A denoising optimization method based on wavelet basis and dynamic adaptive threshold

Abstract

The application discloses a denoising optimization method based on a wavelet base and a dynamic adaptive threshold, and comprises the following steps: step S1: obtaining a DAS-Morlet wavelet base function based on a DAS signal and a Morlet wavelet base; step S2: after a dynamic threshold decision model is constructed based on channel statistics, performing dynamic threshold processing on the DAS-Morlet wavelet signal; and step S3: performing multi-scale fusion on the DAS-Morlet wavelet signal processed by the threshold by adopting a progressive residual model, and outputting a reconstructed DAS signal. The DAS-Morlet wavelet signal is formed by adopting the Morlet wavelet base combined with the DAS characteristics, the dynamic threshold decision model based on the channel statistics is used to perform dynamic threshold processing on the DAS-Morlet wavelet signal, and the progressive residual model is introduced, so that the accuracy of the reconstructed DAS signal is improved.

Description

Technical Field

[0001] This invention relates to the field of signal denoising technology, and in particular to a denoising optimization method based on wavelet basis and dynamic adaptive threshold. Background Technology

[0002] Pipeline transportation, as an efficient long-distance transport method for fluid media, has gradually become an indispensable means of transportation in modern industrial production in many countries due to its multiple advantages such as economy, convenience, safety, and reliability. Tailings, as an inevitable product of the mineral processing plant's separation process, need to be processed into slurry through specific treatments before being transported to tailings ponds for storage and filling. Compared with traditional road, rail, and waterway transportation modes, pipeline transportation, with its unique adaptability, has become an ideal choice for transporting tailings slurry in mineral processing plants. Therefore, monitoring the transportation safety of tailings pipelines is essential and important.

[0003] Traditional methods such as mean filtering do not achieve good results, while deep learning methods are often uninterpretable, making it difficult to understand high-dimensional and deep models, which also require large amounts of data to implement. Models with prior knowledge often perform better, making this a popular research direction. However, when applied to the processing and analysis of DAS signals in tailings pipelines, the following problems still exist: 1. The wavelet kernel is used for feature extraction, without specific analysis and modification for particular situations. Appropriate wavelet basis functions need to be selected, as some wavelet basis functions, such as Lap... 1. The presence of exponential components in wavelet bases such as Lace can lead to significant differences in the distribution of wavelet values; 2. Hard thresholds are discontinuous, while soft thresholds often result in overly smooth signals, especially at high frequencies, leading to loss of detail. This characteristic makes it difficult to separate noise components when dealing with complex noise or non-stationary signals; 3. The DAS distributed fiber optic acoustic vibration system has a real-time acquisition rate of up to 100Mbps, and can acquire tens of thousands of acoustic signals in a single measurement, forming a high-density data matrix. This results in a massive amount of data, requiring specific processing to accelerate the processing capabilities of signal processing algorithms.

[0004] In summary, while wavelet analysis, as a feature extraction method, has certain advantages in current DAS signal processing, it also has some problems. First, the selection of the wavelet kernel needs to be analyzed and modified according to specific situations. Second, in terms of thresholding, the discontinuity of hard thresholding and soft thresholding may lead to excessive signal smoothing, especially when processing high-frequency signals, which can easily result in the loss of details. This makes it difficult to effectively separate noise components in complex noise and non-stationary signal processing. In addition, in practical applications, DAS faces such a large amount of data, requiring specific processing to improve the denoising capability of the signal processing algorithm. Therefore, to solve the above problems, a denoising optimization method based on wavelet basis and dynamic adaptive thresholding is proposed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a denoising optimization method based on wavelet basis and dynamic adaptive threshold. It uses Morlet wavelet basis combined with DAS features to form DAS-Morlet wavelet signal, performs dynamic threshold processing on DAS-Morlet wavelet signal based on dynamic threshold decision model of channel statistics, and introduces asymptotic residual model to improve the accuracy of DAS signal reconstruction.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a denoising optimization method based on wavelet basis and dynamic adaptive threshold, comprising the following steps: Step S1: Based on the DAS signal combined with the Morlet wavelet basis, obtain the DAS-Morlet wavelet basis function; Step S2: Construct a dynamic threshold decision model based on channel statistics, and perform dynamic threshold processing on the DAS-Morlet wavelet signal; Step S3: Use an asymptotic residual model to perform multi-scale fusion on the threshold-processed DAS-Morlet wavelet signal, and output the reconstructed DAS signal.

