Aero-engine control method and system based on adaptive framing

Abstract

The application discloses an aero-engine control method and system based on adaptive composition in the field of aerospace, and provides the aero-engine control method based on adaptive composition, which comprises the following steps: step 1, obtaining data samples according to the mechanical characteristics of a turbine engine, and obtaining a data matrix according to the data samples; step 2, using the Euclidean distance to describe the similarity between the data samples, combining the method of adaptive weight construction, and obtaining the element similarity matrix of the data samples through an iterative algorithm optimization, and simultaneously obtaining the corresponding clustering indication matrix; obtaining observation data and real thrust according to the output of a simulation system, and inputting the observation data and the real thrust into the next iteration, so that the accuracy of clustering is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to an adaptive graph-based aero-engine control method and system in the field of aerospace. BACKGROUND

[0002] The core difficulty of aero-engine model-based control system optimization is how to avoid the multi-mismatch problem between engine thrust and speed caused by engine aging and degradation. Due to the difficulty in establishing the mathematical model of the aero-engine, and the difficulty in accurately obtaining the model parameters in the change of the engine working state, and with the complication of the engine control system, the required observation data, prediction data and control data are also increased, and the traditional engine control system cannot be applied to all cases under such a large number of data gains. In the field of machine learning, spectral clustering and adaptive graphing provide a strategy for high-dimensional data inference. Spectral clustering can make large data information calculation more efficient by constructing a sparse graph, and adaptive graphing can make the similarity matrix obtained according to the similarity between data without artificial construction by designing an optimization problem. Combining these two methods can obtain the optimal solution. Therefore, according to the characteristics of data processing of spectral clustering and adaptive graphing, we can combine machine learning with PID compensator to form a composite direct thrust system.

[0003] In the prior art, the existing aero-engine application in machine learning algorithm uses the nonlinear mapping of neural network to establish a complex model. However, the reconstruction error method can only express the error between the same samples, without considering the difference between multiple samples. Moreover, only simple threshold and scale problems are considered in the optimization process, and reducing the complexity of design simplifies the calculation process, but does not fully utilize the overall structure of the data. Therefore, there is a lack of sufficient exploration in the aero-engine control system. SUMMARY

[0004] The purpose of the present application is to provide an adaptive graph-based aero-engine control method and system, which can effectively express the similarity relationship of each data element and improve the accuracy of the similarity element through adaptive weight construction.

[0005] To achieve the above objectives, this invention provides an aero-engine control method based on adaptive graphing, comprising the following steps: Step 1, obtaining data samples based on the mechanical characteristics of the turbine engine, and obtaining a data matrix based on the data samples; Step 2, using Euclidean distance to describe the similarity between data samples, and combining an adaptive weighting construction method, obtaining the element similarity matrix of the data samples through an iterative algorithm, and simultaneously obtaining the corresponding clustering indicator matrix; Step 3, obtaining the category similarity of data elements through a linear kernel method, and then obtaining the weighted average control quantity u of the data elements through the linear kernel matrix and the data matrix; Step 4, using PID to obtain the deviation between the actual thrust and the predicted thrust, and obtaining the compensation control quantity u. pid A composite thrust control system combining adaptive construction methods is established to control the thrust of the turbofan engine; in step 5, the engine generates corresponding thrust and observation data according to the input of the control system, records the input and enters the next simulation cycle.

[0006] Compared with existing technologies, the advantages of this invention lie in the fact that the proposed method describes the similarity relationship of data elements using Euclidean distance, assigns adaptive weights when constructing the similarity matrix, obtains a clustering indicator matrix through a spectral clustering algorithm, and expresses the linear relationship of data elements using a linear kernel. The weighted average of the data elements and the linear kernel is linearly superimposed with the deviations of the actual and predicted data and then input into the simulation system. The observed data and actual thrust are obtained from the output of the simulation system and input into the next iteration. This process is more efficient and therefore helps to improve the accuracy of clustering.

