在預後與健康管理(Prognostics and Health Management, PHM) 中，預測設備的剩餘可使用壽命(Remaining Useful Life, RUL) 至關重要。其中鋰離子電池電容的退化會大大地受到使用狀況影響，像是在不同加速壽命實驗條件下，會造成不同的鋰離子電池電容退化模式，以及長時間休息後鋰離子電池會有電容量增加的現象，人們稱之為電容再生現象。本文針對四種不同溫度及放電電流條件，探討溫度及放電電流與電容退化之間的關係，並以Chiu (2020) 的分段隨機係數退化模型為基礎，提出了四個分段隨機係數退化模型，本文提出的模型可以在經歷長時間休息之後捕捉到電容退化的趨勢，以及不同實驗條件下電容的退化模式。根據分別由美國航空暨太空總署(NASA) 公布以及長庚大學(CGU) 提供的兩筆鋰離子電池數據集進行案例應用，結果顯示本文提出的分段隨機係模型可以很好的配適不同溫度及放電電流條件下鋰離子電池電容退化資料，並且比未考慮電容再生現象的模型更有效地提高鋰離子電池剩餘可使用壽命預測的準確性。藉此，我們也可以從中獲得剩餘可使用壽命的分配，從該分配推估鋰離子電池的剩餘可使用壽命平均及剩餘可使用壽命分配的第q 分位數，以及相對應的信賴區間。最後，我們假設離子電池在電動車與儲能設備上會經歷的一些使用狀況並預測剩餘可使用壽命，結果顯示本文提出的模型可以較合理地預估剩餘可使用壽命。利用此資訊建議用戶判斷電池適當的置換時間，達到降低成本並使鋰離子電池效用最大化的目的。

In Prognostics and Health Management (PHM), the prediction of Remaining Useful Life (RUL) of the equipment is a key issue. Among them, the degradation of lithium-ion battery capacity will be greatly affected by the conditions of use, such as different accelerated life test conditions, which will cause various degradation patterns of lithium-ion battery capacity. In addition, there is a phenomenon of increased capacity of lithium-ion batteries after a long period of rest time, which is called the capacity regeneration phenomena. Our research explores the relationship between temperature, discharge current rate and capacity degradation for four different temperatures and discharge current rates conditions. Based on the piecewise random coefficient degradation models given by Chiu (2020), we propose four piecewise random coefficient degradation models which can capture the trend of capacity degradation after a long period of rest time and the capacity degradation trend under different test conditions. The case applications are carried out according to the two lithium-ion battery datasets published by National Aeronautics and Space Administration (NASA) and provided by the Cheng Gung University (CGU). The results show that the piecewise random coefficient degradation models proposed in this research can fit the lithium-ion battery capacity degradation data well under different temperature and discharge current rate conditions, and it improves the accuracy of the prediction of the RUL of the lithium-ion battery more effectively than the model that does not consider the capacity regeneration phenomena. Thereby, we can also obtain the distribution of the RUL, and estimate the mean of RUL, q-th quantile of RUL and the corresponding confidence intervals of the tested batteries. Finally, we assume that lithium-ion batteries will experience some usage conditions in electric vehicles and energy storage equipment and then predict the RUL. The results show that the models proposed in this research can reasonably estimate the RUL. Using this information, users are advised to determine the appropriate replacement time for the battery to achieve the goal of reducing costs and maximizing the utility of lithium-ion batteries.

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