Sensor configuration optimization based on the entropy of adjoint concentration distribution for stochastic source term estimation in urban environment

Abstract

Sensor monitoring is foundational to source term estimation (STE). Recently, stochastic STE methods based mainly on Bayesian inference have been attracting attention. However, few studies have developed sensor configuration optimization (SCO) methods aiming to ensure good STE performance in the monitoring area, such that the posterior probability could aggregate around the truths while addressing most sources. This research proposes a deployment method by designing an objective function and applying a simulated annealing (SA) algorithm. The objective function is set as the information joint entropy of the adjoint concentration. The performance of the proposed method was assessed by Bayesian inference STE for 25 unknown sources based on the obtained optimal configuration in a regular block-arrayed building group model. The STE results were compared with those of uniform and random configurations. According to the results, because the optimal configuration can provide the most informative measurements, it yields the best estimations. If we quantize the STE errors and take the average for all unknown sources, the location and strength estimation errors of the optimal configuration significantly decrease by approximately 45% and 99%, respectively, when compared with the random configuration and 39% and 96%, respectively, when compared with the uniform configuration.