Narrow Results

This paper deals with a numerical investigation for the estimation of dynamic system's excitation sources using the independent component analysis (ICA). In fact, the ICA concept is an important technique of the blind source separation (BSS) method. In this case, only the dynamic responses of a given mechanical system are supposed to be known. Thus, the main difficulty of such problem resides in the existence of any information about the excitation forces. For this purpose, the ICA concept, which consists on optimizing a fourth-order statistical criterion, can be highlighted. Hence, a numerical procedure based on the signal sources independency in the ICA concept is developed. In this work, the analytical or the finite element (FE) dynamic responses are calculated and exploited in order to identify the excitation forces applied on discrete (mass-spring) and continuous (beam) systems. Then, estimated results obtained by the ICA concept are presented and compared to those achieved analytically or by the FE and the modal recombination methods. Since a good agreement is obtained, this approach can be used when the vibratory responses of a dynamic system are obtained through sensor's measurements.

Part I of this paper presents analytic solutions for reconstructing the excitation forces that act on the interior surfaces of a finite solid rectangular enclosure with the fluid loading effect taken into consideration, given vibroacoustic data in the exterior region. The reason for selecting a simple structure is to facilitate the reconstruction of excitation forces. To validate these analytic solutions, we apply the reciprocity principle and demonstrate that when the resultant excitation forces are used to excite the enclosure from the inside, the same vibroacoustic responses in the exterior region in exterior region can be obtained. To illustrate this point, we consider the case in which the top panel of a rectangular box is connected to the side walls through simply-supported boundary conditions, and the rest surfaces are rigid. The top surface of this box may be excited into vibrations by any type of excitation forces from the inside with the fluid loading effect taken into consideration. Note that for arbitrarily shaped structures under arbitrary boundary conditions, numerical solutions can be obtained. Therefore, it is possible to determine the excitation forces acting inside an enclosure based on the vibroacoustic information collected in the exterior. The knowledge of the excitation forces is critically important, because it can lead to optimal mitigation strategies to mitigate undesirable noise and vibrations.

Part II of this study presents numerical simulations of reconstructing the excitation forces acting on the interior surface of an enclosure, based on the vibroacoustic information collected in the exterior region. Various types of excitation forces such as distributed, line, and point forces are considered. Moreover, fluid loading inside the enclosure is considered in the numerical simulations. Analytical proofs show that fluid loading has no impact on excitation forces, but has significant impacts on structural vibrations. This is especially true when the density of fluid medium inside an enclosure is high. Results demonstrate that when excitation forces are continuous, the accuracy in reconstruction may be very high. When excitation forces contain abrupt changes or discontinuities, for example, line and point force, the accuracy in reconstruction may be significantly reduced. This is because many expansion terms are required to properly describe the discontinuities of excitations. On the other hand, discretization grids are fixed a priori. When fixed discretization grids are used together with an increasing number of expansion terms, aliasing may occur that may completely distort the reconstructed excitation forces.

Part II of this paper discusses experimental validations of the reconstructed excitation forces acting inside a vibrating structure with the fluid-loading effect taken into consideration. Specifically, the characteristics of the excitation forces such as their locations, types, amplitudes, and spectra are reconstructed by using the modified Helmholtz Equation Least Squares (HELS) method, based on a single set of measurements of the normal surface velocity on the exterior surfaces, as if one could see through such a solid structure. Since the fluid-loading effect has a direct impact on the vibration responses of a structure, it is not possible to derive analytic solutions to vibration responses of the structure. Therefore, numerical solutions are sought by using the boundary element method (BEM). The fluid-loading effect, a.k.a., the reverberation sound field inside the structure is calculated based on the absorption coefficients and surface areas of the interior objects. The reconstructed excitation forces are then compared to the benchmark values and satisfactory agreements are obtained.