Random multi-parameter load spectrum compilation method based on principal component analysis

Abstract

The application discloses a random multi-parameter load spectrum compiling method based on principal component analysis, and utilizes the principal component analysis method to convert multi-parameter random load into several independent load histories, i.e., multi-parameter principal component load histories, by taking the multi-parameter measured load spectrum of a component as basic compiling data, and then performs peak-valley value extraction processing to obtain the peak-valley value sequence and non-peak-valley value point set of the principal component load, performs rain flow cycle counting to obtain the rain flow cycle matrix of the principal component load history, reconstructs the load history from the rain flow cycle matrix, inserts the non-peak-valley value points randomly to obtain the principal component load reconstructed history, and linearly solves the principal component load history to obtain a new multi-parameter random load spectrum. The application fully considers the multi-parameter load correlation and multi-axis damage information in the random multi-parameter load spectrum compiling process, and provides a basis for fatigue damage analysis of practical complex mechanical components and multi-axis fatigue test.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of mechanical structure fatigue test load spectrum compilation, and particularly relates to a complex mechanical component multi-parameter random load spectrum compilation method, which provides a load basis for multi-axial fatigue damage analysis and multi-axial fatigue test of mechanical components under random multi-parameter load, and is an important step for life test and evaluation of key components of engineering complex structures under multi-parameter actual service load. BACKGROUND

[0002] At present, the research on load spectrum at home and abroad is mostly focused on the compilation of single-parameter load spectrum, and has been widely applied in the fields of aerospace, vehicles, engineering machinery and the like. However, in actual engineering application, most mechanical components are subjected to random multi-parameter load for a long time, that is, the components are subjected to more than one kind of load, and the components are prone to multi-axial fatigue damage and then failure. For example, the complex components such as engine case components, automobile universal joints and front suspensions are subjected to typical random non-proportional multi-axial load in actual service. Although the application of single-parameter load statistical method and load spectrum compilation method is relatively mature, it is no longer applicable to the components subjected to complex multi-parameter load. In order to fully and scientifically examine the life of the components, a multi-parameter load spectrum compilation method must be developed.

[0003] When the life examination test of complex mechanical components is carried out, the loaded load spectrum must reflect the actual working characteristics of the components to a certain extent. In addition, if the fatigue damage information contained in the measured load spectrum is not fully considered, it will lead to a certain difference between the compiled load spectrum and the actual service load in load characteristics and fatigue life performance. For multi-parameter load spectrum compilation, not only the damage information of single-axis load should be retained, but also the correlation between multi-parameter loads and multi-axial damage information should be fully considered. At present, there is no clear and universally recognized multi-parameter load spectrum compilation method for components at home and abroad, and only a few institutions and scholars have carried out research on this to different degrees. The Fraunhofer Institute in Germany has developed the CARLOS multi-parameter standard load sequence for the multi-parameter load borne by automobile structures, but the specific method has not been published. The research on multi-parameter load spectrum in China started late, mainly adopts the given matching principle to randomly combine the load and cycle, lacks theoretical basis and does not consider the correlation and phase relationship between loads.

[0004] In summary, the existing multi-parameter load spectrum compilation method still has certain limitations, and there is no clear and universally recognized component multi-parameter load spectrum compilation method. The requirements of fatigue damage information retention in the spectrum are also satisfied to different degrees. Under the action of multi-parameter load, it is still an urgent key engineering problem to compile a component multi-parameter load spectrum that fully considers the correlation between multi-parameter loads and multi-axis damage information, which is also of great significance to the fatigue damage analysis and fatigue test research of complex mechanical components in engineering practice.

[0005] Therefore, it is necessary to develop a random multi-parameter load spectrum compilation method that can consider the correlation of multi-parameter loads and retain multi-axis damage information, laying a foundation for the life determination of complex engineering machinery and its parts. SUMMARY

[0006] In order to solve the problems of lacking consideration of multi-parameter load correlation and loss of multi-axis damage information in the existing component multi-parameter load spectrum compilation, the present application provides a random multi-parameter load spectrum compilation method based on principal component analysis. This method is a more intuitive and clear spectrum compilation method, which fully considers the multi-parameter load correlation and multi-axis damage information in the random multi-parameter load spectrum compilation process, provides a basis for fatigue damage analysis and multi-axis fatigue test of complex mechanical components in engineering practice, and is an important step for life test and evaluation of complex mechanical components in engineering practice under actual service load.

