準確地預測電池的剩餘使用壽命對於電池以及有使用電池的設備的預後與健康管理是非常重要。電池壽命資料通常需經過一段長時間後才能取得，因此我們將電容量作為短期內的健康指標來替代壽命資料。有很多環境因素可能會影響電容量退化路徑，尤其是環境溫度。另一個與電容量有關的重要因素稱為電容再生現象，即為電池在經過一段時間休息後，電容量將會增加。我們的研究探討了電池條件例如連續充電 / 放電循環次數、休息天數以及溫度，與電容退化的關係。這個實驗新穎之處為在不同的室溫下收集資料。這個設定反映了電池使用的實際情況。我們提出了分段隨機係數模型來捕捉給定連續充放電循環次數和休息天數下電容退化的趨勢。概似函數中有多個積分會導致計算困難，但是我們使用蒙地卡羅方法來很好地近似積分。結果顯示比不考慮再生效應和其他條件的模型能更有效地提高預測剩餘壽命的準確度。我們還提供了點估計、區間估計和剩餘壽命的分佈。藉由這些估計，建議用戶根據各種電池條件來決定適當的更換時間。

Accurate prediction of the remaining useful life (RUL) of a battery is important to the prognosis and health management of the battery and the equipment using the battery. Since battery lifetime data are usually obtained after a long period of time, we regard battery capacity as the health indicator in the short term to replace the lifetime data. There are many environmental factors that can affect the degradation path of battery capacity, especially the surrounding temperature. Another important factor related to the capacity is called the capacity regeneration phenomena, i.e., the battery capacity will increase after a period of rest time. Our research explores the relationship of the battery conditions, such as continuous charge / discharge cycle number, rest day, and temperature, with the capacity degradation. The practical part of the experiment is that the data was collected under variant room temperature. This setting reflects the reality of battery usage on the field. We propose the piecewise random coefficient models to capture the trend of capacity degradation under the given continuous charge / discharge cycle number and rest day. There are multiple integrations in the likelihood function that cause computational difficulties, however we use the Monte Carlo method to approximate it well. Our models improve the prediction accuracy of the RUL more effectively than those don't consider the regeneration effect. We provide the point estimation, interval estimation, and the distribution of the RUL. With these estimations, users are advised to determine the appropriate replacement time for various battery conditions.

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