Method for mining relationship between device component performance and unit maintenance level

Abstract

The present application relates to the technical field of complex equipment component repair, in particular to a device component performance and unit body maintenance level relationship mining method capable of effectively improving the use efficiency of an aero-engine, which first carries out expansion processing of repair samples, and then selects a support vector machine regression method which is better in the condition of small sample problems to solve the mapping relationship between the component performance before repair, unit body maintenance level and component performance after repair. Since a component is generally composed of multiple unit bodies, each component has multiple maintenance levels, and the mapping relationship between the component performance before repair, unit body maintenance level and component performance after repair is a many-to-one mapping relationship. In order to improve the accuracy of support vector machine regression, a hybrid kernel function method is used to optimize it, and a particle swarm algorithm is used to optimize the related parameters.

Description

Technical fields:

[0001] This invention relates to the field of complex equipment component repair technology, specifically a method for exploring the relationship between equipment component performance and unit maintenance level that can effectively improve the utilization efficiency of aero-engines. Background technology:

[0002] Due to the long maintenance cycles of aero engines and the generally small size of airline fleets, the sample size of aero engine maintenance requests is typically small. Furthermore, since the scope of actual engine maintenance work is usually defined arbitrarily by engineers, the maintenance scope in the engine maintenance request sample is influenced by the engineers' personal preferences, resulting in a small sample size for certain units at certain maintenance levels. To address these issues, the engine maintenance request sample should be expanded based on relevant aero engine maintenance knowledge, conducting knowledge-based research on engine maintenance request sample expansion. While sample expansion can appropriately increase the number of engine maintenance requests, it still remains a small-sample regression problem. Considering the characteristics of this problem, support vector machine regression, which performs well in small-sample regression problems, should be used for research. Since mixing multiple kernel functions can yield a better-performing kernel function, research on support vector machine regression based on mixed kernel functions should be conducted.

[0003] According to relevant airline documents, the EGTM values ​​of each unit of the CFM56-5B engine can be restored under four maintenance levels, as shown in Table 1. This document serves as a reference for aircraft engine maintenance plants. The restored EGTM values ​​are empirical values ​​that characterize the strength of each unit's impact on the overall engine performance under each maintenance level. The table shows that some units, such as bearings N1 and N2, do not restore the EGTM values ​​under any maintenance level. Therefore, it can be concluded that the performance of these units does not affect the overall engine performance. Thus, it can be analyzed that only the performance of five components—the fan, low-pressure compressor, high-pressure compressor, low-pressure turbine, and high-pressure turbine—affects the overall engine performance.

[0004] Table 1. EGTM (°C) of CFM56-5B engine unit restored to its original state under various maintenance levels.

[0005]

[0006] Summary of the Invention:

[0007] This invention addresses the problem of insufficient sample size for aircraft engine repairs by employing a knowledge- and data-driven approach to expand the repair sample size and using support vector machine regression to solve the problem. This provides an efficient method for mining the relationship between equipment component performance and unit maintenance level in aircraft engine component repair issues.

[0008] This invention achieves its purpose through the following measures:

[0009] A method for mining the relationship between equipment component performance and unit maintenance level, characterized by comprising the following steps:

[0010] Step 1: Expand the sample;

[0011] Step 2: Establish a function model for a support vector machine based on a hybrid kernel function:

[0012] A "bias band" with a spacing of ε is created on both sides of the target linear function to tolerate bias. Samples falling within the bias band are not included in the loss calculation; only support vectors falling on the edge of the bias band affect the function model. The optimized model is obtained by minimizing the total loss and maximizing the bias band spacing. Points within the bias band have a loss value of 0 and are considered non-support vectors. Points a and b on the edge of the bias band are boundary support vectors, and their loss values ​​need to be calculated. Points c, d, e, f, and g outside the bias band are non-boundary support vectors and can be considered outliers during measurement.

[0013] Since the optimization objective of SVR is to maximize the isolation band while minimizing the loss, the parameters w and b are determined accordingly. Maximizing the isolation band is... and Equivalent to The cost function that minimizes the loss can be written as: Among them l ε (z) As shown in (1).

[0014]

[0015] Therefore, the cost function of SVR at this time can be expressed as equation (2).

[0016]

[0017] In practice, it is often difficult to determine a suitable ε to ensure that most data are in the bias band. Therefore, a slack variable ξ is introduced to allow a portion of the samples to be outside the bias band. That is, all samples satisfy equation (3).

[0018]

[0019] Let the independent variable be x. i =[U i ,G′ i ] T The dependent variable is the performance after repair, y i =G i Estimated performance after repair Based on the knowledge of support vector machine regression, the estimated value of the corrected performance is... It can be calculated from equation (4):

[0020]

[0021] Where κ(x) i ,x j )=φ(x i ) T φ(x j Let α be the kernel function. Select a suitable kernel function and solve for α. and b;

[0022] α and α can be solved by solving the dual problem of SVR as shown in equation (5).

[0023]

[0024]

[0025]

[0026]

[0027] The above process must satisfy the KKT conditions, that is, it requires

[0028]

[0029] From the above conditions, it can be seen that f(x) = f(x) i )-y i -∈-ξ i When α = 0, i It can take a non-zero value if and only if hour, It can take non-zero values, in other words, only if the sample (x) i ,y i ) does not fall into the interval zone ∈, the corresponding α and Only then can it take a non-zero value.

