Cavitation jet nozzle structure optimization method and system based on BP-SVR prediction model and particle swarm algorithm

Abstract

This invention discloses a method and system for optimizing cavitation jet nozzle structures based on a BP-SVR prediction model and a particle swarm optimization algorithm. Belonging to the field of cavitation jet technology, it solves the problems of existing technologies, such as difficulty in coordinating multi-parameter coupling, high global optimization costs, and low prediction model accuracy. The method includes constructing a symmetric computational domain, building a BP-SVR combined prediction model, using the time-averaged gas volume peak value in the near-target region as the output label for training, and employing a particle swarm optimization (PSO) algorithm for global optimization within the structural parameter constraints to obtain the optimal nozzle structure parameter combination. By constructing a symmetric computational domain, this invention can more directly and accurately characterize the actual cavitation impact and damage capability of the nozzle on the target surface. Furthermore, by constructing and training the BP-SVR combined prediction model and using it as a fitness evaluation function, it achieves rapid global optimization of the design space under multi-parameter coupling conditions, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures.

Description

Technical Field

[0001] This invention belongs to the field of cavitation jet technology, specifically relating to a method and system for optimizing the structure of cavitation jet nozzles based on the BP-SVR prediction model and particle swarm optimization algorithm. Background Technology

[0002] Cavitation water jet technology utilizes the geometric throttling effect of high-pressure water flowing through a nozzle to reduce the local static pressure below the saturated vapor pressure of water, inducing dissolved gases in the water to precipitate and form cavitation bubbles. These cavitation bubbles rapidly collapse after entering the high-pressure zone with the jet, generating localized high-pressure shock waves and micro-jet streams that can strongly erode the target material. With its dual advantages of efficient cleaning and material strengthening, this technology has been widely applied in cavitation shot peening surface strengthening, drilling engineering-assisted rock breaking, rock cutting, organic wastewater treatment, and marine engineering scenarios such as the removal of biological attachments from ship hulls, offshore platforms, and aquaculture cages, showing a very broad application prospect. As the core component of the cavitation jet system, the nozzle's structural parameters directly determine the cavitation intensity, jet concentration, and target impact effect. Therefore, optimizing the nozzle structure is key to improving the overall performance of the cavitation jet system.

[0003] Currently, research on the optimization of cavitation jet nozzle structure mainly focuses on the following technologies:

[0004] Traditional empirical design and experimental optimization methods: Current nozzle development largely relies on the accumulated experience of designers. Geometric parameters such as contraction angle, diffusion angle, throat diameter, and length are adjusted through single-factor experiments or orthogonal experiments, and the cavitation intensity and impact effect under different parameters are compared. For example, YANG et al. (Effect of geometrical parameters on submerged cavitation jet discharged from profiled central-body nozzle[J]. Chinese Journal of Mechanical Engineering, 2013, 26(3):476-482) conducted single-factor simulations on central-body nozzles and pointed out that there is an optimal contraction angle at the nozzle outlet when the central body diameter is fixed; PENG et al. (Cavitation in waterjet under high ambient pressure conditions[J]. Experimental Thermal and Fluid Science, 2017, 89:9-18) simulated the bubble movement law in a convergent-divergent nozzle and analyzed the influence of environment and flow rate on bubble transport efficiency. However, such methods can only achieve independent analysis of a single parameter and cannot reveal the synergistic optimization law under the coupling effect of multiple parameters. The optimization results are highly dependent on subjective experience, and global optimality is difficult to guarantee.

[0005] CFD-based numerical simulation optimization schemes: With the development of computational fluid dynamics, numerical simulations can be used to obtain characteristics such as velocity, pressure, and gas volume fraction of the flow field inside and outside the nozzle, providing theoretical support for structural optimization. For example, Dong et al. (Numerical simulation of flow field of submerged angular cavitation nozzle[J]. Applied Sciences, 2023, 13(1):613) have established a mature simulation framework for the flow field of underwater angular cavitation nozzles. However, when the design variable dimension is high, to cover the entire parameter space for global optimization, a massive number of numerical simulations are required. A single simulation often takes several hours or even days, resulting in extremely high computational resources and time costs, which cannot meet the rapid iteration requirements in engineering scenarios.

[0006] Machine learning-based optimization schemes: In recent years, machine learning has been gradually applied to the modeling of complex flow systems. For example, Zhang Haonan (Optimization of cavitation jet nozzle structure based on machine learning [D]. Northeast Petroleum University, 2021.) used artificial neural networks to complete the structural optimization of the bellows nozzle, verifying the feasibility of machine learning in this field; Yang Xinglin et al. (Optimization of underwater cavitation water jet nozzle structure based on RBF-ANNGA [J]. Shipbuilding Engineering, 2023, 45(11):85-90) combined RBF neural network and genetic algorithm to realize underwater nozzle optimization. However, existing schemes still have obvious limitations: when using BP neural network alone, it is easy to overfit under small sample conditions, and the generalization ability is weak; when using support vector regression (SVR) alone, the nonlinear expression ability of high-dimensional original features is insufficient; at the same time, most studies still use nozzle outlet velocity, free jet region pressure peak or overall cavitation intensity as optimization targets, without considering that the accumulation and collapse of cavitation bubbles near the target surface in actual engineering is the core factor that determines the damage effect, resulting in the optimization results being out of sync with the actual working conditions.

[0007] In summary, the existing technology has the following limitations:

[0008] Low optimization efficiency and high experimental cost: Traditional optimization methods that rely on experience-based design and single-factor / orthogonal experiments often require a large number of experimental samples under multi-parameter coupling conditions, resulting in high experimental costs and insufficient parameter space coverage, which cannot guarantee the global optimality of the optimization results.

