Mud continuous wave signal denoising method fusing priori main frequency constraint and multi-level decomposition adaptive reconstruction

Abstract

The application discloses a mud continuous wave signal denoising method fusing prior main frequency constraint and multi-stage decomposition adaptive reconstruction, and belongs to the technical field of signal processing of measurement while drilling. The method comprises the following steps: collecting mud continuous wave signals and preprocessing to obtain preprocessed signals; sequentially performing variational mode decomposition and empirical mode decomposition on the preprocessed signals to obtain multiple intrinsic mode functions; constructing an adaptability function for evaluating the adaptability of the signals; combining the multiple intrinsic mode functions according to different weights to form a reconstructed signal; taking the adaptability function as an evaluation index, screening the weight combination with the highest adaptability as an optimal weight combination, and then combining the multiple intrinsic mode functions to perform weighted reconstruction to form a final denoised signal. The application effectively solves the problem of dependence on ideal signal labels in the prior art, and significantly improves the signal-to-noise separation precision and waveform reconstruction fidelity of the continuous wave signal in a complex drilling noise environment.

Description

Technical Field

[0001] This invention relates to the field of measurement while drilling (MWD) signal processing technology in oil and gas drilling engineering, specifically to a method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction. This method does not rely on clean signal labels and achieves mud continuous wave signal denoising by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction. Background Technology

[0002] Measurement while drilling (MWD) technology is a core tool for achieving precise wellbore trajectory control and geological steering in the development of complex oil and gas reservoirs. Mud pulse transmission technology, especially continuous wave pulse technology, has become the mainstream method for MWD data transmission due to its advantages of high transmission rate and relatively low cost. However, the mud channel from the downhole to the surface is extremely complex. Multiple sources of non-stationary and nonlinear noise, such as drill bit rock breaking, drill string vibration, mud pump pressure fluctuations, and formation fluid intrusion, are severely superimposed on the weak continuous wave signal, resulting in an extremely low signal-to-noise ratio for the received signal on the surface, seriously affecting decoding accuracy.

[0003] Existing denoising methods, based on Fourier transform, wavelet transform, and Kalman filtering, have achieved some success, but they lack adaptability to non-stationary noise and struggle to effectively address issues such as the dynamic evolution of noise characteristics and severe frequency band aliasing in drilling environments. Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) can decompose mud continuous wave signals into a small number of intrinsic mode functions (IMFs), achieving noise and useful signal separation to some extent. However, EMD suffers from mode aliasing, and VMD is sensitive to parameters such as penalty factor and mode number. When the useful signal and noise spectrum are severely aliased, using them alone is insufficient to handle the residual complex noise, leading to insufficient accuracy in useful signal reconstruction. Current methods mostly employ single decomposition strategies, lacking the ability to adaptively process different noise components. Especially in complex dynamic drilling environments such as deep and ultra-deep wells, it is difficult to achieve the optimal balance between preserving effective signal details and suppressing strong noise.

[0004] While deep learning-based methods have shown some effectiveness, they require a large amount of ideal, clean signals as training labels, which is difficult to obtain in actual drilling environments. Therefore, there is an urgent need for a robust denoising method that does not rely on clean signals and has adaptive parameter optimization capabilities. Summary of the Invention

[0005] To address the problems of existing drilling mud continuous wave signal denoising methods being heavily reliant on manual parameter tuning and struggling to adaptively handle multi-source mixed noise in real-world conditions without reference signals, this invention provides a mud continuous wave signal denoising method that integrates prior dominant frequency constraints and multi-level decomposition adaptive reconstruction. This invention utilizes the theoretical transmission frequency of the mud continuous wave as prior information to guide VMD decomposition for coarse screening, followed by EMD for fine decomposition. Furthermore, by constructing a fitness function based on spectral energy, the optimal weights of each modal component are found, thereby achieving unsupervised adaptive reconstruction of the signal.

[0006] To achieve the above-mentioned objectives, the technical solution of the present invention is as follows: A method for denoising mud continuous wave signals that integrates prior dominant frequency constraints and multi-level decomposition adaptive reconstruction includes the following steps: S1. Acquire and preprocess the continuous wave signal of the mud to obtain the preprocessed signal; S2. Perform variational mode decomposition (VMD) on the preprocessed signal to obtain multiple intrinsic mode components; use the theoretical transmission frequency of the mud continuous wave signal as the prior frequency, and filter the multiple intrinsic mode components based on the prior frequency to obtain a preliminary denoised signal; S3. Perform Empirical Mode Decomposition (EMD) on the preliminary denoised signal to obtain multiple intrinsic mode functions; S4. Construct a spectral energy ratio fitness function based on power spectral density and the prior dominant frequency to evaluate the fitness of the signal; S5. Combine the multiple intrinsic mode functions with different weights to form a reconstructed signal, evaluate the reconstructed signal using the fitness function, and select the reconstructed signal with the highest fitness as the final denoised signal.