[0007] To achieve the above object, the technical scheme adopted by the present application is as follows:

[0008] A random multi-parameter load spectrum compilation method based on principal component analysis, using the measured multi-parameter load spectrum of the component as the basic spectrum data, using the principal component analysis method to convert the multi-parameter random load into several independent load histories, i.e. multi-parameter principal component load histories, then performing peak and valley value extraction processing to obtain the peak and valley value sequence and non-peak and valley point set of the principal component load, performing rainflow cycle counting to obtain the rainflow cycle matrix of the principal component load history, and then reconstructing the load history from the rainflow cycle matrix and randomly inserting non-peak and valley points to obtain the principal component load reconstruction history, and performing linear calculation on the principal component load history to obtain a new multi-parameter random load spectrum.

[0009] A multi-parameter test spectrum compilation method based on principal component analysis, comprising the following steps:

[0010] (1) Standardizing and analyzing the correlation of the random multi-parameter load spectrum of the complex mechanical component, thereby obtaining the correlation coefficient matrix of the random multi-parameter load;

[0011] (2) Using principal component analysis method to convert multi-parameter random load into several independent load history, i.e. principal component load history, and then extracting peak and valley value to obtain peak and valley value sequence and non-peak and valley value point set of the principal component load history of random multi-parameter;

[0012] (3) Rainflow cycle counting is performed on the peak and valley value sequence of the principal component load to obtain rainflow cycle matrix, and the random load history is reconstructed by the rainflow cycle matrix to obtain the reconstructed load history of random multi-parameter principal component;

[0013] (4) Non-peak and valley value points are randomly inserted to obtain the reconstructed load history of random multi-parameter principal component with consistent data amount;

[0014] (5) Linear solution of the principal component load history is performed to obtain a new multi-parameter random load spectrum, and thus the random multi-parameter random load spectrum based on principal component analysis is compiled.

[0015] Further, the specific steps of step (1) are:

[0016] (11) Using multi-parameter measured load spectrum of complex mechanical components as basic spectrum data, the random multi-parameter load data is standardized; assuming that there are p load parameters and n sampling time points, and the load value of the jth load parameter at the ith sampling time point is denoted as f ij , i = 1, 2,..., n; j = 1, 2,..., p, then the measured random multi-parameter load data matrix F is:

[0017]

[0018] The measured random multi-parameter load data matrix F is converted into a standardized random multi-parameter load data matrix F':

[0019]

[0020] wherein, is the average value of the jth column data of the measured random multi-parameter load data matrix F, i.e. and σ j is the standard deviation of the jth column data of the measured random multi-parameter load data matrix F,

[0021] (12) Correlation analysis is performed on each column load of the standardized random multi-parameter load data matrix F' of the complex mechanical components, and thus the correlation coefficient matrix R of the standardized random multi-parameter load can be obtained;

[0022]

[0023] wherein, rjk is the correlation coefficient of the jth column data and the kth column data in the standardized random multi-parameter load data matrix F', i.e., the correlation coefficient of the jth load parameter and the kth load parameter, and the calculation formula is as follows:

[0024]

[0025] wherein f' ij , f' ik are elements in the standardized random multi-parameter load data matrix F', i.e., the standardized load value of the ith sampling time point of the jth load parameter and the kth load parameter.

[0026] Further, the specific steps of the step (2) are as follows:

[0027] (21) The standardized random multi-parameter load data matrix F' is converted into several independent load histories, i.e., principal component load histories F", by using a principal component analysis method, and the calculation formula is as follows:

[0028]

[0029] wherein F i " = [f" i1 f" i2 ... f" ip ] elements are principal component load values of the ith sampling time point of p principal component load parameters; F i ' = [f' i1 f' i2 ... f' ip ] elements are standardized load values of the ith sampling time point of p standardized load parameters; U j = [u 1j u 2j ... u pj ] T is a characteristic vector corresponding to the jth eigenvalue λ j of the correlation coefficient matrix R of the standardized random multi-parameter load, wherein: elements u 1j , u 2j , u pj are specific values of the characteristic vector U j , and T is a matrix transpose symbol;

[0030] (22) Each load time history of the random multi-parameter principal component load history F" obtained in the step (21) is subjected to peak point or valley point judgment, and if yes, it is retained, otherwise it is moved to a non-peak-valley value point set F" R,j (j = 1, 2,..., p), and three-point method is used to judge the data, i.e., three adjacent data points f"i-1,j , f" i,j , f" i+1,j , if the following condition is satisfied:

[0031] [f" i,j -f" i-1,j ][f" i+1,j -f" i,j ]≥0 and f" i,j -f" i-1,j ≠0

[0032] wherein: f" i,j is a non-peak point or a non-valley point; thus obtaining a non-peak-valley point set F" R,j (j = 1, 2,..., p) and a multi-parameter principal component load history peak-valley value sequence {F" RF,1 F" RF,2 ... F" RF,p}, wherein: elements F" RF,1 , F" RF,2 , F" RF,p respectively represent the peak-valley value sequence of each principal component load history.

