A parameter adaptive optimized sparse generalized s-transform time-frequency analysis method

Abstract

This invention discloses a sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization. This method employs a two-stage optimization strategy to optimize the core window parameters of the generalized S-transform and the sparse inversion solution parameters, respectively, and establishes a fitness function for evaluation to obtain the parameter combination that achieves the optimal time-frequency resolution. Finally, the optimized parameters are used to complete high-resolution time-frequency analysis of the signal. The advantages of this method lie in its adaptive parameter finding capability, reducing the subjectivity of manual parameter selection, and its significant advantages in time-frequency resolution and adaptability, providing time-frequency analysis technical support for subsequent seismic data processing and interpretation.

Description

Technical Field

[0001] This invention belongs to the field of geophysical signal processing and relates to a sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization, belonging to the interdisciplinary technical field of time-frequency analysis and seismic signal processing. Background Technology

[0002] Time-frequency analysis, a crucial component and fundamental step in seismic signal processing, aims to transform non-stationary seismic signals into the time-frequency domain, reflecting the relationship between frequency and time. However, commonly used time-frequency analysis methods primarily include S-transform, generalized S-transform, and sparse generalized S-transform. The sparse generalized S-transform involves multiple key parameters, and manually setting these parameters introduces subjectivity, making it difficult to adapt to complex and variable real-world signals. This leads to decreased time-frequency resolution and affects the reliability of subsequent seismic data processing and interpretation. With the increasing demand for high-resolution processing in oil and gas exploration, a time-frequency analysis method capable of adaptively adjusting parameters is needed. Therefore, this invention employs a parameter adaptive optimization method to automatically optimize the key parameters of the sparse generalized S-transform. This allows the transformation process to adjust parameter values ​​according to signal characteristics, reducing the subjectivity of manually finding parameters, effectively improving resolution in both the time and frequency directions, enhancing adaptability to complex seismic signals, and providing a more reliable time-frequency analysis foundation for subsequent seismic interpretation. Summary of the Invention

[0003] The purpose of this invention is to overcome the problem of manually changing parameters in existing technologies, and to propose a sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization. This method outperforms traditional fixed-parameter methods in terms of adaptability, robustness, and time-frequency analysis performance. This invention includes the following steps:

[0004] 1. A sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization, characterized by the following specific steps:

[0005] S1. Input signal y, optimize the window parameters λ and p of the generalized S-transform using the parameter adaptive method. The specific formula of the generalized S-transform is as follows:

[0006]

[0007] In the formula, τ represents the time shift parameter; f represents the frequency variable; λ represents the window width scaling factor; p represents the frequency dependence exponent; and GST is the generalized S-transform result corresponding to the signal y.

[0008] S2. Initialize each parameter within a defined range, with λ and p both having values ​​greater than 0; after initialization, calculate the inertia weight for the current iteration and map the current position of each particle to a set of parameters to be optimized for subsequent time-frequency spectrum calculation and fitness evaluation.

[0009] S3. Evaluate the fitness of the parameter combinations λ and p obtained after each optimization. The specific steps are as follows:

[0010] S31. Perform a sparse generalized S-transform on the signal y using the current corresponding parameters λ and p, thereby obtaining the time-frequency spectrum TFR and y under this set of parameters. rec The specific formula for reconstructing the signal is as follows:

[0011]

[0012] In the formula, y rec Represents a reconstructed signal; The symbol represents the summation symbol; N represents the time sampling point; i represents the index of the current sampling point; j represents the summation variable, iterating through all sampling points that may be connected to sampling point i; W ij This represents the element in the i-th row and j-th column of the known weight matrix W; u ij This represents the element in the i-th row and j-th column of the variable matrix u to be optimized;

[0013] S32. Define the TFR normalized time-frequency energy distribution P, and calculate the Rényi entropy. The original Rényi entropy is a quantity that is better the smaller it is, but the update logic of adaptive optimization is that the score is better the larger it is. Therefore, a new transformation is made here to make it a "better the larger it is" form. The specific formula is as follows:

