基于时间序列分析的电容器退化模型

Degradation Modeling of Capacitors Based on Time Series Analysis

针对高温下电容器电容值下降的问题,基于差分自回归移动平均(ARIMA)模型及分数阶自回归移动平均(ARFIMA)模型,引入时间序列分析法预测电容值的退化轨迹.对于ARIMA模型,当电容器的退化过程服从Wiener分布时,利用过差分预判法(OPM)预判原时间序列的过差分阶数;根据单位根检验、自相关及偏自相关函数的计算结果确定经过一阶差分后的时间序列的平稳性.对于ARFIMA模型,利用重标极差法判定退化数据是否具有长期记忆性;通过最小准则及极大似然法估计模型阶数及其相关参数值.最后,通过残差检验验证OPM-ARIMA及ARFIMA模型在提取有效信息与准确预测两方面的能力,并进一步分析了这两种模型的可行性与有效性.

For the problem of predicting the capacity degradation of capacitors at elevated temperatures, based on the auto-regressive integrated moving average(ARIMA) model and the auto-regressive fractionally integrated moving average(ARFIMA) model, time series analysis methods are introduced to predict the degradation path of capacity. For the ARIMA model, when the degradation process of the capacitors obeys Wiener distribution, the over-differential prediction method(OPM) can be used to predict the difference order of the original time series that cause over-difference. According to the calculation results from unit root test, auto-correlation function and partial auto-correlation function, it will be verified that whether the time series can become stationary through the first order difference. For the ARFIMA model, the re-scaled range analysis is used to determine whether the degradation data has long-term memory. The orders and related parametric estimated values are obtained by using minimum information criterion and maximum likelihood estimation. Finally, the residual test is used to verify the ability of the OPM-ARIMA model and the ARFIMA model for extracting valuable information and accurate prediction. Furthermore, the feasibility and effectiveness of two models are also analyzed.