Wavelet packet-based ultrashort pulse intense laser field higher harmonic voltage detection method and system

Abstract

The invention discloses a wavelet packet-based ultrashort pulse intense laser field higher harmonic voltage detection method and system. The invention relates to the technical field of ultrashort pulse laser detection and analysis. On the basis of a D-S evidence theory algorithm, calculation of information entropy Hi serves as an evaluation index of confidence, decomposition results of different signals under frequency distribution and energy distribution are regarded as different evidences, and basic probabilities (BPA) are distributed; according to the method, the optimal wavelet packet basis expansion can be selected according to frequency distribution and energy distribution of actual signals, so that the wavelet packet decomposition and reconstruction accuracy is improved; the DD-DC neural network model models neurons into a feedback controller of a wavelet packet basis, and an observation result can be directly mapped into a wavelet coefficient, so that a controlled dynamic system does not need to be explicitly represented. The nonlinear compensation strategy can describe the nonlinear characteristics of the signal more accurately. The strategy can capture the characteristics of the signal in the time domain and the frequency domain, and the prediction output is adjusted.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrashort pulse laser detection and analysis, specifically to harmonic measurement, and especially to a method and system for detecting high-order harmonic voltage of an ultrashort pulse strong laser field using wavelet packets. Background Art

[0002] Ultrashort pulse laser technology, due to its unique temporal characteristics and high energy density, has been widely used in various fields such as materials processing, biomedicine, and optical communications. Ultrashort pulse laser technology has been widely used in many fields due to its outstanding performance, demonstrating its strong application potential.

[0003] Despite the widespread application of ultrashort pulse laser technology, there is currently no unified standard for measuring its harmonics. The accuracy and scalability of harmonic measurement (i.e., the scalability of the measurement range) require further verification and improvement.

[0004] Harmonic measurement is closely related to the voltage fluctuation of the laser, and voltage fluctuation can reflect the stability and reliability of the laser system. For example, large voltage fluctuations may indicate unstable power supply or electrical problems inside the laser, which may lead to instability in the laser output power. By analyzing voltage fluctuations, workers can identify factors that affect laser efficiency, such as temperature changes, nonlinear effects, etc. Voltage fluctuation data can serve as an important basis for fault diagnosis. Abnormal voltage fluctuation patterns may be a sign of hardware failure (such as damage to circuit components) or improper setting of operating parameters. In some high-precision applications (such as laser cutting, laser marking, etc.), precise control of the energy output of the laser is crucial. By monitoring and adjusting voltage fluctuations, more precise energy output control can be achieved. However, the harmonic measurement method of ultrashort lasers is still a difficult problem to overcome, and a reasonable standard needs to be determined to improve the accuracy and reliability of voltage fluctuation measurements. To this end, many existing technologies have attempted to solve this phenomenon, such as: (1) The paper "Li Meiyu, Liu Jianfeng, Li Chenyang. Ultra-high harmonic detection algorithm based on CS-RBAPVS [J]. Hydropower Energy Science, 2020, 38(12): 201-205" studied the ultra-high harmonic detection algorithm based on CS-RBAPVS, using discrete Fourier transform coefficients and difference factors to reconstruct the signal and obtain harmonic detection results, but did not detect high-order harmonics; (2) The paper "Liu Jianfeng, Song Ziheng, Zhou Yongliang, et al. Ultra-high harmonic detection algorithm based on deterministic measurement matrix and variable threshold SAMP [J]. Power System Protection and Control, 2020, 48(21):75-83" proposed an ultra-high harmonic detection algorithm based on deterministic measurement matrix and variable threshold SAMP, which improved the accuracy of ultra-high harmonic detection, but could not detect instantaneous energy; (3) There is a lot of instantaneous energy in the short pulse intense laser field, which leads to inaccurate high-order harmonic detection results. Therefore, the latest existing technology, namely the document "He Jing, Wang Tao, Xie Guoya. Ultrashort pulse intense laser field high-order harmonic voltage detection based on wavelet packets [J]. Laser Magazine, 2022, 43(09): 224-228.", proposed the application of wavelet packet technology to the detection of high-order harmonics in ultrashort pulse intense laser fields to improve the accuracy of detection. The main steps can be divided into: S1. Through wavelet packet decomposition and reconstruction, the segmented signal is distributed into various small frequency bands to improve detection accuracy. This makes the signal characteristics within each frequency band more prominent, thereby improving the accuracy of harmonic detection. Through reconstruction, the original signal information can be recovered from the decomposed signal while retaining the detailed characteristics within each frequency band. S2. Optimal Feature Extraction: Utilizing a small number of coefficients to obtain the optimal features of the signal, the signal is segmented into windows and an appropriate wavelet packet basis is selected based on the signal characteristics. This reduces the computational effort while retaining the signal's key information. By segmenting the signal into windows and selecting an appropriate wavelet packet basis based on the signal's characteristics, the accuracy and efficiency of feature extraction can be further improved. S3. Transformation formula compensation: Since the wavelet transformation process may consume a lot of energy, resulting in a difference between the fundamental wave energy and the predicted value, it is necessary to compensate the transformation formula to improve the accuracy of detection.

[0005] However, the latest existing technology has the following technical problems that need to be improved: (1) Regarding the S1 part of this latest state-of-the-art technology: Starting from equation (3) in the literature, the expansion U of the orthogonal function d is theoretically correct. However, in practical applications, the parameters of the wavelet packet decomposition (the number of decomposition layers and the filter) have a significant impact on the decomposition effect. If the parameters are not selected properly, the distribution of the signal in each frequency band will be affected, thereby reducing the detection accuracy. Inaccurate decomposition results will lead to errors in signal feature extraction, which in turn affects the accuracy of harmonic detection. Unreasonable frequency band allocation may cause some important signal components to be ignored or misallocated, resulting in the loss of harmonic information.

[0006] (2) Regarding the S2 part of the latest existing technology: The optimal feature extraction method is based on the assumption that there is a space V in which the orthogonal basis of the function sequence is B. However, this assumption may not hold in actual signal processing, resulting in the failure of the optimal feature extraction method. Because actual signals are often complex and diverse, they may not fully meet the assumptions required by the optimal feature extraction method. Signals in ultrashort pulsed intense laser fields usually have non-stationary, nonlinear and high-frequency characteristics, making it difficult to select a suitable wavelet packet basis. If the assumptions do not hold, the optimal feature extraction method will not be effectively applied, resulting in inaccurate signal feature extraction. The complexity of the signal characteristics may cause the selected wavelet packet basis to not match the signal characteristics, making it impossible to accurately extract the optimal features of the signal.

[0007] (3) Regarding the S3 part of the latest existing technology: The compensation method is linear and cannot accurately describe the nonlinear characteristics of the signal. In particular, when the signal intensity is high or there are instantaneous energy changes, the compensation effect may not be ideal. The signal in the ultrashort pulse intense laser field may contain instantaneous energy changes, which have a significant impact on the compensation effect. If the compensation method cannot accurately describe these instantaneous changes, the compensation effect will be unsatisfactory. The linear compensation method cannot accurately reflect the true energy distribution of the signal, resulting in inaccurate harmonic detection results. Inaccurate compensation of instantaneous energy changes may cause errors or distortion in harmonic detection, which in turn affects subsequent signal processing and analysis.

[0008] In summary, if the calculated sequence of laser instantaneous energy change values is inaccurate, since the laser instantaneous energy change is the basis for calculating voltage fluctuations, any measurement error will be directly transmitted to the calculation result of the voltage fluctuation, resulting in a deviation between the calculated voltage fluctuation and the actual value.

[0009] Voltage fluctuation analysis based on inaccurate data may lead to erroneous trend judgments or anomaly detection results, thereby misleading subsequent system debugging and optimization work. Furthermore, if the voltage fluctuation calculation is inaccurate, the signal used for feedback control will also be distorted, making it difficult for the control system to achieve the expected performance goals, such as maintaining a constant laser output power. Although existing technologies can detect the voltage fluctuations of the laser itself through external devices, this detection data is instantaneous and cannot be used for further prediction. It also cannot establish a nonlinear relationship with the laser characteristics of the laser itself.

[0010] To this end, the present invention proposes a method and system for detecting high-order harmonic voltage of ultrashort pulse intense laser field using wavelet packets. Summary of the Invention

[0011] In view of this, the present invention hopes to provide a method and system for detecting high-harmonic voltages of ultrashort pulsed intense laser fields using wavelet packets to solve or alleviate the technical problems existing in the prior art, namely, how to further and more accurately detect the voltage fluctuation sequence of the laser system. In order to solve this problem, it can be further divided into the following sub-goals: (1) How to further improve the accuracy of wavelet packet decomposition and reconstruction; (2) How to introduce confidence statistics to replace the hypothesis space to avoid situations where the hypothesis conditions are not valid; (3) How to adopt a more reasonable and accurate nonlinear compensation mechanism.

[0012] The technical solution of the present invention is achieved as follows: First, the wavelet packet-based method for detecting high-harmonic voltage in ultrashort pulsed intense laser fields: (I) Overview: The present invention introduces a feature adaptation mechanism and utilizes information entropy and the Dempster combination principle to select the optimal wavelet packet basis expansion, thereby solving the problem that in practical applications, the wavelet packet decomposition and reconstruction process may result in imperfect results due to algorithm implementation errors or improper parameter selection. At the same time, by adopting the DD-DC neural network model, neurons are modeled as feedback controllers of the wavelet packet basis, realizing data-driven adaptive feature extraction and avoiding the mismatch problem that may be caused by the optimal feature extraction method based on assumptions. In addition, this solution also introduces a nonlinear compensation strategy based on Z transform and discrete Fourier transform to more accurately describe the nonlinear characteristics of the signal, especially in cases where the signal strength is high or there are instantaneous energy changes.