[0030] also They cannot both be true at the same time, therefore α and At least one of them is zero.

[0031] From the above formula, we can draw the following conclusion: for each sample (x) i ,y i Not only do they all have (C-α) i )ξ i =0, and α i (f(x i )-y i -∈-ξi ) = 0. Therefore, we obtain α i Then, if 0 < α i If <C, then ξ must exist. i =0, and thus we have equation (7).

[0032]

[0033] Therefore, after solving for α i Then, after multiple calculations, take the average value of b.

[0034] Support vector machine regression analysis commonly uses linear kernel functions, polynomial kernel functions, and Gaussian kernel functions. Combining two kernel functions yields a hybrid kernel function, which combines the advantages of both. However, the Mercer condition must be satisfied when combining two kernel functions. The calculation formulas for the polynomial kernel function (second order), the Gaussian kernel function, and the hybrid kernel function using both polynomial and Gaussian kernel functions are shown in equations (8), (9), and (10):

[0035] K(x1,x2)=(γ1·x1·x2+cofe) 2 (8)

[0036] K(x1,x2)=exp[-γ2||x1-x2|| 2 (9)

[0037] K(x1,x2)=λ·(γ1·x1·x2+cofe) 2 +(1-λ)·exp[-γ2||x1-x2|| 2 (10)

[0038] In the formula, γ1 is the proportionality coefficient of the polynomial kernel function;

[0039] cofe — coefficient of the constant term of the polynomial kernel function;

[0040] γ2 — Gaussian kernel scaling factor;

[0041] λ — Mixed weighting coefficient.

[0042] The final functional model of the support vector machine based on the hybrid kernel function is as follows:

[0043]

[0044] Step 3: In order to improve the accuracy of support vector machine regression, a hybrid kernel function method is used to optimize it, and particle swarm optimization is used to optimize the relevant parameters.

[0045] In step 1 of this invention, to address the issue of a small number of aircraft engine repair samples, a knowledge- and data-driven approach is used to expand the repair sample. This is achieved by applying maintenance level-related knowledge and adding error perturbations.

[0046] (1) Expand upon relevant knowledge of maintenance levels

[0047] According to relevant data from a repair company and the experience of its engineers, visual inspection and minimal repair of all units have no impact on the post-repair performance of the units. Therefore, under these two repair levels, the performance of the components after repair remains consistent with their performance before repair.

[0048] Suppose component A consists of unit a, unit b, and unit c. Units a, b, and c each have four maintenance levels designated 1, 2, 3, and 4. Visual inspection and minimal repair are maintenance levels 1 and 2, respectively, while performance restoration and overhaul are maintenance levels 3 and 4, respectively. If the maintenance levels of units a, b, and c are 1, 2, and 4, respectively, then the maintenance level of component A is denoted as [1, 2, 4]. Since visual inspection and minimal repair of all units have no impact on the post-repair performance of the component, the maintenance level [1, 2, 4] of component A is equivalent to maintenance levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. Therefore, the post-repair performance of component A under maintenance level [1, 2, 4] is the same as that under maintenance levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. This method can significantly increase the number of samples;

[0049] (2) Data augmentation by adding error perturbations

[0050] While knowledge of repair can effectively expand the number of data samples, it can also lead to overfitting when using regression methods. To address this issue, adding error perturbations can modify the post-repair performance of the generated samples, thus resolving the overfitting problem.

[0051] Let the error value be ε, and the performance of the original sample after repair be k. Then the performance of the newly generated sample after repair is k±m·ε, where m is a random number between 0 and 10. Use this data sample to perform a data fitting regression experiment. If overfitting still occurs, let ε = 2·ε and perform the data fitting regression experiment again. Repeat the above process until overfitting no longer occurs in the data fitting regression experiment.

[0052] In step 3 of this invention, it is assumed that in N-dimensional space, the population has m particles, and the positions of the particles are determined by {x}. i =(x i1 ,x i2 ,…,xiN The velocity of each particle is represented by [v], i = 1, 2, ..., m. i =(v i1 ,v i2 ,…,v iN The fitness values ​​of each particle are calculated using the formula [i = 1, 2, ..., m]. The optimal position of each particle in the iteration history is calculated and denoted as its individual optimal value P. best =(p i1 ,p i2 ,…,p iN ), and the current optimal position of all particles, i.e., the local optimum G. best =(g1,g2,…,g n The formulas for updating the particle's velocity and position are as follows:

[0053]

[0054]

[0055] In the formula, d represents the solution vector composed of decision variables, where d = 1, 2, ..., N.

[0056] k — number of iterations;

[0057] c1 — acceleration constant;

[0058] c2 — acceleration constant;

[0059] w — Inertia weighting coefficient;

[0060] —The d-th dimension component of the particle velocity vector i in the k-th iteration;

[0061] —The d-th dimension component of the particle position vector i in the k-th iteration.

