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.

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.

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.

The Process Analytical Technology initiative and Quality by Design paradigm have led to changes in the guidelines and views of how to develop drug manufacturing processes. On this occasion the concept of the design space, which describes the impact of process parameters and material attributes on the attributes of the product, was introduced in the ICH Q8 guideline. The way the design space is defined and can be presented for regulatory approval seems to be left to the applicants, among who at least a consensus on how to characterize the design space seems to have evolved. The large majority of design spaces described in publications seem to follow a “static” statistical experimentation and modeling approach. Given that temporal deviations in the process parameters (i.e., moving within the design space) are of a dynamic nature, static approaches might not suffice for the consideration of the implications of variations in the values of the process parameters. In this paper, different forms of design space representations are discussed and the current consensus is challenged, which in turn, establishes the need for a dynamic representation and characterization of the design space. Subsequently, selected approaches for a dynamic representation, characterization and validation which are proposed in the literature are discussed, also showcasing the opportunity to integrate the activities of process characterization, process monitoring and process control strategy development.

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.