[0007] Preferably, the DAS-Morlet wavelet basis function is represented by the following equation:

[0008]

[0009] In the formula: s is the original wavelet scaling parameter; ζ is the scaling smoothing factor; t is the time variable, representing the sampling time point of the input signal; C is the envelope gain, used to control the steepness of the Sigmoid function; f DAS represents the dominant frequency of the target sound wave; u represents the translation factor, which controls the position of the wavelet on the time axis.

[0010] Preferably, the channel statistics include μ c and σ c The μ c It can be expressed by the following formula:

[0011]

[0012] The σ c It can be expressed by the following formula:

[0013]

[0014] In the formula: T represents time; μ c This indicates that the output feature map F(c,t) for channel c is averaged over the time dimension T; σ c This indicates the degree of fluctuation in the characteristics of channel c.

[0015] Preferably, the dynamic threshold decision model includes: Step S201: Based on the statistic μ c and σ c Dynamically perceive the feature distribution of each channel; Step S202: Introduce a dual-channel attention mechanism to generate the threshold parameter α c η c Step S203: Adjust the threshold parameter α c and η c Perform gradient update and adjustment; Step S203: Based on the statistic μ from step S201 c and σ c and α in step S203 c and η c Thus, a dynamic threshold formula based on channel statistics is obtained.

[0016] Preferably, the dynamic threshold decision model is represented by the following formula:

[0017]

[0018] In the formula: F(c,t) represents the input signal of channel c at time position t, η c Indicates the threshold offset; α c Indicates the degree of softness or hardness.

[0019] Preferably, the progressive residual model includes: Step S301: Input a feature map and use a 1×1 convolution kernel to split the feature map into three sub-feature maps [X1, X2, X3]; Step S302: Input the sub-feature map X1 into a 1×1 convolution kernel for processing and output Y1; Step S303: Input the sub-feature map X2 and the output Y1 from step S302 into a 3×3 convolution kernel and output Y2; Step S304: Input the sub-feature map X3, the output Y1 from step S302, and the output Y2 from step S303 into a 5×5 convolution kernel and output Y3; Step S305: Input the output Y1 from step S302, the output Y2 from step S303, and the output Y3 from step S304 into a 1×1 convolution kernel for feature fusion and output the reconstructed DAS signal.

[0020] Preferably, there are multiple 1×1 convolutional kernels, and the multiple 1×1 convolutional kernels are used for feature map splitting, convolution processing and feature fusion respectively.

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. This invention uses a Morlet wavelet basis that combines DAS features to form a DAS-Morlet wavelet signal. A decision model based on the dynamic threshold of channel statistics is used to perform dynamic threshold processing on the DAS-Morlet wavelet signal. At the same time, an asymptotic residual model is introduced to improve the accuracy of the reconstructed DAS signal.

[0023] 2. The asymptotic residual model used in this invention reduces the computational cost of convolution by using grouped convolutions and the collaboration of 1×1, 3×3, and 5×5 convolution kernels, thereby improving the data processing speed.

[0024] 3. This invention uses the acoustic wave dominant frequency f of the DAS signal. DAS Noise frequency band f noise Physical characteristics are encoded into wavelet basis initialization to enhance the targeting of noise separation.

[0025] 4. This invention employs an adaptive threshold mechanism to dynamically generate α using dual-channel attention. c and η c This addresses the issues of discontinuous hard thresholds and excessively smooth soft thresholds.