[0013] (2) Technical solution: To achieve the above goals, when multiple groups of wavelet functions of a laser system are combined together to form an orthogonal basis library L2(R), the filter coefficient h of the orthogonal scaling function φ(t) is determined. k , the filter coefficient g of the orthogonal function ψ(t) k (where k∈Z, Z is a positive number set), the present invention selects to perform the following steps: 2.1 Step S1, execute feature adaptation mechanism: Based on the DS evidence theory algorithm and information entropy H i The calculation of is used as the confidence evaluation index, and the decomposition results under the frequency distribution and energy distribution of different signals are regarded as different evidences and assigned basic probabilities (BPA). Based on the preset recognition framework O, the Dempster combination principle is used to combine them and finally form the wavelet packet basis expansion U that best reflects the signal characteristics. opt .

[0014] 2.1.1 Step S100, calculate information entropy: For each frequency distribution F i and energy distribution E i The wavelet packet decomposition result under the condition is used to calculate its information entropy H i As an evaluation indicator of confidence: ; Among them, n represents the ordinal number, p ij is the wavelet packet decomposition frequency distribution F i and energy distribution E i The probability distribution P i The probability of the jth component of ; the base of the logarithmic function can be selected as needed (base 2 or natural logarithm).

[0015] 2.1.2 Step S101, calculate the basic probability distribution: The frequency distribution F i and energy distribution E i The decomposition effects are regarded as different evidences, and a basic probability m(A) is assigned to each evidence, where A is a subset in the recognition framework O; the preset recognition framework O contains the set of all possible wavelet packet basis expansions and / or parameter combinations.

[0016] (1) The first method is to use the inverse of information entropy as the basis for allocating basic probabilities: ; Among them, A i is the frequency distribution F i and energy distribution E i The corresponding subset in the recognition framework O, ϵ is a small positive number to prevent the denominator from being zero, and c is a positive adjustment parameter used to control the degree of influence of information entropy on the basic probability.

[0017] (2) The second method is to introduce the generalized least squares (GLS) method to calculate the stability of the decomposition result and use it as the basis for the basic probability distribution m(A); the method is: S1010, define the stability index: for each probability p ij , calculate the residual vector between it and a reference result (such as the average result) to represent it. In order to evaluate the stability, a stability index is defined using the generalized least squares estimate of the residual: Let y i is the i-th decomposition result, is the reference result, then the residual vector e i : ; S1011, calculate the residual variance of generalized least squares : ; Wherein, W is the weight matrix (dedicated to step S1010), T is the transpose operation, m is the number of data points, and p is the number of decomposition results.

[0018] S1012, define stability indicator function: use residual variance The reciprocal of is used as the stability index i : ; in, is a small positive number to prevent the denominator from being zero.

[0019] S1013, convert the stability index into the basic probability distribution m(A): ; Among them, A i is the frequency distribution F i and energy distribution E i The corresponding subset in the recognition frame O. Stability j It represents the stability index of the jth wavelet packet decomposition result.

[0020] 2.1.3 Step S102, execute Dempster combination principle: Combine the basic probabilities of different evidences to obtain the combined basic probability m′(A): ; Among them, m1 and m2 are the basic probability distributions of different evidences, and B and C are subsets in the identification framework O.

[0021] 2.1.4 Step S103, select the optimal wavelet packet basis expansion U: Based on the combined basic probability m'(A), the wavelet packet basis expansion with the highest confidence is selected as the optimal solution, that is: ; Among them, U opt is the optimal wavelet packet basis expansion.

[0022] 2.2 Step S2, DD-DC neural network model performs data-driven: The DD-DC neural network model models neurons as the expansion of the wavelet packet basis U optThe feedback controller FC enables it to directly map the observation results into wavelet coefficients W(a,b) as the final output Y, which represents the characteristics of the signal at different scale parameters a (corresponding to the inverse of frequency) and translation parameters b (position in time or space), thus eliminating the need to explicitly represent the controlled dynamic system as in traditional technologies.

[0023] 2.2.1 Step S200, the input layer performs the input task: Receive orthogonal basis library L2(R) and wavelet packet basis expansion U opt And perform encoding operations so that the neural network can read it normally; initialize the weight w (dedicated to step S2), the bias vector b, and the feedback controller parameters, including the learning rate η and the momentum α; 2.2.2 Step S201: The hidden layer performs the mapping task: The hidden layer consists of multiple neural layers N i , each neural layer N i Including multiple neurons , where l represents the number of layers, j represents the neuron index of the layer; each neuron Perform forward and backward propagation; each neuron It is a feedback controller FC, which adaptively matches and calculates the initial wavelet coefficients ;in: Each neural layer N i neurons All are based on any two orthogonal functions ψ in the orthogonal basis library L2(R) i (t), ψ j The filter coefficient g of (t) ik 、g jk As input, they are responsible for different data processing and feature extraction tasks, and through the interaction and feedback of multiple layers of neurons, they can more accurately perceive and control the environment; at the same time, each neural layer N i Output Y i is fed back to the previous neural layer N i The data is corrected and iterated repeatedly. When the objective function F converges or reaches the predetermined number of iterations, the final output Y is obtained; 2.2.2.1 Step S2010, initialize the feedback controller FC: Each neuron It is a feedback controller FC, which controls the speed and direction of adjustment based on the learning rate η and momentum α parameters, and adaptively matches and calculates the initial wavelet coefficients. ; The feedback controller FC type is: ; Among them, w new represents the updated weight; wold Indicates the current weight; Represents the gradient of the output error E of the current time step t compared to the previous time step t-1 with respect to the weight matrix w; w previous Indicates the previous weight value (used to maintain a certain inertia in momentum optimization); b new represents the updated bias; b old Indicates the current bias; represents the gradient of the error E with respect to the bias b.

[0024] 2.2.2.2 Step S2011, neuron forward propagation: For each neural layer N i Each neuron , receiving input data from the previous layer (for the first neural layer, it corresponds to the input layer), including any two orthogonal functions ψ in the orthogonal basis library L2(R) i (t), ψ j The filter coefficient g of (t) ik 、g jk Each neuron The weight w calculated based on the current feedback controller FC new and bias b new To calculate its output Y i , is regarded as a preliminary estimate or feature representation of the wavelet coefficients W(a,b).

[0025] (1) For one-to-one tasks, the forward propagation is: ; (2) If we consider multiple combinations of inputs and weights (multiple filter coefficients and corresponding weights), the forward propagation is: ; Among them, Y i Represents neurons The output of; f(⋅) represents the Sigmoid activation function, which is used to introduce nonlinearity; g ik represents the input (filter coefficients) from the previous layer; Represents neurons The weight corresponding to the kth input (the superscript (i,j) indicates that this is the weight specific to the jth neuron in the i-th layer); Represents neurons Bias of; symbol ∑ k Represents a weighted summation of all inputs (filter coefficients).

[0026] 2.2.2.3 Step S2012, neuron backpropagation and feedback control: Based on neurons Output Y i , weight w new and bias b new , adaptively matching and calculating the initial wavelet coefficients .

[0027] Considering that this step cannot directly obtain an expected value, a self-supervised learning strategy needs to be introduced: Since W(a,b) is the wavelet transform coefficient, we hope to output Y i After transformation or reconstruction, the signal can maintain consistency or similarity with the original signal. Then, the objective function F(Y i ) Gradient with respect to weight w and bias b: ; Then, we further use the calculated gradient to update the weights and biases to w new ' and b new ', to optimize the objective function F(Y i ): ; Among them, x n is the nth sample of the original signal. Is to use output Y i The nth sample of the reconstructed signal. S is the total number of samples in the signal; Y i (a,b) is the value of the estimated wavelet coefficient at scale a and position b; Then, the combination of energy distribution difference and sparsity penalty is measured: ; Where ExpectedEnergy(a,b) is the expected energy distribution of wavelet coefficients; λ is a parameter that controls the strength of the sparsity penalty.

[0028] 2.2.2.4 Step S2013, Interaction and Feedback within the Neural Layer: In each neural layer N i Different neurons Output Y between i They serve as input to each other, forming interactions within the layer and sharing information, thereby more accurately perceiving and controlling the environment. The output of the neural layer Y i ' is the combined result of the outputs of all neurons in this layer.

[0029] Each neuron Output Y iAs input to other neurons (including itself, if self-feedback is required): ; Where: Y i,j ′ represents the updated output of the jth neuron after considering the interaction within the layer. F' is a nonlinear function (such as Sigmoid activation function) used to introduce nonlinear interaction effects. i,j,k is the influence weight of the kth neuron on the jth neuron. MM is the neural layer N i The number of neurons in .

[0030] Then, the comprehensive output Y of the neural layer i ′ is the weighted sum of all updated neuron outputs: ; in, are the new weights used to combine the outputs of all updated neurons.

[0031] 2.2.2.5 Step S2014, cross-layer feedback and iteration: The neural layer N i Output Y i Feedback to the previous layer (or input layer) for data correction and further processing. Repeat this step until the objective function F converges or reaches a predetermined number of iterations; the optimization function F is based on the square sum of the error E. The process is, for the neural layer N i , loop execution: S20140, error E calculation: ; Where K is the number of output neurons; Y k is the output of the kth output neuron in the previous iteration; is the output of the k-th output neuron in this iteration; S20141, based on the square sum of error E, is guided by the optimization function F: ; The goal of optimization is to minimize the optimization function F; S20142, update each neuron again according to the direction of the error gradient Biases and weights of S20143, feeds the updated neural layer output back to the previous layer (or input layer); S20144, repeat steps S20140 to S20143 until the change of the minimized optimization function F is less than the threshold value, or the predetermined maximum number of iterations is reached; and the last neural layer N i 'The comprehensive output Yi ′ is the final output Y.

