An aircraft interior and exterior trajectory integrated optimization method based on sparse neural network

Abstract

The application relates to the field of aerospace vehicle general design, and discloses an aircraft interior and exterior trajectory integrated optimization method based on a sparse neural network, which comprises the following steps: constructing a design variable set by using design variables of an aircraft, and setting an output response; constructing a sample in combination with the design variable set based on a design space of the design variables, so as to form a training sample set; determining the output response of each sample by using an interior trajectory simulation model and an exterior trajectory simulation model, so as to form an output response set; introducing a norm as a sparse regular term of a total loss function, so as to construct a sparse neural network based on the norm; training the sparse neural network by using the training sample set and the output response set; taking the sparse neural network as a low-precision model, and taking the interior trajectory simulation model and the exterior trajectory simulation model as high-precision models; continuously optimizing the low-precision model in combination with a dynamic trust factor, and finally determining a candidate design point serving as an optimal design scheme.

Description

Technical Field

[0001] This invention relates to the field of overall design of aerospace vehicles, and specifically to an integrated optimization method for the internal and external ballistic trajectories of a vehicle based on sparse neural networks. Background Technology

[0002] In modern aerospace engineering, the overall design of aircraft such as sounding rockets and booster launch vehicles is a highly complex systems engineering project, involving the deep intersection and coupling of multiple disciplines such as aerodynamics, propulsion, structure, ballistics, and control. Among them, ballistic performance optimization is the core link that determines whether the tactical and technical indicators (such as maximum range and flight speed) of the aircraft can be achieved. As a complex dynamic system, there is a very strong coupling relationship between the thrust characteristics provided by the propulsion system (internal ballistics) and the aerodynamic characteristics of the flight trajectory (external ballistics). However, traditional aircraft design methodologies and existing optimization methods are gradually revealing many limitations when facing the increasingly complex design requirements of advanced aircraft, specifically in the following aspects:

[0003] Traditional aircraft design typically follows a sequential process of "power system design - overall parameter freezing - ballistic performance verification." In this model, power system designers often independently design the engine propellant charge structure based on the overall average thrust or total impulse requirements, simplifying the time-varying thrust curve into a constant or trapezoidal thrust. While this simplification reduces the difficulty of coordination in the early design stages, it neglects the dynamic impact of instantaneous thrust changes on the aircraft's center of gravity motion, aerodynamic characteristics, and attitude control.

[0004] To unlock the ultimate performance of an aircraft, integrated internal and external ballistic design requires the simultaneous optimization of numerous design variables. In the internal ballistics, achieving an ideal thrust-pressure curve necessitates refined parameter definition of the propellant geometry (e.g., wing-pole, star-shaped). In the external ballistics, to satisfy complex terminal and process constraints, flight procedures (e.g., angle-of-attack variation patterns) are typically designed in segments. The combined effect often results in a total design variable dimension exceeding 20, drastically increasing computational resource consumption and making it difficult to meet the rapid iterative design requirements of engineering practice.

[0005] Complex physical field mapping relationships exist in aircraft design; traditional polynomial response surface or shallow neural networks often exhibit underfitting when dealing with such deep complex nonlinear mappings; and fully connected deep networks are prone to overfitting when the sample size is limited, and the large number of parameters increases the burden of model storage and inference.

[0006] In summary, existing aircraft trajectory optimization technologies have significant shortcomings in terms of high-dimensional computational efficiency, nonlinear fitting accuracy, and portability for engineering deployment. Summary of the Invention

[0007] The purpose of this invention is to provide an integrated optimization method for the internal and external ballistics of aircraft based on sparse neural networks, in order to solve problems in high-dimensional computational efficiency, nonlinear fitting accuracy, and engineering deployment portability.

[0008] To achieve the above objectives, the present invention employs the following technical solution:

[0009] A method for integrated optimization of the internal and external ballistic trajectories of an aircraft based on sparse neural networks includes:

[0010] Construct a set of design variables using the aircraft's design variables, and set the output response;

[0011] Based on the design space of design variables, samples are constructed in combination with the set of design variables to form a training sample set; the output response of each sample is determined by the internal ballistic simulation model and the external ballistic simulation model to form an output response set.

