Optimal Sensor Allocation with Multiple Linear Dispersion Processes

TL;DR

This paper develops a bilevel optimization framework for optimal sensor placement to estimate emission rates of multiple sources under varying wind conditions, using linear dispersion models and advanced algorithms.

Contribution

It introduces a novel bilevel optimization approach with convergence guarantees for sensor allocation in emission estimation problems.

Findings

Effective algorithms for sensor placement are proposed.

Numerical examples demonstrate the approach's performance.

Convergence guarantees are established for the algorithms.

Abstract

This paper considers the optimal sensor allocation for estimating the emission rates of multiple sources in a two-dimensional spatial domain. Locations of potential emission sources are known (e.g., factory stacks), and the number of sources is much greater than the number of sensors that can be deployed, giving rise to the optimal sensor allocation problem. In particular, we consider linear dispersion forward models, and the optimal sensor allocation is formulated as a bilevel optimization problem. The outer problem determines the optimal sensor locations by minimizing the overall Mean Squared Error of the estimated emission rates over various wind conditions, while the inner problem solves an inverse problem that estimates the emission rates. Two algorithms, including the repeated Sample Average Approximation and the Stochastic Gradient Descent based bilevel approximation, are investigated in solving the sensor allocation problem. Convergence analysis is performed to obtain the performance guarantee, and numerical examples are presented to illustrate the proposed approach.