Comprehensive noise reduction performance evaluation method for nonlinear ultrasonic detection signal noise reduction algorithm

Abstract

The invention provides a comprehensive noise reduction performance evaluation method for a nonlinear ultrasonic detection signal noise reduction algorithm, and the method comprises the steps: firstly constructing a multi-working-condition noise reduction performance pre-screening mechanism based on error band analysis based on early-stage experimental data, and then introducing a radar map as an evaluation tool for the comprehensive noise reduction effect of the signal noise reduction algorithm. The noise reduction effects of a moving average method (MA), a spectral subtraction method (SS), a short-time Fourier transform method (STFT), a wavelet transform method (WT) and an orthogonal matching pursuit algorithm (OMP) are compared, and finally a signal noise reduction algorithm with the optimal comprehensive efficiency is screened out. On the basis of algorithm optimization, quantitative mapping rules between microcrack three-dimensional geometric parameters and relative nonlinear coefficients are analyzed through regression modeling, and the significant level of the correlation degree of the relative nonlinear coefficients and microcrack size parameters is effectively improved; and a high-confidence theoretical support is provided for quantitative nondestructive detection of the microcracks in engineering practice.

Description

TECHNICAL FIELD

[0001] The application provides a nonlinear ultrasonic detection signal denoising algorithm comprehensive denoising performance evaluation method, and belongs to the field of signal preprocessing. BACKGROUND

[0002] As a non-destructive testing method, ultrasonic detection technology transmits ultrasonic waves and receives the received signals after the ultrasonic waves propagate in the detected object, so as to detect the structure, defects and the like in the object, and has a wide application in material detection, industrial production, medical diagnosis and many other fields. The nonlinear ultrasonic detection technology, as a kind of ultrasonic detection technology, has stronger accuracy and sensitivity in detecting micro-crack defects than other detection methods. However, in the actual detection process, the ultrasonic signal is often disturbed by various noises, which may come from the detection equipment itself, environmental factors, the complex structure of the detected object, etc., resulting in a decrease in the quality of the detection signal and affecting the accuracy and reliability of the detection result. With the continuous development of signal processing technology, various denoising algorithms have emerged, such as traditional wavelet threshold denoising algorithm, variational mode decomposition algorithm, etc., which can to a certain extent, denoising processing of ultrasonic signal, but with the increasing requirement of detection accuracy and the increasing complexity of detection environment, it is difficult to evaluate the application effect of the algorithm in the actual detection.

[0003] At present, the performance evaluation of the denoising algorithm usually adopts some single indicators, such as signal-to-noise ratio (SNR), root mean square error (RMSE) and the like, which can reflect the denoising effect from a certain aspect, but cannot comprehensively evaluate the comprehensive performance of the denoising algorithm. For example, when considering the fidelity of the denoised signal, the noise suppression degree and the calculation efficiency of the algorithm and other factors, a single indicator is often difficult to meet the demand, and it is necessary to more comprehensively and accurately evaluate the comprehensive performance of the denoising algorithm to select the most suitable algorithm for application in the actual detection.

[0004] In view of the problem of incomplete performance evaluation of the denoising algorithm in the prior art, the application provides a comprehensive denoising performance evaluation method, which can evaluate the performance of the denoising algorithm from multiple dimensions, including but not limited to the waveform similarity, signal-to-noise ratio, root mean square error and the like of the denoised signal, and combines the radar chart to make the denoising effect of the denoising algorithm more intuitive, so as to provide a more scientific and accurate basis for selecting the optimal denoising algorithm, and meet the comprehensive requirements of the denoising algorithm performance for different actual detection needs. SUMMARY

[0005] When the present application uses the built high-energy nonlinear ultrasonic detection system to detect and implement quantitative characterization of micro-cracks on the surface of metal materials, the increase of micro-crack size will directly lead to the systematic reduction of the measurement accuracy of the nonlinear coefficient by noise signals. In view to this problem, the present application systematically optimizes the signal denoising algorithm: first, based on the early experimental data, a multi-working-condition denoising performance pre-screening mechanism based on error band analysis is constructed, then a radar chart is introduced as an evaluation tool for the comprehensive denoising effect of the signal denoising algorithm, the denoising effects of moving average method (MA), spectrum subtraction method (SS), short-time Fourier transform method (STFT), wavelet transform method (WT) and orthogonal matching pursuit algorithm (OMP) are compared, and finally the signal denoising algorithm with the best comprehensive performance is selected. On the basis of algorithm optimization, the quantitative mapping rule between the three-dimensional geometric parameters of micro-cracks and the relative nonlinear coefficient is analyzed by regression modeling, which effectively improves the significant level of the correlation between the relative nonlinear coefficient and the micro-crack size parameter, and provides high-confidence theoretical support for the quantitative nondestructive testing of micro-cracks in engineering practice. The main theoretical contents are as follows: In order to achieve the above purpose, the present application designs a nonlinear ultrasonic detection signal denoising algorithm comprehensive denoising performance evaluation method, which specifically includes the following steps: Step 1: Preparation before detection An ultrasonic nonlinear detection system is built, including an ultrasonic signal generator, an ultrasonic transducer, a signal acquisition system and a data analysis and processing system; the surface of the metal material to be detected is cleaned to ensure that the surface is flat and clean; the excitation frequency is selected and the excitation signal parameters are set, generally the frequency range is 1 MHz to 10 MHz.

[0006] Step 2: Micro-crack detection The ultrasonic transducer is placed in the wedge block, and the wedge block is tightly contacted with the material surface by applying coupling agent. The ultrasonic excitation card is used to apply excitation signal to the ultrasonic transducer, so that the ultrasonic wave propagates in the metal material; the receiving transducer is used to receive the ultrasonic signal propagating from the metal material, and the received signal data collected by the oscilloscope is imported into the computer through the U disk or data line, so as to obtain the received signal.

[0007] Step 3: Signal processing The noise-containing received signal collected in step 2 is imported into matlab, and codes are written according to the theoretical model of the noise reduction algorithm, and are calculated in turn by five kinds of noise reduction algorithms: in the moving average method, the original sequence is added to the odd window point by point to obtain the MA noise reduction result; in the spectral subtraction algorithm, the noise spectrum is estimated in the starting segment, the amplitude spectrum subtraction is performed according to the subtraction factor 1 and the spectrum bottom limit 0.02, and the SS result is obtained by IFFT reconstruction; in the short-time Fourier algorithm, the 50 μs Hanning window is segmented FFT, and the inverse transform is obtained after the noise threshold mask to obtain the STFT result; in the wavelet transform algorithm, the db4 wavelet is decomposed for four layers, and the adaptive soft threshold coefficient is reconstructed to give the WT result; in the orthogonal matching pursuit algorithm, the Gabor super-complete dictionary is iteratively selected to orthogonalize the atom, and the residual error is reduced to the threshold to obtain the OMP result. The signal is reduced according to the five kinds of noise reduction algorithms, and the received signals processed by the five kinds of noise reduction algorithms are saved.

