An underwater high-pressure bubble initial radius physical information neural network inversion method fusing bubble dynamics equations

Abstract

The application provides an underwater high-pressure bubble initial radius physical information neural network inversion method fusing a bubble dynamics equation. The method fuses the bubble dynamics equation into a physical error function to establish a physical information neural network model, provides initial conditions for calculation according to pulsating bubble radius or low-frequency bubble load, and further improves the accurate analysis capability of the underwater high-pressure bubble experiment. The method realizes accurate calibration of the underwater high-pressure bubble initial radius according to the pulsating bubble radius or load measured by the experiment, reduces the demand for a precision measuring instrument, and can assist in numerical simulation and theoretical analysis and other ways to carry out higher-precision comparative research.

Description

Technical Field

[0001] This invention relates to the field of bubble dynamics technology, and in particular to a neural network inversion method for the physical information of the initial radius of underwater high-pressure bubbles that integrates bubble dynamics equations. Background Technology

[0002] Underwater high-pressure bubbles are a common physical phenomenon in various production and scientific research fields, including underwater detonation of explosives, high-pressure air guns for deep-sea exploration, electric spark discharge bubbles, and laser cavitation bubbles. Underwater high-pressure bubbles typically radiate high-frequency, strong impact loads to the surrounding flow field in the initial stage of their formation. Subsequently, driven primarily by the internal and external pressure difference, they undergo an expansion-contraction-re-expansion pulsation, radiating low-frequency bubble loads to the surrounding flow field during this process.

[0003] Currently, taking underwater detonation of explosives as an example, since the reaction of explosives requires the participation of an oxidizer, the degree of reaction in the oxygen-free environment of underwater will depend on the type of explosive. Furthermore, underwater detonation of explosives usually requires a waterproof membrane or rigid waterproof shell, and a series of existing studies have shown that the outer packaging of explosives also has a certain impact on the reaction process. Therefore, although the amount of explosive used in underwater detonation experiments is known, the actual reaction amount is uncertain and requires calibration. Currently, the industry mostly uses empirical formulas for shock waves to invert and calibrate the initial conditions based on the measured peak value of high-frequency, high-impact loads. However, in existing underwater high-pressure bubble testing equipment and supporting measuring instrument systems, the accurate capture and measurement of high-frequency, high-impact loads has long been difficult to achieve, placing high demands on the performance of the measuring instrument system and resulting in high costs for related supporting facilities.

[0004] In comparison, existing equipment can more easily measure low-frequency bubble loads accurately because their duration is significantly longer than that of high-frequency strong impact loads, thus allowing for more lenient requirements on the equipment's measurement response and sampling frequency. Therefore, inverting the initial conditions of underwater high-pressure bubbles based on low-frequency bubble loads has strong engineering application significance. Furthermore, although it is difficult to measure the pulsating bubble radius in large-scale underwater high-pressure bubble experiments, the obtained pulsating bubble radius can still serve as a reference indicator given the appropriate conditions. Summary of the Invention

[0005] The purpose of this invention is to address the problems in existing technologies by proposing a neural network inversion method for the initial radius of underwater high-pressure bubbles that integrates bubble dynamics equations. This method incorporates bubble dynamics equations into a physical error function to establish a physical information neural network model. It provides initial conditions for calculation based on factors such as the pulsating bubble radius or low-frequency bubble load, thereby improving the accuracy of analysis in underwater high-pressure bubble experiments.

[0006] This invention is achieved through the following technical solution: This invention proposes a neural network inversion method for the initial radius physical information of underwater high-pressure bubbles, which integrates bubble dynamics equations. The method includes the following steps: S1. Integrate the bubble dynamics equations into the physical error function to establish a physical information neural network model; S2. Input the setup conditions for conducting underwater high-pressure bubble experiments into the physical information neural network model established in S1; S3. Input the data fragments of bubble radius or flow field load obtained from the underwater high-pressure bubble experiment into the physical information neural network model established in S1; S4. The physical information neural network model, after receiving data from S2 and S3, learns according to a preset strategy and iterates continuously to obtain the initial radius of the underwater high-pressure bubble. S5. Based on the initial radius of the underwater high-pressure bubble obtained in S4, calculate the bubble radius and flow field load for the entire process using the bubble dynamics equation, and compare the results with experimental data to verify the accuracy.