[0062] The three terms in the velocity update formula represent the inertia term of the particle's motion velocity, the influence term of the particle's historical best position on its velocity, and the influence term of the global optimal solution on the particle's velocity. In particle swarm optimization (PSO) search, the selection of the inertia weight coefficient *w* plays a crucial role in improving the algorithm's accuracy. Using nonlinear weights instead of linearly decreasing weights can improve the algorithm's accuracy. The formula for calculating the nonlinear weights is as follows:

[0063]

[0064]

[0065] In the formula y i —The actual value of the i-th sample;

[0066] Y i —The predicted value of the i-th sample;

[0067] f(x i — The particle's current fitness value;

[0068] f avg —Average fitness value;

[0069] f min —Minimum fitness value;

[0070] The particle swarm optimization algorithm is used to optimize the four parameters (polynomial kernel scaling coefficient γ1, polynomial kernel constant term coefficient cofe, Gaussian kernel scaling coefficient γ2, and mixed weight coefficient λ) in the support vector machine regression model. The steps are as follows:

[0071] (1) First, the input data is normalized and standardized. Then, the processed data is randomly divided into training and testing sets, and the velocity and position of the particles are initialized.

[0072] (2) Set the particle size to m = 50, the maximum number of iterations to k = 100, set the acceleration constants c1 = 1.5 and c2 = 1.2, and initialize the inertial weight coefficient w0 to 1. Set the polynomial kernel function scaling coefficient γ1∈[-1000,1000], the polynomial kernel function constant term coefficient cofe∈[-1000,1000], the Gaussian kernel function scaling coefficient γ2∈[0,2000], and the mixed weight coefficient λ∈[0,1].

[0073] (3) Update the particle's velocity and position using the above formula, and calculate the fitness value f(x) of each particle based on its position. i ), continuously update the global optimal solution f(G) best Continue iterating until the maximum number of iterations is reached.

[0074] This invention first expands the sample of vehicles sent for repair. Then, it selects the Support Vector Machine (SVM) regression method, which performs well under small sample conditions, to solve the mapping relationship between the performance of a component before repair, the maintenance level of a unit, and the performance of the component after repair. Since a component is generally composed of multiple units, and each component has multiple maintenance levels, the mapping relationship between the performance of the component before repair, the maintenance level of a unit, and the performance of the component after repair is a many-to-one mapping relationship. Due to the long interval between repairs for aero-engines, the number of aero-engine repair samples within a finite time is small, making the mapping relationship between the performance of a component before repair, the maintenance level of a unit, and the performance of the component after repair a typical small sample problem. To improve the accuracy of the SVM regression, a hybrid kernel function method is used for optimization, and a particle swarm optimization algorithm is used to optimize the relevant parameters. Attached image description:

[0075] Appendix Figure 1 This is a flowchart of the present invention.

[0076] Appendix Figure 2 This is a schematic diagram of support vector machine regression.

[0077] Appendix Figure 3 This is a comparison chart of the actual and predicted values ​​of the fan performance in this invention.

[0078] Appendix Figure 4 This is a comparison chart of the actual and predicted values ​​of fan performance.

[0079] Appendix Figure 5 This is a comparison chart of the actual and predicted values ​​of fan performance.

[0080] Appendix Figure 6 This is a comparison chart of the actual and predicted performance values ​​of the high-pressure compressor.

[0081] Appendix Figure 7 This is a comparison chart of the actual and predicted performance values ​​of the high-pressure compressor.

[0082] Appendix Figure 8 This is a comparison chart of the actual and predicted performance values ​​of the high-pressure compressor.

[0083] Appendix Figure 9 This is a comparison chart of the actual and predicted performance values ​​of the low-pressure compressor.

[0084] Figure 10 This is a comparison chart of the actual and predicted performance values ​​of the low-pressure compressor.

[0085] Appendix Figure 11 This is a comparison chart of the actual and predicted performance values ​​of the low-pressure compressor.

[0086] Appendix Figure 12 This is a comparison chart of the actual and predicted values ​​of the low-pressure turbine performance.

[0087] Appendix Figure 13 This is a comparison chart of the actual and predicted values ​​of the low-pressure turbine performance.

[0088] Appendix Figure 14 This is a comparison chart of the actual and predicted values ​​of the low-pressure turbine performance.

[0089] Appendix Figure 15 This is a comparison chart of the actual and predicted values ​​of the high-pressure turbine performance.

[0090] Appendix Figure 16 This is a comparison chart of the actual and predicted values ​​of the high-pressure turbine performance.

[0091] Appendix Figure 17 This is a comparison chart of the actual and predicted values ​​of the high-pressure turbine performance. Detailed implementation method:

[0092] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0093] This invention addresses the problem of insufficient sample numbers of aircraft engine repair requests by employing a knowledge- and data-driven approach to expand the sample. This is achieved by incorporating maintenance level-related knowledge and adding error perturbations.

[0094] (1) Expand upon relevant knowledge of maintenance levels

[0095] According to relevant data from a repair company and the experience of its engineers, visual inspection and minimal repair of all units have no impact on the post-repair performance of the units. Therefore, under these two repair levels, the performance of the components after repair remains consistent with their performance before repair.

