A method for rapid performance evaluation of hypersonic interceptor

Abstract

The application discloses a kind of hypersonic interceptor performance rapid evaluation method.The present application uses neural network as proxy model framework, utilizes the engineering experience accumulated by design personnel in the process of model design, fills the mapping law between working condition parameters and target performance, integrates engineering experience into neural network, makes up the problem of low prediction accuracy of small sample data.Finally, the test error of the neural network proxy model obtained by training is within 0.5%, indicating that the neural network proxy model established by the present application can obtain higher precision aerodynamic performance parameter prediction results, and has good generalization ability.

Description

Technical Field

[0001] This invention relates to the field of interceptor aerodynamic performance evaluation technology, and specifically to a rapid performance evaluation method for hypersonic interceptors. Background Technology

[0002] To counter the threat of near-space hypersonic interceptors (speeds exceeding Mach 5), developing and establishing new weapon defense systems is essential, with ground-based interception being an effective deterrent. However, the thin air in near space results in insufficient aerodynamic force for interceptor missiles, and traditional control surface methods cannot meet their maneuverability and overload requirements. To overcome the shortcomings of traditional control surface methods and achieve rapid response to control commands, direct force / aerodynamic composite control is currently the more ideal approach. This method enables the interceptor missile control system to have a faster response speed and overload capacity, effectively improving strike accuracy. By employing a combined aerodynamic and direct force control approach, the interceptor's maneuverability response time can be significantly reduced, greatly enhancing its maneuverability, such as... Figure 1 As shown.

[0003] However, the flow characteristics of the direct force jet and the supersonic incoming flow are extremely complex, involving shock wave interference and shock wave-boundary layer interference, resulting in severe force and moment interference on the interceptor missile. This makes computer simulation of supersonic interceptors with jets very time-consuming and difficult to optimize. The design optimization of supersonic interceptors with jets has the following characteristics: high dimensionality, black box nature, and high cost. These characteristics lead to a huge design space that needs to be explored, and designers must spend a lot of time and money on computer simulations to find the optimal design. To quickly obtain an initial solution, one effective method to solve this problem is to build a surrogate model (also known as a meta-model, response surface model, or simulator) to replace computer simulation, and then apply optimization techniques to obtain the optimal design. By using surrogate model techniques, it is possible to avoid calling costly numerical analysis models extensively, thereby reducing computational costs.

[0004] While some research and experiments have been conducted both domestically and internationally on constructing surrogate models for aerodynamic performance, these studies primarily rely on abundant sample data, resulting in substantial data requirements. For interceptor design problems under jet interference, the availability of data is significantly reduced due to the time-consuming and expensive nature of computer simulations. In small sample cases, the mapping relationship between some design variables and target performance is missing, leading to consistently high prediction errors regardless of hyperparameter selection. Therefore, finding a method for constructing surrogate models with small sample sizes is crucial for accurate prediction of supersonic interceptor performance. Summary of the Invention

[0005] In view of this, the present invention provides a method for rapid evaluation of the performance of hypersonic interceptors. It utilizes the engineering experience accumulated by designers to supplement the missing mapping rules by integrating engineering experience. The summarized experience (the correspondence between design variables and target performance) is incorporated into the neural network to achieve rapid evaluation of the performance parameters of hypersonic interceptors under small sample conditions and improve prediction accuracy.

[0006] The present invention provides a method for rapid performance evaluation of hypersonic interceptors based on neural networks, comprising:

[0007] Step 1, obtain the training dataset; the training dataset includes real simulation data and engineering experience data;

[0008] The method for obtaining real simulation data is as follows: using computational experimental design methods, sample points of operating parameters are obtained within the initial design space, and the corresponding aerodynamic performance response values ​​are obtained through engineering experiments or data simulation.

[0009] The engineering experience data is obtained by having designers use their engineering experience to draw a fitting curve of the relationship between operating parameters and aerodynamic performance using Bézier curves, and then achieve gradient characterization based on the derivative of the control points of the Bézier curves.

