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Johns Hopkins University
The spreading of a released pollutant in a turbulent environment has severe consequences. The ability to identify the unknown source location from remote sensor data is greatly obfuscated by turbulence. This work discusses effective scalar-source localization algorithms in a turbulent channel by exploiting adjoint and ensemble methods, and by utilizing the growing power of high-fidelity simulations. To reconstruct the spatial distribution of the source, a cost functional is defined based on the difference between the true sensor observations and their model predictions. Forward-adjoint simulations provide the gradient of the cost functional to the source distribution, and the source estimation is iteratively updated. When a single sensor is directly downstream, the reconstruction is accurate in the cross-stream directions but elongated in streamwise direction. Using more sensors improves the performance demonstrably. We therefore seek the optimal sensor placement that improves the prediction in streamwise direction, by minimizing the condition number of the Hessian matrix of the cost functional. An iterative approach is adopted that gradually adjusts the sensor(s) while tracking the principal subspace of the Hessian. For a single sensor, the optimal location is near the edge of the scalar plume. This placement distinguishes signals for adjacent sources much more than sensor directly downstream. For fast identification of the source location and intensity, an eigen-ensemble-variational algorithm is formulated, which relies on the left and right singular vectors, or eigen-sources and eigen-measurements of the scalar impulse-response system. The projection of the true source onto an eigen-source is proportional to the projection of the sensor signal onto the corresponding eigen-measurement. The unknown source is identified by minimizing its deviation from this proportionality. We demonstrate effective ways to use an ensemble of trial sources to estimate the pre-requisite eigen-sources and accurately predict the source location. Furthermore, the effect of sensor noise can be evaluated when Gaussian noise is added to the measurement. All together, the developed algorithms provide effective strategies for reconstruction of unknown scalar sources and optimization of sensor networks. The resulting data provide an important benchmark for future research on olfactory search strategies in fully turbulent environments.
Scalar source, inverse problem