Improved wavelet threshold-based vibration signal joint denoising method and device

Abstract

This invention provides a joint noise reduction method and device for vibration signals based on an improved wavelet threshold, belonging to the field of vibration signal processing technology. This invention improves the accuracy and adaptability of signal decomposition by adaptively optimizing the number of modes and penalty factor in variational mode decomposition using a Cordyceps sinensis optimization algorithm. Then, it objectively filters the intrinsic mode function components using the Pearson correlation coefficient, effectively identifying and separating effective components strongly correlated with the original vibration signal, reducing the false rejection of useful information. Finally, it applies an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to the filtered effective components for noise reduction, achieving dynamic adjustment of noise reduction intensity within different frequency bands. This effectively suppresses noise while better preserving the detailed features and transient impact components of the signal. This invention solves the noise residue problem of traditional wavelet threshold methods and improves the signal-to-noise ratio and feature fidelity of vibration signals in strong noise backgrounds.

Description

Technical Field

[0001] This invention relates to the field of vibration signal processing technology, and in particular to a method and device for joint noise reduction of vibration signals based on an improved wavelet threshold. Background Technology

[0002] Vibration signals serve as a crucial source of information for monitoring the operational status of mechanical equipment, diagnosing faults, and assessing structural health; their quality directly impacts the reliability of subsequent analysis and decision-making. However, in real-world industrial settings, acquired vibration signals are often affected by various factors such as background noise, environmental interference, and sensor errors, exhibiting characteristics like non-stationarity, multiple components, and strong noise coupling. This masks effective signal components, severely limiting the accuracy of status identification and fault diagnosis.

[0003] Traditional vibration signal denoising methods mainly include time-domain filtering, frequency-domain filtering, and time-frequency analysis. Among them, wavelet thresholding denoising, with its excellent time-frequency localization capability, shows certain advantages in non-stationary signal processing. However, traditional wavelet thresholding methods often use fixed thresholds or a single threshold function, which is difficult to adapt to the dynamic changes in signal and noise energy distribution in different frequency bands of vibration signals. This can easily lead to loss of signal details or noise residue, and its effectiveness is limited, especially in multi-component, strong interference environments. Summary of the Invention

[0004] This invention provides a method and device for joint noise reduction of vibration signals based on an improved wavelet threshold, which solves the noise residue problem of traditional wavelet threshold methods.

[0005] In a first aspect, the present invention provides a joint denoising method for vibration signals based on an improved wavelet threshold. The method includes: acquiring the vibration signal to be denoised; adaptively optimizing the key parameters of successive variational mode decomposition using the Cordyceps sinensis optimization algorithm to obtain the optimal number of modes and penalty factor; decomposing the vibration signal based on the optimal number of modes and penalty factor to obtain multiple intrinsic mode functions (IMFs); calculating the Pearson correlation coefficient between each IMF component and the vibration signal, and dividing the multiple IMFs into effective components and noise components using a preset threshold; denoising the effective components using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised IMF components; and reconstructing the denoised IMF components to obtain the denoised vibration signal.

[0006] Secondly, this invention provides a joint noise reduction device for vibration signals based on an improved wavelet threshold. The device includes a communication module and a processing module. The communication module acquires the vibration signal to be denoised. The processing module adaptively optimizes the key parameters of successive variational mode decomposition using a Cordyceps sinensis optimization algorithm to obtain the optimal number of modes and penalty factor. Based on the optimal number of modes and penalty factor, it decomposes the vibration signal to obtain multiple intrinsic mode functions (IMFs). It calculates the Pearson correlation coefficient between each IMF component and the vibration signal, and, combined with a preset threshold, divides the multiple IMFs into effective components and noise components. It performs noise reduction on the effective components using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised IMF components. Finally, it reconstructs the denoised IMF components to obtain the denoised vibration signal.

[0007] Thirdly, embodiments of the present invention provide an electronic device including a memory and a processor. The memory stores a computer program, and the processor is used to call and run the computer program stored in the memory to perform the steps of the method as described in the first aspect and any possible implementation thereof.

[0008] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the method as described in the first aspect and any possible implementation thereof.

[0009] This invention provides a joint noise reduction method and device for vibration signals based on an improved wavelet threshold. The invention employs a Cordyceps sinensis optimization algorithm to adaptively optimize the number of modes and penalty factor in variational mode decomposition, improving the accuracy and adaptability of signal decomposition. Then, Pearson correlation coefficient is used to objectively screen the intrinsic mode function components after decomposition, effectively identifying and separating effective components strongly correlated with the original vibration signal, reducing the false rejection of useful information. Finally, the screened effective components are further denoised using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio, achieving dynamic adjustment of noise reduction intensity within different frequency bands. This effectively suppresses noise while better preserving the detailed features and transient impact components of the signal. This invention solves the noise residue problem of traditional wavelet thresholding methods by optimizing the collaborative processing mechanism of decomposition-component screening-adaptive noise reduction, improving the signal-to-noise ratio and feature fidelity of vibration signals in strong noise backgrounds. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic flowchart of a joint noise reduction method for vibration signals based on an improved wavelet threshold provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the iterative curve of an improved CFO optimization algorithm provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the overall process of ICFO-SVMD signal decomposition provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of an improved wavelet threshold function curve provided by an embodiment of the present invention; Figure 5 This is a schematic diagram of an ICFO-SVMD-WTD process provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the time-domain waveforms of the original signal and the signal after adding Gaussian white noise, provided by an embodiment of the present invention; Figure 7 This is a schematic diagram of a vibration signal joint noise reduction device based on an improved wavelet threshold provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0012] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0013] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner to facilitate understanding.

[0014] Furthermore, the terms "comprising" and "having," and any variations thereof, used in the description of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or modules is not limited to the steps or modules listed, but may optionally include other steps or modules not listed, or may optionally include other steps or modules inherent to such process, method, product, or device.

[0015] To make the objectives, technical solutions, and advantages of the present invention clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0016] As described in the background section, vibration signal denoising is a crucial preprocessing step in fields such as mechanical fault diagnosis and structural health monitoring, and its effectiveness directly impacts the accuracy of subsequent feature extraction and state identification. However, vibration signals acquired in actual engineering projects are often interfered with by strong background noise, causing useful signal components to be masked. Traditional denoising methods have significant limitations when processing non-stationary, multi-component signals, making it difficult to achieve an ideal balance between noise suppression and maintaining signal authenticity.

