A method and apparatus for denoising rolling data based on IPOA-VMD combined with wavelet thresholding

Abstract

This application provides a method and apparatus for denoising rolling data based on IPOA-VMD combined with wavelet thresholding. The method includes: first, constructing a simulated bending force signal of a cold rolling work roll and superimposing Gaussian white noise as the test object; second, using an improved IPOA algorithm, adaptively optimizing the number of modes and penalty factor of VMD to improve the mode decomposition quality; then, using permutation entropy to evaluate and screen the complexity of the decomposed IMF components, applying improved wavelet thresholding to the components requiring denoising, and directly participating in reconstruction of the retained components; finally, evaluating the performance using SNR and RMSE. Results show that this method can effectively suppress rolling signal noise while retaining useful feature information well, exhibiting high signal fidelity.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and in particular to a method and apparatus for denoising rolling data based on IPOA-VMD combined with wavelet thresholding. Background Technology

[0002] During cold rolling, various factors such as speed fluctuations and load variations often generate vibration signals with non-stationary characteristics. These signals exhibit strong variability in both the time and frequency domains, with unstable frequency and amplitude, and contain components from multiple frequency bands. These signals are usually accompanied by strong noise components, which may originate from mechanical equipment vibration, external interference, temperature fluctuations, and frictional noise generated during processing. The presence of noise signals often masks useful features in the original signal, especially for weak anomalies such as fault signals or minor performance fluctuations. Noise can prevent these features from being effectively identified, thus affecting the accuracy of subsequent prediction models and the accurate calculation of efficiency coefficients. Therefore, effective noise reduction of production data to remove interference signals is crucial. By reducing noise, more accurate signal features can be extracted, thereby improving the accuracy and reliability of rolling process modeling, enhancing equipment fault prediction capabilities, and ultimately improving the stability and efficiency of the production process.

[0003] Currently, commonly used signal denoising methods mainly include wavelet transform, empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and their combinations. However, in practical applications, traditional methods have obvious drawbacks: wavelet transform relies on manual selection of wavelet basis and decomposition level, resulting in poor adaptability; EMD and its improved methods suffer from severe mode aliasing, prominent endpoint effects, and weak noise resistance; while variational mode decomposition (VMD) can effectively suppress mode aliasing, its decomposition effect is highly dependent on the parameter settings of the number of modes and penalty factor. Improper parameter selection can lead to insufficient or excessive decomposition, directly reducing the denoising effect and signal fidelity.

[0004] In summary, existing technologies cannot simultaneously meet the engineering requirements of strong noise suppression, effective feature preservation, adaptive parameter optimization, and high robustness in the cold rolling industry. Therefore, there is an urgent need to propose a rolling data noise reduction method that is highly adaptive, accurately decomposed, and has excellent noise reduction effect, so as to improve the quality of rolling signals and provide reliable data support for intelligent detection and safe and stable operation of the cold rolling process. Summary of the Invention

[0005] In view of the above problems, this application provides a method and apparatus for denoising rolling data based on IPOA-VMD combined with wavelet thresholding, which aims to overcome the above problems or at least partially solve them.

[0006] In a first aspect, embodiments of this application provide a method for denoising rolling data based on IPOA-VMD combined with wavelet thresholding, the method comprising: Acquire the raw, noisy signal of the on-site rolling data; The optimal combination of VMD parameters is determined by improving the IPOA method, and based on the optimal combination of VMD parameters, VMD processing is performed on the original noisy signal to obtain several intrinsic mode function components. Calculate the permutation entropy of each intrinsic mode function component, and select the components that need noise reduction and those that do not need noise reduction based on the screening threshold. The denoised IMF component is obtained by denoising the component to be denoised based on the improved wavelet threshold function. The denoised IMF component and the undenoised IMF component are decomposed to obtain the denoised signal.

[0007] Furthermore, the determination of the optimal combination of VMD parameters through the improved IPOA method includes: The optimization variables are initialized based on chaotic sequences to generate an original population. The reverse solution of the optimization variables is obtained by refraction back learning and merged with the original population. The top N high-quality solutions are selected as the final initial population. A global search is performed based on the Levy transition strategy, with the minimum permutation entropy as the fitness function, and the position is updated based on the fitness values ​​of each individual in the final initial population. When the preset number of iterations is reached, the optimal combination of VMD parameters is output; the optimal combination of VMD parameters includes the optimal number of modes and the optimal penalty factor.

[0008] Furthermore, the formula for the position update is: In the formula: in, Let be the individual position in the t-th iteration. Current global optimal position This is the mean vector of the current population position. For the number of iterations, The maximum number of iterations, To optimize the number of variables, This is the step scaling factor. The random variable is used to generate the random step size of Levy. For scale parameters, The absolute value of the random variable. It is a constant. The transfer factor changes with iteration.