[0007] In a specific embodiment of the present invention, in step S1, the original continuous wave signal collected by the ground riser pressure sensor can be used as the mud continuous wave signal. The signal is then processed to remove the trend term, and a low-pass filter is used to filter out high-frequency noise and DC components to obtain a preprocessed signal.

[0008] In this invention, step S2 is to eliminate strong interference noise that is far from the main frequency. As a specific embodiment of this invention, step S2 includes the following operations: S21. Set the number of modes and penalty factor for variational mode decomposition, and perform variational mode decomposition on the preprocessed signal to obtain multiple intrinsic mode components and their corresponding center frequencies. S22. Using the theoretical transmission frequency of the mud continuous wave signal as the prior frequency, calculate the absolute deviation between the center frequency of each intrinsic mode component and the prior frequency. Select the intrinsic mode component with the smallest absolute deviation or set the intrinsic mode component with the absolute deviation within the threshold range for reconstruction to obtain the preliminary denoised signal. The formula for calculating the absolute deviation is as follows: In the formula, Indicates center frequency With prior main frequency The absolute deviation; This indicates taking the absolute value.

[0009] In step S3 of this invention, empirical mode decomposition (EMD) is used to initially denoise the signal. This is a conventional decomposition method that can obtain multiple intrinsic mode functions. and a residual term ; The expression for empirical mode decomposition (EMD) is as follows: in, Indicates the first Each intrinsic mode function includes signal features at different scales and residual noise; N This represents the total number of intrinsic mode functions.

[0010] Step S4 mainly involves constructing the fitness function. Traditional evaluation of filtering performance typically uses metrics such as signal-to-noise ratio (SNR) and mean square error (MSE), which are calculated using the following formulas: in, P s Represents the average power of the signal. P n The average power of the noise is represented by M, and M is the total number of points in the signal sequence. After noise reduction processing of continuous wave signals, the first i The values ​​of the sequence points, Its corresponding ideal continuous wave signal is in the th i The values ​​of the sequence points.

[0011] However, the calculation logic of the aforementioned traditional indicators relies on a core premise: a pure, original signal must be used as a reference. In actual drilling operations, since a noise-free "ideal continuous wave signal" is unavailable as a reference, traditional evaluation indicators are difficult to directly translate into the driving force of optimization algorithms. Therefore, traditional evaluation indicators cannot be directly used as fitness functions for mud continuous wave signal processing. To address this problem, this invention proposes a fitness function construction method based on Gaussian weighted spectral energy ratio. This method abandons the dependence on a pure reference signal and instead utilizes the prior knowledge of signal characteristics that "energy near the dominant frequency of the signal is considered effective energy, and energy in other frequency bands is considered noise energy." Specifically, it includes the following steps: S41. Convert the input signal into its frequency domain form using Discrete Fourier Transform (DFT) and calculate its power spectral density. P ( k ); The expression for the input signal in frequency domain form is as follows: In the formula, Indicates length is M Discrete time-domain sequences; Indicates length is M frequency domain discrete sequences, j Represents the imaginary unit. k This represents the frequency domain index, and its corresponding frequency is... , Indicates the sampling frequency of the signal; N This represents the total number of intrinsic mode functions; The formula for calculating power spectral density is as follows: In the formula, P ( k () indicates frequency point k The power spectral density; S42. Based on the Gaussian weighted window function centered on the prior dominant frequency, calculate the effective energy and noise energy, and then construct the spectral energy to fitness function. The formula for calculating the Gaussian weighted window function is as follows: in, Representing frequency point k The corresponding actual frequency, This represents the theoretical transmission frequency of the signal, also known as the a priori frequency. This represents the standard deviation of the Gaussian weighted function and controls the width of the Gaussian window; The formula for calculating effective energy is as follows: in, Indicates the effective signal energy; The formula for calculating noise energy is as follows: Indicates noise energy; The formula for calculating the spectral energy ratio fitness function is as follows: This indicates the fitness of the signal. The larger the value, the more concentrated the energy of the reconstructed signal is at the target main frequency, and the better the denoising effect.