[0032] 2.2.3 Step S202: The output layer performs the output task: Perform decoding on the final output Y to obtain the wavelet coefficients W(a,b): W(a,b) = Decode(Y); Among them, Decode(⋅) represents the decoding operation.

[0033] 2.3 Step S3, nonlinear compensation: Based on Z-transformation and discrete Fourier transform (DFT), instantaneous energy changes are described and nonlinear compensation is performed on the predicted output Y.

[0034] 2.3.1 Step S300, Z transform and discrete Fourier transform: Let y[n] be the discrete time series representation of the predicted output Y; apply the Z transform to y[n] to obtain its Z domain representation Y(z): ; Where z is a complex variable representing the frequency domain shift. n is an integer index representing each sample point or moment in the time series.

[0035] Applying the Discrete Fourier Transform (DFT) to y[n] yields its frequency domain representation Y[k]: ; Where NM is the length of the sequence, k is the frequency domain index, is a complex exponential function; j is an imaginary unit.

[0036] 2.3.2 Step S301, calculate instantaneous energy change: The instantaneous energy E[n] is expressed as the square of the modulus of the sequence y[n]: E[n] = |y[n]| 2 ; The instantaneous energy change can be described by calculating the difference in energy between adjacent moments or using other energy change measurement methods.

[0037] 2.3.3 Step S302, nonlinear compensation: Let fc(⋅) be a nonlinear compensation function that adjusts the predicted output y[n] according to the instantaneous energy change or other features.

[0038] The output y′[n] after nonlinear compensation is expressed as: y′[n]=fc(y[n],E[n])=y[n]+V⋅(E[n]−E ref )2 ; Where: y[n] is the original prediction output. E[n] is the instantaneous energy of the nth sample point. ref is the reference energy value. V is the nonlinear compensation coefficient, which is used to adjust the compensation strength. y′[n] is the output after nonlinear compensation. The role of the nonlinear compensation function fc(⋅) is to adjust the predicted output according to the instantaneous energy change. Specifically, when the instantaneous energy E[n] deviates from the reference energy value E ref When , the compensation function adds a nonlinear term V⋅(E[n]−E ref ) 2 The magnitude of this nonlinear term depends on the energy deviation (E[n]−E ref ) and compensation coefficient V.

[0039] 2.4 Step S4, obtaining voltage fluctuation relationship: After obtaining the output y′[n], the voltage fluctuation of the laser system can be detected by: S400, determining a relationship model between energy and voltage: determining the relationship between the output energy E' of the laser and its driving voltage V'; for many types of lasers, particularly semiconductor lasers, this relationship is linear or approximately linear: E' = k·V', where k is a proportionality factor representing the efficiency factor of the conversion from electrical energy to optical energy; of course, the relationship formula for the laser output energy E' can also be directly provided by the laser manufacturer; S401, perform filtering (moving average filter): ; Among them, y′′[n] is the energy change sequence after smoothing, and NW is the window size.

[0040] S402, detect voltage fluctuation: y′′[n]=k⋅V[n]; Therefore, the voltage fluctuation sequence V[n]=y′′[n] / k is obtained.

[0041] Furthermore, because the output y′[n] itself is a prediction sequence, the voltage fluctuation sequence V[n] is also a series of predicted values. Furthermore, by predicting future voltage fluctuations, we can identify impending equipment failures or performance degradation trends in advance. For example, an abnormal increase in voltage fluctuations could be a precursor to a power supply problem or other hardware failure.

[0042] (3) Mechanism for resolving technical issues: 3.1 The mechanism to solve the problem that "in practical applications, the process of wavelet packet decomposition and reconstruction may lead to imperfect results due to algorithm implementation errors or improper parameter selection": The present invention calculates the information entropy of the wavelet packet decomposition results for each frequency and energy distribution as a confidence assessment metric. Information entropy reflects the degree of chaos and uncertainty in the decomposition results. Lower information entropy indicates more ordered decomposition results and higher confidence. The decomposition results of the frequency and energy distributions are considered as different pieces of evidence, and a basic probability is assigned to each piece of evidence. The inverse of the information entropy or the generalized least squares (GLS) method can be used to calculate the stability of the decomposition results and use this as the basis for assigning basic probabilities. Using the Dempster combination principle, the basic probabilities of different pieces of evidence are combined to obtain a combined basic probability. This process comprehensively considers information from multiple decomposition results, improving the accuracy of selecting the wavelet packet basis expansion. Based on the combined basic probabilities, the wavelet packet basis expansion with the highest confidence is selected as the optimal solution. In this way, even if there are errors in the algorithm implementation or improper parameter selection in actual applications, the characteristic adaptation mechanism can still select the wavelet packet basis expansion that best resembles the true signal characteristics, thereby improving the accuracy of decomposition and reconstruction.

[0043] 3.2 Regarding the mechanism to solve the problem that "the optimal feature extraction method is based on assumptions and the signal characteristics are complex, which may lead to the mismatch between the selected wavelet packet basis and the signal characteristics": In the DD-DC neural network model of the present invention, neurons are modeled as feedback controllers based on the expansion of wavelet packets. This enables neurons to directly map observation results into wavelet coefficients, representing the characteristics of the signal at different scales and translation parameters. The neural network adaptively matches and calculates the initial wavelet coefficients through forward and backward propagation processes. This process can be dynamically adjusted based on the actual signal characteristics, avoiding the mismatch problem that may be caused by the optimal feature extraction method based on assumptions. The hidden layer includes multiple neural layers, each of which contains multiple neurons. These neurons are based on the filter coefficients of any two orthogonal functions in the orthogonal basis library as input, and through the interaction and feedback of multiple layers of neurons, they can more accurately perceive and control the environment. This structure enables the network to process complex and diverse signal characteristics and improve the accuracy of feature extraction.

[0044] 3.3 Regarding the mechanism to solve the problem that “linear compensation methods may not accurately describe the nonlinear characteristics of the signal, especially when the signal strength is high or there are instantaneous energy changes”: The present invention uses Z transform and discrete Fourier transform to describe the instantaneous energy change of the signal. It can capture the characteristics of the signal in the time and frequency domains, providing an accurate basis for nonlinear compensation. A nonlinear compensation function is constructed to adjust the predicted output according to the instantaneous energy change or other characteristics. This nonlinear compensation function can be a nonlinear function based on the square term of the instantaneous energy deviation or other forms to better describe the nonlinear characteristics of the signal. By adjusting the coefficients of the nonlinear compensation function, the compensation effect is optimized. This can be achieved through a training process, so that the nonlinear compensation function can better adapt to the nonlinear characteristics of the actual signal. In this way, even when the signal strength is high or there is an instantaneous energy change, a more accurate prediction output can be obtained through the nonlinear compensation strategy.

[0045] Secondly, the wavelet packet ultrashort pulse intense laser field high harmonic voltage detection system: The system includes a processor and a memory connected to the processor. The memory stores program instructions. When the program instructions are executed by the processor, the processor executes the detection method as described above.

[0046] When in use, the parameter information of the laser system is communicated with the memory, and the processor detects the required voltage fluctuation sequence data based on the above detection method.

[0047] Compared with the prior art, the present invention has the following beneficial effects: First, by introducing a characteristic adaptation mechanism, the present invention can select the optimal wavelet packet basis expansion based on the frequency and energy distribution of the actual signal, thereby improving the accuracy of wavelet packet decomposition and reconstruction. This improvement solves the problem of imperfect results caused by algorithm implementation errors or improper parameter selection in traditional technologies, providing a more reliable foundation for subsequent harmonic detection. Furthermore, the accurate sequence of energy change values can significantly reduce the errors generated during the voltage fluctuation calculation process, more realistically reflecting the operating state and dynamic characteristics of the laser, making the voltage fluctuation calculation more accurate to actual conditions and helping to identify the true voltage fluctuation pattern.

[0048] Second, the adaptive characteristic mechanism of the present invention significantly improves the accuracy of wavelet packet decomposition and reconstruction by calculating information entropy and utilizing the Dempster combination principle to select the optimal wavelet packet basis expansion. This mechanism dynamically adjusts the wavelet packet decomposition parameters based on the actual signal's frequency and energy distribution, thus avoiding the imperfect results often associated with improper parameter selection in conventional techniques. This adaptability enables the present invention to achieve greater robustness and accuracy when processing complex and changing signals.

[0049] Third, this invention utilizes a DD-DC neural network model to achieve data-driven adaptive feature extraction. This model dynamically adjusts the parameters of the neural network based on signal complexity and diversity, thereby avoiding the mismatch issues that can arise from optimal feature extraction methods based on assumptions. This improvement improves the accuracy and efficiency of feature extraction, providing more accurate feature information for harmonic detection. The predictive output voltage fluctuation sequence enables real-time control systems or personnel to more intelligently and accurately adjust key parameters such as the drive current and cooling system, ensuring that laser output power remains optimal.

[0050] Fourth, the DD-DC neural network model of the present invention models neurons as wavelet packet-based feedback controllers, enabling direct mapping of observations into wavelet coefficients, eliminating the need for explicit representation of the controlled dynamic system. This data-driven approach makes feature extraction more efficient and accurate, while avoiding the mismatch issues that can arise from optimal feature extraction methods based on assumptions. The application of the DD-DC neural network model significantly improves the accuracy and reliability of harmonic detection.