[0017] To improve noise reduction performance, various joint noise reduction strategies based on signal decomposition and intelligent optimization have emerged. For example, intelligent optimization algorithms can adaptively determine the parameters of variational mode decomposition, and combined with improved wavelet thresholding methods, effective noise reduction of various monitoring signals can be achieved. Related research shows that combining optimization algorithms with adaptive signal decomposition methods is an effective way to improve noise reduction performance.

[0018] In signal decomposition methods, successive variational mode decomposition (SMD) has attracted widespread attention due to its advantages such as not requiring a preset number of modes and strong adaptability in the decomposition process, demonstrating good performance in various mechanical fault diagnosis and condition monitoring scenarios. However, the performance of this method still highly depends on the selection of key parameters such as the penalty factor and the number of modes. Traditional trial-and-error methods are inefficient and cannot guarantee optimal parameters. Although existing studies have employed various optimization algorithms for parameter optimization, there is still room for improvement in global search capability and convergence accuracy.

[0019] On the other hand, wavelet thresholding, as a classic method, directly affects its denoising performance through the selection criteria and design of the threshold function. Traditional fixed thresholds easily lead to loss of signal details or residual noise; therefore, improving the threshold function and introducing adaptive strategies have become current research focuses. Existing studies have shown that combining adaptive wavelet thresholding with signal decomposition methods can, to some extent, suppress boundary distortion and noise interference, thereby improving the overall performance of signal processing.

[0020] While existing methods have achieved certain results in their respective applications, they still generally suffer from problems such as insufficient parameter optimization, inflexible thresholding strategies, and difficulty in effectively separating noise and signal components when processing complex vibration signals. To address these issues, this paper proposes a joint denoising method based on improved optimization algorithms for successive variational mode decomposition and improved wavelet thresholding. The method improves decomposition accuracy by optimizing key parameters through intelligent optimization algorithms, and further enhances denoising performance and detail preservation by combining adaptive thresholding based on subband signal-to-noise ratio and a continuous transitional thresholding function.

[0021] like Figure 1 As shown, this invention provides a joint noise reduction method for vibration signals based on an improved wavelet threshold. The method includes steps S101-S106.

[0022] S101. Obtain the vibration signal to be denoised.

[0023] In some embodiments, the vibration signal joint noise reduction method based on improved wavelet threshold provided by the present invention is applied to noise reduction scenarios of at least one of the following rotating machinery vibration signals: outer ring, inner ring, and rolling element fault signals of rolling bearings; broken teeth, pitting, and wear fault signals of gearboxes; imbalance, misalignment, and rubbing fault signals of rotor systems; and broadband vibration and impact signals of equipment such as hydraulic pumps, fans, and compressors.

[0024] S102. The Cordyceps sinensis optimization algorithm is used to adaptively optimize the key parameters of successive variational mode decomposition to obtain the optimal number of modes and penalty factor.

[0025] As one possible implementation, step S102 can be specifically implemented as steps S1021-S1024.

[0026] S1021. Set the range of parameters to be optimized.

[0027] The search range for the modality number is an integer between two and ten, and the search range for the penalty factor is a real number between one thousand and three thousand.

[0028] S1022. An improved Cordyceps sinensis optimization algorithm is used for optimization. In the optimization process, chaotic mapping is used to initialize the population, a cross-mutation mechanism is introduced in the iteration, and a thinking innovation strategy is used for fine search in the later stage.

[0029] S1023. The minimum envelope entropy of the decomposed signal components is used as the fitness function to measure the decomposition effect.

[0030] S1024. Run the optimization algorithm to iteratively find the combination of mode number and penalty factor that minimizes the fitness function, and output the combination as the optimal parameters, which include the optimal mode number and penalty factor.

[0031] For example, Sequential Variational Mode Decomposition (SVMD) is an adaptive signal processing method that further optimizes the constraints and solution process based on Variational Mode Decomposition. SVMD does not require pre-setting key parameters such as the number of modes or center frequency, and can automatically decompose complex multi-component signals into a series of single-component eigenmode functions, each representing a specific frequency component of the signal. By continuously extracting modes from the time series and progressively reconstructing the original signal, this method not only improves the adaptability of the decomposition but also significantly reduces the computational complexity, making it suitable for the analysis and processing of various non-stationary signals. The principle of the SVMD algorithm is as follows: (1) For a time series Assume it can be decomposed into: (1); where, for First mode, The residual signal contains the obtained modes. and unprocessed parts .

[0032] (2) To ensure that the assumption in (1) can be realized, construct The minimization constraint of the first mode is shown in equation (2). (2); where, For the Dirac function, For impulse functions, The imaginary unit, For convolution operators, for The center frequency of the first mode, is the rotation factor.

[0033] (3) To ensure that the constraint in equation (2) can be stably realized, a suitable filter should be selected, and the frequency response of the filter should satisfy: (3); among them, The center frequency of the impulse response, For the balancing parameters, a second constraint can be established at this point: (4).

[0034] (4) The two constraints, equations (2) and (4), cannot effectively distinguish between them. First mode and First mode, therefore based on constraints The approach to establishing this is to select a filter whose frequency response satisfies the following: (5); This allows us to establish a third constraint: (6); among them, It is a frequency impulse response.

[0035] (5) To ensure that the signal can be fully reconstructed during decomposition, the following constraints should also be established: (7); Based on the above, the problem of extracting modal components can be represented as a constrained minimization problem: (8); among them, To balance The parameters.

[0036] For example, the principle of the Caterpillar Fungus Optimizer (CFO) algorithm provided in this embodiment of the invention is as follows. The CFO algorithm is a novel metaheuristic algorithm inspired by the life process of Caterpillar fungus. It simulates the unique search and parasitic behavior of Caterpillar fungus, and its core advantages lie in its powerful global search capability and effective strategy to avoid local optima. The algorithm achieves a good balance between global exploration and local exploitation through efficient exploration operators. Furthermore, the "re-parasitism" and "optimal parasitism" mechanisms introduced by the algorithm further simulate the parasitic characteristics of Caterpillar fungus, significantly improving the ability to escape local optima, thereby ensuring the robustness of the search process.

[0037] (1) Exploration operator: In the exploration phase, the algorithm first sorts the Cordyceps sinensis population in descending order based on the fitness value. Then, each individual will randomly select one of the two exploration mechanisms to update its position, and the probability of selecting the two mechanisms is equal.

