A Structured Subspace Learning-Based Performance-Cost Analysis Method for Solid Rockets

Abstract

This invention relates to the fields of aerospace vehicle overall design, and discloses a structured subspace learning-based solid rocket performance-cost analysis method, comprising: constructing a model sample dataset; constructing a structured sparse subspace feature selection model by combining a similarity graph matrix, and solving it to obtain an optimized row sparse orthogonal projection matrix, wherein the row index of the non-zero row corresponds to the feature parameter in the model sample as the selected cost driving factor; constructing a training sample dataset for a surrogate model; calculating the corresponding specific delivery cost as the output response based on the training samples, and training the surrogate model; for each cost driving factor, constructing a prediction sample dataset by random sampling; using a sequential quadratic programming method to find the optimal prediction sample in the prediction sample dataset, and determining the prediction sample with the minimum specific delivery cost as the final solid rocket design scheme.

Description

Technical Field

[0001] This invention relates to the fields of aerospace vehicle overall design, systems engineering and computational intelligence, and specifically to a solid rocket performance-cost analysis method based on structured subspace learning. Background Technology

[0002] Solid rockets, as a type of propulsion device with simple structure, rapid response, and long-term storage capability, are widely used in aerospace launch vehicles. The overall design of traditional solid rockets usually follows an iterative paradigm of "assumption-analysis-correction". Designers pre-determine a set of geometric parameters based on historical experience or low-precision empirical formulas, estimate the thrust curve using a zero-dimensional internal ballistic model, and then calculate the mechanical properties in combination with a mass model.

[0003] However, with the increasing urgency of space missions demanding "low cost, high reliability, and rapid response," traditional methods have revealed significant technical shortcomings, specifically in the following aspects:

[0004] The "curse of dimensionality" and the trap of local optima in design space: Modern solid rocket design involves dozens or even hundreds of coupled variables, including geometry, topology, material properties, propellant formulation, aerodynamic shape, and control strategies. Existing gradient optimization algorithms (such as sequential quadratic programming, SQP) are prone to getting trapped in local optima when dealing with such non-convex, multi-peak objective functions; while global search algorithms (such as genetic algorithms (GA) and particle swarm optimization (PSO) require exponentially more computation to converge when dealing with high-dimensional spaces (50+ variables), making them impractical in engineering.

[0005] The "black box" effect of key driving factors: In the conceptual design phase, where large-scale historical data is lacking, designers often find it difficult to quantify the specific contribution of each design variable to the final performance index. For example, while increasing the combustion chamber pressure can improve the specific impulse, it also increases the shell wall thickness and structural weight. This nonlinear coupling relationship manifests as severe multicollinearity in traditional regression analysis, making it impossible to accurately identify the core physical parameters that truly affect performance.

[0006] The disconnect between cost and performance evaluation systems: The closest existing solutions typically treat "performance optimization" and "cost estimation" as two independent, sequential processes. That is, a high-performance rocket is designed first, and then the cost is calculated using that model. This fragmented process ignores the direct sensitivity of design parameters to manufacturing costs. The lack of a comprehensive, coupled index that can simultaneously characterize both technological capabilities and economic costs is a major shortcoming of current design methodologies.

[0007] To address the challenges of high-dimensional data, feature selection techniques from data mining have been incorporated into engineering design. However, existing unsupervised feature selection methods (such as Principal Component Analysis (PCA), Laplace score (LS), and methods based on...) are limited. Sparse regression with the -norm has inherent flaws when processing solid rocket design data:

[0008] Insufficient sparsity: Traditional sparse learning often employs... or - The norm, as a regularization term, is essentially a regularization of... -Convex relaxation of the norm. This relaxation often results in a projection matrix that is not sparse enough, and the selected feature subset contains a large number of redundant variables, making it impossible to achieve a "hard selection" of core design variables and increasing the computational burden of subsequent optimization.

[0009] Ignoring physical manifold structure: Standard algorithms assume that samples are uniformly distributed in the feature space, ignoring the inherent physical constraints of engineering data (such as geometric continuity and energy conservation). If the feature selection process disrupts the local manifold structure of the data, the selected parameter combinations will be physically unrealizable. Summary of the Invention

[0010] The purpose of this invention is to provide a solid rocket performance-cost analysis method based on structured subspace learning, which solves the strict sparsity problem of feature selection and combines adaptive graph learning technology to maintain the physical structure of the data, thereby achieving accurate optimization of solid rocket performance.