[0009] Numerical simulation is costly and time-consuming: When relying solely on CFD numerical simulation for global search, each simulation calculation requires a large amount of computing resources and time. When the design variable dimension is high, it is impossible to achieve fast global optimization, which is difficult to meet the needs of engineering applications for rapid optimization.

[0010] Using BP networks alone can lead to overfitting under small sample conditions, while using SVR alone is insufficient in terms of feature representation: Existing machine learning methods either suffer from overfitting under small sample conditions (BP networks) or lack the ability to extract deep nonlinear features from high-dimensional inputs (SVR), making it difficult to balance prediction accuracy and generalization ability.

[0011] The evaluation indicators are out of touch with engineering practice and cannot accurately reflect the near-target damage capability: using nozzle outlet flow field parameters or cavitation intensity in the free jet region as optimization targets fails to fully consider the cavitation accumulation and collapse characteristics of the nozzle in the near-target region under actual use scenarios, resulting in limited effectiveness of the optimization results in practical applications.

[0012] To address the common problems in existing cavitation jet nozzle optimization techniques, such as difficulty in coordinating multi-parameter coupling, high global optimization cost, difficulty in balancing the accuracy and generalization of prediction models, and disconnect between evaluation indicators and engineering practice, we propose a cavitation jet nozzle structure optimization method and system based on the BP-SVR prediction model and particle swarm optimization algorithm. Summary of the Invention

[0013] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for optimizing the structure of cavitation jet nozzles based on the BP-SVR prediction model and particle swarm optimization algorithm. This solves the problems commonly found in existing cavitation jet nozzle optimization technologies, such as difficulty in coordinating multi-parameter coupling, high global optimization costs, difficulty in balancing the accuracy and generalization of prediction models, and a disconnect between evaluation indicators and engineering practice.

[0014] This invention is implemented as follows: a cavitation jet nozzle structure optimization method based on the BP-SVR prediction model and particle swarm optimization algorithm, wherein the cavitation jet nozzle structure optimization method based on the BP-SVR prediction model and particle swarm optimization algorithm includes:

[0015] S10, construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle containing the target surface region, and set the nozzle structure optimization variables and their value ranges;

[0016] S20, based on computational fluid dynamics, the flow field simulation of the nozzle structure corresponding to the nozzle structure optimization variables is performed, and the simulation dataset is constructed using the simulation data;

[0017] S30. Construct a BP-SVR combined prediction model. Use the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module. Extract deep nonlinear feature vectors based on the BP feature extraction module. Input the deep nonlinear feature vectors into the SVR proxy modeling module. Use the time-averaged gas volume peak value in the near-target region as the output label for training. Establish a proxy mapping relationship between nozzle structure parameters and near-target cavitation performance. Output the trained BP-SVR combined prediction model.

[0018] S40 uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structural parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structural parameter combination.

[0019] Preferably, the nozzle structure optimization variables are dimensionless parameters, including: throat length ratio, diffuser length ratio, diffuser angle, contraction angle ratio, and target distance ratio.

[0020] Preferably, in step S10, the two-dimensional axisymmetric computational domain of the cavitation jet nozzle includes an upstream extension section of the nozzle inlet, a downstream flow field computational domain, and a near-target impact region. When constructing the two-dimensional axisymmetric computational domain of the cavitation jet nozzle that includes the target region, the upstream extension section of the nozzle inlet extends 20mm upstream of the cavitation jet nozzle inlet to ensure sufficient development of the inlet flow field; the downstream flow field computational domain is set as a symmetrical rectangular region with a length of 120mm and a width of 40mm; the near-target impact region is a symmetrical target region downstream of the nozzle, with a width of 5mm and a length of 10mm; the boundary conditions of the two-dimensional axisymmetric computational domain are set as: pressure inlet 10MPa, pressure outlet, symmetry line, and wall.

[0021] Preferably, the near-target region is a line segment region located at a distance of 1 mm, 2 mm, and 3 mm from the target surface.

[0022] Preferably, in step S20, when performing flow field simulation on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics, the delayed separated eddy simulation (DDES) method based on the k-ε model is adopted, and curvature correction is introduced to solve the two-dimensional unsteady flow field of the cavitation jet nozzle.

[0023] Preferably, the BP-SVR combined prediction model includes a BP feature extraction module, an SVR surrogate modeling module, and a PSO optimization module. The BP feature extraction module is a BP feature extraction network, and the SVR surrogate modeling module is a support vector regression (SVR) model.

[0024] Preferably, the BP feature extraction network includes an input layer, six hidden layers, and an output layer; the number of nodes in the hidden layers is 64, 32, 24, 16, and 8 respectively; the activation function of the BP feature extraction network is the ReLU function; and the output layer outputs a 4-dimensional deep nonlinear feature vector.

[0025] Preferably, the support vector regression (SVR) model uses the RBF kernel function, and the hyperparameters are set as follows: penalty coefficient C = 5.0, kernel function coefficient γ = 0.098, and insensitive loss function coefficient ε = 0.01.

[0026] Preferably, the BP-SVR combined prediction model adopts a two-stage training method: the first stage trains the BP feature extraction network, uses StandardScaler to standardize the input and target variables respectively, trains in a mini-batch supervised learning manner with a batch size of 32, uses the mean squared error loss function as the loss function, uses the Adam optimizer, and sets the learning rate to 0.001; the second stage trains the deep nonlinear feature vectors extracted by the BP feature extraction network into the support vector regression (SVR) model, and the SVR model uses the RBF kernel function for regression fitting.

[0027] On the other hand, the present invention also provides a cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and particle swarm optimization algorithm, wherein the cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and particle swarm optimization algorithm includes:

[0028] The computational domain construction module is used to construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle that includes the target surface region, and to set the nozzle structure optimization variables and their value ranges.

[0029] The simulation dataset generation module performs flow field simulation on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics methods, and constructs a simulation dataset using the simulation data.

