High precision implicit function learning for forecasting supercapacitor state of health based on Gaussian process regression.

State of health (SOH) prediction of supercapacitors aims to provide reliable lifetime control and avoid system failure. Gaussian process regression (GPR) has emerged for SOH prediction because of its capability of capturing nonlinear relationships between features, and tracking SOH attenuations effectively. However, traditional GPR methods based on explicit functions require multiple screenings of optimal mean and covariance functions, which results in data scarcity and increased time consumption. In this study, we propose a GPR-implicit function learning, which is a prior knowledge algorithm for calculating mean and covariance functions from a preliminary data set instead of screening. After introducing the implicit function, the average root mean square error (Average RMSE) is 0.0056 F and the average mean absolute percent error (Average MAPE) is 0.6%, where only the first 5% of the data are trained to predict the remaining 95% of the cycles, thereby decreasing the error by more than three times than previous studies. Furthermore, less cycles (i.e., 1%) are trained while still obtaining low prediction errors (i.e., Average RMSE is 0.0094 F and Average MAPE is 1.01%). This work highlights the strength of GPR-implicit function model for SOH prediction of energy storage devices with high precision and limited property data.