Measure This, Not That: Optimizing the Cost and Model-Based Information Content of Measurements

TL;DR

The paper tackles how to optimally select measurements under budget constraints in model-based design of experiments (MBDoE). It introduces a convex MINLP that maximizes information content, computing the D-optimality objective and its gradient via a SciPy-based ExternalGreyBoxModel integrated into Pyomo, and demonstrates scalability on two large-scale case studies: nonlinear reaction kinetics and a rotary-packed bed CO$_2$ capture system. The results reveal meaningful Pareto fronts between A- and D-optimality and budget, show that A- and D-optimality often choose different sensors, and highlight that relaxed solutions are not always tight, underscoring the value of solving the integer problem. The work advances automated, budget-aware measurement selection for predictive digital twins and sensor-network design, with practical implications for experimental planning and data-driven model validation.

Abstract

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) problem to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, \texttt{SciPy}, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO$_2$ capture. Both case studies show how examining the Pareto-optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

Figures (11)

• Figure 1: Sequential MBDoE workflow extended from franceschini2008model, wang2022pyomo, and references therein to consider measurement optimization. The workflow and numbered arrows are described in the text.
• Figure 2: Time-varying profiles for the concentration of component A (blue line), B (green dash line), C (red dash line).
• Figure 3: Pareto-optimal trade-off between measurement budgets versus (a) A-optimality (trace of FIM) and (b) D-optimality (determinant of FIM) for the kinetics case study considering four optimization strategies: maximizing A-optimality of the MILP problem (red stars), its relaxed LP problem (blue line); maximizing D-optimality of the MINLP problem (green crosses), and its relaxed NLP problem (purple line). In (a), the blue line is an upper bound for the red stars, while in (b) the purple line is an upper bound for the green crosses.
• Figure 4: Computational results for the kinetic case study at different budgets. (a) the number of CyIpopt iterations of D-optimality NLPs, (b) the number of MindtPy iterations of the D-optimality MINLPs, and (c) the computational time for all four optimization strategies. The optimization problems are solved from the lowest budget to the highest budget.
• Figure 5: Rotary bed adsorption-desorption system and the measurements considered for the MO problem. All 14 measurements are indexed by time (not shown). Measurements labeled with numbers (19, 23, 28) correspond to scaled positions on the column.