Air gun array configuration optimization method and system based on deep fusion of SHAP explanatory guidance and particle swarm optimization

Abstract

The invention belongs to the technical field of intelligent optimization of ocean geophysical exploration equipment, and discloses an air gun array configuration optimization method and system based on SHAP explanatory guidance and particle swarm optimization deep fusion, and the system is composed of a physical simulation module, a performance evaluation module, an SHAP online engine module, a dynamic grouping optimization module and a control output module. Experiments show that in 20 iterations, the initial bubble is improved by 73.3% compared with the original configuration and improved by 15.4% compared with PSO, the coefficient of variation is as low as 0.10 (the robustness is optimal), performance breakthrough is synchronously achieved, an interpretability chart is output, and decision basis for'optimal 'and'how fine adjustment' is provided for engineers. The method is suitable for off-line high-precision array design, and an efficient and reliable technical scheme is provided for air gun array optimization. The method has been successfully applied to a certain oilfield exploration project in the Bohai Sea, effectively improves the seismic data quality, and has significant industrial application value.

Description

Technical Field

[0001] This invention belongs to the field of intelligent optimization technology for marine geophysical exploration equipment, and particularly relates to a method and system for optimizing the configuration of air gun arrays based on the deep fusion of SHAP interpretive guidance and particle swarm optimization. Background Technology

[0002] In marine seismic exploration, air gun arrays are key equipment for generating seismic waves, and their performance directly affects the quality of acquired data. The depth configuration of the array is a core parameter affecting far-field wave characteristics (such as initial bubble ratio and spectral characteristics). Traditional air gun array optimization methods mostly rely on trial and error, which suffers from low efficiency and difficulty in obtaining a globally optimal solution. Although particle swarm optimization (PSO) algorithms have been introduced to improve this problem, they still have significant limitations: relying solely on random search and swarm iteration lacks an understanding of the "parameter-performance impact mechanism," making it prone to getting trapped in local optima; and the converged optimization results lack physical interpretability—engineers cannot clearly define the specific role of adjusting the depth of a particular air gun, limiting its widespread adoption in actual production.

[0003] SHAP (SHapley Additive exPlanations), as an interpretable AI tool, is mostly used for post-hoc interpretation of trained models. That is, it is used as an independent analysis tool. Its combination with the optimization process is usually just a simple chain (such as post-optimization analysis). It fails to achieve deep interaction and collaboration with the optimization algorithm, does not guide the optimization process in real time, and cannot play its core value of "revealing the parameter-target mapping relationship", resulting in optimization and interpretation being in a "two-tiered" state.

[0004] Therefore, how to deeply embed interpretable artificial intelligence (XAI) technology into optimization algorithms to achieve an air gun array optimization technology that is "interpretable in optimization process, collaboratively optimized by multiple indicators, and balanced in performance and efficiency" has become an urgent technical challenge to be solved.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] When SHAP is used as a standalone analysis tool, its integration with the optimization process is usually just a simple chain reaction (such as post-optimization analysis). It fails to achieve deep interaction and collaboration with the optimization algorithm, does not guide the optimization process in real time, and cannot play its core value of "revealing the parameter-target mapping relationship", resulting in optimization and interpretation being in a "two-tiered" state. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method and system for optimizing the configuration of air gun arrays based on the deep fusion of SHAP interpretive guidance and particle swarm optimization.

[0008] This invention is implemented as follows: a method for optimizing the configuration of an air gun array based on the deep fusion of SHAP interpretive guidance and particle swarm optimization includes:

[0009] Step 1, Initialization and Simulation: Initialize the particle swarm, with each particle representing a gas gun depth configuration scheme; simulate the far-field pressure wavelet of the gas gun array corresponding to each particle based on the physical mechanism model;

[0010] Step 2, multi-objective fitness assessment;

[0011] Step 3: SHAP value calculated online;

[0012] Step 4, Parameter Interaction Matrix Construction and Dynamic Grouping: Based on the SHAP values ​​of all particles in each dimension, calculate the interaction matrix between parameters. This matrix reveals the coupling relationship between different air gun depth parameters. The community detection algorithm (Louvain algorithm) is used to dynamically group the particles according to this interaction matrix, and particles with strong parameter interactions are grouped into the same group.

[0013] Step 5, SHAP gradient-guided particle update: In the standard PSO velocity update formula, a SHAP gradient term is introduced; particles not only learn from the individual historical best and the global historical best, but also explore along the direction of the fastest performance improvement indicated by the SHAP value (i.e., the gradient direction); after being grouped, particles perform social learning (learning from the group's best) within their respective groups, thereby achieving more refined collaborative exploration.

[0014] Step 6, Iteration and Termination: Repeat steps 2-5 until the termination condition is met (such as reaching the maximum number of iterations), and output the globally optimal depth configuration.

