Figure 3 - uploaded by Tuomas Antero Airaksinen

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# In the left gure, the noise source and planar antinoise sources are marked and labeled. In the right gure, there are point antinoise sources; only left side actuators are marked and labeled. The corresponding actuators on the right side are dened symmetrically on the right side of the cabin.

Source publication

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 nite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pr...

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## Citations

... This is a non-intrusive approach which allows using a solution method for non-stochastic problems without any modification. In [37], this approach was used to develop a method to study the performance of a local noise control that is optimal in a stochastic domain and in [31], the method was further used to find optimal secondary source locations for such local ANC system. However, the method could be used only for performance assessment purposes. ...

... In this paper, we propose a novel ANC method for enclosed cavities. The method is based on [37], but the optimization of secondary source signals is now reformulated such that an arbitrary number of reference microphones is used to adapt optimal ANC to prevailing acoustic field. This means that the system remains optimal even if changes in phase and amplitude of the noise occur. ...

... Especially posture and head position affect the sound pressure that is experienced in ears and these parameters lead to the stochasticity of the computation domain. As in [37], the domain stochasticity variable r = (r 1 , r 2, r 3 ) ...

A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A least squares formulation leads to a quadratic optimization problem. The presented active noise control method gives robust and efficient noise attenuation, which is demonstrated by a numerical study in a passenger car cabin. The numerical results demonstrate that a significant, stable local noise attenuation of 20–32 dB can be obtained at lower frequencies (< 500 Hz) by two microphones, and 8–36 dB attenuation at frequencies up to 1000 Hz, when 8 microphones are used.

A local active noise control method that uses stochastic numerical acoustical modeling is introduced. The frequency domain acoustical simulations are performed by a sequence solutions to Helmholtz equations approximated by FEM. The proposed ANC method maps microphone measurements linearly to the output signals of antinoise actuators. The matrix defining the linear mapping is optimized for each frequency to minimize expected value of the noise. The paper concentrates on defining the quadratic least-squares optimization problem for the minimization of the sound pressure field in the silent region. The formulation leads to a robust and accurate noise control in stochastic domains that has a stochastic noise source. The method is demonstrated numerically by an experiment in a car cabin, and significant noise reduction is demonstrated at lower frequencies.

The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given.

A method to find optimal locations and properties of anti-noise actuators in a local noise control system is considered. The local noise control performance is approximated by an approach based on a finite element method, attempting to estimate the average performance of an optimal active noise control (ANC) system. Local noise control uses a fixed number of circular actuators that are located on the boundary of a three-dimensional enclosed acoustic space. Actuator signals are used to minimize the known harmonic noise at specified locations. The average noise reduction is maximized at two frequency ranges by adjusting the anti-noise actuator configuration, which is a non-linear multi-objective optimization problem. To solve the optimization problem, an unsorted population size evolutionary optimization algorithm (UPS-EMOA) is considered, and its performance is compared to the widely-known NSGA-II method. As a numerical example problem, the ANC in a passenger car cabin is considered. Significantly better noise control is obtained with the optimized actuator locations than only by a engineer’s sophisticated guess.

The paper provides an overview of the structural optimization system development. The basis and also the primary idea for algorithm formulation was the bone remodelling phenomenon leading to the optimization of the trabecular net within the bone. The idea was completed with theorems concerning the surface constant strain energy principle to form the biomimetic optimization system. The paper describes the key element of the optimization procedure: our own mesh generator called Cosmoprojector. It also presents the concept of Finite Element mesh parallel generation as well as Finite Element Analysis in a parallel environment as a recent enhancement of the presented method. Finally, it presents some results of computations obtained with the use of biomimetic structural optimization.