A method for calculating the correlation of aeroengine performance parameters based on partial least squares method

Abstract

The present invention discloses a method for calculating the correlation of performance parameters of an aero-engine based on partial least squares method, which includes the following operations: pre-processing the measured speed spectrum of the engine, extracting the mission segments of the speed spectrum of the engine flight mission profile according to different flight actions, and obtaining several typical flight action mission segments; statistically analyzing the flight performance parameters and engine performance parameters of the typical flight action mission segments, and calculating the correlation coefficients between the flight performance parameters and the engine performance parameters; and using partial least squares method to establish correlation equations for the flight performance and engine performance parameters of the aero-engine. This technology uses partial least squares method to establish the correlation between the various performance parameters of the aero-engine flight mission profile, which has great engineering significance for the prediction of the aero-engine load spectrum and the prediction of the engine life.

Description

Technical Field

[0001] The invention relates to the technical field of aero-engine load spectrum, and in particular to a method for calculating the correlation of aero-engine performance parameters based on a partial least squares method. Background Art

[0002] The stress analysis and life research of aircraft engines rely on the maneuvering flight load spectrum. In order to determine the service life of aircraft engines, fatigue tests of full-scale structures or parts must be carried out in the final design stage of aircraft engines. In order to obtain more reliable test results, full-scale fatigue tests should simulate the real working conditions as accurately as possible. However, due to the randomness of fatigue loads, the real working conditions are ever-changing. In order to be able to randomly load the test components, the load spectrum must be simulated. Due to their performance differences, different engines have greater differences in load spectra when performing the same flight mission. There are many types of flight parameters and engine parameters included in the flight mission profile of aircraft engines, and studies have shown that the key parameters that can characterize the flight state of aircraft and engine fatigue life damage are interrelated. Previous studies have not statistically and quantified the correlation between aircraft flight performance and engine performance. Statistical and establishment of the correlation between aircraft flight performance and engine performance has great engineering significance for the prediction of aircraft engine load spectrum and life prediction. Summary of the invention

[0003] In order to solve the above problems, the present invention proposes a method for calculating the correlation of aircraft engine performance parameters based on partial least squares method.

[0004] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0005] The present invention is a method for calculating the correlation of aircraft engine performance parameters based on partial least squares method, comprising the following operations:

[0006] Step S1, preprocessing the measured engine speed spectrum, including the division of take-off segment, intermediate segment and landing segment, filtering by rainflow counting method, extracting the mission segment of the engine flight mission profile speed spectrum according to different flight actions, and obtaining several typical flight action mission segments;

[0007] Step S2, counting the flight performance parameters and engine performance parameters of the typical flight action mission segment, and calculating the correlation coefficients between the flight performance parameters and the engine performance parameters;

[0008] Step S3: Based on the calculation result of the correlation coefficient, a partial least squares regression method is used to establish a correlation equation for the aircraft engine flight performance and the engine performance parameters.

[0009] A further improvement of the present invention is that the division of the take-off section and the landing section in step S1 is specifically as follows: removing the taxiing section and taking only the ascending section as the take-off section, and setting the critical point where the height does not change as the starting time point of the ascending section; removing the descending taxiing section and taking the descending section as the landing section, and setting the starting point where the height is no longer descending as the time point for starting ground taxiing.

[0010] A further improvement of the present invention is that the flight performance parameters in step S2 include rotation speed, pitch angle, track angle, roll angle, altitude, and Mach number, the engine performance parameters include inlet total temperature, and the correlation coefficient calculation expression between the flight performance parameters and the engine performance parameters is:

[0011]

[0012] Among them, x i is the data value in the first set of samples, is the mean of the first group of samples, y i is the data value in the second set of samples, is the mean of the second group of samples, i is the ordinal number of the data values ​​in each group of samples, n is the total number of data values ​​in each group of samples, and r is the calculated correlation coefficient of the two groups of sample data. When r>0, it means that the two variables are positively correlated, and when r<0, it means that the two variables are negatively correlated; when |r|=1, it means that the two variables are completely linearly correlated.

[0013] A further improvement of the present invention is that in step S3, the flight performance parameters and engine performance parameters in step S2 are screened by the PLSR method for different typical flight action task segments, and the partial least squares regression method is used to establish a correlation equation for different typical flight action task segments based on the screening results.