[0007] Furthermore, the structure of the physical information neural network model in S1 includes a first input layer with a dimension of... The middle two layers, which satisfy the nonlinear characteristics of the bubble dynamics equation, are fully linked. The hidden layer has a dimension of 1, and the final output layer has a dimension of 2. The activation function is the hyperbolic tangent function.

[0008] Furthermore, in step S1, the physical error function incorporated into the bubble dynamics equation is... The root mean square of the relationship that the radius of the pulsating bubble must satisfy The relationship between the variance and bubble migration must satisfy is the standard deviation. The sum of , and Based on the bubble dynamics equation and physical equation, the number of collocation points The calculation yielded: , ; ; in, The number of points used to train a physical information neural network model so that the model output satisfies the physical laws.

[0009] Furthermore, the setup conditions for the underwater high-pressure bubble experiment in step S2 include the type of gas inside the underwater high-pressure bubble and the initial water depth at which the underwater high-pressure bubble is deployed. Initial internal pressure of underwater high-pressure bubbles Distance from the measuring point located at the initial horizontal center of the underwater high-pressure bubble .

[0010] Furthermore, the data segments obtained from the underwater high-pressure bubble experiment in step S3 are time points. and the bubble radius at the corresponding time. Or the flow field load measured at the measuring point .

[0011] Furthermore, in step S3, when the bubble radius obtained from the underwater high-pressure bubble experiment is used for inversion, it includes three periods: the expansion stage of the pulsating bubble, the area near the maximum radius, and the collapse stage; when the flow field load data segment is used for inversion, it should be the segment near the peak value of the flow field load induced by bubble pulsation measured at the measuring point, including the peak value, the rising edge before the peak value, and the falling edge after the peak value.

[0012] Furthermore, in step S4, during the learning process of the physical information neural network model, the coordinate point time is input into the input layer. , obtained in the output layer Corresponding bubble radius and the displacement of the collocation bubble Furthermore, through automatic differentiation technology, and right Find the first and second derivatives to obtain Corresponding bubble pulsation velocity , Pointed bubble pulsation acceleration Bubble migration speed and the acceleration of bubble migration at points .

[0013] Furthermore, the preset strategy in S4 is a segmented learning strategy, which applies to different iteration steps. Corresponding to different error functions Including experimental error function Physical error function and initial condition error function The corresponding rules are as follows: ; Among them, the experimental error function To extract time points from experimental data segments After inputting the model and obtaining the corresponding results, the loads at the distribution points are calculated. Then, it is calculated as follows: , , When the experimental data provides the radius of a pulsating bubble, the experimental error function... Based on the experimentally measured radius of the pulsating bubble Calculate as follows: ; Wherein, the initial condition error function Based on the assumption that the bubble expansion velocity, bubble displacement, and bubble migration velocity are all zero during the instantaneous generation of high-pressure bubbles underwater, the following calculation method was used: .

[0014] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations.

[0015] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations.

[0016] The beneficial effects of this invention are: The proposed method for inverting the physical information of the initial radius of underwater high-pressure bubbles using a neural network, which integrates the bubble dynamics equations, enables precise calibration of the initial radius of underwater high-pressure bubbles based on experimentally measured pulsating bubble radii or loads. This reduces the need for precision measuring instruments and allows for more accurate comparative studies through numerical simulation and theoretical analysis. Attached Figure Description

