A high-speed multi-projectile parallel water-entry stability analysis method

Abstract

The application discloses a high-speed multi-projectile parallel water-entry stability analysis method, which comprises the following steps: determining core parameters affecting water-entry stability; using the core parameter group as a modeling base matrix to establish a projectile flow-solid two-phase calculation domain, dividing the calculation domain grid, setting fluid domain initial and boundary conditions, setting solid material properties and initial working conditions, and performing simulation to obtain the determination of whether the projectile is unstable, and combining existing data to construct a core input parameter matrix; normalizing the data of the core input parameter matrix, dividing the training set and the verification set, using a DNN neural network, defining the core input parameter matrix of the training set as an input parameter, defining the stability state of the later projectile as an output result, and establishing a plurality of fully connected neural networks therebetween; and verifying the trained neural network with the verification set. The application can provide certain help for projectile motion stability determination.

Description

Technical Field

[0001] This invention belongs to the field of cross-medium water entry, specifically relating to a method for analyzing the stability of high-speed multi-ballistic parallel water entry. Background Technology

[0002] The water entry problem, namely the transient process of an object moving from an air medium through a free water surface into a body of water, is a classic and important research direction in fluid mechanics. This process involves complex multiphase flow, compressibility effects, cavitation dynamics, and the coupling effect with structures, accompanied by strong unsteady, nonlinear, and multi-scale physical phenomena, mainly including stages such as initial impact, cavitation generation, development, closure, and even collapse. In-depth research on the water entry mechanism has crucial engineering application value for many fields such as naval weaponry, aerospace, shipbuilding, and ocean engineering. For a long time, scholars at home and abroad have conducted systematic and in-depth research on the single-projectile water entry problem, forming a relatively mature theoretical, experimental, and numerical method system. However, in practical engineering applications, especially in situations such as multi-projectile coordinated strikes, cluster munitions, and high-speed projectile cluster water entry, the parallel or sequential water entry of multiple projectiles is a more common and realistic physical scenario. Compared with single-projectile water entry, the parallel water entry problem of multiple projectiles exhibits a qualitatively increased complexity in its physical mechanism. It not only includes the water entry flow of each projectile itself, but more importantly, it introduces strong hydrodynamic interference between projectiles. This interference is mainly manifested in the following ways: the cavitation generated by the first missile body and its evolution will significantly change the pressure distribution of the flow field around the subsequent missile body; multiple cavitation bodies may interact with each other through compression, fusion, tearing, etc.; the pressure waves and velocity fields generated by the missile body displacing water will affect each other; these factors are coupled together, fundamentally changing the hydrodynamics acting on each missile body, thus causing complex deviations in its trajectory and attitude stability that are difficult to predict using experience with a single missile body, and even inducing collisions between missile bodies.

[0003] Most current research focuses on simple geometric shapes, such as spheres and cylinders, under low-speed or subsonic conditions. However, when entering water at high speeds (generally, in engineering, the velocity of a projectile is considered to be...),... At high speeds, the intense shock wave generated at the projectile's leading edge interferes with the free water surface, producing initial impact loads, cavitation generation mechanisms, and flow separation characteristics drastically different from those at low speeds. The strong cross-domain coupling between aerodynamic and hydrodynamic effects makes it difficult to directly extrapolate and apply the force and trajectory patterns obtained under low-speed conditions. Existing research largely focuses on post-hoc reproduction and mechanistic analysis of flow fields and motions under specific conditions through experiments or CFD simulations. There is a lack of a universal, parameterized stability analysis theory and method applicable to forward prediction. Engineers cannot quickly evaluate the water entry stability envelope of different high-speed, multi-projectile configurations, such as under varying numbers, spacing, and timing, during the weapon system design phase. They can only rely on costly full-scale experiments or massive CFD simulations, resulting in lengthy design cycles, high costs, and difficult optimization. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the stability of multiple high-speed projectiles entering water in parallel. This method can evaluate the motion stability of multiple high-speed projectiles launched in quick succession during the moment of entry into water across a medium and during the underwater navigation phase, thereby providing some assistance in determining the motion stability of high-speed projectiles entering water.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for analyzing the stability of high-speed multiple missiles entering water in parallel includes:

[0007] Step 1: Identify the core parameters affecting water entry stability, including: the ratio of the distance between the projectiles to the average diameter of the two projectiles. The ratio of the distance traveled by the first projectile over a period of time to the length of the second projectile. Froude number corresponding to the projectile body The ratio of the maximum radius of the cavitation generated by the first water-entry projectile to the distance between the two projectiles. The moment of inertia of the second projectile along the axis perpendicular to its cross-sectional diameter. ;

