Lumped Parameter Thermal Network for Automotive Components: Modeling, Simulation, System Identification, and Parameter Estimation

This research paper proposes a framework based on lumped parameter thermal networks (LPTN) to understand the system behavior of thermally stressed component spaces in automotive vehicles. LPTNs offer an energy-based, low-degree-of-freedom model that can represent arbitrary thermal systems inside automotive vehicles. The time response of these low-order models can be calculated using standard ordinary differential equation solvers. The paper showcases the modeling of LPTNs and the calculation of their time response by using an electronic control unit (ECU) of a BMW 7 series. The use of LPTNs instead of exponential functions reduced the MAE in this example by 60.5%. Furthermore, a system identification approach for experimental temperature curves has been developed and implemented. System identification aims to mathematically model system behavior and predict system output. This paper compares least-square estimation (LSE) with constrained minimization (CM), where CM has a higher MAE by 5.3% but remains physically feasible. Additionally, this work proposes a physical parameter estimation framework. The parameter estimation problem is formulated as a minimization problem leveraging a state space representation of the LPTN. The estimation of parameters becomes physically interpretable through the introduction of boundary conditions for identifiable parameters. The framework to solve the minimization is based on sequential least-square quadratic programming and is implemented using the SciPy toolbox. The prediction of an unseen cooling use case by an LPTN with physically estimated parameters displays a MAE of 1.95 K. Measures to tackle the ill-posed character of parameter estimation are proposed. Finally, this paper discusses the use of neural networks in this context.