[0015] Furthermore, the formula for calculating the far-field pressure wavelet of the air gun array is as follows:

[0016]

[0017] in, This represents the synthesized pressure wavelet at time t at the far-field receiving point of the air gun array; Summation symbol, from the first air gun ( Up to the Kth air gun (Accumulate, K represents the total number of air guns in the air gun array;) This indicates that the k-th air gun is located at the far-field receiving point. The single-gun pressure wavelet at a given moment; t represents the time variable (starting from the moment the air gun is fired). This represents the time delay of the pressure wave from the k-th air gun propagating to the far-field receiving point. The phase correction factor (complex form) for the k-th air gun is represented by j, which represents the imaginary unit. The conversion factor between angular frequency and frequency. The fundamental frequency (core vibration frequency) representing the pulsation of the air gun bubbles. Let represent the spatial phase difference between the k-th air gun and the reference air gun (usually the 1st one), and let c represent the speed of sound in seawater.

[0018] Furthermore, the multi-target fitness assessment involves constructing a comprehensive evaluation function to calculate the fitness value of each particle. This function comprehensively considers multiple key geophysical indicators such as initial bubble ratio, spectral flatness within the target frequency band, and energy percentage.

[0019] Furthermore, the SHAP value is calculated online: During the PSO iteration process, the SHAP value of each particle in each dimension (i.e., each air gun depth) is calculated in real time using a direct SHAP value calculation method based on weighted nearest neighbors and numerical differentiation, based on the historical evaluation data (position and fitness) of the current particle swarm periodically (e.g., every 5 generations). This value quantifies the marginal contribution of a single air gun depth change to the overall performance.

[0020] Furthermore, the formula for the parameter interaction matrix (covariance matrix) is as follows:

[0021]

[0022] in: This represents the sequence of SHAP values ​​for the j-th parameter, specifically the set of SHAP values ​​for all particles (airgun array depth configuration scheme) on the j-th parameter (e.g., the depth of the j-th airgun). ,in It is the SHAP value of the j-th parameter of the i-th particle, and N is the total number of particles; The average SHAP value of the j-th parameter; Represents the sequence of SHAP values ​​for the k-th parameter; It is the SHAP value of the k-th parameter of the i-th particle; The average SHAP value of the k-th parameter;

[0023] The quality of community partitioning is measured by "modularity," and the Louvain algorithm achieves optimal partitioning by maximizing modularity.

[0024]

[0025] Where: Q is the modularity (an indicator of the quality of community partitioning), with a value range of [-1, 1], the larger the value, the better the community partitioning; i, j represent nodes i and j; Let be the edge weights between nodes i and j; This represents the total network weight. The normalization coefficients eliminate the influence of network size on modularity, ensuring that parameter interaction networks of different sizes can be compared horizontally. This is a double summation symbol (traversing all node pairs in the network); Let i be the degree of node i; Let j be the degree of node j; For indicator functions ( = (1 if it is 1, 0 otherwise), where and These represent the community affiliation labels of nodes i and j, respectively.

[0026] Particle-dominated community weight The calculation formula, that is, the weight of the i-th particle belonging to community c, is the sum of the absolute values ​​of the SHAP values ​​of all parameters within that community:

[0027]

[0028] Where: i represents the i-th particle, j represents the j-th parameter; c represents the community c; For community c, there is a set of parameter indexes. This indicates that the community c contains all parameters j; This represents the SHAP value of the j-th parameter of the i-th particle. The absolute value; The larger the value of c, the more significant the contribution of the parameters of community c to the performance of particle i; the particle will eventually be classified into... The largest community.

[0029] Furthermore, the SHAP gradient-guided particle update:

[0030] The SHAP gradient field is calculated using "local neighbor particles + linear regression," which is essentially a local trend fitting based on statistical regularities, rather than simple numerical differentiation. For the j-th parameter dimension of the i-th particle, assuming that n neighboring particles are selected, their parameter values ​​are... The corresponding target value is Then the SHAP gradient value of the i-th particle in the j-th dimension can be calculated by linear regression:

[0031]

[0032] SHAP gradient-guided speed updates:

[0033]

[0034] in, This represents the velocity of the i-th particle after the update of the d-th parameter (air gun depth) in the (t+1)-th iteration; This represents the adaptive inertia weight for the t-th iteration; This represents the current velocity of the i-th particle at the d-th parameter in the t-th iteration; Represents individual learning factors. This represents the social learning factor within the group. This represents the SHAP gradient learning factor; , , All are independent random numbers within the interval [0,1]. This represents the value of the d-th parameter for the "optimal individual position" of the i-th particle in the t-th iteration. This represents the current position of the i-th particle at the d-th parameter in the t-th iteration; This represents the value of the d-th parameter for the "best position of the group" to which the i-th particle belongs in the t-th iteration. Let represent the SHAP gradient of the i-th particle at the d-th parameter in t iterations.

[0035] Another objective of this invention is to provide a gas gun array configuration optimization system based on the deep fusion of SHAP interpretive guidance and particle swarm optimization, comprising:

[0036] The physics simulation module is used to simulate the far-field wavelet of an air gun array at a given depth configuration;

[0037] The performance evaluation module is used to calculate indicators such as the initial bubble ratio, spectral flatness, and overall fitness of the wavelet;

[0038] The SHAP online analysis engine module is used to calculate SHAP values ​​and build interaction matrices in real time.

