The remaining useful life (RUL) prediction of Lithium-ion batteries (LIBs) is of great importance to the health management of electric vehicles and hybrid electric vehicles. However, fluctuation and nonlinearity occur during battery degradation, resulting in difficulties in both model adaptability and RUL prediction accuracy. To face the challenge, we propose a sequence decomposition and deep learning integrated prognostic approach for the RUL prediction of LIBs. Complementary ensemble empirical mode decomposition and principal component analysis are applied to separate the local fluctuations and the global degradation trend from the battery aging data. The long short-term memory neural network combined with fully connected layers is designed as a transfer learning model. The hyperparameter optimization and finetuning strategy of the model is developed based on offline training data. In addition, to further realize the reasonable and effective LIB second-life applications, the RUL corresponding to different failure thresholds is predicted. The performance of the proposed integrated approach in degradation modeling and RUL prediction is evaluated on three publicly available LIB datasets with different degradation characteristics, as well as compared with other prediction algorithms under the same conditions. The illustrative results demonstrate that the proposed approach can achieve accurate, adaptive, and robust prediction for both capacity trajectory and RUL.

The construction of spatial basis functions (BFs) is critical to the time/space separation of distributed parameter system (DPS). The spatial BFs constructed by traditional Karhunen-Loeve (KL) may not work satisfactorily for two spatial-dimensional (2-D) DPS, because of a distorted mapping of the original sensor array in the row-wise vectorization process. In this paper, a novel time/space separation based method is proposed to construct dimension embedded BFs (DE-BFs) for modeling 2-D DPS. The DE-BFs are firstly formulated according to the spatial sensor array structure, and sequentially optimized with alternating least squares (ALS) by minimizing the reconstruction error. The mapping relationship between the DE-BFs and the spatial sensor array is well preserved. In addition, the coupling across temporal and different spatial dimensions is sufficiently captured. A satisfactory model accuracy can be achieved by the DE-BFs, even with limited training data. Experiments of a 2-D curing thermal process are used to verify the effectiveness of the proposed method.

Modeling high-spatial dimensional (high-D) distributed parameter systems (DPSs) is very difficult because of the spatially distributed characteristic and complex spatiotemporal coupling. In this article, a new framework based on high-order singular vector decomposition (HOSVD) is proposed to model a high-D DPS. A modified HOSVD is designed for separation of time and multiple spatial variables. It can well preserve the spatially distributed nature of the high-D DPS. It also considers the interaction across different spatial modes, which is an important part of spatiotemporal coupling in the high-D DPS. Experiments of a two-spatial dimensional thermal curing process are used to verify the effectiveness of the proposed method. An average prediction error near 1% of the curing temperature can be achieved.