮”借用力量”的整合評估功效。計畫的第三年將考慮在前兩年的研究中所得之適當模型下，除了基本的貝氏可靠度分析及敏感性分析外，並考慮在最終預測目標達到最精確的評估下，決定貝氏最佳加速試驗之變數水準和各樣本配適。 ;In this proposal, we will discuss the Bayesian reliability inference for the degradation data of rechargeable lithium-ion batteries. Rechargeable batteries have become more and more popularly used due to the competitive advancement of the electronic equipment in recent decades. To study the long-term performance of the rechargeable batteries, more interests are in the remaining performance of a battery over its whole cycle. The current, voltage and capacity are measured during the repeatedly charging/discharging processes from a degradation test of the lithium-ion batteries.The periodic degradation data show similar patterns among discharging cycles but with decreasing trend. Traditional research in engineering usually uses filtering based on state spaces. Statistical modeling and analysis for the rechargeable batteries degradation data are getting more and more attention. Recently, Wang et al. (2019) proposed an accelerated testing version of the trend-renewal process (TRP) model based on the repairable system model to capture the battery capacity function which reveals a new direction in analyzing the lithium-ion battery data. Due to high reliability and high testing cost, experiments with small sample sizes are often encountered in degradation tests of lithium-ion batteries, thus Bayesian approach may provide more useful and accurate inference as an alternative. In this proposal, we consider the Bayesian reliability inference on the ultimate end of performance based on the degradation process test of lithium-ion battery data, by incorporating prior information through different but similar tests of lithium-ion batteries. In the first year, we will begin with the Bayesian analysis based on the accelerated trend renewal process model of Wang et al. (2019) with different trend functions and/or renewal distributions. By adjusting the hyperparameters of the prior distributions, we expect to obtain Bayesian inference for the end of performance of the lithium-ion battery. As the periodic degradation data show similar patterns among discharging cycles but with decreasing trend, in the second year, we shall analyze the data within each cycle and try to combine the models with empirical Bayes approach to come out with a more satisfactory result by means of the concept of "borrowing the strength". In the last year of this sub-project, we will focus on the Bayesian optimal designs, based on models established in the first two years, by determining the appropriate stress levels as well as sample size allocation to get the most accurate estimates of the end of performance in accelerated degradation tests of the lithium-ion batteries.