[0096] Suppose component A consists of unit a, unit b, and unit c. Units a, b, and c each have four maintenance levels designated 1, 2, 3, and 4. Visual inspection and minimal repair are maintenance levels 1 and 2, respectively, while performance restoration and overhaul are maintenance levels 3 and 4, respectively. If the maintenance levels of units a, b, and c are 1, 2, and 4, respectively, then the maintenance level of component A is denoted as [1, 2, 4]. Since visual inspection and minimal repair of all units have no impact on the post-repair performance of the component, the maintenance level [1, 2, 4] of component A is equivalent to maintenance levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. Therefore, the post-repair performance of component A under maintenance level [1, 2, 4] is the same as that under maintenance levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. This method can significantly increase the number of samples.

[0097] (2) Data augmentation by adding error perturbations

[0098] While knowledge of repair can effectively expand the number of data samples, it can also lead to overfitting when using regression methods. To address this issue, adding error perturbations can modify the post-repair performance of the generated samples, thus resolving the overfitting problem.

[0099] Let the error value be ε, and the performance of the original sample after repair be k. Then the performance of the newly generated sample after repair is k±m·ε, where m is a random number between 0 and 10. Use this data sample to perform a data fitting regression experiment. If overfitting still occurs, let ε = 2·ε and perform the data fitting regression experiment again. Repeat the above process until overfitting no longer occurs in the data fitting regression experiment.

[0100] Although the engine repair sample was expanded using a sample expansion method, the problem of mining the correlation between component pre-repair performance and unit maintenance level remains a small-sample problem. To ensure high accuracy in obtaining the many-to-one mapping relationship, Support Vector Machine (SVM) regression was used. SVM regression has the following advantages: it is highly effective for solving classification and regression problems with high-dimensional features, and it still shows significant results when solving regression problems where the feature dimension is greater than the number of samples; because it uses only a subset of samples to determine the hyperplane, it consumes less memory; and it can use a large number of kernel functions, thus flexibly solving various nonlinear classification and regression problems. Since the problem of mining the correlation between component pre-repair performance and unit maintenance level is a multi-dimensional, small-sample problem, SVM regression is a very suitable choice.

[0101] Support Vector Machine (SVM) theory was proposed in 1995 and applied to the analysis of nonlinear and high-dimensional problems under small sample conditions. Furthermore, SVM can effectively avoid problems encountered by traditional regression algorithms, such as the catastrophe of dimensionality and overlearning.

[0102] SVM includes Support Vector Machine Classification and Support Vector Machine Regression (SVR), both of which are widely used in many fields. The principle of SVR is as follows: a "bias band" is created on both sides of the linear function of the target, with a spacing of ε (tolerance bias, which can be manually set). Samples falling within the bias band are not included in the loss calculation; only support vectors falling on the edges of the bias band affect the function model. Finally, the optimized model is obtained by minimizing the total loss and maximizing the bias band margin. Figure 2 As shown, points within the deviation band have a loss value of 0 and are considered non-support vectors. Points a and b at the edge of the deviation band are boundary support vectors (also called support vectors), and their loss values ​​need to be calculated. Points c, d, e, f, and g located outside the deviation band are non-boundary support vectors and can be considered outliers during measurement.

[0103] Since the optimization objective of SVR is to maximize the isolation band while minimizing the loss, the parameters w and b are determined accordingly. Maximizing the isolation band is... and Equivalent to The cost function that minimizes the loss can be written as: Among them l ε (z) can be shown in equation (1).

[0104]

[0105] Therefore, the cost function of SVR at this time can be expressed as equation (2).

[0106]

[0107] In practice, it is often difficult to determine a suitable ε to ensure that most data are in the bias band. Therefore, a slack variable ξ is introduced to allow a portion of the samples to be outside the bias band. That is, all samples satisfy equation (3).

[0108]

[0109] Let the independent variable be x. i =[U i ,G′ i ] T The dependent variable is the performance after repair, y i =G i Estimated performance after repair Based on the knowledge of support vector machine regression, the estimated value of the corrected performance is... It can be calculated from equation (4).

[0110]

[0111] Where κ(x) i ,x j )=φ(x i ) T φ(x j Let α be the kernel function. To solve this problem, it is necessary to select a suitable kernel function and solve for α. and b.

[0112] α and α can be solved by solving the dual problem of SVR as shown in equation (5).

[0113]

[0114]

[0115]

[0116] The above process must satisfy the KKT conditions, that is, it requires

[0117]

[0118] From the above conditions, it can be seen that f(x) = f(x) i )-y i -∈-ξ i When α = 0, i It can take a non-zero value if and only if hour, It can take non-zero values. In other words, it only takes a value if the sample (x) is zero. i ,y i ) does not fall into the interval zone ∈, the corresponding α and Only then can it take a non-zero value.

[0119] Furthermore, f(x) i )-y i -∈-ξ i =0 and They cannot both be true at the same time, therefore α and At least one of them is zero.

[0120] From the above formula, we can draw the following conclusion: for each sample (x) i ,y i Not only do they all have (C-α) i )ξ i =0, and α i (f(x i )-y i -∈-ξ i ) = 0. Therefore, we obtain α i Then, if 0 < α i If <C, then ξ must exist. i =0, and thus we have equation (7).