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the noise reduction process of the present invention;

[0028] Figure 2 This is a schematic diagram of the asymptotic residual module of the present invention;

[0029] Figure 3 A comparison chart showing the denoising effects of different algorithms;

[0030] Figure 4 for Figure 3 Comparison chart of SNR parameters. Detailed Implementation

[0031] This invention discloses a denoising optimization method based on wavelet basis and dynamic adaptive threshold, comprising the following steps:

[0032] Step S1: Based on the DAS signal and the Morlet wavelet basis, obtain the DAS-Morlet wavelet basis function;

[0033] like Figure 1As shown, this application is applicable to the monitoring of pipeline systems such as tailings pipelines. The DAS system is deployed on the outer wall of the pipeline for easy monitoring of the pipeline network system. With wavelet domain parameter adaptive calibration as the core, firstly, the multi-scale propagation characteristics of the DAS signal are encoded into the wavelet basis initialization process, so that the center frequency of the Morlet wavelet basis matches the effective acoustic frequency of the DAS signal, forming the DAS-Morlet wavelet basis function. This ensures that the Morlet wavelet kernel can accurately capture the target frequency band, realizing signal decomposition guided by physical priors, separating the noise-dominant frequency band from the weak signal-carrying frequency band. That is, by combining the Morlet wavelet basis with DAS characteristics, the DAS signal is modulated with prior information to separate different noise signals. Then, a dynamic thresholding method based on channel statistics is used to dynamically threshold the DAS-Morlet wavelet basis function to suppress noise. Finally, the DAS-Morlet wavelet signal is fused at multiple scales through an asymptotic residual model to accelerate signal processing and finally construct a complete denoised signal.

[0034] An improvement is made using the Morlet wavelet basis as the fundamental wavelet basis. The Morlet wavelet formula is as follows:

[0035]

[0036] In the formula: C is the envelope gain, and t is the time variable.

[0037] Let f be the effective acoustic frequency in the DAS signal. DAS The dominant frequency of DAS noise is f noise By modifying the frequency parameters of the Morlet wavelet, the center frequency of the Morlet wavelet is made to match f. DAS To facilitate accurate capture of the target frequency band by the Morlet wavelet kernel, then:

[0038]

[0039] Adjusting the Morlet wavelet scale, then:

[0040] s eff =s-ζ(ζ∈[-0.5,0.5]) (3)

[0041] In the formula: s eff The effective scale is s; s is the original wavelet scale parameter; ζ is the scale smoothing factor used to adjust the wavelet scale; the effective scale is s. eff It is used to enhance the time-frequency focusing of the Morlet wavelet basis, solve the problem of overlap between noise and effective signal frequency bands, and facilitate the suppression of high-frequency noise.

[0042] When f noise Greater than f DASAt that time, ζ is increased to compress the wavelet scale corresponding to high-frequency noise. Through smooth adjustment of ζ, the time-frequency focusing property of the Morlet wavelet basis is adapted to the acoustic and noise frequency band separation characteristics of the DAS signal. Furthermore, applying a Sigmoid activation function to the exponential term helps to limit the wave value distribution range and avoid gradient explosion. Then ψ DAS (t) is transformed into:

[0043]

[0044] For ψ DAS (t) After scaling, the DAS-Morlet wavelet basis function ψ DAS (t) is represented as:

[0045]

[0046] In the formula: s∈[1,N k ], N k The number of channels represents different scale and translation combinations; u is the translation factor, which restricts the position of the wavelet on the time axis, u∈[0,K-1], where K represents the total number of time points of the signal in the discrete sampling case; C is the envelope gain, which controls the steepness of the Sigmoid function; f DAS t is the dominant frequency of the target acoustic wave; t is a time variable, representing the sampling time point of the input signal.

[0047] Step S2: Construct a dynamic threshold decision model based on channel statistics and perform dynamic threshold processing on the DAS-Morlet wavelet signal;

[0048] The dynamic threshold decision model includes:

[0049] Step S201: Based on the statistic μ c and σ c Dynamically sense the characteristic distribution of each channel;

[0050] Channel processing is performed using the DAS-Morlet wavelet basis function. The DAS-Morlet wavelet basis serves as the wavelet convolution kernel, performing a one-dimensional convolution operation on each input channel to generate an output feature map F(c,t)∈R^(c×T), where c is the number of channels and T is the time point. Then, global statistics are calculated along the channel dimension to model spatial correlation. Therefore:

[0051]

[0052] In the formula: T represents time; μ cF(c,t) represents the average of the output feature map F(c,t) of channel c over the time dimension T, used to capture the global feature intensity of that channel; F(c,t) represents the output value at time point t after the input signal is convolved with the c-th DAS-Morlet wavelet kernel in one dimension.

