Parameter Estimation Using Extended Kalman Filter and Ultrasonic Pulse Time of Flight to Locate Transient, Concentrated Heating Sources

Abstract

The objective of this dissertation is to estimate the location and characteristics of concentrated heating sources on a surface. The heating sources are transient as they may be moving and varying temporally in magnitude. This work is applicable to numerous industries including manufacturing and aerospace. Of particular interest is estimating the transition region for hypersonic vehicles (Mach 5+) where a change in body-surface temperature has been measured at the transition between laminar and turbulent flow. The system analyzed could be employed with ultrasonic transducers mounted on the inside of the aeroshell, measuring the time of flight for ultrasonic pulses transmitted from one transducer to another, a correlation between temperature changes in the aeroshell and ultrasonic pulse time of flight based on the temperature dependence of sound, a 3D model to estimate the expected temperature response, and an inversion method using the extended Kalman filter to estimate the boundary layer transition region location. Unlike other temperature measurement devices, mounting the ultrasonic sensors on the inside of the aeroshell, away from the boundary of interest, does not disturb the phenomenon that is being measured. This dissertation and the underlying research and published works contribute to science in five areas: 1) by successfully employing the extended Kalman filter for a transient heat transfer problem, 2) by incorporating a 3D thermal model into the inverse method, 3) by exploring the sensitivity of ultrasound sensors to heating source location, boundary conditions, and thermal conductivity, 4) by addressing uncertainty through modifications to the extended Kalman filter to achieve more robust performance, and 5) by detailing an innovative measurement model that produces a closed-form Jacobian. The solution is able to track a moving source and the adaptive extended Kalman filter converges to the correct location faster than the extended Kalman filter. Convergence results for the ellipse model are unsatisfactory, however, the model's efficiency and low wall-times warrant further study.