[0010] Step 2: Construct a neural network and initialize its parameters. The input to the neural network is the operating parameters of the interceptor, and the output is the performance parameters of the interceptor. The loss function consists of a data term loss function based on real simulation data and an empirical term loss function based on engineering experience data. The data term loss function is the mean square error between the neural network's predicted value and the true value. The empirical term loss function is the mean square error of the gradients of the neural network's input and output and the corresponding gradients of the Bézier curves.

[0011] Step 3: Using the training dataset obtained in Step 1, train the neural network constructed in Step 2 to obtain the trained neural network.

[0012] Step 4: Use the trained neural network to evaluate the aerodynamic performance of the hypersonic interceptor.

[0013] Preferably, the operating parameters include: shape parameters, operating condition parameters, and aerodynamic characteristic data.

[0014] Ideally, for a specific hypersonic interceptor, its shape parameters are set as invariants.

[0015] The main operating parameters include Mach number Ma, angle of attack α, altitude h, and roll angle. Rudder deflection angle DEL, attitude control jet pressure ratio p zj The pressure ratio of the attitude control jet to p zgj ;

[0016] The main aerodynamic characteristic parameters include fundamental aerodynamic quantities, such as the overall projectile normal force coefficient c. y1 The pitching moment coefficient of the entire missile m z1 Normal force coefficient Δc caused by rudder deflection y1(δ) The pitching moment coefficient Δm caused by rudder deflection z1(δ) ; and aerodynamic disturbances, including: the increase in the normal force coefficient Δc of the entire projectile caused by the jet. y1(j) The increase in pitching moment Δm caused by the jet stream z1(j) The influence of the jet stream on the normal force coefficient Δ(Δc) caused by rudder deflection y1(δ) ) j The influence of jet flow on the pitching moment coefficient Δ(Δm) caused by rudder deflection z1(δ) ) j .

[0017] A preferred method for acquiring engineering experience data is as follows: Add Bézier curve control points to the coordinate system. Designers can obtain the fitted curve by increasing or decreasing the number of control points and dragging their positions. After completing the knowledge drawing, designers save the coordinates of the control points of the current experience knowledge curve, thus completing the entire knowledge acquisition process.

[0018] Preferably, the neural network is a Bayesian neural network, a backpropagation neural network, or an evolutionary neural network.

[0019] A preferred approach is to initially set the weights w and biases b of the Bayesian neural network by sampling from a standard Gaussian distribution and scaling the sampled values.

[0020] A = μ + σε;

[0021] Where A represents the weight w or bias b; μ and σ are the weight or bias Gaussian distributions N(μ, σ) and N(μ, σ), respectively. 2 The mean and variance of ; ε represents the standard normal distribution.

[0022] Ideally, the loss function of a Bayesian neural network consists of two parts: a data term and an empirical term. A lower loss function value indicates better model training performance. The formula for the loss function is as follows:

[0023] Loss Function = loss data +loss exp

[0024] Where, loss data The loss function for the data items is as follows:

[0025]

[0026] Wherein q(w i |θi ) represents the weight parameter w given a normal distribution. i The distribution of θ; i p(w) represents the prior distribution of the weights. i ) represents the prior of the weights; p(D|w i ) represents the likelihood of the observed data given the network parameters;

[0027] loss exp The empirical loss function is as follows:

[0028]

[0029] loss exp =(Model ij -Know ij ) 2

[0030] Among them, Model ij This represents the output node y of the Bayesian neural network. i To input node x j Partial derivatives, Know ij Indicates the output node y i x between input nodes j The gradient of the Bezier curve.