[0051] Fifth, the nonlinear compensation strategy of the present invention can more accurately describe the nonlinear characteristics of the signal. This strategy captures the signal's characteristics in both the time and frequency domains and adjusts the predicted output, thereby improving the accuracy of harmonic detection. Especially in situations with high signal strength or transient energy variations, the nonlinear compensation strategy can significantly reduce errors and distortion, providing more reliable data support for subsequent signal processing and analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0053] Figure 1 Schematic diagram of the method flow of the present invention; Figure 2 Schematic diagram of step S1 of the present invention; Figure 3 Schematic diagram of the neural network architecture of step S2 of the present invention; Figure 4 The hidden layer architecture of step S2 of the present invention; Figure 5 Schematic diagram of a single neural layer architecture in step S2 of the present invention; Figure 6Schematic diagram of the interaction between neural layers in step S2 of the present invention; Figure 7 Schematic diagram of the process of step S3 of the present invention; Figure 8 This is a gradient visualization diagram of the wavelet coefficient prediction in steps S2011 to S2012 of the present invention, wherein part A represents step S2011 and part B represents step S2012; the X-axis represents the wavelet packet basis expansion U opt (normalized); the Z axis is the filter coefficient g ik 、g jk (normalized), the Y axis is the predicted wavelet coefficients (normalized); Figure 9 This is a gradient visualization diagram of the wavelet coefficient prediction in steps S2013 and S2014 of the present invention, wherein part A represents step S2013 and part B represents step S2014; the X-axis represents the wavelet packet basis expansion U opt (normalized); the Z axis is the filter coefficient g ik 、g jk (normalized), the Y axis is the predicted wavelet coefficients (normalized). DETAILED DESCRIPTION

[0054] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar improvements without violating the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0055] Explanation of related terms: In the name "Detection of high-order harmonic voltage of ultrashort pulse intense laser field based on wavelet packet", "harmonic voltage" refers to "detection of voltage fluctuation under high-order harmonic of ultrashort pulse intense laser field based on wavelet packet".

[0056] Example 1: Figure 1 As shown, this embodiment discloses a method for detecting high-order harmonic voltage of ultrashort pulse strong laser field using wavelet packets; when multiple groups of wavelet functions of a laser system are combined together to form an orthogonal basis library L2(R), the filter coefficient h of the orthogonal scaling function φ(t) is determined. k, the filter coefficient g of the orthogonal function ψ(t) k (where k∈Z, Z is a positive number set), this scheme chooses to execute the following steps S1~S3: In this embodiment, if Figure 2 As shown, regarding step S1, the characteristic adaptation mechanism is executed: based on the DS evidence theory algorithm, the information entropy H i The calculation of is used as the confidence evaluation index, and the decomposition results under the frequency distribution and energy distribution of different signals are regarded as different evidences and assigned basic probabilities (BPA). Based on the preset recognition framework O, the Dempster combination principle is used to combine them and finally form the wavelet packet basis expansion U that best reflects the signal characteristics. opt .

[0057] Among them, DS evidence theory is a mathematical method for dealing with uncertainty and incomplete information, which allows multiple pieces of evidence to be combined to draw more reliable conclusions. Information entropy H i It is an indicator to measure the uncertainty of information. It is used as a confidence evaluation indicator here to help judge the reliability of the decomposition results. Through the characteristic adaptive mechanism, the wavelet packet basis expansion U that best reflects the signal characteristics is selected. opt , thereby improving the accuracy of wavelet packet decomposition and reconstruction.

[0058] Specifically, in step S100, information entropy is calculated: for each frequency distribution F i and energy distribution E i The wavelet packet decomposition result under the condition is used to calculate its information entropy H i As an evaluation indicator of confidence: ; Among them, n represents the ordinal number, p ij is the wavelet packet decomposition frequency distribution F i and energy distribution E i The probability distribution P i The probability of the jth component of ; the base of the logarithmic function can be selected as needed (base 2 or natural logarithm); the logarithmic function is used to measure the "surprise" or "information content" of probability. The smaller the probability, the larger the logarithmic term and the greater the contribution to information entropy. The negative sign indicates that information entropy is a measure of the uncertainty of the probability distribution. The larger the value, the higher the uncertainty.

[0059] Among them, the probability p ij The method to obtain is: 1) For each decomposition coefficient, calculate its energy E ij =∑ k ∣c ij (k)∣ 2 ; Among them, c ij(k) is the decomposition coefficient of the i-th layer, j-th node, and k-th sample.

[0060] 2) Normalize the energy of each decomposition coefficient to obtain the probability of energy distribution: ; The denominator is the sum of the energies of all decomposition coefficients, ensuring that the sum of all probabilities is 1.

[0061] It's easy to understand that calculating information entropy allows us to assess the confidence level of wavelet packet decomposition results for different frequency and energy distributions. Decomposition results with high confidence levels are more likely to reflect the true characteristics of the signal, allowing for improved accuracy in subsequent decomposition and reconstruction. Information entropy, as a confidence metric, captures the complexity of a signal's frequency and energy distribution. By selecting decomposition results with high confidence levels, we can better capture the signal's characteristics and avoid situations where assumptions are incorrect.

[0062] Specifically, step S101, calculate the basic probability distribution: the frequency distribution F i and energy distribution E i The decomposition effects are considered as different pieces of evidence, and each piece of evidence is assigned a basic probability m(A), where A is a subset of the identification framework O. The identification framework O contains the set of all possible wavelet packet basis expansions and / or parameter combinations. The basic probability is assigned based on two methods: one is based on the inverse of information entropy, and the other is based on the stability of the decomposition results calculated by the generalized least squares (GLS) method. Specifically: (1) The first method is to use the inverse of information entropy as the basis for allocating basic probabilities: ; Among them, A i is the frequency distribution F i and energy distribution E i The corresponding subset in the recognition frame O, is a small positive number to prevent the denominator from being zero, and c is a positive adjustment parameter used to control the influence of information entropy on basic probability.

[0063] (2) The second method is to introduce the generalized least squares (GLS) method to calculate the stability of the decomposition result and use it as the basis for the basic probability distribution m(A); the method is: S1010, define the stability index: for each probability p ij , calculate the residual vector between it and a reference result (the average result is selected in this embodiment). In order to evaluate the stability, a stability index is defined using the generalized least squares estimate of the residual: Let y i is the i-th decomposition result, is the reference result, then the residual vector ; S1011, calculate the residual variance of generalized least squares ; Wherein, W is the weight matrix (dedicated to step S1010), T is the transpose operation, m is the number of data points, and p is the number of decomposition results.

[0064] S1012, define stability indicator function: use residual variance The reciprocal of ; in, is a small positive number to prevent the denominator from being zero.

[0065] S1013, Converting Stability Indicators into Basic Probability Distributions ; Among them, A i is the frequency distribution F i and energy distribution E i The corresponding subset in the recognition frame O. Stability j It represents the stability index of the jth wavelet packet decomposition result.

[0066] As can be understood, the generalized least squares method evaluates the stability of the decomposition result by considering the residuals and the weight matrix to calculate the residual variance. The stability index reflects the degree of closeness of the decomposition result to the reference result. The higher the stability, the greater the basic probability. Normalization ensures that the sum of all basic probabilities is 1. By assigning basic probabilities based on information entropy or stability, the confidence of different decomposition results can be more accurately assessed. Decomposition results with high confidence are more likely to reflect the true characteristics of the signal and can be used in subsequent decomposition and reconstruction to improve accuracy. The generalized least squares method considers the residuals and the weight matrix, which can more comprehensively evaluate the stability of the decomposition result. Decomposition results with high stability are more reliable and help avoid situations where the assumptions are not met.

[0067] Specifically, step S102 executes the Dempster combination principle: the Dempster combination principle is a method for fusing information from different sources or sensors. It is based on Bayesian theory but can handle uncertainty and conflicting information. In this step, the basic probabilities of different evidences are combined to obtain the combined basic probability. ; Among them, m1 and m2 are different evidences (i.e. different frequency distributions F i and energy distribution E i ), is an empty set; B and C are subsets in the identification framework O. The numerator represents the sum of the products of all basic probability assignments that satisfy B∩C=A. This reflects the degree of joint support for A when two pieces of evidence both support a subset A. The denominator is used for normalization and takes into account the case where two pieces of evidence completely conflict (i.e., B∩C= ). This conflict lowers the overall confidence and therefore needs to be subtracted from 1.

[0068] The Dempster combination principle can be used to integrate information from different pieces of evidence, improving the accuracy of the selection of wavelet packet basis expansions. This method can resolve conflicts between pieces of evidence and avoid bias or misjudgment caused by a single piece of evidence. The combined basis probability m′(A) provides a more reliable basis for the subsequent selection of the optimal wavelet packet basis expansion.

[0069] Specifically, step S103 selects the optimal wavelet packet basis expansion U: based on the combined basic probability m'(A), the wavelet packet basis expansion with the highest confidence is selected as the optimal solution, that is: ; Among them, U opt is the optimal wavelet packet basis expansion. That is, within the recognition framework O, there are multiple possible wavelet packet basis expansions. The combined basis probability m′(U), obtained through the Dempster combination principle, reflects the confidence level of each expansion. Selecting the wavelet packet basis expansion with the highest confidence level as the optimal solution is an optimization strategy based on Bayesian decision theory.