[0008] Step 4: Noise reduction effect evaluation The data output by each algorithm is first calculated for the mean SNR, RMSE, NCC, and then the original distribution S, c, R, IQR is retained, a total of seven-dimensional indicators; after linear normalization, a radar chart is drawn, the same crack is compared in the same figure, the OMP polygon area is the largest, the SNR, S, c, R, IQR five items are the best, the NCC and RMSE are the second best, and the best noise reduction algorithm is determined according to the comprehensive performance. The core evaluation process is as follows: 1. Mean type index calculation For the signal-to-noise ratio SNR, the root mean square error RMSE, and the waveform similarity NCC, the stability of the algorithm is quantified by using the aggregation statistical method. Specifically, the arithmetic mean of the results processed by a single noise reduction algorithm in 20 experiments is obtained, and the mean value of SNR, RMSE and NCC is taken as the characterization index of the noise reduction performance of the algorithm.

[0009] 2. Statistical distribution type index processing For the four statistical characteristic parameters of variance S, dispersion coefficient c, range R, and interquartile range IQR, the original calculation results of 20 experimental data of a single noise reduction algorithm are retained, and the four statistical characteristic parameters are calculated based on these data.

[0010] 3. Data normalization and visualization strategy All indicators need to be linearly normalized before drawing the radar chart, mapping to the [0, 1] interval to eliminate dimensional differences. The SNR, RMSE, NCC nodes are the results of linear normalization of the mean of the corresponding indicators of 20 results after using the algorithm. The S, c, R, IQR nodes corresponding to the signal denoising algorithm are obtained by linearly normalizing the evaluation results of the data set of 20 repeated experiments using 5 signal denoising algorithms for a group of microcracks. Based on the above steps, the radar chart for performance evaluation of signal denoising algorithm using 5 signal denoising algorithms for a microcrack is drawn. Through multi-dimensional index comparison, quantitative evaluation of robustness and signal fidelity of the denoising algorithm can be realized.

[0011] In step 3, further comprising: moving average method (MA), spectral subtraction method (SS), short-time Fourier transform method (STFT), wavelet transform method (WT) and orthogonal matching pursuit algorithm (OMP) algorithm mathematical model, as follows: Moving average method (MA, Moving Average) is commonly used for long defect detection such as millimeter-level defect noise suppression in homogeneous materials such as steel plates, pipes, etc. In the field of online monitoring of equipment, moving average method can be used for real-time monitoring in vibration environment to quickly eliminate random interference of sensor acquisition signal. In the field of signal preprocessing, moving average method can be used as a pre-filter for advanced algorithms such as wavelet transform and EMD, reducing the complexity of subsequent algorithms.

[0012] The moving average method calculates the arithmetic mean of each data point and its adjacent points in the signal sequence by setting a fixed length interval containing an odd number of points, takes the result as the average value of the current point, and moves the window point by point to complete the whole signal processing. For the original detection signal , the window width is , and the signal after using the moving average method for denoising is:

[0013] In the formula, the parameter represents the half-width of the sliding window, represents the original signal sequence, and represents the original signal value at time point n, represents the data point position index of the current processing, and represents the relative position index in the sliding window.

[0014] Moving average method has the advantages of high computational efficiency, easy parameter adjustment and white noise suppression in signal processing. Its algorithm only needs simple addition, subtraction and division operations, and has excellent real-time processing performance, especially suitable for industrial online monitoring and other scenes with strict time effectiveness requirements; by adjusting the window width flexibly, a dynamic balance between noise suppression and signal fidelity can be achieved. However, this method also has obvious limitations: although the symmetric window design avoids phase shift, real-time processing still needs to wait for the window data to be filled, resulting in signal lag, which may affect the time domain positioning accuracy; if the window width is too large, the reflection wave characteristics of small defects are easily attenuated, resulting in loss of high-frequency details; in addition, its suppression effect on broadband structural noise caused by material lattice scattering is weak, and such scenes need to be combined with wavelet transform and other time-frequency analysis methods for joint noise reduction to make up for the deficiency. Since the signal moving average method requires the window width to be an odd number of data points, the sampling points need to be ensured to be an odd number of points when the signal is sampled subsequently.

[0015] Spectral subtraction (SS) is commonly used in scenes such as industrial workshops with stable background noise, which can eliminate fixed-frequency noise generated by motors, fans, etc. Secondly, it can be used for preprocessing in high signal-to-noise ratio scenes as a pre-filter for complex algorithms such as wavelet transform and neural networks. In addition, spectral subtraction can also be used for preliminary screening of thick-walled materials. In the detection of thick-walled parts such as pipes and castings, it can quickly suppress surface scattering noise.

[0016] For ultrasonic signals wherein, is the effective signal, is the noise, by calculating the amplitude spectrum of the noisy signal and the noise estimation spectrum , the frequency spectrum of the effective signal can be obtained as:

[0017] In the formula, is the subtraction factor (usually 1-2), is the spectral floor factor (usually 0.01-0.1). In the detection of micro-cracks in metal materials, is usually taken as , which can reduce the damage to the effective signal and preserve high-frequency components. Therefore, when introducing the algorithm to reduce noise in the signal subsequently, .

[0018] The spectral subtraction method has high calculation efficiency, only involves Fourier transform method and simple arithmetic operation, and is suitable for real-time processing. Secondly, it has strong hardware compatibility and can meet the real-time demand of industrial field detection for embedded devices. Finally, it can suppress steady-state noise and has a significant effect on eliminating fixed frequency interference in ultrasonic detection. However, spectral subtraction can cause random frequency point residual noise, which is manifested as a "tremolo" tail in the time domain. In addition, the use of noisy signal phase to reconstruct the signal directly by the spectral subtraction method leads to distortion of the phase information, which may affect the defect positioning accuracy, so the results of the spectral subtraction method need to be further evaluated.

[0019] The short-time Fourier transform method is commonly used for layered defect detection of layered materials, online detection systems and pulse echo mode detection. The short-time Fourier transform method divides the ultrasonic signal into multiple time-frequency segments by sliding time window, performs Fourier transform on each time-frequency segment, generates a time-frequency two-dimensional matrix to represent the local frequency characteristics of the signal, and then realizes noise reduction through noise estimation and spectral subtraction. The mathematical expression of the short-time Fourier transform method is:

[0020] In the formula, is the original time domain signal, is the time window function, is the time window center position, is the frequency, i is the imaginary unit, is the integral dummy variable, which represents the time variable inside the window function.