[0031] Ideally, the training object of a Bayesian neural network is the probability distribution parameters N(μ, σ) of the weights and biases. 2 (This refers to the numerical values ​​of weights and biases, not the values ​​of weights and biases.) The training method is as follows:

[0032] First, calculate the gradient of the expected value μ of the probability distribution with respect to the loss function:

[0033]

[0034] Then calculate the gradient of the variance σ of the probability distribution with respect to the loss function:

[0035]

[0036] Finally, the probability distribution parameters are updated:

[0037] μ←μ-αΔ μ

[0038] σ←σ-αΔ σ

[0039] Where α represents the learning rate, μ represents the expected value of the corresponding weights / biases, σ represents the variance of the corresponding weights / biases, and ∈ represents a standard normal distribution; the calculation process is repeated until the model training error or the number of training algebras reaches the specified requirement.

[0040] Preferably, in step 3, the accuracy of the trained neural network is verified using simulation software or wind tunnel testing; if the accuracy meets the requirements under both conditions with and without jet interference, then step 4 is executed based on the trained neural network; if the accuracy does not meet the requirements, new sample points are added to the training dataset, and the training is repeated until the accuracy is met; wherein, the response value corresponding to the newly added sample point is obtained by simulation software.

[0041] Beneficial effects:

[0042] (1) This invention addresses the problem of small sample size and high prediction error in the aerodynamic performance evaluation of interceptors under jet interference. It proposes a rapid aerodynamic performance evaluation method for interceptors based on a neural network surrogate model. By analyzing the traditional design process of interceptors, important operating parameters are summarized. Then, the engineering experience accumulated by designers during the model design process is used to fill the mapping relationship between design variables and target performance. Engineering experience combined with small sample data is used to construct a loss function, improving the training effect of the neural network surrogate model. Both in the training and testing processes, the neural network surrogate model with experience integration exhibits superior prediction accuracy. The final trained neural network surrogate model has a test error within 0.5%, indicating that the neural network surrogate model established in this invention can obtain high-precision aerodynamic performance parameter prediction results and has good generalization ability.

[0043] (2) This invention uses Bézier curves to describe the engineering experience of the mapping law between design variables and target performance accumulated by designers in the process of model design. Bézier curves can accurately quantify the influence law of specific shapes between variables and can represent any continuous function within a specified interval. Designers can draw any empirical shape by simply dragging the control points and derive it in the form of mathematical formulas. The description is accurate and highly operable. At the same time, the gradient description based on the control points of Bézier curves is also more convenient.

[0044] (3) The present invention uses a Bayesian neural network as a surrogate model, which has a strong ability to fit nonlinear problems. At the same time, the confidence of the model prediction results is given through Bayesian theory, which can more intuitively reflect the accuracy of the method of the present invention.

[0045] (4) The present invention performs reparameterization operation on the weights and biases of the Bayesian neural network, so that the Bayesian neural network can complete the derivative operation of the loss function without affecting the derivative result.

[0046] (5) This invention utilizes the derivative information of engineering experience to calculate the gradient relationship between specified operating parameters and performance parameters, and combines the automatic differentiation method to transform engineering experience into an empirical term in the loss function. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the air jet flight of a supersonic interceptor.

[0048] Figure 2 This is a flowchart of the method of the present invention.

[0049] Figure 3 It is a third-order Bézier curve.

[0050] Figure 4 To obtain interface diagrams for engineering experience.

[0051] Figure 5 This is the neuron structure of a Bayesian neural network.

[0052] Figure 6 This is a training method based on Bayesian neural networks. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] This invention provides a method for rapid performance evaluation of hypersonic interceptors, the flowchart of which is shown below. Figure 2 As shown, it includes the following steps:

[0055] Step 1, interceptor parameterization modeling:

[0056] This invention supplements the missing mapping rules by consulting designers and seeking relevant engineering experience, and integrates the summarized experience (the correspondence between design variables and target performance) into the surrogate model.

[0057] Parametric modeling of hypersonic interceptors primarily involves analyzing the influencing factors of different aerodynamic performance assessments, using these factors as inputs to a surrogate model. This invention is mainly based on designers' understanding and actual design processes, summarizing the physical correlation between operating parameters and aerodynamic performance. Operating parameters exhibiting this correlation are used as input variables to the surrogate model, ultimately outputting aerodynamic performance parameters.

