S-G filtering ultrasonic signal noise reduction method based on nonlinear least square method guidance

Abstract

The invention relates to an S-G filtering ultrasonic signal noise reduction method, in particular to an S-G filtering ultrasonic signal noise reduction method based on nonlinear least square method guidance. The invention aims to solve the problem of effective signal distortion possibly existing in an ultrasonic signal noise reduction process. The method comprises the following steps of: 1, performing nonlinear least square waveform fitting processing; 2, performing multi-scale grading and reference signal guide regularization; and step 3, implementing multi-scale adaptive S-G filtering. The invention belongs to the technical field of ultrasonic signal noise reduction.

Description

Technical Field

[0001] This invention relates to an SG-filtered ultrasonic signal noise reduction method, belonging to the field of ultrasonic signal noise reduction technology. Background Technology

[0002] Ultrasonic nondestructive testing (NDT) technology, due to its high resolution, strong penetration, and non-destructive nature, is widely used in engineering fields with high reliability requirements, such as aerospace, nuclear industry, and energy equipment. In the service condition assessment of engineering components, time-of-flight (TOF), as a crucial parameter in ultrasonic testing, directly reflects material stress, thickness, and other characteristics, playing a vital role in quantitative assessment. However, the accuracy of TOF is highly dependent on the quality of the acquired signal; especially when the signal waveform is incomplete or subject to noise interference, the measurement results can be severely affected. Therefore, improving the quality of ultrasonic signals, and thus enhancing the accuracy of TOF measurements, is a key step in achieving accurate identification of the final condition of engineering materials.

[0003] However, the quality of ultrasonic signals from coarse-grained materials (such as austenitic stainless steel) faces significant challenges. The coarse grain structure within these materials generates strong scattering noise (called grain scattering noise), severely interfering with or even drowning out the effective wave packets in the acquired signal. The spectral characteristics of this noise highly overlap with the typical operating bandwidth (1-10 MHz) of ultrasonic transducers and persist even in repeated measurements. This renders traditional denoising methods such as time averaging or linear filtering ineffective, failing to improve the signal-to-noise ratio of the acquired signal and leading to errors in Time-of-Flight (TOF) estimation. Therefore, researching effective particle noise removal techniques has become a crucial step in improving the quality of ultrasonic signals and the accuracy of TOF measurements in the detection of coarse-grained materials.

[0004] Chinese patent application CN112147226B discloses a method for determining the optimal decomposition level for laser ultrasonic signals using wavelet denoising. This method proposes a technique for determining the optimal decomposition level of laser ultrasonic signals based on wavelet entropy. First, it acquires ultrasonic signals through laser excitation and reception and performs time-domain averaging. Then, it uses the dmey wavelet basis function to perform layer-by-layer wavelet decomposition of the signal and determines the optimal decomposition level by comparing the wavelet entropy of adjacent decomposition levels. This method can adaptively determine the optimal decomposition level for the characteristics of each ultrasonic signal, thereby achieving better denoising performance. However, this method may have limited ability to preserve signal details in complex noise backgrounds, and the choice of wavelet basis function has a significant impact on the denoising effect, lacking a more refined mechanism for balancing noise suppression and signal fidelity.

[0005] Chinese patent application CN119397174A discloses a method and system for denoising and enhancing nonlinear ultrasonic detection signals. This method decomposes the nonlinear ultrasonic signal using CEEMDAN and classifies and integrates intrinsic mode components (IMFs) using sample entropy. Subsequently, variational mode decomposition is performed on the integrated components to obtain new IMFs. These IMFs are divided into training and test sets and input into a gated recurrent unit (GRU) model for training, ultimately achieving denoising and feature enhancement of the nonlinear ultrasonic signal. This method can effectively reduce noise interference in concrete damage detection and enhance nonlinear features.

[0006] However, this method relies on complex signal decomposition and machine learning models, which may have shortcomings such as long model training time, sensitivity to initial parameters, and insufficient robustness when dealing with non-stationary and nonlinear signals. Summary of the Invention

[0007] To address the potential problem of effective signal distortion during ultrasonic signal denoising, this invention proposes an SG-filtered ultrasonic signal denoising method guided by nonlinear least squares.

[0008] The technical solution adopted by the present invention to solve the above problems is as follows: The steps of the present invention include: Step 1: Nonlinear least squares waveform fitting processing; Step 2: Multi-scale hierarchical classification and reference signal-guided regularization; Step 3: Implement multi-scale adaptive SG filtering.