[0021] In signal processing, STFT selects the time period of the defect-free reflection, the initial segment of the signal is used to estimate the noise spectrum, then the noisy signal and the noise spectrum are compared to construct a soft threshold filter, and time-frequency conversion is realized; finally, inverse transform reconstruction is performed to retain the effective frequency band and perform inverse STFT to recover the time domain signal. In order to avoid spectral leakage, Hanning window is used for noise reduction; The short-time Fourier transform method can simultaneously locate the time domain position of transient defect reflection wave in ultrasonic signal and analyze its frequency domain characteristics through time-frequency joint analysis capability, and can adapt to the non-stationary scattering noise suppression requirement caused by anisotropy in composite material detection. The signal denoising algorithm based on Fourier transform has strong hardware compatibility in embedded systems such as ultrasonic flaw detector, and the calculation efficiency is significantly better than that of wavelet transform. However, due to the restriction of Heisenberg uncertainty principle, the fixed time window design of short-time Fourier transform leads to an inherent contradiction between the time resolution of high-frequency components and the resolution of low-frequency components, and the length of the window function needs to balance the noise suppression effect and signal fidelity. In addition, the edge effect caused by time window truncation further restricts its application in high-precision detection scenarios.

[0022] Wavelet Transform (WT) is often used for defect identification of thick-walled components such as nuclear power plant pipes. In the detection of interlaminar debonding of carbon fiber composite materials, the use of time-frequency localization characteristics can efficiently split overlapping signals, and has good effect on signal reconstruction.

[0023] The core mechanism of wavelet transform denoising is to implement multi-scale decomposition of time domain signals through the Mallat fast wavelet transform algorithm (MALLAT), and the key is that the wavelet coefficients corresponding to the noise are usually weaker than the wavelet coefficients of the effective signal components. By setting an appropriate threshold, the wavelet coefficient components below the threshold are filtered out, thereby retaining and reconstructing the target signal. This method separates noise by Figure 1 The process shown in the figure realizes noise separation, mainly including three core links of signal decomposition, threshold screening and coefficient reconstruction, and finally achieves the purpose of removing interference and retaining effective information.

[0024] The core implementation of wavelet transform depends on the joint action of the scale function and the wavelet function : the scale function is responsible for extracting the overall characteristics of the signal, while the wavelet function is used to capture the detailed characteristics. Through the multi-scale decomposition and reconstruction mechanism, the two achieve effective differentiation of signal characteristics and noise components, and finally complete noise suppression through threshold processing. The specific expressions are as follows:

[0025]

[0026] wherein, , is the scale function, , is the wavelet function, and parameters l and k adjust the time-frequency scale transformation characteristics and time dimension displacement characteristics of the wavelet respectively. When l takes different discrete integer values, it corresponds to different scale levels in the multi-resolution analysis framework, at which time the scale function and the wavelet function generate corresponding function subspaces respectively.

[0027] The actual effectiveness of wavelet threshold denoising mainly depends on the optimized configuration of the wavelet basis function, the threshold determination criterion and the threshold processing rule. As typical processing methods, hard threshold and soft threshold respectively realize the truncated retention or gradual compression of wavelet coefficients through nonlinear quantization operation, and their mathematical expressions are shown as follows. The corresponding coefficient distribution characteristics are shown in Figures 2(a) and 2(b), wherein the hard threshold keeps the effective coefficient amplitude unchanged, and the soft threshold further smooths the signal by introducing a shrinkage effect.

[0028]

[0029]

[0030] where, and are new wavelet coefficients after threshold processing, are original wavelet coefficients, is a threshold value, is a sign function, taking +1 when w>0, -1 when w<0, and 0 when w = 0.

[0031] In the noise reduction of ultrasonic testing signals for metal materials, Daubechies wavelet basis function combined with adaptive soft threshold strategy is often used to effectively separate structural noise and system noise. Daubechies wavelet is a class of orthogonal compactly supported wavelet proposed by mathematician Ingrid Daubechies. Its core feature is to be implicitly defined by filter coefficients of finite length, rather than explicit mathematical closed expression. The construction of this kind of wavelet (such as db2, db4, etc.) depends on low-pass filter coefficients and high-pass filter coefficients where, derived from the low-pass filter through the relationship is the wavelet order. The scaling function N and the wavelet function are generated by two-scale recursive equations:

[0032]

[0033] where, the support interval is strictly limited within , which can ensure the locality of calculation while avoiding the Gibbs phenomenon caused by global oscillation in the traditional Fourier transform method.

[0034] The core advantage of Daubechies wavelet lies in its orthogonality and high-order vanishing moments. Orthogonality makes the sub-band components after signal decomposition independent of each other, thus supporting lossless reconstruction; while N high-order vanishing moments (i.e. the wavelet function is zero for low-order polynomials ​The integral of the product of the derivative of the signal and the derivative of the wavelet is always zero, which enables it to sparsely represent piecewise smooth signals and effectively distinguish noise from real features. For example, in image denoising, high-order wavelets (such as db8) can improve smoothness by suppressing high-frequency noise, but may blur details; low-order wavelets (such as db2) are more suitable for preserving edge information, but their noise reduction capability is limited. Therefore, in the subsequent content of the invention, in order to improve the noise reduction capability of the algorithm while preserving as much detail as possible, db4 wavelet is used for noise reduction, which can well balance frequency localization and computational efficiency.

[0035] The orthogonal matching pursuit algorithm (OMP) is commonly used for metal material micro-defect detection, and can be well applied to the detection of sub-millimeter micro-cracks in aerospace aluminum alloy components by matching the transient impact echo characteristics of Gabor atoms. The OMP algorithm is a greedy algorithm based on the principle of signal sparse decomposition, which selects the atom (basis function) most related to the signal residual by iteration, and orthogonalizes the selected atoms, gradually approximating the sparse representation of the original signal to achieve noise reduction. The OMP algorithm can be represented as solving the following optimization problem:

[0036] In the formula, y is the noisy ultrasonic signal, A is the atom matrix, x is the sparse coefficient, is the maximum reconstruction error. In the specific use of the OMP algorithm, first select the atom with the largest inner product with the current residual from the super-complete atom library (such as the Gaussian atom library), to realize atom matching. Then update the residual by Gram-Schmidt orthogonalization to avoid redundant interference between atoms. Finally, stop the decomposition according to the preset sparsity or residual threshold.

[0037] In step 4, further comprising: for multi-dimensional evaluation of the comprehensive noise reduction performance of the signal denoising algorithm, researching and proposing a multi-dimensional index quantization evaluation system based on radar chart, introducing radar chart (Radar Chart) as a direct display of the comprehensive noise reduction performance of the signal denoising algorithm. As shown in the radar chart Figure 3 The radar chart, also known as spider chart or star plot, is a graphical form for visualizing multivariate data. Its core feature is to distribute multiple variables (dimensions) radially around a central point at equal angles, forming a polar coordinate system similar to a radar scan or spider web. The value of each variable extends from the center outward, and the data points are connected by a polyline to form a closed polygon, which directly displays the data distribution in different dimensions and the overall distribution characteristics.