[0053]

[0054] In the formula: σ c This represents the degree of fluctuation in the characteristics of channel c, reflecting the robustness of the characteristics within that channel, i.e., its sensitivity to noise; this is indicated by the statistic μ. c and σ c Dynamically sense the characteristic distribution of different channels.

[0055] Step S202: Introduce a dual-channel attention mechanism to generate the threshold parameter α c η c ;

[0056] Threshold parameter α c and η c By adjusting the gradient update, the threshold function is made to adaptively select the ratio of soft to hard thresholds and the threshold size based on the statistical characteristics of the input signal, thus balancing the denoising intensity and detail preservation.

[0057] Step S203: Adjust the threshold parameter α c and η c Perform gradient update adjustments;

[0058] α c The gradient is expressed by the following equation:

[0059]

[0060] Where: y c,t The output signal after dynamic thresholding is represented by L, which is the loss function, and the denoised output y is represented by y. c,t With true clean signals The difference,

[0061]

[0062] η c The gradient is expressed by the following equation:

[0063]

[0064] in:

[0065]

[0066] Dynamic parameter α c Trend of change:

[0067]

[0068] The above formula shows that:

[0069] When |F(c,t)| approaches η c At that time, α c →0 (approaching the hard threshold), reducing high-frequency signal attenuation;

[0070] When |F(c,t)|>>η c At that time, α c →1 (approaching the soft threshold) suppresses strong noise.

[0071] Step S203: Based on the statistic μ from step S201 c σ c and α in step S203 c η c Thus, a dynamic threshold formula based on channel statistics is obtained.

[0072] The dynamic threshold decision model is represented by the following equation:

[0073]

[0074] In the formula: F(c,t) represents the input signal of channel c at time position t, which is the characteristic coefficient after wavelet transform. As the original signal to be denoised, the amplitude of F(c,t) determines whether thresholding is required; when the amplitude of F(c,t) is less than η c When the signal is zero, the signal is directly set to zero because this segment of the signal is mainly composed of noise, and setting it to zero is equivalent to directly removing the noise; when the amplitude of F(c,t) is not less than η c When processing the signal, since the signal exceeding the threshold mainly consists of useful signals but is still mixed with noise, directly retaining the original value would retain all the noise, and directly setting it to zero would lose the useful signal. Therefore, we choose to subtract α from |F(c,t)|. c η c The sign function sgn(F(c,t)) is used to preserve the sign of the input signal, ensuring that the signal denoised by the wavelet basis function is in phase with the original signal; η c This represents the threshold offset, which determines whether the signal is truncated; α c This indicates the degree of softness or hardness in threshold processing, balancing noise reduction intensity with detail preservation.

[0075] The above formula (13) is obtained through η c and α c An independent threshold parameter is generated for each channel to accommodate the differences between high-frequency (noise-heavy) and low-frequency (signal-strong) frequencies. α cBy dynamically adjusting the ratio of soft to hard noise reduction to balance noise reduction intensity and detail preservation, and finally using a dynamic thresholding process based on channel statistics, the fixed rules of traditional threshold denoising are transformed into a learnable dynamic process, enabling the model to adapt to the signal characteristics of different channels and different time points.

[0076] Step S3: Use an asymptotic residual model to perform multi-scale fusion on the threshold-processed DAS-Morlet wavelet signal and output the reconstructed DAS signal.

[0077] The asymptotic residual model is used to achieve synergistic optimization of multi-scale feature fusion and computational acceleration.