[0030] The model training module is used to construct the BP-SVR combined prediction model. It uses the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module, extracts deep nonlinear feature vectors based on the BP feature extraction module, and inputs the deep nonlinear feature vectors into the SVR proxy modeling module. It uses the time-averaged gas volume peak value in the near-target region as the output label for training, establishes the proxy mapping relationship between the nozzle structure parameters and the near-target cavitation performance, and outputs the trained BP-SVR combined prediction model.

[0031] The optimization solution module uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structure parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structure parameter combination.

[0032] Compared with the prior art, the embodiments of this application have the following main advantages:

[0033] This invention constructs a two-dimensional axisymmetric computational domain encompassing the target surface region, using the peak time-averaged gas volume near the target surface (1-3 mm from the target surface) as the optimization evaluation index. This overcomes the disconnect between traditional methods that target free jet flow field parameters and engineering realities, enabling a more direct and accurate characterization of the nozzle's actual cavitation impact damage capability on the target surface. Furthermore, it extracts deep nonlinear features of the nozzle structural parameters using a BP neural network, then inputs this feature vector into an SVR model to complete regression modeling, constructing a BP-SVR combined prediction model. This model effectively balances deep feature extraction capabilities with the advantage of small-sample generalization, overcoming the tendency of a single BP network to overfit under small-sample conditions and the limitations of a single SVR model for high-dimensional primitives. Overcoming the limitations of insufficient initial feature representation, this method achieves a balance between high prediction accuracy and strong generalization ability. Furthermore, it combines this combined surrogate model with the particle swarm optimization algorithm, using the trained BP-SVR model to replace the high-cost numerical simulation as the fitness evaluation function. This enables rapid global optimization of the design space under multi-parameter coupling conditions, significantly reducing the experimental and simulation costs in the optimization process. It solves the problems of low optimization efficiency, long computation cycle, and difficulty in meeting the rapid optimization needs of engineering using traditional methods. Overall, it forms a complete engineering optimization closed loop of numerical simulation dataset construction, deep feature extraction, surrogate modeling, and global optimization, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures.

[0034] Compared to full three-dimensional flow field simulation, this invention uses a two-dimensional axisymmetric computational domain instead of a three-dimensional structure. Utilizing the axisymmetric characteristics of the nozzle structure, only a two-dimensional plane needs to be solved. While ensuring the flow field's physical characteristics are not distorted, the computational load of a single simulation is reduced by an order of magnitude. This makes it possible to generate large-scale training simulation datasets in a short time, providing efficient data support for subsequent data-driven intelligent optimization. Furthermore, by materializing a 5mm wide and 10mm long symmetrical target area downstream of the two-dimensional axisymmetric computational domain, this invention, for the first time, realistically recreates the physical conditions of jet impact on the target surface in numerical simulation. This setup can accurately capture the flow separation, pressure reflection, and asymmetric collapse behavior of cavitation bubbles in a confined space after the jet impacts the wall, overcoming the shortcomings of traditional targetless free jet simulations that cannot simulate the real impact process. Thanks to the aforementioned two-dimensional axisymmetric computational domain of the cavitation jet nozzle containing the target area, this invention can use the near-target surface time-averaged gas volume peak as the optimization target. This indicator is directly related to the damage mechanism of cavitation jets on the target surface, namely the accumulation and collapse effect of cavitation bubbles near the target surface, thus replacing the traditional free jet region parameters that cannot reflect actual destructive capabilities. This collaborative design of simulation domain and evaluation indicators ensures that the optimized nozzle structure parameters can be directly converted into efficient cleaning or demolition capabilities on the engineering site, thereby avoiding the technical disconnect between good simulation results and poor on-site results.

[0035] In this embodiment of the invention, the constructed BP-SVR combined prediction model effectively addresses the inherent shortcomings of single models in the field of cavitation jets by deeply fusing the representation learning ability of neural networks with the small-sample generalization advantage of support vector regression. Specifically, the BP-SVR combined prediction model employs a two-stage architecture of deep feature extraction and high-precision regression. It utilizes a BP feature extraction network with six hidden layers as the front-end feature extractor, and through layer-by-layer nonlinear mapping using the ReLU activation function, transforms the original 4D structural parameters into 4D deep feature vectors rich in physical information, overcoming the limitation of traditional SVR in handling high-dimensional nonlinear features. Subsequently, the support vector regression SVR model is used as the back-end regressor. Leveraging its advantage of minimizing structural risk under small-sample conditions, it overcomes the overfitting tendency of BP networks, achieving high-precision modeling of complex cavitation flow fields. Furthermore, by introducing StandardScaler normalization, the dimensional differences between nozzle structural parameters are eliminated, accelerating model convergence and improving stability. Combining Mini-batch with Adam optimizer further enhances the training efficiency and robustness of the model with limited samples. The two-stage decoupled training strategy (training BP first, then SVR) simplifies the parameter tuning difficulty and ensures the optimal matching between the feature space and the regression space. Attached Figure Description

[0036] Figure 1 A schematic diagram of the implementation process of the cavitation jet nozzle structure optimization method based on the BP-SVR prediction model and particle swarm algorithm is shown.

[0037] Figure 2 This is a schematic diagram of the cavitation jet nozzle structure provided by the present invention.

[0038] Figure 3 This is a diagram of the BP-SVR combined prediction model architecture provided by the present invention.