[0039] The dynamic grouping optimization module is used to perform particle grouping and SHAP gradient-guided PSO updates;

[0040] The control and output module is used to control the iterative process and output the final optimization result.

[0041] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, the computer program being executed by the processor causing the processor to perform the steps of the air gun array configuration optimization method based on SHAP interpretive guidance and particle swarm optimization deep fusion.

[0042] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the air gun array configuration optimization method based on SHAP interpretive guidance and particle swarm optimization deep fusion.

[0043] Another objective of this invention is to provide an information data processing terminal for implementing the air gun array configuration optimization system based on the deep fusion of SHAP interpretive guidance and particle swarm optimization.

[0044] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0045] To address the disconnect between existing technologies where SHAP is merely used as a post-optimization interpretation tool and the PSO optimization process, resulting in a "two-tiered" architecture, this invention proposes a deeply integrated architecture of "real-time SHAP computation - interactive analysis - dynamic grouping - gradient guidance." This architecture embeds an interpretability analysis engine (SHAP real-time analysis engine module) into the core loop of the optimization iteration, enabling simultaneous performance evaluation and parameter contribution analysis in each iteration. Experimental verification demonstrates that this architecture successfully transforms SHAP from a static "interpreter" into a dynamic "guide," fundamentally solving the "black box optimization" problem. This ensures that the optimization direction is physically interpretable from the outset, resolving the long-standing pain points of traditional PSO's blind search and engineers' inability to understand parameter adjustment logic. Figure 5 The SHAP feature importance diagram provided by the embodiments of the present invention is shown, which can clearly show the degree of influence of each air gun depth on the initial bubble ratio, providing engineers with a direct basis for fine-tuning, and solving the problem of the traditional optimization results "knowing what but not why".

[0046] To address the inefficiencies of traditional trial-and-error methods and the lag in the sequential optimization-interpretation process, this invention deeply integrates SHAP interpretability AI technology into and dominates the entire Particle Swarm Optimization (PSO) process through "online computation, dynamic interaction, and gradient guidance." Table 2 shows that the method of this invention (guided fusion SHAP-PSO) and PSO, as well as the simple sequential SHAP-PSO method, consistently achieves the highest initial bubble ratio regardless of the number of iterations (5, 20, or 50). The guided fusion SHAP-PSO achieves an initial bubble ratio of 17.82 after 5 iterations, reaches 19.22 after 20 iterations, and remains unchanged after 50 iterations, indicating convergence after 20 iterations. This achieves the optimal balance between performance and convergence efficiency in offline design scenarios requiring high precision. Table 4 shows similar trends under other seeds. Tables 3 and... Figure 6-8 The method of this invention exhibits optimal spectral flatness and effective bandwidth.

[0047] To overcome the shortcomings of standard PSO, such as being prone to getting trapped in local optima and lacking directional guidance, this invention incorporates two core methodological innovations. First, the SHAP gradient is directly embedded as a guiding term into the PSO velocity update formula. This ensures that the particle's search direction not only relies on historical best practices (individual best pbest and group best gbest) but also integrates the "fastest performance improvement direction" based on current local sample statistics, thus giving the algorithm the intelligence to escape local optima and explore more promising regions. Second, based on the SHAP interaction matrix, the Louvain community discovery algorithm is used to dynamically group particles. This strategy automatically identifies and aggregates subsets (communities) with strong interactions between parameters, allowing particles within a group to focus more on the collaborative optimization of internal parameters during social learning, achieving a shift from "global coarse learning" to "local fine collaboration." Table 4 shows that the guided SHAP-PSO has the lowest coefficient of variation (0.10), fully demonstrating that this method significantly improves the algorithm's robustness and search stability under different initial conditions.

[0048] Practical application examples further demonstrate that the technical solution of this invention has achieved a breakthrough in optimizing performance indicators. In terms of performance, as shown in Table 5, in a practical application in an oilfield in the Bohai Sea, the method of this invention optimized the initial bubble ratio of the air gun array from 24.39 to 30.19, and the spectral flatness also improved from 0.886 to 0.895, directly improving the quality of seismic exploration data. This indicates that the method of this patent has transformed from "theoretically optimal" to "engineerably usable," providing a technical paradigm for marine seismic exploration that combines scientific rigor and practicality.

[0049] This invention achieves the simultaneous output of "high-precision optimization" and "high-transparency interpretation" in the field of intelligent optimization of marine geophysical exploration equipment, and has both important theoretical innovation and direct industrial application value.

