Combining Non-Parametric and Parametric Models for Stable and Computationally Efficient Battery Health Estimation

Abstract

Equivalent circuit models for batteries are commonly used in electric vehicle battery management systems to estimate state of charge and other important latent variables. They are computationally inexpensive, but suffer from a loss of accuracy over the full range of conditions that may be experienced in real-life. One reason for this is that the model parameters, such as internal resistance, change over the lifetime of the battery due to degradation. However, estimating long term changes is challenging, because parameters also change with state of charge and other variables. To address this, we modelled the internal resistance parameter as a function of state of charge and degradation using a Gaussian process (GP). This was performed computationally efficiently using an algorithm [1] that interprets a GP to be the solution of a linear time-invariant stochastic differential equation. As a result, inference of the posterior distribution of the GP scales as 𝒪(n) and can be implemented recursively using a Kalman filter.

The challenge and opportunity of battery lifetime prediction from field data

“…A challenge with these approaches is that careful tuning is required to achieve robust performance. To address this, Aitio and Howey [82] show that applying Gaussian process regression to identify functional dependencies of model parameters can give smoother and more dependable results when using drive cycle data. Equivalent circuit models are popular since they are easy to implement and parametrize, although recent work has shown that similar computational efficiency can be achieved with models based on porous-electrode theory [83][84][85].…”

“…For example, Zhang et al [61] use an equivalent circuit model to infer capacity from non-constant current data, then use this to parametrize a capacity fade curve. Aitio and Howey [82] use a Gaussian process to accurately infer the SOC dependency of resistance from synthetic drive-cycle data.…”

Free Radicals: Making a Case for Battery Modeling

“…Integrating physics-based models with recently developed machine learning tools enables some exciting opportunities to improve performance whilst maintaining transparency. Data-driven approaches offer flexible techniques for fitting functions, and the integration of this with physics models 41,42 presents a new frontier that could enable approaches that are more accurate, generalizable, and interpretable.…”

Hybrid physics-based and data-driven modeling with calibrated uncertainty for lithium-ion battery degradation diagnosis and prognosis

“…An ECM uses an electrical circuit with components of resistors, capacitors, inductors, and voltage sources to mimic the electrical response of a cell to external loads, without explicitly modeling the underlying reactions and mass transport. Due to their simplicity and low computational requirements, ECMs are widely adopted for real-time SOH estimation in battery management systems [5,11]. Since all the underlying complicated physics and electrochemistry are lumped into a simple circuit, an ECM's fidelity can dramatically drop in less normal operating conditions such as fast charging, which are exactly the scenarios that cause significant degradation.…”