[0014] The beneficial effects of the present invention are: 1. A new method for calculating the correlation between aircraft engine performance parameters proposed in the present invention establishes a correlation model between flight performance parameters and engine performance parameters in a flight mission profile, and statistically and quantifies the correlation between the rotational speed and other flight performance parameters and engine performance parameters.

[0015] 2. The present invention adopts the partial least squares regression method in multiple regression to regress and fit the flight performance parameters and engine performance parameters, retaining the complex multiple correlations between the various performance parameters of the flight profile.

[0016] 3. The method for calculating the correlation of aircraft engine performance parameters based on partial least squares method proposed in the present invention can be applied to aircraft engine stress analysis, engine performance research, life research and the compilation of subsequent test run spectra, laying a foundation and having certain engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the implementation of the present invention;

[0018] Figure 2 Schematic diagram of the division of the take-off section and the landing section in an embodiment of the present invention;

[0019] Figure 3 is a diagram of the speed spectrum rainflow filtering result in an embodiment of the present invention;

[0020] Figure 4 is a partial enlarged view of a load segment in an embodiment of the present invention;

[0021] Figure 5 is a graph of overall VIP values ​​in an embodiment of the present invention;

[0022] Figure 6 It is a VIP value diagram after dividing the task segments in the embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0024] like Figure 1 As shown, the method for calculating the correlation of aircraft engine performance parameters based on partial least squares method of the present invention includes the following operations:

[0025] Step S1, preprocessing the measured engine speed spectrum, including the division of take-off segment, intermediate segment and landing segment, filtering by rainflow counting method, extracting the mission segment of the engine flight mission profile speed spectrum according to different flight actions, and obtaining several typical flight action mission segments;

[0026] Step S2, counting the flight performance parameters and engine performance parameters of the typical flight action mission segment, and calculating the correlation coefficients between the flight performance parameters and the engine performance parameters;

[0027] Step S3: Based on the calculation result of the correlation coefficient, a correlation equation is established for the flight performance and engine performance parameters of the aircraft engine using the partial least squares regression method.

[0028] Figure 2 This is a schematic diagram of the take-off and landing sections of a flight mission profile of a certain type of aircraft engine. The entire division process is represented by the combination of its rotation speed, altitude, Mach number, and pitch angle. Figure 2It can be seen that the flight mission profile includes the aircraft startup taxiing segment, the ascending segment, the intermediate segment, the descending segment and the landing taxiing segment. Since startup taxiing and landing taxiing are stages that must be experienced in each flight mission, and the aircraft speed changes dramatically during startup taxiing, but the changes and execution of startup taxiing and landing taxiing are basically irrelevant to the flight mission, the present invention does not consider the impact of startup taxiing and landing taxiing on the engine speed. The measured flight parameters will be disturbed during the collection process, so the rain flow counting method is used to filter the original speed spectrum. The filtering result is as follows Figure 3 and Figure 4 shown.

[0029] This embodiment adopts a complex action recognition method based on basic actions to recognize complex actions in actual flight, specifically: complex actions are summarized into five basic actions: level flight, ascent, descent, turn, and roll, as shown in Table 1;

[0030] Table 1 Flight parameter ranges of basic actions

[0031]

[0032] The flight parameters based on the basic actions are combined into complex overall flight actions according to the cumulative change, change range, sequence, etc. The first step is to identify the time series of the basic flight actions. The second step is to determine the time series of the complex actions according to the composition structure and sequence of the basic actions. The third step is to refine the time identified in the second step according to the cumulative change of the parameters during the complex action process to obtain the complex action. Combined with the actual use of the aircraft model, the flight actions are divided into 6 typical flight action task segments including three complex actions and three basic actions. Among them, the three complex actions are circling, ascending turn, and descending turn, and the three basic actions are level flight, ascending, and descending. The above complex actions are decomposed into basic actions as shown in Table 2 below:

[0033] Table 2 Complex flight action breakdown table

[0034]

[0035] The flight performance parameters and engine performance parameters of six typical flight action mission segments were statistically analyzed, and the correlation coefficients between the flight performance parameters and the engine performance parameters were calculated.

[0036] The correlation coefficient is an indicator to measure the degree of correlation between multiple parameters. It is generally represented by the letter r. Its value is generally between -1 and 1. The correlation coefficient is not an equidistant measurement value, but a sequential data. When calculating the correlation coefficient, a larger sample size is required to obtain a more reliable correlation coefficient value. In mathematical statistics, formula (1) is usually used to calculate the correlation coefficient of two groups of sample data. When calculating the correlation coefficient of two groups of samples, the sample sizes of the two groups of data must be the same.

