The accurate prognostics of lithium-ion battery state of health (SOH) and remaining useful life (RUL) have great significance for reducing the costs of maintenance. The methods based on the physical models cannot perform satisfactorily as the systems become more and more complex. With the development of digital acquisition and storage technology, the data of battery cells can be obtained. This makes the data-driven methods get more and more attention. In this paper, to overcome the problem that the trend fitting deteriorates rapidly when test data are far from the training data for multiple-step-ahead estimation, a prognostic method fusing the wavelet de-noising (WD) method and the hybrid Gaussian process function regression (HGPFR) model for predicting the RUL of the lithium-ion battery is proposed. Gaussian process regression (GPR) is a typical representative for the Bayesian structure with non-parameter expression and uncertainty presentation. In this case, the effects on predictive results are compared and analyzed using the proposed method and the HGPFR model with different lengths of training data. Besides, in consideration of the degradation characteristics for the lithium-ion battery data set, the selections of the wavelet de-noising method are performed with corresponding experimental analyses. Furthermore, we set the hype-parameter for the mean function and co-variance function, and then develop a method for parameter optimization to make the proposed model suitable for the data. Moreover, a numerical simulation based on the data repository of Department of Engineering Science (DES) university of Oxford and Center for Advanced Life Cycle Engineering (CALCE) of University of Maryland is carried out, and the results are analyzed. For the data repository, an accuracy of 2.2% is obtained compared with the same value of 6.7% for the HGPFR model. What is more, the applicability and stability are verified with the prognostic results by the proposed method.

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