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

[0018] Figure 1 This is a schematic diagram of the process for a neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations, as described in this invention. Figure 2 This is a comparison chart of the pulsating bubble radius result corresponding to the initial radius obtained by inversion based on the pulsating bubble radius in Embodiment 1 of the present invention, and the experimental value and ideal theoretical value; Figure 3This is a comparison chart of the load results corresponding to the initial radius obtained by the inversion of bubble pulsation load in Embodiment 2 of the present invention with the experimental value and the ideal theoretical value; Figure 4 This is a comparison chart of the pulsating bubble radius result corresponding to the initial radius obtained by bubble pulsating load inversion according to Embodiment 2 of the present invention with the experimental value and the ideal theoretical value. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Combination Figures 1-4 This invention proposes a neural network inversion method for the initial radius physical information of underwater high-pressure bubbles, which integrates bubble dynamics equations. The method includes the following steps: S1. Integrate the bubble dynamics equations into the physical error function to establish a physical information neural network model; The structure of the physical information neural network model in S1 includes a first input layer with a dimension of [missing information]. The middle two layers, which satisfy the nonlinear characteristics of the bubble dynamics equation, are fully linked. The hidden layer has a dimension of 1, and the final output layer has a dimension of 2. The activation function is the hyperbolic tangent function.

[0021] In step S1, the physical error function is incorporated into the bubble dynamics equation. The root mean square of the relationship that the radius of the pulsating bubble must satisfy The relationship between the variance and bubble migration must satisfy is the standard deviation. The sum of , and Based on the bubble dynamics equation and physical equation, the number of collocation points The calculation yielded: , ; ; in, The number of points used to train a physical information neural network model so that the model output satisfies the physical laws. , , , The values ​​are, in order, the enthalpy difference between the inner and outer surfaces of the bubble, the sound velocity in water, the added mass coefficient, and the drag coefficient, corresponding to the model output results.

[0022] S2. Input the setup conditions for conducting underwater high-pressure bubble experiments into the physical information neural network model established in S1; The setup conditions for the underwater high-pressure bubble experiment in step S2 include the type of gas inside the underwater high-pressure bubble and the initial water depth at which the underwater high-pressure bubble is deployed. Initial internal pressure of underwater high-pressure bubbles Distance from the measuring point located at the initial horizontal center of the underwater high-pressure bubble .

[0023] S3. Input the data fragments of bubble radius or flow field load obtained from the underwater high-pressure bubble experiment into the physical information neural network model established in S1; The data segments obtained from the underwater high-pressure bubble experiment in step S3 are time points. and the bubble radius at the corresponding time. Or the flow field load measured at the measuring point .

[0024] In step S3, when the bubble radius obtained from the underwater high-pressure bubble experiment is used for inversion, it includes three periods: the expansion stage of the pulsating bubble, the area near the maximum radius, and the collapse stage. When the flow field load data segment is used for inversion, it should be the segment near the peak value of the flow field load induced by bubble pulsation measured at the measuring point, including the peak value, the rising edge before the peak value, and the falling edge after the peak value.

[0025] S4. The physical information neural network model, after receiving data from S2 and S3, learns according to a preset strategy and iterates continuously to obtain the initial radius of the underwater high-pressure bubble. In step S4, during the learning process of the physical information neural network model, the coordinate point time is input into the input layer. , obtained in the output layer Corresponding bubble radius and the displacement of the collocation bubble Furthermore, through automatic differentiation technology, and right Find the first and second derivatives to obtain Corresponding bubble pulsation velocity , Pointed bubble pulsation acceleration Bubble migration speed and the acceleration of bubble migration at points .

[0026] The default strategy in S4 is a segmented learning strategy, which varies with different iteration steps. Corresponding to different error functions Including experimental error function Physical error function and initial condition error function The corresponding rules are as follows: ; Among them, the experimental error function To extract time points from experimental data segments After inputting the model and obtaining the corresponding results, the loads at the distribution points are calculated. Then, it is calculated as follows: , , When the experimental data provides the radius of a pulsating bubble, the experimental error function... Based on the experimentally measured radius of the pulsating bubble Calculate as follows: ; Wherein, the initial condition error function Based on the assumption that the bubble expansion velocity, bubble displacement, and bubble migration velocity are all zero during the instantaneous generation of high-pressure bubbles underwater, the following calculation method was used: .

[0027] S5. Based on the initial radius of the underwater high-pressure bubble obtained in S4, calculate the bubble radius and flow field load for the entire process using the bubble dynamics equation, and compare the results with experimental data to verify the accuracy.