[0070] By selecting the wavelet packet basis expansion with the highest confidence, the accuracy of wavelet packet decomposition and reconstruction can be improved. This method avoids situations where assumptions are not true because the selection is based on the combined probability of actual evidence rather than a single hypothesis or model. The selection of the optimal wavelet packet basis expansion helps better capture and analyze the high-order harmonic characteristics of ultrashort pulsed intense laser fields, improving the sensitivity and reliability of the detection method.

[0071] In this embodiment, if Figure 3 As shown, regarding step S2, the DD-DC neural network model performs data driving: the DD-DC neural network model models neurons as the expansion U of the wavelet packet basis optThe feedback controller FC enables it to directly map the observation results into wavelet coefficients W(a,b) as the final output Y, which represents the characteristics of the signal at different scale parameters a (corresponding to the inverse of the frequency) and translation parameters b (position in time or space). This eliminates the need to explicitly represent the controlled dynamic system as in traditional technologies (because traditional technologies usually require the establishment of a detailed controlled dynamic system model, including the system's state equations, output equations, and possible disturbance and uncertainty models. The establishment of these models often requires a lot of professional knowledge and experimental data, and the complexity of the model increases significantly with the increase of the system dimension. In the DD-DC neural network model, since the observation results are directly mapped to wavelet coefficients through data-driven means, the need for explicit modeling is avoided, thereby greatly simplifying the complexity of the model).

[0072] It should be pointed out that the DD-DC neural network model is a data-driven dynamic control method that combines the learning ability of neural networks with the time-frequency analysis ability of wavelet packets. In this model, neurons are no longer just traditional information processing units, but are modeled as feedback controllers FC based on the expansion of the wavelet packet basis Uopt. That is, neurons can directly adjust their outputs based on observations to match the time-frequency characteristics of the signal. opt The feedback controller enables neurons to use the time-frequency analysis capability of wavelet packets to more accurately capture the characteristics of signals.

[0073] Specifically, such as Figure 3 As shown, in step S200, the input layer performs the input task: receiving: (1) Orthogonal basis library L2(R), which is the basis of signal representation and contains orthogonal functions for signal decomposition and reconstruction; (2) Wavelet packet basis expansion U opt , is the wavelet packet basis combination obtained by optimal selection, which is used to more efficiently represent the time-frequency characteristics of the signal.

[0074] Then, the above parameters are encoded so that the neural network can read them normally; the weights w (dedicated to step S2), the bias vector b, and the feedback controller parameters, including the learning rate η and the momentum α, are initialized; Specifically, such as Figure 4 As shown, in step S201, the hidden layer performs the mapping task: the hidden layer includes multiple neural layers N i , each neural layer N i Including multiple neurons , where l represents the number of layers, j represents the neuron index of the layer; each neuron Perform forward and backward propagation; each neuron It is a feedback controller FC, which adaptively matches and calculates the initial wavelet coefficients ;in: Each neural layer N i neurons All are based on any two orthogonal functions ψ in the orthogonal basis library L2(R) i (t), ψ j The filter coefficient g of (t) ik 、g jk As input, they are responsible for different data processing and feature extraction tasks, and through the interaction and feedback of multiple layers of neurons, they can more accurately perceive and control the environment; at the same time, each neural layer N i Output Y i is fed back to the previous neural layer N i The data is corrected and iterated repeatedly. When the objective function F converges or reaches the predetermined number of iterations, the final output Y is obtained; It's understandable that through the interaction and feedback of multiple layers of neurons, neural networks can more accurately capture the time-frequency characteristics of signals, improving the accuracy of wavelet packet decomposition and reconstruction. Neurons, acting as feedback controllers, can adaptively adjust their output based on the input signal, enhancing the adaptability of the neural network. This neural network does not rely on specific system assumptions, such as linearity or time invariance, and is therefore more adaptable to complex signal environments.

[0075] Specifically, in step S2010, the feedback controller FC is initialized: each neuron It is a feedback controller FC, which controls the speed and direction of adjustment based on the learning rate η and momentum α parameters, and adaptively matches and calculates the initial wavelet coefficients. ; The feedback controller FC form is: ; Among them, w new represents the updated weight; w old Indicates the current weight; Represents the gradient of the output error E of the current time step t compared to the previous time step t-1 with respect to the weight matrix w; w previous Indicates the previous weight value (used to maintain a certain inertia in momentum optimization); b new represents the updated bias; b old Indicates the current bias; represents the gradient of the error E with respect to the bias b.

[0076] The principle of the above feedback controller is that each neuron Each of these functions as a feedback controller, FC, responsible for adjusting its weights and biases based on the input signal and the current network state to minimize the output error. The feedback controller iteratively updates the weights and biases, allowing the neural network to gradually approach the optimal solution to the objective function. Through continuous adjustments by the feedback controller, neurons are able to adaptively match the calculated initial wavelet coefficients, reflecting the signal characteristics at different scales and translation parameters.

[0077] Specifically, step S2011, as Figure 5 As shown, the neuron forward propagation: for each neural layer N i Each neuron , receiving input data from the previous layer (for the first neural layer, it corresponds to the input layer), including any two orthogonal functions ψ in the orthogonal basis library L2(R) i (t), ψ j The filter coefficient g of (t) ik 、g jk Each neuron The weight w calculated based on the current feedback controller FC new and bias b new To calculate its output Y i , is regarded as a preliminary estimate or feature representation of the wavelet coefficients W(a,b).

[0078] (1) For one-to-one tasks, the forward propagation is: ; (2) If we consider multiple combinations of inputs and weights (multiple filter coefficients and corresponding weights), the forward propagation is: ; Among them, Y i Represents neurons The output of; f(⋅) represents the Sigmoid activation function, which is used to introduce nonlinearity; g ik represents the input (filter coefficients) from the previous layer; Represents neurons The weight corresponding to the kth input (the superscript (i,j) indicates that this is the weight specific to the jth neuron in the i-th layer); Represents neurons Bias of; symbol ∑ k Represents a weighted summation of all inputs (filter coefficients).

[0079] The output of the neuron Y i It can be regarded as a preliminary estimate or feature representation of the wavelet coefficient W(a,b), and its gradient can be visualized as Figure 7As shown in part (A), it can be seen that in the initial estimation state, there are spikes and cliffs, and the global minimum is not clear, so further back propagation and iteration are still required. However, in this step, the complex features in the signal can be captured through the nonlinear transformation and weight adjustment of the neural network, thereby improving the accuracy of wavelet packet decomposition and reconstruction. Traditional wavelet packet decomposition methods may rely on certain assumptions (such as the stationarity and sparsity of the signal). However, in practical applications, these assumptions may not hold. However, through the adaptive learning and nonlinear processing capabilities of the neural network of this embodiment, it can better adapt to the changes and complexity of the signal, thereby avoiding the situation where the assumptions do not hold.

[0080] It should be noted that although the above expression does not show the wavelet packet basis expansion U opt As the input form, but it has been implicitly expressed; first, the wavelet packet basis expansion U opt It is the expansion obtained by selecting the optimal basis (i.e. the basis that can best represent the signal sparsely) when performing wavelet packet decomposition on the signal. It consists of a series of wavelet packet basis functions (i.e. orthogonal functions) and corresponding coefficients, which reflect the characteristics of the signal at different frequencies and time scales. In neural networks, U opt It is not input directly as a whole, but indirectly through its components (i.e. basis functions and coefficients). i (t), ψ j (t)) filter coefficients (such as g ik 、g jk ) can be regarded as U opt The neural network implicitly captures the relationship between U by learning the relationship between these input data (i.e., filter coefficients) and output (i.e., wavelet coefficients or feature representations). opt The signal characteristics represented.

[0081] Furthermore, this approach leverages the sparse representation capabilities of wavelet packet decomposition while combining the adaptive learning and nonlinear processing capabilities of neural networks to improve the accuracy and robustness of signal processing. Furthermore, since the neural network input is the filter coefficients (rather than the entire signal), this helps reduce computational complexity and memory usage, improving processing efficiency.

[0082] It's understandable that the nonlinear transformations and weight adjustments of neural networks can more accurately capture the characteristics of the wavelet coefficients in the signal, thereby improving the accuracy of wavelet packet decomposition and reconstruction. Neural networks possess powerful adaptive learning and nonlinear processing capabilities, enabling them to better adapt to signal variations and complexity. This enhances the robustness of wavelet packet decomposition and reconstruction methods, enabling them to maintain good performance in various application scenarios. Using the neuron output as a preliminary estimate or feature representation of the wavelet coefficients facilitates subsequent feature extraction and analysis.

[0083] Specifically, such as Figure 5 As shown, step S2012, neuron back propagation and feedback control: based on neuron Output Y i , weight w new and bias b new , adaptively matching and calculating the initial wavelet coefficients .

[0084] Preferably, considering that this step cannot directly obtain an expected value, it is necessary to introduce a self-supervised learning strategy: Since W(a,b) is the wavelet transform coefficient, we hope to output Y i After transformation or reconstruction, the signal can maintain consistency or similarity with the original signal. Then, the objective function F(Y i ) Gradient with respect to weight w and bias b: ; Then, we further use the calculated gradient to update the weights and biases to w new ' and b new ', to optimize the objective function ; Among them, x n is the nth sample of the original signal. Is to use output Y i The nth sample of the reconstructed signal. S is the total number of samples in the signal; Y i (a,b) is the value of the estimated wavelet coefficient at scale a and position b; Then, we measure the combination of energy distribution difference and sparsity penalty. The principle is that if the estimated wavelet coefficients are highly consistent with the expected energy distribution, the decomposition result is accurate and can well represent the original signal. On the contrary, if the difference is large, it may be equivalent to errors or deficiencies in the decomposition process: ; The first term measures the difference between the estimated wavelet coefficients and the expected energy distribution of the wavelet coefficients. The second term is a sparsity penalty term that encourages the wavelet coefficients to remain sparse. λ is a parameter that controls the strength of the sparsity penalty. ExpectedEnergy(a,b) is the expected energy distribution of the wavelet coefficients.