[0011] To achieve the above objectives, the present invention employs the following technical solution:

[0012] A structured subspace learning-based method for solid rocket performance-cost analysis includes:

[0013] Construct a model sample dataset based on the characteristic parameters of different categories of solid rockets;

[0014] An adaptive similarity graph is constructed using model samples from the model sample dataset as nodes; the weight of the edges between nodes is the similarity between the corresponding model samples; and a similarity graph matrix is ​​constructed using the similarity between the model samples.

[0015] A structured sparse subspace feature selection model is constructed based on the model sample dataset and similarity graph matrix, including the objective function and constraints.

[0016] The similarity graph matrix, feature attention matrix and row sparse orthogonal projection matrix in the objective function are solved alternately under constraints to obtain the optimized row sparse orthogonal projection matrix. The row index of the non-zero row corresponds to the feature parameter in the model sample, which is the selected cost driver factor.

[0017] Based on all the selected cost drivers and the model sample dataset, a training sample dataset for the proxy model is constructed; for each training sample, its corresponding specific delivery cost is determined, and the specific delivery cost is used as the output response of the training sample to obtain the output response set;

[0018] Construct a proxy model; train the proxy model using the training sample dataset and the output response set;

[0019] A corresponding value space is set for each cost driver factor; a prediction sample dataset is constructed by random sampling, and a specific delivery cost corresponding to each prediction sample is determined by using a trained surrogate model; the prediction sample with the minimum specific delivery cost is selected as the final solid rocket design scheme by searching the prediction sample dataset.

[0020] Furthermore, the construction process of the model sample dataset is as follows:

[0021] First, based on publicly available technical manuals or simulation inversion data, collect characteristic parameters of multiple solid rocket models to construct multiple initial model samples, thus obtaining a model sample dataset.

[0022] Data cleaning is performed on the initial model samples, including handling missing values, removing outliers, standardization, and encoding.

[0023] The model sample dataset is expanded using a random sampling method.

[0024] Furthermore, missing value handling refers to filling missing feature parameters in each model sample with the mean of the same feature parameter in other model samples, or filling them with KNN interpolation; outlier removal refers to removing outlier model samples from all initial model samples using box plots; standardization refers to Z-score standardization of the feature parameters of continuous variables in the model samples; and encoding refers to one-hot encoding of the qualitative feature parameters in the model samples.

[0025] Furthermore, the model sample dataset is expanded using random sampling methods, including:

[0026] For each feature parameter in all model samples, its distribution interval is calculated; Latin hypercube sampling is performed on the distribution intervals of all feature parameters, and each set of feature parameters obtained from the sampling is used as a new model sample and added to the model sample dataset; then, the Shapiro-Wilk test is performed on the model sample dataset. If the model sample distribution conforms to a normal distribution, the construction of the model sample dataset is completed; otherwise, the dataset is expanded again.

[0027] Furthermore, the objective function of the structured sparse subspace feature selection model is as follows:

[0028] ;

[0029] The constraints are as follows:

[0030] ;

[0031] in Indicates minimization. Indicates the number of model samples in the model sample dataset; superscript Indicates the transpose operation; express Norm; express Norm; To find the trace of the matrix; Represents a diagonalized matrix; Indicates the first in the model sample dataset The model sample and the first One model sample; Similarity graph matrix The Middle OK The elements of the column represent The similarity between them; For row sparse orthogonal projection matrices; The weight matrix for the feature parameters, with elements on its diagonal. Indicates the first Importance weights of each feature parameter; Feature attention matrix Depend on All diagonal elements constitute; The control parameters for the graph have a range of values. ; The global variance maximization term The weight control parameter has a value range of 100%. ; Represents the similarity graph matrix The Middle Row similarity vector; Represents a vector consisting entirely of 1s; It is the identity matrix; Represents a row sparse orthogonal projection matrix The number of zero rows in the middle and lower bounds.