[0050] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0051] The technical solution of this invention can be directly transformed into a core optimization module in marine seismic exploration equipment design software, or integrated into an intelligent air gun array design system. Its expected benefits include: ① Improved exploration efficiency: By optimizing the air gun array configuration, the quality of seismic wavelets (such as initial bubble ratio and spectral characteristics) is significantly improved, thereby increasing the accuracy of subsurface structure imaging and reducing oil and gas exploration risks and well drying rates. ② Reduced design costs: The traditional trial-and-error process relying on expert experience is transformed into an efficient and automated intelligent design process, significantly shortening the array design cycle and saving manpower and time costs. ③ Formation of technological barriers and new products: Professional design software with independent intellectual property rights can be developed or high-end technical services can be provided, forming a differentiated competitive advantage in the marine exploration software market and creating new business growth points. Its application in large-scale offshore oil and gas field exploration projects or equipment manufacturing enterprises has considerable economic benefits and market prospects.

[0052] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0053] Currently, both domestically and internationally, the field of air gun array optimization generally adopts traditional trial-and-error and standard optimization algorithms (such as PSO). There is a lack of research or patent publications that deeply embed and dominate the entire Particle Swarm Optimization (PSO) optimization process using "online computation, dynamic interaction, and gradient guidance," and perform dynamic community grouping based on parameter interaction. This invention achieves a deep integration and closed-loop application of interpretable AI and intelligent optimization algorithms in air gun array configuration problems, filling the technological gap in this field regarding "real-time interpretable guided intelligent optimization."

[0054] (3) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0055] The field of marine seismic exploration has long faced the following core technical challenges: First, traditional trial-and-error methods and simple PSO algorithms are prone to getting stuck in local optima, making it difficult to obtain the globally optimal air gun array configuration; second, the optimization results lack physical interpretability, making it difficult for engineers to clearly understand the specific effects of parameter adjustments, thus limiting the implementation of the technology; third, the coupling relationship between parameters during the optimization process is difficult to quantify, resulting in low efficiency in collaborative optimization. These challenges have long constrained breakthroughs in the performance and intelligent development of air gun arrays, and the industry has been eager to find a solution that balances "optimization efficiency, global optimality, and physical interpretability." This invention, through a particle update mechanism guided by SHAP gradients and a dynamic grouping strategy based on the SHAP interaction matrix, not only solves the local optimum problem (with a coefficient of variation as low as 0.10 and optimal robustness), but also reveals the parameter-performance mapping relationship and the coupling mechanism between parameters through SHAP values ​​and the interaction matrix, giving the optimization results clear physical meaning and successfully overcoming this long-standing technical bottleneck.

[0056] (4) Does the technical solution of the present invention overcome technical bias?

[0057] This invention overcomes two technical biases. First, it overcomes the bias that "interpretability inevitably leads to high computational overhead and compromises optimization efficiency." This invention, through the design of an efficient online SHAP approximation calculation method and a reasonable triggering cycle (e.g., every 5 generations), keeps the interpretation cost within an acceptable range. Experiments show (Table 3) that although the time per iteration increases, the algorithm achieves better performance with fewer iterations. In offline design scenarios, the overall "performance-time-benefit" efficiency is significantly improved. Second, it overcomes the traditional sequential mindset that "optimization algorithms and interpretability analysis should be performed independently." This invention demonstrates that deeply integrating the two and achieving real-time interactive guidance not only preserves their respective advantages but also generates a synergistic effect of "1+1>2," resulting in better, more stable, and more understandable optimization results, providing a new paradigm for complex system optimization. Attached Figure Description

[0058] Figure 1 This is a flowchart of the air gun array configuration optimization method based on the deep fusion of SHAP interpretive guidance and particle swarm optimization provided in the embodiments of the present invention.

[0059] Figure 2 This is a block diagram of the air gun array configuration optimization system based on the deep fusion of SHAP interpretive guidance and particle swarm optimization, provided in an embodiment of the present invention.

[0060] Figure 3 This is an overall architecture diagram of the system provided in the embodiments of the present invention.

[0061] Figure 4 This is a flowchart of the guided fusion SHAP-PSO optimization provided in an embodiment of the present invention.

[0062] Figure 5 This is a SHAP feature importance diagram provided in the embodiments of the present invention, showing the degree of influence of each air gun depth on the initial bubble ratio.

[0063] Figure 6 This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 5 iterations, including far-field pressure wavelet, spectral flatness, and convergence.

[0064] Figure 7 This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 20 iterations, including far-field pressure wavelet, spectral flatness, and convergence.

[0065] Figure 8This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 50 iterations, including far-field pressure wavelet, spectral flatness, and convergence. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0067] like Figure 1 As shown, the air gun array configuration optimization method based on the deep fusion of SHAP interpretive guidance and particle swarm optimization provided by this embodiment of the invention includes the following steps:

[0068] S101, Initialization and Simulation: Initialize the particle swarm, with each particle representing a gas gun depth configuration scheme; simulate the far-field pressure wavelet of the gas gun array corresponding to each particle based on the physical mechanism model;

[0069] S102, Multi-objective fitness assessment;

[0070] S103, SHAP value online calculation;

[0071] S104, Parameter Interaction Matrix Construction and Dynamic Grouping:

[0072] Based on the SHAP values ​​of all particles in each dimension, the interaction matrix between parameters is calculated, which reveals the coupling relationship between different air gun depth parameters. The community detection algorithm (Louvain algorithm) is used to dynamically group the particles according to the interaction matrix, and particles with strong parameter interactions are grouped together.