[0012] By introducing The norm serves as a sparse regularization term for the total loss function, thus constructing a system based on... Norm-based sparse neural networks; training sparse neural networks using training sample sets and output response sets;

[0013] The sparse neural network is used as a low-precision model, while the internal ballistic simulation model and the external ballistic simulation model are used as high-precision models. A set of candidate design points is constructed based on the design space. The comprehensive index of the candidate design points is calculated by combining the dynamic trust factor and the low-precision model to screen the candidate design points. The output response of the screened candidate design points is determined by the high-precision model, thereby updating the training sample set and the output response set. Then, the low-precision model is retrained. Finally, the candidate design points as the optimal design scheme are determined from the predicted output of the low-precision model at each iteration.

[0014] Furthermore, the design variable set contains multidimensional design variables; the construction process of the training sample set is as follows:

[0015] Construct the objective function for sample optimization:

[0016] ;

[0017] in, This represents the sample distribution in the training sample set; The design space for design variables consists of the range of values ​​corresponding to each design variable. Indicates that when the condition is met Under the constraints of Maximize; Indicates that when the condition is met Under the constraints Minimize; Indicates the first training sample set Sample The Euclidean distance between them; each sample represents a specific value from a set of design variables;

[0018] An initial sample is generated based on the design space using the Latin hypercube sampling method; when generating the sample, the sampling frequency is enhanced at the boundary of the design space.

[0019] Under the constraints of the objective function, a genetic algorithm is used to optimize the position of the samples; when the genetic algorithm converges, the optimal sample distribution is obtained, and all the samples at this point constitute the training sample set.

[0020] Furthermore, the output response includes multidimensional response parameters of the aircraft; the process of constructing the output response set is as follows:

[0021] An internal ballistic simulation model is constructed. The internal ballistic simulation model is used to simulate the internal ballistics for each sample in the training sample set using the level set method. During the simulation, the combustion surface evolution follows the Hamilton-Jacobi equation, thus obtaining the thrust-time curve.

[0022] An external ballistic simulation model is constructed. The external ballistic simulation model is used to calculate the corresponding output response by taking the thrust-time curve as input and combining it with the aerodynamic database and the aerodynamic model of the aircraft. The output responses corresponding to all samples constitute the output response set. The aerodynamic database refers to the interpolation table of aerodynamic parameters with respect to velocity and angle of attack.

[0023] Furthermore, the sparse neural network is a fully connected neural network comprising an input layer, a hidden layer, and an output layer; wherein: the number of neurons in the input layer is the same as the dimension of the design variables in the design variable set; three hidden layers are set, and the number of neurons in the output layer is consistent with the dimension of the response parameters in the output response;

[0024] The total loss function includes the mean squared error. and sparse regularization terms The details are as follows:

[0025] ;

[0026] in, This is the total loss function; This represents the weight matrix of the sparse neural network as a whole. Batch size; For the first The output response corresponding to each sample; For sparse neural networks targeting the first The predicted output for each sample; is the regularization coefficient, and its value range is . ; For sparse neural networks Layer weight matrix; This represents the total number of layers in the sparse neural network. for of Norms, in their specific form, are as follows:

[0027] ;

[0028] in, For sparse neural networks The first in the layer The first neuron at the location of the first neuron The weights of the vectors of each neuron; These are the sparse neural network's first... The number of neuron locations and the number of neuron vectors in the layer; The sparsity index is used to express the sparsity index. .

[0029] Furthermore, during training, sparse neural networks employ the following gradient update formula:

[0030] ;

[0031] in, To find the partial derivative operator; express Norm;

[0032] Based on the gradient update formula and in conjunction with the AdamW optimizer, the sparse neural network is trained using the training sample set and the output response set to realize the weight matrix. Precise updates and sparsification;

[0033] The learning rate is adjusted using a cosine annealing strategy, and a pruning threshold is set. When training a network:

[0034] like Then a mandatory order And freeze the sparse neural network's first... The first in the layer The first neuron at the location of the first neuron The connections between a neuron vector and other neuron vectors prevent it from participating in subsequent forward propagation and backward updates.

[0035] Furthermore, a candidate design point set is constructed based on the design space. A comprehensive index of the candidate design points is calculated using a dynamic trust factor and a low-precision model to screen the candidate design points, including:

[0036] Candidate design points are obtained by Latin hypercube sampling within the design space of the design variables; all candidate design points constitute a candidate design point set.

