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This paper documents an inverse visible element Rayleigh integral (VERI) approach. The VERI is a fast though approximate method for predicting sound radiation that can be used in the place of the boundary element method. This paper extends the method by applying it to the inverse problem where the VERI is used to generate the acoustic transfer matrix relating the velocity on the surface to measurement points. Given measured pressures, the inverse VERI can be used to reconstruct the vibration of a radiating surface. Results from an engine cover and diesel engine indicate that the method can be used to reliably quantify the sound power and also approximate directivity.

This paper revisits the popular Rayleigh integral approximation, and also considers a second approximation, the high frequency boundary element method which is similar to the Rayleigh integral. Both methods are approximations to the boundary integral equation, and can solve problems in a fraction of the time required by the conventional boundary element method. The development of both methods from the Helmholtz integral equation is demonstrated and the differences between the two methods are delineated. Both methods were compared on practical examples including a running engine, gearbox, and construction cab. It was concluded that both methods can reliably predict the sound power for many problems but are inaccurate for sound pressure computations.

This paper explores the use of inverse numerical acoustics to reconstruct the surface vibration of a noise source. Inverse numerical acoustics is mainly used for source identification. This approach uses the measured sound pressure at a set of field points and the Helmholtz integral equation to reconstruct the normal surface velocity. The number of sound pressure measurements is considerably less than the number of surface vibration nodes. A brief guideline on choosing the number and location of the field points to provide an acceptable reproduction of the surface vibration is presented. The effect of adding a few measured velocities to improve the accuracy will also be discussed. Other practical considerations such as the shape of the field point mesh and effect of experimental errors on reconstruction accuracy will be presented. Examples will include a diesel engine and a transmission housing.

This paper explores the use of inverse boundary element method to identify aeroacoustic noise sources. In the proposed approach, sound pressure at a few locations out of the flow field is measured, followed by the reconstruction of acoustic particle velocity on the surface where the noise is generated. Using this reconstructed acoustic particle velocity, the acoustic response anywhere in the field, including in the flow field, can be predicted. This approach is advantageous since only a small number of measurement points are needed and can be done outside of the flow field, and a relatively fast computational time. As an example, a prediction of vortex shedding noise from a circular cylinder is presented.

Numerical acoustics has traditionally been relegated to a prediction only role. However, recent work has shown that numerical acoustics techniques can be used to diagnose noise problems. The starting point for these techniques is the acoustic transfer vector (ATV). First of all, ATV's can be used to conduct contribution analyses which can assess which parts of a machine are the predominant noise sources. As an example, the sound power contribution and radiation efficiency from parts of a running diesel engine are presented in this paper. Additionally, ATV's can be used to reliably reconstruct the vibration on a machine surface. This procedure, commonly called inverse numerical acoustics (INA), utilizes measured sound pressures along with ATV's to reconstruct the surface velocity. The procedure is demonstrated on an engine cover for which the reconstructed vibration had excellent agreement with experimental results.