[0121]

[0122] Therefore, after solving for α i Then, after multiple calculations, take the average value of b.

[0123] Support vector machine regression analysis commonly uses linear kernel functions, polynomial kernel functions, and Gaussian kernel functions. Combining two kernel functions yields a hybrid kernel function, which combines the advantages of both. However, the Mercer condition must be satisfied when combining two kernel functions. The calculation formulas for the polynomial kernel function (second order), the Gaussian kernel function, and the hybrid kernel function using both polynomial and Gaussian kernel functions are shown in equations (8), (9), and (10):

[0124] K(x1,x2)=(γ1·x1·x2+cofe) 2 (8)

[0125] K(x1,x2)=exp[-γ2||x1-x2|| 2 (9)

[0126] K(x1,x2)=λ·(γ1·x1·x2+cofe) 2 +(1-λ)·exp[-γ2||x1-x2|| 2 (10)

[0127] In the formula, γ1 is the proportionality coefficient of the polynomial kernel function;

[0128] cofe — coefficient of the constant term of the polynomial kernel function;

[0129] γ2 — Gaussian kernel scaling factor;

[0130] λ — Mixed weighting coefficient.

[0131] The final functional model of the support vector machine based on the hybrid kernel function is as follows:

[0132]

[0133] Theoretical analysis reveals that the main parameters of this function are the polynomial kernel function scaling factor γ1, the polynomial kernel function constant term coefficient cofe, the Gaussian kernel function scaling factor γ2, and the mixed weight coefficient λ. These four parameters significantly influence the selection of support vectors and the prediction accuracy of support vector machine regression. This invention uses a particle swarm optimization algorithm to optimize these four parameters, thereby improving the algorithm's accuracy.

[0134] Particle swarm optimization (PSO) simulates the foraging behavior of bird flocks. Based on the principle that birds transmit information to other birds when they find food, thus changing the search routes of other birds, this intelligent optimization algorithm is designed. It seeks a globally optimal solution within a certain range by continuously modifying the search routes through constantly changing local optima. Assume that in N-dimensional space, the population has m particles, and the positions of the particles are determined by {x...} i =(x i1 ,x i2 ,…,x iN The velocity of each particle is represented by [v], i = 1, 2, ..., m. i =(v i1 ,v i2 ,…,v iN The fitness values ​​of each particle are calculated using the formula [i = 1, 2, ..., m]. The optimal position of each particle in the iteration history is calculated and denoted as its individual optimal value P. best =(p i1 ,p i2 ,…,p iN ), and the current optimal position of all particles, i.e., the local optimum G. best =(g1,g2,…,g n The formulas for updating the particle's velocity and position are as follows:

[0135]

[0136]

[0137] In the formula, d represents the solution vector composed of decision variables, where d = 1, 2, ..., N.

[0138] k — number of iterations;

[0139] c1 — acceleration constant;

[0140] c2 — acceleration constant;

[0141] w — Inertia weighting coefficient;

[0142] —The d-th dimension component of the particle velocity vector i in the k-th iteration;

[0143] —The d-th dimension component of the particle position vector i in the k-th iteration.

[0144] The three terms in the velocity update formula represent the inertia term of the particle's motion velocity, the influence term of the particle's historical best position on its velocity, and the influence term of the global optimal solution on the particle's velocity. In particle swarm optimization (PSO) search, the selection of the inertia weight coefficient *w* plays a crucial role in improving the algorithm's accuracy. Using nonlinear weights instead of linearly decreasing weights can improve the algorithm's accuracy. The formula for calculating the nonlinear weights is as follows:

[0145]

[0146]

[0147] In the formula y i —The actual value of the i-th sample;

[0148] Y i —The predicted value of the i-th sample;

[0149] f(x i — The particle's current fitness value;

[0150] f avg —Average fitness value;

[0151] f min —Minimum fitness value;

[0152] The particle swarm optimization algorithm is used to optimize the four parameters (polynomial kernel scaling coefficient γ1, polynomial kernel constant term coefficient cofe, Gaussian kernel scaling coefficient γ2, and mixed weight coefficient λ) in the support vector machine regression model. The steps are as follows:

[0153] (1) First, the input data is normalized and standardized. Then, the processed data is randomly divided into training and testing sets, and the velocity and position of the particles are initialized.

[0154] (2) Set the particle size to m = 50, the maximum number of iterations to k = 100, set the acceleration constants c1 = 1.5 and c2 = 1.2, and initialize the inertial weight coefficient w0 to 1. Set the polynomial kernel function scaling coefficient γ1∈[-1000,1000], the polynomial kernel function constant term coefficient cofe∈[-1000,1000], the Gaussian kernel function scaling coefficient γ2∈[0,2000], and the mixed weight coefficient λ∈[0,1].

[0155] (3) Update the particle's velocity and position using the above formula, and calculate the fitness value f(x) of each particle based on its position. i ), continuously update the global optimal solution f(G) best Continue iterating until the maximum number of iterations is reached.