[0037] Setting dynamic trust factors The initial value is determined, and then the iteration is performed according to the preset number of iterations; the specific process of each iteration is as follows:

[0038] Calculate each candidate design point using a low-precision model Predicted output and determine the predicted output. Expectations and the corresponding standard deviation ; Calculate the expected improvement value of the standard :

[0039] ;

[0040] in, This represents the current optimal prediction output. Initially, the prediction output of a candidate design point is randomly selected as the target. ; Indicates the standard change. The standard normal cumulative distribution function is... It is the probability density function;

[0041] Calculate each candidate design point The minimum Euclidean distance to all other candidate design points in the candidate design point set is calculated and normalized. The result is denoted as: Then calculate the comprehensive index. :

[0042] ;

[0043] in, Indicates dynamic trust factor;

[0044] Comprehensive index of all candidate design points Sort in descending order and select the top... Candidate design points corresponding to each comprehensive indicator These were selected as candidate design points.

[0045] Furthermore, the selected candidate design points determine the output response using a high-precision model, thereby updating the training sample set and the output response set. Then, the low-precision model is retrained, including:

[0046] For the former Candidate design points corresponding to each comprehensive indicator The corresponding output response is obtained by calling the high-precision model. ;Will As the new optimal prediction output ; Calculate prediction error :

[0047] ;

[0048] in, Indicates the preceding Among the candidate design points corresponding to the comprehensive index, the first one is... Candidate design points The corresponding output response is obtained through high-precision model calculation; for The predicted output obtained by inputting into a low-precision model; ;

[0049] Set error threshold And make a judgment:

[0050] if ,Will Updated to ;if ,but Updated to ;

[0051] Will As a new sample, it is added to the training sample set; at the same time, Add it to the output response set to update the training sample set and the output response set;

[0052] The sparse neural network is retrained using the updated training sample set and output response set.

[0053] Further, determine the current iteration count; if the preset maximum iteration count has been reached, or if the iterations are consecutive... The next iteration satisfies If the prediction fails, the iteration stops; the optimal prediction output from each iteration is used. In the middle, select The candidate design point corresponding to the maximum value is taken as the optimal design scheme; This is a preset value.

[0054] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the integrated optimization method for internal and external ballistics of an aircraft based on a sparse neural network.

[0055] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the integrated optimization method for internal and external ballistics of an aircraft based on a sparse neural network.

[0056] Compared with the prior art, the present invention has the following technical features:

[0057] 1. Breakthrough in optimizing high-dimensional design space: based on Norm-based sparse neural networks reduce the number of parameters in surrogate models by more than 60% while maintaining extremely high fitting accuracy to multidimensional complex nonlinear spaces. Combined with an adaptive multi-precision collaborative optimization framework, the optimization process, which originally required tens of thousands of physical simulations, can converge in just a few dozen simulations, improving computational efficiency by 1-2 orders of magnitude.

[0058] 2. Improved accuracy of strongly coupled internal and external ballistic design: This invention eliminates the range prediction bias caused by the simplification of the thrust model (average thrust) in traditional serial design through integrated modeling. The application of the Level-Set method makes the simulation of the burning surface retreat of complex charges closer to the real physical process, with higher nonlinear fitting accuracy.

[0059] 3. Advantages of lightweight model and engineering deployment: Sparse neural networks not only require less storage space but also significantly reduce inference computation. This allows the optimized model to be easily integrated into commonly used industrial design software such as CATIA and MATLAB, and even deployed in aircraft onboard computers.

[0060] 4. Robustness and generalization ability: based on Norm sparsification is similar to a feature selection mechanism that can automatically identify and retain the key features that have the greatest impact on aircraft performance, suppress noise interference, and thus improve the model’s generalization ability in unknown design regions. Attached Figure Description

[0061] Figure 1 This is a schematic flowchart of the method of the present invention;

[0062] Figure 2 This is a diagram of the sparse neural network architecture in this invention;

[0063] Figure 3 This is the total loss curve of the sparse neural network during training in the example;

[0064] Figure 4 The example shows the curve of the learning rate of the sparse neural network changing with the number of iterations.

[0065] Figure 5 The thrust fitting curve of the aircraft is obtained after designing the aircraft using the optimal design scheme in the example. Detailed Implementation

[0066] This invention provides an integrated optimization method for the internal and external trajectories of aircraft based on sparse neural networks. It adopts an overall technical approach of data generation, model training, sparse optimization, and optimization application, specifically including the following steps:

[0067] Step 1: Construct a set of design variables using the aircraft's design variables and set the output response.