[0009] Furthermore, the VMD processing of the original noisy signal based on the optimal VMD parameter combination yields several intrinsic mode function components, including: The original noisy signal is decomposed into multiple bandpass mode components with different center frequencies; For each bandpass mode component, convolve it with the Hilbert kernel to obtain the analytic signal corresponding to each bandpass mode component; Based on complex exponential modulation, the spectrum of each analytical signal is shifted to the fundamental frequency to obtain the analytical signal after the spectrum shift. The gradient norm of the analytic signal after each spectral basis shift is defined as the bandwidth of each modal component, and the VMD variational optimization model is constructed with the minimum sum of the bandwidths of all modal components as the optimization objective. Based on the Lagrange augmented function, the VMD variational optimization model is solved, and finally all the intrinsic mode components and their corresponding center frequencies after VMD decomposition are obtained.

[0010] Further, the calculation of the permutation entropy of each intrinsic mode function component, and the selection of components requiring denoising and those not requiring denoising based on a screening threshold, includes: Calculate the permutation entropy of each intrinsic mode function component; Determine whether the permutation entropy of each intrinsic mode function component is greater than the screening threshold. If it is, the intrinsic mode function component is a component that needs noise reduction; otherwise, the intrinsic mode function component is a component that does not need noise reduction.

[0011] Furthermore, the improved wavelet threshold function is: in, The original wavelet cardinality; The wavelet cardinality after thresholding; For the threshold; It is a regulating factor.

[0012] Furthermore, the wavelet basis of the improved wavelet threshold function is dbN, the vanishing moment order is 3, and the decomposition level is 5.

[0013] Secondly, embodiments of this application provide a rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding. The device is used to implement the above-described method and includes: The acquisition module is used to acquire the raw, noisy signal of the on-site rolling data; The decomposition module is used to determine the optimal combination of VMD parameters by improving the IPOA method, and to perform VMD decomposition on the original noisy signal based on the optimal combination of VMD parameters to obtain several intrinsic mode function components. The filtering module is used to calculate the permutation entropy of each intrinsic mode function component and filter out the components that need to be denoised and the components that do not need to be denoised according to the filtering threshold. The noise reduction module is used to denoise the components to be denoised based on the improved wavelet threshold function to obtain the denoised IMF components; The reconstruction module is used to reconstruct the denoised IMF components and the denoised IMF components to obtain the denoised signal.

[0014] Compared with the prior art, the specific beneficial effects of the present invention are as follows: First, this invention constructs a Pelican Optimization Algorithm (IPOA) based on multi-strategy fusion improvement. Through chaotic sequence initialization, refraction inverse learning mechanism and Levy transition strategy, it significantly improves population diversity and global search capability, thereby enabling the rapid and accurate determination of the optimal number of modes and penalty factor of VMD algorithm, avoiding decomposition errors caused by manual experience setting, and laying the foundation for subsequent accurate decomposition.

[0015] Second, this invention uses the optimal parameter combination obtained through IPOA optimization to perform VMD decomposition on noisy signals, which can adaptively decouple complex rolling signals into several band-limited intrinsic mode components (IMFs). Compared with traditional EMD or fixed-parameter VMD, this method significantly suppresses the problems of mode aliasing, frequency band confusion, and boundary effects that exist in traditional EMD and VMD methods, making the frequency distribution of each IMF component more concentrated and the characteristics clearer.

[0016] Third, this invention achieves adaptive screening of IMF components by introducing permutation entropy, which can accurately distinguish between noise-dominant components and effective information components. It performs wavelet threshold denoising only on high-noise components, suppressing noise to the maximum extent while fully preserving useful features. This solves the signal distortion problem caused by blind denoising in traditional methods and effectively avoids the omission of effective information or the residue of noise. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a waveform diagram of the cold rolling bending roll force signal in the embodiment; Figure 2 This is a flowchart of the VMD algorithm in the embodiment; Figure 3 This is a flowchart of the Pelican Optimization Algorithm (IPOA) based on multi-strategy fusion improvement in the embodiment; Figure 4 This is a curve comparison chart of the soft threshold function, hard threshold function, and improved threshold function in the embodiments; Figure 5 This is a flowchart of the rolling data denoising method using IPOA-VMD combined with wavelet thresholding proposed in this invention. Figure 6 These are the denoising results based on different decomposition levels of the dbN wavelet basis; Figure 7 These are the denoising results based on different decomposition levels of the symN wavelet basis; Figure 8 These are noise reduction results based on different decomposition levels of the coifN wavelet basis; Figure 9 It is the IPOA-VMD decomposition result of cold rolling bending roll force simulation data; Figure 10 (a)-(b) are , At that time, the intrinsic mode function spectrum obtained by decomposing the signal using the IPOA-VMD algorithm proposed in this invention is shown; where (a) is the spectrum of IMF1-5 and (b) is the spectrum of IMF6-11. Figure 11 It is the cosine similarity of each IMF component; Figure 12 It is the permutation entropy of each IMF component; Figure 13 It is the effect of IPOA-VMD combined with wavelet noise reduction; Figure 14 It is the effect of VMD combined with wavelet denoising. Detailed Implementation