[0037]

[0038] Among them, x i is the data value in the first set of samples, is the mean of the first group of samples; y i is the data value in the second set of samples, is the mean of the second group of samples. r is the calculated correlation coefficient of the two groups of sample data. When r>0, it means that the two variables are positively correlated, and when r<0, it means that the two variables are negatively correlated; when |r|=1, it means that the two variables are completely linearly correlated, that is, they satisfy the functional relationship. Table 3 shows the corresponding relationship between the correlation coefficient value and the degree of correlation;

[0039] Table 3 Correlation table

[0040]

[0041] The speed representing the aerodynamic load in the measured load spectrum of the aircraft engine is selected; the normal overload coefficient representing the maneuvering load; the pitch angle, track angle, roll angle, altitude, and Mach number representing the aircraft performance; the low-pressure turbine after-gas temperature and inlet total temperature representing the engine performance are selected. All these load parameters of all flight mission profiles are extracted, and the correlation coefficient calculation method based on mathematical statistics is used. The load parameters are regarded as linearly related variables, and the correlation coefficient is calculated using formula (1). The six typical flight mission segments are obtained. The results are shown in Table 4:

[0042] Table 4 Calculation results of flight / engine performance correlation coefficient

[0043]

[0044]

[0045] It can be seen from the correlation coefficient results in the table that there are many parameters in the flight mission profile of aircraft engines and there is a strong correlation between various parameters.

[0046] Six variables including heading angle, pitch angle, roll angle, altitude, Mach number and inlet total temperature are selected as independent variables. When using partial least squares regression method to establish the correlation between flight performance and engine performance, the independent variables must be screened first. The present invention uses PLSR method for variable screening. The variable projection importance index VIP value of the six independent variables is used to measure the importance of the independent variable set to explain the dependent variable set.

[0047] Depend on Figure 5It can be seen that the VIP value ranges from 0.2 to 1.5, and the VIP values ​​of the heading angle and pitch angle are both lower than 0.5, which can be ignored compared with the three variables of roll angle, Mach number, and inlet total temperature. However, in the actual use of aircraft engines, the altitude and heading angle have a greater impact on the rotation speed, and the impact of the roll angle on the rotation speed is related to the flight action. At the same time, considering that there are two actions with constant altitude in the flight action: circling and level flight, which affect the VIP value, the VIP values ​​of these six typical flight actions are further refined and analyzed, and finally the VIP value of each flight action is obtained.

[0048] The variable projection importance index is used to calculate the six typical flight action mission profiles. The results are as follows: Figure 6 As shown. In the ascending flight action, the heading angle and the rolling angle are much lower than the other parameter values, so the heading angle and the rolling angle can be ignored in the regression calculation of the ascending flight action; in the descending flight action, the heading angle and the rolling angle are much lower than the other parameter values, so the heading angle and the rolling angle can be ignored in the regression calculation of the descending flight action; in the level flight action, the heading angle, the pitch angle, and the rolling angle are much lower than the other values ​​and the height value remains unchanged in the level flight, so the heading angle, the pitch angle, the rolling angle, and the height can be ignored in the regression calculation of the level flight action; in the circling flight action, only the heading angle is much lower than the other values ​​and the height remains unchanged in the circling action, so the heading angle and the height can be ignored in the regression calculation of the circling flight action; in the ascending turn and descending turn flight actions, the VIP values ​​of the six parameter values ​​are similar, so the regression calculation of the ascending turn and descending turn flight actions needs to consider all parameter values.

[0049] In summary, under different flight maneuvers, the correlations between flight performance parameters and engine performance parameters are different and need to be performed separately during fitting.

