Constrained Bayesian optimization and spatio-temporal surveillance for sensor network design in the presence of measurement errors

ABSTRACT

The optimal placement of sensors is studied to construct a surveillance sensor network for a complicated stochastic system with random measurement errors. The problem is formulated as a joint problem of constrained black-box optimization for the fast detection of an anomaly event and spatio-temporal change-point detection for a low false alarm rate. An algorithm is proposed called Confidence-Set based Constrained Bayesian Optimization (CSCBO) that models performance measures as Gaussian Processes (GPs) and provides a flexible and easy-to-implement framework for handling noisy black-box constraints. As the decision variables of this problem are high-dimensional binary variables, the Wasserstein similarity metric is introduced as a distance measure among different solutions to capture the similarity among solutions properly. Finally, a newly proposed detection statistic for spatio-temporal surveillance is combined with CSCBO to identify the optimal sensor placement while controlling the false alarm rate. The combined procedure is applied to the Altamaha River.

KEYWORDS:

• Water quality monitoring
• sensor network
• Bayesian optimization
• spatio-temporal analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available in the Georgia River Network, the Summit to the Sea, and the Altamaha River Basin Management Plan, GA EPD, at https://garivers.org/altamaha-river/, http://coastgis.marsci.uga.edu/summit/altamaha.htm and https://epd.georgia.gov, reference number Altamaha River Basin Management Plan 2003, Georgia Department of Natural Resources Environmental Protection Division. These data were derived from the resources available in the public domain as listed above.

Additional information

Funding

The work reported herein was supported by the National Science Foundation [Grant CMMI-1538746].