# Improved Electrochemical-Mechanical Parameter Estimation Technique for Lithium-Ion Battery Models
## 1 Introduction  
Lithium-ion batteries (LIBs) have become the dominant energy storage technology for various applications, ranging from consumer electronics to grid storage and electric vehicles [1, 2]. Accurate modeling of LIBs is essential for predicting performance, optimizing efficiency, and ensuring safe operation. Battery models can be broadly categorized into empirical, equivalent circuit models (ECMs) [3, 4] and physics-based models [5]. The latter offers a more comprehensive representation of the multiphysics processes occurring in batteries; however, this increased accuracy comes at the cost of higher computational complexity due to the coupling of Partial Differential Equations (PDEs). Among physics-based models, the Doyle-Fuller-Newman (DFN) model [6] stands out as the most prominentdue to its ability to accurately describe lithium-ion transport, charge transfer, and electrochemical reactions within the battery. It serves as a fundamental reference for advanced battery simulations and optimization studies, making it a cornerstone in battery modeling research. However, this requires the precise estimation of electrochemical and mechanical parameters, which influence battery behavior under operating conditions. When it comes to battery modeling, it is important to distinguish between the manufacturer's perspective and the end user or system integrator's perspective. Manufacturers typically have access to comprehensive internal data, including detailed material properties, geometric specifications, and electrochemical parameters obtained through dedicated design, optimization, and characterization campaigns. In contrast, end users--such as developers of battery management systems or integrators of battery packs--often have limited access to such internal information. Therefore, parameter identification plays a crucial role in battery modeling, ensuring that simulation results align with actual behavior. Some parameters can be directly measured using experimental setups [7; 8], while others are more challenging or expensive to determine, requiring estimation methods. Many studies performed battery parameter estimation through voltage curve fitting [9; 10; 11], where experimental discharge and charge curves are matched to simulated ones. This method is widely used due to its simplicity and effectiveness in capturing electrochemical characteristics. The drawback is the reduced accuracy when dealing with a large number of parameters that are not strictly sensitive to the voltage profile--called \"voltage-insensitive\" after a dedicated sensitivity analysis [12]. Other works leverage the multi-objective approach in order to capture a larger number of sensitive parameters. COBRAPRO [13] is a MATLAB-based open-source toolbox with an integrated parameter estimation routine for physics-based battery models. It minimizes a multi-objective cost function considering the voltage profile and SOC depending on the concentration of lithium ions in the electrodes. PyBOP [14] is a Python library designed to work with PyBaMM, offering a flexible framework for parameter estimation. It uses both gradient-based and free derivative optimization methods to fit model parameters to experimental data, supporting custom objective functions. [PERSON] et al. [15] proposed a coupled electro-thermal model using Genetic Algorithms (GAs) and minimizing the multi-objective function through Pareto fronts. Recently, significant focus has been placed on the mechanical response of LIBs during operation, leading to the development of various techniques to measure and model the reversible battery deformation induced by the electrochemical processes [16; 17; 18; 19; 20]. However, existing parameter estimation methods largely overlook this mechanical behavior. In this study, the effect of the mechanical measurements of the reversible battery deformation on parameter estimation is deeply investigated through an optimization model developed in COMSOL Multiphysics.