[0039] Figure 4 This is a schematic diagram of the cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and particle swarm algorithm provided by the present invention. Detailed Implementation

[0040] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0041] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0042] Existing cavitation jet nozzle optimization techniques generally suffer from problems such as difficulty in coordinating multi-parameter coupling, high global optimization costs, difficulty in balancing prediction model accuracy and generalization, and a disconnect between evaluation indicators and engineering realities. To address these issues, we propose a cavitation jet nozzle structure optimization method and system based on a BP-SVR prediction model and particle swarm optimization algorithm. In short, the method first constructs a two-dimensional axisymmetric computational domain for the cavitation jet nozzle, including the target surface region, and sets the nozzle structure optimization variables and their value ranges. Then, based on computational fluid dynamics methods, flow field simulations are performed on the nozzle structure corresponding to the optimization variables. Simulation datasets are constructed using the simulation data, and finally, a BP-SVR combined prediction model is built. The nozzle structure parameters in the simulation dataset are used as input to the BP feature extraction module. Based on the BP feature extraction module, deep nonlinear feature vectors are extracted. These deep nonlinear feature vectors are then input to the SVR surrogate modeling module. The time-averaged gas volume peak value in the near-target region is used as the output label for training. A surrogate mapping relationship between the nozzle structure parameters and the near-target cavitation performance is established. The trained BP-SVR combined prediction model is used as the fitness evaluation function. The particle swarm optimization (PSO) algorithm is used to perform global optimization within the structural parameter constraints to obtain the optimal nozzle structure parameter combination that maximizes the time-averaged gas volume peak value in the near-target region. The optimal nozzle structure parameter combination is then output. This invention constructs a two-dimensional axisymmetric computational domain encompassing the target surface region, using the peak time-averaged gas volume near the target surface (1-3 mm from the target surface) as the optimization evaluation index. This overcomes the disconnect between traditional methods that target free jet flow field parameters and engineering realities, enabling a more direct and accurate characterization of the nozzle's actual cavitation impact damage capability on the target surface. Furthermore, it extracts deep nonlinear features of the nozzle structural parameters using a BP neural network, then inputs this feature vector into an SVR model to complete regression modeling, constructing a BP-SVR combined prediction model. This model effectively balances deep feature extraction capabilities with the advantage of small-sample generalization, overcoming the tendency of a single BP network to overfit under small-sample conditions and the limitations of a single SVR model for high-dimensional primitives. Overcoming the limitations of insufficient initial feature representation, this method achieves a balance between high prediction accuracy and strong generalization ability. Furthermore, it combines this combined surrogate model with the particle swarm optimization algorithm, using the trained BP-SVR model to replace the high-cost numerical simulation as the fitness evaluation function. This enables rapid global optimization of the design space under multi-parameter coupling conditions, significantly reducing the experimental and simulation costs in the optimization process. It solves the problems of low optimization efficiency, long computation cycle, and difficulty in meeting the rapid optimization needs of engineering using traditional methods. Overall, it forms a complete engineering optimization closed loop of numerical simulation dataset construction, deep feature extraction, surrogate modeling, and global optimization, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures.

[0043] This invention provides a method for optimizing the structure of cavitation jet nozzles based on the BP-SVR prediction model and particle swarm optimization algorithm. Figure 1A schematic diagram illustrating the implementation process of a cavitation jet nozzle structure optimization method based on a BP-SVR prediction model and particle swarm optimization algorithm is shown. The cavitation jet nozzle structure optimization method based on the BP-SVR prediction model and particle swarm optimization algorithm specifically includes:

[0044] S10, construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle containing the target surface region, and set the nozzle structure optimization variables and their value ranges;

[0045] In this embodiment of the invention, an angled cavitation jet nozzle can be used as the optimization target. Figure 2 A schematic diagram of the cavitation jet nozzle structure is shown. Figure 2 In the cavitation jet nozzle structure, the following geometric elements are included: throat diameter d (fixed at 1 mm), contraction section length L1, throat length L2, diffuser section length L3, contraction angle α (fixed at 13.5°), diffuser angle β, and distance T from nozzle orifice to target surface. d To eliminate the influence of differences in geometric scale and dimensions on the analysis results, dimensionless parameters were used as the nozzle structure optimization variables, and four dimensionless parameters were selected. The nozzle structure optimization variables include: throat length ratio. , length ratio of diffusion section Diffusion angle and contraction angle ratio and target range ratio Among them, the throat length ratio ranges from 3 to 6; the diffuser length ratio ranges from 2 to 7; the contraction angle ratio ranges from 3 to 6; and the target distance ratio ranges from 10 to 30.

[0046] In step S10, the two-dimensional axisymmetric computational domain of the cavitation jet nozzle includes an upstream extension section of the nozzle inlet, a downstream flow field computational domain, and a near-target impact region. When constructing the two-dimensional axisymmetric computational domain of the cavitation jet nozzle that includes the target region, the upstream extension section of the nozzle inlet extends 20mm upstream of the nozzle inlet to ensure sufficient development of the inlet flow field. The downstream flow field computational domain is set as a symmetrical rectangular region with a length of 120mm and a width of 40mm. The near-target impact region is a symmetrical target region downstream of the nozzle, with a width of 5mm and a length of 10mm. The boundary conditions of the two-dimensional axisymmetric computational domain are set as: pressure inlet 10MPa, pressure outlet, symmetry line, and wall. Based on the traditional nozzle flow field computational domain, a near-target impact region (5mm wide and 10mm long) is added downstream of the nozzle to construct a two-dimensional axisymmetric computational domain that includes the target condition. This allows the optimization objective to directly correspond to the actual usage scenario, which is the key to constructing the simulation dataset. It should be noted that the target region refers to the area 10-30mm away from the nozzle outlet.

[0047] S20. Flow field simulation is performed on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics methods, and a simulation dataset is constructed using simulation data. It should be noted that the "nozzle structure parameters" refer to the complete set of parameters describing the nozzle geometry and operating conditions, including fixed and variable parameters; the "nozzle structure optimization variables" refer to the subset of parameters that are allowed to be adjusted during the optimization process. When constructing the simulation dataset, the nozzle structure parameters are used as input to the prediction model; when performing particle swarm optimization, global optimization is performed only within the range of values ​​for the nozzle structure optimization variables.

