Grey-box modelling of lithium-ion batteries using neural ordinary differential equations

Abstract

Grey-box modelling combines physical and data-driven models to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling, as differential equations given by physical laws and neural networks can be combined in a single modelling framework. This simplifies the simulation and optimization and allows to consider irregularly-sampled data during training and evaluation of the model. We demonstrate this approach using two levels of model complexity; first, a simple parallel resistor-capacitor circuit; and second, an equivalent circuit model of a lithium-ion battery cell, where the change of the voltage drop over the resistor-capacitor circuit including its dependence on current and State-of-Charge is implemented as NODE. After training, both models show good agreement with analytical solutions respectively with experimental data.

Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model

“…In the present contribution, we continue our previous work [17] by further improving the GB model. For this purpose, we increased the amount of physical knowledge in the model.…”

“…[14] expanded the approach to solving differential equations with constraints. In our previous work [17], we showed how to consider external variables u(t) (here, the dynamic battery current as input variable) directly based on a simple application example. The differential equation according to Equation (2) is generalised:…”

“…Therefore, we have to provide a function describing the change in the external variables with time. We could for example interpolate the measured data [17]. Figure 1 As stated in Refs.…”

“…Figure 1 As stated in Refs. [14,17], NODEs can be used for GB modelling. The differential equations derived from physical insights in the system and NODEs can be combined in one equation system.…”

“…NODEs approximate the remaining deviation between the physical model and the experiment. In our previous work [17] an ECM serves as a basis for a GB model of a lithium-ion battery. NODEs model the voltage drop across the included resistor-capacitor (RC) circuit.…”