Sparse Sensor Allocation for Inverse Problems of Detecting Sparse Leaking Emission Sources

2025-09-05

AI Summary

This paper addresses the optimal sensor placement problem for sparse leakage source detection. We propose a bilevel optimization framework that jointly incorporates non-negativity constraints and parametric uncertainty in the forward model. At the upper level, sensor locations are optimized to minimize the integral mean squared error (IMSE) under wind field uncertainty; at the lower level, emission rates are estimated via non-Gaussian, non-negative Bayesian inversion. To enable scalable computation, we design a GPU-accelerated algorithm integrating repeated sample average approximation (rSAA) and stochastic gradient-based bilevel approximation (SBA). Experiments demonstrate that our method consistently achieves significantly lower IMSE across diverse initial sensor deployments, thereby enabling synergistic optimization of sensing configuration and source strength inference. The implementation is open-sourced and supports efficient large-scale computation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements

Abstract

This paper investigates the sparse optimal allocation of sensors for detecting sparse leaking emission sources. Because of the non-negativity of emission rates, uncertainty associated with parameters in the forward model, and sparsity of leaking emission sources, the classical linear Gaussian Bayesian inversion setup is limited and no closed-form solutions are available. By incorporating the non-negativity constraints on emission rates, relaxing the Gaussian distributional assumption, and considering the parameter uncertainties associated with the forward model, this paper provides comprehensive investigations, technical details, in-depth discussions and implementation of the optimal sensor allocation problem leveraging a bilevel optimization framework. The upper-level problem determines the optimal sensor locations by minimizing the Integrated Mean Squared Error (IMSE) of the estimated emission rates over uncertain wind conditions, while the lower-level problem solves an inverse problem that estimates the emission rates. Two algorithms, including the repeated Sample Average Approximation (rSAA) and the Stochastic Gradient Descent based bilevel approximation (SBA), are thoroughly investigated. It is shown that the proposed approach can further reduce the IMSE of the estimated emission rates starting from various initial sensor deployment generated by existing approaches. Convergence analysis is performed to obtain the performance guarantee, and numerical investigations show that the proposed approach can allocate sensors according to the parameters and output of the forward model. Computationally efficient code with GPU acceleration is available on GitHub so that the approach readily applicable.

Problem

• Optimizing sensor placement for detecting sparse emission sources
• Addressing non-negativity and uncertainty in emission rate estimation
• Minimizing estimation error through bilevel optimization framework

Innovation

• Bilevel optimization for sensor allocation
• Non-Gaussian sparse source inversion
• GPU-accelerated computational efficiency