[0038] 1) Wave advance operator: When an individual selects the wave advance operator, the search process aims to simulate a wave-like dynamic behavior. The mathematical model of this behavior can be described as follows: (9); in, Indicates the first The location of each Cordyceps during the search phase; It is the number of variables in the problem; This is the location of the Cordyceps sinensis with the minimum fitness value; and They represent the first The and the first The position of the first Cordyceps sinensis. Since the suitability of Cordyceps sinensis is arranged from highest to lowest, the first... The performance of the first Cordyceps sinensis was better than that of the second. Cordyceps sinensis is better. Alpha is defined as: (10); 2) Spiral rising operator: In the spiral rising operator stage, the search mechanism used by Cordyceps sinensis is described by the following mathematical formula: (11); in, The search step size for Cordyceps sinensis at this stage is calculated as follows: (12); in, It is a random number that is uniformly distributed in the range [0,1]. It is a random integer that is either 1 or 2. It is randomly selected for the whole; It is the current iteration number. It represents the maximum number of iterations. This represents the search radius of the cordyceps, used to perform a local search around it to find the optimal solution. When At this point, the cordyceps will perform a detailed search within a small region. Furthermore, as it gradually approaches the maximum iteration, this parameter will gradually approach 1. This gradual adjustment ensures that if the search gets stuck in a local optimum, increasing the parameter will prevent further problems. This can enhance the algorithm's ability to avoid local optima in the later stages of iteration.

[0039] (2) During the larval parasitism process, the CFO algorithm guides population renewal by simulating the strategic choices of Cordyceps sinensis between "optimal parasitism" and "reparasitism". The mathematical modeling of this selective parasitism effectively enhances the algorithm's ability to converge to a higher success rate.

[0040] 1) Re-parasitic behavior: In this stage, individual Cordyceps sinensis continue to utilize the resources of the same host larva. To improve parasitic reliability, more adapted individuals will re-parasitize the larva. This process is represented by the following formula: (13); in, Indicates the first The parasitic stage of Cordyceps sinensis; This is its position in the exploration phase; It is a random scalar obtained from a standard normal distribution. Because It is highly likely to be close to zero, therefore the displacement is small in most cases; however, in a few cases, It will take a larger value, thus producing a significant displacement, pushing Cordyceps sinensis into a new exploration area, which helps to break out of the local optimum.

[0041] 2) Optimal parasitic behavior, unlike "reparasitic behavior" which targets the same host, primarily occurs when Cordyceps sinensis encounters larvae already parasitized by other individuals. In this case, the individual's core strategy shifts to actively seeking better global growth conditions, and its behavioral principles are defined as follows: (14); where, parameter The calculation method is as follows: (15); among them, It is a random number uniformly distributed in the range [0,1]; parameter This allows for a larger search step size for Cordyceps sinensis in the early stages of iteration, but as the number of iterations increases, It gradually approaches zero, thus achieving a smooth transition from large-scale exploration to small-scale utilization.

[0042] For example, this invention can improve the Cordyceps sinensis optimization algorithm. To further enhance the global optimization capability and convergence accuracy of the original CFO, this paper introduces three improvement mechanisms based on the original CFO's "fluctuating progress-spiral ascent-reparasitism-optimal parasitism" framework: the Chebyshev chaotic mapping initialization strategy, the cross-fertilization mutation strategy, and the Thinking Innovation Strategy (TIS). The improved algorithm enhances the diversity of the initial population, the escape capability of the mid-stage search, and the stability of the late-stage convergence at different stages, thereby achieving an adaptive balance between global exploration and local development. The improvement principle is described below.

[0043] (1) Chebyshev Chaotic Initialization Strategy: The original CFO algorithm uses uniform random initialization, which easily leads to uneven distribution of individuals in the search space, resulting in insufficient diversity in the early search stage. To enhance the coverage of the initial population, this invention uses Chebyshev chaotic mapping for initialization. This mapping has ergodicity and pseudo-randomness, which can make the search individuals evenly distributed in the global scope, thereby improving the global exploration capability of the algorithm.

[0044] Let the search space dimension be . Population size is , No. The chaotic sequence of individuals is generated by the Chebyshev mapping: (16); among them, For the first The value of the next chaotic iteration is normalized and mapped to the search interval. The initial position of the individual can be obtained: (17) This strategy effectively improves the diversity and coverage of the initial solutions, avoids the algorithm from getting trapped in early local optima, and provides a high-quality initial distribution for the subsequent search phase.

[0045] (2) Cross-sectional and cross-sectional fusion and variation strategy To further improve the global jump-out capability and search accuracy of the CFO during the mid-term search phase, this invention introduces a cross-sectional fusion mutation operator between the exploration and parasitic phases. This strategy combines three mechanisms: global learning, individual perturbation, and Levy flight, achieving dynamic balance through adaptive control parameters. The mutation position update formula is as follows: (18); (19); among them, These are the weighting coefficients. Let Levy distribution step size be , and These represent the current and maximum number of iterations, respectively.

[0046] This strategy enables the algorithm to maintain a large-scale global exploration in the early stages of the search, while gradually enhancing local development capabilities in the later stages, effectively avoiding premature convergence.

[0047] (3) Innovative Thinking Strategy: To improve the stability of local exploitation and convergence in the later stages of the algorithm, this paper introduces an innovative thinking strategy. This strategy guides individuals to conduct a "rethinking" re-search near the global optimum by introducing cognitive perturbation and dynamic adjustment coefficients, thereby achieving better local exploitation. Its mathematical expression is as follows: (20); among them, , This represents the current globally optimal individual position. As a dynamic adjustment factor, .

[0048] (twenty one); This strategy introduces "thinking jumps" at the end of the algorithm to achieve adaptive perturbation, which can generate new potential solutions near the global optimum, thereby improving the convergence accuracy and stability of CFO.

[0049] For example, the performance verification of the improved CFO optimization algorithm provided in this embodiment of the invention is as follows. To verify the effectiveness of the improved CFO algorithm proposed in this invention, we conducted a system simulation experiment in the MATLAB R2023b environment. The experiment set the population size N=30 and the maximum number of iterations T=100. A total of 12 standard test functions were selected as evaluation benchmarks, including 4 unimodal functions (F1-F4), 5 multimodal functions (F5-F9), and 3 fixed-dimensional composite functions (F10-F12) to comprehensively evaluate the performance of the algorithm on different types of problems. The mathematical expressions, search spaces, and theoretical optimal values ​​of each test function are summarized in Table 1.