[0019] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0020] Example 1: Refer to Figure 5 This embodiment provides a method for denoising rolling data based on IPOA-VMD combined with wavelet thresholding, including the following steps: Step 1: Acquire the raw, noisy signal of the on-site rolling data; In actual cold rolling processes, production signals are affected by various interferences, resulting in non-stationary characteristics. In this embodiment, the original signals containing noise in the production site are processed. Furthermore, during the experimental phase, based on the characteristics of the bending force of the work rolls in the production site, a set of simulated work roll bending force signals is artificially synthesized as pure signals, and 25dB of Gaussian white noise is added to obtain simulated noisy signals, which serve as test data for subsequent parameter analysis and noise reduction experiments. Figure 1 Figures (a)-(c) show the time-domain waveforms of the established pure signal, the noisy signal, and the simulated signal after adding white noise, respectively. Figure 1 It can be seen that noise severely interferes with the local fluctuation characteristics and trends of the signal, obscuring the key information of the signal.

[0021] Step 2: Determine the optimal combination of VMD parameters by improving the IPOA method, and perform VMD processing on the original noisy signal based on the optimal combination of VMD parameters to obtain several intrinsic mode function components; the optimal combination of VMD parameters includes the optimal number of modes and the optimal penalty factor; Empirical Mode Decomposition (EMD) can decompose complex nonlinear signals into several intrinsic mode functions (IMFs), each representing an independent frequency component. EMD decomposes based on the local characteristics of the signal itself, exhibiting good adaptability and local time-frequency analysis capabilities. However, EMD also suffers from severe mode aliasing, endpoint effects, and a lack of theoretical support. In 2014, Dragomiretskiy proposed Variational Mode Decomposition (VMD) based on EMD. This method introduces variational theory and frequency domain modeling, decomposing the signal into several frequency-based mode functions by minimizing the sum of the bandwidths of the mode components, effectively overcoming the mode aliasing problem commonly found in EMD. In the VMD decomposition process, each obtained mode component can be regarded as a band-limited intrinsic mode function (BIMF), whose expression is: (1) in, It is a phase function that is not monotonically decreasing; The envelope is not less than zero, and the envelope and the instantaneous angular frequency are... The rate of change of is extremely slow compared to the rate of change of the phase function; The VMD algorithm will analyze the real-valued signal. Consider as multiple bandpass mode functions with different center frequencies The core idea is to achieve high-resolution mode decomposition by minimizing the bandwidth of each mode function through variational optimization methods, while ensuring that the original signal can be reconstructed by the sum of all modes. For example... Figure 2 As shown, the specific steps include: A1: For each bandpass mode component to be extracted By convolving with the Hilbert kernel, the analytic signal corresponding to the bandpass mode component is obtained, thereby extracting the one-sided spectral form of the mode component; The analytic signal after Hilbert transform is: (2) in, This represents the convolution operation. Represents the Hilbert nucleus. It is a unit impulse function. It is the imaginary unit.

[0022] A2: Based on complex exponential modulation, the spectrum of each analytical signal is shifted to the fundamental frequency to obtain the analytical signal after the spectrum shift; To further estimate the frequency domain distribution characteristics of the modal signal, a complex exponential term is used. The first The spectrum of each modal component is shifted to the fundamental frequency position, thereby normalizing the center frequency of each modal component to near zero frequency; The analytic signal after the spectral basis shift is: (3) in, Indicates the center frequency.

[0023] A3: Define the gradient norm 2 of the analytic signal after each spectral basis shift as the bandwidth of each bandpass mode component, and construct a VMD variational optimization model with the minimum sum of bandwidths of all mode components as the optimization objective. Specifically, based on the Gaussian smoothing criterion, the gradient norm (i.e., the second norm) of the analytic signal is defined as the bandwidth. With the objective of minimizing the sum of the bandwidths of each mode under the constraint of the modal reconstruction signal, the following VMD variational optimization model is established: (4) in, This represents the individual intrinsic mode components obtained after decomposition; The center frequency corresponding to each intrinsic mode component; It is the first-order time derivative; The unit impulse function (Dirac function); This indicates a constraint condition.