[0007] As a further improvement to the present invention, the specific content of step 1 is as follows.

[0008] Set the data sample as Where n represents the number of samples, d represents the dimension of the sample features, and the various features of the samples include...

[0009] x = [H, Ma, W] f (k-2), W f (k-1),A8(k-2),A8(k-1),A8(k),N L (k-1), N H (k-1), T 43 (k-1), P6(k-1), T6(k-1), FG(k-1), N L (k), N H (k), P 22 (k), T 22 (k), P3(k), T 43 (k), P6(k), T6(k), FG r ]

[0010] Where k is the time marker, H is the flight altitude, Ma is the flight Mach number, and W is the flight speed. f Fuel flow rate, A8 is the adjustable nozzle throat area, FG r For reference thrust; low-pressure speed N L High pressure and high speed N H Fan outlet pressure P 22 Fan outlet temperature T 22 Compressor outlet pressure P3, high-pressure turbine outlet temperature T 43 The combination of at least two of the following parameters constitutes the observation parameter combination: low-pressure turbine outlet temperature P6, low-pressure turbine outlet temperature T6, and thrust FG. In the next iteration of the entire composite thrust system, the dimension will increase by one dimension from the original dimension because the actual thrust will be added to the observation data.

[0011] As a further improvement to the present invention, the specific content of step 2 is as follows.

[0012] The element similarity of the data matrix is ​​expressed using Euclidean distance, while adaptively acquiring the element similarity between samples. Specifically, a weighted undirected graph H is constructed for the samples.<V,E> Each sample is a vertex in H, and the set of edges is E = {e i，j} represents sample x i and x j The Euclidean distance between them is used to obtain adaptive weights w = {w i，j} is used to optimize the similarity matrix.

[0013] As a further improvement of the present invention, in step 2, the similarity matrix obtained after optimization is a clustering indicator matrix, denoted as S, and the weight vectors w = {w... i，j}, L S Let F represent the Laplacian matrix of the similarity matrix, and let F represent the indicator matrix of the Laplacian matrix. Then the objective function for this step is as follows:

[0014]

[0015] Where n represents the number of data points, w i，j s represents the adaptive weights between two data points. i，j Representing data x i To x j The similarity between elements; the first row of the above formula is the sum of three terms, the second row is the range of values, the first term describes the similarity of the data through Euclidean distance and assigns adaptive weights to balance the size of the elements in the similarity matrix; the second term is to avoid trivial solutions, so the norm of the indicator matrix F is added, which can be intuitively interpreted as: if two data points are close, they are also close to each other in the similarity graph, where 1 represents a vector of all 1s; the third term... It performs spectral clustering on similar graphs and constructs a clustering indicator matrix for subsequent linear kernel calculation; tr(.) represents the trace of the matrix, and α and β are hyperparameters used to control the regularization term.

[0016] As a further improvement of the present invention, the Lagrange multiplier method and the alternating iterative update method are used to solve the objective function in step 2.

[0017] As a further improvement of the present invention, in step 3, the linear kernel matrix is ​​obtained based on the clustering indicator matrix, and then weighted and averaged with the data matrix to obtain the control quantity u, the expression of which is:

[0018]

[0019] Where n represents the number of data points, X represents the data matrix, 1 represents an all-one vector, F represents the clustering indicator matrix, and u represents the control variable.

[0020] As a further improvement of the present invention, the thrust compensation amount u is obtained by using PID in step 4. pid This is combined with an adaptive mapping method to form a composite thrust control system, where u and u pid Linear superposition is performed to obtain the total output of the composite thrust system, u. pid The expression is:

[0021]

[0022] Where, e(k)=FG r -FG(k-1) represents the control variable.