[0050] Table 1 Test Functions

[0051] Experimental results show that the improved CFO algorithm exhibits superior performance on most test functions. For unimodal functions, such as F1 and F2, the algorithm can stably converge to near the theoretical optimum, and the average error is significantly lower than that of the comparative algorithms, indicating good convergence accuracy. For multimodal functions, the improved CFO demonstrates stronger global exploration and the ability to escape local optima. Especially in complex multimodal problems such as F6, its optimization results are significantly better than the original CFO and classic algorithms such as GWO, demonstrating stronger robustness.

[0052] Based on the data in Table 1 and Figure 2 The convergence curve analysis shows that the improved CFO algorithm has significant advantages in terms of solution accuracy, convergence speed, and stability, effectively alleviating the limitations of traditional optimization algorithms in handling complex, multi-modal, and high-dimensional problems, such as premature convergence and insufficient search efficiency. This is mainly attributed to the three strategies introduced: enhancing population diversity in the early stages of the search, improving global exploration and local escape capabilities in the middle stages, and achieving smoother and faster convergence behavior in the later stages.

[0053] For example, the steps for optimizing SVMD parameters using the improved CFO algorithm provided in this embodiment of the invention are as follows. SVMD is an advanced signal decomposition method, and its performance largely depends on the selection of two key parameters: the penalty factor α and the number of modes K. Improper setting of these two parameters may lead to problems such as mode aliasing, over-decomposition, or under-decomposition, thereby affecting the accuracy of signal decomposition. Traditional parameter selection methods typically rely on empirical trial and error, which is inefficient and makes it difficult to guarantee obtaining the optimal solution. Therefore, this invention employs an improved CFO optimization algorithm to optimize the K and α values ​​of SVMD in order to quickly and accurately obtain the optimal parameter combination.

[0054] Combining the advantages of the improved CFO optimization algorithm, this invention proposes an ICFO-SVMD signal decomposition method based on the CFO algorithm. This invention enhances the algorithm's global search capability by introducing Chebyshev chaotic mapping, cross-sectional fusion mutation strategy, and innovative thinking strategy, avoiding the trap of local optima, and achieving efficient exploration and precise convergence of the parameter space. This yields the optimal K and α values ​​for SVMD, ensuring the signal can be effectively decomposed. The overall process of ICFO-SVMD signal decomposition is as follows: Figure 3 As shown.

[0055] S103. Based on the optimal number of modes and the penalty factor, the vibration signal is decomposed to obtain multiple intrinsic mode functions.

[0056] As one possible implementation, step S103 can be specifically implemented as steps S1031-S1033.

[0057] S1031. Input the optimal number of modes and the penalty factor into the successive variational mode decomposition model to construct the vibration signal as a constrained variational problem.

[0058] S1032. Solve the constrained variational problem iteratively using the alternating direction multiplier method.

[0059] S1033. After the iteration is completed, a series of intrinsic mode functions with a number equal to the optimal mode number are output. Each intrinsic mode function represents a specific frequency component in the vibration signal.

[0060] S104. Calculate the Pearson correlation coefficient between each intrinsic mode function component and the vibration signal, and combine it with a preset threshold to divide the multiple intrinsic mode functions into effective components and noise components.

[0061] As one possible implementation, step S104 can be specifically implemented as steps S1041-S1044.

[0062] S1041. Calculate the Pearson correlation coefficient between each intrinsic mode function and the vibration signal in sequence.

[0063] S1042. Based on the Pearson correlation coefficient corresponding to each intrinsic mode function and the preset correlation threshold, a comparative analysis is performed to determine the comparison result.

[0064] S1043. If the comparison result shows that the Pearson correlation coefficient is greater than or equal to the correlation threshold, then the intrinsic mode function is determined to be strongly correlated with the vibration signal, and the intrinsic mode function is determined to be an effective component.

[0065] S1044. If the comparison result shows that the Pearson correlation coefficient is less than the correlation threshold, then the intrinsic mode function is determined to be strongly correlated with the noise, and the intrinsic mode function is determined to be the noise component.

[0066] Optionally, the vibration signal joint denoising method based on improved wavelet thresholding provided in this embodiment of the invention can, after step S104, directly set the eigenmode functions of the components determined to be noise components to zero; or, perform secondary wavelet thresholding denoising on the noise components to obtain useful information components in the noise components. The useful information components are then superimposed back into the effective component set to participate in vibration signal reconstruction.

[0067] S105. The effective components are denoised using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised components of the intrinsic mode function.

[0068] As one possible implementation, step S105 can be specifically implemented as steps S1051-S1056.

[0069] S1051. Perform wavelet transform on each effective component to obtain high-frequency wavelet coefficient subbands distributed across multiple scales.

[0070] S1052. Calculate the signal-to-noise ratio for each high-frequency wavelet coefficient sub-band.

[0071] S1053. Determine the adaptive scaling factor of each high-frequency wavelet coefficient sub-band based on the signal-to-noise ratio of each high-frequency wavelet coefficient sub-band.

[0072] S1054. Based on the adaptive scaling coefficients of each high-frequency wavelet coefficient sub-band and the preset basic threshold, the adaptive threshold of each high-frequency wavelet coefficient sub-band is obtained by multiplying them.

[0073] Among them, the higher the adaptive threshold corresponding to the high-frequency wavelet coefficient sub-band with low signal-to-noise ratio, the lower the adaptive threshold corresponding to the high-frequency wavelet coefficient sub-band with high signal-to-noise ratio.

[0074] S1055. Based on the adaptive threshold of each high-frequency wavelet coefficient sub-band, the wavelet coefficients of each high-frequency wavelet coefficient sub-band are thresholded to obtain the processed wavelet coefficients of each high-frequency wavelet coefficient sub-band.

[0075] S1056. After processing the wavelet coefficients of each high-frequency wavelet coefficient subband, perform inverse wavelet transform on the wavelet coefficients to reconstruct the noise-reduced vibration signal.

[0076] S106. Reconstruct the denoised intrinsic mode function components to obtain the denoised vibration signal.

[0077] As one possible implementation, embodiments of the present invention can directly add the denoised intrinsic mode function components in the time domain at corresponding time points to obtain the denoised vibration signal.

[0078] For example, in practical engineering applications, the acquired signals are usually mixed with various random noises, and their relationship is generally described by the additive noise model of equation (22). (22); among them, For real and useful signals; This is the noise term.