[0050] The partial least squares regression method is as follows: Suppose there is a single dependent variable Y∈R n , independent variable X = |x1, x2, ..., x p |, x p ∈R n Partial least squares regression extracts components t1 and u1 from the independent variable X and the single dependent variable Y respectively. When extracting components, for the needs of regression analysis, it is required to meet the following requirements:

[0051] (1) t1 and u1 should carry as much variation information as possible in their respective data tables;

[0052] (2) The correlation between t1 and u1 can be maximized. After the first components t1 and u1 are extracted, partial least squares regression is performed to regress the independent variable X on t1 and the dependent variable Y on t1. If the regression equation has achieved satisfactory accuracy, the algorithm terminates; otherwise, the residual information of the independent variable X explained by t1 and the residual information of the dependent variable Y explained by t1 are used for the second round of component extraction. This process is repeated until a satisfactory accuracy is achieved. If a total of m components t1, t2, ..., t1 are extracted for the independent variable X, then the algorithm is terminated. m , partial least squares regression will be implemented by implementing a single dependent variable Y for t1, t2, …, t m The regression is then expressed as a single dependent variable Y with respect to the original variables x1, x2, …, x p The regression equation is obtained, and the partial least squares regression modeling is completed. According to the above principles, the partial least squares regression method can be summarized into the following steps:

[0053] Step (1) standardize the independent variable X and the single dependent variable Y to obtain the standardized independent variable matrix E0 and dependent variable matrix F0;

[0054] Step (2) extracts a component from the independent variable matrix E0, t1=E0W1, where: W1 is the eigenvector corresponding to the maximum eigenvalue of E′0, F0, E0, F′0, E′0 and F′0 are the transpose of the independent variable matrix and the transpose of the dependent variable matrix respectively, and F0 is the dependent variable matrix.

[0055] Using the regression of the independent variable matrix E0 on t1: E0 = t1P1 + E1, that is: E1 = E0 - t1P1, where: P1 = E′0t1 / ‖t1‖ 2 .

[0056] Check convergence. If the single dependent variable Y has a j If the regression equation has achieved satisfactory accuracy, proceed to the next step; otherwise, let E1 = E0, repeat step (2), and perform regression analysis on the residual matrix.

[0057] Step (3) In the hth step (h = 2, ..., m), the regression equation meets the accuracy requirement and the components t1, t2, ..., t m , implement the dependent variable matrix F0 at t1, t2, …, t m Regression on the , we get F0 = r1t1 + r2t2 + ... + r m t m , where m=1~∞, r is the regression coefficient.

[0058] Since t1, t2, …, t mThey are all linear combinations of the independent variable matrix E0, so the dependent variable matrix F0 can be written as a linear combination of the independent variable matrix E0. That is:

[0059] v0=r1E0W1+r2E0Q2+…+r m E0W m (2)

[0060] Step (4) is to reduce the regression equation of the dependent variable matrix E0 to the regression equation of the single dependent variable Y on the independent variable X according to the inverse process of standardization.

[0061] According to the above analysis, the heading angle (ω1), pitch angle (ω2), roll angle (ω3), Mach number (Ma), altitude (H), inlet total temperature (T) are used as independent variables, and the speed (n1) is used as the dependent variable. The flight profile data under different flight actions are iteratively calculated by partial least squares regression. The following regression equation is obtained using formula (2) and the standardized inverse process:

[0062] Level flight: n1 = -38.04M a -0.33T (3);

[0063] Ascent: n1 = -0.35ω2-63.48M a +0.04H-0.11T (4);

[0064] Descending: n1=0.15ω2+-16.87M a +0.01H+0.20T (5);

[0065] Circling: n1 = -0.01ω2 + 0.02ω3 - 0.56M a -0.03T (6);

[0066] Ascending turn: n1 = -0.07ω1 + 0.35ω2 + 0.02ω3 - 0.13M a +0.05H-0.03 (7)

[0067] Descending turn: n1 = 0.02ω1-0.56ω2-0.02ω3+26.70M a +0.06H-1.14T (8)

[0068] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have the same meaning as in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined similarly here.