[0023] To achieve the above objectives, this invention also provides an aero-engine control system based on adaptive graphing, including a feature extraction module, a similarity matrix construction module, a linear similarity control quantity construction module, and a simulation loop module. The feature extraction module is used to form a data matrix by combining features such as envelope data, iteration parameters, and observation data with the number of samples, thereby enabling mathematical calculations of the model. The similarity matrix construction module is used to obtain a similarity matrix of data sample elements through Euclidean correlation and adaptive graphing optimization. The linear similarity control quantity construction module is used to obtain a control quantity by weighted averaging the linear similarity matrix constructed from the similarity matrix with the original matrix, for controlling the engine. The simulation loop module is used to obtain corresponding thrust and observation data after controlling the system input, and then input the data into the next simulation loop.

[0024] Compared with the prior art, the beneficial effect of the present invention is that it is used to input engine control quantities into the simulation system to obtain real thrust and observation data, and then use them as input for the next iteration, thereby reducing errors and achieving the optimal solution. Attached Figure Description

[0025] Figure 1 This is a diagram showing the working cross-section of the turbofan engine components and air passage in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of the adaptive graphing composite engine thrust model of the present invention.

[0027] Figure 3 The results are simulation results of the step response at the operating point within the envelope of this invention.

[0028] Figure 4 This is a comparison chart of the actual thrust and the predicted thrust of the present invention. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings:

[0030] like Figures 1-3 The aero-engine control method based on adaptive graphing, as shown, includes the following steps:

[0031] Step 1: Obtain data samples based on the mechanical characteristics of the turbine engine, and then obtain a data matrix based on the data samples;

[0032] Set the data sample as Where n represents the number of samples, d represents the dimension of the sample features, and the various features of the samples include...

[0033] x = [H, Ma, W] f (k-2), W f (k-1),A8(k-2),A8(k-1),A8(k),N L (k-1), N H (k-1), T 43 (k-1), P6(k-1), T6(k-1), FG(k-1), N L (k), N H (k), P 22 (k), T 22 (k), P3(k), T 43 (k), P6(k), T6(k), FG r ]

[0034] Where k is the time marker, H is the flight altitude, Ma is the flight Mach number, and W is the flight speed. f Fuel flow rate, A8 is the adjustable nozzle throat area, FG r For reference thrust; low-pressure speed N L High pressure and high speed N H Fan outlet pressure P 22 Fan outlet temperature T 22Compressor outlet pressure P3, high-pressure turbine outlet temperature T 43 The combination of at least two of the following parameters constitutes the observation parameter combination: low-pressure turbine outlet temperature P6, low-pressure turbine outlet temperature T6, and thrust FG. In the next iteration of the entire composite thrust system, the dimension will increase by one dimension from the original dimension because the actual thrust will be added to the observation data.

[0035] Step 2: Use Euclidean distance to describe the similarity between data samples. Combined with the adaptive weight construction method, use an iterative algorithm to optimize and obtain the element similarity matrix of the data samples, and at the same time obtain the corresponding clustering indicator matrix.

[0036] The element similarity of the data matrix is ​​expressed using Euclidean distance, while adaptively acquiring the element similarity between samples. Specifically, a weighted undirected graph H is constructed for the samples.<V,E> Each sample is a vertex in H, and the set of edges is E = {e i，j} represents sample x i and x j The Euclidean distance between them is used to obtain adaptive weights w = {w i，j} is used to optimize the similarity matrix.

[0037] The optimized similarity matrix is ​​the clustering indicator matrix, denoted as S, and the weight vectors for different aero-engines are w = {w i，j}, L S Let F represent the Laplacian matrix of the similarity matrix, and let F represent the indicator matrix of the Laplacian matrix. Then the objective function for this step is as follows:

[0038]

[0039] Where n represents the number of data points, w i，j s represents the adaptive weights between two data points. i，j Representing data x i To x j The similarity between elements; the first row of the above formula is the sum of three terms, the second row is the range of values, the first term describes the similarity of the data through Euclidean distance and assigns adaptive weights to balance the size of the elements in the similarity matrix; the second term is to avoid trivial solutions, so the norm of the indicator matrix F is added, which can be intuitively interpreted as: if two data points are close, they are also close to each other in the similarity graph, where 1 represents a vector of all 1s; the third term... It performs spectral clustering on similar graphs and constructs a clustering indicator matrix for subsequent linear kernel calculation; tr(.) represents the trace of the matrix, and α and β are hyperparameters used to control the regularization term.