[0033] Further, the specific steps of step (3) are:

[0034] (31), performing rainflow cycle counting on the random principal component load peak-valley value sequence {F" RF,1 F" RF,2 ... F" RF,p} obtained in step (22) to obtain a rainflow cycle matrix {RFM1 RFM2... RFM p} of the multi-parameter principal component load history, wherein: elements RFM1, RFM2, RFM p respectively represent the rainflow cycle matrix of each principal component load history;

[0035] wherein the rainflow cycle counting is based on the principle of material stress-strain hysteresis loop to extract the load full cycle of the load history, four points in the load history are read continuously, i.e. two peaks and two valleys, and the basis for full cycle selection is that the absolute value of the difference between the middle two points is less than the absolute value of the difference between the front two points and the absolute value of the difference between the rear two points, i.e. satisfying:

[0036]

[0037] (32), obtaining a rainflow cycle matrix {RFM1 RFM2... RFM p} respectively, the time history reconstruction based on rainflow statistics, that is, the random insertion and connection of the cycle load in the rainflow cycle matrix to form a new random load spectrum, and thus obtain the multi-parameter principal component load reconstruction history {F″ RFR,1 F″ RFR,2 ... F″ RFR,p} respectively, wherein: elements F″ RFR,1 , F″ RFR,2 , F″ RFR,p respectively represent the reconstruction history of each principal component load; wherein the peak-to-valley value of the inserted load cycle must be able to contain the peak-to-valley value of the pre-inserted load cycle.

[0038] Further, the specific steps of step (4) are:

[0039] The non-peak-to-valley value point set F″ R,j (j = 1, 2,..., p) obtained in step (22) is randomly inserted into the random principal component load reconstruction history {F″ RFR,1 F″ RFR,2 ... F″ RFR,p} of step (32) respectively, wherein after the random insertion of the non-peak-to-valley value point, the point is still not a peak-to-valley value point, that is, the non-peak-to-valley value point is only randomly inserted into the peak-to-valley half cycle containing the load value of the point, thereby obtaining a random multi-parameter principal component load reconstruction history {F′ RFR,1 F′ RFR,2 ... F′ RFR,p} with consistent data quantity, wherein: elements F′ RFR,1 , F′ RFR,2 , F′ RFR,p respectively represent the reconstruction history of each principal component load with consistent data quantity.

[0040] Further, the specific steps of step (5) are:

[0041] (51), linear solution of the principal component load history is performed on the random multi-parameter principal component load reconstruction history {F′ RFR,1 F′ RFR,2 ... F′R FR,p} obtained in step (4), and a new random multi-parameter standardized reconstruction load spectrum is obtained by back calculation, and the calculation formula is as follows:

[0042] [f RFR,i1 f RFR,i2 ... f RFR,ip ] = [f′ RFR,i1 f′ RFR,i2 ... f′ RFR,ip ]U -1

[0043] wherein, F′RFR,i = [f RFR,i1 f RFR,i2 ... f RFR,ip ] the element in the matrix is the reconstructed value of the i th sampling time point of the j th principal component load parameter of the p principal component load parameters; RFR,i = [f RFR,i1 f RFR,i2 ... f RFR,ip ] the element in the matrix is the reconstructed value of the i th sampling time point of the j th standardized load parameter of the p standardized load parameters; is the eigenvector matrix of the correlation coefficient matrix R of the standardized random multi-parameter load in step (21);

[0044] (52), for the random multi-parameter standardized reconstructed load spectrum {F RFR,1 F RFR,2 ...F RFR,p} obtained in step (51), wherein: the elements F RFR,1 , F RFR,2 , F RFR,p respectively represent the standardized reconstructed history of each principal component load, and the average value of the j th column data of the measured random multi-parameter load data matrix F in step (11) and the standard deviation σ j of the j th column data of the measured random multi-parameter load data matrix F are denormalized to obtain the completed multi-parameter load spectrum based on principal component analysis, and the calculation formula is as follows:

[0045]

[0046] wherein, f RFR,ij is the reconstructed value of the i th sampling time point of the j th standardized load parameter of the multi-parameter standardized reconstructed load spectrum, and f F,ij is the load value of the i th sampling time point of the j th load parameter of the completed multi-parameter load spectrum based on principal component analysis.