[0079] Traditional time-domain or frequency-domain linear filtering methods have limitations when processing non-stationary, multi-component signals. They often struggle to effectively suppress noise while perfectly preserving the key time-frequency local features of the signal. Wavelet transform possesses excellent time-frequency localization properties, enabling multi-scale decomposition of signals. This allows the low-frequency component to characterize the overall trend of the signal, while the high-frequency component portrays details and abrupt changes. This invention performs wavelet decomposition on a noisy signal, then thresholds the high-frequency coefficients in the wavelet coefficient domain to suppress wavelet coefficients contributed by noise, and finally obtains a denoised signal through wavelet reconstruction.

[0080] For example, improving the wavelet threshold: The selection of the wavelet threshold directly determines the balance between noise reduction intensity and signal fidelity, and is one of the core issues in wavelet threshold denoising. If the threshold is set too high, it can easily cause excessive smoothing of signal details; while if the threshold is too low, residual noise will be significant. The "universal threshold" derived based on the maximum likelihood criterion under the Gaussian noise model is expressed as follows: (23); among them, The noise standard deviation is typically obtained by estimating the median of the high-frequency subband coefficients. This is the signal length.

[0081] The universal threshold can achieve asymptotically optimal mean square error (MSE) performance under the Gaussian white noise assumption, thus exhibiting good robustness. However, this threshold is significantly conservative with respect to noise, which can easily lead to problems such as detail attenuation and edge blurring in practical signal processing, especially in structurally rich vibration signals.

[0082] To overcome this deficiency and improve structural fidelity while maintaining the robustness of the universal threshold, this invention introduces the concept of adaptive attenuation within a fixed threshold framework to modulate the original threshold. The improved threshold is: (24); among them, This is the adjustment coefficient, and its value is... It is used to control the actual effective size of the threshold under different local structural conditions, so as to achieve adaptive adjustment of the threshold.

[0083] In recent years, the uniform fixed threshold used in traditional Visu Shrink has proven difficult to adapt to the differences in signal / noise energy distribution across different frequency bands. Therefore, related research has begun to introduce the idea of ​​sub-band adaptive thresholding in the wavelet domain, that is, estimating the noise variance and signal variance separately within each sub-band and dynamically adjusting the threshold based on local statistical characteristics. Based on this idea, this invention further transforms the noise and signal energy estimation for each sub-band into the form of sub-band signal-to-noise ratio. Let a certain sub-band coefficient... The total energy is (25); The corresponding signal energy can then be estimated as: (26); Based on this, the normalized signal-to-noise ratio factor is constructed: (27); among them, This indicates that the subband is primarily dominated by noise. The smaller the value, the stronger the structural component in the subband.

[0084] To achieve adaptive adjustment for different structural strengths, this invention adopts the following scaling relationship: (28); Through the above processing, when the sub-band is dominated by noise, i.e. When the threshold remains almost unchanged, it retains the strong noise suppression properties of the original general threshold; however, when the subband contains obvious signal structures, the threshold decreases accordingly, thus effectively preventing excessive attenuation of details. Compared with traditional fixed threshold strategies, this invention achieves a better balance between noise suppression capability and structural fidelity.

[0085] For example, improving the threshold function: Traditional wavelet thresholding methods mainly include two categories: soft thresholding and hard thresholding. Soft thresholding has the advantages of good continuity and avoidance of artifacts, but it will produce systematic bias for coefficients with large amplitudes; hard thresholding is unbiased for large coefficients, but there is discontinuity at the threshold, which can easily lead to ringing and artifacts. Therefore, constructing an improved threshold function with good continuity, low bias and adjustability while retaining the advantages of both methods is an important way to improve the quality of wavelet denoising.

[0086] Based on this, the present invention designs an improved threshold function with "soft-hard continuous transition" characteristics. The threshold function is defined as follows: (29); among them, For threshold parameters; As a regulating factor, it controls the strength of threshold contraction; These are the original wavelet coefficients.

[0087] The curves of traditional soft and hard thresholding functions and the wavelet thresholding function improved in this invention are shown in the figure. Figure 4 As shown.

[0088] This invention provides a joint denoising method for vibration signals based on an improved wavelet threshold. It employs a Cordyceps sinensis optimization algorithm to adaptively optimize the number of modes and penalty factor in variational mode decomposition, improving the accuracy and adaptability of signal decomposition. Then, the Pearson correlation coefficient is used to objectively screen the intrinsic mode function components after decomposition, effectively identifying and separating effective components strongly correlated with the original vibration signal, reducing the false rejection of useful information. Finally, the screened effective components are further denoised using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio, achieving dynamic adjustment of denoising intensity within different frequency bands. This effectively suppresses noise while better preserving the detailed features and transient impact components of the signal. This invention solves the noise residue problem of traditional wavelet thresholding methods by optimizing the collaborative processing mechanism of decomposition-component screening-adaptive denoising, improving the signal-to-noise ratio and feature fidelity of vibration signals in strong noise backgrounds.

[0089] Optionally, the vibration signal joint noise reduction method based on improved wavelet threshold provided in this embodiment of the invention further includes steps S201-S204 after step S106.

[0090] S201. Calculate the signal-to-noise ratio improvement of the denoised vibration signal and the vibration signal.

[0091] S202. Calculate the root mean square error between the noise-reduced vibration signal and the reference pure signal.

[0092] S203. Calculate the envelope spectrum of the noise-reduced vibration signal and evaluate the prominence of the fault characteristic frequency components.

[0093] S204. Based on one or more of the following: signal-to-noise ratio improvement, root mean square error, envelope spectrum, and salience, generate a quantitative evaluation result for this noise reduction process.

[0094] Thus, by introducing a multi-dimensional quantitative evaluation system, this invention transforms subjective judgments of noise reduction effectiveness into objective and comparable data indicators. It not only assesses the intensity and fidelity of noise reduction through signal-to-noise ratio improvement and root mean square error, but also directly verifies the effectiveness of the method in the core application scenario of fault diagnosis through envelope spectrum analysis. This comprehensively and reliably demonstrates the overall performance and engineering practical value of the proposed joint noise reduction method.

[0095] Optional, such as Figure 5 As shown, the vibration signal joint denoising method based on improved wavelet threshold provided in this embodiment of the invention further includes steps 1 to 6.

[0096] Step 1: Obtain the raw signal.

[0097] Step 2: Using the minimum envelope entropy as the fitness function for optimizing SVMD parameters using ICFO, adaptive optimization is performed on the two key parameters of SVMD—the number of decomposition modes K and the penalty factor α—to obtain the optimal parameter combination [K, α].