[0024] A4: Based on the Lagrange augmented function, solve the VMD variational optimization model to obtain all intrinsic mode components and their corresponding center frequencies after VMD decomposition, thus completing the adaptive mode decomposition of the signal. Specifically, to further solve the above VMD variational optimization model, Lagrange multipliers are introduced while preserving the constraints. and secondary penalty factor This transforms the original optimization problem into an unconstrained optimization problem, whose corresponding augmented Lagrangian function is: (5) in, Represents the L2 norm; The VMD algorithm introduces Lagrange multipliers. and secondary penalty factor The original constraint minimization problem is transformed into the corresponding augmented Lagrangian function form, thus transforming the problem-solving process into finding the saddle point of the Lagrangian function. One commonly used method for solving constrained variational problems is the Alternating Direction Method of Multipliers (ADMM), which is favored for its good convergence and computational efficiency. This method updates each sub-variable sequentially through alternating iterations, gradually approximating the optimal solution to the unconstrained problem. Specifically, the VMD algorithm updates each eigenmode component sequentially in each iteration. Its corresponding center frequency and frequency domain Lagrange multipliers Achieve optimal variational decomposition of the original signal: (6) To simplify the expression, the first iteration will be... The latest center frequency of each modal component Recorded as By using Passavar's theorem and Planchel's theorem, the constrained variational problem in the time domain is transformed into the frequency domain, thus obtaining the frequency domain form of the objective function: (7) in, Represents frequency variables. This represents the k-th modal component obtained in the (n+1)-th iteration. Represents the original signal The frequency domain representation, Lagrange multipliers The frequency domain representation of .

[0025] Based on equation (7), using replace This further simplifies the frequency shift in the first term, resulting in equation (8).

[0026] (8) Furthermore, by utilizing the Hermie symmetry of real signals, the integration domain in equation (8) can be restricted to the non-negative frequency range (0 to ∞), and the L2 norm metric can be transformed into an integral form, resulting in the objective function shown in equation (9): (9) Therefore, the solution to the VMD variational optimization model is: (10) Due to the center frequency Only in the bandwidth estimation term, then The iterative update formula is: (11) and The solution process is the same. Transforming equation (11) into the frequency domain, we can obtain: (12) Using the double ascent method Update: (13) The termination condition for the loop iteration is given by equation (14): (14) in, This represents the convergence accuracy or tolerance threshold, and is a very small positive number. This represents the updated intrinsic mode components. This represents the intrinsic mode components before the update; Secondly, according to the decomposition steps of the VMD algorithm, the number of modes needs to be preset before performing mode decomposition on the signal. and penalty factors Among them, the number of modes This determines the number of sub-bands the signal is divided into. Setting the value too high may lead to excessive signal decomposition and increased redundancy; conversely, setting it too low may prevent the extraction of detailed frequency information, resulting in mode aliasing or loss of frequency band information. This parameter is used to adjust the bandwidth of the modal components, and its value affects the spectral concentration and decomposition accuracy. Therefore, to achieve high-quality signal decomposition, it is essential to select appropriate parameter combinations. To achieve the optimal balance between the number of modes and the degree of bandwidth compression, this application proposes an improved pelican optimization algorithm based on multi-strategy fusion, namely the improved IPOA algorithm.

[0027] The Pelican Optimization Algorithm (POA) is a swarm intelligence metaheuristic optimization method inspired by two typical behaviors of pelicans during hunting: diving to catch prey and flapping wings to disturb the water surface. These behaviors are used to achieve global exploration and local exploitation, respectively, thereby searching for the globally optimal solution in continuous optimization problems. The core of the POA algorithm lies in using two behaviors to correspond to two search methods: Phase I (dive hunting): This phase focuses on global exploration, causing individuals to approach or adjust their direction towards the "prey" with a certain degree of randomness. The search principle is shown in equation (15). (15) in, Indicates the current position of the individual. This represents the candidate positions obtained from the Phase I update. Represents a random vector. This indicates the current globally optimal position. Represents a random integer. This represents element-wise multiplication, where each dimension has a different random step size; Stage II (Surface flapping): This stage favors local development, refining the solution by perturbation near the current solution to enhance convergence. Its search principle is shown in equation (16). (16) In the formula, This is the position after stage I. These are candidate positions obtained from the Stage II perturbation. This is the step size coefficient; To address the issues that traditional Proof-of-Action (POA) algorithms may suffer from inadequate population diversity, exploration / exploitation imbalance, and premature convergence in complex multimodal problems, leading to local optima, this invention improves upon the traditional POA algorithm in three aspects: initialization, search mechanism, and optimization efficiency. Figure 3 As shown, the improved POA algorithm specifically includes the following steps: B1: Initialize optimization variables based on chaotic sequences, generate the original population, and use refraction back learning to obtain the inverse solution of the optimization variables, merge it with the original population, and select the top N high-quality solutions as the final initial population. To avoid uneven distribution and insufficient population diversity in random initialization, a more uniform chaotic sequence initialization is adopted, the principle of which is shown in equation (17): (17) in, For the first The chaotic sequence values ​​generated in the next iteration The chaotic sequence value for the next iteration. , This represents the number of iterations. Then, refraction reverse learning is used to expand the search space and increase the probability of selecting high-quality individuals. The principle is as follows: (18) in, This represents the original candidate solutions (i.e., the original population). For the reverse solution of refraction, This represents the range of values ​​for this variable dimension. A coefficient representing the number of iterations; B2: A global search is performed based on the Levy transition strategy, with the minimum permutation entropy as the fitness function, and the position is updated based on the fitness value of each individual in the population; Specifically, a Levy transition-guided global search is used to replace the original global search method, thereby achieving a balance between long-step exploration and short-step development, improving the ability to escape local optima. The position update formula is as follows: (19) In the formula: (20) (twenty one) (twenty two) in, The globally optimal position vector up to the current iteration. This is the mean vector of the current population position. To optimize iteration numbering, The maximum number of iterations, The number of decision variables, This is the step scaling factor. The random variable is used to generate the random step size of Levy. For scale parameters, The absolute value of the random variable. Take 1.5, The transfer factor changes with iteration.