[0047] The present application is based on the single-parameter load spectrum compilation idea, and the rainflow cycle and load history reconstruction are performed on the multi-parameter principal component load spectrum, so that the random multi-parameter load spectrum is compiled by comprehensively considering the load correlation and multi-axis damage information. Compared with the existing multi-parameter load spectrum compilation method, the present application has the following beneficial effects:

[0048] (1) simple and intuitive, clear steps and accurate description;

[0049] The random multi-parameter component load spectrum is used as basic coding data, the principal component analysis of the multi-parameter load history is carried out, the rain flow cycle counting and load history reconstruction are carried out for the independent multi-parameter principal component load history, the non-peak-valley point is randomly inserted to obtain the principal component load reconstruction history, the linear solution of the principal component load is carried out, and the new multi-parameter random load spectrum is obtained by backstepping, the load correlation and multi-axis damage information are comprehensively considered, and the preparation method is more reasonable relative to the single-parameter load spectrum.

[0050] (2) has wide engineering application value;

[0051] The multi-parameter load spectrum preparation method provided by the application is simple and has wide engineering application value.

[0052] (3) research new multi-axis damage model and multi-axis fatigue life analysis method;

[0053] The random multi-parameter load spectrum preparation method prepared by the application can reflect the actual load characteristics and damage characteristics of the component, can provide load spectrum preparation basis for researching multi-axis damage and multi-axis fatigue life analysis method under the actual service condition of the specific mechanical component, and can preliminarily carry out multi-axis fatigue test of material level according to the multi-parameter fatigue test spectrum prepared by the application, so that the design and development cost and time are reduced.

[0054] As shown above, the application provides a basis for multi-axis fatigue damage analysis of engineering actual complex mechanical components under random multi-parameter load, and provides a basis for multi-parameter fatigue test evaluation of the complex mechanical components. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 It is the specific technical roadmap of the application;

[0056] Figure 2 It is the random multi-parameter load spectrum of three load compositions of example 1;

[0057] Figure 3 It is the random multi-parameter load spectrum data standardization result of example 1;

[0058] Figure 4 It is the random multi-parameter principal component load history of example 1;

[0059] Figure 5 It is the random multi-parameter principal component load peak-valley value sequence of example 1;

[0060] Figure 6 It is the random multi-parameter principal component load local peak-valley value sequence of example 1.

[0061] Figure 7 is the random multi-parameter principal component load rainflow cycle matrix of Example 1;

[0062] Figure 8 is the random multi-parameter principal component load reconstructed peak-valley value sequence of Example 1;

[0063] Figure 9 is the random multi-parameter principal component load reconstructed history of Example 1;

[0064] Figure 10 is the random multi-parameter standardized load reconstructed history of Example 1;

[0065] Figure 11 is the random multi-parameter load spectrum based on principal component analysis of Example 1. DETAILED DESCRIPTION

[0066] The present application will be further described below in conjunction with examples and drawings.

[0067] Example 1

[0068] As shown in the specific technical roadmap of the present application, the present application is now analyzed by a random multi-parameter load spectrum of a component composed of three load paths, Figure 1 A multi-parameter test spectrum preparation method based on principal component analysis, comprising the following steps:

[0069] (1) Standardizing and analyzing the correlation of the random multi-parameter load spectrum of a complex mechanical component, thereby obtaining a correlation coefficient matrix of the random multi-parameter load;

[0070] The specific steps of step (1) are:

[0071] (11) Taking the multi-parameter measured load spectrum of a complex mechanical component as the basic spectrum data, as

[0072] Figure 2 is the random multi-parameter load spectrum composed of three load paths of Example 1, which has three load parameters and 3050 sampling time points, i.e., p = 3, n = 3050 in this example; the random multi-parameter load data is standardized; assuming that there are p load parameters and n sampling time points, the load value of the jth load parameter at the ith sampling time point is denoted as f ij , i = 1, 2,..., 3050; j = 1, 2, 3, p = 3, n = 3050 in this example, then the measured random multi-parameter load data matrix F:

[0073]

[0074] ​The measured random multi-parameter load data matrix F is converted into a standardized random multi-parameter load data matrix F′:

[0075]