[0073] S105, SHAP gradient-guided particle update:

[0074] In the standard PSO velocity update formula, a SHAP gradient term is introduced; particles not only learn from their individual historical best and global historical best, but also explore along the direction of fastest performance improvement indicated by the SHAP value (i.e., the gradient direction); after being grouped, particles perform social learning (learning from the group's best) within their respective groups, thereby achieving more refined collaborative exploration;

[0075] S106, Iteration and Termination: Repeat S102-S105 until the termination condition is met (such as reaching the maximum number of iterations), and output the globally optimal depth configuration.

[0076] The formula for calculating the far-field pressure wavelet of the air gun array provided in this embodiment of the invention is as follows:

[0077]

[0078] in, This represents the synthesized pressure wavelet at time t at the far-field receiving point of the air gun array; Summation symbol, from the first air gun ( Up to the Kth air gun The numbers are accumulated, where K represents the total number of air guns in the air gun array, and k represents the air gun number index (from 1 to K). This indicates that the k-th air gun is located at the far-field receiving point. The single-gun pressure wavelet at a given moment; t represents the time variable (starting from the moment the air gun is fired). This represents the time delay of the pressure wave from the k-th air gun propagating to the far-field receiving point. Let j represent the phase correction factor (complex form) of the k-th air gun, and j be the imaginary unit commonly used in engineering (equivalent to i in mathematics), satisfying j² = -1. , The fundamental frequency (core vibration frequency) representing the pulsation of the air gun bubbles. Let represent the spatial phase difference between the k-th air gun and the reference air gun (usually the 1st), and let c represent the speed of sound in seawater. The symbol ' / ' represents the mathematical multiplication operator, and ' / ' represents the mathematical division operator.

[0079] The multi-target fitness assessment provided in this embodiment of the invention involves constructing a comprehensive evaluation function to calculate the fitness value of each particle. This function comprehensively considers multiple key geophysical indicators such as initial bubble ratio, spectral flatness within the target frequency band, and energy proportion.

[0080] The online SHAP value calculation provided in this embodiment of the invention is as follows: During the PSO iteration process, the SHAP value of each particle in each dimension (i.e., each air gun depth) is calculated in real time based on the historical evaluation data (position and fitness) of the current particle swarm at regular intervals (e.g., every 5 generations) using a direct SHAP value calculation method based on weighted nearest neighbors and numerical differentiation. This value quantifies the marginal contribution of a single air gun depth change to the overall performance.

[0081] The formula for the parameter interaction matrix (covariance matrix) provided in this embodiment of the invention is as follows:

[0082]

[0083] in: This represents the sequence of SHAP values ​​for the j-th parameter, specifically the set of SHAP values ​​for all particles (airgun array depth configuration scheme) on the j-th parameter (e.g., the depth of the j-th airgun). ,in It is the SHAP value of the j-th parameter of the i-th particle, and N is the total number of particles; The average SHAP value of the j-th parameter; Represents the sequence of SHAP values ​​for the k-th parameter; It is the SHAP value of the k-th parameter of the i-th particle; The average SHAP value of the k-th parameter;

[0084] The quality of community partitioning is measured by "modularity," and the Louvain algorithm achieves optimal partitioning by maximizing modularity.

[0085]

[0086] Where: Q is the modularity (an indicator of the quality of community partitioning), with a value range of [-1, 1], the larger the value, the better the community partitioning; i, j represent nodes i and j; Let be the edge weights between nodes i and j; This represents the total network weight. The normalization coefficients eliminate the influence of network size on modularity, ensuring that parameter interaction networks of different sizes can be compared horizontally. This is a double summation symbol (traversing all node pairs in the network); Let i be the degree of node i; Let j be the degree of node j; For indicator functions ( = (1 if it is 1, 0 otherwise), where and These represent the community affiliation labels of nodes i and j, respectively.

[0087] Particle-dominated community weight The calculation formula, that is, the weight of the i-th particle belonging to community c, is the sum of the absolute values ​​of the SHAP values ​​of all parameters within that community:

[0088]

[0089] Where: i represents the i-th particle, j represents the j-th parameter; c represents the community c; For community c, there is a set of parameter indexes. This indicates that the community c contains all parameters j; This represents the SHAP value of the j-th parameter of the i-th particle. The absolute value; The larger the value of c, the more significant the contribution of the parameters of community c to the performance of particle i; the particle will eventually be classified into... The largest community.