[0040] In step 2, the Lagrange multiplier method and the alternating iterative update method are used to solve the objective function.

[0041] Step 3: Obtain the category similarity of data elements through the linear kernel method, and then obtain the weighted average control quantity u of data elements through the linear kernel matrix and the data matrix;

[0042] The control quantity u is obtained by weighting the linear kernel matrix obtained from the clustering indicator matrix and then the data matrix. Its expression is as follows:

[0043]

[0044] Where n represents the number of data points, X represents the data matrix, 1 represents an all-one vector, F represents the clustering indicator matrix, and u represents the control variable.

[0045] Step 4: Use PID control to obtain the deviation between the actual thrust and the predicted thrust, and obtain the compensation control quantity u. pid Establish a composite thrust control system that combines adaptive construction methods to control the thrust of a turbofan engine;

[0046] Using PID to obtain thrust compensation amount u pid This is combined with an adaptive mapping method to form a composite thrust control system, where u and u pid Linear superposition is performed to obtain the total output of the composite thrust system, u. pid The expression is:

[0047]

[0048] Where, e(k)=FG r -FG(k-1) represents the control variable.

[0049] Step 5: The engine generates corresponding thrust and observation data based on the input from the control system, records the input, and enters the next simulation cycle.

[0050] The aero-engine control system based on adaptive graphing includes a feature extraction module, a similarity matrix construction module, a linear similarity control quantity construction module, and a simulation loop module. The feature extraction module combines features such as envelope data, iteration parameters, and observation data with the number of samples to form a data matrix, thereby enabling mathematical calculations for the model. The similarity matrix construction module obtains a similarity matrix of data sample elements through Euclidean correlation and adaptive graphing optimization. The linear similarity control quantity construction module obtains the control quantity by weighted averaging the linear similarity matrix constructed from the similarity matrix with the original matrix, which is used to control the engine. The simulation loop module receives the corresponding thrust and observation data after controlling the system input and then feeds the input data into the next simulation loop.

[0051] In this invention, it is assumed that the data sample is Where n represents the number of samples and d represents the sample dimension, then

[0052] x = [H, Ma, W] f (k-2), W f (k-1),A8(k-2),A8(k-1),A8(k),N L (k-1), N H (k-1), T 43 (k-1), P6(k-1), T6(k-1), FG(k-1), N L (k), N H (k), P 22 (k), T 22 (k), P3(k), T 43 (k), P6(k), T6(k), FG r ]

[0053] Where k is the time marker, H is the flight altitude, Ma is the flight Mach number, and W is the flight speed. f Fuel flow rate, A8 is the adjustable nozzle throat area, FG r For reference thrust; the combination of observation parameters is as follows: low-pressure rotational speed N L High pressure and high speed N H Fan outlet pressure P 22 Fan outlet temperature T 22 Compressor outlet pressure P3, high-pressure turbine outlet temperature T 43 Let P6 be the low-pressure turbine outlet temperature, T6 be the low-pressure turbine outlet temperature, and FG be the thrust. Let s be... i，j This represents data x from two aero engines. i To x j The similarity between elements, S represents the similarity matrix, and the weight vector w = {w... i,j}, L S Let F represent the Laplacian matrix of the similarity matrix, and let F represent the indicator matrix of the Laplacian matrix. Then the objective function for this step is as follows:

[0054]

[0055] The first term describes the similarity of the data using Euclidean distance and assigns adaptive weights to balance the size of the elements in the similarity matrix. The second term, to avoid trivial solutions, incorporates the norm of the indicator matrix F. The intuitive explanation is: if two data points are close, they are also close to each other in the similarity graph. Here, 1 represents an all-1 vector, the third term performs spectral clustering on the similarity graph to construct a clustering indicator matrix, which is used for subsequent linear kernel calculations. tr(.) represents the trace of the matrix, and α and β are hyperparameters used to control the weights of the regularization terms.