[0076] wherein, is the average value of the jth column data of the measured random multi-parameter load data matrix F, i.e. and σ j is the standard deviation of the jth column data of the measured random multi-parameter load data matrix F, As Figure 3 is the standardization result of the random multi-parameter load spectrum data of Example 1;

[0077] (12) Correlation analysis is performed on each column load of the standardized random multi-parameter load data matrix F′ of the complex mechanical component, and thus a correlation coefficient matrix R of the standardized random multi-parameter load is obtained;

[0078]

[0079] wherein, r jk is the correlation coefficient of the jth column data and the kth column data in the standardized random multi-parameter load data matrix F′, i.e. the correlation coefficient of the jth load parameter and the kth load parameter, wherein j, k = 1, 2, 3, and the calculation formula is as follows:

[0080]

[0081] wherein, f′ ij , f′ ik are elements in the standardized random multi-parameter load data matrix F′, i.e. the standardized load value of the ith sampling time point of the jth load parameter and the kth load parameter.

[0082] (2) The multi-parameter random load is converted into several independent load histories, i.e. principal component load histories, by using the principal component analysis method, and then peak-valley value extraction processing is performed thereon to obtain a peak-valley value sequence and a non-peak-valley value point set of the random multi-parameter principal component load history;

[0083] The specific steps of the step (2) are as follows:

[0084] (21) The standardized random multi-parameter load data matrix F′ is converted into several independent load histories, i.e. principal component load histories F″, by using the principal component analysis method, and the calculation formula is as follows:

[0085]

[0086] wherein, F i ″= [f″i1 f′ i2 f′ i3 The element in the middle is the principal component load value of the i-th sampling time point of the 3 principal component load parameters; F i ′=[f′ i1 f′ i2 f′ i3 The element in the middle is the standardized load value of the i-th sampling time point of the 3 standardized load parameters; U j =[u 1j u 2j u 3j ] T is the eigenvector corresponding to the j-th eigenvalue λ j of the correlation coefficient matrix R of the standardized random multi-parameter load, wherein: the elements u 1j , u 2j , u 3j are specific numerical values of the eigenvector U j , and T is the matrix transpose symbol; thus, the random multi-parameter principal component load history of Example 1 shown in Figure 4 can be obtained.

[0087] (22) For each load time history of the random multi-parameter principal component load history F′′ obtained in step (21), peak point or valley point judgment is performed, if yes, it is retained, otherwise it is moved to the non-peak-valley point set F′′ R,j (j=1, 2, 3), three-point method is used to judge the data, that is, three adjacent data points f′′ i-1,j , f′′ i,j , f′′ i+1,j are read in turn, if the following conditions are met:

[0088] [f′′ i,j -f′′ i-1,j ][f′′ i+1,j -f′′ i,j ]≥0 and f′′ i,j -f′′ i-1,j ≠0

[0089] f′′ i,j , it is a non-peak point or a non-valley point; thus, the non-peak-valley point set F′′ R,j (j=1, 2, 3) of the principal component load history and the peak-valley sequence {F′′ RF,1 F′′ RF,2 F′′ RF,3} of the random multi-parameter principal component load history of Example 1 shown in Figure 5 can be obtained, wherein: the elements F′′ RF,1 , F′′ RF,2 , F′′ RF,3These represent the peak-to-valley sequence of the loading history for each principal component, such as... Figure 6 This is the local peak-valley value sequence of the random multi-parameter principal component load in Example 1;

[0090] (3) Rainflow cycle counting is performed on the principal component load peak-valley value sequence to obtain its rainflow cycle matrix. Random load history is reconstructed from the rainflow cycle matrix to obtain the random multi-parameter principal component load reconstruction history.

[0091] The specific steps of step (3) are as follows:

[0092] (31) For the random principal component load peak-valley value sequence {F″ obtained in step (22) RF,1 F″ RF,2 F″ RF,3 Rainflow cycle counting is performed to obtain the rainflow cycle matrix {RFM1 RFM2 RFM3} of the multi-parameter principal component load history, where: elements RFM1, RFM2, and RFM3 represent the rainflow cycle matrix of each principal component load history.

[0093] Rainflow cycle counting is based on the principle of material stress-strain hysteresis loop to extract the full load cycle from the load history. It continuously reads four points in the load history: two peaks and two troughs. The selection criterion for the full cycle is that the absolute value of the difference between the two middle points must be less than the absolute values ​​of the differences between the two preceding points and the two following points, i.e., satisfying the following condition:

[0094]

[0095] Therefore, the rainflow cycle matrix of the random multi-parameter principal component load history in Example 1 can be obtained respectively, as follows: Figure 7 The image shows the rainflow cycle matrix of the random multi-parameter principal component load portion of Example 1 (sorted according to amplitude).