[0058] Specifically, through communication with designers, this invention categorizes the parameters involved in the aerodynamic performance evaluation of hypersonic interceptors into three types. The first type: shape parameters. Since this invention focuses on a specific hypersonic interceptor, shape parameters are set as invariants in the performance evaluation experiments. The second type: operating condition parameters, mainly including Mach number Ma, angle of attack α, altitude h, and roll angle. Rudder deflection angle DEL, attitude control jet pressure ratio p zj Attitude and orbit control jet pressure ratio p zgj Examples are shown in Table 1.

[0059] Table 1. Operating Condition Variables Table

[0060]

[0061] The third category: aerodynamic characteristic data, the main parameters of which include the overall normal force coefficient c. y1 The pitching moment coefficient of the entire missile m z1 Normal force coefficient Δc caused by rudder deflection y1(δ) The pitching moment coefficient Δm caused by rudder deflection z1(δ) Four fundamental aerodynamic quantities, and the increase in the normal force coefficient ΔC of the entire projectile caused by the jet. y1(j) The increase in pitching moment Δm caused by the jet stream z1(j) The influence of the jet stream on the normal force coefficient Δ(Δc) caused by rudder deflection y1(δ) ) j The influence of jet flow on the pitching moment coefficient caused by rudder deflection, Δ(Δm) z1(δ) ) j The four aerodynamic disturbance quantities are shown in Table 2.

[0062] Table 2 Aerodynamic Variables Table

[0063]

[0064] Different aerodynamic coefficients are correlated with Mach number, altitude, angle of attack, Reynolds number, and roll angle. The correlation table is shown in Table 3, where "×" indicates no correlation, "√" indicates correlation, and "√√" indicates strong correlation. In the absence of jet influence, the input parameters are five (Ma, α, h, ...). DEL), with output parameters consisting of four basic aerodynamic quantities. Under jet-effect conditions, the input and output parameters are seven (Ma, α, h, ...). DEL, p zj p zgj ).

[0065] Table 3. Correlation between operating conditions and aerodynamic characteristics

[0066] variable Normal force Pitch moment Rudder control force Jet control force Mach number √ √√ √ √ high √ √√ √ √√ Angle of Attack √√ × √ √ Posture control opening × × × √√ Attitude and Orbit Control Assembly × × × √√ Rudder deflection angle × × √√ × Reynolds number √ √√ √ √ Roll angle √ × √ √

[0067] This invention, based on the correlation between operating parameters and aerodynamic characteristics, analyzes the input and output parameters of the interceptor proxy model. Different proxy models are constructed for different aerodynamic performance parameters; for example, the normal force proxy model has input parameters such as Mach number, altitude, attack angle, Reynolds number, and roll angle.

[0068] Step 2, construct the interceptor proxy model:

[0069] Constructing an interceptor proxy model first requires determining the proxy model method and model parameters. Considering the high dimensionality and strong nonlinearity of the supersonic interceptor problem, this invention uses a neural network as the model framework for the proxy model. Neural networks have the advantage of strong fitting ability for nonlinear problems; Bayesian neural networks, backpropagation neural networks, evolutionary neural networks, etc., can be used. Bayesian neural networks are preferred because, in addition to their strong nonlinear fitting ability, they can also provide the confidence level of the model's prediction results through Bayesian theory, which more intuitively reflects the accuracy of the method in this invention. This embodiment uses a Bayesian neural network as an example to describe the solution of this invention in detail. A Bayesian neural network is a probabilistic estimation model. During initialization, in addition to the number of neural network layers, the number of nodes per layer, and the activation function, it is also necessary to set the probability distribution of the network weights and biases.

[0070] The probabilistic model for network weights and biases is generally set to a Gaussian distribution. However, if the weights and biases of a Bayesian neural network are directly derived from a Gaussian distribution N(μ, σ), then... 2 The sampling obtained from the standard Gaussian distribution will make μ and σ non-differentiable. The present invention performs a reparameterization operation on them: sampling from the standard Gaussian distribution and scaling the sampled values ​​to obtain w, as shown in equation (1).

