Laser-assisted see-through technology for locating sound sources inside a structure.

A laser-assisted see-through technology is developed to locate sound sources inside a structure and to analyze the interior sound field. Six lasers were employed to measure simultaneously the normal velocities on the exterior surface. These input data were used to locate sound sources inside a solid structure using a passive sonic detection and ranging algorithm, and then to reconstruct the interior sound field using the Helmholtz equation least squares method, and finally to observe the changes of the interior sound field over time through computer tomography. If signals are time invariant, all these can be accomplished with two lasers, one being fixed and another moving around to measure the normal surface velocity sequentially to establish transfer function with respect to the stationary laser. Once the transfer functions are established, they can be multiplied by any segment of time-domain signals measured by the fixed laser to acquire multiple normal surface velocities, as if they were measured simultaneously. This laser-assisted see-through technology has been validated experimentally and employed to observe the aerodynamically-induced sound field generated by a blower inside a projector. This development is important as it signifies a significant advancement in sound source localization, and opens the door to a class of applications presently unattainable.

Noninvasive Determination of Blood Pressure by Heart Sound Analysis Compared With Intra-Arterial Monitoring in Critically Ill Children-A Pilot Study of a Novel Approach.

OBJECTIVES: To develop a novel device to predict systolic and diastolic blood pressure based on measured heart sound signals and evaluate its accuracy in comparison to intra-arterial blood pressure readings. STUDY DESIGN: Prospective, observational pilot study. SETTING: PICU. PATIENTS: Critically ill children (0-18 yr) undergoing continuous blood pressure monitoring via radial artery intra-arterial catheters were enrolled in the study after informed consent. The study included medical, cardiac, and surgical PICU patients. INTERVENTIONS: Along with intra-arterial blood pressure, patient's heart sounds were recorded simultaneously by a highly sensitive sensor taped to the chest. Additional hardware included a data acquisition unit and laptop computer. Subsequently, advanced signal processing technologies were used to minimize random interfering signals and extract and separate S1 and S2 signals. A computerized model was then developed using artificial neural network systems to estimate blood pressure from the extracted heart sound analysis. MEASUREMENTS AND MAIN OUTCOMES: We found a statistically significant correlation for systolic (r = 0.964; R = 0.928) and diastolic (r = 0.935; R = 0.868) blood pressure readings (n = 491) estimated by the novel heart-sound signal-based method and those recorded by intra-arterial catheters. The mean difference of the individually paired determinations of the blood pressure between the heart-sound-based method and intra-arterial catheters was 0.6 ± 7 mm Hg for systolic blood pressure and -0.06 ± 5 mm Hg for diastolic blood pressure, which was within the recommended range of 5 ± 8 mm Hg for any new blood pressure devices. CONCLUSIONS: Our findings provide proof of concept that the heart-sound signal-based method can provide accurate, noninvasive blood pressure monitoring.

Analyzing excitation forces acting on a plate based on measured acoustic pressure.

This paper presents a theoretical study on "seeing" through an elastic structure to uncover the root cause of sound and vibration by using nearfield acoustical holography (NAH) and normal modes expansion. This approach is of generality because vibro-acoustic responses on the surface of a vibrating structure can always be reconstructed, exactly or approximately. With these vibro-acoustic responses, excitation forces acting on the structure can always be determined, analytically or numerically, given any set of boundary conditions. As an example, the explicit formulations for reconstructing time-harmonic excitation forces, including point, line and surface forces, and their arbitrary combinations acting on a rectangular thin plate in vacuum mounted on an infinite baffle are presented. The reason for choosing this example is that the analytic solutions to vibro-acoustic responses are available, and in-depth analyses of results are possible. Results demonstrate that this approach allows one to identify excitation forces based on measured acoustic pressures and reveal their characteristics such as locations, types and amplitudes, as if one could "see" excitation forces acting behind the plate based on acoustic pressure measured on the opposite side. This approach is extendable to general elastic structures, except that in such circumstance numerical results must be sought.

Analyzing panel acoustic contributions toward the sound field inside the passenger compartment of a full-size automobile.

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.

Reconstructing transient acoustic radiation from an arbitrary object with a uniform surface velocity distribution.

This paper presents the general formulations for reconstructing the transient acoustic field generated by an arbitrary object with a uniformly distributed surface velocity in free space. These formulations are derived from the Kirchhoff-Helmholtz integral theory that correlates the transient acoustic pressure at any field point to those on the source surface. For a class of acoustic radiation problems involving an arbitrarily oscillating object with a uniformly distributed surface velocity, for example, a loudspeaker membrane, the normal surface velocity is frequency dependent but is spatially invariant. Accordingly, the surface acoustic pressure is expressible as the product of the surface velocity and the quantity that can be solved explicitly by using the Kirchhoff-Helmholtz integral equation. This surface acoustic pressure can be correlated to the field acoustic pressure using the Kirchhoff-Helmholtz integral formulation. Consequently, it is possible to use nearfield acoustic holography to reconstruct acoustic quantities in entire three-dimensional space based on a single set of acoustic pressure measurements taken in the near field of the target object. Examples of applying these formulations to reconstructing the transient acoustic pressure fields produced by various arbitrary objects are demonstrated.