[0048] In this embodiment of the invention, a structured mesh is generated for the constructed two-dimensional axisymmetric computational domain during flow field simulation. To ensure a balance between computational accuracy and efficiency, this embodiment of the invention employs a targeted mesh control strategy:

[0049] Localized mesh refinement in key areas: Mesh refinement is applied to the throat, cavitation cavity, outlet section, and near-wall region where the flow field gradient changes drastically. Specifically, boundary layer meshes are used in the near-wall region to ensure accurate capture of boundary layer flow and the initial location of cavitation. The throat and cavitation cavity, as the core areas where cavitation occurs, have their complex eddy structures analyzed by increasing mesh density.

[0050] Grid independence verification: To avoid numerical errors interfering with the training of the BP-SVR combined prediction model, this invention conducted rigorous grid independence verification. By comparing the flow field characteristics under different grid numbers, a total grid number of 8.0 × 10⁻⁶ was ultimately selected. 4 The proposed meshing scheme was validated. The maximum average velocity error under this scheme was controlled within 5%, and further increasing the mesh density had less than 1% impact on the flow field results.

[0051] By adopting the above grid strategy, we can ensure the high fidelity of the simulation data, provide reliable training samples for the subsequent BP-SVR combined prediction model, and keep the cost of a single simulation calculation within a reasonable range, thus meeting the needs of intelligent optimization algorithms for large-scale sample calls.

[0052] Compared to full three-dimensional flow field simulation, this invention uses a two-dimensional axisymmetric computational domain instead of a three-dimensional structure. Utilizing the axisymmetric characteristics of the nozzle structure, only a two-dimensional plane needs to be solved. While ensuring the flow field's physical characteristics are not distorted, the computational load of a single simulation is reduced by an order of magnitude. This makes it possible to generate large-scale training simulation datasets in a short time, providing efficient data support for subsequent data-driven intelligent optimization. Furthermore, by materializing a 5mm wide and 10mm long symmetrical target area downstream of the two-dimensional axisymmetric computational domain, this invention, for the first time, realistically recreates the physical conditions of jet impact on the target surface in numerical simulation. This setup can accurately capture the flow separation, pressure reflection, and asymmetric collapse behavior of cavitation bubbles in a confined space after the jet impacts the wall, overcoming the shortcomings of traditional targetless free jet simulations that cannot simulate the real impact process. Thanks to the aforementioned two-dimensional axisymmetric computational domain of the cavitation jet nozzle containing the target area, this invention can use the near-target surface time-averaged gas volume peak as the optimization target. This indicator is directly related to the damage mechanism of cavitation jets on the target surface, namely the accumulation and collapse effect of cavitation bubbles near the target surface, thus replacing the traditional free jet region parameters that cannot reflect actual destructive capabilities. This collaborative design of simulation domain and evaluation indicators ensures that the optimized nozzle structure parameters can be directly converted into efficient cleaning or demolition capabilities on the engineering site, thereby avoiding the technical disconnect between good simulation results and poor on-site results.

[0053] In this embodiment of the invention, when simulating the flow field of the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics methods, the Delayed Detached Eddy Simulation (DDES) method based on the k-ε model is adopted, and curvature correction is introduced to solve the two-dimensional unsteady flow field of the cavitation jet nozzle. The final simulation dataset contains 150 sets of nozzle structure parameters, each set of samples contains 4 dimensionless input parameters, and the samples in each set are evenly distributed in the parameter space, covering different combinations of structural parameters, providing reliable data support for subsequent model training.

[0054] It should be noted that, in another optional embodiment, flow field simulation of the nozzle structure corresponding to the nozzle structure optimization variables is performed based on computational fluid dynamics methods. When constructing the simulation dataset using simulation data, the numerical simulation method in the construction of the simulation dataset can be replaced with other turbulence calculation methods, such as the standard k-ε RANS method, the SST k-ω method, and large eddy simulation (LES), etc. A near-target surface gas phase volume fraction simulation dataset can still be constructed; the difference lies in the different trade-offs between computational accuracy and computational cost. Furthermore, Gaussian noise data augmentation can be used to construct the simulation dataset. Gaussian noise data augmentation methods can include SMOTE oversampling, Latin hypercube sampling (LHS) in parameter space, or data generation methods based on generative adversarial networks (GANs), all of which can achieve the goal of improving sample diversity and model robustness.

[0055] S30. Construct a BP-SVR combined prediction model. Use the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module. Extract deep nonlinear feature vectors based on the BP feature extraction module. Input the deep nonlinear feature vectors into the SVR surrogate modeling module. Use the time-averaged gas volume peak value in the near-target region as the output label for training. Establish a surrogate mapping relationship between the nozzle structure parameters and the near-target cavitation performance. Output the trained BP-SVR combined prediction model. The near-target region is the line segment region at a distance of 1 mm, 2 mm, and 3 mm from the target surface.

[0056] It should be noted that, in another optional embodiment, the BP feature extraction network of the BP-SVR combined prediction model can be replaced with other deep learning feature extraction networks, such as convolutional neural networks (CNN), residual networks (ResNet), or long short-term memory networks (LSTM). As long as the original input structural parameters can be mapped into low-dimensional deep feature vectors, they can be combined with SVR to complete regression modeling. The SVR surrogate modeling module can also be replaced with other regression models such as Gaussian process regression (GPR) and extreme gradient boosting (XGBoost).

