Bayesian Analysis of Interpretable Aging across Thousands of Lithium-ion Battery Cycles

TL;DR

This work tackles aging diagnosis in lithium-ion batteries by performing a nonlinear Bayesian identifiability analysis of the Doyle-Fuller-Newman (DFN) model across 95 NCA/LiC$_6$–SiO$_x$ cells from Tesla Model 3. Using Markov chain Monte Carlo (MCMC) on discharge data at C/5, 1C, and 2C across 7776 diagnostic cycles, the authors estimate the four key parameters $D_{s,n}$, $D_{s,p}$, $k_n$, and $k_p$ and map their trajectories to state of health (SOH). They find that anode diffusion ($D_{s,n}$) is identifiable throughout life, while cathode diffusion ($D_{s,p}$) and the anode rate constant ($k_n$) become identifiable only after substantial aging; the cathode rate constant ($k_p$) remains unidentifiable. The parameter evolution is linked to aging via power-law relationships, enabling SOH-based aging predictions, though the authors note missing physics and suggest extensions (e.g., Hybrid MPET, CIET) to improve identifiability and predictive capability. Overall, the study demonstrates how parameter identifiability insights can enhance aging diagnostics and motivate higher-fidelity modeling for lithium-ion batteries. The approach provides a framework for tracking physically meaningful degradation pathways and predicting future cell behavior from parameter trajectories, with potential applicability to other chemistries and datasets. $D_{s,i}$, $k_i$, and SOH are central to these insights.$

Abstract

The Doyle-Fuller-Newman (DFN) model is a common mechanistic model for lithium-ion batteries. The reaction rate constant and diffusivity within the DFN model are key parameters that directly affect the movement of lithium ions, thereby offering explanations for cell aging. This work investigates the ability to uniquely estimate each electrode's diffusion coefficients and reaction rate constants of 95 Tesla Model 3 cells with a nickel cobalt aluminum oxide (NCA) cathode and silicon oxide--graphite (LiC$_\text{6}$--SiO$_{\text{x}}$) anode. The parameters are estimated at intermittent diagnostic cycles over the lifetime of each cell. The four parameters are estimated using Markov chain Monte Carlo (MCMC) for uncertainty quantification (UQ) for a total of 7776 cycles at discharge C-rates of C/5, 1C, and 2C. While one or more anode parameters are uniquely identifiable over every cell's lifetime, cathode parameters become identifiable at mid- to end-of-life, indicating measurable resistive growth in the cathode. The contribution of key parameters to the state of health (SOH) is expressed as a power law. This model for SOH shows a high consistency with the MCMC results performed over the overall lifespan of each cell. Our approach suggests that effective diagnosis of aging can be achieved by predicting the trajectories of the parameters contributing to cell aging. As such, extending our analysis with more physically accurate models building on DFN may lead to more identifiable parameters and further improved aging predictions.

Figures (7)

• Figure 1: Schematic of the DFN model for an NCA/LiC$_6$--SiO$_{\text{x}}$ cell during discharge. The solid diffusion coefficients and reaction rate constants are listed under the sections whose physics they principally affect.
• Figure 2: (a) Generation of high-fidelity battery models through parameterization and comparison with real experiments and (b) comparison of cycling behavior of an aged cell and pristine cell.
• Figure 3: MCMC sampling of the 2-dimensional confidence region: (a) 500 samples, (b) 2000 samples, (c) 5000 samples.
• Figure 4: Estimation of the posterior distribution by sampling the parameter space. After a few hundred iterations, the approximate posterior distributions resemble the true distributions with some noise. The true PDF was estimated by sampling the confidence region for 1,000,000 iterations: $k_{p}$ through (a) 500 samples, (b) 2000 samples, (c) 5000 samples, and $D_{s,p}$ through (d) 500 samples, (e) 2000 samples, (f) 5000 samples.
• Figure 5: Changing identifiability trends as the cell degrades. For a pristine cell, only $D_{s,n}$ is identifiable. At end-of-life, $D_{s,n}$, $D_{s,p}$, and $k_n$ become identifiable while $k_p$ remains unidentifiable.