Passive sonic detection and ranging for locating sound sources.

A passive sonic detection and ranging (SODAR) technology is developed to locate sound sources that emit arbitrarily time-dependent signals in a typical environment encountered in practice in real time. This passive SODAR is built on a comprehensive approach including the pre-processing of input data to enhance the signal-to-noise ratio, acoustic modeling of sound radiation from a point source, iterative triangulations, and post-processing of output data to ensure the accuracy in source localization. Moreover, it employs an optimization process to extend the source detection range and improve the source localization accuracy in a highly non-ideal environment that involves a large number of unspecified reflected and diffracted sound waves. This is accomplished through computations based on the source locations predicted by the individual units of four microphones that are not lying on the same plane. Experimental results confirm that passive SODAR works for arbitrarily time-dependent signals that include continuous, transient, impulsive, random, narrow-, and broadband sounds with frequencies above 20 Hz. The minimum number of microphones that are required in passive SODAR is six. These microphones can be mounted anywhere as long as they are not on the same plane and the lines of sight from sound sources remain unblocked.

Panel acoustic contribution analysis.

Formulations are derived to analyze the relative panel acoustic contributions of a vibrating structure. The essence of this analysis is to correlate the acoustic power flow from each panel to the radiated acoustic pressure at any field point. The acoustic power is obtained by integrating the normal component of the surface acoustic intensity, which is the product of the surface acoustic pressure and normal surface velocity reconstructed by using the Helmholtz equation least squares based nearfield acoustical holography, over each panel. The significance of this methodology is that it enables one to analyze and rank relative acoustic contributions of individual panels of a complex vibrating structure to acoustic radiation anywhere in the field based on a single set of the acoustic pressures measured in the near field. Moreover, this approach is valid for both interior and exterior regions. Examples of using this method to analyze and rank the relative acoustic contributions of a scaled vehicle cabin are demonstrated.

Blind extraction and localization of sound sources using point sources based approaches.

This paper presents theoretical models for blind sound source localization and separation of the signals emitted by arbitrary point sources in free space. Source localizations are achieved by a model based approach that accounts for the spherical spreading of an acoustic wave and utilizes an iterative triangulation, based on the signals measured by a three-dimensional microphone array. Once source locations are determined, the source signals are separated by using the point source separation (PSS) method, which is valid for all types of signals, including harmonic, continuous, transient, random, narrowband and broadband. General solutions for signals separation are presented. Theoretically, PSS can reconstruct the individual source signals exactly. This is because it employs the free-space Green's function, which defines the exact correlation among individual sources and measurement microphones. To validate PSS, numerical simulations are carried out and results are compared with those obtained by FastICA (Independent Component Analysis) code. The impacts of various parameters such as the microphone configuration, type of source signals, signal to noise ratio, number of microphones and source localization errors on the quality of signals separation by using PSS and FastICA are examined. The advantages and disadvantages of PSS and FastICA are compared and discussed.

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

Experimental validation of alternate integral-formulation method for predicting acoustic radiation based on particle velocity measurements.

This paper presents experimental validation of an alternate integral-formulation method (AIM) for predicting acoustic radiation from an arbitrary structure based on the particle velocities specified on a hypothetical surface enclosing the target source. Both the normal and tangential components of the particle velocity on this hypothetical surface are measured and taken as the input to AIM codes to predict the acoustic pressures in both exterior and interior regions. The results obtained are compared with the benchmark values measured by microphones at the same locations. To gain some insight into practical applications of AIM, laser Doppler anemometer (LDA) and double hotwire sensor (DHS) are used as measurement devices to collect the particle velocities in the air. Measurement limitations of using LDA and DHS are discussed.

Locating arbitrarily time-dependent sound sources in three dimensional space in real time.

This paper presents a method for locating arbitrarily time-dependent acoustic sources in a free field in real time by using only four microphones. This method is capable of handling a wide variety of acoustic signals, including broadband, narrowband, impulsive, and continuous sound over the entire audible frequency range, produced by multiple sources in three dimensional (3D) space. Locations of acoustic sources are indicated by the Cartesian coordinates. The underlying principle of this method is a hybrid approach that consists of modeling of acoustic radiation from a point source in a free field, triangulation, and de-noising to enhance the signal to noise ratio (SNR). Numerical simulations are conducted to study the impacts of SNR, microphone spacing, source distance and frequency on spatial resolution and accuracy of source localizations. Based on these results, a simple device that consists of four microphones mounted on three mutually orthogonal axes at an optimal distance, a four-channel signal conditioner, and a camera is fabricated. Experiments are conducted in different environments to assess its effectiveness in locating sources that produce arbitrarily time-dependent acoustic signals, regardless whether a sound source is stationary or moves in space, even toward behind measurement microphones. Practical limitations on this method are discussed.

