Electro-chemical battery model validation

The VIRTUAL VEHICLE Research GmbH is Europe’s largest R&D center for virtual vehicle technology, the innovation catalyst for future vehicle technologies. Their focus is on the linking of numerical simulations and hardware testing, creating automated testing and validation procedures.


The fastly growing e-cars market excites the need for advanced methods for design and analysis specifically for this sector. VIRTUAL VEHICLE works on modelling the vehicle battery electric behavior, allowing improvements in the battery design. For the “Single-Particle” model (SPM), an optimal setting for the model’s 31 parameters was found in the previous research to obtain the best-known match with the measured data.

In this study, the goal was to enrich existing data with comprehensive statistical insights. In the initial stage, the problem was split into a series of iteratively created surrogates. First iterations were dedicated to searching for domain limits and identification of parameter ranges for a stable battery model. Then, the domain was restricted to the effect on statistical aspects of results from iteration to iteration.

Another part of the project investigated the close surroundings of the optimum used as the reference. The statistical analysis examined the robustness of the solution and gave the answers to whether or not some parameters may be omitted from the model. Also, it revealed there is still room for fine tuning of parameters to achieve the match between modelled and measured battery cycle.

Fig. 1. Electric vehicle battery (photo by Gereon Meyer CC BY-SA 4.0)


Coupling of the Uptimai tool with VIRTUAL VEHICLE’s FEMToolbox software for battery cycle simulation was easily done without the need of interfering with neither simulation nor UQ code. The already existing interface of the VIRTUAL VEHICLE’s software was modified to pass data to the Uptimai tool after post-processing of the simulation results. Uptimai algorithm used these outputs created for altering input parameters to build a surrogate model of the behaviour of the simulated battery cycle. Results presented here are for the model created for the close surroundings (20% of the complete input range) of the reference point.

The Uptimai algorithm was used to process simulation results into the metamodel of agreement between measured and computed battery-cell cycles. The level of agreement was defined as normalized Root Mean Square Error (RMSE), observed for each simulation. The metamodel consists of dependencies between input parameter changes and the simulation results, allowing a detailed description of the battery cycle.

Specific response to changes in particular input variables was observed using the Uptimai Increment plot. This feature allows treating each dependency separately but is also able to perform a cross-comparison of variables against each other. Fig. 2 depicts the total response to the three most influential variables. Note the peak in results caused by the cumulative effect of these variables close to their upper boundary. This combination of input parameter values should be avoided when seeking a better battery cycle model.

Fig. 2. Extremity localized on the increment function plot

The Uptimai Sensitivity Analysis confirmed the tight connection of variables through high-order interactions, which in sum create a considerable portion of the uncertainty of results. For the most influential variable ocv_Li(ci)_1, interactions are responsible for 2/3 of variance in results caused by this input variable. Although the surrogate model was much simpler than in the above-mentioned case of the iterative approach, mutual interactions of up to four variables had to be investigated.

Fig. 3. Sensitivity Analysis of the reduced domain

Also, another surrogate model was created for seven input variables indicated as statistically negligible in all previously done UQ analyses. It confirmed that even in this highly focused domain some variables, especially D_1, are not able to affect the results (see Fig. 3). As proven by the Uptimai Histogram Plots (Fig. 5), the cumulative response of all variables in the reduced domain is much lower than the effect of the most influential input. However, since the nominal point of the reduced domain was set to the so far known optimum, findings of this very precise surrogate were used to obtain an even better result. The new optimum increases the quality of the battery cycle model by more than 20%.

Fig. 4. Comparison of effects of the most influential variable of the full domain against all variables of the reduced domain


  • Definition of valid design space. The Uncertainty Quantification was able to explore and identify correct ranges for the input domain where the Single-Particle model always converges.
  • Suggestions for stable optimum – addressing ranges of input parameters responsible for better-than-average results allowed to improve the current optimum by 20%.
  • Deep statistical insights into the Single-Particle model behaviour with identification of the most influential input variables.