Uncertainty-Aware State of Energy Estimation for Lithium-Ion Batteries via Hybrid Kernel Sparse Gaussian Process

This work develops a hybrid kernel sparse Gaussian process regression integrated with kernel density estimation (HCSGPR-UQ) to resolve three critical drawbacks of conventional lithium-ion battery State of Energy (SOE) estimators: degraded accuracy under dynamic loads, high computational overhead, and inadequate uncertainty quantification. A composite covariance kernel is built by weighting the radial basis function (RBF) and Matérn 5/2 kernels to simultaneously model global smooth SOE decay trends and local nonlinear fluctuations induced by abrupt current/temperature variations. Inducing-point sparse approximation is adopted to accelerate model inference, while kernel density estimation (KDE) generates nonparametric prediction bounds for quantitative uncertainty evaluation. Validations are carried out on a 75 Ah traction lithium-ion cell across −5 °C to 35 °C under Dynamic Stress Test (DST) and Beijing Bus Dynamic Stress Test (BBDST) cycles. Experimental results reveal that the proposed method yields mean absolute errors (MAEs) of only 0.32% (DST) and 0.38% (BBDST), runs roughly 15× faster than full Gaussian process regression (GPR), and attains a 94.7% coverage probability for nominal 95% prediction intervals. Balancing estimation precision, real-time inference speed and statistical reliability, the proposed framework delivers a viable online SOE estimation solution for vehicle battery management systems (BMSs).