[0028] This invention proposes a method for inverting the initial radius of underwater high-pressure bubbles using a physical information neural network that integrates bubble dynamics equations. First, the method establishes a physical information neural network model by using the bubble dynamics equations as a physical error function. Second, it inputs known conditions such as the water depth, initial internal pressure, and distance between measuring points of the underwater high-pressure bubble. Then, it inputs data fragments of the high-pressure bubble radius or induced flow field load measured in experiments into the neural network for learning. After learning, the neural network outputs the initial radius of the underwater high-pressure bubble. Finally, it substitutes the initial radius of the underwater high-pressure bubble into the calculation to obtain the flow field load induced by the high-pressure bubble, and compares this calculation with experimental data for verification. This invention improves the interpretability and convergence speed of the neural network in training and learning for the flow field load induced by underwater high-pressure bubbles by embedding the bubble dynamics equations as a physical error function into a deep neural network. It can invert the initial radius of underwater high-pressure bubbles using only a small sample of data, further improving the accuracy of research in fields such as underwater reactions of high-energy materials like explosives, deep-sea exploration air guns, electric spark bubbles, and laser bubbles.

[0029] Two embodiments are presented here, which realize the inversion of the initial radius of underwater high-pressure bubbles based on the pulsating bubble radius and the bubble pulsating load, respectively.

[0030] Example 1: This embodiment uses the method proposed in this invention to invert the initial radius of underwater high-pressure bubbles based on the pulsating bubble radius. In this embodiment, the initial radius of the underwater high-pressure bubble generated by explosive detonation is calibrated. The explosive used is a detonator containing 1.125g of PBX9501 explosive, encased in rigid packaging. The setup conditions are as follows: , , The parameters are obtained from the JWL equation of state corresponding to PBX9501 explosive. The method proposed in this invention uses only three data points—the expansion stage, the area near the maximum radius, and the collapse stage—to invert and obtain an initial radius of 5.43 mm, corresponding to an equivalent reaction amount of 1.204 g of PBX9501 explosive. The corresponding pulsating bubble radius is shown below. Figure 2 As shown, the pulsating bubble radius corresponding to the ideal 1.125g PBX9501 explosive is closer to the experimental value. This embodiment demonstrates that the method proposed in this invention can not only achieve high-precision inversion with a small amount of data, but also demonstrate the enhancing effect of rigid packaging on the equivalent reaction amount of explosive.

[0031] Example 2: This embodiment, based on bubble loading, uses the method proposed in this invention to invert the initial radius of underwater high-pressure bubbles. In this embodiment, the initial radius of the underwater high-pressure bubble generated by explosive detonation is calibrated. This experiment, after precise calibration, uses 0.227 kg of TNT explosive. The setup conditions are as follows: , , The parameters are obtained from the JWL equation of state corresponding to TNT explosive. The method proposed in this invention, based on the load data points marked in purple in the figure, inverts to obtain an initial radius of 0.03217 m, corresponding to an equivalent reaction amount of 227.3 g of TNT explosive, with a relative error of 0.1%. The corresponding pulsating bubble radius is shown below. Figure 3 As shown, its corresponding load is as follows Figure 4 As shown, this demonstrates the extremely high precision of the method described in this invention.

[0032] The results of the above embodiments demonstrate that by embedding the bubble dynamics equation as a physical error function into a deep neural network, the interpretability and convergence speed of the neural network in training and learning for flow field loads induced by underwater high-pressure bubbles are improved. This allows for high-precision inversion of the initial radius of underwater high-pressure bubbles using only a small segment of sample data. This invention can further improve the accuracy of research in fields such as underwater reactions of high-energy materials like explosives, deep-sea exploration air guns, electric spark bubbles, and laser bubbles.

[0033] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations.

[0034] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations.