[0096] (32) The rainflow circulation matrix {RFM1 RFM2 RFM3} obtained in step (31) is reconstructed based on rainflow statistics, that is, the cyclic loads in the rainflow circulation matrix are randomly inserted and connected to form a new random load spectrum, thereby obtaining the multi-parameter principal component load reconstruction history {F″ RFR,1 F″ RFR,2 F″ RFR,3},like Figure 8 As shown, where: element F″ RFR,1 、F″ RFR,2 、F″ RFR,3 These represent the reconstruction history of each principal component load; the peak and valley values ​​of the inserted load cycle must be able to contain the peak and valley values ​​of the pre-inserted load cycle.

[0097] (4) Randomly inserting non-peak-valley points to obtain random multi-parameter principal component load reconstruction history with consistent data amount;

[0098] The specific steps of the step (4) are:

[0099] The non-peak-valley point set F" R,j The non-peak-valley load values in the set F" RFR,1 F" RFR,2 F" RFR,3} are randomly inserted into the random principal component load reconstruction history {F" Figure 9 , respectively, wherein after the non-peak-valley points are randomly inserted, the points are still not peak-valley points, that is, the non-peak-valley points are only randomly inserted into the peak-valley value half cycle containing the load values of the points, thereby obtaining a random multi-parameter principal component load reconstruction history {F' FR,1 F' RFR,2 F' RFR,3} with consistent data amount as shown in RFR,1 , F' RFR,2 , F' RFR,3 respectively, wherein: the elements F' RFR,1 , F' RFR,2 , F' RFR,3 respectively, wherein: the elements F'

[0100] (5) Linear solution of the principal component load history is performed to obtain a new multi-parameter random load spectrum, thereby obtaining a completed random multi-parameter random load spectrum based on principal component analysis;

[0101] The specific steps of the step (5) are:

[0102] (51), the linear solution of the principal component load history is performed on the random multi-parameter principal component load reconstruction history {F' RFR,1 F' RFR,2 F ′RFR,3} obtained in the step (4), and a new random multi-parameter standardized reconstruction load spectrum of Example 1 as shown in Figure 10 is obtained by reverse calculation, and the calculation formula is as follows:

[0103] [f RFR,i1 f RFR,i2 f RFR,i3 ]=[f′ RFR,i1 f′ RFR,i2 f′ RFR,i3 ]U -1 , (i = 1, 2,..., 3050; j = 1, 2, 3)

[0104] , F' RFR,i = [f' RFR,i1 f' RFR,i2 f' RFR,i3the middle element of F is the reconstructed value of the i th sampling time point of the j th principal component load parameter; F RFR,i = [f RFR,i1 f RFR,i2 f RFR,i3 the middle element of F is the reconstructed value of the i th sampling time point of the j th standardized load parameter; is the eigenvector matrix of the correlation coefficient matrix R of the standardized random multi-parameter load in step (21);

[0105] (52), for the random multi-parameter standardized reconstructed load spectrum {F RFR,1 F RFR,2 F RFR,3} obtained in step (51), wherein: the elements F RFR,1 , F RFR,2 , F RFR,3 respectively represent the standardized reconstructed history of each principal component load, and the average value of the j th column data of the measured random multi-parameter load data matrix F in step (11) and the standard deviation σ j of the j th column data of the measured random multi-parameter load data matrix F are denormalized to obtain the compiled multi-parameter load spectrum based on principal component analysis, and the calculation formula is as follows:

[0106]

[0107] wherein, f RFR,ij is the reconstructed value of the i th sampling time point of the j th standardized load parameter of the multi-parameter standardized reconstructed load spectrum, and f F,ij is the load value of the i th sampling time point of the j th load parameter of the compiled multi-parameter load spectrum based on principal component analysis.

[0108] The above is only a specific embodiment of the present application, and the purpose, technical solution and beneficial effects of the present application are further described in detail. Finally, it should be noted that: the above is only a preferred embodiment of the present application, and does not limit the present application in any form. For researchers and technicians in the technical field, non-innovative modifications, changes and modifications of the technical solution of the present application based on the above content without departing from the scope of the technical solution of the present application should also be regarded as within the protection scope of the present application.