[0014]

[0015]

[0016] In the formula, α represents the order of Rényi entropy, usually taken as α=3, which is the third-order Rényi entropy; Represents the normalized energy value P n Raise α to the power of α; n represents the index of the event or state, summing over all possible events; Represents the logarithmic term to the base 2; E represents the score of time-frequency energy concentration, denoted as H. α The reciprocal of (P); ε represents a local constant, usually taken as 10. −8 Or 10 −10 To prevent the denominator from being 0 when the error is 0;

[0017] S33. Subsequently, the obtained time spectrum is reconstructed, and the specific formula for the reconstruction quality score is as follows:

[0018]

[0019] In the formula, R represents the reconstruction quality score; Represents the L2 norm; This represents the magnitude of the difference between the two; This represents the energy level of the signal y(t);

[0020] S34. Use the fitness function to evaluate the fitness of the parameter combinations λ and p after each iteration of steps S1-S2. The iteration ends when the maximum number of iterations is reached. The parameter combination with the highest final score is the optimal parameter obtained in this stage. The specific formula of the fitness function is as follows:

[0021]

[0022] In the formula, score1 represents the overall score; 0.85 and 0.15 represent weighting coefficients;

[0023] S4. Based on the optimization in step S3, further optimize the core parameters γ, μ, and ε of the sparse generalized S-transform. The optimization process of these three parameters is roughly the same as that of the above parameters λ and p. After initializing the three parameters, repeat the above steps S31-S33. The specific formulas for γ, μ, and ε acting on the sparse generalized S-transform are as follows:

[0024] , res < ε

[0025]

[0026] In the formula, γ represents the weight of the L2 regularization term, which controls the smoothness and complexity of the solution; ε represents the residual convergence threshold; μ represents the weight of the data fidelity term, which controls the degree of model fit to the observed data; ω represents the sparsity constraint parameter; res represents the reconstruction residual energy of the current iteration; y i This represents the known measurement value of the i-th sampling point; This represents taking the absolute value;

[0027] S5. The fitness function score2 is used to evaluate the fitness of the parameter combinations γ, μ, and ε after each iteration. The iteration ends when the maximum number of iterations is reached. The parameter combination with the highest final score is the optimal parameter obtained in this stage. The time-frequency energy clustering score E and the reconstruction quality score R are the same as those used when optimizing parameters λ and p. The specific formulas are as follows:

[0028]

[0029]

[0030] In the formula, T represents the efficiency or speed score; Ct represents the actual running time for the algorithm to complete one task.

[0031] S6. Substitute the five optimized parameters from steps S1-S5 into the sparse generalized S-transform formula to obtain the optimal time spectrum of the original signal.

[0032] The sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization of the present invention has the following advantages:

[0033] (1) It can automatically search for better parameter combinations based on the characteristics of the input signal, thereby reducing the subjectivity of manual parameter tuning and improving the objectivity and stability of parameter selection;

[0034] (2) The time-frequency energy concentration, signal reconstruction accuracy and solution stability can be uniformly incorporated into the optimization process, ensuring the time-frequency spectrum focusing capability while taking into account the signal fidelity;

[0035] (3) For complex non-stationary signals such as seismic signals, this method can better match local time-frequency characteristics and improve the ability to identify weak anomalies and local frequency components. Attached Figure Description

[0036] To more clearly illustrate the technical solutions and embodiments of the present invention, the accompanying drawings used in the technical description and embodiments are briefly introduced below. The drawings are provided to further understand the embodiments of the present invention and constitute a part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention.