[0056] The weight w can be adaptively determined based on the data elements as follows:

[0057]

[0058] To solve equation (1), we use the Lagrange multiplier method and an iterative update approach. The solution process is as follows:

[0059] Step 1: Fix S and F, update w:

[0060] When S and F are fixed, the second and third terms of equation (1) are constants. Therefore, only the first term of equation (1) is considered. As mentioned before, w i，j The value can be updated according to equation (2).

[0061] Step 2: Fix F, keep w stationary, update S:

[0062] Let d i =[d i,j ] n×1 This represents the Euclidean distance vector from the i-th data point to all other data points, where the j-th element is d. i，j According to the formula We make h i =[h i，j ] n×1 Let i represent the metric vector whose i-th element belongs to another class, and whose j-th element is... We will by s i，j (j = 1, ..., n) can be written in vector form as s i =[s i，j ] n×1 Then, the above formula (1) is expressed in vector form as follows:

[0063]

[0064] The final formula can be obtained by simplifying it using vector form:

[0065]

[0066] From equation (4), we can see that each s i It can be solved independently, therefore its corresponding Lagrange equation can be written as:

[0067]

[0068] Where λ and ξ are Lagrange multipliers. i Having k non-zero values, taking the derivative of the Lagrange function and setting its value to 0, we can obtain:

[0069]

[0070] Where (α) + =max(α, 0), according to 1 T s i =1, because parameters α and λ are unknown parameters, assume d i The elements in the array are sorted in ascending order as d i，1 , ..., d i，k Similarly, h i The elements are sorted in ascending order as h i，1 ..., h i，k Since each point only selects its k best nearest neighbors, s i，k >0 and s i，k+1 =0, therefore the following inequality holds:

[0071]

[0072] According to 1 T s i =1, satisfies We can obtain:

[0073]

[0074] Therefore, vector s can be obtained. i The j-th value is:

[0075]

[0076] At the same time, in order to determine the value of k, because s i There are k non-zero values, let's assume Substituting λ into the equation, we obtain the following inequality:

[0077] q i，k <λ≤q i，k+1 #(10)

[0078] By simplification, we can obtain:

[0079]

[0080] Using the algorithm described above, we can determine each k, and then determine s. i Thus, the similarity matrix S is obtained.

[0081] Step 3: Keep S and w fixed, update F:

[0082] If we only take the terms related to F in equation (2), then the optimized F can be in the following form:

[0083]

[0084] LS Expanding on equation (13), it can be further written in the following form:

[0085]

[0086] Where D = diag(S) represents the degree matrix corresponding to S, and diag(·) is a diagonal matrix function. Then equation (13) can be expressed as:

[0087]

[0088] The optimal solution for F in equation (14) is formed by the eigenvectors corresponding to the smallest c eigenvalues ​​of matrix M. The second and third steps above need to be repeated iteratively until convergence.

[0089] The weighted average control quantity u of the data elements is obtained through the linear kernel matrix and the data matrix, and the expression is:

[0090]

[0091] The deviation between the actual thrust and the predicted thrust is obtained by using PID control to obtain the compensation control quantity u. pid A composite thrust control system combining adaptive construction methods is established to control the thrust of the turbofan engine. The expression is as follows:

[0092]

[0093] The engine generates corresponding thrust based on the input from the control system and combines the observed data.

[0094] The feature extraction module in this invention is used to extract multiple features from samples in a sample set; the similarity matrix construction module is used to construct a similarity matrix of data using the Euclidean distance of data samples, combined with adaptive graphing kernel and adaptive weights, to express the similarity relationship between data; the linear similarity control quantity construction module is used to obtain a clustering indicator matrix by performing spectral clustering on the obtained similarity matrix, and then obtain a linear weighted average control quantity u based on linear kernel correlation and the data matrix, and combine it with PID to obtain the deviation control quantity u. pid As input to the simulation system, the simulation loop module is used to input engine control quantities into the simulation system to obtain real thrust and observation data, which are then used as input for the next iteration to reduce errors and achieve the optimal solution.