[0085] The initial wavelet coefficients formed in this step The gradient visualization form is as follows Figure 7 As shown in part (B), we can see that the peaks and cliffs have been optimized, but the global minimum is not clear and needs further optimization.

[0086] It can be understood that by calculating the mean square error (MSE) as the objective function and continuously updating the weights and biases to minimize this objective function, the network can better learn the characteristics of the original signal, thereby improving the accuracy of reconstruction. Through self-supervised learning strategies and optimizing the objective function, the reconstructed signal can maintain consistency or similarity with the original signal, thereby improving the accuracy of wavelet packet decomposition and reconstruction.

[0087] Furthermore, due to the use of a self-supervised learning strategy, there is no need to assume that the expected wavelet coefficients are known, thus avoiding the situation where the assumption is not true. Its principle is to optimize the network parameters by comparing the consistency of the reconstructed signal with the original signal, rather than directly relying on the expected wavelet coefficients. Therefore, even if the expected wavelet coefficients are unknown, accurate wavelet coefficients can be obtained through the optimization process.

[0088] Furthermore, by combining the energy distribution difference and sparsity penalty, the estimated wavelet coefficients can be made to conform to the desired energy distribution while maintaining sparsity, thereby improving the efficiency and accuracy of wavelet packet decomposition. The energy distribution difference term encourages the estimated wavelet coefficients to be consistent with the desired energy distribution, while the sparsity penalty term encourages the wavelet coefficients to maintain sparsity. The combination of the two can make the estimated wavelet coefficients more accurate and effective.

[0089] It should be further pointed out that sparse representation is a signal processing method that represents a signal using as few nonzero coefficients as possible, thereby simplifying the signal representation and reducing computational complexity. In wavelet packet decomposition, sparsity is equivalent to only a few basis functions making a significant contribution to the signal representation, which helps to extract the signal's key features. Overfitting is a common problem in machine learning and signal processing, which refers to a model that performs well on training data but poorly on test data. By introducing a sparsity penalty, the model can be encouraged to select fewer basis functions to represent the signal, thereby avoiding overfitting and improving the model's generalization ability. Measuring energy distribution differences alone may lead to overly complex models containing too many nonzero coefficients; using a sparsity penalty alone may sacrifice model accuracy, resulting in an inability to fully capture signal features. By combining the two, a sparse representation of the signal can be achieved while maintaining model accuracy, achieving a balance.

[0090] Further, such as Figure 5 As shown, it also includes step S2013, interaction and feedback within the neural layer: in each neural layer N i Different neurons Output Y between i They serve as input to each other, forming interactions within the layer and sharing information, thereby more accurately perceiving and controlling the environment. The output of the neural layer Y i ' is the combined result of the outputs of all neurons in this layer.

[0091] Each neuron Output Y i As input to other neurons (including itself, if self-feedback is required): ; Where: Y i,j ′ represents the updated output of the jth neuron after considering the interaction within the layer. The form of the visualized gradient is as follows Figure 8 As shown in part (A), we can see that compared with the previous step, the peaks and cliffs have been greatly optimized, but there is still a certain search space for the global minimum. F' is a nonlinear function (such as the Sigmoid activation function) used to introduce nonlinear interaction effects. i,j,k is the influence weight of the kth neuron on the jth neuron. MM is the number of neurons in the neural layer N i The number of neurons in .

[0092] Then, the comprehensive output Y of the neural layer i ′ is the weighted sum of all updated neuron outputs: ; in, are the new weights used to combine the outputs of all updated neurons.

[0093] It is understandable that through the interaction between neurons within a layer, the information within the neural layer can be more fully utilized, improving the accuracy of wavelet packet decomposition and reconstruction. The interaction within the layer allows each neuron to receive the output of other neurons as input, thereby more comprehensively considering the characteristics of the signal and improving the accuracy of decomposition and reconstruction.

[0094] The introduction of nonlinear functions (such as the Sigmoid activation function) enhances the network's expressive power, enabling it to process more complex signal characteristics. Nonlinear functions can introduce nonlinear interactions, making neuron outputs no longer simply linear combinations of inputs, but capable of representing more complex nonlinear relationships. Through intra-layer interactions and integrated output mechanisms, the network can more flexibly adapt to signal changes and complexity, avoiding situations where assumptions are violated. These intra-layer interactions and integrated outputs enable the network to dynamically adjust the contribution of each neuron to the output, thereby more flexibly adapting to signal changes and complexity.

[0095] Further, such as Figure 6 As shown, it also includes step S2014, cross-layer feedback and iteration: the neural layer N i Output Y i Feedback to the previous layer (or input layer) for data correction and further processing. Repeat this step until the objective function F converges or reaches a predetermined number of iterations; the optimization function F is based on the square sum of the error E. The process is, for the neural layer N i , loop execution: S20140, error E calculation: ; Where K is the number of output neurons; Y k is the output of the kth output neuron in the previous iteration; is the output of the k-th output neuron in this iteration; S20141, based on the square sum of error E, is guided by the optimization function F: ; The goal of optimization is to minimize the optimization function F; S20142, update each neuron again according to the direction of the error gradient Biases and weights of S20143, feeds the updated neural layer output back to the previous layer (or input layer); S20144, repeat steps S20140 to S20143 until the change of the minimized optimization function F is less than the threshold value, or the predetermined maximum number of iterations is reached; and the last neural layer N i 'The comprehensive output Y i ′ is the final output Y, and its gradient is visualized as follows Figure 8 As shown in part (B), the three-dimensional gradient surface is very smooth, without any abrupt peaks or cliffs. This indicates that the objective function changes continuously and predictably. This smooth surface helps the optimization algorithm stably find the extreme value. It also has a unimodal structure and consistently points to the minimum point. This proves that this model can always gradually approach the optimal solution by moving in the direction of the negative gradient.

[0096] It can be understood that through cross-layer feedback and iteration, the output of the neural layer is continuously corrected to bring it closer to the desired output, thereby improving the accuracy of wavelet packet decomposition and reconstruction. Cross-layer feedback allows the neural layer to use information from the previous layer (or input layer) to make corrections and adjustments, and the iterative process allows these corrections and adjustments to continue until the optimal solution is reached or the termination condition is met.

[0097] Through continuous iteration and optimization, the model can better adapt to signal changes and complexity, improving its generalization capabilities. The iterative process enables the model to dynamically adjust weights and biases, allowing for more flexible adaptation to signal characteristics and changes. Through cross-layer feedback and iteration, the model can, to a certain extent, offset the impact of invalid assumptions, improving its robustness. Cross-layer feedback and iteration enable the model to continuously correct and adjust its output, thereby offsetting errors introduced by invalid assumptions.

[0098] Specifically, in step S202, the output layer performs an output task: performing a decoding operation on the final output Y to obtain the wavelet coefficients W(a,b): W(a,b) = Decode(Y); wherein Decode(⋅) represents a decoding operation.

[0099] In this embodiment, if Figure 7 As shown, regarding step S3, nonlinear compensation: based on Z-transformation and discrete Fourier transform (DFT), instantaneous energy changes are described and nonlinear compensation is performed on the predicted output Y.

[0100] Specifically, step S300, Z transform and discrete Fourier transform: let y[n] be the discrete time series representation of the predicted output Y; apply Z transform to y[n] to obtain its Z domain representation Y(z): ; Where z is a complex variable representing the frequency domain shift. n is an integer index representing each sample point or moment in the time series.

[0101] Applying the Discrete Fourier Transform (DFT) to y[n] yields its frequency domain representation Y[k]: ; Where NM is the length of the sequence, k is the frequency domain index, is a complex exponential function; j is an imaginary unit.

[0102] Specifically, in step S301, the instantaneous energy change is calculated: the instantaneous energy E[n] is expressed as the square of the modulus of the sequence y[n]: E[n] = |y[n]| 2 ; Instantaneous energy changes can be described by calculating the difference in energy between adjacent moments or using other energy change measurement methods.

[0103] Specifically, in step S302, nonlinear compensation: let fc(⋅) be a nonlinear compensation function, which adjusts the predicted output y[n] according to the instantaneous energy change or other characteristics.

[0104] The output y′[n] after nonlinear compensation is expressed as: y′[n]=fc(y[n],E[n])=y[n]+V⋅(E[n]−E ref ) 2 ; Where: y[n] is the original prediction output. E[n] is the instantaneous energy of the nth sample point. ref is the reference energy value. V is the nonlinear compensation coefficient, which is used to adjust the compensation strength. y′[n] is the output after nonlinear compensation. The role of the nonlinear compensation function fc(⋅) is to adjust the predicted output according to the instantaneous energy change. Specifically, when the instantaneous energy E[n] deviates from the reference energy value E ref When , the compensation function adds a nonlinear term V⋅(E[n]−E ref ) 2 The magnitude of this nonlinear term depends on the energy deviation (E[n]−E ref ) and compensation coefficient V to adjust the predicted output to make it more consistent with the actual signal characteristics.

[0105] It is understood that nonlinear compensation can correct prediction errors caused by signal nonlinearity or noise, improving the accuracy of wavelet packet decomposition and reconstruction. By introducing a nonlinear compensation function, the predicted output is adjusted according to the instantaneous energy change, making the compensated output closer to the actual signal.