[0035] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0036] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0037] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0038] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0039] The above provides a detailed description of the neural network inversion method for the initial radius physical information of underwater high-pressure bubbles that integrates bubble dynamics equations. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A neural network inversion method for the initial radius physical information of underwater high-pressure bubbles, integrating bubble dynamics equations, characterized in that, The method includes the following steps: S1. Integrate the bubble dynamics equations into the physical error function to establish a physical information neural network model; S2. Input the setup conditions for conducting underwater high-pressure bubble experiments into the physical information neural network model established in S1; S3. Input the data fragments of bubble radius or flow field load obtained from the underwater high-pressure bubble experiment into the physical information neural network model established in S1; S4. The physical information neural network model, after receiving data from S2 and S3, learns according to a preset strategy and iterates continuously to obtain the initial radius of the underwater high-pressure bubble. S5. Based on the initial radius of the underwater high-pressure bubble obtained in S4, calculate the bubble radius and flow field load for the entire process using the bubble dynamics equation, and compare the results with experimental data to verify the accuracy. The structure of the physical information neural network model in S1 includes a first input layer with a dimension of [missing information]. The two middle layers, which satisfy the nonlinear characteristics of the bubble dynamics equations, are fully connected. The hidden layer has a dimension of 1, and the final output layer has a dimension of 2. The activation function is the hyperbolic tangent function; where, n Total number of time points; In step S1, the physical error function is incorporated into the bubble dynamics equation. The root mean square of the relationship that the radius of the pulsating bubble must satisfy The relationship between the variance and bubble migration must satisfy is the standard deviation. The sum of , and Based on the bubble dynamics equation and physical equation, the number of collocation points The calculation yielded: ， ； ； in, The number of points used to train a physical information neural network model so that the model output results satisfy physical laws; This represents the speed of sound in water. This indicates the velocity of the bubble pulsation at the designated point. Indicates the radius of the matching bubble. Indicates the migration speed of the dotted bubble. This represents the enthalpy difference between the inner and outer surfaces of the bubble. This represents the acceleration of the bubble pulsation at the point of intersection. Indicates the additional quality coefficient. This represents the acceleration of the bubble migration at the collocation point. Indicates the drag coefficient. It represents the acceleration due to gravity.

2. The method according to claim 1, characterized in that, The setup conditions for the underwater high-pressure bubble experiment in step S2 include the type of gas inside the underwater high-pressure bubble and the initial water depth at which the underwater high-pressure bubble is deployed. Initial internal pressure of underwater high-pressure bubbles Distance from the measuring point located at the initial horizontal center of the underwater high-pressure bubble .

3. The method according to claim 2, characterized in that, The data segments obtained from the underwater high-pressure bubble experiment in step S3 are time points. and the corresponding bubble radius at the time Or the flow field load measured at the measuring point .

4. The method according to claim 3, characterized in that, In step S3, when the bubble radius obtained from the underwater high-pressure bubble experiment is used for inversion, it includes three periods: the expansion stage of the pulsating bubble, the area near the maximum radius, and the collapse stage. When the flow field load data segment is used for inversion, it should be the segment near the peak value of the flow field load induced by bubble pulsation measured at the measuring point, including the peak value, the rising edge before the peak value, and the falling edge after the peak value.

5. The method according to claim 4, characterized in that, In step S4, during the learning process of the physical information neural network model, the coordinate point time is input into the input layer. , obtained in the output layer Corresponding bubble radius and the displacement of the collocation bubble Furthermore, through automatic differentiation technology, and right Find the first and second derivatives, and we get Corresponding bubble pulsation velocity , Pointed bubble pulsation acceleration Bubble migration speed and the acceleration of bubble migration .

6. The method according to claim 5, characterized in that, The default strategy in S4 is a segmented learning strategy, which varies with different iteration steps. Corresponding to different error functions Including experimental error function Physical error function and initial condition error function The corresponding rules are as follows: ； Among them, the experimental error function To extract time points from experimental data segments After inputting the model and obtaining the corresponding results, the loads at the distribution points are calculated. Then, it is calculated as follows: ， ， in, The value r represents the density of water; r represents the distance from the measuring point to the center of the bubble. When the experimental data provides the radius of a pulsating bubble, the experimental error function... Based on the experimentally measured radius of the pulsating bubble Calculate as follows: ； Wherein, the initial condition error function Based on the assumption that the bubble expansion velocity, bubble displacement, and bubble migration velocity are all zero during the instantaneous generation of high-pressure bubbles underwater, the following calculation method was used: 。 7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-6.

Images