[0032] Furthermore, the similarity graph matrix, feature attention matrix, and row sparse orthogonal projection matrix in the objective function are solved alternately under constraints to obtain the optimized row sparse orthogonal projection matrix, including:

[0033] Step 1, fix and ,renew ;

[0034] Constructing the Laplacian matrix ,in Let be the degree matrix; the objective function simplifies to:

[0035] ;

[0036] in To represent maximization, the auxiliary matrix Defined as: ; It is a constant, and its value is not less than ; This represents the model sample dataset;

[0037] Update by solving the objective function ;

[0038] Step 2, fix and ,renew ;

[0039] At this point, the objective function transforms into a function about Quadratic programming problem:

[0040] ;

[0041] constraint: ; superscript Represents the Hadamah altar;

[0042] The objective function is solved using the augmented Lagrange multiplier method to update... ;

[0043] Step 3, fix and ,renew ;

[0044] For each model sample, calculate its optimal similarity to other model samples. :

[0045] ;

[0046] in, Indicates the first One model sample, ; Utilize optimal similarity right Update;

[0047] After the , and By alternating updates, the final optimized row sparse orthogonal projection matrix is ​​obtained. .

[0048] Furthermore, the specific delivery cost corresponding to each training sample as follows:

[0049] ;

[0050] in, This indicates the cost per rocket launched by a solid rocket. For the effective payload mass of a solid rocket, This indicates the effective flight distance of a solid rocket.

[0051] Furthermore, the Kriging model is adopted as the surrogate model.

[0052] 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 solid rocket performance-cost analysis method based on structured subspace learning.

[0053] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the solid rocket performance-cost analysis method based on structured subspace learning.

[0054] Compared with the prior art, the present invention has the following technical features:

[0055] 1. Clear Identification of Cost Drivers: Through verification through embodiments, this invention reveals that the scale parameters of solid rockets (rocket diameter, launch mass, and overall rocket length) are key cost drivers affecting performance-cost. This differs from the traditional design approach that simply pursues high specific impulse, indicating that in solid rocket design, the performance / cost benefits gained through geometric scaling out outweigh those from fine-tuning internal ballistic parameters. In subsequent optimization design, these cost drivers can be prioritized for optimization to reduce costs.

[0056] 2. Algorithm robustness and sparsity: Compared with traditional methods, the method used in this invention... - Norm constraints avoid the fluctuations in results caused by regularization parameter adjustment, and directly provide a discrete and definite set of key parameters, eliminating ambiguity in design decisions.

[0057] 3. Adaptive noise reduction capability: The feature attention module can automatically identify and suppress noise in simulation data (such as measurement errors or random fluctuations of minor parameters), making the analysis results more focused on the physical essence.

[0058] 4. Strong engineering applicability: This method does not rely on labeled historical data (since new solid rocket models often lack historical cost labels, unsupervised learning is more advantageous) and can be widely applied to the early concept design and scheme demonstration stages of spacecraft such as sounding rockets and solid rocket boosters. Attached Figure Description

[0059] Figure 1 A flowchart illustrating the method of this invention;

[0060] Figure 2 This is a convergence graph of the objective function value in an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram showing some cost driving factors and their corresponding importance weights in an embodiment of the present invention;

[0062] Figure 4 This is a parameter sensitivity experiment diagram from an embodiment of the present invention. Detailed Implementation

[0063] To address the problems in existing solid rocket and launch system designs, such as the complex coupling relationship between performance parameters and life-cycle costs, and the difficulty in accurately quantifying and identifying key cost drivers during the conceptual design phase, this invention provides a structured subspace learning-based solid rocket performance-cost analysis method, comprising the following steps:

[0064] Step 1: Construct a model sample dataset based on the characteristic parameters of different categories of solid rockets; the categories of the characteristic parameters include physical scale, material properties, control system, aerodynamic properties, and propulsion system.

[0065] The physical scale features 10 parameters, including rocket diameter, overall rocket length, slenderness ratio, launch mass, combustion chamber volume, shell wall thickness, nozzle throat diameter, nozzle exit diameter, propellant mass, and structural coefficient; the material properties feature 8 parameters, including shell material type, material density, tensile strength, elastic modulus, insulation layer density, lining thickness, nozzle throat lining ablation rate, and reference material cost index; the control system features 12 parameters, including guidance mode, circular error probability, servo type, control surface span, control surface chord length, and static stability margin. The aerodynamic characteristics include: speed, control system bandwidth, IMU drift rate, anti-interference level, TVC (thrust vector control) maximum swing angle, actuator power consumption, and control section mass; there are 10 characteristic parameters of aerodynamic characteristics, including zero-lift drag coefficient, lift line slope, maximum Mach number, bottom drag coefficient, wave drag coefficient, maximum dynamic pressure, aerodynamic heating heat flux, pressure core position, roll damping torque, and angle of attack limit; there are 8 characteristic parameters of the propulsion system, including propellant formulation type, theoretical specific impulse, burning rate coefficient, pressure index, characteristic velocity, nozzle expansion ratio, propellant anisotropy, and loading coefficient.

