Numerical Solutions for Optimal Control Problems Under SPDE Constraints

Abstract

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 variable/field 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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 05, 2006
Accession Number
ADA458787

Entities

People

  • Yanzhao Cao

Organizations

  • Florida A&M University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Complex Numbers
  • Differential Equations
  • Equations
  • Equations Of State
  • Helmholtz Equations
  • Impedance
  • Mathematics
  • Measurement
  • Monte Carlo Method
  • Noise
  • Numbers
  • Partial Differential Equations
  • Random Variables
  • Scientific Research
  • Uncertainty

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Aerospace Engineering
  • Computational Fluid Dynamics (CFD)