[0098] Step 3: Decompose the noisy signal using the optimized SVMD optimal parameter combination [K, α] to obtain a series of intrinsic mode functions.

[0099] Step 4: Next, calculate the Pearson correlation coefficient between each IMF component and the original signal. The formula for calculating the Pearson correlation coefficient is shown in the equation. Based on the magnitude of the Pearson correlation coefficient, the IMF components are divided into effective components and noise components. (30); among them, The original signal, For the first One IMF component, and These are their means, This is the signal length.

[0100] Step 5: Denoising is performed on the effective IMF components using an improved wavelet threshold function.

[0101] Step 6: Reconstruct the denoised components to finally achieve signal denoising.

[0102] For example, to verify the effectiveness of the proposed method in the analysis of vibration signals of rotating machinery, simulation experiments were conducted on simulated vibration signals in the Matlab environment. Vibration signals of rotating machinery typically contain various complex noise components caused by background noise, component friction, and external interference. To ensure that the simulation test conditions closely resemble actual engineering applications, the following composite simulation signal containing various typical fault characteristics was constructed. Conduct the test: (31); in, It is a time variable. In this simulated signal, the components... The simple harmonic motion of the rotor was simulated; components This is a typical amplitude modulation signal used to simulate periodic impact modulation phenomena caused by rolling bearing failures, etc.; component To dampen oscillations, a high-frequency natural vibration induced by instantaneous impact on components is simulated. Finally, a noise term is added to simulate noise interference under actual working conditions.

[0103] The constructed signal combination can effectively simulate the scenario of multiple fault characteristics and complex noise coexisting in actual vibration signals. To verify the applicability and superiority of the proposed ICFO-SVMD-improved wavelet threshold joint denoising method in nonlinear and non-stationary vibration signals, the constructed simulation signal was selected as the research object, and comparative experiments were conducted under different noise intensities (SNR = 1dB, 5dB, 10dB, 15dB, and 20dB). Taking the 20dB noise condition as an example, the time-domain waveforms of the original signal and the signal after adding Gaussian white noise are as follows: Figure 6 As shown, the addition of noise significantly obscures the signal's periodic impulses and decaying oscillations, resulting in a significant decrease in signal clarity.

[0104] An improved Cordyceps sinensis optimization algorithm was used to adaptively optimize the key parameters of SVMD—the penalty factor α and the number of decomposed modes K—where the search interval for K is [2, 10] and the search interval for α is [1000, 3000]. After ICFO optimization, the optimal parameter combination [9, 2736] was obtained. Substituting the optimal parameter combination into SVMD, the noisy simulation signal was decomposed to obtain several intrinsic mode functions (IMFs). The Pearson correlation coefficient between each IMF component and the original noiseless signal was calculated, as shown in Table 2. Using the correlation coefficient threshold as a criterion, modes with high correlation were classified as effective components, while the remaining modes were regarded as noise-dominant components and removed. Improved wavelet threshold denoising was applied to the retained effective IMF components, and they were then reconstructed.

[0105] Table 2 Correlation coefficients of each IMF component

[0106] Comparing the original signal with the signal time-domain waveform processed by the ICFO-SVMD-improved wavelet threshold denoising algorithm, the periodic characteristics and high-frequency oscillation components of the signal become clearer after denoising, the noise is effectively suppressed, and key information is preserved.

[0107] To further quantitatively evaluate the denoising performance of the proposed method, this invention compares and analyzes it with several classic algorithms, including traditional wavelet thresholding, VMD, SVMD, CFO-SVMD, and the VMD-wavelet method with unoptimized parameters. Comparing the time-domain waveforms of the noisy simulation signal processed by different denoising algorithms provides a direct assessment of the performance differences between the methods. Compared to the other five comparison methods, the signal processed by the proposed ICFO-SVMD-improved wavelet thresholding method has the closest overall waveform to the original clean signal, exhibiting the best noise suppression and feature fidelity. The signal processed by the traditional wavelet thresholding method is generally smooth, but the impulse amplitude is significantly attenuated; the signal decomposed and reconstructed by VMD or SVMD still retains a large amount of high-frequency noise spikes; while the combined methods such as VMD-WTD and CFO-SVMD improve the denoising effect to some extent, waveform distortion or detail blurring still exists at the impulse peaks. The signal processed by this invention retains the complete impulse component amplitude, the transient high-frequency oscillations are clearly distinguishable, and the signal baseline is stable with almost no residual noise fluctuations.

[0108] To intuitively evaluate the denoising performance of different methods, this invention uses signal-to-noise ratio (SNR) and root mean square error (RMSE) as evaluation metrics for comparative analysis. SNR reflects the intensity relationship between signal and noise, while RMSE measures the deviation between the denoised signal and the original signal. Generally, a RMSE closer to zero is considered to indicate a higher SNR and better denoising performance. The calculation formulas are as follows: (32); (33); Table 3 summarizes the SNR and RMSE performance of each method under different noise intensities. The data in Table 3 shows the SNR and RMSE performance of various noise reduction methods under different noise intensities. Under all noise conditions, the present invention exhibits the highest signal-to-noise ratio and the smallest root mean square error, demonstrating excellent noise reduction performance.

[0109] In summary, the comprehensive quantitative indicators in Table 3 provide precise evidence from a data perspective, validating the superior performance and reliability of the proposed joint denoising method in terms of signal fidelity and noise suppression.

[0110] Table 3 Noise Reduction Effect Evaluation Indicators

[0111] For example, experimental verification using rolling bearing data is provided. To further verify the applicability and effectiveness of the proposed ICFO-SVMD-improved wavelet threshold joint denoising method in actual engineering vibration signals, this invention provides rolling bearing vibration data for experimental verification. This dataset is widely used for fault diagnosis and denoising algorithm performance testing. The experimental object is a 6205-2RS deep groove ball bearing, and its main geometric parameters are shown in Table 4. To simulate noise interference under real working conditions, this invention additionally superimposes -2dB Gaussian white noise onto the original measured signal to improve the rigor of the denoising verification.

[0112] Table 4 lists the main geometric parameters of the bearing, including the inner and outer ring diameters, rolling element diameters, and fault characteristic frequencies. The outer ring fault characteristic frequency is approximately 103.4 Hz. To ensure the time-frequency accuracy of subsequent analysis, a sampling frequency of 12800 Hz was set for the experiment, with approximately 25600 sampling points, which can fully cover the operating cycle and fault characteristic responses of typical rotating machinery.

