Ultrasonic cavitation noise extraction based on fence sampling

The composition of the ultrasonic cavitation sound field is complex, including fundamental, harmonic, subharmonic, super-harmonic, and broadband transient noise. Fundamental waves, harmonics, etc., may interfere with the analysis and research of broadband transient cavitation noise, so it is necessary to filter out these interferences in the sound field. This article conducts measurement experiments on the ultrasonic cavitation sound field generated by high-power ultrasonic cleaning transducers. By utilizing the characteristics of the fence effect, the acoustic signal in the ultrasonic cavitation sound field is resampled through fence sampling so that the fundamental and harmonic components are fused at 0 Hz and filtered out. The ultrasonic cavitation noise is successfully extracted, and its signal structure is the same as the noise component structure in the original signal.


Introduction
In recent years, there have been more and more industrial and daily applications of ultrasonic cavitation in liquid media, such as ultrasonic cleaning, ultrasonic decontamination, Baijiu brewing, and other fields.Ultrasonic cavitation is a phenomenon where liquid media is subjected to ultrasonic waves, resulting in negative pressure in certain areas and the generation of bubbles [1].
Cavitation noise is one of the important characteristics of ultrasonic cavitation, which is generated by steady-state cavitation bubble pulsation and transient cavitation bubble rupture caused by the highpower operation of ultrasonic transducers in liquid media [2].It is a part of the sound field in ultrasonic cavitation.The study of ultrasonic cavitation noise in the ultrasonic cavitation sound field can help understand the specific cavitation intensity, cavitation threshold, and distribution of cavitation, providing strong and reliable references for practical applications.
For the study of ultrasonic cavitation noise, people usually study its spectral components, calculate the noise level of harmonics related to cavitation activities, or calculate the integration of continuous spectra generated by transient cavitation to represent cavitation intensity.However, there is relatively little extraction of cavitation noise.In 2000, Frohly et al. studied the relationship between cavitation noise and cavitation intensity in ultrasonic cavitation.They used the power spectra of cavitation noise harmonics and higher-order harmonics, as well as the power spectra of continuous spectra, to represent cavitation intensity at different ultrasonic powers [3].In 2005, Sobotta and Jung measured the cavitation noise of ultrasonic cleaning equipment, analyzed the cavitation noise spectrum, and studied the variation of sound pressure at the driving ultrasound frequency f0 at different transducer surface sound intensities [4].In 2016, Hertz Eichenrod et al. conducted experimental verification on the distribution function of the cavitation noise spectrum, verifying that cavitation noise is not a Gaussian distribution [5].In 2017, Köchel et al. studied the signal processing methods of cavitation noise and the relationship between harmonics and cavitation [6].In 2019, the international standard "Measurement of Cavitation Noise in Ultrasonic Cleaning Tanks and Ultrasonic Reactors" (IEC/TS 63001:2019) was published.This standard specifies that cavitation intensity is characterized by the LCN and spectral components of cavitation noise in the measurement of ultrasonic cleaning equipment [7].In 2021, Wu et al. extracted the continuous spectrum of ultrasonic cavitation noise by designing an adaptive notch filter [8].They measured the cavitation noise level of ultrasonic cleaning transducers using cavitation noise spectrum analysis in 2022, studying the changes in cavitation intensity in ultrasonic cleaning tanks [9].In 2022, Wu et al. studied the representation methods of cavitation emphasis and reviewed various approaches, including cavitation noise analysis [10].
If ultrasound cavitation noise can be effectively extracted, it is more conducive to the study of cavitation and more accurate calculation of relevant parameters such as cavitation threshold and cavitation intensity.This article utilizes the component characteristics of cavitation noise to resample the acoustic signal collected in the ultrasonic cavitation sound field.Ultimately, it extracts a singlecomponent ultrasonic cavitation noise signal with the same noise component structure as the original acoustic signal collected.