[0038] Radar charts compress high-dimensional data into a two-dimensional plane, intuitively presenting overall performance and local differences, thus achieving comprehensive data visualization. By analyzing the polygon area and vertex positions of the radar chart, the quality of different objects can be quickly determined; furthermore, sharp or concave vertices in the radar chart can visually reflect extreme values, highlighting key features. Therefore, radar charts are highly suitable for comprehensively evaluating the denoising effect of signal denoising algorithms.

[0039] To systematically evaluate the comprehensive performance of different noise reduction algorithms in signal post-processing during nonlinear ultrasonic detection of microcracks, this invention constructs a multi-dimensional quantitative index system covering signal fidelity (signal-to-noise ratio). SNR Root mean square error RMSE Feature correlation (waveform similarity) NCC ), statistical stability (standard deviation) S Coefficient of Dispersion c Range R、 Interquartile range IQR There are a total of 7 core indicators. Each indicator is linearly normalized (normalization interval [0,1], where 1 represents optimal performance) to eliminate the impact of dimensional differences on the overall evaluation. By introducing radar charts as an evaluation tool, the limitations of traditional single-indicator comparisons can be overcome, comprehensively reflecting the algorithm's overall ability to suppress noise and maintain the stability of detection data.

[0040] For standard deviation S Coefficient of Dispersion c Range R Interquartile range IQR Signal-to-noise ratio (SNR) and other signal noise reduction metrics SNR Root mean square error RMSE Waveform similarity NCC Of these seven data fluctuation assessment indicators, signal-to-noise ratio (SNR) and waveform similarity (NCC) are positive indicators (the higher the better), while standard deviation... S Coefficient of Dispersion c Range R Interquartile range IQR and root mean square error RMSE All are negative indicators (the smaller the better). Positive and negative indicators need to be treated differently. The linear normalization treatments for positive and negative indicators are shown in the following equations:

[0041]

[0042] in, For data X The normalized result after normalization and These represent the maximum and minimum values ​​in the corresponding data set.

[0043] When drawing a radar chart, it is necessary to create a polar coordinate system based on the normalized results of different evaluation node indicators and draw the axis by dividing the angle equally according to the number of indicators. Then, standard scale is applied and the normalized values ​​are mapped. Finally, the data points of the same object are connected to form a closed polygon. Different objects are distinguished by color or line type to realize the drawing of the radar chart.

[0044] Currently, commonly used signal denoising algorithms for nonlinear ultrasonic nondestructive testing include moving average (MA), spectral subtraction (SS), wavelet transform (WT), short-time Fourier transform (STFT), and orthogonal matched pursuit (OMP), each with its own advantages and applicable scenarios. The signal-to-noise ratio (SNR) is generally used as the metric for evaluating the denoising performance of these algorithms. SNR ), root mean square error ( RMSE ) and waveform similarity ( NCC The evaluation will be conducted using [the following] criteria. Specific indicator definitions are as follows:

[0045]

[0046]

[0047] in, This indicates the original signal that the detection system has not processed by a signal denoising algorithm. This is the signal after applying a signal denoising algorithm.

[0048] The other four indicators are defined as follows: Standard Deviation S Standard deviation is a core indicator in statistics used to quantify the dispersion of data, characterizing the degree to which each observation in a data set deviates from the arithmetic mean. As the arithmetic square root of variance, standard deviation provides a direct measure of data volatility by eliminating dimensional differences. A larger value indicates a more dispersed data distribution, while a smaller value reflects that the data is more concentrated around the mean. The formula for the unbiased estimate of standard deviation after Bessel correction is as follows:

[0049] in, n For sample size, This is the average of the relative nonlinear coefficients obtained from multiple experiments on arbitrary microcracks. For the first i The relative nonlinear coefficient value obtained from the second test.

[0050] Coefficients of Dispersion of the Sample c The coefficient of variation, also known as the variance coefficient, is a dimensionless indicator used in statistics to measure the dispersion of data. It is defined as the sample standard deviation.S Ratio to the sample mean The mathematical expression is as follows:

[0051] The interquartile range is a robust statistic for describing the degree of dispersion of data, which is defined as the difference between the third quartile (Q3) and the first quartile (Q1), that is, Q Q3-Q1 Q IQR = Q Q3-Q1 Q Wherein, for a data set with data capacity N, Q1 is located at the 0.25(N+1) position, Q3 is located at the 0.75(N+1) position, and the difference can be calculated based on this to obtain Q1 and Q3, so as to obtain the interquartile range. n Q n Q n Q Q IQR

[0052] The range, also known as the full range, is the simplest indicator for describing the degree of dispersion of data, which is defined as the difference between the maximum value and the minimum value in the array, that is: R R=Max-Min R = X Max-Min max X min The advantages and beneficial effects of the present application are that: a signal denoising algorithm comprehensive performance evaluation method for nonlinear ultrasonic detection is proposed, a seven-dimensional index system covering signal-to-noise ratio, waveform similarity, root mean square error, standard deviation, dispersion coefficient, range and interquartile range is constructed, and radar chart is combined to realize visual and quantitative comparison of denoising efficiency of multiple algorithms, breaking through the limitations of traditional single index evaluation. The method system selects the optimal denoising algorithm (such as OMP), effectively improves the fidelity and stability of the nonlinear characteristic signal of micro-cracks, and significantly enhances the correlation strength between the size parameters and the relative nonlinear coefficient of micro-cracks. Experimental verification shows that the present application has good applicability and robustness in many types of components such as aluminum alloy plates and steel torsion shafts, providing reliable technical support for accurate identification and quantitative evaluation of micro-cracks under complex working conditions, and has wide engineering popularization value. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 Wavelet denoising signal processing flow.

[0054] Figure 2(a) is a hard threshold function.

[0055] ​​​​​​​​​​Fig. 2(b) is a soft threshold function.

[0056] Figure 3 for the radar chart example.

[0057] Figs. 4(a)-4(i) are comparative results after algorithm processing of the micro crack length detection experiment of the aluminum alloy flat plate.

[0058] Figs. 5(a)-5(i) are comparative results after algorithm processing of the micro crack width detection experiment of the aluminum alloy flat plate.

[0059] Figs. 6(a)-6(i) are comparative results after algorithm processing of the micro crack depth detection experiment of the aluminum alloy flat plate.

[0060] Figs. 7(a)-7(g) are comparative results after algorithm processing of the micro crack length detection experiment of the 45# steel torsion axial.

[0061] Figs. 8(a)-8(h) are comparative results after algorithm processing of the micro crack width detection experiment of the 45# steel torsion axial.

[0062] Figs. 9(a)-9(f) are comparative results after algorithm processing of the micro crack depth detection experiment of the 45# steel torsion axial.

[0063] Figs. 10(a)-10(g) are comparative results after algorithm processing of the micro crack length detection experiment of the 45# steel torsion axial.

