Nondestructive testing methods are used to inspect and test materials and components for discontinuities or differences in mechanical characteristics. Phased array signal processing techniques have been widely used in different applications, but less research has been conducted on contactless nondestructive testing with passive arrays. This paper presents an application of beamforming techniques analysis using a passive synthetic microphone array to calculate the origin and intensity of sound waves in the ultrasonic frequency range. Acoustic cameras operating in the audible frequency range are well known. In order to conduct measurements in higher frequencies, the arrangement of microphones in an array has to be taken into consideration. This arrangement has a strong influence on the array properties, such as its beam pattern, its dynamics, and its susceptibility to spatial aliasing. Based on simulations, optimized configurations with 16, 32, and 48 microphones and 20 cm diameter were implemented in real experiments to investigate the array resolution and localize ultrasonic sources at 75 kHz signal frequency. The results show that development of an ultrasonic camera to localize ultrasonic sound sources is beneficial.
Ultrasonic arrays [
In the field of air acoustics on the other hand acoustic camera systems are increasingly popular for detection, visualization and analysis of sound sources. These systems are based on beamforming, where an array of passive receivers is used to enhance identification of air acoustic emissions by summing the received signals of all microphones with individual delays [
While beamforming with passive acoustic arrays is often used in sonar [
The arrangement of the microphones is one of the most important factors to enhance the results of beamforming. Knowing the principles of microphone arrays, the optimization of array design parameters makes it possible to investigate configurations that need fewer microphones for a desired application. In this chapter, the theoretical background for array shape selection is explained.
The response pattern of a passive microphone array with M microphones depends on its individual sensors and on their arrangement in space. The array pattern describes the response of the array to plane waves with wave vector
Beam pattern calculated for ring (dashed line) and linear (solid line) arrays at 75 kHz. In order to have good separation between the lobes, small beam width is desired.
The width of the main lobe defines the array resolution which is a significant parameter that affects the sound source localization results and is influenced by the array geometry. The Rayleigh criterion is a well-known definition of resolution at the diffraction limit which was first defined in optics [
In order to optimize the application of the microphone arrays, it is important to have good source separation and as low as possible levels of the side lobes, which means that large diameters would be preferred. On the other hand, it is important to have small microphone spacing to achieve a wide angle between the side lobes or to avoid side lobes when analyzing high frequencies. To overcome this, a variety of microphone configurations (linear, cross-shape, periodic grid, circle, and spiral) have been investigated in the literature [
Higher frequency means lower wavelength and it therefore increases local resolution. On the other hand, the attenuation of airborne sound increases with increasing frequency. For a first demonstration we therefore chose a center frequency of 75 kHz which is clearly in the ultrasonic range but still low enough such that special wide-band microphones are available. In order to attain a resolution
(a) Ring array with 32 elements and (b) spiral V = 8.2 array with 32 elements and 20 cm diameter.
According to the Rayleigh criterion in (
Figures
Simulated reconstruction result with sum and delay beamforming for a ring array with 32 elements (Figure
Simulated reconstruction result by sum and delay beamforming for a V = 8.2 spiral array with 32 elements (Figure
In order to evaluate the performance of the array design, experimental tests were conducted in the ultrasonic frequency range at 75 kHz and for comparison also in the acoustic frequency range at 10 kHz and 20 kHz. In both cases the sound source was placed behind a screen with two apertures of 1 cm diameter and a center-to-center separation of 15 mm. A commercial acoustic camera with 48 microphones was available for the experiment in the acoustic frequency range. For the experiment in the ultrasonic frequency range, a single microphone in combination with a mechanical positioning device was used to collect the data at the 32 microphone positions as depicted in Figure
In order to examine the resolution in the acoustic frequency range, we conducted measurements with a commercial acoustic camera (Gfai tech GmbH, Berlin, Germany). A Bluetooth speaker was placed in a wooden box with two holes of 1 cm diameter and 1.5 cm center-to-center separation. The speaker was excited with 10 kHz and 20 kHz continuous wave sinus signals from a signal generator. A commercial 48-channel planar spiral configuration (83 cm diameter) and a ring configuration (75 cm diameter) with data acquisition and evaluation unit were used to detect and localize the signals coming from two holes (Figure
(a) Schematic set-up of the measurement; (b) the spiral configuration of the commercial microphone array.