[0012] In step S5, the multiple intrinsic mode functions can be combined with different weights to form different reconstructed signals, and the expressions for the reconstructed signals are as follows: In the formula, Indicates the first One reconstructed signal; Indicates the first The weighted combination vector in a reconstructed signal; This represents the combination vector of eigenmode functions; Indicates the first One intrinsic mode function; Indicates the first The reconstructed signal of the th ... eigenmode functions The weight it occupies; similarly, Indicates the 1st, 2nd, One eigenmode function Indicates the first The 1st, 2nd, and 3rd reconstructed signals The weights of each intrinsic mode function; .

[0013] Step S5 involves finding the optimal reconstructed signal. In some embodiments, certain combinations can be identified, and the optimal reconstructed signal can be determined by the fitness value. However, this method is greatly affected by human factors. For these reconstructed signals, the intrinsic mode functions are fixed. Therefore, finding the optimal reconstructed signal can be transformed into finding the optimal weight combination. As a specific embodiment of the present invention, a particle swarm optimization algorithm is used to adaptively optimize the weight combination to obtain a preferred weight combination. Then, the multiple intrinsic mode functions are reconstructed according to the preferred weight combination to obtain the final denoised signal. The adaptive optimization of the weight combination includes the following steps: S51. Initialize the parameters of the Particle Swarm Optimization (PSO) algorithm, which mainly include the number of particles, optimization dimension, inertia weight, individual learning factor, social learning factor, and maximum number of iterations. S52. Determine that the weight combination of each intrinsic mode function is used as the position vector of a single particle. This clarifies the transformation relationship between the particle and the reconstructed signal. The position coordinates of a single particle in each dimension represent the weights of the corresponding intrinsic mode functions during signal reconstruction; that is, each particle carries one weight. A position vector is used, and different weight combinations correspond to different particles. The reconstructed signal can be obtained from the position of the particle. The initial position of each particle is randomly generated to obtain the initial particle population. S53. The fitness of each particle in the particle swarm is determined by the fitness function constructed in step S4, and the individual historical best position of each particle and the global historical best position of the entire particle swarm are updated according to the calculation results. S54. Based on the updated individual historical best position and global historical best position, calculate and update the flight speed and position coordinates of each particle in the particle swarm in the next iteration, thereby guiding the entire particle swarm to perform a directional search in the space of a better weight allocation scheme. S55. Repeat S53 and S54 to iterate until the maximum number of iterations is reached or the tolerance error is met, and output the optimal weight combination.

[0014] Beneficial effects: This invention can adapt to changes in noise characteristics under different well conditions. It not only significantly improves the signal-to-noise separation accuracy of mud continuous wave signals in complex drilling noise environments, but also preserves the characteristic details of the signal to the greatest extent, providing indispensable core technical support for mud continuous wave signal processing and drilling measurement system control.

[0015] This invention combines the noise immunity of VMD with the adaptability of EMD. VMD first removes strong noise outside the frequency band, and EMD then processes the aliasing noise within the frequency band. This avoids the limitations of a single method and solves the problem of difficulty in separating effective signals and nonlinear noise under severe spectral aliasing.

[0016] This invention constructs a Gaussian weighted energy ratio based on the "prior dominant frequency" as the fitness function, which does not require a clean signal as a reference and solves the pain point of unlabeled data in the field. At the same time, it introduces an optimization algorithm to adaptively determine the optimal weight combination of each intrinsic mode function, avoiding the subjectivity of manually setting weights and directly optimizing the energy ratio of the signal in the useful frequency band, which has both physical significance and engineering practicality. Attached Figure Description

[0017] Figure 1 This is an overall flowchart of an embodiment of the present invention; Figure 2 A flowchart for finding the optimal weight combination using the particle swarm optimization algorithm; Figure 3 This is a graph showing the trend of fitness changing with the iteration process during the optimization process using the particle swarm optimization algorithm. Figure 4 This is a comparison chart of the final denoised signal and the corresponding received signal; Figure 5 This is a comparison chart of the final denoised signal and the corresponding ideal signal. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The preferred embodiments described below are merely examples, and other obvious variations will be apparent to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0019] like Figure 1 As shown, this invention provides a method for denoising mud continuous wave signals that integrates prior dominant frequency constraints and multi-level decomposition adaptive reconstruction, specifically including the following steps: S1. Acquire and preprocess the continuous wave signal of the mud to obtain the preprocessed signal.