[0028] B3: When the preset number of iterations is reached, output the optimal number of modes and the optimal penalty factor; In this embodiment, the optimal number of modes K=11 and the optimal penalty factor α=2386.

[0029] Step 3: Calculate the permutation entropy of each intrinsic mode function component, and select the components that need to be denoised and the components that do not need to be denoised according to the screening threshold. Furthermore, the intrinsic mode function components (IMF components) obtained from VMD decomposition based on the optimal parameter combination (number of modes, penalty factor) determined in the previous step may still contain noise components and weak useful information simultaneously. Simply discarding high frequencies or eliminating low-correlation components can easily lead to loss of effective information and affect the accuracy of signal reconstruction. To fully preserve the effective information, permutation entropy is introduced to sieve the IMFs into components requiring denoising and those not requiring denoising. For components requiring denoising, an improved wavelet threshold function is used for denoising to suppress noise to the greatest extent while retaining useful components. For components not requiring denoising, their original form is maintained and they directly participate in signal reconstruction. Specifically, to effectively filter the IMF components after VMD decomposition, the permutation entropy (PE) metric is introduced to evaluate sequence complexity. Permutation entropy measures the distribution of the relative ordering patterns of embedded vectors in a time series, reflecting the randomness and uncertainty of the signal. The specific calculation process for permutation entropy includes: If the input original time series is: (twenty three) Reconstructing the original time series yields the reconstruction matrix. for: (twenty four) in, Represents the number of reconstructed vectors. , Represents the embedding dimension. Represents the delay time; for The elements in each row vector are sorted according to their numerical values ​​to obtain the corresponding symbol arrangement (sequential pattern), i.e. Then, calculate the probability of occurrence of all different symbol sequences (i.e., different order patterns). Entropy is used to measure the randomness and complexity of a sequence. The definition of permutation entropy is: (25) in, The permutation entropy of the m-th symbol sequence; To facilitate comparisons across different dimensions, normalization is performed to obtain the final permutation entropy value: (26) in, This represents the permutation entropy before normalization; The value range is [0,1]. The smaller the value, the more ordered and deterministic the sequence is, and vice versa. Based on extensive experimental results, a screening threshold was set. The value is 0.6, which is the permutation entropy of each IMF component. In contrast, when the permutation entropy of an IMF component is greater than 0.6, the IMF component is a noise component, which requires noise reduction; conversely, when the permutation entropy of an IMF component is less than or equal to 0.6, the IMF component is an effective information component, which does not require noise reduction.

[0030] Step 4: Denoise the component to be denoised based on the improved wavelet threshold function to obtain the denoised IMF component; Wavelet Transform (WT) is a time-frequency analysis method based on the concept of multi-scale analysis, capable of analyzing the local features of signals at different scales. Unlike the traditional Fourier Transform, which only provides frequency domain information, wavelet Transform, by introducing scaling and translation operations, maps the signal to a two-dimensional representation that includes both time and frequency, thus enabling multi-resolution analysis of non-stationary signals. The wavelet transform basis functions are called "wavelet functions," which possess good time-frequency locality and satisfy certain mathematical conditions. Based on the continuity of the scale and translation factors, wavelet transforms can be divided into two categories: Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). Discrete Wavelet Transform (DWT) expands the wavelet basis functions in the discrete domain by discretely sampling the scale and translation factors.

[0031] Wavelet threshold denoising (WTD) is a nonlinear denoising method based on discrete wavelet transform. Its core principle is to apply threshold compression to the decomposed wavelet cardinality to suppress noise components. Common processing methods include soft thresholding and hard thresholding. Soft thresholding processes the wavelet cardinality through smooth compression: coefficients with absolute values ​​less than the threshold are directly set to zero, while coefficients exceeding the threshold are scaled down proportionally to reduce their amplitude. In contrast, hard thresholding is more direct, only removing coefficients below the threshold while leaving the rest unchanged. Soft thresholding provides better continuity, helping to avoid abrupt changes during signal reconstruction.

