T-shape data and probabilistic remaining useful life prediction for Li-ion batteries using multiple non-crossing quantile long short-term memory

Abstract

This paper introduces and formalizes the concept of T-shape data, which arises in several engineering and natural contexts, where the initial data are richer and cover a wider range of operations than the data acquired in the following time. The specific context considered is the Li-ion battery experimental testing before the actual operation, where the T-shape data is cast as right-censored data in the application of battery remaining useful life (RUL) prediction. Existing RUL prediction techniques focused on RUL point estimation and provided rough calculations concerning the RUL distribution, thus are insufficient for battery degradation information. Based on the T-shape structure, this paper investigates a time-varying construction of the RUL probability density function. The proposed computationally efficient method, the multiple non-crossing quantiles Long Short-Term Memory (MNQ-LSTM), learns long-term dependencies among battery RUL and operation process quantities, including operating conditions. With several predicted quantile levels, the construction of the RUL conditional probability density function can capture the underlying survival distribution and statistical inferences of battery RUL with richer and more accurate information. Numerical results verify the performance of the proposed MNQ-LSTM with T-shape data. Compared to the conventional LSTM, Gaussian process regression, and a hybrid deep learning model of convolutional neural network and the bi-directional gated recurrent unit, the proposed model outperforms and can achieve the coefficient of determination up to 95.74% regarding point predictions. 100% testing results of battery RUL are not outside the range of 90% prediction intervals even in the worst case of 80% T-shape data.