Data-driven calibration techniques for thermal models in battery systems rely on the systematic adjustment of model parameters to align simulation outputs with experimental measurements. The process involves parameter identification, error quantification, and iterative optimization to minimize discrepancies between predicted and observed thermal behavior. This approach enhances the accuracy of thermal models, which are critical for predicting battery performance, safety, and lifespan.

Thermal models for batteries typically include partial differential equations that describe heat generation, conduction, convection, and radiation. These models depend on several parameters, such as thermal conductivity, specific heat capacity, and heat transfer coefficients, which may not be precisely known a priori. Experimental datasets, collected under controlled conditions, provide the necessary ground truth for calibrating these parameters. The calibration process begins with the selection of key parameters that significantly influence thermal behavior. Sensitivity analysis helps identify which parameters have the most substantial impact on model outputs, allowing prioritization during calibration.

Parameter identification involves determining the values of unknown or uncertain parameters that best fit the experimental data. This is often framed as an inverse problem where the goal is to minimize the difference between simulated and measured temperatures. Common techniques include least squares regression, maximum likelihood estimation, and Bayesian inference. Least squares regression adjusts parameters to minimize the sum of squared residuals between model predictions and experimental data. Maximum likelihood estimation finds parameter values that maximize the probability of observing the experimental data given the model. Bayesian inference incorporates prior knowledge about parameters and updates their probability distributions based on new data.

Error minimization is achieved through optimization algorithms that iteratively adjust parameters to reduce the discrepancy between simulations and experiments. Gradient-based methods, such as the Levenberg-Marquardt algorithm, are widely used due to their efficiency in finding local minima. These methods require computing the gradient of the error function with respect to the parameters, which can be obtained numerically or through adjoint methods. When the error surface is non-convex or contains multiple local minima, global optimization techniques like genetic algorithms or particle swarm optimization may be employed. These methods explore a broader parameter space but are computationally more expensive.

Experimental datasets for calibration should cover a range of operating conditions, including different charge and discharge rates, ambient temperatures, and cooling scenarios. This ensures the calibrated model remains accurate across diverse scenarios. Data preprocessing is essential to remove noise and outliers, which can distort parameter estimates. Techniques like moving average filters or wavelet denoising are commonly applied to smooth temperature measurements without losing critical features.

Cross-validation is used to assess the generalizability of the calibrated model. The dataset is split into training and validation subsets, with the model calibrated on the training data and tested on the validation data. A well-calibrated model should perform comparably on both subsets, indicating robustness. If the model performs poorly on the validation data, it may be overfitted to the training data, necessitating adjustments like regularization or the inclusion of additional physics-based constraints.

Uncertainty quantification is another critical aspect of data-driven calibration. Even with optimized parameters, discrepancies between simulations and experiments may persist due to model simplifications or measurement errors. Techniques like Monte Carlo sampling or polynomial chaos expansion propagate parameter uncertainties through the model to estimate confidence intervals for predictions. This provides a more comprehensive understanding of model reliability and guides further refinements.

A practical example involves calibrating a lumped-parameter thermal model for a lithium-ion battery cell. The model may include heat generation terms based on joule heating and entropic effects, with parameters like internal resistance and entropy coefficient requiring calibration. Experimental data from thermocouples attached to the cell surface during cycling provides the reference temperatures. The calibration process adjusts the parameters until the simulated surface temperatures match the measurements within an acceptable tolerance.

Another example is calibrating a detailed three-dimensional thermal model for a battery pack. Here, parameters like thermal conductivity between cells and cooling plate heat transfer coefficients are tuned using infrared thermography data. The complexity of the model necessitates efficient optimization strategies, possibly leveraging parallel computing to handle the computational load.

Data-driven calibration is not a one-time process but should be repeated as new data becomes available or operating conditions change. Continuous monitoring and updating of the model ensure its accuracy over the battery's lifecycle. This is particularly important for applications like electric vehicles, where thermal management is crucial for safety and performance.

Challenges in data-driven calibration include the trade-off between model complexity and computational cost. Highly detailed models may provide better accuracy but require extensive data and computational resources for calibration. Simplified models are faster to calibrate but may lack predictive power in certain scenarios. The choice depends on the specific application and available resources.

Another challenge is the availability of high-quality experimental data. Inconsistent measurements, insufficient sensor coverage, or uncontrolled environmental conditions can hinder calibration efforts. Investing in precise instrumentation and controlled testing environments pays off in the form of more reliable models.

In summary, data-driven calibration of thermal models involves parameter identification and error minimization using experimental datasets. Sensitivity analysis guides parameter selection, while optimization algorithms adjust their values to align simulations with measurements. Cross-validation and uncertainty quantification ensure model robustness, and iterative updates maintain accuracy over time. This approach is essential for developing reliable thermal models that support battery design, operation, and safety across various applications. The techniques discussed here provide a foundation for achieving high-fidelity thermal predictions without relying on machine learning, focusing instead on physics-based models refined through empirical data.