Optimization of a Moving Sensor Trajectory for Observing a Point Scalar Source in Turbulent Flow

TL;DR

This paper develops an optimization strategy for sensor trajectories to improve the estimation of a scalar source in turbulent flow, using adjoint sensitivity analysis and a novel cost functional.

Contribution

It introduces a new trajectory optimization method leveraging adjoint scalar fields and a parameter-free cost functional for better source estimation in turbulent flows.

Findings

Optimized sensor trajectories significantly improve source estimation accuracy.

The sensitivity ratio serves as an effective diagnostic for performance evaluation.

A new cost functional predicts scalar source time dependence without adjustable parameters.

Abstract

We propose a strategy for optimizing a sensor trajectory in order to estimate the time dependence of a localized scalar source in turbulent channel flow. The approach leverages the view of the adjoint scalar field as the sensitivity of measurement to a possible source. A cost functional is constructed so that the optimal sensor trajectory maintains a high sensitivity and low temporal variation in the measured signal, for a given source location. This naturally leads to the adjoint-of-adjoint equation based on which the sensor trajectory is iteratively optimized. It is shown that the estimation performance based on the measurement obtained by a sensor moving along the optimal trajectory is drastically improved from that achieved with a stationary sensor. It is also shown that the ratio of the fluctuation and the mean of the sensitivity for a given sensor trajectory can be used as a diagnostic tool to evaluate the resultant performance. Based on this finding, we propose a new cost functional which only includes the ratio without any adjustable parameters, and demonstrate its effectiveness in predicting the time dependence of scalar release from the source.