[0057] It should be noted that existing technologies generally focus on parameters such as nozzle exit velocity, peak pressure in the free jet region, or overall cavitation intensity. However, in actual engineering scenarios such as concrete demolition and marine debris removal, the substantial damage to the target material is not caused by the free jet itself, but by the violent aggregation and collapse of cavitation bubbles as they approach the target surface. Traditional evaluation indicators, due to neglecting the wall confinement effect and pressure reflection effect, cannot accurately characterize the conversion efficiency of jet energy into impact kinetic energy, leading to significant deviations between optimization results and actual operational effects. The near-target region defined in this invention directly corresponds to the high-frequency occurrence zone of cavitation bubble collapse. By selecting line segments at 1mm, 2mm, and 3mm from the target surface to construct the near-target region, and using the near-target region as the monitoring location, a precise setting is based on the impact dynamics characteristics of the cavitation jet. Within this range, the cavitation bubble volume expands to its limit and is about to collapse, and the peak value of its gas phase volume fraction directly reflects the number and energy density of collapsed cavitation bubbles per unit time. By using the peak time-averaged gas volume near the target surface as the optimization objective (output label), this invention forces the optimization algorithm to select nozzle structure parameters that promote cavitation transport to the target surface and concentrated collapse near the wall, rather than simply pursuing jet velocity. Experimental verification shows that the nozzle structure optimized based on this index has significantly better impact damage resistance under actual working conditions than nozzles optimized based on traditional indexes, truly realizing the transformation from flow field simulation optimization to engineering effectiveness optimization.

[0058] S40 uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structural parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structural parameter combination.

[0059] It should be noted that, in another optional embodiment, the Particle Swarm Optimization (PSO) algorithm can be replaced by other intelligent optimization algorithms, such as Genetic Algorithm (GA), Differential Evolution (DE), Whale Optimization (WOA), or Bayesian Optimization (BO). As long as the output of the BP-SVR surrogate model can be used as the fitness evaluation function for global search within the given constraints, the same optimization objective can be achieved.

[0060] This invention constructs a two-dimensional axisymmetric computational domain encompassing the target surface region, using the peak time-averaged gas volume near the target surface (1-3 mm from the target surface) as the optimization evaluation index. This overcomes the disconnect between traditional methods that target free jet flow field parameters and engineering realities, enabling a more direct and accurate characterization of the nozzle's actual cavitation impact damage capability on the target surface. Furthermore, it extracts deep nonlinear features of the nozzle structural parameters using a BP neural network, then inputs this feature vector into an SVR model to complete regression modeling, constructing a BP-SVR combined prediction model. This model effectively balances deep feature extraction capabilities with the advantage of small-sample generalization, overcoming the tendency of a single BP network to overfit under small-sample conditions and the limitations of a single SVR model for high-dimensional primitives. Overcoming the limitations of insufficient initial feature representation, this method achieves a balance between high prediction accuracy and strong generalization ability. Furthermore, it combines this combined surrogate model with the particle swarm optimization algorithm, using the trained BP-SVR model to replace the high-cost numerical simulation as the fitness evaluation function. This enables rapid global optimization of the design space under multi-parameter coupling conditions, significantly reducing the experimental and simulation costs in the optimization process. It solves the problems of low optimization efficiency, long computation cycle, and difficulty in meeting the rapid optimization needs of engineering using traditional methods. Overall, it forms a complete engineering optimization closed loop of numerical simulation dataset construction, deep feature extraction, surrogate modeling, and global optimization, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures.

[0061] in, Figure 3 The architecture diagram of the BP-SVR combined prediction model is shown. In this embodiment of the invention, the BP-SVR combined prediction model includes a BP feature extraction module, an SVR surrogate modeling module, and a PSO optimization module. The BP feature extraction module is a BP feature extraction network (Back Propagation Neural Network, BP network), the SVR surrogate modeling module is a support vector regression SVR model, and the PSO optimization module is used to perform global optimization within the structural parameter constraints using the particle swarm optimization (PSO) algorithm to obtain the optimal nozzle structure parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structure parameter combination. The BP feature extraction network includes an input layer, 6 hidden layers, and an output layer; the number of nodes in the hidden layers is 64, 32, 24, 16, and 8 respectively. The BP feature extraction network uses the ReLU function as its activation function, and the output layer outputs a 4-dimensional deep nonlinear feature vector.

[0062] It should be noted that the BP feature extraction network input layer contains four input nodes, denoted as O1, O2, O3, and O4, corresponding to the four original nozzle structural parameters. After the input variables are nonlinearly mapped through multiple hidden layers, a 4-dimensional feature layer is formed at the end of the network, with output nodes denoted as C1, C2, C3, and C4. This 4-dimensional feature layer is used to characterize the deep coupling relationship between the nozzle structural parameters and the cavitation jet performance. The extracted 4-dimensional deep nonlinear feature vectors C1, C2, C3, and C4 serve as inputs to the subsequent SVR model to establish a surrogate mapping relationship between the structural parameters and the near-target cavitation performance. Subsequently, based on the trained BP-SVR combined prediction model, the optimal combination of structural parameters is searched in the design space using the subsequent Particle Swarm Optimization (PSO) algorithm, thereby achieving performance prediction and optimization design of the nozzle structure.

[0063] In this embodiment of the invention, the Support Vector Regression (SVR) model uses the RBF kernel function, and the hyperparameters are set as follows: penalty coefficient C = 5.0, kernel function coefficient γ = 0.098, and insensitive loss function coefficient ε = 0.01. The BP-SVR combined prediction model employs a two-stage training method: the first stage trains the BP feature extraction network, using StandardScaler to standardize the input and target variables respectively, and trains using mini-batch supervised learning with a batch size of 32. The loss function is the mean squared error loss function, the optimizer is the Adam optimizer, the learning rate is set to 0.001, and the random seed is set to 42. The second stage trains the deep nonlinear feature vectors extracted by the BP feature extraction network into the SVR model, which uses the RBF kernel function for regression fitting. In the second stage, the final linear regression output layer of the BP feature extraction network is removed, retaining only the initial feature extraction part. Let the original input sample be X, and the nonlinear mapping process of the BP feature extraction network is represented as follows: , This represents the nonlinear mapping process of the BP feature extraction network. This represents the extracted low-dimensional deep features.

