Denoising of laser cladding crack acoustic emission signals based on wavelet thresholding method.

Due to the influence of thermal stress and other factors during laser cladding, cracks will appear in the cladding layer. To reduce cladding loss, an effective method is to detect cracks early and adjust fusion parameters promptly. The paper utilized acoustic signal detection technology to collect crack defect signals during the laser cladding process. Subsequently, the collected acoustic signals were subjected to time-frequency analysis and wavelet thresholding denoising. Then by applying a custom thresholding approach for each level of wavelet coefficients, the crack signals were denoised. The results showed that this method achieved better denoising effects compared to other signal denoising methods and preserved the crack information to a greater extent, confirming the feasibility of the custom thresholding denoising approach. It helps to achieve online detection and acoustic signal analysis of cracks during the cladding process.


Introduction
Laser cladding is a technology that uses a laser as a heat source to combine different types of cladding materials with the surface of the substrate, forming a metallurgical bond to significantly enhance substrate surface properties, thereby improving its working life and reliability [1].However, laser cladding will be affected by many conditions, such as cladding powder, cladding process, and matrix material.Due to the complexity of these factors, the cladding layer is prone to surface and internal defects, such as cracks, pores, and inclusions.These defects not only reduce the performance of the cladded workpiece but may also lead to its rejection [2].
Cracks are one of the most significant defects affecting the quality of the cladding layer [3].This is due to the internal stress generated during the cladding process, which makes the cladding layer prone to cracking [4].When the residual stress within the cladding layer exceeds the material's yield strength limit, cracks are formed, releasing energy in the form of transient elastic waves, resulting in sound.Therefore, by collecting and analyzing the sound signals from cladding cracks, we can potentially achieve effective detection and identification of defects in laser cladding layers.This method can help in the early detection of crack defects and enable appropriate measures to repair or adjust the cladding process, ensuring the quality and reliability of the cladded workpieces [5,6].
Currently, the defect detection methods for cladded components mainly include ultrasonic testing, magnetic particle testing, dye penetrant testing, and acoustic signal testing [7].The first three methods require consideration of the shape and material of the workpiece and may cause contamination to the workpiece.In comparison, acoustic signal testing has certain advantages.It is a dynamic detection method that can effectively detect internal defects in cladding components.However, acoustic signal testing also faces some challenges.It is susceptible to noise interference, thus requiring noise reduction processing to improve the accuracy and reliability of the detection [8].
In this paper, the samples with and without cladding cracks were prepared with the same process parameters.Through preprocessing and time-frequency analysis, the acoustic signals collected in the process of cladding were divided into crack signals and normal signals.Finally, the appropriate wavelet basis function, layer number of decomposition, and threshold function were selected to denoise the acoustic signals during the cladding process [9].

Experimental
The cladding powders used in the experiment are 1712 austenitic stainless steel powder (for preparing cladding layers without cracks, 50～180 μm) and Ni60 powder (for preparing cladding layers with cracks, 50～106 μm).The substrate material is quenched and tempered 27SiMn steel.Different laser cladding layers were prepared by BS-OF-3000-15-4F laser cladding equipment (Xi'an Bisheng Technology Co, LTD).The cladding power is 3000 W. Before the experiment, a non-contact miniature microphone was installed around the test object to collect the sound signals.The experimental procedure is as follows: (1) First, the surface of the 27SiMn substrate steel plate was polished smooth and flat and then cleaned with anhydrous ethanol, dried, and placed in the laser cladding area.
(2) During the experiment, 50 g cladding powder was taken each time and dried in an oven at 60 ℃ for 2 hours to remove moisture.Then the dried powder was poured into the power feeder.
(3) Disperse and secure the microphone around the substrate, and connect it to the computer via a USB interface.During the experiment, the sound signals were collected and recorded by the recording software.
(4) The cladding process was conducted at an overlap rate of 40%.When the laser has cooled down, the entire laser cladding system is turned off.