[0066] Therefore, in the model sample dataset of this invention, each model sample has 48 dimensions; that is, the form of the model sample is: [physical scale features, material property features, control system features, aerodynamic property features, and propulsion system features]. The physical scale features are used to reflect the geometric scale and mass scale of the solid rocket; the material property features are used to determine the structural weight coefficient and manufacturing cost; the control system features are used to reflect the precise control capability and electronic system complexity; the aerodynamic property features are parameters that affect the range and flight stability; and the propulsion system features are parameters that determine the power performance.

[0067] The process of constructing the model sample dataset is as follows:

[0068] Step 1.1: First, based on publicly available technical manuals or simulation inversion data, collect multiple sets of characteristic parameters of different solid rocket models to construct multiple sets of initial model samples, thus obtaining a model sample dataset; that is, construct a model sample for the characteristic parameters of each type of solid rocket.

[0069] Step 1.2 involves data cleaning of the initial model samples, including missing value handling, outlier removal, standardization, and encoding.

[0070] Missing value handling refers to filling missing feature parameters in each model sample with the mean of the same feature parameter in other model samples, or filling them with KNN interpolation.

[0071] Outlier removal refers to the process of removing outlier model samples from all initial model samples using the box plot method (IQR criterion).

[0072] Standardization refers to Z-score standardization of the feature parameters of continuous variables in the model samples to eliminate dimensional differences.

[0073] Encoding refers to the unique thermal encoding of qualitative feature parameters in the model samples, such as "formulation type".

[0074] Step 1.3, expand the model sample dataset as follows:

[0075] For each feature parameter in all model samples, its distribution interval is calculated; the distribution intervals of all feature parameters are randomly sampled using Latin hypercube sampling, and each set of feature parameters obtained from each sampling is used as a new model sample and added to the model sample dataset; then the Shapiro-Wilk test is performed on the model sample dataset. If the model sample distribution conforms to a normal distribution, it indicates that the construction of the model sample dataset is reasonable; otherwise, it is expanded again.

[0076] In one embodiment of the present invention, 50 sets of initial model samples were collected, and after outlier removal, 40 sets remained. After expansion, a total of 108 sets of model samples were collected.

[0077] Step 2: Using the model samples in the model sample dataset as nodes, construct an adaptive similarity graph; the weight of the edges between nodes is the similarity between the corresponding model samples; construct a similarity graph matrix using the similarity between the model samples. Similarity graph matrix The Middle OK Column elements Indicates the first The model sample and the first The similarity of individual model samples.

[0078] Step 3: Construct a structured sparse subspace feature selection model based on the model sample dataset and the similarity graph matrix, including the objective function and constraints; this model is used to learn the similarity graph matrix. Feature attention matrix Sparse orthogonal projection matrix .

[0079] The objective function of the structured sparse subspace feature selection model is as follows:

[0080] ;

[0081] The constraints of the structured sparse subspace feature selection model are as follows:

[0082] ;

[0083] in, Indicates the number of model samples in the model sample dataset; superscript This indicates the transpose operation, and the same applies below; express Norm; express Norm; To find the trace of the matrix; Represents a diagonalized matrix; Indicates the first in the model sample dataset The model sample and the first One model sample; row sparse orthogonal projection matrix Used to project feature parameters from model samples into a multidimensional subspace; The weight matrix for the feature parameters, with elements on its diagonal. Indicates the first Importance weights of each feature parameter; Feature attention matrix Depend on All diagonal elements constitute; The graph control parameter controls the sparsity of the adaptive similarity graph, and its value range is [value range missing]. ; The global variance maximization term The weight control parameter has a value range of 100%. ; Represents the similarity graph matrix The Middle Row similarity vector; Represents a vector consisting entirely of 1s; It is the identity matrix; This represents the number of selected feature parameters, i.e., the row sparse orthogonal projection matrix. The number of zero rows in the middle and lower bounds.