[0068] This step aims to transform abstract engineering design problems into mathematically operable parametric models.

[0069] Step 1.1: Construct the design variable set.

[0070] To achieve deep coupling optimization of internal and external trajectories, this invention constructs a system containing... Design variable set of dimensional design variables ,in Indicates the first One design variable.

[0071] The design variables include the aircraft's internal ballistic dynamics parameters and external ballistic flight control parameters; the internal ballistic dynamics parameters are the relevant parameters of the propellant grain in the aircraft's engine combustion chamber; for example, for a wing-shaped propellant grain, the ballistic dynamics parameters include wing length, wing tilt angle, wing width, etc.; the external ballistic flight control parameters are the parameters used to control the aircraft's ballistic trajectory and energy management strategy, including basic thrust, launch velocity tilt angle, boost phase angle of attack, glide phase angle of attack, etc.

[0072] Step 1.2, set the output response.

[0073] Output response The response parameters in are Dimensions, for example, response parameters include the aircraft's performance indicators and physical constraint indicators; where performance indicators include, for example, flight distance; and physical constraint indicators include, for example, terminal velocity, maximum normal overload, etc. Indicates the first One response parameter.

[0074] Step 2: Based on the design space of the design variables, construct samples in combination with the set of design variables to form a training sample set; determine the output response of each sample through the internal ballistic simulation model and the external ballistic simulation model to form an output response set.

[0075] Step 2.1: Construct the training sample set and the output response set.

[0076] While traditional Latin hypercube sampling (LHS) ensures uniformity of projection in each dimension, it is prone to local clustering of samples in high-dimensional spaces.

[0077] For m-dimensional design variables, in order to obtain representative training samples within the design space of the design variables, this invention adopts an enhanced space-filling sampling strategy based on the maximum-minimum distance criterion, aiming to maximize the minimum distance between any two samples in the training sample set, as detailed below:

[0078] Step 2.1.1, construct the objective function for sample optimization, as follows:

[0079] ;

[0080] in, This represents the sample distribution in the training sample set; The design space for design variables consists of the range of values ​​corresponding to each design variable. Indicates that when the condition is met Under the constraints of Maximize; Indicates that when the condition is met Under the constraints Minimize; Indicates the first training sample set Sample The Euclidean distance between them; each sample is a specific value of a set of design variables; that is, after assigning a value to each design variable in the set of design variables, it becomes a sample.

[0081] Step 2.1.2: Generate initial samples based on the design space using the Latin hypercube sampling method. When generating samples, the sampling frequency should be increased at the boundaries of the design space to generate more samples at the boundaries. For example, if a design variable is divided into k intervals, the sampling frequency is higher in the first and kth intervals than in the other k-2 intervals. This is because the design variables of an aircraft often undergo nonlinear abrupt changes at the boundaries of their value ranges.

[0082] Step 2.1.3: Under the constraints of the objective function, the position of the sample is optimized using a genetic algorithm. The objective function can minimize the distance between samples while satisfying the spatial orthogonality constraint, thereby ensuring that the projection of the sample on any two-dimensional subplane also has good distribution characteristics.

[0083] Step 2.1.4: After the genetic algorithm converges, the optimal sample distribution is obtained. At this point, all the samples constitute the training sample set.

[0084] Step 2.1.5: Construct the internal ballistic simulation model. The internal ballistic simulation model is used to simulate the internal ballistics for each sample in the training sample set using the level-set method. During the simulation, the combustion surface evolution follows the Hamilton-Jacobi equations, thus obtaining the thrust-time curve. .

[0085] Step 2.1.6, construct the external ballistic simulation model; the external ballistic simulation model is used to plot the thrust-time curve. Using the aerodynamic database and the aerodynamic model of the aircraft as input, the corresponding output response is calculated. Thus, the output responses corresponding to all samples together constitute the output response set; wherein the aerodynamic database refers to the interpolation table of aerodynamic parameters with respect to velocity and angle of attack; the aerodynamic parameters include lift coefficient and drag coefficient.

[0086] Step 2.2: Remove outliers from the training sample set and the output response set; then perform normalization processing. Outlier removal refers to removing a sample whose internal or external ballistic simulation results do not conform to the actual physical laws.

[0087] Step 3, by introducing The norm serves as a sparse regularization term for the total loss function, thus constructing a system based on... Norm-based sparse neural networks; training sparse neural networks using training sample sets and output response sets.