[0071] w=μ+σε (1)

[0072] Where w represents the weights of the neural network, μ represents the mean of the probability distribution of these weights, σ ​​represents the variance of the probability distribution of these weights, and ε represents the standard normal distribution, i.e., ε ~ N(0, I). Similarly, the formula for calculating the bias b is obtained.

[0073] In reparameterization, the transformation from ε to w involves only linear operations (translation and scaling). The sampling operation is outside the neural network computation graph. For the neural network, ε is simply a constant and does not affect the derivative of the loss function with respect to μ and σ. This method completes the initialization of the Bayesian neural network.

[0074] Step 3, Experience / Data Acquisition:

[0075] The process involves acquiring training data required for training the surrogate model. This training data includes real simulation data and engineering experience data. Real simulation data can be obtained by using computational design of experiments to acquire sample points within the initial design space, and then using simulation software to obtain the actual response values ​​of performance indicators (objective function and constraints) at the initial (new) sample points. For acquiring engineering experience, this invention proposes a method based on Bézier curves: based on the operating parameters determined in step one, and after communication with designers, engineering experience curves are obtained using Bézier curve tools, and the derivative of these curves is calculated to complete the gradient representation of the engineering experience.

[0076] Specifically, this includes:

[0077] (1) Empirical acquisition based on Bézier curves

[0078] The principle behind Bézier curves is the Bernstein polynomial (it can be proven from the Bernstein polynomial that all continuous functions on the interval [a, b] can be approximated by polynomials). Therefore, Bézier curves can represent any continuous function within a specified interval. The basic principle is illustrated using a third-order Bézier curve as an example.

[0079] like Figure 3 As shown, let P0, P2 is three distinct points on a parabola. The two tangent lines passing through points P0 and P2 intersect at point P1. The tangent at point P0P1 and P2P1 intersects at point P0P1 and P2P1 respectively. and And the following proportions hold true:

[0080]

[0081] With P0 and P2 fixed, introduce a parameter t and let the above ratio be... That is:

[0082]

[0083]

[0084]

[0085] Further derivation:

[0086]

[0087] For each value of t in the range [0, 1], there will be a point. A series The resulting fitted curve is the Bézier curve fitted by control points P0, P1, and P2. When multiple control points are introduced, the expression for an (n-1)th order Bézier curve with n control points can be obtained:

[0088]

[0089] Among them B (t) Let t be the fitted point for a certain value, and n be the number of control points. For permutations and combinations, Pi is the coordinate of the i-th control point, and t is a series of values ​​in [0, 1]. The parametric equation of a cubic Bézier curve is shown in the following formula:

[0090] B (t) =P0(1-t) 3 +3P1(1-t)2 t+3P2(1-t)t 2 +P3t 3

[0091] By combining the expression for the Bézier curve, it can be found that the fitted curve consists of a series of control points P. i As defined, the number of points on the curve is determined by t. This invention utilizes the characteristic that curves are defined by control points. Operated by technicians, by increasing or decreasing the number of control points and dragging their positions, an engineering experience data fitting curve can be obtained, with operating parameters as independent variables and aerodynamic performance as the dependent variable. After experts complete the drawing of the experience curve, they save the control point coordinates, completing the entire experience acquisition process. Figure 4 Example of obtaining curve fitting data from engineering experience data, when... Figure 4 (a) Drag control point 2 to Figure 4 (b) At the position, the fitted curve is from Figure 4 (a) changed into Figure 4 (b) Drag control point 4 in sequence to form Figure 4 (c) Drag point 6 to form Figure 4 (d) Fitted curve.

[0092] (2) Gradient-based empirical representation

[0093] According to the analytical formula of Bézier curves, the observation points on the fitted curve are determined by the coordinates of the control points and the sampling density of t. Therefore, the x and y coordinates of the observation points on the fitted curve are defined by the x and y coordinates of the control points. Here, using the chain rule and t as an intermediate variable, we calculate the derivative values ​​of the observation points on the fitted curve, as shown in the following formula:

[0094]

[0095] in This refers to the x and y coordinates of the i-th control point, which ultimately yields t sets of gradients.

