Prognostics for State of Health of Lithium-Ion Batteries Based on Gaussian Process Regression

Table 1

Prediction errors comparison of different methods for batteries Nos. 5, 6, and 7.

(a)

Battery number	Error criteria	Basic GPR	LGPFR	QGPFR	Combination LGPFR	Combination QGPFR	SMK-GPR
5	MAPE (%)	12.10	23.0	1.90	1.60	2.10	1.65
	RMSE (%)	13.03	1.71	1.50	1.36	1.80	1.38
6	MAPE (%)	27.0	10.30	7.70	10.20	29.0	10.60
	RMSE (%)	22.51	6.90	5.12	6.86	20.44	7.08
7	MAPE (%)	19.20	1.90	5.40	1.70	2.60	1.91
	RMSE (%)	20.70	1.59	5.52	1.73	2.69	1.88

(b)

Battery number	Error criteria	P-MGPR	SE-MGPR	Model I	Model II	Model III
5	MAPE (%)	1.55	1.38	0.80	0.94	0.91
	RMSE (%)	1.36	1.20	0.74	0.83	0.83
6	MAPE (%)	2.96	2.93	1.00	0.99	2.18
	RMSE (%)	2.12	2.11	0.82	0.81	1.71
7	MAPE (%)	1.09	1.02	0.74	0.73	1.12
	RMSE (%)	1.14	1.07	0.82	0.81	1.71

Note. Some experimental results are obtained from [24, 27]; LGPFR: Gaussian process functional regression with linear mean function [24]; QGPFR: Gaussian process functional regression with quadratic polynomial mean function [24]; Combination LGPFR: LGPFR with combination of squared exponential covariance function and periodic covariance function [24]; Combination QGPFR: QGPFR with combination of squared exponential covariance function and periodic covariance function [24]; SMK-GPR: the GPR method with spectral mixture kernels [27]; SE-MGPR: multiscale GPR methods with squared exponential function [27]; P-MGPR: multiscale GPR methods with periodic covariance function [27].