[0156] Example 1:

[0157] Based on relevant research on component performance evaluation, engines can be divided into five components: fan, low-pressure compressor, high-pressure compressor, low-pressure turbine, and high-pressure turbine. Since the characteristics of these five components differ, research on the mapping relationship between pre-repair performance, maintenance level, and post-repair performance requires regression studies on each of the five components separately. Maintenance-related data for an airline's engines from September 2016 to July 2021 were selected as the data for this study. Based on the relevant flight parameters and component performance evaluation studies before engine component repair, the relevant degradation of engine components can be obtained, thereby evaluating the performance of the components before repair. By studying the relevant flight parameters and component performance evaluation studies after engine repair, the post-repair performance of the engine can be evaluated. The performance of the five components, including the fan, was evaluated based on the first 20 flight records of 76 engines manufactured by an airline. The average value of the fan performance evaluation value was denoted as P. fan,ave If the performance evaluation value of a certain engine fan is denoted as P... fan The relative performance of this engine is denoted as P. fan,rel =P fan / P fan,ave The relative performance of the low-pressure compressor, high-pressure compressor, high-pressure turbine, and low-pressure turbine can be calculated similarly. This invention uses relative component performance in all related studies to reduce the impact of performance differences between engine components.

[0158] To effectively evaluate the model's fit, the mean absolute error (MAE) is used to assess the model's accuracy. Its calculation formula is shown in equation (16).

[0159]

[0160] To verify the superiority of the hybrid kernel function-based support vector machine regression algorithm in predicting the performance of components after repair, a comparative experiment was conducted using a polynomial kernel function-based support vector machine regression algorithm and a Gaussian kernel function-based support vector machine regression algorithm. Before using the hybrid kernel function-based support vector machine regression algorithm for prediction, particle swarm optimization was used to optimize the polynomial kernel function scaling coefficient γ1, the polynomial kernel function constant term coefficient cofe, the Gaussian kernel function scaling coefficient γ2, and the hybrid weight coefficient λ. To ensure the validity of the comparison, before using the polynomial kernel function-based support vector machine regression algorithm for prediction, particle swarm optimization was used to optimize the polynomial kernel function scaling coefficient γ1 and the polynomial kernel function constant term coefficient cofe; before using the Gaussian kernel function-based support vector machine regression algorithm for prediction, particle swarm optimization was used to optimize the Gaussian kernel function scaling coefficient γ2. The mean absolute error (MAE) of the three algorithms under optimal parameter conditions was recorded, and the prediction accuracy of the three algorithms was compared. By optimizing the algorithm parameters to ensure that all three algorithms are optimal in solving this problem, the relative error values ​​of the three algorithms in predicting the performance of components after repair were compared.

[0161] The above comparative experiments were conducted on the five components: fan, low-pressure compressor, high-pressure compressor, high-pressure turbine, and low-pressure turbine. The experimental results are as follows:

[0162] First, fan optimization calculations were performed. Using a polynomial kernel function and a particle swarm optimization algorithm, the optimal parameters were found to be γ = -10 and cofe = 55.24, resulting in an MAE of 0.0097. The figure shows a comparison between the predicted (black) and actual (red) fan performance values ​​obtained using the polynomial kernel function and support vector machine regression. Using a Gaussian kernel function and a particle swarm optimization algorithm, the optimal parameter γ = 0.89 was obtained, resulting in an MAE of 0.0125. The figure also shows a comparison between the predicted (black) and actual (red) fan performance values ​​obtained using the Gaussian kernel function and support vector machine regression.

[0163] Using a hybrid kernel function, the optimal parameters obtained through particle swarm optimization are γ1 = -6.90, cofe = -100, γ2 = 3.93, and λ = 0.1, resulting in an MAE of 0.0078. The figure shows a comparison between the predicted (black) and actual (red) fan performance values ​​obtained through support vector machine regression using the hybrid kernel function.

[0164] Secondly, optimization calculations were performed on the high-pressure compressor. Using a polynomial kernel function and a particle swarm optimization algorithm, the optimal parameters were found to be γ = -2.77 and cofe = 8.49, resulting in an MAE of 0.0146. The figure shows a comparison between the predicted (red) and actual (black) high-pressure compressor performance values ​​obtained using a polynomial kernel function and support vector machine regression. Using a Gaussian kernel function and a particle swarm optimization algorithm, the optimal parameter γ = 95.13 was obtained, resulting in an MAE of 0.0091. Figure 7 The image shows a comparison between the predicted (red) and actual (black) values ​​of the high-pressure compressor performance obtained by using Gaussian kernel function and support vector machine regression.

[0165] Using a hybrid kernel function, the optimal parameters obtained through particle swarm optimization are γ1 = 4.21, cofe = 97.73, γ2 = 33.24, and λ = 0.1, resulting in a MAE of 0.0078. Figure 8 The image shows a comparison between the predicted (red) and actual (black) values ​​of the high-pressure compressor performance obtained through support vector machine regression using a hybrid kernel function. The comparison reveals that the support vector machine regression based on the hybrid kernel function performs better than the other two algorithms, and its predictions are closer to the actual values.