[0078] The asymptotic residual model includes:

[0079] Step S301: Input the feature map and use a 1×1 convolution kernel to split the feature map into three sub-feature maps [X1, X2, X3];

[0080] Step S302: Input the sub-feature map X1 into a 1×1 convolution kernel for processing, and output Y1;

[0081] Step S303: Input the sub-feature map X2 and the output Y1 from step S302 into a 3×3 convolution kernel to output Y2;

[0082] Step S304: Input the sub-feature map X3, the output Y1 from step S302, and the output Y2 from step S303 into a 5×5 convolution kernel to output Y3;

[0083] Step S305: Input Y1 output from step S302, Y2 output from step S303, and Y3 output from step S304 into a 1×1 convolution kernel for feature fusion, and output the reconstructed DAS signal.

[0084] The number of 1×1 convolutional kernels is multiple, and the multiple 1×1 convolutional kernels are used to perform feature map splitting, convolution processing and feature fusion respectively.

[0085] The number of 1×1 convolution kernels in this application is three.

[0086] In step S301, the 1×1 convolutional kernel achieves channel grouping; in step S302, the 1×1 convolutional kernel suppresses high-frequency random noise; in step S303, the 3×3 convolutional kernel processes intermediate-frequency structural noise; in step S304, the 5×5 convolutional kernel captures low-frequency global noise; the asymptotic residual model adopts a decomposed and fused residual structure to decompose the noise estimation error into subspaces of different scales, and uses multi-scale convolutional kernels of 1×1, 3×3, and 5×5 to achieve spatial dimension expansion instead of channel grouping expansion of ordinary residual modules, thereby achieving the goal of hierarchical reception domain expansion.

[0087] like Figure 2As shown, in the asymptotic residual model, the first group of 1×1 convolutional kernels only receives the input feature map, groups the feature map, and outputs three sub-feature maps X1, X2, and X3. Feature map X1 is input to the second group of 1×1 convolutional kernels, which are used to process and suppress high-frequency random noise. After capturing and eliminating the high-frequency random noise in feature map X1, the second group of 1×1 convolutional kernels outputs the high-frequency denoised signal Y1. Feature map X2 and the high-frequency denoised signal Y1 are input to a 3×3 convolutional kernel, which is used to process and suppress intermediate-frequency structural noise. After capturing and eliminating the intermediate-frequency noise in feature maps X2 and Y1, the 3×3 convolutional kernel outputs the intermediate-frequency denoised signal Y2. Feature map X3 and the high-frequency denoised signal Y1 are input to a 3×3 convolutional kernel, which is used to process and suppress intermediate-frequency structural noise. After capturing and eliminating the intermediate-frequency noise in feature maps X2 and Y1, the 3×3 convolutional kernel outputs the intermediate-frequency denoised signal Y2. The signal Y1 and the mid-frequency denoised signal Y2 are input together into a 5×5 convolution kernel. The 5×5 convolution kernel is used to process and suppress low-frequency global noise. After capturing and eliminating low-frequency global noise in feature maps X3, Y1 and Y2, the 5×5 convolution kernel outputs Y3. The first group of 1×1 convolutions is pre-compressed to reduce the number of channels in the subsequent 3×3 and 5×5 convolutions, so that the computation of 5×5 convolution is reduced to 37% of that of ordinary residuals. The high-frequency denoised signal Y1 output by the 1×1 convolution kernel, the mid-frequency denoised signal Y2 output by the 3×3 convolution kernel, and the low-frequency global denoised signal Y3 output by the 5×5 convolution kernel are input together into a third group of 1×1 convolution kernels. Cross-scale feature interaction is achieved by adding the third group of 1×1 convolution kernels point by point, which improves the computational efficiency and realizes feature fusion.

[0088] Verification Test

[0089] SNR and RMSE are complementary metrics. SNR focuses on the degree of noise suppression; RMSE (root mean square error) focuses on the accuracy of signal restoration. The lower the RMSE value, the smaller the difference between the denoised signal and the real signal, meaning higher restoration accuracy and better denoising effect. Figure 3 , Figure 4 As shown in Table 1, the SNR and RMSE obtained by U-net, CCRN, EDCC-EMD and this application are illustrated.