[0064] Figs. 11(a)-11(h) are comparative results after algorithm processing of the micro crack width detection experiment of the 45# steel torsion axial.

[0065] Figs. 12(a)-12(f) are comparative results after algorithm processing of the micro crack depth detection experiment of the 45# steel torsion axial. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0067] Embodiment one: Take the 7075-T6 aluminum alloy plate micro-crack, torsion shaft axial micro-crack and torsion shaft circumferential micro-crack detection as an example, based on the nonlinear ultrasonic detection principle, the experimental metal material surface micro-crack nonlinear ultrasonic detection system is built, equipped with an ultrasonic excitation transducer with a center frequency of 2.5 MHz and an ultrasonic receiving transducer with a center frequency of 5 MHz. The excitation is set to a 10-cycle, 2.5 MHz sinusoidal wave signal, which is modulated by Hanning window to avoid spectrum leakage; set appropriate sampling rate, interval time.

[0068] A series of 7075-T6 aluminum alloy plate samples are prepared, which have different sizes of micro-crack features on the surface, and the size is 200mm(length l)×200mm(width w)×20mm(thickness h), and the micro-crack group is uniformly distributed on the surface of the plate sample in the form of 3×3 array. Among them, the corresponding research size of each row of micro-cracks increases from left to right, and the transverse and longitudinal micro-crack spacing is 50mm. For the length change micro-crack plate, the length of the micro-crack on it changes in the range of 1-9mm with 1mm step, while the width and depth are uniformly set to 0.5mm. When studying the width and depth parameters, the corresponding size value range is 0.1mm-0.9mm, and the incremental step is 0.1mm, at this time the length is 5mm and the other size is 0.5mm.

[0069] The ultrasonic transducer is installed on the wedge block, and the coupling is stable by applying a constant pressure on the wedge block through the tool; 20 times of repeated sampling are performed at the same position for each pre-made micro-crack, the trigger mode is set to "one-shot" pulse wave, and 10000 point data of the received wave band are stored; the original received signal collected in the experiment is saved into the industrial computer through USB acquisition.

[0070] The original received waveform of each micro-crack is sequentially imported into the same script in Matlab: first, 9-point window sliding average is used to get MA result; then, the first 250 points are used to estimate noise spectrum, and spectrum subtraction is completed with reduction factor 1 and spectrum bottom limit 0.02, and inverse Fourier transform is used to get SS result; then, 50μs Hanning window and 50% overlap are used for signal segmentation FFT, and inverse transform is used after masking with 1.2 times of noise mean, to get STFT result; then, db4 wavelet is decomposed for 4 layers, and WT result is obtained after general soft thresholding and reconstruction; finally, orthogonal matching pursuit is performed on Gabor super-complete dictionary with residual 5% as stopping criterion to obtain OMP result; the five results are saved as 10000-point sequences for subsequent index calculation.

[0071] In the evaluation of the noise reduction effect, according to the evaluation strategy proposed in the application, the original 2700 groups (27 micro-cracks x 20 times x 5 algorithms) of original data are compressed into three types of size parameter trend representation, the theoretical need to show a single aluminum alloy plate 9 micro-cracks corresponding to 900 groups of original data are compressed into a single graph presentation, and the error bandwidth and the stability of the noise reduction algorithm performance are preliminarily established by color coding. The SNR, RMSE and NCC of the same crack are calculated 20 times respectively and averaged, and the relative nonlinear coefficient sequence of 20 times is reserved for calculating the standard deviation, dispersion coefficient, range and quartile distance; after seven-dimensional index linear normalization [0, 1], the radar chart is drawn according to the polar coordinate 12 equal division axis, connected into a closed polygon and the area is calculated.

[0072] Based on the post-processing of the experimental results of the nonlinear ultrasonic detection of the micro-cracks on the aluminum alloy plate, the error band dynamic expansion of the four algorithms MA, SS, STFT and WT shows a strong nonlinear coupling relationship with the size change of the micro-cracks. When the length, width and depth of the micro-cracks on the surface of the 7075-T6 aluminum alloy plate increase from the size lower limit of the micro-crack samples in the experiment to the size upper limit, the error bandwidth of the four algorithms expands about (4.2-8.7) times, and at this time the error band expansion rate is positively correlated with the size of the micro-cracks, revealing the performance degradation phenomenon of the traditional noise reduction algorithm in the nonlinear ultrasonic detection of the micro-cracks on the surface of the plane metal component represented by the 7075-T6 aluminum alloy plate under strong noise interference. The mechanism is that the increase of the micro-crack size causes double negative effects: on the one hand, the increase of the micro-crack size leads to the expansion of the grain boundary scattering cross section, causing the increase of the grain distribution disorder degree and leading to the increase of the structural noise intensity; on the other hand, the increase of the micro-crack size leads to the further amplification of the micro-crack to the system noise, causing more noise to be mixed in the detection signal. The time-frequency non-stationary characteristics of this composite noise make it difficult for traditional time / frequency domain noise reduction methods to effectively separate the characteristic signal.

[0073] To comprehensively compare and evaluate the comprehensive noise reduction performance of the five algorithms introduced in the present application for the nonlinear ultrasonic detection of micro-cracks on the surface of aluminum alloy plates, based on the length, width and depth of the micro-cracks on the aluminum alloy plate, the signal reduction results obtained after the signal reduction are used to construct a seven-dimensional radar evaluation system covering signal fidelity, feature correlation and statistical stability. The radar charts for comparing the comprehensive noise reduction performance of each algorithm for the same micro-crack detection signal reduction are shown in Figures 4(a)-4(i), 5(a)-5(i) and 6(a)-6(i). Among them, Figures 4(a)-4(i) respectively represent the noise reduction effect of different algorithms for different lengths of micro-cracks when the length of the micro-crack increases from 1 mm to 9 mm; among them, Figure 4(a) is for a 1 mm long micro-crack, Figure 4(b) is for a 2 mm long micro-crack, Figure 4(c) is for a 3 mm long micro-crack, Figure 4(d) is for a 4 mm long micro-crack, Figure 4(e) is for a 5 mm long micro-crack, Figure 4(f) is for a 6 mm long micro-crack, Figure 4(g) is for a 7 mm long micro-crack, Figure 4(h) is for an 8 mm long micro-crack, and Figure 4(i) is for a 9 mm long micro-crack. Figures 5(a)-5(i) respectively represent the noise reduction effect of different algorithms for detecting different width micro-cracks when the width of the micro-crack increases from 0.1 mm to 0.9 mm; among them, Figure 5(a) is for a 0.1 mm long micro-crack, Figure 5(b) is for a 0.2 mm long micro-crack, Figure 5(c) is for a 0.3 mm long micro-crack, Figure 5(d) is for a 0.4 mm long micro-crack, Figure 5(e) is for a 0.5 mm long micro-crack, Figure 5(f) is for a 0.6 mm long micro-crack, Figure 5(g) is for a 0.7 mm long micro-crack, Figure 5(h) is for a 0.8 mm long micro-crack, and Figure 5(i) is for a 0.9 mm long micro-crack. Figures 6(a)-6(i) respectively represent the noise reduction effect of different algorithms for detecting different depth micro-cracks when the depth of the micro-crack increases from 0.1 mm to 0.9 mm; among them, Figure 6(a) is for a 0.1 mm long micro-crack, Figure 6(b) is for a 0.2 mm long micro-crack, Figure 6(c) is for a 0.3 mm long micro-crack, Figure 6(d) is for a 0.4 mm long micro-crack, Figure 6(e) is for a 0.5 mm long micro-crack, Figure 6(f) is for a 0.6 mm long micro-crack, Figure 6(g) is for a 0.7 mm long micro-crack, Figure 6(h) is for a 0.8 mm long micro-crack, and Figure 6(i) is for a 0.9 mm long micro-crack.

