Sensor Placement Optimization.pdf

Sensor placement optimization for Gaussian processes with integral observations is crucial in various applications, including ultrasonic detection of fouling in closed pipes. The goal is to estimate an unknown spatial function based on a collection of observations that are integrals of that function along known paths.

Model-based and geometric strategies for sensor placement are extended to support integral observations. Model-based solutions evaluate the expected improvement of the function estimate for possible locations, while geometric approaches optimize for locations using line arrangements and fitness functions derived from the arrangement.

The behavior of various sensor placement strategies is empirically characterized for 2D geometries, including ultrasonic localization of fouling in closed metal pipes. Each receiver records multiple integrals corresponding to different helical paths along the surface, making sensor optimization an interesting problem.

Gaussian processes are specified by a prior mean function and a prior symmetric positive-definite kernel function, with hyperparameters determining the prior correlation structure. The predictive distribution for conjugate normal likelihood is obtained in closed form, allowing for predictions of the function at test points conditioned on observed data.

The use of integral observations with Gaussian processes enables the estimation of unknown functions based on linear operators, such as derivatives or integrals. This is particularly useful in applications where observations are collected by pairs of transmitting and receiving sensors, and the underlying function has a point-wise effect on some property of the propagating signal.

Optimizing sensor locations before any measurements are made is essential in typical scenarios that require engineering effort for setting up the sensing configuration. The techniques developed can be extended for active selection of additional sensors conditional on current measurements, allowing for more efficient and effective sensing configurations.