[0008] Step 2: Using the aforementioned core parameters as the modeling basis matrix, establish the projectile fluid-solid two-phase computational domain, mesh the computational domain, set the initial and boundary conditions of the fluid domain, set the solid material properties and initial working conditions, and obtain the modeling results through simulation. , To determine whether the projectile is unstable, and to construct the core input parameter matrix based on existing data;

[0009] Step 3: Normalize the data of the core input parameter matrix, divide it into training set and validation set, use DNN neural network, define the core input parameter matrix of the training set as input parameter, define the stability state of the subsequent projectile as output result, and establish several fully connected neural networks in between.

[0010] Step 4: Validate the trained neural network using a validation set, that is, compare the output of the DNN network with the actual results. If the accuracy is met, the model training is complete.

[0011] The significant advantages of this invention compared to existing technologies are:

[0012] (1) It can effectively improve computational efficiency and quickly realize design iteration. A single CFD simulation of a working condition takes several hours to several days. Exploring the influence of parameters is extremely costly, while a trained DNN model only takes milliseconds to perform a forward prediction. Stability scanning of tens of thousands of parameter combinations can be completed in seconds.

[0013] (2) Traditional methods rigorously solve physical equations, but when faced with the extreme complexity of "high speed + multiple missiles + parallelism", the computational cost increases exponentially, and the strong coupling effect makes it difficult to intuitively extrapolate the results. DNN can learn the complex relationships of extremely complex nonlinear relationships such as transonic shock waves, cavitation interaction, and multi-body interference from limited high-fidelity data, without the need to explicitly model every physical detail.

[0014] (3) Due to the inconsistent weights of the core parameters influencing water ingress stability, the deep learning neural network we constructed abandoned the traditional mean squared error (MSE) loss function and instead adopted the cross-entropy loss function. This will more accurately allocate the influence weights of the core parameters based on existing research results, avoiding the decisive influence of some large-value core parameters on the results, thus ignoring the influence of small-value parameters on the final results. Attached Figure Description

[0015] Figure 1 A simplified schematic diagram of a supercavitating projectile.

[0016] Figure 2 This is a schematic diagram of the overall process.

[0017] Figure 3 A schematic diagram showing the setup of the simulation domain.

[0018] Figure 4 This is a schematic diagram of the data preprocessing process.

[0019] Figure 5 This is a phase diagram of the projectile entering the water.

[0020] Figure 6 This is a curve showing the lateral force coefficients of a twin-engine projectile.

[0021] Figure 7 A framework diagram for building a DNN neural network.

[0022] Figure 8 Flowchart for network model validation. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] The following provides specific implementation parameters and a supercavitating projectile model, and performs high-speed multi-projectile parallel water entry stability analysis. The authenticity of this method is further verified by cross-medium water entry simulation calculation and the construction of a DNN neural network.

[0025] To save computational resources, the supercavitating projectile in this example is simplified to a cylinder, and the geometric parameters of the two projectiles are completely identical. The initial velocities of the two projectiles are set to... , into the water corner The two projectiles are [length] ,diameter The aspect ratio is 5, and the material chosen is structural steel with a density of 7. ,like Figure 1 As shown. The implementation process of this invention is as follows. Figure 2 As shown.

[0026] Step 1: Identify the core parameter affecting water ingress stability: dimensionless number Defined as the ratio of the distance between the projectiles to the average diameter of the two projectiles, i.e. ,in The maximum diameter of the two projectiles. The distance between the axes of the two projectiles; dimensionless number Defined as the ratio of the distance traveled by the first projectile over a period of time to the length of the second projectile, i.e. The launch timing difference between the two projectiles The initial velocity of the first projectile upon entering the water was The Froude number corresponding to the projectile. ,in The initial velocity of the projectile, The acceleration due to gravity; the dimensionless number Gr is defined as the ratio of the maximum radius of the cavitation bubble generated by the first water-entering projectile to the distance between the two projectiles, i.e. ,in The maximum radius of the cavitation bubble evolved from the first projectile; the moment of inertia of the second projectile along the axis perpendicular to its cross-sectional diameter. ,in The mass of the second projectile;