[0074] The visualization results of the above radar charts show that the OMP algorithm has good applicability for the nonlinear ultrasonic detection of micro-cracks on the surface of 7075-T6 aluminum alloy plates with different lengths, widths and depths used in the experiment. In the seven-dimensional index space, it forms a significant polygon, and the comprehensive performance index (the area of the radar chart polygon) is obviously the largest in the detection of the length, width and depth of the micro-cracks on the surface of the aluminum alloy plate, and the standard deviation S , the dispersion coefficientc , variance R , interquartile range IQR , signal-to-noise ratio improvement SNR The five parameters are basically optimal, only the waveform similarity of the signal denoising index NCC and the root mean square error RMSE The index is slightly inferior to the signal moving average method MA. In addition, in the variance S , coefficient of variation c and signal-to-noise ratio improvement SNR The normalized value of the OMP algorithm in the three evaluation indexes is the largest, which further confirms its good applicability to capture the nonlinear acoustic response caused by the size change of the surface micro-cracks of the plane type metal component represented by the 7075-T6 aluminum alloy plate, and can well filter out the system noise as Gaussian white noise and the material structure noise as random noise.

[0075] Based on quantitative analysis, the size-relative nonlinear coefficient relationship curve after denoising by the OMP algorithm shows significant optimization characteristics: the quadratic fitting determination coefficients of micro-crack length, width and depth with relative nonlinear coefficient are obviously improved, which again confirms the low volatility characteristics of the data after denoising and the effectiveness of the OMP algorithm in retaining the nonlinear characteristic signals in the nonlinear ultrasonic detection of the micro-cracks on the surface of the metal plate, making it an optimal solution with precision advantage and engineering applicability.

[0076] Example two: The surface axial micro-crack nonlinear ultrasonic detection of the curved surface type metal component represented by the 45 steel torsion shaft, the signal denoising algorithm efficiency comprehensive evaluation is carried out according to the nonlinear ultrasonic detection experimental results of the axial micro-cracks on the surface of the torsion shaft, the detection steps and methods are the same as case one, and the detection results are as follows: In order to comprehensively compare and evaluate the comprehensive noise reduction performance of the five algorithms introduced in the present application for the nonlinear ultrasonic detection of the surface axial micro-cracks of the 45 steel torsion shaft, based on the length, width and depth of the micro-cracks of the 45 steel torsion shaft surface axial micro-cracks, the detection signal noise reduction result index parameters are obtained, and the comprehensive noise reduction performance comparison radar chart of each algorithm for the same micro-crack detection signal noise reduction is drawn as shown in Figures 7(a)-7(g), 8(a)-8(h) and 9(a)-9(f). Among them, Figures 7(a)-7(g) respectively represent the noise reduction effect of different algorithms under different lengths of micro-cracks when the length of the micro-crack increases from 4mm to 10mm; among them, Figure 7(a) is a 4mm long micro-crack, Figure 7(b) is a 5mm long micro-crack, Figure 7(c) is a 6mm long micro-crack, Figure 7(d) is a 7mm long micro-crack, Figure 7(e) is an 8mm long micro-crack, Figure 7(f) is a 9mm long micro-crack, and Figure 7(g) is a 10mm long micro-crack; Figures 8(a)-8(h) respectively represent the noise reduction effect of different algorithms under different widths of micro-cracks when the width of the micro-crack increases from 0.15mm to 0.5mm; among them, Figure 8(a) is a 0.15mm long micro-crack, Figure 8(b) is a 0.2mm long micro-crack, Figure 8(c) is a 0.25mm long micro-crack, Figure 8(d) is a 0.3mm long micro-crack, Figure 8(e) is a 0.35mm long micro-crack, Figure 8(f) is a 0.4mm long micro-crack, Figure 8(g) is a 0.45mm long micro-crack, and Figure 8(h) is a 0.5mm long micro-crack; Figures 9(a)-9(f) respectively represent the noise reduction effect of different algorithms under different depths of micro-cracks when the depth of the micro-crack increases from 0.15mm to 0.4mm; among them, Figure 9(a) is a 0.15mm long micro-crack, Figure 9(b) is a 0.2mm long micro-crack, Figure 9(c) is a 0.25mm long micro-crack, Figure 9(d) is a 0.3mm long micro-crack, Figure 9(e) is a 0.35mm long micro-crack, and Figure 9(f) is a 0.4mm long micro-crack.

[0077] The visualization results of the above radar charts show that similar to the post-processing results of the detection signals of the 7075-T6 aluminum alloy flat plate micro-cracks, the OMP algorithm for the nonlinear ultrasonic detection of the surface axial micro-cracks of the 45 steel torsion shaft containing different lengths, widths and depths also shows strong adaptability, and is significantly better than other algorithms, and can also well filter out system noise and material structure noise in this application scenario. In addition, the adaptive atom selection mechanism of the OMP algorithm is still applicable in the nonlinear ultrasonic detection signal noise reduction of the surface axial micro-cracks of the 45 steel torsion shaft, and can always dynamically match the nonlinear harmonic components caused by the micro-cracks in the iteration process.

[0078] Based on the above analysis, the OMP algorithm can also be applied to the nonlinear ultrasonic testing of the axial micro-cracks on the surface of the curved metal component represented by the 45 steel torsion shaft.

[0079] Example three: The post-processing comparative data of the nonlinear ultrasonic testing results of the circumferential micro-cracks of the 45 steel torsion shaft show that the dynamic expansion of the error band of the MA, SS, STFT and WT algorithms is also strongly coupled with the change of the micro-crack size. The detection steps and methods are the same as in case one and case two, and the detection results are as follows: When the length, width and depth of the circumferential micro-cracks of the 45 steel torsion shaft are increased from the size lower limit to the size upper limit of the micro-crack samples in the experiment, the error band width of the four algorithms is expanded by about (4.6-13.5) times, and at this time the error band expansion rate is positively correlated with the micro-crack size. This phenomenon shows that the traditional noise reduction algorithm has obvious noise sensitivity characteristics in the nonlinear ultrasonic testing of the circumferential micro-cracks on the surface of the curvature structural component represented by the 45 steel torsion shaft, and its robustness will also be significantly degraded under strong background noise conditions.