[0090] Table 1 Comparison of SNR and RMSE results for the four algorithms

[0091] Dry Records U-net CCRN EDCC-EMD The method of this application SNR (dB) -7.0031 -1.9768 3.5764 6.5891 15.3415 RMSE (rad) 0.1034 0.0923 0.0658 0.0422 0.0235

[0092] The noisy records in Table 1 represent the original noisy signals. As shown in Table 1, the SNR of the method in this application is higher than that of the other three methods, meaning that the denoising effect of this application is better than that of the other three methods. The SNR value increases from -7.0031dB in the noisy records to 15.3415dB in the method of this application, indicating that the signal is cleaner after denoising using the denoising method of this application. The RMSE value of the method in this application is significantly lower than that of the other methods, indicating that the signal restored by this application is close to the true value and the model has high accuracy. The RMSE decreases from 0.1034 in the noisy records to 0.0235 in this application, indicating that the prediction accuracy is significantly improved after denoising.

[0093] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural transformations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A denoising optimization method based on wavelet basis and dynamic adaptive threshold, characterized in that, Includes the following steps: Step S1: Based on the DAS signal and the Morlet wavelet basis, obtain the DAS-Morlet wavelet basis function; Step S2: Construct a dynamic threshold decision model based on channel statistics and perform dynamic threshold processing on the DAS-Morlet wavelet signal; Step S3: Use the progressive residual model to perform multi-scale fusion on the threshold-processed DAS-Morlet wavelet signal and output the reconstructed DAS signal. The asymptotic residual model includes: Step S301: Input the feature map and use a 1×1 convolution kernel to split the feature map into three sub-feature maps [X1, X2, X3]; Step S302: Input the sub-feature map X1 into a 1×1 convolution kernel for processing, and output Y1; Step S303: Input the sub-feature map X2 and the output Y1 from step S302 into a 3×3 convolution kernel to output Y2; Step S304: Input the sub-feature map X3, the output Y1 from step S302, and the output Y2 from step S303 into a 5×5 convolution kernel to output Y3; Step S305: Input Y1 output from step S302, Y2 output from step S303, and Y3 output from step S304 into a 1×1 convolution kernel for feature fusion, and output the reconstructed DAS signal.

2. The denoising optimization method based on wavelet basis and dynamic adaptive threshold according to claim 1, characterized in that, The DAS-Morlet wavelet basis function is expressed by the following equation: （5） In the formula: s is the original wavelet scaling parameter; ζ is the scaling smoothing factor; t is the time variable, representing the sampling time point of the input signal; C is the envelope gain, used to control the steepness of the Sigmoid function; f DAS represents the dominant frequency of the target sound wave; u represents the translation factor, which controls the position of the wavelet on the time axis.

3. The denoising optimization method based on wavelet basis and dynamic adaptive threshold according to claim 1, characterized in that, The channel statistics include and The It can be expressed by the following formula: （6） The It can be expressed by the following formula: （7） In the formula: T represents time; This represents the output feature map for channel c. Take the average over the time dimension T; This indicates the degree of fluctuation in the characteristics of channel c.

4. A denoising optimization method based on wavelet basis and dynamic adaptive threshold as described in claim 3, characterized in that, The dynamic threshold decision model includes: Step S201: Based on statistics and Dynamically sense the characteristic distribution of each channel; Step S202: Introduce a dual-channel attention mechanism to generate threshold parameters , ; Step S203: Adjust the threshold parameter and Perform gradient update adjustments; Step S203: Based on the statistics from step S201 and and step S203 and Thus, a dynamic threshold formula based on channel statistics is obtained.

5. A denoising optimization method based on wavelet basis and dynamic adaptive threshold as described in claim 1, characterized in that, The dynamic threshold decision model is represented by the following equation: （13） In the formula: This represents the input signal of channel c at time position t. Indicates the threshold offset; Indicates the degree of softness or hardness.

6. A denoising optimization method based on wavelet basis and dynamic adaptive threshold as described in claim 1, characterized in that, The number of 1×1 convolutional kernels is multiple, and the multiple 1×1 convolutional kernels are used to perform feature map splitting, convolution processing and feature fusion respectively.

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