[0027] Step 2: Construct the modeling basis matrix from the above core parameters. The form of the modeling basis matrix is ​​consistent with that of the core parameter input matrix. The modeling basis matrix is ​​used to parametrically model core parameters that are insufficient or not fully considered in the publicly available data. Establish a fluid-solid two-phase computational domain, divide the computational domain into meshes, and use overlapping mesh technology in dynamic meshing outside the projectile. The projectile wall in contact with the fluid phase needs good matching. Set the initial and boundary conditions of the fluid domain, set the material properties of the solid structure, and assign it initial working conditions, such as an initial velocity of 0.5%. 100 m / s, all projectiles enter the water vertically. In this embodiment, two different... ,Right now , The launch interval is ; , Froude numbers are represented as ,in It is the acceleration due to gravity, take ; After simulation calculation, it was determined to be... ; after 3D modeling, the result is The specific simulation domain settings are as follows: Figure 3 As shown, the final simulation results are as follows: Figure 5 As shown, the lateral force coefficient Both values ​​are less than 1%, meaning there is no instability under either operating condition. Among publicly available data, the data with statistical examples is... , , , , However, the lateral force coefficient of the second projectile... It is generally believed that a lateral force coefficient exceeding 5% indicates a risk of instability, and exceeding 8% makes instability highly likely. Therefore, in this example, the final result is instability. The specific lateral force coefficient curve is shown below. Figure 6 As shown in Table 1 below, the core parameter values ​​are transformed into a core input parameter matrix.

[0028] Table 1 Core Parameter Input Matrix

[0029]

[0030] Step 3: Solve the operating conditions and combine them with publicly available data. First, perform normalization processing, that is, normalize the values ​​of all input core parameters to... Between these two sets, the training and validation sets are randomly divided in a ratio of 0.8:0.2 to prevent overfitting after using all the data for training, which would further reduce prediction accuracy. The specific preprocessing procedure is as follows: Figure 4As shown; this invention employs a DNN neural network, defining the core parameter matrix within the training set as the input parameters and the stability state of the subsequently launched projectile as the output result, for supervised learning; a connection is established between the parameter input layer and the result output layer containing A fully connected neural network with n hidden layers uses gradient descent with the chain rule and backpropagation. The complete chain rule update process can be represented as:

[0031]

[0032]

[0033] in, for Cross-entropy loss is a manually defined loss function used to measure the difference between the predicted output layer and the true value. In other words, it's a human-chosen method to describe the absolute difference between the predicted and true solutions of the neural network. In this embodiment, the cross-entropy loss function is chosen; the specific formula will be mentioned later. The core purpose of deep learning neural networks is to adjust biases... With weight This allows the loss function to continuously decrease, eventually approaching the true value; For the current index layer; For the first The error term matrix of the layer represents the loss function with respect to the th layer. The gradient of the layer-weighted input is the core intermediate variable for backpropagation; For the first The weighted input matrix of the layer, ; For the first The activation output matrix of the layer, superscript This is the matrix transpose symbol. Indicates the first The weight matrix of the layer, Indicates the first The bias matrix of the layer, This represents element-wise multiplication (Hadamard product). Where, when hour, Input the matrix for the core parameters. In the initial stage of deep learning, the Dropout method is set to regularize the data; the specific formula is as follows:

[0034]

[0035] in, Indicates the first The original activation output matrix of the layer, Indicates the first The output matrix of the layer after Dropout. For the first The mask value tensor (0 or 1) of the layer neurons. To preserve the probability, a scaling compensation is manually applied to the denominator to ensure the expected value remains unchanged. In this embodiment, the probability of retaining the intermediate hidden layer in the first three layers is set to 0.7, and the probability of retaining the intermediate hidden layer in the last two layers is set to 0.8.

[0036] During backpropagation, differentiation is required. To reduce the computational cost of backpropagation and improve computational speed, this embodiment uses ReLU as the activation function between hidden layers of the neural network, and its derivative is:

[0037]

[0038] in, This is represented as a weighted input matrix for a certain layer. Furthermore, ReLU itself is nonnegative, giving it a natural advantage in handling engineering data, and no activation function is set between the final hidden layer and the output layer; regarding learning parameter settings, the learning rate of the input parameters... The Decay pattern is used in conjunction with the Adam optimizer, meaning that the learning rate of each parameter increases with the number of iterations. The learning rate will gradually decrease, and the Adam optimizer can further adaptively adjust the learning rate for each parameter; the neural network is initialized in the first iteration:

[0039]

[0040] in, The initial matrix of first-order moment (momentum) has the same dimension as the input parameters and is initially set to 0. It is the second-order moment (uncentered variance) initial matrix, with the same dimension as the input parameters, and is initially set to 0. This is the number of training iterations (time steps), counted starting from 0. For each training iteration... (No. Step update), calculate the current gradient:

[0041]

[0042] in, For loss function For the set of all parameters The gradient of . Where the subscript Representing the Time step, i.e. It is the first The set of all hyperparameters at the end of the step (all weights W and biases b). It is the first The gradient matrix is ​​obtained by step calculation.