Source localization with the acoustic camera (spiral configuration). (a) at 10 kHz; (b) at 20 kHz.
Source localization with the acoustic camera (ring configuration). (a) at 10 kHz; (b) at 20 kHz.
Theoretically, the angular resolution would improve when the acoustic array would be positioned closer to the source, but because of the diameter of the arrays of 83 cm and 75 cm, a distance to the object below 40 cm would not improve the reconstruction result but leads to source localization instability. Experimentally, it is not recommended to perform the measurement closer than the diameter, but the localization may even work to a certain distance.
The appearance of the side lobes around the main lobe especially in Figure
For the experiment in the ultrasonic frequency range, an ultrasonic transducer with 6 cm aperture and a center frequency of 75 kHz (15% bandwidth) was used to send the signals. A schematic set up is shown in Figure
Schematic set-up of the measurement in the ultrasonic frequency range.
To detect the direction of the sources defined by the holes an ultrasonic receiving array is needed. For the experiments which will be presented here, we employed a broadband microphone with a constant sensitivity up to 100 kHz frequency and a diameter of 3 mm (Type 40 DP, 1/8” Pressure Microphone, G.R.A.S. Sound & Vibration, Denmark). The microphone was mounted to a motorized 3-axis mechanical positioning device which was located in front of the screen. While the distance to the screen (z-coordinate) was kept constant, the microphone was moved in x and y directions with a manipulator to 32 specific positions to build the passive synthetic spiral and ring arrays.
One of the obstacles when designing high frequency microphone arrays is the small interelement spacing. For the choice of the array configurations (see Section
The ultrasonic time signal of each position was captured, digitized, and stored in a computer. A sampling frequency of 20 MS/s was chosen; the length of the time interval was 1 ms. For each microphone configuration, the measurement was performed at three different screen–microphone distances, 0.5 D, 0.65 D, and 0.9 D, respectively, to investigate ultrasound localization at distances less than the diameter of the array (D = 20 cm). The shorter distances were chosen for comparison because ultrasonic sources have short wavelength which increases the attenuation as a function of distance. As an example for a typical shape of the received signals, the time signal captured with the first microphone of the spiral V = 8.2 from the origin at 0.9 D measurement distance and the averaged frequency spectra of the signals of all microphones calculated by fast Fourier transformation are depicted in Figure
(a) Recorded time signal of the first microphone at the spiral positions (V = 8.2) at 0.9 D distance from the source and (b) averaged spectra of the time signals calculated by fast Fourier transformation.
With a program written in MATLAB, the experimental data were delayed and summed to perform the time domain localization as explained in Section
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 32 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 8.2) with 32 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
To get a better overview, we repeated the measurements with 16 and 48 microphone positions and kept the diameter of the arrays constant to 20 cm. Figures
Results of post processing experimental data.
Ring | 16 Microphones | 32 Microphones | 48 Microphones | |||
---|---|---|---|---|---|---|
d | MSL (dB) | API | MSL (dB) | API | MSL (dB) | API |
0.5 D | - | - | -0.20 | 0.65 | -0.25 | 0.66 |
0.65 D | - | - | -2.00 | 0.74 | -1.50 | 0.75 |
0.9 D | -0.89 | 1.08 | -4.10 | 1.10 | -4.10 | 1.12 |
| ||||||
Spiral 8.2 | 16 Microphones | 32 Microphones | 48 Microphones | |||
| ||||||
d | MSL (dB) | API | MSL (dB) | API | MSL (dB) | API |
0.5 D | - | - | -1.45 | 1.54 | -4.10 | 1.67 |
0.65 D | - | - | -4.40 | 1.65 | -6.00 | 1.68 |
0.9 D | -2.24 | 2.00 | -5.65 | 1.89 | -6.20 | 1.94 |
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 16 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 8.2) with 16 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic ring array with 48 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
Beamforming result at 75 kHz frequency calculated from the experimental data acquired with the synthetic spiral array (V = 8.2) with 48 elements. Z-distance of the microphone to the screen: (a) 0.5 D; (b) 0.65 D; (c) 0.9 D.