[0080] In order to comprehensively evaluate the comprehensive applicability and stability of the five algorithms introduced in the application for the nonlinear ultrasonic detection of the circumferential micro-cracks on the surface of the curved metal member, the radar charts based on the experimental data post-processing results are shown in Figures 10(a)-10(g), 11(a)-11(h) and 12(a)-12(f). Among them, Figures 10(a)-10(g) respectively show the noise reduction effect of different algorithms under different lengths of micro-cracks when the micro-crack length increases from 4 mm to 10 mm; among them, Figure 10(a) is a 4 mm long micro-crack, Figure 10(b) is a 5 mm long micro-crack, Figure 10(c) is a 6 mm long micro-crack, Figure 10(d) is a 7 mm long micro-crack, Figure 10(e) is an 8 mm long micro-crack, Figure 10(f) is a 9 mm long micro-crack, and Figure 10(g) is a 10 mm long micro-crack; Figures 11(a)-11(h) respectively show the noise reduction effect of different algorithms for detecting different width micro-cracks when the micro-crack width increases from 0.15 mm to 0.5 mm; among them, Figure 11(a) is a 0.15 mm long micro-crack, Figure 11(b) is a 0.2 mm long micro-crack, Figure 11(c) is a 0.25 mm long micro-crack, Figure 11(d) is a 0.3 mm long micro-crack, Figure 11(e) is a 0.35 mm long micro-crack, Figure 11(f) is a 0.4 mm long micro-crack, Figure 11(g) is a 0.45 mm long micro-crack, and Figure 11(h) is a 0.5 mm long micro-crack; Figures 12(a)-12(f) respectively show the noise reduction effect of different algorithms for detecting different depth micro-cracks when the micro-crack depth increases from 0.15 mm to 0.4 mm; among them, Figure 12(a) is a 0.15 mm long micro-crack, Figure 12(b) is a 0.2 mm long micro-crack, Figure 12(c) is a 0.25 mm long micro-crack, Figure 12(d) is a 0.3 mm long micro-crack, Figure 12(e) is a 0.35 mm long micro-crack, and Figure 12(f) is a 0.4 mm long micro-crack.

[0081] Based on the visualization results of the above radar charts, it can be seen that the OMP algorithm also has good applicability for the nonlinear ultrasonic detection signal noise reduction of the 45 steel torsion shaft surface circumferential micro-cracks with different lengths, widths and depths used in the experiment, which is significantly better than other signal noise reduction algorithms, which will not be repeated here.

[0082] Combined with the radar chart of the signal denoising effect evaluation of the micro-crack detection on the surface of the 7075-T6 aluminum alloy flat plate and the micro-crack detection on the surface of the 45 steel torsion shaft obtained by the previous OMP algorithm for the experimental result processing and evaluation, it can be verified by the cross-piece that the OMP algorithm has the universal advantage in the nonlinear ultrasonic detection of the micro-crack on the surface of the metal component, which can not only ensure the stability of the data distribution after denoising, but also has significant comprehensive optimization performance in improving the signal quality, suppressing the noise interference and keeping the waveform structure consistency, and the synergistic improvement characteristics of the noise suppression effect and the signal guarantee ability are systematically verified. The algorithm shows strong adaptability to the component geometry, micro-crack size parameters and material properties, which is due to the adaptive feature extraction mechanism based on the K-SVD framework, which can effectively separate the micro-crack nonlinear response and multi-source noise in the time-frequency domain.

Claims

1. A method for evaluating the comprehensive denoising performance of a nonlinear ultrasonic detection signal denoising algorithm, characterized in that, The method comprises the following steps: Step 1: Pre-detection preparation An ultrasonic nonlinear detection system is built, including an ultrasonic signal generator, an ultrasonic transducer, a signal acquisition system and a data analysis and processing system; the surface of the metal material to be detected is cleaned to ensure that the surface is flat and clean; the excitation frequency is selected and the excitation signal parameters are set, and the selected frequency range is generally 1 MHz to 10 MHz; Step 2: Micro-crack detection The ultrasonic transducer is placed in the wedge block, and the wedge block is tightly contacted with the material surface by applying coupling agent; the ultrasonic transducer is excited by the ultrasonic excitation card to make the ultrasonic wave propagate in the metal material; the received signal data collected by the oscilloscope is imported into the computer through a U disk or a data line, and the received signal is obtained; Step 3: Signal processing The received signal containing noise collected in step 2 is imported into matlab, and codes are written according to the noise reduction algorithm model, and five kinds of noise reduction algorithms are calculated in turn: in the moving average method, the original sequence is added to the odd window point by point to obtain the noise reduction result of MA; in the spectral subtraction algorithm, the noise spectrum is estimated in the initial segment, and the amplitude spectrum subtraction is performed according to the subtraction factor 1 and the spectrum bottom limit 0.02, and the SS result is obtained by IFFT reconstruction; in the short-time Fourier algorithm, the signal is segmented by 50 μs Hanning window and FFT is performed, and the STFT result is obtained after inverse transformation after noise threshold masking; In the wavelet transform algorithm, the WT result is given after the self-adaptive soft threshold coefficient is reconstructed after four-layer decomposition of db4 wavelet; In the orthogonal matching pursuit algorithm, the atoms are orthogonalized by iteration in the Gabor super-complete dictionary, and the OMP result is obtained after the residual error is reduced to the threshold, and the received signal after the processing of the five kinds of noise reduction algorithms is saved; Step 4: Noise reduction effect evaluation The data output by each algorithm is first calculated for mean SNR, RMSE and NCC, and then the original distribution S, c, R and IQR are retained, and a total of seven-dimensional indexes are obtained; After linear normalization, a radar chart is drawn, and the same crack is compared with five kinds of noise reduction algorithms in the same chart to determine the best noise reduction algorithm in terms of comprehensive performance.

2. The method according to claim 1, wherein the method is characterized by: In step 3, further comprising: the moving average method calculates the arithmetic mean of each data point and its adjacent points in the signal sequence by setting a fixed length interval containing an odd number of points, takes the result as the average value of the current point, and moves the window point by point to complete the whole signal processing; for the original detection signal , the window width is , the signal after using the moving average method for noise reduction is : ； wherein the parameters denotes the half-width of the sliding window, denotes the original signal sequence, denotes the original signal value at time point n, denotes the data point position index currently processed, denotes a certain time point in the signal sequence, denotes the relative position index within the sliding window.