[0043] Update the first-order moment estimate (momentum term) and the second-order moment estimate (adaptive term):

[0044]

[0045]

[0046] in, This is the first-order moment decay rate hyperparameter, which controls the degree to which historical gradient information is retained; it is usually set to 0.9. For the first First-moment estimation of the step (mean gradient with decay). It is the second-order moment decay rate hyperparameter, which controls the degree to which historical gradient squared information is preserved, and is usually set to 0.999. For the first Second-order moment estimation of the step (mean squared gradient with decay).

[0047] Calculate the first and second moments after deviation correction:

[0048]

[0049]

[0050] As time goes by Increase Approaching 1, This is the first-order moment estimate after bias correction. In the early stages of training ( When the value is small, the correction range is large; This is the second-order moment estimate after bias correction. The next step is to update various hyperparameters of the model, such as weights. paranoia wait:

[0051]

[0052] For the first The dynamic learning rate of the step; The numerical stability constant is typically set to 10⁻ 8 To prevent the denominator from being zero. It is the first Take the square root of each element of the corrected second moment; For the first The step refers to the various hyperparameters of the model in the previous step. For the first The updated model has various hyperparameters.

[0053] Regarding the final selection of the loss function, the cross-entropy loss function is adopted, and the specific formula is as follows:

[0054]

[0055] in, Let cross-entropy be the loss function. Total number of categories; It is a Boolean number for the category Its value is 1 if it is true, otherwise it is 0. The model predicts that the sample belongs to a certain category. The probability of; For a specific category The weights are set. In this embodiment, There are five categories of core parameters. This cross-entropy loss function can more accurately allocate the influence weights of core parameters based on existing research findings, avoiding the decisive influence of some large-valued core parameters on the results, thus ignoring the influence of small-valued parameters in the final result. , , , , In a specific embodiment of this invention, during the high-speed, multi-projectile parallel entry into water process, This core parameter has a significant impact on the stability of parallel water inflow, and the initial weights... , The impact on the stability of parallel water inflow is relatively small, and the initial weights are... The total weight sum is 1, that is , The weight name of the current index, for example The specific structure of a DNN neural network is as follows: Figure 7 As shown;

[0056] Step 4: Validate the trained neural network using a validation set, i.e., compare the predicted solutions of the DNN network with the actual solutions. It is generally assumed that if the accuracy requirement is met... If the accuracy is low, then the model is considered to have completed training. The initial value is used, and the iteration decay amplitude of the decay mode is further reduced. Then, the simulation data is supplemented to retrain the DNN neural network until the accuracy reaches the requirement. That is, the construction and training of a neural network model for evaluating the stability of high-speed multiple missiles entering water in parallel is completed. The specific verification flowchart is as follows. Figure 8 As shown. Finally, the DNN neural network training is completed, resulting in a high-speed, multi-projectile parallel water entry stability analysis method.

[0057] Clearly, compared to physical experiments and the need for repeated cross-medium parallel water entry simulations for each new operating condition, the deep learning neural network model constructed in this study provides an efficient and accurate solution. This model can not only autonomously learn extremely complex nonlinear relationships such as cavitation and cavitation-bubble interaction from limited simulation and literature data, but the trained model can also achieve rapid forward prediction, greatly improving prediction speed. Furthermore, to more accurately reflect the differences in the weights of each core parameter's influence on stability, the model abandons the traditional mean squared error loss function and instead uses the cross-entropy loss function for optimization, ensuring that the training process is not dominated by parameters with large numerical magnitudes, thus more reasonably evaluating the contribution of all key parameters. In summary, the method of this invention can achieve accurate and rapid prediction and analysis of the stability of high-speed multi-missile parallel water entry based on a trained neural network model.