[0088] Step 3.1, design the structure of the sparse neural network.

[0089] The sparse neural network is a fully connected neural network (DNN), comprising an input layer, hidden layers, and an output layer; wherein:

[0090] The number of neurons in the input layer is the same as the dimension of the design variables in the design variable set, i.e., m neurons.

[0091] The hidden layers are set to three layers, with the number of neurons in the first to the third hidden layers being 256, 128, and 64, respectively.

[0092] The number of neurons in the output layer is consistent with the dimension of the response parameters in the output response, i.e., n neurons.

[0093] The sample is input into a sparse neural network to obtain the corresponding prediction output, which is the predicted value of the response parameter.

[0094] Step 3.2: Design the activation function and initialize the sparse neural network.

[0095] Hidden layers employ nonlinear activation functions (such as ReLU or Tanh) to give sparse neural networks the ability to fit nonlinear physical fields.

[0096] The network parameters (weights) of sparse neural networks are initialized using XavierInitialization to ensure the stability of gradient flow during the initial training phase.

[0097] Step 3.3, Construction of the total loss function.

[0098] By introducing The norm is used as a sparse regularization term to construct the total loss function; [the following is introduced] After the norm, the structure based on A sparse neural network with a norm; the regularization term forces the sparse neural network to automatically eliminate redundant connections during training, achieving "training is pruning".

[0099] The total loss function includes the mean squared error (MSE) and a sparse regularization term. The details are as follows:

[0100] ;

[0101] in, This is the total loss function; This represents the weight matrix of the sparse neural network as a whole. Batch size is the number of samples used in each training batch. For the first The output response for each sample For sparse neural networks targeting the first The predicted output for each sample; is the regularization coefficient, and its value range is . ; For sparse neural networks Layer weight matrix; This represents the total number of layers in the sparse neural network (including input, hidden, and output layers); for of Norms, in their specific form, are as follows:

[0102] ;

[0103] in, For sparse neural networks The first in the layer The first neuron at the location of the first neuron The weights of the vectors of each neuron; These are the sparse neural network's first... The number of neuron locations and the number of neuron vectors in the layer; The sparsity index is used to express the sparsity index. .

[0104] Step 3.4, Constructing the gradient update formula for sparse neural networks.

[0105] against Taking advantage of the non-differentiability and non-convexity of the norm at zero, this invention constructs a new gradient update formula during the training of the sparse neural network, achieving accurate updates to the weights. The construction process of the gradient update formula is as follows:

[0106] Total loss function Seeking information about weights Partial derivatives:

[0107] ;

[0108] in, To find the partial derivative operator; for Gradient expansion is as follows:

[0109] ;

[0110] in, express Norms, for example for of norm Power of 1.

[0111] Therefore, the complete gradient update formula is as follows:

[0112] .

[0113] Step 3.5: Based on the gradient update formula, and in conjunction with the AdamW optimizer, the sparse neural network is trained using the training sample set and the output response set to realize the weight matrix. Precise updates and sparsification; setting the epoch to 500 and using cosine annealing to adjust the learning rate; setting a pruning threshold. (e.g., value) During network training:

[0114] like Then a mandatory order And freeze the sparse neural network's first... The first in the layer The first neuron at the location of the first neuron The connection between a neuron vector and other neuron vectors prevents it from participating in subsequent forward propagation and backward updates, thus achieving the pruning process.

[0115] Step 3.6: When the total loss function converges, the trained sparse neural network is obtained. At this point, for a new sample, it is input into the sparse neural network to obtain the predicted output, namely the predicted values ​​of the aircraft's performance indicators and physical constraint indicators (predicted values ​​of response parameters).

[0116] Step 4: Use the sparse neural network as a low-precision model and the internal ballistic simulation model and external ballistic simulation model as high-precision models; construct a candidate design point set based on the design space, and calculate the comprehensive index of the candidate design points by combining the dynamic trust factor and the low-precision model to screen the candidate design points; determine the output response of the screened candidate design points through the high-precision model, thereby updating the training sample set and the output response set, and then retraining the low-precision model; finally, determine the candidate design points as the optimal design scheme from the predicted output of the low-precision model at each iteration.