[0095] This invention employs a similarity matrix to describe the similarity relationships of multi-dimensional data. Through adaptive learning and weight balancing of the similarity matrix elements, a clustering indicator matrix is ​​generated. This matrix, using a linear kernel, describes the linear relationships between data elements to obtain the control quantity. This control quantity is then fused with the deviation values ​​generated by the PID controller before being input into the engine. The engine-generated data is then used for iterative processing. This overcomes the shortcomings of previous multi-aero-engine control systems that, when combined with machine learning, ignored the relationships between different data. By constructing a holistic similarity matrix of multiple data sets through shared adaptive weights, a better data representation can be obtained, improving the accuracy of prediction data. A weighted average is obtained by superimposing the linear kernel, data fusion, and PID results, inducing general characteristics of the data, which are then input into the engine to obtain the input for the next iteration. This process is repeated until convergence.

[0096] This invention has the following advantages:

[0097] Spectral clustering can make computation on massive datasets more efficient by constructing sparse graphs, while adaptive graph construction can design an optimization problem to obtain the similarity matrix based on the similarity relationships between data points without manual construction. Combining these two methods can yield the optimal solution. Therefore, based on the characteristics of spectral clustering and adaptive graph construction in data processing, we can combine machine learning with a PID compensator to form a composite direct thrust system.

[0098] Based on the mechanical characteristics of the turbine engine, envelope data is obtained, along with various features such as the number of sensor types and combinations of observation parameters. A data matrix is ​​then derived based on the number of samples. Using the Euclidean distance between samples and an adaptive weighting method, a clustering algorithm is used to optimize and obtain the element similarity matrix of the data samples, simultaneously yielding the corresponding clustering indicator matrix. Since the indicator matrix is ​​a real-valued clustering matrix, it follows linear similarity. Therefore, the category similarity of data elements can be obtained using a linear kernel method. The weighted average control variable u of the data elements is then obtained using the linear kernel matrix and the original matrix. Finally, the deviation between the actual thrust and the predicted thrust is obtained using PID control to acquire the compensation control variable u. pid A composite thrust control system incorporating an adaptive construction method is established to control the thrust of a turbofan engine. The engine generates a corresponding thrust and combines it with observed data based on the input from the control system, records the input, and then proceeds to the next simulation cycle.

[0099] This invention is not limited to the above embodiments. Based on the technical solutions disclosed herein, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. An aero-engine control method based on adaptive graphing, characterized in that, Includes the following steps: Step 1: Obtain data samples based on the mechanical characteristics of the turbine engine, and then obtain a data matrix based on the data samples; Step 2: Use Euclidean distance to describe the similarity between data samples. Combined with the adaptive weight construction method, use an iterative algorithm to optimize and obtain the element similarity matrix of the data samples, and at the same time obtain the corresponding clustering indicator matrix. Step 3: Obtain the category similarity of data elements using the linear kernel method, and then obtain the weighted average control value of the data elements using the linear kernel matrix and the data matrix. ; Step 4: Use PID control to obtain the deviation between the actual thrust and the predicted thrust, and obtain the compensation control quantity. Establish a composite thrust control system that combines adaptive construction methods to control the thrust of a turbofan engine; Step 5: The engine generates corresponding thrust and observation data based on the input from the control system, records the input, and enters the next simulation cycle.