Preprocessing and time-frequency analysis of acoustic signals.
Two different cladding layer samples were obtained through laser cladding experiments and acoustic signal acquisition experiments.The color detection of the two different cladding layer samples.Figure 1(a) and (c), and the corresponding acoustic signal waveforms obtained from the respective transducers in Figure 1(b) and (d).
Compared to Figure 1(c), the cracked cladding layer sample in Figure 1(a) shows numerous cracks that are almost spread throughout the sample.Comparing the waveform of signals in Figure 1(b) and  (d), there are many mutations in the crack signal, and the signal mutation point can be understood as the waveform at the occurrence of a crack event.However, in Figure 1(b), it can be observed that the crack signal contains a lot of noise interference, making some crack signals less prominent and unable to clearly distinguish whether they are signals of crack faults.Therefore, we need to perform frequency domain analysis and denoising processing on the original crack signals to facilitate subsequent waveform analysis.The two signals were transformed into frequency domain signals using the Fast Fourier Transform (FFT) [10], which are shown in Figure 2. The normal signal and crack signal frequencies are mainly concentrated between 1200 and 8000 Hz, and there are many peak signals in this frequency domain.When amplifying the frequency waveform between 7500 and 8000 Hz, it can be observed that the crack signal frequency amplitude is greater than the frequency amplitude of the normal signal.Therefore, it can be inferred that the crack signal is a multi-peak burst signal, and the frequency range of crack faults is in the medium to high-frequency range.However, the specific frequency range of crack faults is still unclear and requires further analysis.

Wavelet threshold denoising analysis of laser cladding acoustic signals
In this study, the wavelet thresholding method was applied to denoise the crack signals.In the denoising process, the selection of wavelet basis function, decomposition level, and threshold function directly affects the denoising effect of the signal.

Wavelet basis function.
Selecting an appropriate wavelet basis function yields better results for the wavelet decomposition of the signal.Since there is no single wavelet basis function that can achieve the optimal decomposition effect for all types of signals, several commonly used wavelet basis functions were selected for a comparative analysis of denoising indicators (Figure 4). Figure 4 compares the Signal-to-Noise Ratio (SNR) and Root Mean Square Error (RMSE) of 11 wavelet basis functions.Generally, in the denoising process, a higher SNR and a smaller RMSE indicate a better denoising effect [11].From Figure 4, it can be observed that the db12 wavelet basis function has the best denoising effect.Additionally, the dbN series of wavelets have properties such as orthogonality, compact support, symmetry, and vanishing moments, which enable them to better preserve the characteristics of the crack signal.

Layer number of decomposition.
When the wavelet decomposition level is higher, the better it reflects the differences in characteristics between noise and signal, and it is more conducive to denoising.However, a larger number of decomposition levels results in more noticeable signal distortion after reconstruction, which may reduce the effectiveness of signal denoising to some extent.Based on the db12 wavelet basis function, decomposing the crack signal into 3, 4, and 5 layers, the denoising effects are shown in Figure 5. Comparing the SNR and RMSE of different decomposition levels, the denoising effect is best for the 3-layer decomposition.

Threshold function.
After the coefficient threshold is determined, the noise coefficient of the signal needs to be filtered out through the appropriate threshold function.The commonly used threshold functions are the hard thresholding function and the soft thresholding function [12].Comparing the denoising effects of the two threshold functions (Figure 6), The result shows that the hard threshold achieves the best denoising effect.