[0009] Furthermore, step 1 specifically includes: benchmark model The model is as follows: (1), In formula (1), the parameter vector These represent signal amplitude, wave packet center time, pulse width, angular frequency, and phase, respectively. Given a set of time sampling points Corresponding original signal value Its goal is to find the best estimate of the model parameters. This makes the baseline model function Compared with the original data To minimize the sum of squared errors between them, define the error function vector. , its first Each component is Minimize the objective function That is, the sum of squares of the error vector: (2), Searching for Minimize parameters In each iteration, the LM algorithm estimates the parameters based on the current parameters. Calculate the step size for updating a parameter The update step size is obtained by solving a system of linear equations: (3), In formula (3), It is the error function vector Regarding parameter vectors At the current estimate The Jacobian matrix at the location, whose elements are ; This is the current error vector; It is the identity matrix; It is the damping coefficient, which is adaptively adjusted based on the effect of each iteration, balancing the fast convergence of the Gauss-Newton method and the global convergence of the gradient descent method, by iteratively updating the parameters. The process continues until the convergence criterion is met, at which point the optimal parameter estimate is finally obtained. The final reference signal can then be constructed. Its expression is: (4).

[0010] Furthermore, step 2 specifically includes: For the original signal Discrete wavelet transform is performed to achieve multi-scale decomposition. The 'db4' wavelet basis function is used to decompose the signal into appropriate levels. The coefficients obtained from the decomposition include the scale coefficients at the lowest resolution. and detail coefficient sequences at various scales Combinations: (5), In formula (5), It is the scaling factor. These are wavelet coefficients. and These are the scaling function and the wavelet function, respectively. Random noise is mainly concentrated in the detail coefficients at higher scales. ; Use a soft thresholding function for detail coefficients at each scale Application threshold The processed coefficients are obtained. : (6), (7), In formulas (6) and (7), The additional scaling factor is the signal length. Enhance high-frequency noise suppression, pass Robust estimation is performed, and after thresholding, a multi-scale coefficient set is obtained. Introducing baseline-guided multi-scale regularization; The reference waveform obtained by the nonlinear least squares method Perform DWT of the same order to obtain the corresponding coefficient set. By calculating the energy weights of the reference waveform at each scale: (8), The energy weights of the lowest frequency scaling coefficients are as follows: (9), Perform a least squares operation with regularization in the coefficient domain to ensure that the processed coefficients are close to the threshold result without deviating excessively from the baseline: (10) In formula (10), Represents the original scaling coefficients unaffected by the threshold; regularization parameter By controlling the strength of the baseline prior, this optimization problem has an explicit analytical solution: (11), The method described above yielded the following results. and The low-frequency scaling coefficients will shift towards the reference waveform, while the high-frequency detail coefficients will retain the characteristics after thresholding.

[0011] Furthermore, step 3 specifically includes: Directly in the wavelet coefficient domain for each coefficient sequence Applying an adaptive SG filter, the window length of the SG filter It is adaptive, dynamically adjusting based on the characteristics of the original signal or the pre-processed signal, limiting the window length to a safe range: (12) In formula (12), The length of the SG filter window. For dynamic range, The standard deviation of noise. To regulate A linear ratio between the coefficient sequence and the window length. The filtered sequence is obtained by applying the SG filter. Take a third-order polynomial, for the window size The smoothing value for each coefficient is: (13) In formula (13), the weights Derived from local least squares fitting, after filtering at each scale, the following is obtained: Perform inverse wavelet transform to reconstruct the time-domain signal, and obtain the reconstructed signal. : (14) right A uniform filter with a small window is applied for final smoothing. The final output of the algorithm is obtained. The signal that completes noise reduction: (15).

[0012] This invention constructs the required reference waveform model by employing a nonlinear least squares method for optimization. This allows for the capture of several ultrasonic echoes required for stress measurement. Combined with physical constraints, the construction of the reference signal effectively avoids overfitting and ensures the complete preservation of valid signal echoes.

[0013] However, the reference signal obtained by NLS fitting is a parameterized ideal waveform (such as a Gaussian-modulated cosine waveform). Although it can capture the general shape and location of the main echoes, it may differ from the ideally denoised echoes in local details and precise waveform. This difference can still affect the accuracy of subsequent envelope extraction. Therefore, further filtering is needed to obtain a more accurate waveform shape. The beneficial effects of this invention are: 1. Compared with other conventional noise reduction methods, this invention extracts a physically meaningful reference waveform through nonlinear least squares waveform fitting (NLS) to provide a correction reference for subsequent filtering. This not only effectively removes highly non-Gaussian particulate noise, but also avoids signal distortion caused by blind noise reduction, and preserves the characteristics and details of the original signal to the maximum extent, ensuring the integrity and accuracy of the signal. 2. This invention introduces multi-scale regularization guided by a reference waveform. In the wavelet decomposition process, this invention uses the time-frequency characteristics of the reference waveform as physical prior information, which allows the low-frequency scale coefficients to shift towards the reference waveform, effectively correcting low-frequency drift. At the same time, the high-frequency detail coefficients are denoised by soft thresholding, eliminating noise, thus preserving the transient characteristics of the signal while denoising. 3. This invention directly applies multi-scale adaptive Savitzky-Golay (SG) filtering in the wavelet coefficient domain. By dynamically adjusting the window length of the SG filter according to the signal characteristics, this method can better adapt to the local characteristics of the signal, effectively preserve the peak features and edge information of the signal while smoothing noise, avoid the limitations of traditional SG filters in signal edge processing, and improve the noise reduction effect and signal fidelity. Attached Figure Description