[0032] Soft threshold function for: (27) Hard threshold function for: (28) In the formula: (29) in, For wavelet cardinality, For the threshold, For signal length, The standard deviation of noise; Soft thresholding functions possess excellent smoothing properties, which are beneficial for maintaining signal continuity. However, while reducing noise, they often cause excessive energy suppression, leading to a certain degree of distortion. Hard thresholding methods can more effectively preserve the main feature information of a signal; however, due to their abrupt processing, they may cause signal discontinuities. Therefore, this application proposes an improved thresholding function that lies between soft and hard thresholding functions. It possesses the continuity of soft thresholding functions while preserving the amplitude preservation capability of hard thresholding functions as much as possible. The specific formula is shown below: In the formula, The original wavelet cardinality; The wavelet cardinality after thresholding; For the threshold; The adjustment factor is shown below. The curves comparing the soft threshold function, hard threshold function, and improved threshold function are as follows: Figure 4 As shown.

[0033] In wavelet thresholding denoising, the selection of wavelet basis functions and the setting of the decomposition level have a significant impact on the final result. Different wavelet basis functions possess different mathematical properties, among which the vanishing moment order is a key indicator of their ability to capture signal details. Wavelet functions with higher vanishing moment orders are more effective at separating high-frequency noise from useful components, improving denoising accuracy and stability. However, higher orders also bring greater computational burden, affecting actual computational efficiency. Similarly, the wavelet decomposition level determines the decomposition depth of the signal in the frequency domain. Increasing the number of levels is beneficial for extracting finer-grained feature information, but excessive decomposition may lead to the miscompression or loss of useful signals. Therefore, in order to select the most suitable wavelet function configuration for the rolling data signal targeted by this invention, simulated noisy signals established in the experimental stage were used as experimental data, and three wavelet basis functions, dbN, symN, and coifN, were used for experimental analysis. Figures 6-8 The RMSE metrics for noisy simulation signals after denoising using different wavelet bases and different decomposition levels are shown in Tables 1 to 3.

[0034] The noise reduction amplitude reflects the degree of change in signal energy before and after noise reduction. Specifically, RMSE is used as the indicator of noise reduction effectiveness, and its calculation formula is as follows: in, For noise reduction amplitude, Data before noise reduction RMSE, Data after noise reduction RMSE.

[0035] in, It is a noise-free signal. This is the data after noise reduction. The smaller the RMSE value, the better the noise reduction effect.

[0036] Table 1. Noise Reduction Amplitude (%) of dBN Wavelet Basis Table 2. Noise Reduction Amount (%) of symN Wavelet Basis Table 3. Noise Reduction Amount (%) of coifN Wavelet Basis Experimental results show that, under the same number of decomposition levels, different wavelet bases exhibit different denoising capabilities. When using the same wavelet base, the effect of the number of decomposition levels on denoising performance shows a clear "first increase, then decrease" trend. This indicates that too shallow a decomposition level is insufficient to adequately decompose noise, while too deep a level can easily lead to the loss of useful information and affect reconstruction accuracy. In the dbN wavelet base, when the vanishing moment order is 3 and the number of decomposition levels is 5, The minimum value was 1.0659, with a noise reduction rate of 76.898%, indicating the best noise reduction effect.

[0037] Step 5: Reconstruct the denoised IMF component and the denoised IMF component to obtain the denoised signal.