[0166] Secondly, optimization calculations were performed on the low-pressure compressor. Using a polynomial kernel function and a particle swarm optimization algorithm, the optimal parameters were found to be γ = -0.70 and cofe = -100, resulting in an MAE of 0.2275. Figure 9 This is a comparison between the predicted (red) and actual (black) values ​​of the low-pressure compressor performance obtained using a support vector machine regression with a polynomial kernel function. Using a Gaussian kernel function and a particle swarm optimization algorithm, the optimal parameter γ = 809.10 was obtained, resulting in a MAE of 0.0119. Figure 10 This is a comparison between the predicted (red) and actual (black) values ​​of the low-pressure compressor performance obtained by using Gaussian kernel function and support vector machine regression.

[0167] Using a hybrid kernel function, the optimal parameters obtained through particle swarm optimization are γ1 = -2.83, cofe = 78.30, γ2 = 98.72, and λ = 0.1, resulting in a MAE of 0.0090. Figure 11 This is a comparison between the predicted (red) and actual (black) values ​​of the low-pressure compressor performance obtained by using a support vector machine regression with a hybrid kernel function.

[0168] Secondly, optimization calculations were performed on the low-pressure turbine. Using a polynomial kernel function and a particle swarm optimization algorithm, the optimal parameters were obtained as γ = -1.28 and cofe = -99.76, resulting in a MAE of 0.0227. Figure 12This is a comparison between the predicted (red) and actual (black) values ​​of low-pressure turbine performance obtained through support vector machine regression using a polynomial kernel function. Using a Gaussian kernel function and particle swarm optimization, the optimal parameter γ = 70.79 was obtained, resulting in a MAE of 0.0160. Figure 13 This is a comparison between the predicted (red) and actual (black) values ​​of low-pressure turbine performance obtained by using Gaussian kernel function and support vector machine regression.

[0169] Using a hybrid kernel function, the optimal parameters obtained through particle swarm optimization are γ1 = 4.42, cofe = 47.68, γ2 = 4.50, and λ = 0.1, resulting in a MAE of 0.0136. Figure 14 This is a comparison between the predicted (red) and actual (black) values ​​of low-pressure turbine performance obtained through support vector machine regression using a hybrid kernel function.

[0170] Finally, optimization calculations for the high-pressure turbine were performed. Using a polynomial kernel function and a particle swarm optimization algorithm, the optimal parameters were obtained as γ = 0.90 and cofe = 51.04, resulting in an MAE of 0.0299. Figure 15 This is a comparison between the predicted (red) and actual (black) values ​​of high-pressure turbine performance obtained through support vector machine regression using a polynomial kernel function. Using a Gaussian kernel function and particle swarm optimization, the optimal parameter γ = 74.60 was obtained, resulting in a MAE of 0.0083. Figure 16 This is a comparison between the predicted (red) and actual (black) values ​​of high-pressure turbine performance obtained using Gaussian kernel function and support vector machine regression. Using a hybrid kernel function and particle swarm optimization algorithm, the optimal parameters are found to be γ1 = -4.17, cofe = -42.71, γ2 = 100, λ = 0.29, resulting in an MAE of 0.0078. Figure 17 This is a comparison between the predicted (red) and actual (black) values ​​of high-pressure turbine performance obtained through support vector machine regression using a hybrid kernel function.

[0171] This invention first expands the sample of vehicles sent for repair. Then, it selects the Support Vector Machine (SVM) regression method, which performs well under small sample conditions, to solve the mapping relationship between the performance of a component before repair, the maintenance level of a unit, and the performance of the component after repair. Since a component is generally composed of multiple units, and each component has multiple maintenance levels, the mapping relationship between the performance of the component before repair, the maintenance level of a unit, and the performance of the component after repair is a many-to-one mapping relationship. Due to the long interval between repairs for aero-engines, the number of aero-engine repair samples within a finite time is small, making the mapping relationship between the performance of a component before repair, the maintenance level of a unit, and the performance of the component after repair a typical small sample problem. To improve the accuracy of SVM regression, a hybrid kernel function method is used for optimization, and a particle swarm optimization algorithm is used to optimize the relevant parameters. Finally, the algorithm is evaluated and verified using actual data.

