针对电池健康度建模中参数难估计问题，提出自动优化正则化的迭代拟合方法。
Regularised Iterative Generalised Least Squares with Optimal Selection of the Hyper-Parameter for Identifying Nonlinear Phenomenological Models
- 引入岭回归改善参数共线性导致的数值不稳定问题。
- 通过信息论指标自动选择每轮迭代的最优正则化系数。
- 可处理异方差与序列相关数据，适合物理机理模型参数估计场景。
在当前以经验方法为主导的领域（如锂离子电池健康状态预测）中，基于准物理思维构建的机理模型需从实验数据中估计参数。此类模型常因结构导致参数完全或部分共线，难以可靠估计。为保持理想模型形式的同时提升数值稳定性，本文提出一种岭回归方案，并设计了一种基于信息论准则的自动化方法，用于在每轮迭代中优化岭回归的超参数。相关公式需通过定点迭代求解，分析表明其收敛速度极快。该最优超参数选择机制被整合进高效的正则化迭代广义最小二乘框架中，可同时拟合异方差和序列相关数据。仿真验证了整体方法的有效性。
原文摘要 · Abstract (English)
In some fields currently dominated by empirical approaches, such as state of health (SoH) prediction for lithium-ion batteries, phenomenological models motivated by quasi-physical thinking contain parameters to be estimated from experimental data. Often the structure of such models yields fully or partially confounded parameters, which are difficult or even impossible to estimate reliably. To preserve the desired model formulation and simultaneously improve the numerical conditioning for the problem we introduce a ridge regression scheme. An automated method is provided, based on information theoretic measures of model performance, which optimises the ridge regression hyper-parameter at each iteration. The formulae presented require fixed point iteration to solve for the hyper-parameter. Given a suitable starting value, analysis demonstrates convergence is very rapid. The optimal hyper-parameter selection mechanism is incorporated within an efficient regularised iterative generalised least squares mechanism, capable of fitting both heteroscedastic and serially correlated data as required. Simulation confirms the efficacy of the overall method.
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