[0106] Nonlinear compensation enhances a system's adaptability and robustness to signal variations, preventing assumptions from being violated. This is because the nonlinear compensation function dynamically adjusts based on the actual energy changes in the signal, offsetting deviations caused by signal nonlinearity or noise to a certain extent. Nonlinear compensation improves signal quality, facilitating subsequent analysis and processing. Nonlinear compensation reduces noise and distortion, making the compensated signal closer to the original, thereby improving signal quality.

[0107] In this embodiment, regarding step S4, the voltage fluctuation relationship is obtained: after the output y′[n] is obtained, the voltage fluctuation of the laser system can be detected; the method is: Specifically, S400 determines a relationship model between energy and voltage: determining a relationship between the output energy E' of the laser and its driving voltage V'. For many types of lasers, particularly semiconductor lasers, this relationship is linear or approximately linear: E'=k·V', where k is a proportionality factor representing an efficiency factor for converting electrical energy to optical energy. Of course, the relationship formula for the laser output energy E' can also be directly provided by the laser manufacturer. Specifically, in S401, filtering (moving average filter) is performed: ; Among them, y′′[n] is the energy change sequence after smoothing, and NW is the window size.

[0108] Specifically, in S402 , voltage fluctuation is detected: y′′[n]=k⋅V[n]; Therefore, the voltage fluctuation sequence V[n]=y′′[n] / k is obtained.

[0109] Furthermore, an accurate sequence of energy change values can significantly reduce the errors generated during the voltage fluctuation calculation process, more realistically reflecting the operating state and dynamic characteristics of the laser, making the voltage fluctuation calculation closer to the actual situation and helping to identify the true voltage fluctuation pattern. An accurate sequence of energy change values can help more accurately detect abnormal fluctuations in voltage. Voltage fluctuation analysis based on an accurate sequence of energy change values can better adjust and optimize the laser's control system parameters, achieving more stable output power control.

[0110] An accurate sequence of energy variation values helps to more precisely evaluate the laser's energy conversion efficiency, thereby guiding how to optimize the driver circuit design to achieve higher electro-optical conversion efficiency. By accurately analyzing voltage fluctuations, it is possible to identify unnecessary energy loss points and take measures to reduce these losses, thereby reducing overall energy consumption.

[0111] It is understandable that predicting future voltage fluctuations can help real-time control systems more intelligently adjust key parameters such as the drive current and cooling system, ensuring that the laser output power always remains at an optimal state. By predicting and compensating for possible future voltage fluctuations, laser output power fluctuations caused by power supply instability can be reduced, thereby improving the overall stability and reliability of the system. Predicting voltage fluctuations helps optimize energy usage strategies and avoid unnecessary energy loss. For example, when voltage fluctuations are large, the laser output power can be temporarily reduced to save energy. Based on the prediction of future voltage fluctuations, more efficient power conversion mechanisms can be designed to further improve the energy conversion efficiency of the laser.

[0112] Furthermore, in applications requiring extremely high precision, such as laser micromachining and ophthalmic surgery, predicting voltage fluctuations can help maintain consistent and accurate laser output, reducing errors caused by voltage variations. By predicting future voltage fluctuations, process parameters can be adjusted in advance, ensuring that the entire machining or operation proceeds smoothly and meets the expected quality standards.

[0113] Embodiment 2: This embodiment further provides a specific solution for the identification framework O as described in embodiment 1.

[0114] The identification framework O contains all possible wavelet packet basis expansions and their parameter combinations (established through historical data): O={(b k ,θ k )|k=1,2,…,K} Among them, b k Represents the kth wavelet packet basis expansion. k represents the parameter combination corresponding to the kth wavelet packet basis expansion. K represents the total number of possible wavelet packet basis expansions and their parameter combinations.

[0115] In order to specifically represent the wavelet packet basis expansion, the formula form of discrete wavelet transform (DWT) or continuous wavelet transform (CWT) can be used, combined with the hierarchical structure of wavelet packet decomposition.

[0116] For example, for discrete wavelet packet transform: ; Among them, d j,k (n) represents the wavelet packet coefficient at the jth layer and the kth subband. k (l) represents the wavelet packet filter coefficient corresponding to the kth subband. x(n) represents the original signal.

[0117] For the parameter combination θ k , including the number of levels of wavelet packet decomposition, filter coefficients and sampling rate: ; Among them, L k The number of levels of the kth wavelet packet decomposition. is a positive integer that determines the depth of the wavelet packet decomposition. A greater number of levels yields more subbands and a higher frequency resolution, but also increases computational complexity. M represents the filter coefficient set corresponding to the k-th wavelet packet basis expansion. k is the number of filter coefficients, h k,l is the lth filter coefficient. The filter coefficient determines the frequency characteristics of the wavelet packet transform, and different filter coefficients will lead to different decomposition results. Represents the sampling rate of the kth wavelet packet transform. The sampling rate determines the discretization degree of the signal and affects the time and frequency resolution of the wavelet packet transform.

[0118] It's understandable that the wavelet packet transform provides a more flexible and sophisticated signal analysis method than traditional wavelet transforms. By selecting different wavelet packet basis expansions, we can analyze signals at different frequency and time resolutions. The recognition framework O includes all possible wavelet packet basis expansions, ensuring that we can select the optimal basis expansion during signal analysis, thereby improving the accuracy and robustness of the analysis.

[0119] Because the algorithmic form of the identification framework O uses an enumeration or parameterization to describe the wavelet packet basis expansion and its parameter combinations, this form is universal and can be applied to different wavelet packet transform algorithms and application scenarios. By defining the identification framework O, we can provide a unified foundation and framework for subsequent steps such as basic probability allocation and feature adaptation mechanisms, providing flexible and diverse options for signal analysis. This form not only improves the accuracy and robustness of the analysis.

[0120] Example 3: This example further provides an intelligent dynamic data-driven solution for controlling the learning rate η and momentum α of the feedback controller FC as in Example 1: ; Among them, E t represents the residual (or error) at step t, E t−1 represents the residual at step t−1. λ is a step adjustment coefficient used to control the speed and amplitude of learning rate adjustment. E t / E t−1 Reflects the rate of change of the residual. If the residual decreases (i.e. E t / E t−1 <1, the learning rate can be kept constant or slightly increased (depending on the value of λ); if the residual increases (i.e., E t / E t−1>1), the learning rate will be reduced to slow down the update pace and avoid overshoot. In this way, the learning rate can be adaptively adjusted according to the dynamic changes of the residual.

[0121] sgn(x) is the sign function. When x>0, sgn(x)=1; when x<0, sgn(x)=−1; when x=0, sgn(x)=0. μ is also a step coefficient used to control the speed and amplitude of momentum adjustment. t −E t−1 Reflects the change in the residual. If the residual decreases (i.e. E t −E t−1 <0), the momentum can be maintained or slightly increased (because sgn(E t −E t−1 )=−1, so the new weight α t+1 =α t ⋅(1+μ)); if the residual increases (i.e. E t −E t−1 >0), the momentum will decrease (because sgn(E t − Et−1 )=1, so α t+1 =α t ⋅(1−μ)) to slow down the inertia of the update step and avoid excessive oscillation. In this way, the momentum can be adaptively adjusted according to the dynamic changes of the residual.

[0122] By dynamically adjusting the learning rate and momentum based on the residual, it can better adapt to changes during training. When the residual is large, the learning rate and momentum may be reduced to avoid overshoot and oscillation. When the residual is small, the learning rate may remain the same or slightly increase, and the momentum may be adjusted accordingly to accelerate convergence. Traditional fixed learning rate and momentum methods can cause the feedback controller FC to diverge. However, the residual backtracking method can monitor training results in real time, adjust parameters in a timely manner, and effectively reduce the risk of divergence.

[0123] As the residual gradually decreases, the learning rate can be appropriately increased and the momentum adjusted accordingly to accelerate convergence. This intelligent acceleration mechanism fully utilizes useful information during training to improve training efficiency. By dynamically adjusting the learning rate and momentum, this solution helps the model escape local optimal solutions and further explore the space for global optimal solutions.

[0124] Example 4: This example further provides a neural network training method as in step S2 of Example 1. The method includes the following steps: P1. Data Engineering: Collect the wavelet coefficients in the historical data as the dependent variable Y and find the orthogonal basis library L2(R) corresponding to it, that is, any two orthogonal functions ψ i (t), ψ jThe filter coefficient g of (t) ik 、g jk Constitute the historical independent variable X, and then establish a data set D: D=[(X1,Y1),(X2,Y2),...,(X n ,Y n )]; Among them, (X i ,Y i ) is the i-th sample, and n is the number of samples.

[0125] Divide the dataset D into training set D train , test set D test , validation set D val . Use 70% of the data as training set D train , 15% as validation set D val To adjust the model parameters, the remaining 15% is used as the test set D test To evaluate the model performance.

[0126] P2, training process: Use the model architecture shown in step S2, and use the training set D train During the training process, the model adjusts the neuron bias b, weight w, parameter λ, number of neurons MM and influence weight w i,j,k To minimize the prediction error, the mapping relationship between input features and fault types is learned.

[0127] After each training, use the test set D test Validation and testing are performed to evaluate its predictive performance and generalization ability.

[0128] P3, optimization and iteration: based on the validation set D val Evaluate the model's prediction performance and localization accuracy to identify potential areas for improvement. Adjust the model's bias b, weight w, parameter λ, number of neurons MM, and influence weight w based on the direction of the performance difference. i,j,k , to improve the model's prediction performance and positioning accuracy. Continuous training continues until the model converges or reaches a predetermined number of iterations.

