Time-dependent global sensitivity analysis of the Doyle-Fuller-Newman model

Abstract

The Doyle-Fuller-Newman model is arguably the most ubiquitous electrochemical model in lithium-ion battery research. Since it is a highly nonlinear model, its input-output relations are still poorly understood. Researchers therefore often employ sensitivity analyses to elucidate relative parametric importance for certain use cases. However, some methods are ill-suited for the complexity of the model and appropriate methods often face the downside of only being applicable to scalar quantities of interest. We implement a novel framework for global sensitivity analysis of time-dependent model outputs and apply it to a drive cycle simulation. We conduct a full and a subgroup sensitivity analysis to resolve lowly sensitive parameters and explore the model error when unimportant parameters are set to arbitrary values. Our findings suggest that the method identifies insensitive parameters whose variations cause only small deviations in the voltage response of the model. By providing the methodology, we hope research questions related to parametric sensitivity for time-dependent quantities of interest, such as voltage responses, can be addressed more easily and adequately in simulative battery research and beyond.

Figures (13)

• Figure 1: The number of publications on Scopus mentioning "lithium-ion battery" and "sensitivity analysis" in either title, abstract, or keywords over the past years, indicating a clear upwards trend.
• Figure 2: Visualization of a parameter space spanned by the three parameters $\xi_1$, $\xi_2$, and $\xi_3$. The hypercross structure sampled by OAT methods and its enveloping hypersphere inhabit only a fraction of the entire volume. This fraction decreases very rapidly as the number of parameters increases saltelli_why_2019.
• Figure 3: A visual summary of the main differences between the PC method and the KL method.
• Figure 4: Schematic depiction of the DFN model during discharge.
• Figure 5: An overview of the parameter ranges covered in this study and in similar works by Zhang et al. zhang_parameter_2014, Li et al. li_parameter_2020, Liu et al. liu_simulation_2020, Gao et al. gao_global_2021, and Streb et al. streb_improving_2022. The parameter ranges obtained from the LiionDB agree well with most of the literature ranges, albeit with a tendency of being more extensive. However, some parameter intervals are smaller than their counterparts from literature. For $L_\text{neg}$, this can be explained by the availability of only two data points. The discrepancy between our value range for $c_{\text{l},0}$ and the interval of Liu et al. is relativized by the fact that various literature sources were utilized to construct the range. The obtained interval for $t^+$ extends into the negative numbers, which is not considered in any of the selected literature.