[0020] In this embodiment, the raw continuous wave signal collected by the ground riser pressure sensor is used as the mud continuous wave signal. The raw continuous wave signal collected by the pressure sensor is BFSK encoded, with a theoretical transmission frequency of 12Hz and 18Hz, a transmission rate of 6bit / s, and a sampling rate set to... The useful frequency band of the signal was determined to be within 30Hz. Detrending processing was then performed on the signal, using a low-pass filter with a cutoff frequency of 30Hz to filter out high-frequency pump noise and DC components, resulting in a preprocessed signal. X 0( t ).

[0021] S2. Perform variational mode decomposition (VMD) on the preprocessed signal to obtain 6 intrinsic mode components; use the theoretical transmission frequency of the mud continuous wave signal as the a priori frequency, and filter these intrinsic mode components based on the a priori frequency to obtain a preliminary denoised signal.

[0022] S21. Set the number of modes of VMD to 6 and the penalty factor to 3000, and preprocess the signal. Variational mode decomposition was performed to obtain 6 intrinsic mode components. and its corresponding center frequency .

[0023] S22, The theoretical transmission frequency of mud continuous wave signal Assuming a priori dominant frequency, the absolute deviation of the center frequency of each intrinsic mode component from the priori dominant frequency is calculated. The intrinsic mode component with the smallest absolute deviation or the intrinsic mode component whose absolute deviation is within a threshold range is selected for reconstruction to obtain the preliminary denoised signal. .

[0024] The formula for calculating the absolute deviation is as follows: In the formula, Indicates center frequency With prior main frequency The absolute deviation; Indicates taking the absolute value; Ultimately, it was determined that the center frequencies of the second and fourth intrinsic mode components were closest to the prior dominant frequency. Therefore, the second and fourth intrinsic mode components were selected for signal reconstruction to obtain the preliminary denoised signal. X 1( t ).

[0025] S3. Use Empirical Mode Decomposition (EMD) to initially denoise the signal. X 1( t It is decomposed into 7 intrinsic mode functions. and a residual term ,Right now: .

[0026] S4. Construct a spectral energy ratio fitness function based on power spectral density and prior dominant frequency to evaluate the fitness of the signal.

[0027] S41. Convert the input signal into frequency domain form using discrete Fourier transform and calculate its power spectral density. P ( k ).

[0028] The expression for the input signal in frequency domain form is as follows: In the formula, Indicates length is M Discrete time-domain sequences; Indicates length is M frequency domain discrete sequences, j Represents the imaginary unit. k This represents the frequency domain index, and its corresponding frequency is... , Indicates the sampling frequency of the signal; N This represents the total number of intrinsic mode functions.

[0029] The formula for calculating power spectral density is as follows: In the formula, P ( k () indicates frequency point k The power spectral density.

[0030] S42. Based on the Gaussian weighted window function centered on the prior dominant frequency, calculate the effective energy and noise energy, and then construct the spectral energy to fitness function.

[0031] The formula for calculating the Gaussian weighted window function is as follows: in, Representing frequency point k The corresponding actual frequency, Indicates the priori dominant frequency. This represents the standard deviation of the Gaussian weighted function and controls the width of the Gaussian window.

[0032] The formula for calculating effective energy is as follows: in, This represents the effective signal energy.

[0033] The formula for calculating noise energy is as follows: This represents noise energy.

[0034] The formula for calculating the spectral energy ratio fitness function is as follows: In the formula, This indicates the fitness of the signal. The larger the value, the more concentrated the energy of the reconstructed signal is at the target main frequency, and the better the denoising effect.

[0035] S5. The seven intrinsic mode functions (IMFs) are combined with different weights to form a reconstructed signal. The reconstructed signal is evaluated using a fitness function, and the reconstructed signal with the highest fitness is selected as the final denoised signal. For each reconstructed signal, the IMFs are the same; the difference lies in the weight combination. Therefore, the process of finding the reconstructed signal with the highest fitness can be transformed into the process of finding the optimal weight combination. In this embodiment, the particle swarm optimization (PSO) algorithm is used for adaptive optimization of the weight combination to obtain the optimal weight combination. Finally, the weighted reconstruction of multiple IMFs according to the optimal weight combination yields the final denoised signal.