Claims

1. A random multi-parameter load spectrum development method based on principal component analysis, characterized by, With the multi-parameter measured load spectrum of the component as the basic data, the multi-parameter random load is converted into several independent load histories by using the principal component analysis method, i.e. the principal component load history, and then the peak and valley values of the principal component load history are extracted to obtain the peak and valley value sequence and the non-peak and valley point set of the principal component load history, the rainflow cycle counting is performed to obtain the rainflow cycle matrix of the principal component load history, the load history is reconstructed from the rainflow cycle matrix, and the non-peak and valley points are randomly inserted to obtain the reconstructed principal component load history, and the linear solution of the principal component load history is performed to obtain the new multi-parameter random load spectrum; The method comprises the following steps: (1) standardizing and analyzing the correlation of the random multi-parameter load spectrum of the complex mechanical component to obtain the correlation coefficient matrix of the random multi-parameter load; (2) converting the multi-parameter random load into several independent load histories by using the principal component analysis method, i.e. the principal component load history, and then extracting the peak and valley values of the principal component load history to obtain the peak and valley value sequence and the non-peak and valley point set of the principal component load history; (3) performing the rainflow cycle counting on the peak and valley value sequence of the principal component load to obtain the rainflow cycle matrix thereof, and reconstructing the random load history from the rainflow cycle matrix to obtain the reconstructed principal component load history of the random multi-parameter load; (4) randomly inserting the non-peak and valley points to obtain the reconstructed principal component load history of the random multi-parameter load with consistent data quantity; (5) performing the linear solution of the principal component load history to obtain the new multi-parameter random load spectrum, and thus obtaining the prepared random multi-parameter random load spectrum based on the principal component analysis; The specific steps of the step (1) are as follows: (11), with the multi-parameter measured load spectrum of complex mechanical components as the basic data for compiling the spectrum, the random multi-parameter load data is standardized; assuming that there are p load parameters and n sampling time points, and the load value of the jth load parameter at the ith sampling time point is denoted as f ij , i = 1, 2,..., n; j = 1, 2,..., p, then the measured random multi-parameter load data matrix F: The measured random multi-parameter load data matrix F is converted into the standardized random multi-parameter load data matrix F': wherein is the average of the data in the jth column of the measured random multi-parameter load data matrix F, and σ j is the standard deviation of the data in the jth column of the measured random multi-parameter load data matrix F, (12) analyzing the correlation of each column load of the standardized random multi-parameter load data matrix F' of the complex mechanical component to obtain the correlation coefficient matrix R of the standardized random multi-parameter load; wherein r jk is the correlation coefficient of the jth column data and the kth column data in the standardized random multi-parameter load data matrix F', i.e. the correlation coefficient of the jth load parameter and the kth load parameter, and the calculation formula is as follows: wherein f′ ij , f′ ik are the elements of the standardized random multi-parameter load data matrix F′, i.e. the standardized load value of the i-th sampling time point of the j-th load parameter and the k-th load parameter; The specific steps of the step (2) are as follows: (21) converting the standardized random multi-parameter load data matrix F' into several independent load histories by using the principal component analysis method, i.e. the principal component load history F'', and the calculation formula is as follows: wherein F i = [f i1 ... f i2 ... f ip ] are the principal component load values of the i-th sampling time point of the p principal component load parameters, respectively; F i = [f i1 ... f i2 ... f ip ] are the standardized load values of the i-th sampling time point of the p standardized load parameters, respectively; U j = [u 1j ... u 2j ... u pj ] T is the eigenvector corresponding to the j-th eigenvalue λ j of the correlation coefficient matrix R of the standardized random multi-parameter load, wherein: elements u 1j , u 2j , u pj are specific numerical values of the eigenvector U j , and T is the matrix transpose symbol; (22), for each load time history of the random multi-parameter principal component load history F" obtained in step (21), peak or valley point judgment is carried out respectively, if yes, it is retained, otherwise it is moved to the non-peak-valley point set F" R,j (j = 1, 2,..., p), three-point method judgment is carried out on the data, that is, three adjacent data points f" i-1,j , f" i,j , f" i+1,j are read in turn, if the following conditions are met: [f" i,j -f" i-1,j ][f" i+1,j -f" i,j ]≥0 and f" i,j -f" i-1,j ≠0 wherein: F" i,j is a non-peak point or a non-valley point; thereby obtaining a non-peak-valley point set F" of the principal component load history R,j (j = 1, 2, …, p) and a multi-parameter principal component load history peak-valley value sequence {F" RF,1 F" RF,2 ... F" RF,p}, wherein: the elements F" RF,1 , F" RF,2 , F" RF,p respectively represent the peak-valley value sequence of each principal component load history; The specific steps of the step (3) are as follows: (31) For the random principal component load peak-valley value sequence {F″ obtained in step (22) RF,1 F″ RF,2 ... F″ RF,p Perform rainflow cycle counting to obtain the rainflow cycle matrix {RFM1 RFM2 ... RFM} of the multi-parameter principal component loading history. p }, where: elements RFM1, RFM2, RFM p These represent the rainflow cycle matrices representing the loading history of each principal component; The rainflow cycle counting is based on the principle of material stress-strain hysteresis loop to extract the load full cycle of the load history, and four points in the load history are continuously read, i.e. two peak values and two valley values, and the full cycle selection is based on the fact that the absolute value of the difference between the middle two points is smaller than the absolute values of the differences between the front two points and the rear two points, i.e. the following condition is met: (32), the rainflow cycle matrix {RFM1 RFM2... RFM p} obtained from step (31) are respectively subjected to rainflow statistics-based time history reconstruction, i.e. the random insertion and connection of the cycle loads in the rainflow cycle matrix to form a new random load spectrum, thereby obtaining a multi-parameter principal component load reconstruction history {F" RFR,1 F" RFR,2 ... F" RFR,p}, wherein: elements F" RFR,1 , F" RFR,2 , F" RFR,p respectively represent the reconstruction history of each principal component load; wherein the peak-to-valley values of the inserted load cycles must be able to contain the peak-to-valley values of the pre-inserted load cycles.