3. The method of claim 1, wherein the method further comprises: determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal; and determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 3, further comprising: in the spectral subtraction algorithm, for the ultrasound signal wherein, is the effective signal, is the noise, by calculating the noisy signal amplitude spectrum and the noise estimate spectrum the spectrum of the effective signal is obtained as: ； wherein is an over-reduction factor (usually taken as 1-2), is a spectral floor factor, in the case of micro-crack detection in metallic materials, taken as .

4. The method of claim 1, wherein the method further comprises: determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal; and determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 3, further comprising: the short-time Fourier transform method divides the ultrasonic signal into multiple time-frequency segments through a sliding time window, performs Fourier transform on each time-frequency segment, generates a time-frequency two-dimensional matrix to represent the local frequency characteristics of the signal, and then realizes noise reduction through noise estimation and spectral subtraction; the mathematical expression of the short-time Fourier transform method is: ； wherein is the original time domain signal, is a time window function, is the time window center position, is the frequency, i is the imaginary unit, is the integration dummy variable, representing the time variable inside the window function; In signal processing, STFT selects the time period of the defect reflection, the initial segment of the signal is used to estimate the noise spectrum, then the noise signal and the noise spectrum are compared, a soft threshold filter is constructed, time-frequency conversion is realized, and finally inverse transformation reconstruction is performed, the effective frequency band is retained, and inverse STFT is performed to recover the time domain signal; in order to avoid spectral leakage, Hanning window is used for noise reduction; The short-time Fourier transform method realizes the time-frequency joint analysis in signal noise reduction, synchronously locates the time domain position of the transient defect reflection wave in the ultrasonic signal, and analyzes the frequency domain characteristics.

5. The method of claim 1, wherein the method further comprises: determining the performance of the nonlinear ultrasonic detection signal denoising algorithm based on the signal-to-noise ratio of the denoised signal. In step 3, further comprising: wavelet transform method depends on scale function and wavelet function : scale function is responsible for the general features of the signal, wavelet function is used to capture the details; both through multi-scale decomposition and reconstruction mechanism, the signal characteristics and noise components are distinguished, and finally the noise suppression is completed through threshold processing; the specific expressions are as follows: ； ； wherein , is a scaling function, , is a wavelet function, parameters l and k adjust the time-frequency scaling transform property and the time dimension displacement property of the wavelet respectively; when l takes different discrete integer values, corresponding to different scale levels in the multi-resolution analysis framework, the scaling function and the wavelet function generate corresponding function subspaces respectively.

6. The method of claim 5, wherein the method further comprises: determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal; and determining the signal-to-noise ratio of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. Wavelet threshold de-noising depends on the optimal configuration of wavelet basis function, threshold decision criterion and threshold processing rule; hard threshold and soft threshold respectively realize the truncated reservation or gradual compression of wavelet coefficients through nonlinear quantization operation, and the mathematical expressions are as follows; among them, the hard threshold keeps the effective coefficient amplitude unchanged, and the soft threshold further smooths the signal by introducing shrinkage effect; ； ； wherein and is a new wavelet coefficient after threshold processing, is an original wavelet coefficient, is a threshold value, is a sign function, taking +1 when w > 0, -1 when w < 0, and 0 when w = 0. In the noise reduction of ultrasonic testing signal for metal material, the Daubechies wavelet base function is combined with the adaptive soft threshold strategy to separate the structural noise and the system noise, wherein, Through the relationship From the low-pass filter, N is the wavelet order; the scale function and the wavelet function is generated by the two-scale recursive equation: ； ； wherein the support interval is defined by in the range.

7. The method of claim 1, wherein the method further comprises: determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal; and determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 3, further comprising: the orthogonal matching pursuit algorithm OMP algorithm is expressed as solving the optimization problem as follows: ； where y is the noisy ultrasound signal, A is the dictionary of atoms, x is the sparse coefficients, is the maximum reconstruction error; in operation, first, the atom with the largest inner product with the current residual is selected from the overcomplete atom library, realizing atom matching; then the residual is updated by Gram-Schmidt orthogonalization; finally, decomposition is stopped according to the preset sparsity or residual threshold.

8. The method of claim 1, wherein the method further comprises: determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal; and determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 4, further comprising: for standard deviation S , coefficient of dispersion c , range R , interquartile range IQR and signal noise reduction index signal-to-noise ratio SNR , root mean square error RMSE , waveform similarity NCC These 7 data fluctuation evaluation indexes, signal-to-noise ratio SNR and waveform similarity NCC are positive indexes, the larger the better; while standard deviation S , coefficient of dispersion c , range R , interquartile range IQR and root mean square error RMSE are negative indexes, the smaller the better, and the positive and negative indexes need to be distinguished and processed; the linear normalization processing of the positive and negative indexes is shown in the following formula respectively: ； ； wherein, is data X is the normalized result after normalization, and are the maximum and minimum values in the corresponding data set, respectively. When drawing the radar chart, it is necessary to create a polar coordinate system based on the normalized results of different evaluation node indicators and draw the axis according to the number of indicators, then standardize and map the normalized values, and finally connect the data points of the same object to form a closed polygon, and different objects are distinguished by color or line type to realize the drawing of the radar chart.

9. The method of claim 1, wherein the method further comprises: determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal; and determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 4, further comprising: using signal-to-noise ratio for evaluating the noise reduction effect evaluation index of the signal noise reduction algorithm SNR , root mean square error RMSE and waveform similarity NCC to evaluate, and the specific index definitions are as follows: ； ； ； wherein, represents the original signal detected by the detection system without processing by the signal denoising algorithm, is the signal after the signal denoising algorithm has been used.

10. The method of claim 1, wherein the method further comprises: determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal; and determining a signal-to-noise ratio (SNR) of the nonlinear ultrasonic detection signal after the nonlinear ultrasonic detection signal is processed by the nonlinear ultrasonic detection signal noise reduction algorithm. In step 4, further comprising four other evaluation indicators: The unbiased estimation standard deviation formula after Bessel correction is as follows: ； wherein, n is the sample volume, is the average of the relative nonlinearity coefficients obtained from multiple experiments for any microcrack, is the relative nonlinearity coefficient value obtained from the nth test, i is the relative nonlinearity coefficient value obtained from the nth test. coefficient of dispersion of a sample c Also known as the coefficient of variation, defined as the sample standard deviation S divided by the sample mean The mathematical expression is as follows: ； The interquartile range is a robust statistic that describes the dispersion of data, defined as the difference between the third quartile Q 3 and the first quartile Q 1, i.e. IQR = Q 3- Q 1 wherein, for a data set with data capacity n , Q 1 is located at the 0.25( n +1) position, Q 3 is located at the 0.75( n +1) position, difference calculation is performed to obtain Q 1 and Q 3, thereby obtaining interquartile range IQR ; range R is the difference between the maximum and minimum values in an array, i.e.: R = X max - X min。

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