[0129] Example 5: This example further provides the nonlinear term V⋅(E[n]−E ref ) 2 Intelligent dynamic assignment method; The core point is that the nonlinear compensation coefficient V is an adjustable parameter, and the value of V should be such that the nonlinear compensation can effectively correct the prediction error without introducing too much noise; when the instantaneous energy E[n] deviates from the reference energy E[n], the energy E[n] will be ref When the nonlinear term V⋅(E[n]−E ref) 2 The prediction output will be adjusted based on the degree of deviation. If V is too large, it may lead to overcompensation and introduce unnecessary noise; if it is too small, it may not be able to effectively correct the prediction error.

[0130] Therefore, this embodiment introduces the following solution to dynamically assign compensation to the nonlinear compensation coefficient V: ; Where: V n is the value of V at the nth iteration. n+1 is the value of V at the n+1th iteration. v is the learning rate, a positive number that controls the size of the update step. is the performance index function J(V) when V=V n The gradient at ; the performance indicator function J(V) can be a nonlinear term V⋅(E[n]−E ref ) 2 Mean square error compared to the previous task result; In each iteration, the gradient of the performance indicator function J(V) with respect to V is calculated, and the value of V is updated using the gradient descent formula described above. If the convergence condition is met (such as the gradient is close to 0 or the maximum number of iterations is reached), the iteration is stopped; otherwise, the iteration continues until the optimal solution is obtained.

[0131] All of the above embodiments merely represent implementation methods of the present invention in practical applications. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the scope of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the appended claims.

[0132] For those skilled in the art, it can be further appreciated that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0133] At the same time, those skilled in the art will understand that all or part of the processes in all the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media provided in this application and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double-speed data rate SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

Claims

1. The wavelet packet ultrashort pulse intense laser field high harmonic voltage detection method includes combining multiple groups of wavelet functions of a laser system together to form an orthogonal basis library L2(R), and determining the filter coefficient h of the orthogonal scaling function φ(t) k , the filter coefficient g of the orthogonal function ψ(t) k , characterized in that: Perform the following steps: S1, with information entropy H i The calculation of is used as the confidence evaluation index, and the decomposition results under the frequency distribution and energy distribution of different signals are regarded as different evidences and assigned basic probabilities. Based on the recognition framework O, the Dempster combination principle is used to combine them to form the wavelet packet basis expansion U that reflects the signal characteristics. opt ; S2, using the DD-DC neural network model, the wavelet packet basis expansion U opt Mapped into wavelet coefficients W(a,b) as the final output Y, representing the characteristics of the signal at different scale parameters a and translation parameters b; S3, based on Z transform and discrete Fourier transform, describes the instantaneous energy change and performs nonlinear compensation on the predicted output Y; S4, detecting voltage fluctuation of the laser system; the method is: S400, determining the relationship between the output energy E' of the laser and its driving voltage V': E'=k·V', where k is the proportionality coefficient, which represents the efficiency factor of the conversion from electrical energy to light energy; S401, perform filtering: ; Among them, y′′[n] is the energy change sequence after smoothing, and NW is the window size; S402 , detecting voltage fluctuations: y′′[n]=k⋅V[n]; obtaining a voltage fluctuation sequence V[n]=y′′[n] / k.

2. The detection method according to claim 1, wherein: The execution steps of S1 include: S100, for each frequency distribution F i and energy distribution E i The wavelet packet decomposition result under the condition is used to calculate its information entropy H i As an evaluation indicator of confidence: ; Among them, n represents the ordinal number, p ij is the wavelet packet decomposition frequency distribution F i and energy distribution E i The probability distribution P i The probability of the jth component of ; S101, the frequency distribution F i and energy distribution E i The decomposition effect is considered as different evidence and each evidence is assigned a basic probability m(A), where A is a subset in the recognition framework O: ； Among them, A i is the frequency distribution F i and energy distribution E i The corresponding subset in the recognition frame O, is a positive number to prevent the denominator from being zero, and c is a positive adjustment parameter; S102: Execute the Dempster combination principle to combine the basic probabilities of different pieces of evidence to obtain a combined basic probability m′(A): ; in, is an empty set, m1 and m2 are basic probability distributions of different evidences, B and C are subsets in the identification framework O; S103, based on the combined basic probability m'(A), select the wavelet packet basis expansion with the highest confidence as the optimal solution: .

3. The detection method according to claim 1, wherein: In the S2, the DD-DC neural network model models the neurons as the expansion U of the wavelet packet basis opt The feedback controller FC, the DD-DC neural network model includes: S200, input layer: receiving the orthogonal basis library L2(R) and the wavelet packet basis expansion U opt And perform encoding operations; initialize weight w, bias vector b and the feedback controller FC parameters, including learning rate η and momentum α; S201, the hidden layer includes multiple neural layers N i , each neural layer N i Including multiple neurons , where l represents the number of layers, j represents the neuron index of the layer; each neuron Perform forward and backward propagation; each neuron The feedback controller FC is used to adaptively match and calculate the initial wavelet coefficients. .

4. The detection method according to claim 3, wherein: In said S201, each neural layer N i neurons All are based on any two orthogonal functions ψ in the orthogonal basis library L2(R) i (t), ψ j The filter coefficient g of (t) ik 、g jk As input, the execution process includes: S2010, initialize the feedback controller FC: ； Among them, w new represents the updated weight; w old Indicates the current weight; Represents the gradient of the output error E of the current time step t compared to the previous time step t-1 with respect to the weight matrix w; w previous Indicates the last weight value; b new represents the updated bias; b old Indicates the current bias; represents the gradient of the error E with respect to the bias b; S2011, Forward Propagation: ; Among them, Y i Represents neurons The output of; f(⋅) represents the Sigmoid activation function; g ik Represents the input from the previous layer; Represents neurons The weight corresponding to the kth input; Represents neurons Bias; S2012, Backpropagation and Feedback Control: Calculate the objective function F(Y) of the mean square error (MSE) between the reconstructed signal and the original signal i ) Gradient of weight w and bias b; then, further use the calculated gradient to update the weight and bias to w new ' and b new '; and measures the combination of energy distribution difference and sparsity penalty: ； Where ExpectedEnergy(a,b) is the expected energy distribution of wavelet coefficients; λ is a parameter that controls the intensity of sparsity penalty; is the initial wavelet coefficient; Y i (a,b) is the value of the estimated wavelet coefficient at scale a and position b.

5. The detection method according to claim 4, wherein: In the above S201, the interaction and feedback within the neural layer are also included: each neuron Output Y i,j As input to other neurons: ； Where: Y i,j ′ represents the updated output of the jth neuron after considering the interaction within the layer; F' is a nonlinear function; w i,j,k is the influence weight of the kth neuron on the jth neuron; MM is the neural layer N i The number of neurons in the i ′: ;in, is the new weight.

6. The detection method according to claim 5, characterized in that: The interaction and feedback within the neural layer in S201 also includes a self-supervised learning strategy, the method is: The objective function F(Y i ) Gradient with respect to the weight w and the bias b: ; Update weights and biases to w new ' and b new ', to optimize the objective function F(Y i ): ； Among them, x n is the nth sample of the original signal; Is to use output Y i The nth sample of the reconstructed signal; S is the total number of samples of the signal; and then the combination of energy distribution difference and sparsity penalty is measured.

7. The detection method according to claim 5, wherein: In the S201, it also includes S2014, cross-layer feedback and iteration, for the neural layer N i , loop execution: S20140, calculation error E: ; Where K is the number of output neurons; Y k is the output of the kth output neuron in the previous iteration; is the output of the k-th output neuron in this iteration; S20141, calculate the sum of squared error E metric for bootstrapping; S20142, update each neuron again according to the direction of the error gradient Biases and weights of S20143, feeds the updated neural layer output back to the previous layer; S20144, repeat steps S20140 to S20143 until the change of the minimized optimization function F is less than the threshold value, or the predetermined maximum number of iterations is reached; and the last neural layer N i 'The comprehensive output Y i ’ as the final output Y.

8. The detection method according to claim 3, wherein: In the S2, the method further includes S202, performing a decoding operation on the final output Y to obtain wavelet coefficients W(a, b): W(a,b) = Decode(Y); Among them, Decode(⋅) represents the decoding operation.

9. The detection method according to any one of claims 1 to 8, characterized in that: The execution steps of S3 include: S300, let y[n] be the discrete time series representation of the predicted output Y; apply the Z transform to y[n] to obtain its Z domain representation Y(z): ; Where z is a complex variable representing the shift in the frequency domain; n is an integer index; Applying the discrete Fourier transform to y[n] yields the frequency domain representation Y[k]: ； Where NM is the length of the sequence, k is the frequency domain index, is a complex exponential function; j is an imaginary unit; S301, the instantaneous energy E[n] is expressed as the square of the modulus of the sequence y[n]: E[n] = |y[n]| 2 ; S302, let fc(⋅) be the nonlinear compensation function; the output y′[n] after nonlinear compensation is expressed as: y′[n]=fc(y[n],E[n])=y[n]+V⋅(E[n]−E ref ) 2 ; Where: y[n] is the original prediction output; E[n] is the instantaneous energy of the nth sample point; E ref is the reference energy value; V is the nonlinear compensation coefficient; y′[n] is the output after nonlinear compensation.

10. A system for implementing the detection method according to any one of claims 1 to 9, characterized in that: The system includes a processor and a memory connected to the processor, wherein program instructions are stored in the memory, and when the program instructions are executed by the processor, the processor executes the detection method according to any one of claims 1 to 9.

Images