[0096] In this way, the derivative values ​​of engineering experience can be obtained. Some of the obtained aerodynamic performance experiences are shown in Tables 4 and 5.

[0097] Table 4. Engineering Experience Table for Normal Force

[0098]

[0099] Note: k is the gradient.

[0100] Table 5 Engineering Experience Table of Pitch Moment Coefficient

[0101]

[0102] Step 4, construct the loss function:

[0103] To uncover patterns and information embedded in engineering experience and integrate them into the training process of neural networks, this invention defines a novel loss function formula. The loss function value consists of two parts: a data term and an empirical term. A lower loss function value indicates better model training performance. The loss function formula is as follows:

[0104] Loss Function = loss data +loss exp

[0105] Where Loss Function refers to the loss function of the neural network, loss data The loss function refers to a loss function constructed based on real simulation data (small sample data). exp This refers to a loss function constructed based on engineering experience data.

[0106] (1) Data Items

[0107] For other neural network models, the training process involves predicting the output value of each set of training data based on the current neural network, comparing it with the actual output value in the training data, and using the error obtained from the comparison as a data term of the loss function.

[0108] For Bayesian neural network models, the training process involves finding the maximum posterior probability (MAP) of the weight parameters w. Directly calculating the posterior probability p(W|D) is difficult, so researchers often use variational inference and Monte Carlo sampling to estimate it. This embodiment uses variational inference, employing a Gaussian distribution q(W|θ) controlled by a set of parameters θ(μ, σ) to approximate the posterior p(W|D). KL divergence is used to measure the similarity between the two distributions q(W|D) and p(W|D). The smaller the KL divergence, the more similar the two distributions. This transforms the problem of calculating the posterior probability into an optimization problem of finding the optimal θ. The KL divergence formula is as follows:

[0109]

[0110] After decomposition and transformation, the original equation becomes:

[0111] KL(q(W|θ)||p(W|D))

[0112] =∫E q(w|θ) ln(q(w|θ))-∫q(w|θ)ln(P(w))dw-∫q(w|θ)ln(P(D|w))dw

[0113] The smaller the KL divergence, the more similar the two distributions are, so we only need to minimize it. Considering that the weights of the neural network are independent, the formula can be further simplified to:

[0114]

[0115] q(w i |θ i p(w) represents the distribution of the weight parameters given the parameters of a normal distribution. i ) represents the prior of the weight, p(D|w i ) represents the likelihood of the observed data given the network parameters.

[0116] (2) Experience Items

[0117] The empirical term is calculated by using an automatic differentiation method to calculate the gradient relationship between the input parameter nodes (e.g., Mach number, angle of attack) and the output parameter nodes (e.g., total ballistic normal force) of the neural network. This gradient relationship is then compared with the gradient relationship in actual engineering experience (i.e., the gradient relationship of the Bézier curve obtained in the previous step), and the mean square error is calculated to obtain the empirical loss function term.

[0118] The automatic differentiation used in the empirical term of the loss function decomposes a complex mathematical operation into a series of simple basic operations, each of which can be obtained by looking up a table. Automatic differentiation has two forms: forward mode and reverse mode. This invention uses the reverse mode. This method first traverses the entire graph in the forward direction, calculating the value of each node; then it traverses the entire graph in the reverse direction (from top to bottom), calculating the partial derivatives of the nodes. Through automatic differentiation, we can quickly obtain the differential between the output and input variables. Applying this method to neural networks, we can quickly obtain the differential between any node in the output layer and any node in the input layer. Therefore, we can obtain the loss function for the empirical term. exp for:

[0119]

[0120] loss exp =(Model ij -Know ij ) 2

[0121] M0del ij This represents the output node y of the Bayesian neural network. i To input node x j Partial derivatives, Know ij Indicates the output node y i x between input nodes j Engineering experience (Bezier curve gradient relationship).

