Automation of Strategic Data Prioritization in System Model Calibration: Sensor Placement

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by O(nlog(2)(n)) for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit's practical use.