TUOMAS AIRAKSINEN
Department of Mathematical Information Technology, University of Jyväskylä, P. O. Box 35 (Agora), FI-40014 University of Jyväskylä, Finland
ERKKI HEIKKOLA
Numerola Oy, P. O. Box 126, FI-40101 Jyväskylä, Finland
JARI TOIVANEN
Institute for Computational and Mathematical Engineering, Durand Building, Stanford University, Stanford, CA 94305, USA

Received 13 May 2010
Accepted 23 November 2010

A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the finite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pressure field in the silent region are given by the solution of a quadratic optimization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a model problem, a significant noise reduction is demonstrated at lower frequencies.

Local sound control; stochastic domain; Helmholtz equation; finite element method; passenger car; quadratic optimization