[0117] This invention utilizes low-precision and high-precision models to construct a multi-precision collaborative framework. This framework continuously updates the low-precision model while simultaneously optimizing candidate design points to determine the optimal design scheme. The low-precision model employs the sparse neural network trained in step 2, characterized by its fast computation speed (milliseconds) but inherent errors. The high-precision model comprises the internal and external ballistic simulation models from steps 2.1.5 and 2.1.6. While characterized by slow computation (minutes / hours), the high-precision model's output response is considered the true value. This invention also incorporates a dynamic trust factor. This enables iterative updates to low-precision models.

[0118] Step 4.1: Candidate design points are obtained by Latin hypercube sampling within the design space of the design variables; all candidate design points constitute a candidate design point set; the number of candidate design points can be greater than the number of samples in the training sample set; in this example, the size of the candidate design point set is 10000.

[0119] Step 4.2, Set the dynamic trust factor The initial value is determined, and then the iteration is performed according to the preset number of iterations; the specific process of each iteration is as follows:

[0120] Calculate each candidate design point using a low-precision model Predicted output And determine the predicted output. Expectations and the corresponding standard deviation ; Calculate the expected improvement value of the standard :

[0121] ;

[0122] in, This represents the current optimal prediction output. Initially, the prediction output of a candidate design point can be randomly selected as the optimal prediction output. It will be updated in subsequent iterations; Indicates the standard change. The standard normal cumulative distribution function is... Let be the probability density function.

[0123] Step 4.3, calculate each candidate design point The minimum Euclidean distance to all other candidate design points in the candidate design point set is calculated and normalized. The result is denoted as: Then calculate the comprehensive index. :

[0124] ;

[0125] in, This represents the dynamic trust factor, whose initial value is set to... .

[0126] Step 4.4: Comprehensive index of all candidate design points Sort in descending order and select the first... Candidate design points corresponding to each comprehensive indicator The corresponding output response is obtained by calling a high-precision model to calculate these candidate design points. ;Will As the new optimal prediction output ;in, Configured according to actual needs, for example, in the embodiments. Set to 5.

[0127] Step 4.5, calculate the prediction error, as follows:

[0128] ;

[0129] in, Indicates the preceding Among the candidate design points corresponding to the comprehensive index, the first one is... Candidate design points The corresponding output response is obtained through high-precision model calculation; for The predicted output obtained by inputting into a low-precision model.

[0130] Set error threshold And make a judgment:

[0131] if This indicates that the current low-precision model is relatively accurate, and at this time... Increase; for example, can Updated to ;if Then Reduce; for example, it can be reduced. Updated to In the embodiment, it is set .

[0132] Step 4.6, It is added to the training sample set as a new sample; at the same time, Add it to the output response set to update the training sample set and the output response set;

[0133] By retraining the sparse neural network using the updated training sample set and output response set, the sparse neural network can be continuously updated and optimized.

[0134] Step 4.7, determine the current iteration count; if the preset maximum iteration count has been reached, or if consecutive iterations have occurred... The next iteration satisfies If the prediction fails, the iteration stops; the optimal prediction output from each iteration is used. In the middle, select The candidate design point corresponding to the maximum value is taken as the optimal design scheme; that is, the aircraft can be optimized according to the design variables contained in the candidate design point; where This is a preset value, for example, 100 times.

[0135] In one embodiment of the present invention, the internal ballistic dynamics parameters in the design variables include wing length (length of the star point / wingplate in the cross-section of the propellant grain), wing tilt angle (angle of inclination of the wingplate relative to the central axis), wing width (width of the star point tip), circumscribed circle diameter (maximum diameter of the propellant grain cross-section), throat diameter (diameter of the nozzle throat), nozzle expansion ratio (ratio of nozzle exit area to throat area), and cylindrical section length (length of the axial main propellant section of the propellant grain); the external ballistic flight control parameters in the design variables include basic thrust, launch velocity tilt angle, boost phase angle of attack, and glide phase angle of attack.

[0136] In the embodiment, the number of neurons in the first to third layers of the sparse neural network are 256, 128, and 64, respectively. Compared with existing fully connected neural networks, this invention introduces... After applying the norm, the sparsity of the network parameters reached over 62.0%, the inference time was reduced from 35ms / sample to 14ms / sample, the computational load was reduced by 61.3%, and the memory usage was reduced by 62.3%. Therefore, the storage requirements and inference computation of the sparse neural network were significantly reduced, while retaining the key feature paths that have the greatest impact on the performance of the aircraft.