[0064] In this embodiment of the invention, the constructed BP-SVR combined prediction model effectively addresses the inherent shortcomings of single models in the field of cavitation jets by deeply fusing the representation learning ability of neural networks with the small-sample generalization advantage of support vector regression. Specifically, the BP-SVR combined prediction model employs a two-stage architecture of deep feature extraction and high-precision regression. It utilizes a BP feature extraction network with six hidden layers as the front-end feature extractor, and through layer-by-layer nonlinear mapping using the ReLU activation function, transforms the original 4D structural parameters into 4D deep feature vectors rich in physical information, overcoming the limitation of traditional SVR in handling high-dimensional nonlinear features. Subsequently, the support vector regression SVR model is used as the back-end regressor. Leveraging its advantage of minimizing structural risk under small-sample conditions, it overcomes the overfitting tendency of BP networks, achieving high-precision modeling of complex cavitation flow fields. Furthermore, by introducing StandardScaler normalization, the dimensional differences between nozzle structural parameters are eliminated, accelerating model convergence and improving stability. Combining Mini-batch with Adam optimizer further enhances the training efficiency and robustness of the model with limited samples. The two-stage decoupled training strategy (training BP first, then SVR) simplifies the parameter tuning difficulty and ensures the optimal matching between the feature space and the regression space.

[0065] Finally, experimental verification showed that the BP-SVR combined prediction model constructed in this invention exhibits excellent performance:

[0066] Extremely high goodness of fit: the coefficient of determination (R²) on both the training and test sets. 2 The values ​​reached 0.998 and 0.964 respectively, indicating that the model can explain more than 96.4% of the performance fluctuations and almost perfectly captures the nonlinear mapping relationship between parameters and performance.

[0067] Extremely low prediction error: the mean squared error (MSE) on the test set is only 0.013, and the mean absolute error (MAE) is only 0.090. This means that the model's predictions for unknown structures deviate very little from the actual simulation values, making it sufficient to replace high-cost CFD simulations as the fitness function for particle swarm optimization (PSO) and support the global optimization process.

[0068] In this embodiment of the invention, after the BP-SVR combined prediction model is trained, it replaces the high-cost numerical simulation. The PSO optimization module uses the Particle Swarm Optimization (PSO) algorithm to perform a global optimization search for the nozzle structure parameters. The optimization objective is to maximize the peak value of the near-target time-averaged gas volume, and the optimal parameter combination is iteratively searched under the constraints of the value ranges of each design variable. The main parameters of the PSO algorithm are set as follows: particle swarm size 50, inertia weight 0.729, individual learning factor and social learning factor both set to 1.494, and random seed set to 42.

[0069] The PSO algorithm quickly completes the solution space search and locks into high-fitness regions in the early stages of iteration, and basically reaches a stable convergence state around the 6th iteration. The optimal nozzle structure parameters are ultimately obtained as the throat length ratio. , length ratio of diffusion section Target distance ratio The predicted peak value of the near-target average gas volume was 89.25%; CFD simulation verified that the result was 86.32%, with a relative error of only about 3.28.

[0070] On the other hand, embodiments of the present invention also provide a cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and particle swarm optimization algorithm. Figure 4 A schematic diagram of a cavitation jet nozzle structure optimization system based on a BP-SVR prediction model and a particle swarm optimization algorithm is shown. The cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and the particle swarm optimization algorithm specifically includes:

[0071] The computational domain construction module 100 is used to construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle containing the target surface region, and to set the nozzle structure optimization variables and their value ranges.

[0072] The simulation dataset generation module 200 performs flow field simulation on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics methods, and constructs a simulation dataset using the simulation data.

[0073] The model training module 300 is used to construct the BP-SVR combined prediction model. It uses the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module, extracts deep nonlinear feature vectors based on the BP feature extraction module, inputs the deep nonlinear feature vectors into the SVR proxy modeling module, and uses the time-averaged gas volume peak value in the near-target region as the output label for training. It establishes a proxy mapping relationship between the nozzle structure parameters and the near-target cavitation performance, and outputs the trained BP-SVR combined prediction model.

[0074] The optimization solution module 400 uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structural parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structural parameter combination.

[0075] In summary, this invention provides a method and system for optimizing cavitation jet nozzle structures based on a BP-SVR prediction model and particle swarm optimization algorithm. By constructing a symmetric computational domain, this invention can more directly and accurately characterize the actual cavitation impact damage capability of the nozzle on the target surface. Furthermore, by constructing and training a BP-SVR combined prediction model and using it as a fitness evaluation function, it achieves rapid global optimization of the design space under multi-parameter coupling conditions, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures. Specifically, by constructing a two-dimensional axisymmetric computational domain including the target surface region, and using the time-averaged peak gas volume near the target surface (1-3 mm from the target surface) as the optimization evaluation index, this invention overcomes the problem of disconnection from engineering practice caused by traditional methods that target free jet flow field parameters, enabling a more direct and accurate characterization of the nozzle's actual cavitation impact damage capability on the target surface. Finally, by extracting deep nonlinear features of the nozzle structure parameters through a BP neural network, and then applying these features to... By inputting the SVR model to complete regression modeling, a BP-SVR combined prediction model was constructed, effectively balancing the ability of deep feature extraction with the advantage of small-sample generalization. This overcomes the limitations of a single BP network being prone to overfitting under small-sample conditions and the insufficient ability of a single SVR to express high-dimensional original features, achieving a unity of high prediction accuracy and strong generalization ability. Furthermore, this combined surrogate model was combined with the particle swarm optimization algorithm, using the trained BP-SVR model to replace the high-cost numerical simulation as the fitness evaluation function. This enabled rapid global optimization of the design space under multi-parameter coupling conditions, significantly reducing the experimental and simulation costs in the optimization process. It solved the problems of low optimization efficiency, long computation cycle, and inability to meet the rapid optimization needs of engineering using traditional methods. Overall, a complete engineering optimization closed loop was formed, consisting of numerical simulation dataset construction, deep feature extraction, surrogate modeling, and global optimization, providing a reliable technical approach for the intelligent and efficient optimization of cavitation jet nozzle structures.