[0113] Table 4 Basic Bearing Parameters

[0114] The ICFO-SVMD-improved wavelet thresholding method proposed in this invention is used to process the measured signal. Using minimum envelope entropy as the fitness function, the penalty factor α and the number of modes K in SVMD are jointly optimized using an improved Cordyceps sinensis optimization algorithm. The search interval for K is set to [2, 15], and the search interval for α is set to [1000, 1500]. The optimal parameter combination [10, 1400] obtained through ICFO optimization is substituted into SVMD for decomposition, yielding a series of intrinsic mode functions (IMFs). Based on the Pearson correlation coefficient between each IMF and the original signal, modes with high correlation are retained, while other noise-dominated modes are removed. For the effective IMF components, improved wavelet thresholding denoising is applied to effectively suppress noise components, resulting in a reconstructed denoised signal.

[0115] For example, the actual test data of the gearbox is used to verify the applicability of the proposed ICFO-SVMD-improved wavelet threshold joint noise reduction method under actual working conditions. The present invention uses a power transmission simulation test bench (DDS) to collect gearbox fault signals. The test bench mainly consists of a motor, a motor controller, a planetary gearbox, a reduction gearbox and a load. The main parameters of the gearbox used in the test are detailed in Table 5.

[0116] In terms of fault settings, a broken sun gear tooth fault was set up in the experiment, and the experiment was conducted under constant speed and no-load conditions. During data acquisition, the sampling frequency was set to 12800Hz, and the number of sampling points was 25600. To more closely resemble the noise interference in actual industrial scenarios, -2dB Gaussian white noise was added to the raw experimental signal obtained in the laboratory.

[0117] Table 5 Planetary Gearbox Parameters

[0118] This invention, by applying the ICFO-SVMD-improved wavelet threshold denoising method, significantly suppresses noise components in the signal, making the main fault characteristic frequencies clearer. This indicates that the denoising method effectively eliminates noise-induced interference while preserving the key frequency components of the signal, thereby improving signal resolvability. Especially in fault diagnosis, a clear envelope spectrum helps in accurately identifying fault modes. This result verifies the effectiveness and superiority of the proposed method in practical engineering signals.

[0119] Since the data collected in the experiment was not a pure signal, SNR and RMSE could not be used as evaluation metrics for the signal. In order to further quantify the noise reduction effect, Residual Variance Ratio (RVR) and Signal-to-Noise Ratio (SER) were introduced as evaluation metrics.

[0120] (1) Residual variance ratio, which is the proportion of residual noise energy in the signal after quantization and noise reduction. The lower the value, the better the noise reduction effect. (34).

[0121] (2) Signal energy ratio: the change in signal energy before and after quantization and denoising. The higher the value, the more effectively the noise component is suppressed and the energy characteristics of the original signal are better preserved. (35); among them, For noise variance, Signal variance Represents a signal sequence. It is a noise sequence.

[0122] This invention selected typical methods such as VMD, SVMD, SVMD-WTD, and VMD-WTD for comparative analysis, and the experimental results are shown in Table 6. The experimental data show that, compared with other methods, the signal waveform processed by the algorithm in this paper is smoother, and noise components are significantly suppressed, making it particularly suitable for denoising non-stationary and nonlinear signals.

[0123] Table 6. Quantitative evaluation of the denoising effect of different algorithms

[0124] This invention proposes a joint vibration signal denoising method based on an improved Cordyceps sinensis optimization algorithm, successive variational mode decomposition, and improved wavelet threshold. It aims to solve the contradiction between noise suppression and signal fidelity in traditional denoising methods when processing non-stationary, multi-component vibration signals, and has the following technical effects.

[0125] (1) By introducing ICFO to optimize the key parameters of SVMD: the number of modes K and the penalty factor α, the accuracy of signal decomposition is significantly improved. At the same time, the wavelet threshold based on the sub-band signal-to-noise ratio (Sub-band SNR) is used to effectively enhance the noise suppression and signal detail preservation capabilities.

[0126] (2) Experimental results verify the superiority of the present invention under different noise intensities. In the tests of simulated signals and measured signals, the method provided by the present invention exhibits a higher signal-to-noise ratio and a lower root mean square error than the traditional method, effectively suppressing noise and preserving the key features of the signal, especially showing stronger robustness and accuracy in high-noise environments.

[0127] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0128] Figure 7 A schematic diagram of a vibration signal joint noise reduction device based on an improved wavelet threshold provided by an embodiment of the present invention is shown. The noise reduction device 300 includes a communication module 301 and a processing module 302.

[0129] The communication module 301 is used to acquire the vibration signal to be noise-reduced.

[0130] The processing module 302 is used to adaptively optimize the key parameters of successive variational mode decomposition using the Cordyceps sinensis optimization algorithm to obtain the optimal number of modes and penalty factor; based on the optimal number of modes and penalty factor, decompose the vibration signal to obtain multiple intrinsic mode functions; calculate the Pearson correlation coefficient between each intrinsic mode function component and the vibration signal, and combine it with a preset threshold to divide the multiple intrinsic mode functions into effective components and noise components; perform noise reduction processing on the effective components using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised intrinsic mode function components; and reconstruct the denoised intrinsic mode function components to obtain the denoised vibration signal.

[0131] Figure 8This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device 400 includes: a processor 401, a memory 402, and a computer program 403 stored in the memory 402 and executable on the processor 401. When the processor 401 executes the computer program 403, it implements the steps in the above-described method embodiments. Alternatively, when the processor 401 executes the computer program 403, it implements the functions of each module / unit in the above-described device embodiments.

[0132] For example, the computer program 403 may be divided into one or more modules / units, which are stored in the memory 402 and executed by the processor 401 to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 403 in the electronic device 400.

[0133] The processor 401 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0134] The memory 402 can be an internal storage unit of the electronic device 400, such as a hard disk or memory of the electronic device 400. The memory 402 can also be an external storage device of the electronic device 400, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD) card, flash card, etc., equipped on the electronic device 400. Furthermore, the memory 402 can include both internal and external storage units of the electronic device 400. The memory 402 is used to store the computer program and other programs and data required by the terminal. The memory 402 can also be used to temporarily store data that has been output or will be output.

