Model Complexity Reduction in Bayesian Sensor Calibration and Its Relation to Principal Component Analysis
Year: 2025
Type: article
Abstract: Calibration is a costly, necessary part of sensor manufacturing. Bayesian sensor calibration leverages prior knowledge in the form of a sample of sensor response functions from a sensor ensemble such as a fabrication lot. Based on a response model withMparameters, it allows to infer the measurand of interest and its predictive uncertainty from output signals of specimens of the ensemble after their lean calibration with a small numberNof measurements, possibly with${N}\lt {M}$. This article answers the question of whether it is possible to reduce model complexity by choosing models with parameter number$\widetilde {\textit {M}}\lt {M}$, while guaranteeing a required predictive accuracy. Reduced models are obtained by projections of a high-dimensional model, termed full model, onto a subspace of its parameter space. An I-optimality-based loss function implementing the Bayesian calibration approach is derived. For givenNand$\widetilde {\textit {M}}$, it allows to find an optimal reduced model and, at the same time, the optimal experimental design of the calibration. The approach is applied to 48 specimens of a CMOS Hall sensor system cross-sensitive to temperature and mechanical stress. Starting from an 11-parameter full model, reduced models with$\widetilde {\textit {M}}={2},{4}$, and 5 are identified for calibration routines with${N}={2},{4}$, and 6 measurements, respectively. Despite the significantly smaller parameter numbers, the resulting root mean square (rms) predictive uncertainties of 102, 77.0, and 64.8$\mu $T, respectively, are increased by less than${1}\%$from the full-model values. A general conclusion is that model order reduction (MOR) in the present Bayesian framework invariably entails an uncertainty increase, similar to principal component analysis (PCA).
Source: IEEE Sensors Journal
Authors: Tim Samuel Winter, Oliver Paul
Institution: University of Freiburg
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $2,645
OpenAlex ID: W4408423434