CN114139307A - Random multi-parameter load spectrum compilation method based on principal component analysis - Google Patents

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

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CN114139307A
CN114139307A CN202111381796.6A CN202111381796A CN114139307A CN 114139307 A CN114139307 A CN 114139307A CN 202111381796 A CN202111381796 A CN 202111381796A CN 114139307 A CN114139307 A CN 114139307A
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孙志刚
赵如涛
李亚松
常亚宁
宋迎东
牛序铭
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a random multi-parameter load spectrum compilation method based on principal component analysis, which takes a member multi-parameter actual measurement load spectrum as basic compilation spectrum data, utilizes a principal component analysis method to randomly load multiple parameters into a plurality of mutually independent load courses, namely multi-parameter principal component load courses, then carries out peak-valley value extraction processing on the multi-parameter actual measurement load spectrum to obtain a peak-valley value sequence and a non-peak-valley value point set of a principal component load, carries out rain circulation counting to obtain a rain circulation matrix of the principal component load course, carries out load course reconstruction on the rain circulation matrix and randomly inserts non-peak-valley value points to obtain a principal component load reconstruction course, and carries out linear calculation on the principal component load course to obtain a new multi-parameter random load spectrum by reverse extrapolation. The invention realizes the full consideration of the multi-parameter load correlation and the multi-axis damage information in the random multi-parameter load spectrum compilation process, and provides a foundation for the fatigue damage analysis and the multi-axis fatigue test of the actual complex mechanical component of the engineering.

Description

Random multi-parameter load spectrum compilation method based on principal component analysis
Technical Field
The invention belongs to the technical field of mechanical structure fatigue test load spectrum compilation, and particularly relates to a multi-parameter random load spectrum compilation method for a complex mechanical component, which provides a load basis for multi-axial fatigue damage analysis and multi-axial fatigue test of the mechanical component under random multi-parameter load and is an important step for life test evaluation of key parts of a engineering complex structure under multi-parameter actual service load.
Background
At present, the research on load spectrums at home and abroad mostly focuses on compiling single-parameter load spectrums and is widely applied to the industrial fields of aerospace, vehicles, engineering machinery and the like. However, in practical engineering applications, most mechanical components are subjected to random multi-parameter loads for a long time, that is, the components are subjected to more than one load, and the components are prone to multi-axial fatigue damage and then fail. Complex components such as aircraft engine casings, automotive gimbals and front suspensions are subject to typical random non-proportional multi-axis loads in actual service. Although the application of the single-parameter load statistical method and the load spectrum compiling method is mature, the method is not suitable for the components bearing complex multi-parameter loads any more, and a multi-parameter load spectrum compiling method must be developed for carrying out sufficient and scientific service life assessment on the components.
When the service life assessment test is carried out on the complex mechanical component, the loaded load spectrum of the complex mechanical component must reflect the actual working characteristics of the component to a certain extent. In addition, if the fatigue damage information contained in the actually measured load spectrum cannot be fully considered, the compiled load spectrum and the actual service load have certain differences in load characteristics and fatigue life performance. For the multi-parameter load spectrum compilation, not only the damage information of the single-axis load needs to be reserved, but also the correlation among the multi-parameter loads and the multi-axis damage information need to be fully considered. At present, no clear and generally accepted component multi-parameter load spectrum compiling method exists at home and abroad, only a few organizations and scholars carry out researches on the component multi-parameter load spectrum compiling method in different degrees, the German Fraunhofer Hoff society carries out researches on multi-parameter loads borne by an automobile structure, a CARLOS multi-parameter standard load sequence is developed, but no specific method is published; the research aiming at the multi-parameter load spectrum in China starts late, the random combination of the load and the cycle is mainly carried out by adopting a given matching principle, the theoretical basis is lacked, and the correlation and the phase relation among the loads are not considered.