[0135] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A joint noise reduction method for vibration signals based on an improved wavelet threshold, characterized in that, include: Acquire the vibration signal to be denoised; The Cordyceps sinensis optimization algorithm is used to adaptively optimize the key parameters of successive variational mode decomposition to obtain the optimal number of modes and penalty factor; Based on the optimal number of modes and the penalty factor, the vibration signal is decomposed to obtain multiple intrinsic mode functions; Calculate the Pearson correlation coefficient between each intrinsic mode function component and the vibration signal, and combine it with a preset threshold to divide the multiple intrinsic mode functions into effective components and noise components; The effective components are denoised using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised components of the intrinsic mode function. The denoised intrinsic mode function components are reconstructed to obtain the denoised vibration signal.

2. The vibration signal joint noise reduction method based on improved wavelet threshold according to claim 1, characterized in that, The method employs a Cordyceps sinensis optimization algorithm to adaptively optimize the key parameters of successive variational mode decomposition, obtaining the optimal number of modes and penalty factor, including: Set the range of parameters to be optimized, where the search range for the number of modes is an integer between two and ten, and the search range for the penalty factor is a real number between one thousand and three thousand. An improved Cordyceps sinensis optimization algorithm was used for optimization. In the optimization process, chaotic mapping was used to initialize the population, a cross-mutation mechanism was introduced in the iteration, and a creative thinking strategy was used for fine search in the later stage. The minimum envelope entropy of the decomposed signal components is used as the fitness function to measure the decomposition effect. The optimization algorithm is run to iteratively find the combination of mode number and penalty factor that minimizes the fitness function, and the combination is output as the optimal parameters, which include the optimal mode number and penalty factor.

3. The vibration signal joint noise reduction method based on improved wavelet threshold according to claim 1, characterized in that, Based on the optimal mode number and penalty factor, the vibration signal is decomposed to obtain multiple intrinsic mode functions, including: By inputting the optimal number of modes and the penalty factor into the successive variational mode decomposition model, the vibration signal is constructed as a constrained variational problem. This constrained variational problem is solved iteratively using the alternating direction multiplier method. After iteration, a series of intrinsic mode functions with a number equal to the optimal mode number are output. Each intrinsic mode function represents a specific frequency component in the vibration signal.

4. The joint noise reduction method for vibration signals based on improved wavelet thresholding according to claim 1, characterized in that, The calculation of the Pearson correlation coefficient between each intrinsic mode function component and the vibration signal, and the division of multiple intrinsic mode functions into effective components and noise components based on a preset threshold, includes: Calculate the Pearson correlation coefficient between each intrinsic mode function and the vibration signal in sequence; Based on the Pearson correlation coefficient corresponding to each intrinsic mode function and the preset correlation threshold, a comparative analysis is performed to determine the comparison results; If the comparison result shows that the Pearson correlation coefficient is greater than or equal to the correlation threshold, then the intrinsic mode function is determined to be strongly correlated with the vibration signal, and the intrinsic mode function is determined to be an effective component. If the comparison result shows that the Pearson correlation coefficient is less than the correlation threshold, then the intrinsic mode function is determined to be strongly correlated with the noise, and the intrinsic mode function is identified as the noise component.

5. The vibration signal joint noise reduction method based on improved wavelet threshold according to claim 4, characterized in that, After calculating the Pearson correlation coefficient between each intrinsic mode function component and the vibration signal, and dividing the multiple intrinsic mode functions into effective components and noise components based on a preset threshold, the method further includes: The eigenmode functions identified as noise components are directly set to zero; or, the noise components are subjected to secondary wavelet threshold denoising to obtain the useful information components in the noise components. Useful information components are superimposed back into the effective component set to participate in the reconstruction of vibration signals.

6. The vibration signal joint noise reduction method based on improved wavelet threshold according to claim 1, characterized in that, The effective components are denoised using an improved wavelet threshold function based on adaptive adjustment of subband signal-to-noise ratio to obtain the denoised intrinsic mode function components, including: Wavelet transform is performed on each effective component to obtain high-frequency wavelet coefficient subbands distributed across multiple scales; Calculate the signal-to-noise ratio for each high-frequency wavelet coefficient sub-band; Based on the signal-to-noise ratio of each high-frequency wavelet coefficient sub-band, determine the adaptive scaling factor of each high-frequency wavelet coefficient sub-band; Based on the adaptive scaling factor of each high-frequency wavelet coefficient sub-band and the preset basic threshold, the adaptive threshold of each high-frequency wavelet coefficient sub-band is obtained by multiplying them. Among them, the adaptive threshold of the high-frequency wavelet coefficient sub-band with low signal-to-noise ratio is higher, and the adaptive threshold of the high-frequency wavelet coefficient sub-band with high signal-to-noise ratio is lower. Based on the adaptive threshold of each high-frequency wavelet coefficient sub-band, the wavelet coefficients of each high-frequency wavelet coefficient sub-band are thresholded to obtain the processed wavelet coefficients of each high-frequency wavelet coefficient sub-band. After processing the wavelet coefficients of each high-frequency wavelet coefficient subband, inverse wavelet transform is performed on the wavelet coefficients to reconstruct the noise-reduced vibration signal.

7. The joint noise reduction method for vibration signals based on improved wavelet thresholding according to claim 1, characterized in that, The process of reconstructing the denoised intrinsic mode function components to obtain the denoised vibration signal includes: Based on the denoised intrinsic mode function components, they are directly added together in the time domain at corresponding time points to obtain the denoised vibration signal.

8. The joint noise reduction method for vibration signals based on improved wavelet thresholding according to any one of claims 1 to 7, characterized in that, After reconstructing the components of the denoised intrinsic mode function to obtain the denoised vibration signal, the method further includes: Calculate the signal-to-noise ratio improvement between the noise-reduced vibration signal and the original vibration signal; Calculate the root mean square error between the noise-reduced vibration signal and the reference clean signal; Calculate the envelope spectrum of the noise-reduced vibration signal and assess the prominence of the fault characteristic frequency components; The quantitative evaluation result of this noise reduction process is generated based on one or more of the signal-to-noise ratio improvement, root mean square error, envelope spectrum, and prominence.

9. The joint noise reduction method for vibration signals based on improved wavelet thresholding according to any one of claims 1 to 7, characterized in that, The method is applicable to noise reduction scenarios for at least one of the following rotating machinery vibration signals: fault signals of the outer ring, inner ring, and rolling elements of rolling bearings; fault signals of broken teeth, pitting, and wear in gearboxes; fault signals of imbalance, misalignment, and rubbing in rotor systems; and broadband vibration and impact signals from equipment such as hydraulic pumps, fans, and compressors.

10. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor being configured to invoke and run the computer program stored in the memory to perform the method as described in any one of claims 1 to 9.

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