Mathematical models are increasingly used in pharmaceutical process development within quality-by-design (QbD) frameworks to reduce experimental effort and enable rational process design. However, model validation is still often based on deterministic performance indicators, which do not explicitly account for experimental variability, measurement noise, and model uncertainty. This work proposes an uncertainty-aware framework for model validation in pharmaceutical processes that quantifies predictive reliability in probabilistic terms, consistent with regulatory concepts. The framework explicitly integrates uncertainty in operating conditions, measurements, and model parameters, and evaluates model performance based on the probability that prediction satisfy predefined acceptance criteria rather than on single-point accuracy indicators. An in-silico case study of crystallization was performed to demonstrate the approach, where synthetic experimental data with controlled uncertainty wer... [more]

Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so they can be rescaled. A further singular value decomposition can be performed to identify degenerate sets of equations and remaining scaling issues. This work presents an EO model of a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. The IDAES diagnostics tools were successfully applied to this flowsheet to identify problems to im... [more]

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power−voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg−Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss−Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed b... [more]