Numerical Solutions for Optimal Control Problems Under SPDE Constraints
Final technical rept.
FLORIDA AGRICULTURAL AND MECHANICAL UNIV TALLAHASSEE
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The primary source of aircraft noise is the fan noise from the engines natural approaches to reducing this noise involve acoustic shape optimization of the inlet and impedance optimization of the liner. This project will use optimal control to systematically determine the inlet shape and the linear material impedance factor that minimize the fan noise. A novel feature of this approach is that we automatically incorporate uncertainty and data measurement errors. Specifically we assume that the acoustic wave number is a random variablefield instead of a constant. This means that the computed answers are valid, not merely for a single configuration, but for a wide range. Our numerical results show significant noise reduction with the optimal impedance factor. Since the wave number is random, the underlying partial differential equation-Helmholtz equation in our case, is a stochastic partial differential equation. In this project, we have constructed efficient Monte Carlo methods as well as stochastic finite element methods to solve stochastic partial differential equations. Rigorous error estimates are obtained and numerical simulations are conducted to support the error analysis.
- Statistics and Probability