[0122] Step 5, Model Training:

[0123] Using the calculated loss function value, backpropagation of the error is performed to train the neural network model parameters.

[0124] A Bayesian neural network is a surrogate model that trains the parameters of a neural network using the Bayesian method. Unlike traditional point estimation neural networks, a Bayesian neural network is a probabilistic estimation model, where the network weights and biases are in the form of a probability distribution. Figure 5 This is the computational method for neurons in a Bayesian neural network. First, a prior assumption is introduced, assuming the model parameters (weights / biases) follow a certain distribution (usually a standard normal distribution). Then, specific weight / bias values ​​are obtained through sampling. Finally, the values ​​are calculated based on the neuron's input, weights / biases, and activation function f. act The output of the neuron node is calculated.

[0125] like Figure 6 As shown, the forward feed process of a Bayesian neural network is not much different from that of a traditional neural network. However, by introducing prior probabilities, the method for estimating the neural network parameters changes from maximum likelihood estimation to maximum a posteriori probability estimation (MAP). The training objects are the probability distribution parameters N(μ, σ) of the weights and biases. 2 This refers to the numerical values ​​of the weights and biases, not the weights and biases. The calculation process is as follows:

[0126] First, calculate the gradient of the expected value μ of the probability distribution with respect to the loss function:

[0127]

[0128] Then calculate the gradient of the variance σ of the probability distribution with respect to the loss function:

[0129]

[0130] Finally, the probability distribution parameters are updated:

[0131] μ←μ-αΔ μ

[0132] σ←σ-αΔ σ

[0133] Where α represents the learning rate, μ represents the expected value of the corresponding weights / biases, σ represents the variance of the corresponding weights / biases, and ∈ represents a standard normal distribution. The calculation process is repeated until the model training error or the number of training algebras reaches the specified requirement.

[0134] Step 6, Precision Verification:

[0135] The accuracy of the surrogate model is verified using simulation software and wind tunnel tests. If the accuracy meets the requirements under both conditions with and without jet interference, the Bayesian neural network construction is complete; otherwise, proceed to step seven.

[0136] Step 7, Add new sample points:

[0137] The simulation software is used to add sample points. After adding sample points, the process proceeds to step three, where the simulation software is called to obtain the response values ​​at the newly added sample points. Then, the surrogate model is trained to improve the model accuracy until the accuracy requirements are met.

[0138] Step 8, Performance Evaluation:

[0139] The aerodynamic performance of hypersonic interceptors can be rapidly evaluated using a trained neural network surrogate model.

[0140] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for rapid performance evaluation of hypersonic interceptors based on neural networks, characterized in that, include: Step 1, obtain the training dataset; the training dataset includes real simulation data and engineering experience data; The method for obtaining real simulation data is as follows: using computational experimental design methods, sample points of operating parameters are obtained within the initial design space, and the corresponding aerodynamic performance response values ​​are obtained through engineering experiments or data simulation. The engineering experience data is obtained by having designers use their engineering experience to draw a fitting curve of the relationship between operating parameters and aerodynamic performance using Bézier curves, and then achieve gradient characterization based on the derivative of the control points of the Bézier curves. Step 2: Construct a neural network and initialize its parameters. The input to the neural network is the operating parameters of the interceptor, and the output is the performance parameters of the interceptor. The loss function consists of a data term loss function based on real simulation data and an empirical term loss function based on engineering experience data. The data term loss function is the mean square error between the neural network's predicted value and the true value. The empirical term loss function is the mean square error of the gradients of the neural network's input and output and the corresponding gradients of the Bézier curves. Step 3: Using the training dataset obtained in Step 1, train the neural network constructed in Step 2 to obtain the trained neural network. Step 4: Use the trained neural network to evaluate the aerodynamic performance of the hypersonic interceptor.