Wavelet threshold denoising results.
After comparing and analyzing the denoising effects of various wavelet thresholding parameters, the final selection is to use the Db12 wavelet basis function for a 3-level wavelet decomposition of the crack signal.The hard thresholding function is applied to filter the wavelet coefficients of the crack signal using the threshold calculated by the SURE (Stein Unbiased Risk Estimation) algorithm.Finally, obtain the denoised crack signal.Taking crack signal 3 as an example, the denoising result using wavelet thresholding.Figure 7 shows the processing results after denoising.The wavelet coefficients after a 3-level wavelet decomposition using Db12 wavelet in Figure 7(a).The low-frequency components are mostly noise coefficients, while the high-frequency components exhibit relatively significant crack coefficients with smaller noise coefficients.Figure 7(b) shows the wavelet coefficients after thresholding, where some coefficients are preserved while others are set to zero.The comparison between the crack signal after threshold processing and the original crack signal is in Figure 7(c).The waveform of crack signal 3 is represented in blue, while the waveform of the denoised signal is represented in red.Comparing the waveforms before and after denoising, it can be observed that the noise signal has been completely removed.However, the denoised signal reconstruction also exhibits a partial loss of crack waveform.This is because the threshold calculated by the SURE algorithm is 0.599, which effectively filters out all the noise coefficients but is relatively large compared to the crack coefficients in the high-frequency range.It can be seen that this threshold filters out all the coefficients from the first and second levels from  An analysis was conducted on the sources of crack signal loss, indicating that the threshold was set too high, and the magnitude of wavelet coefficients varies across different levels.Therefore, it is necessary to design appropriate thresholds for each level of wavelet coefficients.Instead of the SURE thresholding algorithm, custom thresholds for each level of wavelet coefficients are used for denoising the crack signal based on their actual magnitudes.Figure 8 shows the resulting noise reduction results.
A comparative analysis was conducted on the denoised crack signals, and the results indicate that after the denoising process, the noise signals were mostly filtered out, and the characteristics of the crack signals were also well preserved.This indicates that using the Db12 wavelet for a 3-level wavelet decomposition, along with custom thresholding rules and the hard thresholding function, the wavelet thresholding method exhibits a good denoising effect on laser cladding crack signals.By comparing Figure 8 with Figure 7(c), it can be observed that the results obtained by using the custom threshold for noise removal are superior to those obtained using the SURE threshold algorithm.It effectively preserves the crack information while filtering out the noise signal to a greater extent.This demonstrates the effectiveness and accuracy of the custom thresholding method and lays the foundation for the analysis of laser cladding crack signals.

Conclusion
In this paper, normal acoustic signals and crack acoustic signals during the laser cladding process were recorded using a microphone.Both types of signals were subjected to time-frequency analysis and wavelet thresholding denoising.the wavelet thresholding method with Db12 wavelet basis function, 3level wavelet decomposition, and hard thresholding function was determined.The crack signals were denoised using a custom thresholding approach for each level of wavelet coefficients.This denoising method showed better results compared to other signal denoising methods while preserving the crack information to a greater extent.This demonstrates the feasibility of the custom thresholding denoising method, which is helpful for online detection and analysis of crack acoustic signals during the cladding process.

Figure 1 .
Figure 1.Laser cladding sample and original signal: (a) Dye penetration inspection result of crack cladding layer sample (Single layer 4 channels); (b) crack signal; (c) Dye penetration inspection result of normal cladding layer sample (Single layer 3 channels); (d) Normal signal.

Figure 2 .
Figure 2. Noise reduction signal frequency: (a) crack signal; (b) Normal signal.Since the crack signal collected by the experiment is non-stationary, it indicates that there are fluctuations in the frequency domain concerning time.Therefore, the crack signals were subjected to Continuous Wavelet Transform (CWT) processing.Figure 3 shows the time-frequency spectrogram of the crack signals after CWT processing, with the waveforms of some crack signals in the left column,

Figure 3 .
Figure 3. Partial time-frequency analysis of crack signal: (a) Section 1; (b) The first section analyzes the time-frequency picture; (c) Section 2; (d) The second section analyzes the time-frequency picture.

Figure 4 .
Figure 4. Signal denoising effect under different wavelet basis functions.

Figure 6 .
Figure 6.Signal denoising effect under different threshold functions.

Figure 7 (
b), which contain crack coefficients.As a result, some crack signals are mistakenly filtered out as noise signals.