[0038] Experimental Case: Using the work roll bending force signal synthesized during the experimental phase as the simulated noisy signal, a noise reduction experiment was conducted based on the IPOA-VMD joint wavelet noise reduction model. The following experimental steps were performed: 1. Let the input data after adding noise be... VMD hyperparameter optimization is performed using IPOA, and the number of modes is determined. The optimal solution is 11, and the penalty factor is... The optimal solution is 2386; 2. Through optimal parameter combination ( The VMD algorithm is executed to decompose the noise simulation signal into several intrinsic mode function (IMF) components, such as... Figure 9 As shown, it is divided into 11 IMF components. Its spectrum is as follows: Figure 10 As shown; 3. Figure 11The results show the cosine similarity between each IMF component and the signal. The results reveal significant differences in the similarity between different IMF components and the signal. IMF2 exhibits the highest cosine similarity at 0.846481, significantly higher than the other components, indicating that IMF2 has the highest consistency with the reference signal in the feature direction and contains the most important effective information. Secondly, the cosine similarities of IMF3 and IMF4 are 0.418676 and 0.419707, respectively, indicating that these two components also retain relatively obvious target features, but their correlation is weaker than that of IMF2. The cosine similarities of IMF6, IMF7, and IMF8 are 0.257292, 0.255193, and 0.249323, respectively, indicating that they have some similarity to the reference signal, but their contribution is relatively limited. In contrast, the cosine similarity of IMF5, IMF9, and IMF10 is relatively low, especially that of IMF9 and IMF10, which are close to 0 (0.026157 and 0.029538 respectively). This indicates that these components have weak correlation with the reference signal and contain less effective feature information. Therefore, the main feature information of the target signal is concentrated in IMF2, IMF3, and IMF4, with some existing in IMF6–IMF8, while the remaining components have weak representational ability for the target features. Therefore, in subsequent signal reconstruction, feature extraction, or fault identification processes, IMF2, IMF3, and IMF4 can be prioritized as the main analysis objects, combined with IMF6–IMF8 for auxiliary analysis, in order to improve feature representation ability and reduce interference from irrelevant components. 4. To more intuitively illustrate the relationship between the entropy values ​​of each IMF component, this invention employs a 3D view, such as... Figure 12 As shown, the trend layer IMF1 signal changes slowly at low frequency and is close to DC, so it can be directly retained. The main period layer IMF2 and IMF10 signals have stable periods and relatively fixed frequencies, so they can be directly retained. The four signals IMF3, IMF4, IMF6, and IMF7 have dense oscillations and high frequencies, so they need to be denoised first. The three signals IMF5, IMF8, and IMF9 have local energy concentration, intermittent fluctuations, and are non-stationary, so they need to be denoised. 5. The wavelet threshold function is used to denoise the IMF components that need denoising after permutation entropy filtering. Then, the denoised signal is reconstructed by combining these components with the signal that does not need denoising. The signal denoising effect is as follows: Figure 13 As shown.

[0039] To further verify the noise reduction effect, traditional VMD combined with wavelet denoising was used for comparison, and the results are shown in Table 4. The effect of traditional VMD combined with wavelet denoising is shown in Table 4. Figure 14 From Table 4, Figure 10 and Figure 11It can be seen that optimizing the VMD parameters using the IPOA algorithm significantly improves the noise reduction effect. Among the two methods, the IPOA-VMD combined wavelet noise reduction method performs best, with a signal-to-noise ratio of 27.4136 dB. The signal-to-noise ratio (SNR) is 0.3903, significantly better than the VMD combined with wavelet denoising method. Compared with the unoptimized VMD combined with wavelet denoising, its SNR is improved from 24.8634 dB to 27.4136 dB, an improvement of 10.26%. The value decreased from 0.4067 to 0.3903, a reduction of approximately 4.03%. In summary, the IPOA-VMD combined wavelet denoising method can effectively denoise rolling signals while preserving useful feature information and suppressing invalid noise interference, thus exhibiting high signal fidelity.

[0040] Table 4 Comparison of Signal-to-Noise Ratio and RMSE between the two methods The signal-to-noise ratio (SNR) in Table 4 measures the proportion of noise in a signal, and its calculation formula is as follows: in, It is a noise-free signal. This is the data after noise reduction. The signal-to-noise ratio (SNR) measures the proportion of noise in a signal; the higher the SNR, the smaller the noise proportion, and the better the noise reduction effect.

[0041] Example 2: This application also provides a rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding. The device is used to implement the method of the above embodiment, and the device includes: The acquisition module is used to acquire the raw, noisy signal of the on-site rolling data; The decomposition module is used to determine the optimal combination of VMD parameters by improving the IPOA method, and to perform VMD decomposition on the original noisy signal based on the optimal combination of VMD parameters to obtain several intrinsic mode function components. The filtering module is used to calculate the permutation entropy of each intrinsic mode function component and filter out the components that need to be denoised and the components that do not need to be denoised according to the filtering threshold. The noise reduction module is used to denoise the components to be denoised based on the improved wavelet threshold function to obtain the denoised IMF components; The reconstruction module is used to reconstruct the denoised IMF components and the denoised IMF components to obtain the denoised signal.

[0042] The rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding in this application embodiment can be an electronic device or a component in an electronic device, such as an integrated circuit or a chip. The electronic device can be a terminal or other devices besides a terminal. For example, the electronic device can be a GPU BOX, mobile phone, tablet computer, laptop computer, handheld computer, in-vehicle electronic device, mobile internet device (MID), augmented reality (AR) / virtual reality (VR) device, robot, wearable device, ultra-mobile personal computer (UMPC), netbook or personal digital assistant (PDA), etc. It can also be a server, network attached storage (NAS), personal computer (PC), television (TV), ATM or self-service machine, etc. This application embodiment does not make specific limitations.

[0043] The rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding in this application embodiment can be a device with an operating system. This operating system can be Android, Linux, Windows, or other possible operating systems; this application embodiment does not specifically limit it.

[0044] The rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding provided in this application embodiment can achieve... Figure 1 The various processes implemented in the method implementation examples will not be described again here to avoid repetition.

[0045] Example 3: This application also provides an electronic device, which includes: at least one processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the rolling data noise reduction method based on IPOA-VMD combined with wavelet thresholding of the foregoing embodiment.