[0084] Among them, the The norm is a mixture norm, used to calculate the norm of each row of a matrix. Norm, and then calculate norm Norm, thus counting the number of non-zero rows.

[0085] In the above objective function, This is a local popularity preservation term; it is used to indicate that if two model samples are close in distance in a multidimensional subspace, then the two model samples should have a high degree of similarity; this will force the structured sparse subspace feature selection model to learn a structure that conforms to the intrinsic geometric distribution of the model samples; The maximum entropy regularization term, without which the optimization result often causes each model sample to connect only to its nearest neighbor model sample, leading to an overly sparse and unrobust adaptive similarity graph; introducing the maximum entropy regularization term forces a more uniform connection distribution in the adaptive similarity graph; the global variance maximization term... This encourages the projected feature parameters to retain as much global information as possible.

[0086] Of the constraints mentioned above, constraint 1 is a probabilistic constraint on the adaptive similarity graph, ensuring that the similarity graph matrix... This is the normalized result; constraint 2 is an orthogonal constraint, ensuring the row sparse orthogonal projection matrix. It forms an orthogonal basis to avoid degeneracy; constraint 3 is an attention weight constraint; constraint 4 is... Norm constraints are used to enforce row sparse orthogonal projection matrices. The number of non-zero rows is This means that selection was made directly through physical means. Using a single feature parameter, rather than filtering by a soft threshold; the selected... The feature parameters corresponding to the row indices of non-zero rows are the cost driver factors, representing the key factors affecting performance-cost.

[0087] Step 4: Solve the similarity graph matrix, feature attention matrix, and row sparse orthogonal projection matrix in the objective function alternately under constraints to obtain the optimized row sparse orthogonal projection matrix. ; Row sparse orthogonal projection matrix In The feature parameters corresponding to the row indices of the non-zero rows in the model samples are the selected cost drivers.

[0088] The process of solving the structured sparse subspace feature selection model is as follows:

[0089] Step 4.1, first set , and The value of ; in one embodiment of the present invention, The value is 12. The value is 0.005. The value is 0.01; the Euclidean distance between model samples in the model sample dataset is calculated based on the KNN algorithm, and the normalized result of the Euclidean distance is used as the similarity between model samples, thereby improving the similarity graph matrix. Perform initialization.

[0090] Step 4.2, since the objective function contains non-convex... Due to norm constraints and variable coupling, a direct analytical solution cannot be obtained; therefore, this invention employs an alternating iterative optimization strategy, updating the solution in three cyclical steps:

[0091] Step 1, fix and ,renew .

[0092] when and When fixed, the problem becomes: Subspace learning under constraints; constructing the Laplacian matrix ,in Let be the degree matrix; the objective function simplifies to:

[0093] ;

[0094] Where the auxiliary matrix Defined as: ;here It is a sufficiently large constant whose value is not less than , here set ,ensure Zhengding; This represents the model sample dataset.

[0095] At this point, the objective function is a typical trace maximization problem with row sparsity constraints; The optimal solution does not require gradient descent, but can be obtained through the following closed-form solution:

[0096] Calculate the auxiliary matrix The diagonal elements are used to represent the score of each feature parameter; then the elements with the largest diagonal values ​​are selected. Each index constitutes an index set. ;make non If all rows are 0, then The non-zero rows are formed by the auxiliary matrix The principal eigenvectors of the corresponding submatrices are used to construct this; this step directly utilizes... The combination of properties avoids the traditional The norm requires complex approximate solutions.

[0097] Step 2, fix and ,renew .

[0098] The problem then becomes finding the optimal weight matrix. The objective function is transformed into a function about Quadratic programming problem:

[0099] ;

[0100] constraint: ; superscript It represents the Hadamaji.

[0101] At this point, the objective function is a standard convex quadratic programming problem, which can be solved using the Augmented Lagrange Multiplier Method (ALM). This step automatically increases the importance weights of feature parameters that contribute significantly to preserving the data structure, based on the current projection effect, and suppresses noise.

[0102] Step 3, fix and ,renew .

[0103] For each model sample, calculate its optimal similarity to other model samples. This is a Euclidean distance projection problem with entropy regularization, and its analytical solution is in the well-known Softmax form:

[0104] ;

[0105] in, Indicates the first One model sample, .