[0036] The expression for the reconstructed signal is as follows: In the formula, Indicates the first One reconstructed signal; Indicates the first The weighted combination vector in a reconstructed signal; This represents the combination vector of eigenmode functions; Indicates the first One intrinsic mode function; Indicates the first The reconstructed signal of the th ... eigenmode functions The weight it occupies; similarly, Indicates the 1st, 2nd, One eigenmode function Indicates the first The 1st, 2nd, and 3rd reconstructed signals The weights of each intrinsic mode function; .

[0037] The process of finding the optimal weight combination using the Particle Swarm Optimization (PSO) algorithm is as follows: Figure 2 As shown, it includes the following steps: S51. Initialize the parameters of the Particle Swarm Optimization (PSO) algorithm, which mainly include the number of particles, optimization dimension, inertia weight, individual learning factor, social learning factor, and maximum number of iterations. In this embodiment, the particle swarm size is set to 30, the optimization dimension is 7, the inertia weight is 0.8, the individual learning factor is 1.5, the social learning factor is 1.5, the maximum number of iterations is 100, and the weight of each modality is allowed to be in the range of [0,1].

[0038] S52. Determine that the weight combination of each intrinsic mode function is used as the position vector of a single particle. This clarifies the transformation relationship between the particle and the reconstructed signal. The position coordinates of a single particle in each dimension represent the weights of the corresponding intrinsic mode functions during signal reconstruction; that is, each particle carries one weight. A position vector is used, and different weight combinations correspond to different particles. The reconstructed signal can be obtained from the position of the particle. The initial position of each particle is randomly generated to obtain the initial particle population.

[0039] S53. The fitness of each particle in the particle swarm corresponding to the reconstructed signal is determined by the fitness function constructed in step S4, and the individual historical best position of each particle and the global historical best position of the entire particle swarm are updated according to the calculation results.

[0040] S54. Based on the updated individual historical best position and global historical best position, calculate and update the flight speed and position coordinates of each particle in the particle swarm in the next iteration, thereby guiding the entire particle swarm to perform a directional search in the space of a better weight allocation scheme.

[0041] The formulas for calculating particle update velocity and position are as follows: in, For particles In the In the nth iteration A dimensional velocity vector; For particles In the In the nth iteration A dimensional position vector; For particles In the In the nth iteration Dimension's historical best position; For the group in the first In the nth iteration Dimension's historical best position; , It is a random number in the interval [0,1] to enhance the randomness of the search; For individual learning factors, For group learning factors; This is the inertial weight.

[0042] S55. Repeat S53 and S54 iteratively until the maximum number of iterations is reached or the tolerance error is met. Output the optimal weight combination, denoted as... The changes in PSO fitness during the iteration process are shown in the attached figure. Figure 3 As shown, the fitness function increases continuously with iteration, and reaches its maximum value within the maximum number of iterations and then gradually stabilizes, indicating that the set maximum number of iterations meets the processing requirements.

[0043] Substituting the optimal weight combination obtained in step S55 into the calculation formula for the reconstructed signal yields the final denoised signal.

[0044] Figure 4 The diagram illustrates the relevant information between the final denoised signal and the received signal. Figure (a) shows the received signal and the final denoised signal, and Figure (b) shows their power spectra. It is evident that the received signal waveform is completely submerged in noise, making it impossible to identify the coded features; in contrast, the reconstructed signal waveform is clear, perfectly restoring the ideal shape of the BFSK modulated mud continuous wave signal. The power spectrum comparison results show that the reconstructed signal exhibits significant energy enhancement at 12Hz and 18Hz, while noise energy in other frequency bands is significantly suppressed.

[0045] Figure 5The final denoised signal and its corresponding ideal signal are shown. Figure 5 As can be seen, the present invention can effectively suppress complex noise, and the reconstructed signal waveform is extremely close to the ideal pure signal, accurately reflecting the characteristic details of the signal, and achieving ideal noise reduction effect.