[0046] This application also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps in the rolling data noise reduction method based on IPOA-VMD combined with wavelet thresholding disclosed in the foregoing embodiments of this application.

[0047] This application also provides a computer program product that, when run on an electronic device, enables the processor to implement the rolling data noise reduction method based on IPOA-VMD combined with wavelet thresholding as disclosed in the foregoing embodiments of this application.

[0048] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0049] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, apparatuses, electronic devices, and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0050] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0051] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0052] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0053] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0054] The above provides a detailed description of a rolling data denoising method, apparatus, and electronic device based on IPOA-VMD combined with wavelet thresholding provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for denoising rolling data based on IPOA-VMD combined with wavelet thresholding, characterized in that, The method includes: Acquire the raw, noisy signal of the on-site rolling data; The optimal combination of VMD parameters is determined by improving the IPOA method, and based on the optimal combination of VMD parameters, VMD processing is performed on the original noisy signal to obtain several intrinsic mode function components. Calculate the permutation entropy of each intrinsic mode function component, and select the components that need noise reduction and those that do not need noise reduction based on the screening threshold. The denoised IMF component is obtained by denoising the component to be denoised based on the improved wavelet threshold function. The denoised IMF component and the undenoised IMF component are decomposed to obtain the denoised signal.

2. The method of claim 1, wherein, The method of determining the optimal combination of VMD parameters by improving the IPOA method includes: The optimization variables are initialized based on chaotic sequences to generate an original population. The reverse solution of the optimization variables is obtained by refraction back learning and merged with the original population. The top N high-quality solutions are selected as the final initial population. A global search is performed based on the Levy transition strategy, with the minimum permutation entropy as the fitness function, and the position is updated based on the fitness values ​​of each individual in the final initial population. When the preset number of iterations is reached, the optimal combination of VMD parameters is output; the optimal combination of VMD parameters includes the optimal number of modes and the optimal penalty factor.

3. The method of claim 1, wherein, The formula for updating the position is: In the formula: in, Let be the individual position in the t-th iteration. Current global optimal position This is the mean vector of the current population position. For the number of iterations, The maximum number of iterations, To optimize the number of variables, This is the step scaling factor. The random variable is used to generate the random step size of Levy. For scale parameters, The absolute value of the random variable. It is a constant. The transfer factor changes with iteration.

4. The method of claim 2, wherein, The VMD-based optimal parameter combination is used to perform VMD processing on the original noisy signal to obtain several intrinsic mode function components, including: The original noisy signal is decomposed into multiple bandpass mode components with different center frequencies; For each bandpass mode component, convolve it with the Hilbert kernel to obtain the analytic signal corresponding to each bandpass mode component; Based on complex exponential modulation, the spectrum of each analytical signal is shifted to the fundamental frequency to obtain the analytical signal after the spectrum shift. The gradient norm of the analytic signal after each spectral basis shift is defined as the bandwidth of each modal component, and the VMD variational optimization model is constructed with the minimum sum of the bandwidths of all modal components as the optimization objective. Based on the Lagrange augmented function, the VMD variational optimization model is solved, and finally all the intrinsic mode components and their corresponding center frequencies after VMD decomposition are obtained.

5. The method of claim 4, wherein, The calculation of the permutation entropy of each intrinsic mode function component, and the selection of components requiring denoising and those not requiring denoising based on a screening threshold, includes: Calculate the permutation entropy of each intrinsic mode function component; Determine whether the permutation entropy of each intrinsic mode function component is greater than the screening threshold. If it is, the intrinsic mode function component is a component that needs noise reduction; otherwise, the intrinsic mode function component is a component that does not need noise reduction.

6. The method of claim 1, wherein, The improved wavelet threshold function is: wherein, is the original wavelet basis; is the thresholded wavelet basis; is the threshold; is the adjustment factor.

7. The method of claim 6, wherein, The improved wavelet threshold function has a wavelet basis of dbN, a vanishing moment order of 3, and a decomposition level of 5.

8. A rolling data noise reduction device based on IPOA-VMD combined with wavelet thresholding, characterized in that, The apparatus for implementing the method as described in any one of claims 1-7 comprises: The acquisition module is used to acquire the raw, noisy signal of the on-site rolling data; The decomposition module is used to determine the optimal combination of VMD parameters by improving the IPOA method, and to perform VMD decomposition on the original noisy signal based on the optimal combination of VMD parameters to obtain several intrinsic mode function components. The filtering module is used to calculate the permutation entropy of each intrinsic mode function component and filter out the components that need to be denoised and the components that do not need to be denoised according to the filtering threshold. The noise reduction module is used to denoise the components to be denoised based on the improved wavelet threshold function to obtain the denoised IMF components; The reconstruction module is used to reconstruct the denoised IMF components and the denoised IMF components to obtain the denoised signal.

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