In order to make sure that the two maxima obtained by beamforming in Figures
Beamforming result at 75 kHz frequency, calculated with experimental data from the spiral configuration at 18 cm distance from the screen. (a) Left hole covered; (b) right hole covered.
This research work presents first steps towards an ultrasonic microphone array for NDT applications. Ring and spiral configurations with 32 elements and 20 cm diameter were designed and simulated to examine the array resolution and localize ultrasonic sources at 75 kHz. The simulations demonstrated that the ring array outperforms the spiral array with respect to the resolution but delivers more artefacts especially in case of two coherent sources. A set of experiments in the ultrasonic frequency range at 75 kHz was performed to corroborate the simulations. As ultrasonic multichannel data acquisition systems would be expensive, we performed the ultrasonic experiments in this study with a single microphone and a single data acquisition system. This microphone was moved to the required positions with the help of a motor driven mechanical positioning system. A screen with two holes with 15 mm center-to-center separation distance placed in front of an ultrasonic transducer was used as the test source. Delay and sum beamforming in time domain served as a simple method for the simulations and for the processing of the ultrasonic experimental data. The measurement at 0.9 D distance between array and screen showed very good results without extreme appearance of side lobes. The number of microphones is very important as it defines the necessary number of channels of the electronics and therefore the overall costs of the system. A comparison to the performance of ring or spiral systems with 16 and 48 microphones showed that 32 microphones are a good compromise at the chosen geometrical conditions.
In order to demonstrate the influence of the operating frequency, a source with the same geometry (a screen with two holes with a center-to-center separation distance of 15 mm) but with lower frequency (10 kHz and 20 kHz) was examined with a commercial acoustic camera equipped with 48 microphones. The best result was obtained with frequency domain beamforming in this case. Nevertheless, it was clearly demonstrated that higher frequency provides higher local resolution as even sophisticated post-processing cannot compensate for all artefacts and broadening effects.
The results of this study have shown that source localization by beamforming is possible in the ultrasonic frequency range above 40 kHz, and that it is possible to improve the local resolution by using ultrasonic frequency. In future studies, the influence of parameters such as measurement distance, array configuration, pulse length, and frequency ranges will have to be investigated and optimized in more detail. Localization of ultrasonic sources with arrays could be very promising in the context of NDT as for example in leakage detection in automotive or aerospace industry. Industrial processes such as welding processes for example do not only emit acoustic signals but also signals in the ultrasonic frequency range. Process monitoring at increased frequency could benefit from a higher signal to noise ratio due to a lower level of reverberation and environmental noise signals as well as a higher local resolution. This could be exploited by application of passive contactless ultrasonic arrays.
The measured MATLAB data used to support the findings of this study are available from the corresponding author upon request.
Some parts of the work were presented as an oral presentation at DAGA Conference 2018 in Munich and Fraunhofer Vision Technologietag 2018 in Jena.
The authors declare that they have no conflicts of interest.
A part of this work has been funded by the German Ministry of Economics and Technology in the frame of the program ZIM (Zentrales Innovationsprogramm Mittelstand), contact ZF4234102LT6, cooperative project BeamUS500, and IZFP project part BeamUS500-Sensor. The authors gratefully acknowledge Nico Brosta and Katharina Bonaventura for helping with ultrasonic data acquisition and MATLAB programming.