Principles of fence sampling
After the ultrasonic transducer is in a high-power operating state and causes transient cavitation, a complex sound field will be formed, including the fundamental wave driving the ultrasound, the harmonics generated by the high-power nonlinear operation of the ultrasonic transducer, the harmonics generated by the regular pulsation of steady-state cavitation bubbles, and the transient cavitation noise generated by the rupture of transient cavitation bubbles.Among the components of these sound waves, the frequencies of the fundamental and harmonic waves are determined by the driving noise frequency of the ultrasonic transducer.It can be considered that their frequencies are ordered, with their spectra represented as line spectra.The transient cavitation noise is disordered, and its spectrum exhibits a continuous spectrum.The acoustic spectrum in the ultrasonic cavitation field is shown in Figure 1, where the fundamental, harmonic, subharmonic, super-harmonic, and continuous spectral components can be clearly seen.If there is a sine signal f (t) with a frequency of f0 ( ) When the signal is sampled at a sampling rate of f0 or f0/n, the resulting sampling result is a straight line with a value of C.Where C=Asinφ.The schematic diagram of f (t) sampling results using a sampling rate of f0/n is shown in Figure 2. Using a sampling rate of f0/n, the original signal is "blocked" behind the field of view like a fence.The fence effect refers to the phenomenon where the spectrum calculated by the discrete Fourier transform is limited to an integer multiple of the fundamental frequency, and the output can only be seen at the corresponding discrete point [11].In order to extract noise signals from the ultrasonic cavitation sound field, the characteristics of the fence effect can be utilized to resample the collected acoustic signals in the ultrasonic cavitation sound field based on the frequency characteristics of the cavitation noise signal.This article refers to this sampling as fence sampling.It prevents the fundamental and harmonic waves from being visible but does not affect the signal structure of the noise signal.
Therefore, fence sampling can be used to resample the acoustic signal in the ultrasonic cavitation noise field, effectively filtering out the ordered signal and extracting the noise signal from it.

Ultrasonic cavitation noise extraction
When the ultrasonic transducer is operating at high power and its fundamental frequency is a sine signal, a hydrophone with sufficient bandwidth and sensitivity that can withstand ultrasonic cavitation corrosion is placed in the ultrasonic cavitation sound field.The acoustic signal p(t) in the ultrasonic cavitation noise field received by the hydrophone is collected.p(t) can be seen as the sum of ordered signal porder (t) and noise signal pnoise(t), i.e ( ) ( ) ( ) (2) where ( ) ( ) (3) in the formula, Ai is the amplitude of the i-th constituent signal in the ordered signal; fi is the frequency of the i-th constituent signal in an ordered signal; φi is the phase of the i-th constituent signal in an ordered signal.
Firstly, FFT is performed, and the acoustic signal p(t) in the collected ultrasonic cavitation noise field is sampled to obtain P( f ).Based on the obtained spectrum, the subharmonic frequency of the lowest frequency to be filtered is determined, and this frequency is set as the sampling rate fs-fence for fence sampling.
After determining the sampling rate fs-fence for fence sampling, the acoustic signal p(t) in the ultrasonic cavitation noise field is sampled using fs-fence to obtain the fence sampling signal pfence(t).FFT is performed on pfence(t) to obtain Pfence( f ), with the formula:  f) is filtered out to obtain the noise signal spectrum Pcavitation( f ).Then, inverse Fourier transform is performed on it to obtain the ultrasonic cavitation noise signal pcavitation(t).The formula is:

Results and discussion
The ultrasonic cleaning transducer is placed in the center of the sink (sink size: length 113 cm, width 68 cm, height 77 cm, organic glass material, sink wall thickness 3 cm).Sufficient water is added to a depth of 40 cm.The working frequency of the ultrasonic cleaning transducer is 24 kHz, with a length of 35 cm, a width of 17.5 cm, a height of 10 cm, and a maximum output power of 2000 W. The schematic diagram of the experimental system is shown in Figure 3.The experimental system consists of a signal transmission system, a signal reception and acquisition system, and a motion control positioning system.The signal transmission system includes a signal source, power amplifier, and ultrasonic cleaning transducer.The signal source and power amplifier control the ultrasonic cleaning transducer to emit sound waves and generate ultrasonic cavitation sound fields in water.The signal reception and acquisition system includes a digital oscilloscope, an acquisition card, a computer, and a hydrophone, which monitors and collects signals from the hydrophone.The motion control system includes a computer and a motion control device, which controls the motion control device to accurately locate the hydrophone at the measurement position and analyze and calculate the collected hydrophone reception signal.
The signal source and power amplifier are controlled to ensure the high-power normal operation of the ultrasonic cleaning transducer.The ultrasonic cavitation sound field signal received by the hydrophone is shown in Figure 4. Usually, when an ultrasonic transducer operates at high power to generate transient cavitation, the nonlinear operation and steady-state cavitation bubble pulsation of the ultrasonic transducer will excite n-fold harmonics (nf0), n/2-fold harmonics (nf0/2), and n/3-fold harmonics (nf0/3) in the sound field, where n is an integer greater than or equal to 1.At this point, the energy magnitude of the fundamental frequency and the aforementioned harmonics in the ultrasonic cavitation sound field is much larger compared to other m/n times super-harmonics.Therefore, in order to better extract ultrasonic cavitation noise, 1/6 of the fundamental frequency is selected as the fence sampling frequency, i.e., fsfence = 4 k.The fence sampling signal of the ultrasonic cavitation sound field is sampled at fs-fence, and the time-domain diagram of the fence sampling signal obtained is shown in Figure 5.By filtering the fence sampling signal and removing the 0 Hz component, the ultrasonic cavitation noise to be extracted can be obtained.The time-domain diagram of ultrasonic cavitation noise is shown in Figure 6.From Figure 6, it can be seen that the extracted acoustic signal is a typical noise signal.Then, FFT was performed on the collected ultrasonic cavitation sound field and the extracted ultrasonic cavitation noise, respectively, to obtain their spectral maps, as shown in Figure 7. From Figure 7, it can be seen that the extracted ultrasonic cavitation noise and the noise component spectrum of the acoustic signal in the ultrasonic cavitation sound field approximately overlap in the frequency band of 30 kHz~130 kHz.The parts that do not overlap are affected by the sampling frequency of the fence sampling.It can be concluded that the extracted ultrasonic cavitation noise signal and the noise component of the original signal have the same signal structure within the overlapping frequency band.Therefore, using fence sampling can effectively control the harmonics generated by the nonlinear operation of transducers in the ultrasonic cavitation sound field and effectively extract the cavitation noise signal in the ultrasonic cavitation sound field.

Conclusions
This article uses a clever method of fence sampling to control the harmonics generated by the nonlinear operation of transducers in the ultrasonic cavitation sound field and extracts the ultrasonic cavitation noise.Within a certain frequency band, the signal structure is the same as the noise component of the acoustic signal in the ultrasonic cavitation sound field.This method can quickly extract ultrasonic cavitation noise by suppressing the nonlinear interference components of transducers in the ultrasonic cavitation sound field.It then conducts research related to cavitation noise through the extracted ultrasonic cavitation noise, such as cavitation intensity, cavitation distribution, etc.Meanwhile, the extraction of ultrasonic cavitation noise is related to the sampling frequency of the fence.An appropriate sampling frequency needs to be used based on specific sound field conditions and extraction needs.

Figure 1 .
Figure 1.Schematic diagram of sound signal spectrum in ultrasonic cavitation sound field.
can be observed from Pfence( f ) that all the line spectra of the ordered signals contained in the original signal disappear and are fully integrated into the 0 Hz component of Pfence( f ).At this point, the value C of the 0 Hz component is: component in Pfence( f ) is set to zero, or the 0 Hz component of Pfence(

Figure 4 .
Figure 4. Time domain diagram of ultrasonic cavitation sound field acoustic signal.

Figure 5 .
Figure 5.Time domain diagram of fence sampling signal.

Figure 6 .
Figure 6.Time domain map of ultrasonic cavitation noise.