[0137] Figure 3The figure shows the total loss curve (i.e., the value of the total loss function) of the sparse neural network during training in the embodiment. It can be seen that the total loss function converges around the 20th iteration on both the training sample set and another validation set constructed through the design space, and the value of the total loss function is close to 0, indicating that the sparse neural network proposed in this invention introduces… The norm and the optimization of the gradient update formula can effectively improve the fitting accuracy, while also significantly improving the computational efficiency.

[0138] Figure 4 The figure shows the learning rate of the sparse neural network in the embodiment as a function of the number of iterations. It can be seen that the learning rate gradually decreases as the number of iterations increases, which verifies the rationality of the training process in this scheme.

[0139] Figure 5 The figure shows the thrust fitting curve of the aircraft after designing it using the optimal design scheme in this embodiment. Comparing the thrust curve obtained by the optimal design scheme with that obtained by internal ballistic simulation, the results show that the two are highly consistent, proving that the sparse neural network accurately learns the nonlinear law of burnout. Compared with the traditional serial design scheme based on average thrust, the aircraft optimized by this method has a 5.14% increase in range and a 0.92% reduction in engine mass.

[0140] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A sparse neural network-based integrated optimization method for the internal and external trajectories of an aircraft, characterized in that, The method comprises the following steps: constructing a design variable set by using design variables of the aircraft, and setting an output response; constructing samples based on a design space of the design variables, and forming a training sample set in combination with the design variable set; determining the output response of each sample by using an interior ballistic simulation model and an exterior ballistic simulation model, and forming an output response set; By introducing a sparse regular term as a total loss function, a sparse neural network based on norm is constructed; the sparse neural network is trained by using a training sample set and an output response set; taking the sparse neural network as a low-precision model, and taking the interior ballistic simulation model and the exterior ballistic simulation model as high-precision models; constructing a candidate design point set based on the design space, calculating a comprehensive index of the candidate design points in combination with a dynamic trust factor and the low-precision model, and screening the candidate design points, which comprises the following steps: obtaining the candidate design points by using Latin hypercube sampling in the design space of the design variables; all the candidate design points constitute the candidate design point set; Setting a dynamic trust factor The initial value of the dynamic trust factor is set, and then iterations are performed according to a preset number of iterations; the specific process of each iteration is as follows: Calculate each candidate design point using a low-precision model Predicted output And determine the predicted output. Expectations and the corresponding standard deviation ; Calculate the expected improvement value of the standard : ； wherein, represents the current optimal prediction output, the prediction output of a randomly selected candidate design point is chosen as the initial value, ; represents the standard variation, is the standard normal cumulative distribution function, is the probability density function; Calculate each candidate design point The minimum Euclidean distance from the candidate design point to all other candidate design points in the candidate design point set is calculated and normalized to obtain a result denoted as ; then the comprehensive index is calculated ； wherein, represents a dynamic trust factor; comprehensive indicators of all candidate design points selecting the candidate design points corresponding to the top comprehensive indicators in descending order as the screened candidate design points; determining the output response of the screened candidate design points by using the high-precision model, updating the training sample set and the output response set, and then retraining the low-precision model; finally, determining the candidate design point as an optimal design scheme from the predicted output of the low-precision model in each iteration.

2. The sparse neural network based integrated intra- and exo-atmospheric trajectory optimization method according to claim 1, wherein, The design variable set comprises multi-dimensional design variables; the training sample set is constructed in the following manner: constructing an objective function for sample optimization: ； in, This represents the sample distribution in the training sample set; The design space for design variables consists of the range of values ​​corresponding to each design variable. Indicates that when the condition is met Under the constraints of Maximize; Indicates that when the condition is met Under the constraints Minimize; Indicates the first training sample set Sample The Euclidean distance between them; each sample represents a specific value from a set of design variables; generating initial samples based on the design space by using a Latin hypercube sampling method; when the samples are generated, the sampling frequency is enhanced at the boundary of the design space; optimizing the positions of the samples by using a genetic algorithm under the constraint of the objective function; when the genetic algorithm converges, the optimal sample distribution is obtained, and all the samples at this time constitute the training sample set.

