Accelerating Bayesian Optimization for Nonlinear State-Space System Identification with Application to Lithium-Ion Batteries

Abstract

This paper studies system identification for nonlinear state-space models, a problem that arises across many fields yet remains challenging in practice. Focusing on maximum likelihood estimation, we employ Bayesian optimization (BayesOpt) to address this problem by leveraging its derivative-free global search capability enabled by surrogate modeling of the likelihood function. Despite these advantages, standard BayesOpt often suffers from slow convergence, high computational cost, and practical difficulty in attaining global optima under limited computational budgets, especially for high-dimensional nonlinear models with many unknown parameters. To overcome these limitations, we propose an accelerated BayesOpt framework that integrates BayesOpt with the Nelder--Mead method. Heuristics-based, the Nelder--Mead method provides fast local search, thereby assisting BayesOpt when the surrogate model lacks fidelity or when over-exploration occurs in broad parameter spaces. The proposed framework incorporates a principled strategy to coordinate the two methods, effectively combining their complementary strengths. The resulting hybrid approach significantly improves both convergence speed and computational efficiency while maintaining strong global search performance. In addition, we leverage an implicit particle filtering method to enable accurate and efficient likelihood evaluation. We validate the proposed framework on the identification of the BattX model for lithium-ion batteries, which features ten state dimensions, 18 unknown parameters, and strong nonlinearity. Both simulation and experimental results demonstrate the effectiveness of the proposed approach as well as its advantages over alternative methods.

Figures (9)

• Figure 1: Illustration of the Nelder--Mead method, adapted from Cheng:CBC:2015.
• Figure 2: Illustration of the accelerated BayesOpt approach. The contours show the landscape of $L(\bm{\theta})$. The green and red stars mark the global and local optima, respectively. The dashed and solid triangular simplexes correspond to the initial and final simplexes of each Nelder--Mead run. During optimization, BayesOpt guides the search toward the global optimum, while Nelder--Mead performs rapid local refinement. Across successive runs, the simplexes gradually shrink, indicating that Nelder--Mead progressively narrows its search region.
• Figure 3: The BattX model comprising four coupled sub-circuits.
• Figure 4: Convergence performance comparison over 50 independent runs. The mean log-likelihood and its variability across runs are shown. The dashed black line indicates the log-likelihood evaluated at the nominal parameter $\bm{\theta}^*$. All methods use the U-IPF-based likelihood evaluator with $N_p=100$ particles.
• Figure 5: Comparison of log-likelihood evaluations using (a) U‑IPF and (b) APF around the nominal $\bm{\theta}^*$ with $N_p$ particles. Each filter is run independently 1,000 times for each value of $N_p$.

Theorems & Definitions (2)

• Remark 1
• Remark 2