[0106] The size depends on the model samples and Distance in the weighted feature space; the closer the distance, the more exponentially the similarity increases; weight control parameters. Similar to "temperature" in thermodynamics: The smaller the size, the more acute the distribution, focusing only on the nearest neighbors; The larger the similarity, the more uniform the distribution; utilizing the optimal similarity. right The graph is then updated to create an adaptive similarity graph that can dynamically adapt to changes in feature weights.

[0107] After the , and By alternating updates, the final optimized row sparse orthogonal projection matrix can be obtained. Because it was enforced constraint, Only in China The rows are non-zero; the row indices of these non-zero rows correspond to the feature parameters in the model samples that are selected as cost drivers.

[0108] In this embodiment, the selected The cost drivers are: rocket diameter, overall rocket length, aspect ratio, launch mass, shell material type, guidance mode, servo type, control surface wingspan, maximum Mach number, propellant formulation type, theoretical specific impulse, and nozzle expansion ratio.

[0109] Step 5: Based on all the selected cost-driving factors and the model sample dataset, construct the training sample dataset for the proxy model; wherein, each model sample in the model sample dataset has all feature parameters except for the cost-driving factors removed, thus forming the training sample in the training sample dataset; for each training sample, determine its corresponding specific delivery cost. The specific calculation formula is as follows:

[0110] ;

[0111] in, This indicates the cost per rocket launched by a solid rocket. For the effective payload mass of a solid rocket, Indicates the effective flight distance of a solid rocket. Also includes the specific delivery cost. The output response (i.e., label) is used as the training sample, thus obtaining the output response set.

[0112] Step 6: Construct the surrogate model; train the surrogate model using the training sample dataset and the output response set; in this embodiment, the Kriging model is used as the surrogate model.

[0113] Step 7: Define a corresponding value space for each cost driver; construct a prediction sample dataset using a random sampling method, i.e., sample the value space of each cost driver, obtaining one prediction sample each time; determine the specific delivery cost corresponding to each prediction sample using the trained surrogate model; and optimize the prediction sample dataset to determine the specific delivery cost. The smallest predicted sample is used as the final solid rocket design scheme, that is, the solid rocket is designed using the specific values ​​of the cost driving factors in the predicted sample; the optimization can be achieved using a sequential quadratic programming algorithm.

[0114] In one embodiment of the present invention, the size of the model sample dataset is 10⁸, and the convergence graph of the objective function value is shown below. Figure 2 As shown; via Figure 2 It can be seen that the objective function value converged after only 2 iterations, indicating that the method has high computational efficiency and strong engineering applicability.

[0115] Final selection of cost drivers and their corresponding importance weights like Figure 3 As shown; according to importance weight It can be seen that rocket diameter, launch mass, and overall rocket length are the main cost drivers. Therefore, constructing training samples based on these cost drivers to build a proxy model, i.e., the subsequent optimization process, can effectively reduce the specific delivery cost of the final solid rocket design.

[0116] Figure 4 In order to obtain the objective function , The sensitivity experiment results for these two parameters demonstrate... , The impact of different values ​​on accuracy (ACC) is illustrated in the example where, , They are respectively , When the objective function is constructed, the accuracy is highest, thus providing a basis for subsequent methods to apply the parameters. , The value of is provided as guidance.