[0090] The SHAP gradient-guided particle update provided in this embodiment of the invention:

[0091] The SHAP gradient field is calculated using "local neighbor particles + linear regression," which is essentially a local trend fitting based on statistical regularities, rather than simple numerical differentiation. For the j-th parameter dimension of the i-th particle, assuming that n neighboring particles are selected, their parameter values ​​are... This represents the value of the k-th neighboring particle selected at the j-th parameter (air gun depth), corresponding to the target value. Then the SHAP gradient value of the i-th particle in the j-th dimension can be calculated by linear regression:

[0092]

[0093] SHAP gradient-guided speed updates:

[0094]

[0095] in, This represents the velocity of the i-th particle after the update of the d-th parameter (air gun depth) in the (t+1)-th iteration; This represents the adaptive inertia weight for the t-th iteration; This represents the current velocity of the i-th particle at the d-th parameter in the t-th iteration; Represents individual learning factors. This represents the social learning factor within the group. This represents the SHAP gradient learning factor; , , All are independent random numbers within the interval [0,1]. This represents the value of the d-th parameter for the "optimal individual position" of the i-th particle in the t-th iteration. This represents the current position of the i-th particle at the d-th parameter in the t-th iteration; This represents the value of the d-th parameter for the "best position of the group" to which the i-th particle belongs in the t-th iteration. Let represent the SHAP gradient of the i-th particle at the d-th parameter in t iterations.

[0096] like Figure 2 As shown, an embodiment of the present invention provides a gas gun array configuration optimization system based on deep fusion of SHAP interpretive guidance and particle swarm optimization, comprising:

[0097] The physics simulation module is used to simulate the far-field wavelet of an air gun array at a given depth configuration;

[0098] The performance evaluation module is used to calculate indicators such as the initial bubble ratio, spectral flatness, and overall fitness of the wavelet;

[0099] The SHAP online analysis engine module is used to calculate SHAP values ​​and build interaction matrices in real time.

[0100] The dynamic grouping optimization module is used to perform particle grouping and SHAP gradient-guided PSO updates;

[0101] The control and output module is used to control the iterative process and output the final optimization result.

[0102] The air gun array configuration optimization system based on the deep fusion of SHAP interpretive guidance and particle swarm optimization described in this embodiment of the invention takes the deep configuration parameters of the air gun array as the optimization object, and achieves automatic search and optimization of air gun array configuration schemes through the synergistic effect of physical simulation, performance evaluation, interpretive analysis and intelligent optimization.

[0103] The system first receives the air gun array depth configuration parameters corresponding to each particle in the current particle swarm from the physics simulation module, and performs numerical simulation of the far-field wavelet of the air gun array under the corresponding configuration conditions based on the acoustic propagation model to obtain the time-domain wavelet signal. This module then transmits the wavelet signal to the performance evaluation module for further extraction of wavelet features and performance evaluation.

[0104] The performance evaluation module performs signal processing and spectral analysis on the far-field wavelet signal, calculates performance indicators such as the initial bubble ratio and spectral flatness of the wavelet, and constructs a comprehensive fitness function based on a preset weighting relationship. This function maps multiple performance indicators to a single optimization target value, which is used to measure the merits of the current air gun array configuration. The comprehensive fitness function serves as optimization feedback input to the subsequent optimization module and interpretive analysis module.

[0105] The SHAP online analysis engine module takes historical particle search data and their corresponding overall fitness as input to construct an interpretable model between configuration parameters and fitness. It then calculates the SHAP value of each configuration parameter in real time for the current iteration, quantifying the marginal contribution of parameters at different depths to the overall fitness. Furthermore, the SHAP online analysis engine module constructs an interaction matrix between parameters to characterize the cooperative or conflicting relationships between different parameters, providing a basis for subsequent dynamic grouping and search direction adjustments.

[0106] The dynamic grouping optimization module dynamically groups the dimensional parameters in the particle swarm based on the SHAP value and parameter interaction matrix, classifying parameters that contribute significantly or have close interactions into the same subgroup. During the particle swarm optimization process, a guiding term based on SHAP gradient information is introduced to directionally correct the particle velocity and position update process, causing particles to preferentially search along directions that contribute more to fitness improvement. This reduces the uncertainty caused by dimensional coupling in the search space and improves convergence efficiency and stability.

[0107] The control and output module is used to coordinate the operation of the above modules, control the particle swarm initialization, iterative update, termination criterion judgment and other processes, and output the optimal air gun array configuration result and its corresponding performance index when the termination condition is met, so as to realize the closed-loop collaborative operation from physical modeling, performance evaluation, interpretive analysis to intelligent optimization.

[0108] Through the above mechanism, this invention achieves the deep embedding of interpretability analysis results into the particle swarm optimization process, so that the optimization search not only relies on random exploration and historical experience, but can also be guided by parameter contribution information, thereby improving search efficiency and result stability while ensuring optimization effect.

[0109] Figure 3 This is an overall architecture diagram of the system provided in the embodiments of the present invention.

[0110] Figure 4 This is a flowchart of the guided fusion SHAP-PSO optimization provided in an embodiment of the present invention.

[0111] Figure 5 This is a SHAP feature importance diagram provided in the embodiments of the present invention, showing the degree of influence of each air gun depth on the initial bubble ratio.