[0037] Figure 1 This is a flowchart of the processing of the sparse generalized S-transform time-frequency analysis method with parameter adaptive optimization;

[0038] Figure 2 This is a schematic diagram showing the time-frequency analysis of the synthesized FM signal using this method;

[0039] Figure 3 This is a schematic diagram of the time-frequency analysis of a single seismic signal using this method. Detailed Implementation

[0040] To more clearly illustrate the technical advantages of this invention, synthetic signals and seismic signals are used as examples, and the embodiments of this invention are further described in detail with reference to the accompanying drawings. The specific implementation methods of this invention are as follows:

[0041] S1. Input signal y, optimize the window parameters λ and p of the generalized S-transform using the parameter adaptive method;

[0042] S2. Initialize each parameter within a defined range, with λ and p both having values ​​greater than 0; after initialization, calculate the inertia weight for the current iteration and map the current position of each particle to a set of parameters to be optimized for subsequent time-frequency spectrum calculation and fitness evaluation.

[0043] S3. Evaluate the fitness of the parameter combinations λ and p obtained after each optimization;

[0044] S4. Perform a sparse generalized S-transform on the signal y using the current corresponding parameters λ and p, thereby obtaining the time-frequency spectrum (TFR) and y under this set of parameters. rec ;

[0045] S5. Define the TFR normalized time-frequency energy distribution P, and calculate the Rényi entropy. The original Rényi entropy is a quantity that is better the smaller it is, but the update logic of adaptive optimization is that the score is better the larger it is. Therefore, a new transformation is made here to make it into the form of "better the larger it is".

[0046] S6. Then, the obtained time spectrum is reconstructed.

[0047] S7. Use the fitness function to evaluate the fitness of the parameter combinations λ and p after each iteration of steps S1-S2. When the maximum number of iterations is reached, the iteration ends. The parameter combination with the highest score is the optimal parameter obtained in this stage.

[0048] S8. Based on the optimization in step S3, further optimize the core parameters γ, μ, and ε of the sparse generalized S-transform. The optimization of these three parameters is roughly the same as the optimization process of the above parameters λ and p. After initializing the three parameters, repeat the above steps S31-S33.

[0049] S9. Use the fitness function score2 to evaluate the fitness of the parameter combinations γ, μ and ε after each iteration. When the maximum number of iterations is reached, the iteration ends. The parameter combination with the highest final score is the optimal parameter obtained in this stage. The time-frequency energy clustering score E and the reconstruction quality score R are the same as the formulas used when optimizing parameters λ and p.

[0050] S10. Substitute the five optimized parameters from steps S1-S5 into the sparse generalized S-transform formula to obtain the optimal time spectrum of the original signal.

[0051] Implementation examples of the present invention:

[0052] Figure 1 This is a flowchart of the processing of the sparse generalized S-transform time-frequency analysis method with parameter adaptive optimization;

[0053] Figure 2The results of time-frequency analysis of the synthesized frequency-modulated signal using this method are shown in Figure (a), which consists of two Chirp signals with frequency ranges of 0~150Hz and 10~200Hz, respectively. Figure (b) shows the time spectrum of the sparse generalized S-transform after parameter optimization. As can be seen from the figure, the focusing and energy focusing properties are high, and the boundary effects that occur at low frequencies are not present.

[0054] Figure 3 The results of time-frequency analysis of a single seismic signal using this method are shown in Figure (a). Figure (a) shows the input one-dimensional seismic signal, which can be seen to correspond to different amplitudes at different times. Figure (b) shows the time spectrum of the sparse generalized S-transform after parameter optimization. As can be seen from the figure, the parameters obtained by the particle swarm optimization algorithm can achieve a good balance between energy concentration, sparsity and signal characterization ability in the time spectrum of the sparse generalized S-transform.