2. The method as described in claim 1, characterized in that, The operating parameters include: external shape parameters, operating condition parameters, and aerodynamic characteristic data.

3. The method as described in claim 2, characterized in that, For a specific hypersonic interceptor, its shape parameters are set as invariants; The main operating parameters include Mach number Ma, angle of attack α, altitude h, and roll angle. Rudder deflection angle DEL, attitude control jet pressure ratio p zj The pressure ratio of the attitude control jet to p zgj ; The main aerodynamic characteristic parameters include fundamental aerodynamic quantities, such as the overall projectile normal force coefficient c. y1 The pitching moment coefficient of the entire missile m z1 Normal force coefficient Δc caused by rudder deflection y1(δ) The pitching moment coefficient Δm caused by rudder deflection z1(δ) ; and aerodynamic disturbances, including: the increase in the normal force coefficient Δc of the entire projectile caused by the jet. y1(j) The increase in pitching moment Δm caused by the jet stream z1(j) The influence of the jet stream on the normal force coefficient Δ(Δc) caused by rudder deflection y1(δ) ) j The influence of jet flow on the pitching moment coefficient Δ(Δm) caused by rudder deflection z1(δ) ) j .

4. The method as described in claim 1, characterized in that, The specific methods for acquiring engineering experience data are as follows: Add Bézier curve control points to the coordinate system. Designers can obtain the fitted curve by increasing or decreasing the number of control points and dragging their positions. After completing the knowledge drawing, designers save the coordinates of the control points of the current experience knowledge curve to complete the entire knowledge acquisition process.

5. The method as described in claim 1, characterized in that, The neural network is a Bayesian neural network, a backpropagation neural network, or an evolutionary neural network.

6. The method as described in claim 5, characterized in that, The initial settings for the weights w and biases b of the Bayesian neural network are as follows: Samples are taken from a standard Gaussian distribution, and the sampled values ​​are scaled to obtain the following: A = μ + σε; Where A represents the weight w or bias b; μ and σ are the weight or bias Gaussian distributions N(μ,σ) and N(μ,σ), respectively. 2 The mean and variance of ; ε represents the standard normal distribution.

7. The method as described in claim 5 or 6, characterized in that, The loss function value of a Bayesian neural network consists of two parts: a data term and an empirical term; the formula for the loss function is as follows: Loss Function=loss data +loss exp Where, loss data The loss function for the data items is as follows: Wherein q(w i |θ i ) represents the weight parameter w given a normal distribution. i The distribution of θ; i p(w) represents the prior distribution of the weights. i ) represents the prior of the weights; p(D|w i ) represents the likelihood of the observed data given the network parameters; loss exp The empirical loss function is as follows: loss exp =(Model ij -Know ij ) 2 Among them, Model ij This represents the output node y of the Bayesian neural network. i To input node x j Partial derivatives, Know ij Indicates the output node y i x between input nodes j The gradient of the Bezier curve.

8. The method as described in claim 7, characterized in that, The training objects of a Bayesian neural network are the probability distribution parameters N(μ,σ) of the weights and biases. 2 The training method is as follows: First, calculate the gradient of the expected value μ of the probability distribution with respect to the loss function: Then calculate the gradient of the variance σ of the probability distribution with respect to the loss function: Finally, the probability distribution parameters are updated: μ←μ-αΔ μ σ←σ-αΔ σ Where α represents the learning rate, μ represents the expected value of the corresponding weights / biases, σ represents the variance of the corresponding weights / biases, and ∈ represents a standard normal distribution; the calculation process is repeated until the model training error or the number of training algebras reaches the specified requirement.

9. The method as described in claim 1, characterized in that, In step 3, the accuracy of the trained neural network is verified using simulation software or wind tunnel tests; if the accuracy meets the requirements under both no jet interference and jet interference conditions, then step 4 is executed based on the trained neural network. If the accuracy does not meet the requirements, new sample points are added to the training dataset, and the training is repeated until the accuracy is met; the response values ​​corresponding to the new sample points are obtained by simulation software.

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