[0058] Obviously, the above embodiments of the present invention are merely examples to clearly illustrate the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for analyzing the stability of high-speed multiple missiles entering water in parallel, characterized in that, include: Step 1: Identify the core parameters affecting water entry stability, including: the ratio of the distance between the projectiles to the average diameter of the two projectiles. The ratio of the distance traveled by the first projectile over a period of time to the length of the second projectile. Froude number corresponding to the projectile body The ratio of the maximum radius of the cavitation generated by the first water-entry projectile to the distance between the two projectiles. The moment of inertia of the second projectile along the axis perpendicular to its cross-sectional diameter. ; Step 2: Using the aforementioned core parameters as the modeling basis matrix, establish the projectile fluid-solid two-phase computational domain, mesh the computational domain, set the initial and boundary conditions of the fluid domain, set the solid material properties and initial working conditions, and obtain the modeling results through simulation. , To determine whether the projectile is unstable, and to construct the core input parameter matrix based on existing data; Step 3: Normalize the data of the core input parameter matrix, divide it into training set and validation set, use DNN neural network, define the core input parameter matrix of the training set as input parameter, define the stability state of the subsequent projectile as output result, and establish several fully connected neural networks in between. Step 4: Validate the trained neural network using a validation set, that is, compare the output of the DNN network with the actual results. If the accuracy is met, the model training is complete.

2. In the high-speed multi-missile parallel water entry stability analysis method according to claim 1, the DNN deep neural network model in step 3 adopts a fully connected neural network, and uses the backpropagation chain rule to solve the hyperparameters by gradient and descent along the gradient. The calculation is as follows using the chain rule: 4.

1. Section The layer output error term is: 4.

2. Section Hidden layer error term: 4.

3. The complete chain rule update process can be represented as: in, The cross-entropy loss function; This represents the total number of network layers. For the current index layer; For the first The error term matrix of the layer represents the loss function with respect to the th layer. Gradient of layer-weighted input; For the first The weighted input matrix of the layer, For the first The activation output matrix of the layer, This represents element-wise multiplication. It is the first The derivative of the layer activation function, where, when hour, For the input feature matrix, Indicates the first Weight matrix of layer +1, superscript This is the matrix transpose symbol. Indicates the first The layer's bias matrix is ​​adjusted by the bias. With weight The hyperparameters are configured to continuously reduce the loss function.

3. The integrated evaluation method for the static stability margin of a supercavitating projectile across media according to claim 1, characterized in that, In the initial stage, the DNN deep neural network model uses Dropout technology to regularize the data. The specific formula is as follows: in, Indicates the first The original activation output matrix of the layer, Indicates the first The output matrix of the layer after Dropout. For the first The mask value tensor of layer neurons, To preserve probability.

4. The method for analyzing the stability of high-speed multi-projectile parallel water entry according to claim 1, characterized in that, The ReLU activation function is used between layers of a deep neural network (DNN) model, and its derivative is: in, It is represented as a weighted input matrix for a certain layer.

5. The method for analyzing the stability of high-speed multi-projectile parallel water entry according to claim 2, characterized in that, The specific formula for the cross-entropy loss is as follows: in, Total number of categories; For the true category Its value is 1 if it is true, otherwise it is 0. The model predicts that the sample belongs to category [class name missing]. The probability of; For a specific category The weights set.

6. The method for analyzing the stability of high-speed multi-projectile parallel water entry according to claim 2, characterized in that, The DNN deep neural network model described in step 3 adopts a decay mode for the learning rate of the input parameters, and combined with the Adam optimizer, it can adaptively adjust the learning rate for each hyperparameter. Perform initialization: in, The first moment: the initial matrix, with the same dimension as the input parameters; It is the second-order moment initial matrix, with the same dimension as the input parameters. It is the number of training iterations; for each training iteration Calculate the current gradient: in, For loss function For the set of all parameters gradient, It is the first The set of all hyperparameters at the end of the step. It is the gradient matrix calculated in step t; Update the first-order moment estimate and the second-order moment estimate: in, The first-order moment decay rate hyperparameter, For the current first moment estimate, It is the second-order moment decay rate hyperparameter. This is the current second-order moment estimate; Calculate the first and second moments after deviation correction: This is the first-order moment estimate after bias correction. This is the second-order moment estimate after bias correction; the next step is to update the model parameters: Let be the dynamic learning rate at step t; It is the numerical stability constant. These are the updated parameters.

7. The method for analyzing the stability of high-speed multi-projectile parallel water entry according to claim 2, characterized in that, The ratio of the distance traveled by the first projectile over a period of time to the length of the second projectile. The calculation formula is: ,in The launch timing difference between the two projectiles. H represents the initial velocity of the first projectile upon entering the water, and H represents the length of the projectile.

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