[0112] Figure 6 This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 5 iterations, including far-field pressure wavelet, spectral flatness, and convergence.

[0113] Figure 7 This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 20 iterations, including far-field pressure wavelet, spectral flatness, and convergence.

[0114] Figure 8 This is a comparison chart showing the effects of the optimization method provided in this embodiment of the invention with other optimization algorithms after 50 iterations, including far-field pressure wavelet, spectral flatness, and convergence.

[0115] 1. Experimental Environment

[0116] Hardware: Intel(R) Xeon(R) CPU E5-2686 v4 @ 2.30GHz 2.30 GHz, 64GB RAM;

[0117] Software: Python 3.12, NumPy 1.26.4, scikit-learn 1.4.2, SciPy 1.13.1, Shap 0.48.0;

[0118] Basic parameters: 6 air gun arrays, individual gun parameters are shown in Table 1.

[0119] Table 1: Parameters of a Single Air Gun Array

[0120] air gun number Pressure (psi) Volume (in³) Initial depth (m) Coordinates (x, y, z) (m) Is it a coherent gun? 1 2000 150 6.0 (0,0,6.0) yes 2 2000 80 6.0 (2,0,6.0) yes 3 2000 115 6.0 (4,0,6.0) no 4 2000 80 6.0 (0,2,6.0) no 5 2000 55 6.0 (2,2,6.0) no 6 2000 40 6.0 (4,2,6.0) no

[0121] 2. Experimental Procedure and Results

[0122] (1) Comparison of optimization results

[0123] The method of this invention (SHAP-PSO with deep fusion) is compared with standard PSO and "tandem SHAP-PSO" (simple SHAP-PSO interpreted by SHAP after optimization), with the benchmarks unified as random seed 20 and original initial bubble ratio (11.09):

[0124] Table 2: Convergence performance comparison (random seed 20, different number of iterations)

[0125] Number of iterations Algorithm type Initial brew ratio Calculation time (s) 5 times Standard PSO 16.48 11.21 Serial SHAP-PSO 14.79 13.22 Guided integration of SHAP-PSO 17.82 11.21 20 times Standard PSO 16.65 39.56 Serial SHAP-PSO 16.37 44.78 Guided integration of SHAP-PSO 19.22 104.80 50 times Standard PSO 16.66 82.87 Serial SHAP-PSO 16.58 95.95 Guided integration of SHAP-PSO 19.22 531.30

[0126] Comparison of basic performance indicators, after 20 iterations, average values ​​of multiple random seeds (higher initial bubble ratio and spectral flatness are better):

[0127] Table 3: Comparison of basic performance indicators (average after 20 iterations and multiple random seeds)

[0128] Performance indicators Objective function type original PSO Serial SHAP-PSO Guided integration of SHAP-PSO Initial brew ratio Not based on PSD 11.09 17.56±1.98 15.96±2.15 17.97±2.40 Initial brew ratio Based on PSD 11.09 16.24±1.80 15.69±1.34 17.12±1.89 Spectral flatness Not based on PSD 0.965 0.982±0.004 0.984±0.003 0.984±0.003 Spectral flatness Based on PSD 0.907 0.959±0.012 0.960±0.011 0.964±0.012 Explainability Not based on PSD - - Explainable Explainable Explainability Based on PSD - - Explainable Explainable Calculation time (s) Not based on PSD - 35.46±2.63 39.87±2.41 107.34±8.64 Calculation time (s) Based on PSD - 37.28±1.89 41.51±2.41 114.81±9.42 Core performance advantages - Optimal efficiency Optimal balance Best overall performance

[0129] The random seed influences the initial search position of the algorithm, and its sensitivity reflects the algorithm's robustness. The performance stability under different random seeds is measured by the "coefficient of variation (standard deviation ÷ mean)" (a smaller coefficient of variation indicates greater stability).

[0130] Table 4: Comparison of algorithm stability (coefficient of variation under different random seeds)

[0131] Random Seed PSO initial brew ratio SHAP-PSO in series, initial foaming ratio Guided fusion of SHAP-PSO initial foam ratio 10 15.28 15.19 19.22 20 16.63 14.07 14.36 30 19.13 15.58 19.09 40 19.18 19.00 19.22 coefficient of variation 0.12 0.15 0.10

[0132] From Table 2 and Figure 6-8 It can be seen that the initial bubble ratio of the guided fusion SHAP-PSO is 17.82 after 5 iterations, reaches 19.22 after 20 iterations, and remains unchanged after 50 iterations, indicating that it converges after 20 iterations. A similar trend is also observed under other seeds. 20 iterations is the performance-efficiency balance point, because the improvement brought by 50 iterations is not significant but the computation time is significantly increased.

[0133] From Table 3 and Figure 6-8It is evident that the guided SHAP-PSO method exhibits the best performance in core performance metrics (initial bubble ratio, spectral flatness) and interpretability. Although the computation time is longer, its overall performance advantage is significant. This demonstrates the superior ability of the method presented in this invention to effectively improve core performance. Despite the increased computation time, this process is completed in the offline design phase, and the performance gains far outweigh the time cost.

