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Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.

Parameter sensitivity analysis of mechanistic battery models has the power to quantify the individual and joint effects of parameters on the performance of lithium-ion cells. This information can be beneficial for industrial cell designs, cell testing, and battery management system (BMS) configurations. The numerical quantification of these parameter sensitivities, however, is challenging in terms of computational costs and is an active field of research. In this paper, based on a 3D multiphysics model, we conduct a global sensitivity analysis for the utilizable cell discharge capacity and the maximum cell temperature at the discharge rate of 1C. The least angle regression version of the polynomial chaos expansion (PCE) concept has been identified as an optimal trade-off between approximation power and computational complexity. As a result, the sensitivities of all parameters in the 3D multiphysics model were studied using a hierarchical design and a stepwise design. We conclude that the cell discharge capacity and the thermal behavior at 1C discharge are most sensitive to the electrode parameters and their pore structure. The results reveal different dependencies and lead to new insights for cell design and operation.

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients.Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

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A model‐based uncertainty quantification (UQ) approach is applied to the manufacturing process of lithium‐ion batteries (LIB). Cell‐to‐cell deviations and the influence of sub‐cell level variations in the material and electrode properties of the cell performance are investigated experimentally and via modeling. The electrochemical battery model of the Doyle–Newman type is extended to cover the effect of sub‐cell deviation of product properties of the LIB. The applied model is parameterized and validated using a stacked pouch cell containing Li(Ni1/3Co1/3Mn1/3)O2 (NMC) and graphite (LixC6). It is integrated into a sampling‐based UQ framework. A nested point estimate method (PEM) is applied to a large number of independent normal distributed parameters. The simulations follow two consecutive nonideal manufacturing process steps: coating and calendering. The nested PEM provides a global sensitivity analysis that shows a change in sensitivity of the investigated parameters depending on the applied C‐rate. Furthermore, the sub‐cell level deviation of parameters in heterogeneous electrodes provokes a nonuniform current distribution in the cell. This alters the variance of the discharge capacity distribution. Therefore, sub‐cell deviation has to be considered to quantify process uncertainties. The applied method is feasible and highly efficient for this purpose.

Abstract:In this study, we show an effective data-driven identification of the State-of-Health of Lithium-ion batteries by Nonlinear Frequency Response Analysis. A degradation model based on support vector regression is derived from highly informative Nonlinear Frequency Response Analysis data sets. First, an ageing test of a Lithium-ion battery at 25 • C is presented and the impact of relevant ageing mechanisms on the nonlinear dynamics of the cells is analysed. A correlation measure is used to identify the most sensitive frequency range for ageing tests. Here, the mid-frequency range from 1 Hz to 100 Hz shows the strongest correlation to Lithium-ion battery degradation. The focus on the mid-frequency range leads to a dramatic reduction in measurement time of up to 92% compared to standard measurement protocols. Next, informative features are extracted and used to parametrise the support vector regression model for the State of Health degradation. The performance of the degradation model is validated with additional cells and validation data sets, respectively. We show that the degradation model accurately predicts the State of Health values. Validation data demonstrate the usefulness of the Nonlinear Frequency Response Analysis as an effective and fast State of Health identification method and as a versatile tool in the diagnosis of ageing of Lithium-ion batteries in general.

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