In summary, the existing multi-parameter load spectrum compiling method has certain limitations, and a clear and generally accepted member multi-parameter load spectrum compiling method is not available, so that the requirement of the fatigue damage information retention for compiling the spectrum is met to different degrees. Under the action of multi-parameter loads, a component multi-parameter load spectrum which fully considers the correlation among the multi-parameter loads and multi-axis damage information is compiled, a key engineering problem which needs to be solved urgently is still solved, and the method has important significance for the fatigue damage analysis and the fatigue test research of complex mechanical components in engineering practice.
Therefore, it is necessary to develop a random multi-parameter load spectrum compiling method capable of considering multi-parameter load correlation and retaining multi-axis damage information, and a foundation is laid for the life determination of complex engineering machinery and parts thereof.
Disclosure of Invention
In order to solve the problems that multi-parameter load related relation consideration and multi-axis damage information loss are lacked in component multi-parameter load spectrum compilation in the prior art, the invention provides a random multi-parameter load spectrum compilation method based on principal component analysis.
In order to achieve the purpose, the invention adopts the technical scheme that:
a random multi-parameter load spectrum compilation method based on principal component analysis is characterized in that a member multi-parameter actual measurement load spectrum is used as basic compilation spectrum data, a principal component analysis method is utilized to randomly load multiple parameters into a plurality of mutually independent load courses, namely multi-parameter principal component load courses, peak-valley values of the multi-parameter actual measurement load courses are extracted and processed to obtain a peak-valley value sequence and a non-peak-valley value point set of a principal component load, rain flow circulation counting is conducted to obtain a rain flow circulation matrix of the principal component load courses, load course reconstruction is conducted on the rain flow circulation matrix, non-peak-valley value points are randomly inserted to obtain a principal component load reconstruction course, linear calculation of the principal component load courses is conducted, and a new multi-parameter random load spectrum can be obtained through reverse extrapolation.
A multi-parameter test spectrum compiling method based on principal component analysis comprises the following steps:
(1) carrying out standardization processing and correlation analysis on a random multi-parameter load spectrum of the complex mechanical component, thereby obtaining a correlation coefficient matrix of the random multi-parameter load;
(2) carrying out random loading on the multi-parameter into a plurality of mutually independent load processes, namely main component load processes, by using a main component analysis method, and then carrying out peak-valley value extraction processing on the main component load processes to obtain a peak-valley value sequence and a non-peak-valley value point set of the random multi-parameter main component load processes;
(3) carrying out rain flow cycle counting aiming at the main component load peak-valley value sequence to obtain a rain flow cycle matrix of the main component load peak-valley value sequence, and carrying out random load process reconstruction on the rain flow cycle matrix to obtain a random multi-parameter main component load reconstruction process;
(4) randomly inserting non-peak and non-valley points to obtain a random multi-parameter principal component load reconstruction process with consistent data quantity;
(5) and carrying out linear calculation on the principal component load process, and carrying out reverse thrust to obtain a new multi-parameter random load spectrum, thereby obtaining the compiled random multi-parameter random load spectrum based on principal component analysis.
Further, the specific steps of the step (1) are as follows:
(11) and measuring the load with multiple parameters of the complex mechanical componentThe spectrum is basic spectrum data, and the standardization processing is carried out on random multi-parameter load data; let p load parameters in total, n sampling time points, and let the load value of the jth load parameter at the ith sampling time point be fijN, · i ═ 1, 2; 1,2, p, then the measured random multi-parameter load data matrix F:
Figure BDA0003365886090000031
converting the measured random multi-parameter load data matrix F into a standardized random multi-parameter load data matrix F':
Figure BDA0003365886090000032
wherein,
Figure BDA0003365886090000033
Figure BDA0003365886090000034
is the average value of j-th column data of the measured random multi-parameter load data matrix F, i.e.