2. The random multi-parameter load spectrum development method based on principal component analysis according to claim 1, characterized in that, The specific steps of the step (4) are as follows: The non-peak-valley point set F" obtained in step (22) R,j The non-peak-valley load values in the random principal component load reconstruction history {F" RFR,1 F" RFR,2 ... F" RFR,p} in step (32) are randomly inserted respectively, wherein after the non-peak-valley points are randomly inserted, the points are still not peak-valley points, i.e. the non-peak-valley points are only randomly inserted into the peak-valley value half cycle containing the load value of the point, thereby obtaining the random multi-parameter principal component load reconstruction history {F' RFR,1 F' RFR,2 ...F' RFR,p} with consistent data quantity, wherein: the elements F' RFR,1 , F' RFR,2 , F' RFR,p respectively represent the reconstruction history with consistent data quantity of each principal component load.

3. The random multi-parameter load spectrum development method based on principal component analysis according to claim 2, characterized in that, The specific steps of the step (5) are as follows: (51) Regarding the reconstruction process of the random multi-parameter principal component loads obtained in step (4) {F′ RFR,1 F′ RFR,2 ... F′ RFR,p Linear solutions to the principal component loading histories are performed, and the new stochastic multi-parameter standardized reconstructed loading spectrum is obtained by reverse calculation. The calculation formula is as follows: [f RFR,i1 f RFR,i2 ... f RFR,ip ]=[f′ RFR,i1 f′ RFR,i2 ... f′ RFR,ip ]U -1 wherein F' = [f' f'... f'], the elements of which are the reconstructed principal component load values of the p principal component load parameters at the i sampling time point; F = [f f... f], the elements of which are the reconstructed standardized load values of the p standardized load parameters at the i sampling time point; and F = [f f... f], the elements of which are the reconstructed principal component load values of the p principal component load parameters at the i sampling time point. RFR,i RFR,i1 RFR,i2 RFR,ip RFR,i RFR,i1 RFR,i2 RFR,ip is the eigenvector matrix of the correlation coefficient matrix R of the standardized random multi-parameter load in step (21).​​​​​​​​ (52) Random multi-parameter normalized reconstructed load spectrum {F RFR,1 F RFR,2 ...F RFR,p}, wherein: elements F RFR,1 , F RFR,2 , F RFR,p respectively represent the normalized reconstructed history of each principal component load, and the average value of the jth column data of the measured random multi-parameter load data matrix F according to step (11) and the standard deviation σ j of the jth column data of the measured random multi-parameter load data matrix F are denormalized to obtain the completed multi-parameter load spectrum based on principal component analysis, and the calculation formula is as follows: wherein f RFR,ij is the reconstructed normalized load value of the i-th sampling time point of the j-th normalized load parameter of the multi-parameter normalized reconstructed load spectrum, f F,ij is the load value of the i-th sampling time point of the j-th load parameter of the completed multi-parameter load spectrum based on principal component analysis.

Images