2. The aero-engine control method based on adaptive graphing according to claim 1, characterized in that: The specific details of step 1 are as follows: Set the data sample as ,in Indicates the number of samples. This represents the dimension of the sample features, which include various features of the sample. x=[H,Ma,W f (k-2),W f (k-1),A8(k-2),A8(k-1),A8(k),N L (k−1),N H (k-1),T 43 (k- 1),P6(k-1),T6(k-1),FG(k-1),N L (k),N H (k),P 22 (k),T 22 (k),P3(k),T 43 (k),P6(k),T6(k),FG r ]: in, For time markers, For flight altitude, For the flight Mach number, f A is the fuel flow rate, and A8 is the adjustable nozzle throat area. Reference thrust; low-pressure speed High pressure speed Fan outlet pressure 22 Fan outlet temperature 22 Compressor outlet pressure 3. High-pressure turbine outlet temperature 43 Low-pressure turbine outlet temperature 6. Low-pressure turbine outlet temperature 6. Thrust The combination of at least two of them constitutes the observation parameter combination. In the entire composite thrust system, in the next iteration, the actual thrust will be added to the observation data, so the dimension will increase by one dimension from the original dimension.

3. The aero-engine control method based on adaptive graphing according to claim 2, characterized in that: The specific details of step 2 are as follows: The element similarity of the data matrix is ​​expressed using Euclidean distance, and the element similarity between samples is adaptively obtained. Specifically, a weighted undirected graph is constructed for the samples. Each sample is A vertex, a set of edges Indicates sample and The Euclidean distance between them is calculated, and adaptive weights are obtained simultaneously. , used to optimize the similarity matrix.

4. The aero-engine control method based on adaptive graphing according to claim 3, characterized in that: In step 2, the similarity matrix obtained after optimization is the clustering indicator matrix, denoted as... Weight vectors of different aero engines , The Laplace matrix representing the similarity matrix. Let the indicator matrix represent the Laplacian matrix, then the objective function for this step is as follows: ； in, Indicates the number of data points. This represents the adaptive weight between two data points. Representing data arrive The similarity between elements; the first row of the above formula is the sum of three terms, the second row is the range of values, the first term describes the similarity of the data through Euclidean distance and assigns adaptive weights to balance the size of the elements in the similarity matrix; the second term is to avoid trivial solutions, so an indicator matrix is ​​added. The norm of , intuitively interpreted, is: if two data points are close, then they are also close to each other in a similarity graph, where . The third term represents a vector consisting entirely of 1s. It involves performing spectral clustering on similar graphs to construct a clustering indicator matrix, which is then used for subsequent linear kernel calculations. This indicates finding the trace of a matrix. and It is a hyperparameter used to control the regularization term.

5. The aero-engine control method based on adaptive graphing according to claim 4, characterized in that: In step 2, the Lagrange multiplier method and the alternating iterative update method are used to solve the objective function.

6. The aero-engine control method based on adaptive graphing according to claim 5, characterized in that: In step 3, the linear kernel matrix is ​​obtained based on the clustering indicator matrix, and then weighted and averaged with the data matrix to obtain the control quantity. Its expression is: ； in, Indicates the number of data points. Represents a data matrix. Represents a vector consisting entirely of 1s. Represents the clustering indicator matrix. Indicates the control quantity.

7. The aero-engine control method based on adaptive graphing according to claim 6, characterized in that: In step 4, the thrust compensation amount is obtained using PID control. This is combined with an adaptive mapping method to form a composite thrust control system, which will and Linear superposition is performed to obtain the total output of the composite thrust system. The expression is: ； in, , indicating the control quantity.

8. An aero-engine control system based on adaptive graphing, characterized in that, It includes a feature extraction module, a similarity matrix construction module, a linear similarity control variable construction module, and a simulation loop module. The feature extraction module is used to form a data matrix by combining the envelope data, iteration parameters, and observation data features with the number of samples, thereby enabling mathematical calculations of the model. The similarity matrix construction module is used to obtain the similarity matrix of data sample elements through Euclidean correlation of data elements and adaptive graph optimization; The linear similarity control quantity construction module is used to obtain the control quantity by weighted averaging the linear similarity matrix constructed from the similarity matrix and the original matrix, which is used to implement control input for the engine. The simulation loop module is used to control the system to obtain the corresponding thrust and observation data after input, and then enter the input data into the next simulation loop.

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