The Helmholtz equation least squares (HELS)-based nearfield acoustical holography (NAH) is utilized to analyze panel acoustic contributions toward the acoustic field inside the interior region of an automobile. Specifically, the acoustic power flows from individual panels are reconstructed, and relative contributions to sound pressure level and spectrum at any point of interest are calculated. Results demonstrate that by correlating the acoustic power flows from individual panels to the field acoustic pressure, one can correctly locate the panel allowing the most acoustic energy transmission into the vehicle interior. The panel on which the surface acoustic pressure amplitude is the highest should not be used as indicative of the panel responsible for the sound field in the vehicle passenger compartment. Another significant advantage of this HELS-based NAH is that measurements of the input data only need to be taken once by using a conformal array of microphones in the near field, and ranking of panel acoustic contributions to any field point can be readily performed. The transfer functions between individual panels of any vibrating structure to the acoustic pressure anywhere in space are calculated not measured, thus significantly reducing the time and effort involved in panel acoustic contributions analyses.

This paper describes how brake squeal has always been a top customer satisfaction and quality control issue for the auto industry because of its extremely unpleasant, high-pitch/high-intensity sound. Over the past decade, hundreds of millions of dollars have been spent on vehicle repairs because of brake squeals. The analysis of brake squeal is extremely difficult because of its unpredictability and irregularity. Even under well-controlled laboratory conditions, brake squeal may not be reproducible and when it does, squeal lasts for a fraction of a second. Currently, analysis of brake squeal is carried out using a scanning laser to measure the out-of-plane and in-plane vibration modes, and operational deflection shape during squeal. In laser diagnostics, it is critical to synchronize scanning with an onset of brake squeal so as to correctly identify the vibration modes. Since brake squeal is unpredictable, it occurs in a twinkling of an eye, and it cannot be repeated for more than a few minutes, a complete scanning over the entire disk brake assembly surface normally can be very time consuming. Apparently, such an approach is not in keeping with the demand on cost-effective NVH diagnostics and abatement.

Automobile brake squeals have always been a major problem for the auto industry because of the high pitch and intensity level. Currently, the vehicle brake squeal diagnostics is carried out by using a scanning laser synchronized with squeals. If squeals occur at multiple frequencies, then filtering must be used so that the scanned out-of-plane vibration corresponds to a single frequency. This process is very time consuming, especially when squeals contain multiple frequencies. Moreover, the results thus obtained are valid at measurement locations only. In this paper, we use Helmholtz equation least-squares (HELS)-based near-field acoustical holography to reconstruct squeal sounds via a custom-designed 48-microphone array conformal to the shape of a brake assembly. This microphone array allows for taking a snapshot of 3D acoustic image on the surface of the brake assembly and produces 3D mappings of all acoustic quantities. In particular, we can identify the out-of-plane vibration modes that are responsible for squeals and reveal the locations where squeals originate from. There is no need for synchronization and filtering. The whole measurement can be done in seconds, and the reconstructed results are valid not only on source surface, but also in the field. [Work supported by NSF.]

This paper describes how nearfield acoustical holography (NAH) allows for reconstructing acoustic quantities such as the acoustic pressure, intensity, and power radiated from a finite object into 3D space based on the acoustic pressures measured on 2D surface. Since NAH provides complete acoustic information cost effectively, it has drawn a great deal of attention in the diagnostics of noise and vibration sources. Three major NAH methods are reviewed and their advantages and disadvantages are compared. While planar NAH is easy to implement, its applications are limited to planar surfaces in a free field only. The Inverse Boundary Element Method (IBEM) is suitable for an arbitrary source surface, but it is difficult to implement due to its strict requirements and intensive computations. The Helmholtz Equation Least Squares (HELS) provides a compromise in reconstruction of acoustic radiation from an arbitrary object by providing an approximate solution using the fewest measurements. Moreover, it is easy to implement, offers great flexibility in measurements and reconstruction, and is very fast. As such, it enables one to obtain a satisfactory reconstruction in the most cost-effective manner.

In most engineering applications, the acoustic fields are usually generated by multiple incoherent sources. When such acoustic fields are sampled and taken as input data to the Helmholtz equation least-squares (HELS) formulations directly, the reconstruction might not be accurate. Hence there is a need to discriminate the contributions from individual sources and separate the composite sound field into a set of spatially coherent subfields that are also mutually incoherent. In this paper, we apply the principal component decomposition technique to the HELS method to reconstruct acoustic radiation from multiple incoherent sources in a free field. The key ingredients of this technique include a diagonalization by singular value decomposition (SVD) of the cross-spectral matrices generated by a number of reference microphones. Each diagonal term corresponds to a subfield that results from a so-called virtual sound source. Even though such virtual sources are not always representative of the actual sources, they are nonetheless incoherent and thus can be used as input to HELS. Experimental validations of this technique on reconstructing acoustic pressure and time-averaged normal acoustic intensity on the surfaces of multiple incoherent sources are presented. [Work supported by NSF.]

The Helmholtz Equation Least Squares (HELS) method [Wu and Yu, J. Acoust. Soc. Am. 104, 2054–2060 (1998); Wu, ibid. 107, 2511–2522 (2000)] are validated experimentally in both exterior and interior regions of a highly nonspherical structure. This is contrary to the common belief that expansion solutions based on spherical coordinates are valid within the region bounded by spheres. Detailed explanations for this phenomenon, known as the Rayleigh hypothesis, are given in a separate paper. Shown here are the experimental validations of the acoustic fields reconstructed by the HELS method for a cabinet with overall dimensions 2.05 m ×1.05 m ×0.75 m. A loudspeaker is placed inside the cabinet. The white noise produced by the speaker is measured by an array of 48 microphones stationed outside. The acoustic pressures in the near- and far-fields are reconstructed and validated with respect to those measured at the same locations. Also reconstructed is the normal component of the time-averaged acoustic intensity, from which the transmission paths are identified. Such transmission paths cannot be revealed based on the acoustic pressure distribution alone because pressure is a scalar quantity. The interior acoustic pressures are reconstructed with the speaker placed outside and microphone array inside the cabinet. [Work supported by NSF.]

The objective of this study is to examine the effectiveness of the HELS method [S. F. Wu and J. Yu, J. Acoust. Am. 104, 2054–2060 (1998); S. F. Wu, ibid. 107, 2511–2522 (2000)] in visualizing the areas that are prone to noise transmission into a full-size vehicle passenger compartment due to engine, powertrain system, tires, and wind excitations. The input to the HELS formulation is the acoustic pressure measured inside the compartment. No vehicle geometry and dimensions are necessary. The optimum number of expansion functions is determined by minimizing the sum of the squared errors with respect to the measured data. Once the HELS formulation is established, the acoustic pressure anywhere including the vehicle interior surface can be determined. The normal component of the surface velocity can be reconstructed in a similar manner. Once these quantities are specified, the normal component of the time-averaged acoustic intensity and acoustic energy flow inside a vehicle passenger compartment can be visualized. This three-dimensional acoustic image can provide valuable insight into vehicle interior noise reduction. The effects of number and locations of measurements on the accuracy of reconstruction are investigated. [Work supported by the Daimler-Chryster Challenge Fund.]