[0134] As shown in Table 4, the guided fusion SHAP-PSO has the lowest coefficient of variation (0.10), the smallest performance fluctuation under different initial conditions, and the best robustness.

[0135] Conclusion: PSO: Suitable for scenarios that "have certain performance requirements and pursue a balance between performance and efficiency," especially under some random seeds, it can approach the performance of deep fusion, and the time cost is only 1 / 3 to 1 / 2 of it; Serial SHAP-PSO: The performance is close to that of standard PSO, but the robustness is worse and the efficiency is slightly lower, with no significant advantages, and it can be eliminated; Guided fusion SHAP-PSO: Suitable for scenarios that "have extremely high performance requirements and can tolerate high computational costs" (such as offline optimization), its robustness and performance upper limit are the best, but "efficiency redundancy" must be accepted.

[0136] Practical application effect

[0137] The method of this invention was applied to an oilfield exploration project, specifically to an air gun array used in offshore seismic exploration. This array consists of 21 (3*7) air guns, with a geophone positioned 1m above each air gun. The array was submerged to a depth of 5m, with a recording sampling interval of 1.0ms, a virtual reflection coefficient of -1, and a sound velocity in seawater of 1521.6m / s. Three optimization algorithms—standard PSO, tandem SHAP-PSO, and guided fusion SHAP-PSO—were each iterated 20 times.

[0138] Table 5 Comparison with the original airgun array configuration

[0139] index original Standard PSO Serial SHAP-PSO Guided integration of SHAP-PSO Initial brew ratio 24.39 26.85 23.82 30.19 Spectral flatness 0.886 0.880 0.883 0.895

[0140] Through sea trials, it has been verified that the far-field wavelet index obtained by using the optimized parameter configuration of this invention is superior. This invention successfully solves the problem of air gun array optimization through an innovative algorithm fusion mechanism, with significant results and high industrial application value.

[0141] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0142] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing array parameter configuration based on interpretive contributions, characterized in that, Including the following control mechanisms: When performing a group search on array configuration parameters, the marginal contribution of each parameter to the performance index is introduced into the search process as an independent control variable. This makes the search direction simultaneously constrained by the historical optimal solution, the group optimal solution, and the trend of the marginal contribution change. As a result, the search process is transformed from a black-box iteration that simply depends on the objective function into an interpretable guided search process constrained by the parameter contribution mechanism.

2. The method according to claim 1, characterized in that, The marginal contribution is calculated using a nearest neighbor fitting model built based on historical samples of the current group. This model characterizes the direction and magnitude of the impact of a single parameter change on the overall performance index change.

3. The method according to claim 1, characterized in that, The performance indicators include at least the amplitude distribution characteristics of the array's far-field response and the energy distribution characteristics of the target frequency band.

4. A population search control method based on adaptive grouping of parameter interaction intensity, characterized in that, This includes the following mechanisms: A parameter interaction network is constructed by utilizing the correlation between the contribution sequences formed by each parameter during the group search process. Based on the community structure of this network, the parameters are automatically divided into several interaction subgroups, and the search individuals are constrained to only perform collaborative searches within their corresponding parameter subgroups, thereby avoiding the erroneous splitting of strongly coupled parameters that would lead to a decrease in search efficiency.

5. The method according to claim 4, characterized in that, In the parameter interaction network, nodes represent parameters, and edge weights represent the covariance strength between parameter contribution sequences.

6. The method according to claim 4, characterized in that, The division of parameter subgroups is achieved by maximizing the community modularity, so that the parameter correlation strength within a subgroup is greater than the parameter correlation strength between subgroups.

7. An optimization method based on the direct participation of interpretive gradients in population dynamics updates, characterized in that, During the group search process, the explanatory gradient term formed by the changing trend of parameter contributions is directly introduced into the state update equation of the search individual, so that the search individual not only moves towards the historical best position, but also adaptively advances along the parameter direction with the fastest performance improvement, thereby realizing active search based on mechanism direction.

8. The method according to claim 7, characterized in that, The explanatory gradient is obtained by fitting a linear trend to the relationship between parameter changes and performance changes in neighborhood samples.

9. The method according to claim 7, characterized in that, The update rate of a search individual is composed of an inertia term, an individual optimal guidance term, a group optimal guidance term, and an interpretative gradient guidance term.

10. An optimization system for implementing the method according to any one of claims 1 to 9, characterized in that, include: The parameter simulation module is used to generate the array response corresponding to a given parameter configuration; The performance evaluation module is used to calculate the overall performance indicators corresponding to the configuration; The interpretive analysis module is used to calculate the marginal contribution of each parameter to performance and its changing trend; The interactive modeling module is used to construct the parameter interaction network and complete parameter grouping; The search control module is used to perform interpretive guidance, group collaboration, and status updates; The results output module is used to output the optimal parameter configuration results.

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