[0055] The above embodiments are only used to illustrate the present invention. The implementation steps of the method can be varied. Any equivalent transformations and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A sparse generalized S-transform time-frequency analysis method with adaptive parameter optimization, characterized in that... The following specific steps are adopted: S1. Input signal y, optimize the window parameters λ and p of the generalized S-transform using the parameter adaptive method. The specific formula of the generalized S-transform is as follows: ； In the formula, τ represents the time shift parameter; f represents the frequency variable; λ represents the window width scaling factor; p represents the frequency dependence exponent; and GST is the generalized S-transform result corresponding to the signal y. S2. Initialize each parameter within a defined range, with λ and p both having values ​​greater than 0; after initialization, calculate the inertia weight for the current iteration and map the current position of each particle to a set of parameters to be optimized for subsequent time-frequency spectrum calculation and fitness evaluation; S3. Evaluate the fitness of the parameter combinations λ and p obtained after each optimization. The specific steps are as follows: S31. Perform one sparse generalized S transform on the signal y with the current corresponding parameters λ and p, thereby obtaining the time-frequency representation TFR under this set of parameters and y rec The specific formula for reconstructing the signal is as follows: ； In the formula, y rec Represents a reconstructed signal; The symbol represents the summation; N represents the time sampling point; i represents the index of the current sampling point; j represents the summation variable, which iterates through all sampling points that may be connected to sampling point i. W ij represents the element of the weight matrix W in the i-th row and j-th column; u ij represents the element of the i-th row and j-th column of the matrix u of variables to be optimized; S32. Define the TFR normalized time-frequency energy distribution P, and calculate the Rényi entropy. The original Rényi entropy is a quantity that is better the smaller it is, but the update logic of adaptive optimization is that the score is better the larger it is. Therefore, a new transformation is made here to make it a "better the larger it is" form. The specific formula is as follows: ； ； In the formula, α represents the order of Rényi entropy, usually taken as α=3, which is the third-order Rényi entropy; Represents the normalized energy value P n Raise α to the power of α; n represents the index of the event or state, summing over all possible events; Represents the logarithmic term to the base 2; E represents the score of time-frequency energy concentration, denoted as H. α The reciprocal of (P); ε represents a local constant, typically taken as 10. −8 Or 10 −10 To prevent the denominator from being 0 when the error is 0; S33. Subsequently, the obtained time spectrum is reconstructed, and the specific formula for the reconstruction quality score is as follows: ； In the formula, R represents the reconstruction quality score; Represents the L2 norm; This represents the magnitude of the difference between the two. This represents the energy level of signal y; S34. Use the fitness function to evaluate the fitness of the parameter combinations λ and p after each iteration of steps S1-S2. The iteration ends when the maximum number of iterations is reached. The parameter combination with the highest final score is the optimal parameter obtained in this stage. The specific formula of the fitness function is as follows: ； In the formula, score1 represents the overall score; 0.85 and 0.15 represent weighting coefficients; S4. Based on the optimization in step S3, further optimize the core parameters γ, μ, and ε of the sparse generalized S-transform. The optimization process of these three parameters is roughly the same as that of the above parameters λ and p. After initializing the three parameters, repeat the above steps S31-S33. The specific formulas for γ, μ, and ε acting on the sparse generalized S-transform are as follows: ,res<e; ； In the formula, γ represents the weight of the L2 regularization term, which controls the smoothness and complexity of the solution; ε represents the residual convergence threshold; and μ represents the weight of the data fidelity term, which controls the degree of fit of the model to the observed data. ω represents the sparse constraint parameter; res represents the reconstruction residual energy of the current iteration; y i This represents the known measurement value of the i-th sampling point; This represents taking the absolute value; S5. The fitness function score2 is used to evaluate the fitness of the parameter combinations γ, μ, and ε after each iteration. The iteration ends when the maximum number of iterations is reached. The parameter combination with the highest final score is the optimal parameter obtained in this stage. The time-frequency energy clustering score E and the reconstruction quality score R are the same as those used when optimizing parameters λ and p. The specific formulas are as follows: ； ； In the formula, T represents the efficiency or speed score; Ct represents the actual running time for the algorithm to complete one task. S6. Substitute the five optimized parameters from steps S1-S5 into the sparse generalized S-transform formula to obtain the optimal time spectrum of the original signal.

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