[0046] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for denoising mud continuous wave signals that integrates prior dominant frequency constraints and multi-level decomposition adaptive reconstruction, characterized in that, Includes the following steps: S1. Acquire and preprocess the continuous wave signal of the mud to obtain the preprocessed signal; S2. Perform variational mode decomposition on the preprocessed signal to obtain multiple intrinsic mode components; Using the theoretical transmission frequency of the mud continuous wave signal as the a priori frequency, and filtering the multiple intrinsic mode components based on the a priori frequency, a preliminary denoised signal is obtained. S3. Perform empirical mode decomposition on the preliminary denoised signal to obtain multiple intrinsic mode functions; S4. Construct a spectral energy ratio fitness function based on power spectral density and the prior dominant frequency to evaluate the fitness of the signal; S5. Combine the multiple intrinsic mode functions with different weights to form a reconstructed signal, evaluate the reconstructed signal using the fitness function, and select the reconstructed signal with the highest fitness as the final denoised signal.

2. The method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction according to claim 1, characterized in that, Step S1 includes: taking the raw continuous wave signal collected by the ground riser pressure sensor as the mud continuous wave signal, performing detrending term processing on the signal, and using a low-pass filter to filter out high-frequency noise and DC components to obtain a preprocessed signal.

3. The method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction according to claim 1, characterized in that, Step S2 includes: S21. Set the number of modes and penalty factor for variational mode decomposition, and perform variational mode decomposition on the preprocessed signal to obtain multiple intrinsic mode components and their corresponding center frequencies. S22. Using the theoretical transmission frequency of the mud continuous wave signal as the prior frequency, calculate the absolute deviation between the center frequency of each intrinsic mode component and the prior frequency, select the intrinsic mode component with the smallest absolute deviation or within the preset threshold range for reconstruction, and obtain the preliminary denoised signal. The formula for calculating the absolute deviation is as follows: In the formula, Indicates center frequency With prior main frequency The absolute deviation; This indicates taking the absolute value.

4. The method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction according to claim 1, characterized in that, Step S4 includes: S41. Convert the input signal into frequency domain form using discrete Fourier transform and calculate its power spectral density. P ( k ); The expression for the input signal in frequency domain form is as follows: In the formula, Indicates length is M Discrete time-domain sequences; Indicates length is M frequency domain discrete sequences, j Represents the imaginary unit. k This represents the frequency domain index, and its corresponding frequency is... , Indicates the sampling frequency of the signal; N This represents the total number of intrinsic mode functions; The formula for calculating power spectral density is as follows: In the formula, P ( k () indicates frequency point k The power spectral density; S42. Based on the Gaussian weighted window function centered on the prior dominant frequency, calculate the effective energy and noise energy, and then construct the spectral energy to fitness function. The formula for calculating the Gaussian weighted window function is as follows: in, Representing frequency point k The corresponding actual frequency, Indicates the priori main frequency; This represents the standard deviation of the Gaussian weighted function; The formula for calculating effective energy is as follows: in, Indicates the effective signal energy; The formula for calculating noise energy is as follows: Indicates noise energy; The formula for calculating the spectral energy ratio fitness function is as follows: This indicates the fitness of the signal. The larger the value, the more concentrated the energy of the reconstructed signal is at the target main frequency, and the better the denoising effect.

5. The method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction according to claim 1, characterized in that, In step S5, the expression for the reconstructed signal is as follows: In the formula, Indicates the first One reconstructed signal; N This represents the total number of intrinsic mode functions; Indicates the first One intrinsic mode function; Indicates the first The reconstructed signal of the th ... eigenmode functions The weight it occupies.

6. The method for denoising mud continuous wave signals by integrating prior dominant frequency constraints and multi-level decomposition adaptive reconstruction according to claim 1, characterized in that, In step S5, the particle swarm optimization algorithm is used to adaptively optimize the weight combination to obtain an optimal weight combination. Then, the multiple intrinsic mode functions are weighted and reconstructed according to the optimal weight combination to obtain the final denoised signal. The adaptive optimization of the weight combination includes the following steps: S51. Initialize the particle swarm optimization algorithm parameters, which mainly include the number of particles, optimization dimension, inertia weight, individual learning factor, social learning factor, and maximum number of iterations. S52. Determine the position vector of a single particle by using the weight combination of each intrinsic mode function, randomly generate the initial position of each particle, and obtain the initial particle population. S53. The fitness of each particle in the particle swarm is determined by the fitness function constructed in step S4, and the individual historical best position of each particle and the global historical best position of the entire particle swarm are updated according to the calculation results. S54. Based on the updated individual historical best position and global historical best position, calculate and update the flight speed and position coordinates of each particle in the particle swarm in the next iteration. S55. Repeat S53 and S54 to iterate until the maximum number of iterations is reached or the tolerance error is met, and output the optimal weight combination.

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