Optimal Sensor Allocation with Multiple Linear Dispersion Processes

2024-01-19

AI Summary

This paper addresses the multi-source emission rate estimation problem in two-dimensional space, where source locations are known but the number of sensors is significantly smaller than the number of potential emitters, under uncertain wind fields. Method: We formulate a linear atmospheric dispersion forward model accounting for wind uncertainty and, for the first time, tightly integrate multi-source linear inversion with bilevel optimization. We propose a stochastic gradient-based bilevel approximation algorithm with theoretical convergence guarantees, combining sample average approximation (SAA) and inverse problem solving to overcome limitations of deterministic or single-wind-direction assumptions. Contribution/Results: Theoretical analysis establishes rigorous convergence properties. Numerical experiments demonstrate that our method reduces mean squared error by 37% on average compared to baseline approaches, significantly enhancing robustness and accuracy of emission source reconstruction under diverse wind conditions.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Optimal sensor placement for estimating multiple emission sources
• Solving bilevel optimization with limited sensors versus sources
• Minimizing estimation error across varying wind conditions

Innovation

• Bilevel optimization for sensor allocation
• Sample Average Approximation algorithm
• Stochastic Gradient Descent approximation