[0014] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of a two-dimensional axisymmetric finite element model; Figure 3 This is a diagram demonstrating the noise reduction effect of the MARSG-NLS method; Figure 4 This is a schematic diagram comparing the structures before and after noise reduction. Detailed Implementation

[0015] Example The experiment used a GH4742 nickel-chromium-cobalt high-temperature alloy cylindrical specimen, with a precisely measured reference length of 65.00 mm. The experimental system consisted of a Tektronix AFG31000 series arbitrary function generator, an Aigtek ATA-2041 signal amplifier, a Tektronix MSO64B mixed-signal oscilloscope, a piezoelectric ceramic transducer, and a central processing unit equipped with an Intel i7-11th generation processor.

[0016] During operation, the GH4742 cylindrical specimen is placed horizontally, and the excitation transducer and receiving transducer are tightly attached to the two end faces of the specimen using acoustic coupling agent. The host control signal generator generates a Gaussian-modulated cosine pulse, which is converted into ultrasonic waves by the excitation transducer and penetrates the specimen. A five-cycle Gaussian-modulated cosine function, with a modulated signal center frequency of approximately 1.22 MHz, is used to simulate the excitation signal used in the actual experiment. The specific expression is as follows:

[0017] The receiving transducer captures the transmitted signal, which is then amplified by a signal amplifier and acquired and digitized by a mixed-signal oscilloscope to obtain a raw time-domain signal containing strong scattering noise.

[0018] After acquiring the original signal, the MARSG-NLS noise reduction algorithm proposed in this invention is executed on the host computer. The specific processing steps are as follows: The first step is to perform nonlinear least squares (NLS) waveform fitting. The acquired noisy signal is used as the algorithm input, and a Gaussian-modulated cosine wave function is defined. As the physical model for fitting, the Levenberg-Marquardt (LM) iterative optimization algorithm is used to solve for the parameter vector θ that minimizes the sum of squared errors between the model waveform and the original signal data. After this process, a noise-free reference signal waveform is generated. This waveform reflects the ideal shape of the main echo components in the original signal.

[0019] The second step involves performing multi-scale decomposition and reference signal-guided regularization. This is done by comparing the original noisy signal with the reference signal generated in the previous step. Discrete wavelet transform (DWT) was performed using the 'db4' wavelet basis. First, a soft thresholding function was applied to the high-frequency detail coefficient sequence after decomposition of the noisy signal for initial denoising. Then, a reference signal was used... The wavelet coefficients are used to perform guided correction on the low-frequency scaling coefficients of noisy signals. This correction is achieved by solving a least-squares optimization problem with regularization terms, with the goal of making the processed low-frequency coefficients closer to the corresponding coefficients of the reference signal while retaining their own characteristics, so as to correct the low-frequency drift caused by noise.

[0020] The third step is to implement multi-scale adaptive SG filtering (MARSG). This step is performed directly in the wavelet coefficient domain. For each scale coefficient sequence after regularization correction (including low-frequency scale coefficients and high-frequency detail coefficients at each level), an adaptive Savitzky-Golay (SG) filter is applied. The window size of this filter is dynamically adjusted, automatically selecting the optimal window size based on the local characteristics of the current coefficient sequence (such as smoothness or abrupt changes). A larger window is used for strong smoothing in regions with gentle coefficient changes, while a smaller window is used to preserve details in regions with drastic coefficient changes (corresponding to the edges of the echo).

[0021] The fourth step is signal reconstruction and parameter calculation. All wavelet coefficients after MARSG filtering are reconstructed using inverse discrete wavelet transform (IDWT) to obtain the final denoised time-domain signal. The waveform of the signal exhibits a clear and well-defined echo packet.

[0022] Finally, to calculate the specimen length, the noise-reduced signal was analyzed. The Hilbert transform is applied to extract the envelope. Two adjacent sharp echo peaks are identified from the envelope, and the time difference between these two peaks is precisely measured and denoted as the time of flight (TOF). Based on the physical properties of the GH4742 material (elastic modulus E≈201GPa, density ρ≈8230kg / m3), the longitudinal wave velocity c≈4940m / s is calculated. The measured TOF value and the sound velocity c are substituted into the length calculation formula. After multiple measurements and averaging, the final calculated length of the specimen was 65.21 mm, with an actual length error of only 0.32%. This demonstrates higher accuracy in the actual length measurement of coarse-grained material specimens. This example not only verifies the optimization effect of the MARSG-NLS method on the measurement accuracy of parameters such as length or thickness in the context of particle noise, but also proves the feasibility of this method in industrial environments.