[0076] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0077] It should be understood that the disclosed apparatus can be implemented in other ways, given the several embodiments provided in this application. For example, the apparatus embodiments described above are merely illustrative; the division of units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or communication connections shown or discussed may be through some interfaces; the indirect coupling or communication connections between devices or units may be telecommunications or other forms.

[0078] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. A method for optimizing the structure of a cavitation jet nozzle based on a BP-SVR prediction model and a particle swarm optimization algorithm, characterized in that, The method includes: S10, construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle containing the target surface region, and set the nozzle structure optimization variables and their value ranges; S20, based on computational fluid dynamics, the flow field simulation of the nozzle structure corresponding to the nozzle structure optimization variables is performed, and the simulation dataset is constructed using the simulation data; S30. Construct a BP-SVR combined prediction model. Use the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module. Extract deep nonlinear feature vectors based on the BP feature extraction module. Input the deep nonlinear feature vectors into the SVR proxy modeling module. Use the time-averaged gas volume peak value in the near-target region as the output label for training. Establish a proxy mapping relationship between nozzle structure parameters and near-target cavitation performance. Output the trained BP-SVR combined prediction model. S40 uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structural parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structural parameter combination.

2. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 1, characterized in that: The nozzle structure optimization variables adopt dimensionless parameters, including: throat length ratio, diffuser length ratio, diffuser angle, contraction angle ratio, and target distance ratio.

3. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 2, characterized in that: In step S10, the two-dimensional axisymmetric computational domain of the cavitation jet nozzle includes the upstream extension section of the nozzle inlet, the downstream flow field computational domain, and the near-target impact region. When constructing the two-dimensional axisymmetric computational domain of the cavitation jet nozzle that includes the target region, the upstream extension section of the nozzle inlet extends 20mm upstream of the cavitation jet nozzle inlet to ensure that the inlet flow field is fully developed. The downstream flow field computational domain is set as a symmetrical rectangular region with a length of 120 mm and a width of 40 mm; the near-target impact region is a symmetrical target region downstream of the nozzle, with a width of 5 mm and a length of 10 mm; the boundary conditions of the two-dimensional axisymmetric computational domain are set as follows: pressure inlet 10 MPa, pressure outlet, symmetry line and wall.

4. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 1, characterized in that: The near-target area is a line segment region located 1mm, 2mm, and 3mm away from the target surface.

5. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 1, characterized in that: In step S20, when performing flow field simulation on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics, the delayed separated eddy simulation (DDES) method based on the k-ε model is adopted, and curvature correction is introduced to solve the two-dimensional unsteady flow field of the cavitation jet nozzle.

6. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 1, characterized in that: The BP-SVR combined prediction model includes a BP feature extraction module, an SVR surrogate modeling module, and a PSO optimization module. The BP feature extraction module is a BP feature extraction network, and the SVR surrogate modeling module is a support vector regression SVR model.

7. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 6, characterized in that: The BP feature extraction network includes an input layer, six hidden layers, and an output layer; the number of nodes in the hidden layers are 64, 32, 24, 16, and 8 respectively. The BP feature extraction network uses the ReLU function as its activation function, and the output layer outputs a 4-dimensional deep nonlinear feature vector.

8. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 7, characterized in that: The Support Vector Regression (SVR) model uses the RBF kernel function, with the hyperparameters set as follows: penalty coefficient C = 5.0, kernel function coefficient γ = 0.098, and insensitive loss function coefficient ε = 0.

01.

9. The cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in claim 8, characterized in that: The BP-SVR combined prediction model adopts a two-stage training approach: In the first stage, the BP feature extraction network is trained, and the input and target variables are standardized using StandardScaler. The training is conducted using a mini-batch supervised learning method with a batch size of 32, a mean squared error loss function, and an Adam optimizer with a learning rate of 0.

001. In the second stage, the deep nonlinear feature vectors extracted by the BP feature extraction network are input into the support vector regression (SVR) model, which uses the RBF kernel function for regression fitting.

10. A cavitation jet nozzle structure optimization system based on BP-SVR prediction model and particle swarm optimization algorithm, used to implement the cavitation jet nozzle structure optimization method based on BP-SVR prediction model and particle swarm optimization algorithm as described in any one of claims 1-9, characterized in that: The cavitation jet nozzle structure optimization system based on the BP-SVR prediction model and particle swarm optimization algorithm includes: The computational domain construction module is used to construct a two-dimensional axisymmetric computational domain for the cavitation jet nozzle that includes the target surface region, and to set the nozzle structure optimization variables and their value ranges. The simulation dataset generation module performs flow field simulation on the nozzle structure corresponding to the nozzle structure optimization variables based on computational fluid dynamics methods, and constructs a simulation dataset using the simulation data. The model training module is used to construct the BP-SVR combined prediction model. It uses the nozzle structure parameters in the simulation dataset as the input of the BP feature extraction module, extracts deep nonlinear feature vectors based on the BP feature extraction module, and inputs the deep nonlinear feature vectors into the SVR proxy modeling module. It uses the time-averaged gas volume peak value in the near-target region as the output label for training, establishes the proxy mapping relationship between the nozzle structure parameters and the near-target cavitation performance, and outputs the trained BP-SVR combined prediction model. The optimization solution module uses the trained BP-SVR combined prediction model as the fitness evaluation function and employs the particle swarm optimization (PSO) algorithm to perform global optimization within the structural parameter constraints in order to obtain the optimal nozzle structure parameter combination that maximizes the peak value of the time-averaged gas phase volume near the target surface, and outputs the optimal nozzle structure parameter combination.

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