Claims

1. A method for mining the relationship between equipment component performance and unit maintenance level, characterized in that, Includes the following steps: Step 1: Sample expansion is performed by applying knowledge of maintenance levels and adding error perturbations. Expanding based on maintenance level knowledge means treating component repair combinations involving both maintenance levels as equivalent, based on the experience that visual inspection and minimal repair do not affect post-repair performance, thus significantly increasing the sample size. Expanding the data by adding error perturbations involves adding random error perturbations to the post-repair performance of the generated samples and iteratively adjusting the error values ​​through fitting regression experiments until the overfitting problem is resolved. Step 2: Establish a function model for a support vector machine based on a hybrid kernel function: A "bias band" was created on both sides of the linear function of the target, with a spacing of [missing information]. Points within the bias band have a loss value of 0 and are considered non-support vectors; points at the edge of the bias band... and points For boundary support vectors, their loss values ​​need to be calculated for points located outside the bias band. ,point ,point ,point and points These are non-boundary support vectors, which are considered outliers during measurement. The optimization objective of SVR is to maximize the isolation zone while minimizing the loss, and the parameters are determined accordingly. and Maximizing the isolation zone is ,and Equivalent to The cost function that minimizes the loss is denoted as ,in As shown in (1); （1）， In the formula, This is the error value. This is the inertia weighting coefficient. The position of the particle. For the first The actual value of each sample; The cost function of SVR is expressed as equation (2). （2）， Introducing slack variables All samples satisfy equation (3). （3）， Let the independent variable be... The dependent variable is the performance after repair. Estimated performance after repair Estimated performance after repair The result is obtained from equation (4): （4）， in For the kernel function, select a suitable kernel function and solve for it. , and b; Solve from equation (5) and , （5）， The solution must satisfy the KKT conditions, that is, it requires... （6）， If and only if hour, It can take a non-zero value if and only if hour, It can take non-zero values, that is, only if the sample Do not fall into In the spacer band, the corresponding and Only then can it take a non-zero value. and They cannot both be true at the same time, therefore and At least one of them is zero. The following conclusions can be drawn: For each sample They all ,and After obtaining Afterwards, if Then there must be Therefore, we have equation (7): （7）， The solution is obtained After that, after multiple calculations, take... The average value; The calculation formulas for the second-order polynomial kernel function, Gaussian kernel function, and mixed kernel function using polynomial and Gaussian kernel functions used in support vector machine regression analysis are shown in equations (8), (9), and (10): （8）， （9）， （10）， In the formula, It is the proportionality coefficient of the polynomial kernel function. These are the coefficients of the constant term in the polynomial kernel function. It is the scaling factor of the Gaussian kernel function; These are the mixed weight coefficients, resulting in the following function model for the support vector machine based on the mixed kernel function: （12）， Step 3: Optimize the support vector machine using a hybrid kernel function method, and use the particle swarm optimization algorithm to optimize the relevant parameters.

2. The method for mining the relationship between equipment component performance and unit maintenance level according to claim 1, characterized in that, Step 1 expands upon relevant knowledge of repair levels, specifically as follows: Components From unit unit and unit Composition, unit unit and unit Each component has four maintenance levels designated 1, 2, 3, and 4. Visual inspection and minimal repair are maintenance levels 1 and 2, respectively; performance restoration and overhaul are maintenance levels 3 and 4, respectively. unit unit and unit The maintenance levels are 1, 2 and 4 respectively, then the components The maintenance levels are denoted as [1, 2, 4]. Since visual inspection and minimum repair of all units have no impact on the post-repair performance of the components, the components... The maintenance level [1, 2, 4] is equivalent to maintenance levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. Therefore, the component... Post-repair performance and components under repair levels [1, 2, 4] The performance after repair is the same under the repair levels [1, 1, 4], [2, 2, 4], and [2, 1, 4]. Data augmentation is achieved by adding error perturbations, specifically by setting the error value to... The performance of the original sample after repair was The performance of the newly generated sample after repair is: , Using random numbers between 0 and 10, and conducting data fitting and regression experiments with this data sample, if overfitting still occurs, then let... Then, perform data fitting and regression experiments, and repeat the above process until overfitting no longer occurs in the data fitting and regression experiments.

3. The method for mining the relationship between equipment component performance and unit maintenance level according to claim 1, characterized in that, In step 3, assuming that... In 3D space, a population has There are 1 particle, and the position of the particle is determined by... To represent, the flight speed of each particle is determined by... The fitness value of each particle is calculated using a fitness function, and the optimal position of each particle in the iteration history is calculated and denoted as the individual optimal value. And the current optimal position of all particles, i.e., the local optimum. The formulas for updating the particle's velocity and position are as follows: （12）， （13）， In the formula, It is the solution vector composed of decision variables; It is the number of iterations; and It is the acceleration constant; It is the inertia weighting coefficient; It is in the Particle velocity in the next iteration The first vector Dimensional components; It is in the Particle position in the next iteration The first vector Dimensional components; The three terms in the velocity update formula represent the inertia term of the particle's motion velocity, the influence term of the particle's historical best position on the velocity, and the influence term of the global optimal solution on the particle's velocity. Nonlinear weights are used instead of linearly decreasing weights to improve the algorithm's accuracy. The formula for calculating the nonlinear weights is as follows: （14）， （15）， In the formula, It is the first The actual value of each sample; It is the first Predicted values ​​for each sample; This is the particle's current fitness value; It is the average fitness value; It is the minimum fitness value; The particle swarm optimization algorithm is used to evaluate the four parameters in the support vector machine regression model: the polynomial kernel function and the scaling factor. Coefficients of the constant term of the polynomial kernel function Gaussian kernel function scaling factor and mixed weighting coefficients The optimization process is as follows: (1) First, the input data is normalized and standardized, and then the processed data is randomly divided into training set and test set, and the velocity and position of the particles are initialized. (2) Set the particle size to The maximum number of iterations is Set the acceleration constant , The inertia weighting coefficient Initialize to 1, set the polynomial kernel function scaling factor. Coefficients of the constant term of the polynomial kernel function Gaussian kernel function scaling factor and mixed weighting coefficients ; (3) Update the particle's velocity and position using the above formula, and calculate the fitness value of each particle based on its position. Continuously update the global optimal solution Iterate continuously until the maximum number of iterations is reached.

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