[0117] 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 method for solid rocket performance-cost analysis using structured subspace learning, characterized in that, include: Construct a model sample dataset based on the characteristic parameters of different categories of solid rockets; An adaptive similarity graph is constructed by using model samples in the model sample dataset as nodes. The weight of the edge between nodes is the similarity between the model samples corresponding to the nodes; Construct a similarity graph matrix using the similarity between model samples; A structured sparse subspace feature selection model is constructed based on the model sample dataset and the similarity graph matrix, including the objective function and constraints; the objective function is as follows: ； The constraints are as follows: ； in Indicates minimization. Indicates the number of model samples in the model sample dataset; superscript Indicates the transpose operation; express Norm; express Norm; To find the trace of the matrix; Represents a diagonalized matrix; Indicates the first in the model sample dataset The model sample and the first One model sample; Similarity graph matrix The Middle OK The elements of the column represent The similarity between them; For row sparse orthogonal projection matrices; The weight matrix for the feature parameters, with elements on its diagonal. Indicates the first Importance weights of each feature parameter; Feature attention matrix Depend on All diagonal elements constitute; The control parameters for the graph have a range of values. ; The global variance maximization term The weight control parameter has a value range of 100%. ; Represents the similarity graph matrix The Middle Row similarity vector; Represents a vector consisting entirely of 1s; It is the identity matrix; Represents a row sparse orthogonal projection matrix The number of zero rows in the middle and lower bounds; The similarity graph matrix, feature attention matrix and row sparse orthogonal projection matrix in the objective function are solved alternately under constraints to obtain the optimized row sparse orthogonal projection matrix. The row index of the non-zero row corresponds to the feature parameter in the model sample, which is the selected cost driver factor. Based on all the selected cost drivers and the model sample dataset, a training sample dataset for the proxy model is constructed; for each training sample, its corresponding specific delivery cost is determined, and the specific delivery cost is used as the output response of the training sample to obtain the output response set; Construct a proxy model; train the proxy model using the training sample dataset and the output response set; For each cost driver, a corresponding value space is set; A prediction sample dataset is constructed using a random sampling method. A trained surrogate model is used to determine the specific delivery cost corresponding to each prediction sample. The prediction sample with the minimum specific delivery cost is selected as the final solid rocket design scheme by searching the prediction sample dataset.

2. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 1, characterized in that, The process of constructing the model sample dataset is as follows: First, based on publicly available technical manuals or simulation inversion data, collect characteristic parameters of multiple solid rocket models to construct multiple initial model samples, thus obtaining a model sample dataset. Data cleaning is performed on the initial model samples, including handling missing values, removing outliers, standardization, and encoding. The model sample dataset is expanded using a random sampling method.

3. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 2, characterized in that, Missing value handling refers to filling missing feature parameters in each model sample with the mean of the same feature parameter in other model samples, or filling them with KNN interpolation; outlier removal refers to removing outlier model samples from all initial model samples using box plots; standardization refers to Z-score standardization of the feature parameters of continuous variables in the model samples; encoding refers to one-hot encoding of the qualitative feature parameters in the model samples.

4. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 2, characterized in that, The model sample dataset is expanded using random sampling methods, including: For each feature parameter in all model samples, its distribution interval is calculated; Latin hypercube sampling is performed on the distribution intervals of all feature parameters, and each set of feature parameters obtained from the sampling is used as a new model sample and added to the model sample dataset; then, the Shapiro-Wilk test is performed on the model sample dataset. If the model sample distribution conforms to a normal distribution, the construction of the model sample dataset is completed; otherwise, the dataset is expanded again.

5. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 1, characterized in that, The similarity graph matrix, feature attention matrix, and row sparse orthogonal projection matrix in the objective function are solved alternately under constraints to obtain the optimized row sparse orthogonal projection matrix, including: Step 1, fix and ,renew ; Constructing the Laplacian matrix ,in Let be the degree matrix; the objective function simplifies to: ； in To represent maximization, the auxiliary matrix Defined as: ; It is a constant, and its value is not less than ; This represents the model sample dataset; Update by solving the objective function ; Step 2, fix and ,renew ; At this point, the objective function transforms into a function about Quadratic programming problem: ； constraint: ; superscript Represents the Hadamah altar; The objective function is solved using the augmented Lagrange multiplier method to update... ; Step 3, fix and ,renew ; For each model sample, calculate its optimal similarity to other model samples. : ； in, Indicates the first One model sample, ; Utilize optimal similarity right Update; After the , and By alternating updates, the final optimized row sparse orthogonal projection matrix is ​​obtained. .

6. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 1, characterized in that, The specific delivery cost for each training sample as follows: ； in, This indicates the cost per rocket of a solid rocket. For the effective payload mass of a solid rocket, This indicates the effective flight distance of a solid rocket.

7. The solid rocket performance-cost analysis method based on structured subspace learning according to claim 1, characterized in that, The Kriging model is used as the surrogate model.

8. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes a computer program, it implements the solid rocket performance-cost analysis method based on structured subspace learning as described in any one of claims 1-7.

9. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by a processor, it implements the solid rocket performance-cost analysis method based on structured subspace learning as described in any one of claims 1-7.

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