3. The sparse neural network based integrated intra- and exo-atmospheric trajectory optimization method according to claim 1, wherein, The output response comprises multi-dimensional response parameters of the aircraft; the output response set is constructed in the following manner: constructing an interior ballistic simulation model; the interior ballistic simulation model is used for simulating the interior ballistic by using a level set method for each sample in the training sample set; in the simulation process, the evolution of the burning surface follows a Hamilton-Jacobi equation, so as to obtain a thrust-time curve; constructing an exterior ballistic simulation model; the exterior ballistic simulation model is used for solving the corresponding output response by taking the thrust-time curve as input, combining an aerodynamic database and an aerodynamic model of the aircraft; the output responses corresponding to all the samples jointly constitute the output response set; the aerodynamic database refers to an interpolation table of aerodynamic parameters with respect to speed and attack angle.

4. The sparse neural network based integrated intra- and exo-atmospheric trajectory optimization method according to claim 1, wherein, The sparse neural network is a fully connected neural network comprising an input layer, a hidden layer and an output layer; wherein: the number of neurons in the input layer is the same as the dimension of the design variables in the design variable set; the hidden layer is provided with three layers; and the number of neurons in the output layer is consistent with the dimension of the response parameters in the output response; The total loss function includes mean square error and a sparse regularization term as follows: ； in, This is the total loss function; This represents the weight matrix of the sparse neural network as a whole. Batch size; For the first The output response corresponding to each sample; For sparse neural networks targeting the first The predicted output for each sample; is the regularization coefficient, and its value range is . ; For sparse neural networks Layer weight matrix; This represents the total number of layers in the sparse neural network. for of Norms, in their specific form, are as follows: ； wherein, is a weight of a neuron vector of a neuron at a neuron position in a layer of a sparse neural network; is a weight of a neuron vector of a neuron at a neuron position in a layer of a sparse neural network; is a weight of a neuron vector of a neuron at a neuron position in a layer of a sparse neural network; is a weight of a neuron vector of a neuron at a neuron position in a layer of a sparse neural network; are respectively a number of neuron positions and a number of neuron vectors of a layer of a sparse neural network; are respectively a number of neuron positions and a number of neuron vectors of a layer of a sparse neural network; is a sparse index, .

5. The sparse neural network based integrated aircraft's interior and exterior trajectory optimization method of claim 4, wherein, the following gradient update formula is used when the sparse neural network is trained: ； wherein is a partial derivative operator; denotes norm; Based on the gradient update formula, cooperate with AdamW optimizer, use the training sample set and output response set to train the sparse neural network, realize the accurate update and sparsification of the weight matrix of the sparse neural network Adopt cosine annealing strategy to adjust learning rate, set cutting threshold When training the network: If , then the court orders , and freezes the connections between the th neuron vector at the th neuron position in the th layer of the sparse neural network and other neuron vectors so that it no longer participates in subsequent forward propagation and backward update.

6. The sparse neural network based integrated intra- and exo-atmospheric trajectory optimization method according to claim 1, wherein, the screened candidate design points are determined by using the high-precision model to determine the output response, so as to update the training sample set and the output response set, and then retrain the low-precision model, which comprises the following steps: For the former synthetic indicator, the candidate design point corresponding to the output response calculated by calling the high-precision model ; take as the new optimal prediction output ; calculate the prediction error : ； in, Indicates the preceding Among the candidate design points corresponding to the comprehensive index, the first one is... Candidate design points The corresponding output response is obtained through high-precision model calculation; for The predicted output obtained by inputting into a low-precision model; ; Setting an error threshold and a determination is made: If , will be updated to ; if , will be updated to ; if , will be updated to ; Add to the training sample set as a new sample; meanwhile, add to the output response set, to realize the update of the training sample set and the output response set; retraining the sparse neural network by using the updated training sample set and output response set.

7. The sparse neural network based aircraft integrated trajectory optimization method of claim 6, wherein, Determine the current iteration count; if the preset maximum iteration count has been reached, or if the iterations are consecutive... The next iteration satisfies If the prediction fails, the iteration stops; the optimal prediction output from each iteration is used. In the middle, select The candidate design point corresponding to the maximum value is taken as the optimal design scheme; This is a preset value. 8.A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the method for integrated optimization of the interior and exterior ballistic trajectories of the aircraft based on the sparse neural network according to any one of claims 1-7.

9. A computer readable storage medium having stored therein a computer program; characterized in that, The computer program is executed by the processor to implement the sparse neural network-based integrated optimization method for the internal and external ballistics of the aircraft according to any one of claims 1-7.

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