[0069] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the correlation of aircraft engine performance parameters based on partial least squares method, characterized in that: The following operations are included: Step S1, preprocessing the measured engine speed spectrum, including the division of take-off segment, intermediate segment and landing segment, filtering by rainflow counting method, extracting the mission segment of the engine flight mission profile speed spectrum according to different flight actions, and obtaining several typical flight action mission segments; Step S2, counting the flight performance parameters and engine performance parameters of the typical flight action mission segment, and calculating the correlation coefficients between the flight performance parameters and the engine performance parameters; Step S3, establishing a correlation equation for the flight performance parameters and the engine performance parameters of the aircraft engine using a partial least squares regression method according to the calculation result of the correlation coefficient; In step S3, for different typical flight action task segments, the flight performance parameters and engine performance parameters in step S2 are screened using the PLSR method, and a correlation equation is established for different typical flight action task segments using the partial least squares regression method according to the screening results; Select the rotation speed representing the aerodynamic load in the measured load spectrum of the aircraft engine; the normal overload coefficient representing the maneuvering load; the pitch angle, track angle, roll angle, altitude, and Mach number representing the aircraft performance; the low-pressure turbine after-gas temperature and inlet total temperature representing the engine performance; extract all these load parameters of all flight mission profiles, and use the correlation coefficient calculation method based on mathematical statistics to regard the load parameters as linearly related variables; The partial least squares regression method is used to establish the correlation equations between the flight performance parameters and engine performance parameters of the aircraft engine, including: Step (1) standardize the independent variable X and the single dependent variable Y to obtain the standardized independent variable matrix E0 and dependent variable matrix F0; Step (2) extract a component from the independent variable matrix E0, t1 = E0W1, where: W1 is the eigenvector corresponding to the maximum eigenvalue of E′0, F0, E0, F′0, E0 and F0 are the transpose of the independent variable matrix and the transpose of the dependent variable matrix respectively, and F0 is the dependent variable matrix; Using the regression of the independent variable matrix E0 on t1: E0 = t1P1 + E1, that is: E1 = E0 - t1P1, where: P1 = E′0t1 / ‖t1‖ 2 ; Check convergence. If the single dependent variable Y has a j If the regression equation has achieved satisfactory accuracy, proceed to the next step; otherwise, let E1 = E0, repeat step (2), and perform regression analysis on the residual matrix; Step (3) In the hth step (h = 2, ..., m), the regression equation meets the accuracy requirement and the components t1, t2, ..., t m , implement the dependent variable matrix F0 at t1, t2, …, t m Regression on the , we get F0 = r1t1 + r2t2 + ... + r m t m , where m = 1 ~ ∞, r is the regression coefficient; Since t1, t2, …, t m They are all linear combinations of the independent variable matrix E0, so the dependent variable matrix F0 can be written as a linear combination of the independent variable matrix E0; that is: F0=r1E0W1+r2E0W2+…+r m E0W m (2) Step (4) according to the inverse process of standardization, the regression equation of the dependent variable matrix F0 is reduced to the regression equation of the single dependent variable Y on the independent variable X; According to the above analysis, the heading angle (ω1), pitch angle (ω2), roll angle (ω3), Mach number (Ma), altitude (H), inlet total temperature (T) are used as independent variables, and the speed (n1) is used as the dependent variable. The flight profile data under different flight actions are iteratively calculated by partial least squares regression. The following regression equation is obtained using formula (2) and the standardized inverse process: Level flight: n1 = -38.04M a -0.33T(3); rise: n1=-0.35ω2-63.48M a +0.04H-0.11T(4); decrease: n1=0.15ω2+-16.87M a +0.01H+0.20T(5); Circling: n1=-0.01ω2+0.02ω3-0.56M a -0.03T(6); Ascending turn: n1=-0.07ω1+0.35ω2+0.02ω3-0.13M a +0.05H-0.03(7) Descending turn: n1 = 0.02ω1-0.56ω2-0.02ω3+26.70M a +0.06H-1.14T(8).

2. The method for calculating the correlation of aircraft engine performance parameters based on partial least squares method according to claim 1, characterized in that: The division of the take-off segment and the landing segment in step S1 is specifically as follows: removing the taxiing segment and taking only the ascending segment as the take-off segment, and setting the critical point where the altitude does not change as the starting time point of the ascending segment; removing the descending taxiing segment and taking the descending segment as the landing segment, and setting the starting point where the altitude is no longer descending as the time point for starting ground taxiing.

3. The method for calculating the correlation of aircraft engine performance parameters based on partial least squares method according to claim 1, characterized in that: In step S2, the flight performance parameters include rotation speed, pitch angle, track angle, roll angle, altitude, and Mach number, and the engine performance parameters include inlet total temperature. The correlation coefficient calculation expression between the flight performance parameters and the engine performance parameters is: Among them, x i is the data value in the first set of samples, is the mean of the first group of samples, y i is the data value in the second set of samples, is the mean of the second group of samples, i is the ordinal number of the data values ​​in each group of samples, n is the total number of data values ​​in each group of samples, and r is the calculated correlation coefficient of the two groups of sample data. When r>0, it means that the two variables are positively correlated, when r<0, it means that the two variables are negatively correlated, and when |r|=1, it means that the two variables are completely linearly correlated.

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