High heat flux point source sensitivity and localization analysis for an ultrasonic sensor array

State estimation procedures using the extended Kalman filter are investigated for a transient heat transfer problem in which a high heat flux point source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. This work is an integral part of an effort to develop a system capable of locating the boundary layer transition region on a hypersonic vehicle aeroshell. Results from thermal conduction experiments involving one-way ultrasonic pulse time of flight measurements are presented. Uncertainties in the experiments and sensitivity to heating source location are discussed. One key finding is that sensitivity to heating source location is greater in the direction normal to the ultrasonic pulse propagation path. Scaled sensitivities to boundary conditions and thermal conductivity are presented and analyzed for all possible source locations using a square sensor grid. While sensitivity to the primary heat flux was determined to be the highest, sensitivity to the other parameters is either on the same order of magnitude or one order of magnitude less. Two different measurement models are compared for heating source localization: (1) directly using the one-way ultrasonic pulse time of flight as the measurement vector and (2) indirectly obtaining distance from the one-way ultrasonic pulse time of flight and then using these obtained distances as the measurement vector in the extended Kalman filter. Heating source localization results and convergence behavior are compared for the two measurement models. Two areas of sensitivity analyses are presented: (1) heat source location relative to sensor array position, and (2) sensor noise. The direct measurement model produced the best results when considering accuracy of converged solution, ability to converge to the correct solution given different initial guesses, and smoothness of convergence behavior.