Reconstruction of vibroacoustic responses of a highly nonspherical structure using Helmholtz equation least-squares method.

The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

Methods for reconstructing acoustic quantities based on acoustic pressure measurements.

This paper presents an overview of the acoustic imaging methods developed over the past three decades that enable one to reconstruct all acoustic quantities based on the acoustic pressure measurements taken around a target source at close distances. One such method that has received the most attention is known as near-field acoustical holography (NAH). The original NAH relies on Fourier transforms that are suitable for a surface containing a level of constant coordinate in a source-free region. Other methods are developed to reconstruct the acoustic quantities in three-dimensional space and on an arbitrary three-dimensional source surface. Note that there is a fine difference between Fourier transform based NAH and other methods that is largely overlooked. The former can offer a wave number spectrum, thus enabling visualization of various structural waves of different wavelengths that travel on the surface of a structure; the latter cannot provide such information, which is critical to acquire an in-depth understanding of the interrelationships between structural vibrations and sound radiation. All these methods are discussed in this paper, their advantages and limitations are compared, and the need for further development to analyze the root causes of noise and vibration problems is discussed.

Reconstruction of transient acoustic radiation from a sphere.

Transient near-field acoustical holography (NAH) formulation is derived from the Helmholtz equation least squares (HELS) method to reconstruct acoustic radiation from a spherical surface subject to transient excitations in a free field. To facilitate derivations of temporal solutions, we make use of the Laplace transform and expansion in terms of the spherical Hankel functions and spherical harmonics, with their coefficients settled by solving a system of equations obtained by matching an assumed-form solution to the measured acoustic pressure. To derive a general form of solution for a temporal kernel, we replace the spherical Hankel functions and their derivatives by polynomials, recast infinite integrals in the inverse Laplace transform as contour integrals in a complex s-plane, and evaluate it via the residue theorem. The transient acoustic quantities anywhere including the source surface are then obtained by convoluting the temporal kernels with respect to the measured acoustic pressure. Numerical examples of reconstructing transient acoustic fields from explosively expanding, impulsively accelerating, and partially accelerating spheres, and that from a sphere subject to an arbitrarily time-dependent excitation are depicted. To illustrate the effectiveness of HELS-based transient NAH formulations, all input data are collected along an arbitrarily selected line segment and used to reconstruct transient acoustic quantities everywhere.

Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography.

In this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half-space by using hybrid near-field acoustic holography (NAH) and modified Helmholtz equation least squares (HELS) formulations. In hybrid NAH, we combine modified HELS with an inverse boundary element method (IBEM) to reconstruct a vibroacoustic field. The main advantage of this approach is that the majority of the input data can be regenerated but not measured, thus the efficiency is greatly enhanced. In modified HELS, we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed-form solution to the measured acoustic pressure. Here the system of equations is ill conditioned and Tikhonov regularization is implemented through singular value decomposition (SVD) and the generalized cross-validation (GCV) method. Numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than does a modified HELS, but a modified HELS is more efficient than is hybrid NAH [Work supported by NSF].

On the choice of expansion functions in the Helmholtz equation least-squares method.

This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.

Hybrid near-field acoustic holography.

Hybrid near-field acoustical holography (NAH) is developed for reconstructing acoustic radiation from an arbitrary object in a cost-effective manner. This hybrid NAH is derived from a modified Helmholtz equation least squares (HELS) formula that expands the acoustic pressure in terms of outgoing and incoming waves. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching the assumed-form solution to measured acoustic pressures through the least squares. Measurements are taken over a conformal surface around a source at close range so that the evanescent waves can be captured. Next, the modified HELS is utilized to regenerate as much acoustic pressures on the conformal surface as necessary and take them as input to the Helmholtz integral formulation implemented numerically by boundary element method (BEM). The acoustic pressures and normal velocities on the source surface are reconstructed by using a modified Tikhnov regularization (TR) with its regularization parameter determined by generalized cross validation (GCV) method. Results demonstrate that this hybrid NAH combines the advantages of HELS and inverse BEM. This is because a majority of the input data are regenerated but not measured, thus the efficiency of reconstruction is greatly enhanced. Meanwhile, the accuracy of reconstruction is ensured by the Helmholtz integral theory and modified TR together with GCV method, provided that HELS converges fast enough on the measurement surface. Numerical examples of reconstructing acoustic quantities on the surface of a simplified engine block are demonstrated. [Work supported by NSF.]

Combined Helmholtz equation-least squares method for reconstructing acoustic radiation from arbitrarily shaped objects.

A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.