[0023] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for denoising ultrasonic signals using SG filtering guided by nonlinear least squares, characterized in that, The specific steps include: Step 1: Nonlinear least squares waveform fitting processing; Step 2: Multi-scale hierarchical classification and reference signal-guided regularization; Step 3: Implement multi-scale adaptive SG filtering.

2. The ultrasonic signal noise reduction method based on nonlinear least squares guided by the SG filter according to claim 1, characterized in that, Step 1 specifically includes: benchmark model The model is as follows: （1）， In formula (1), the parameter vector These represent signal amplitude, wave packet center time, pulse width, angular frequency, and phase, respectively. Given a set of time sampling points Corresponding original signal value Its goal is to find the best estimate of the model parameters. This makes the baseline model function Compared with the original data To minimize the sum of squared errors between them, define the error function vector. , its first Each component is Minimize the objective function That is, the sum of squares of the error vector: （2）， Searching for Minimize parameters In each iteration, the LM algorithm estimates the parameters based on the current parameters. Calculate the step size for updating a parameter The update step size is obtained by solving a system of linear equations: （3）， In formula (3), It is the error function vector Regarding parameter vectors At the current estimate The Jacobian matrix at position is composed of elements. ; This is the current error vector; It is the identity matrix; It is the damping coefficient, which is adaptively adjusted based on the effect of each iteration, balancing the fast convergence of the Gauss-Newton method and the global convergence of the gradient descent method, by iteratively updating the parameters. The process continues until the convergence criterion is met, at which point the optimal parameter estimate is finally obtained. The final reference signal can then be constructed. Its expression is: （4）。 3. The ultrasonic signal noise reduction method based on nonlinear least squares guided by the SG filter according to claim 1, characterized in that, Step 2 specifically includes: For the original signal Discrete wavelet transform is performed to achieve multi-scale decomposition. The 'db4' wavelet basis function is used to decompose the signal into appropriate levels. The coefficients obtained from the decomposition include the scale coefficients at the lowest resolution. and detail coefficient sequences at various scales Combinations: （5）， In formula (5), It is the scaling factor. These are wavelet coefficients. and These are the scaling function and the wavelet function, respectively. Random noise is mainly concentrated in the detail coefficients at higher scales. ; Use a soft thresholding function for detail coefficients at each scale Application threshold The processed coefficients are obtained. : （6）， （7）， In formulas (6) and (7), The additional scaling factor is the signal length. Enhance high-frequency noise suppression, pass Robust estimation is performed, and after thresholding, a multi-scale coefficient set is obtained. Introducing baseline-guided multi-scale regularization; The reference waveform obtained by the nonlinear least squares method Perform DWT of the same order to obtain the corresponding coefficient set. By calculating the energy weights of the reference waveform at each scale: （8）， The energy weights of the lowest frequency scaling coefficients are as follows: （9）， Perform a least squares operation with regularization in the coefficient domain to ensure that the processed coefficients are close to the threshold result without deviating excessively from the baseline: （10） In formula (10), Represents the original scaling coefficients unaffected by the threshold; regularization parameter By controlling the strength of the baseline prior, this optimization problem has an explicit analytical solution: （11）， The method described above yielded the following results. and The low-frequency scaling coefficients will shift towards the reference waveform, while the high-frequency detail coefficients will retain the characteristics after thresholding.

4. The ultrasonic signal noise reduction method based on nonlinear least squares guided by the SG filter according to claim 1, characterized in that, Step 3 specifically includes: Directly in the wavelet coefficient domain for each coefficient sequence Applying an adaptive SG filter, the window length of the SG filter It is adaptive, dynamically adjusting based on the characteristics of the original signal or the pre-processed signal, limiting the window length to a safe range: （12）， In formula (12), The length of the SG filter window. For dynamic range, The standard deviation of noise. To regulate A linear ratio between the coefficient sequence and the window length. The filtered sequence is obtained by applying the SG filter. Take a third-order polynomial, for the window size The smoothing value for each coefficient is: （13）， In formula (13), the weights Derived from local least squares fitting, after filtering at each scale, the following is obtained: Perform inverse wavelet transform to reconstruct the time-domain signal, and obtain the reconstructed signal. : （14）， right A uniform filter with a small window is applied for final smoothing. The final output of the algorithm is obtained. The signal that completes noise reduction: （15）。

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