Figure BDA0003365886090000035
And σjFor the standard deviation of the j-th column data of the measured random multi-parameter payload data matrix F,
Figure BDA0003365886090000036
(12) carrying out correlation analysis on each column of loads of a standardized random multi-parameter load data matrix F' of the complex mechanical component, thereby obtaining a correlation coefficient matrix R of the standardized random multi-parameter loads;
Figure BDA0003365886090000037
wherein r isjkIs standardizedThe correlation coefficient between the jth column data and the kth column data in the random multi-parameter load data matrix F', that is, the correlation coefficient between the jth load parameter and the kth load parameter, is calculated as follows:
Figure BDA0003365886090000038
wherein, f'ij、f′ikThe normalized load values of the ith sampling time point of the jth load parameter and the kth load parameter are elements in a normalized random multi-parameter load data matrix F'.
Further, the specific steps of the step (2) are as follows:
(21) the standardized random multi-parameter load data matrix F 'is converted into a plurality of mutually independent load processes by using a principal component analysis method, namely a principal component load process F', and the calculation formula is as follows:
Figure BDA0003365886090000041
wherein, Fi″＝[f″i1 f″i2 ... f″ip]The middle elements are respectively the principal component load values of the ith sampling time point of the p principal component load parameters; fi′＝[f′i1 f′i2 ... f′ip]The middle elements are respectively the normalized load values of the ith sampling time point of the p normalized load parameters; u shapej＝[u1j u2j ... upj]TMatrix Rjth eigenvalue lambda of correlation coefficient for normalizing random multi-parameter loadjA corresponding feature vector, wherein: element u1j、u2j、upjAre respectively a feature vector UjT is a matrix transposition symbol;
(22) respectively judging peak points or valley points aiming at each path of load time history of the random multi-parameter principal component load history F 'obtained in the step (21), if so, keeping, otherwise, moving to a non-peak-valley point set F', and otherwise, moving to a non-peak-valley point setR,j(j ═ 1,2,. and p), and three-point method judgment is carried out on the data, namely three adjacent data points f ″ "are read in sequencei-1,j、f″i,j、f″i+1,jIf the following conditions are met:
[f″i,j-f″i-1,j][f″i+1,j-f″i,j]f ≥ 0i,j-f″i-1,j≠0
Wherein: f ″)i,jThen it is the peak or valley point; thus obtaining the main component load course non-peak-valley value point set F ″)R,j(j ═ 1,2,. said., p) and a sequence of multi-parameter principal component load history peak-to-valley values { F ″ "RF,1 F″RF,2 ... F″RF,p}, wherein: element F ″)RF,1、F″RF,2、F″RF,pRespectively representing the peak-to-valley sequence of each principal component load course.
Further, the specific steps of the step (3) are as follows:
(31) and aiming at the random main component load peak-valley value sequence { F') obtained in the step (22)RF,1 F″RF,2 ... F″RF,pPerforming rain flow circulation counting to obtain a rain flow circulation matrix (RFM) of multi-parameter principal component load history1 RFM2 ... RFMp}, wherein: element RFM1、RFM2、RFMpA rain flow circulation matrix respectively representing each principal component load course;
the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of a material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following steps: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely the following conditions are met:
Figure BDA0003365886090000051
(32) and the rain flow circulation matrix { RFM) obtained in step (31)1 RFM2 ... RFMpRespectively carrying out time histories based on rain flow statisticsReconstructing, namely randomly inserting and connecting the cyclic loads in the rain flow cyclic matrix to form a new random load spectrum, thereby obtaining a multi-parameter principal component load reconstruction process { F ″)RFR,1 F″RFR,2 ... F″RFR,p}, wherein: element F ″)RFR,1、F″RFR,2、F″RFR,pRespectively representing the reconstruction process of each principal component load; wherein the peak to valley values of the inserted load cycle must be able to contain the pre-inserted load cycle peak to valley values.
Further, the specific steps of the step (4) are as follows:
collecting the non-peak-valley value points F' obtained in the step (22)R,j(j ═ 1, 2.. said., p) in which the off-peak-to-valley load values were randomly inserted into the random principal component load reconstruction history { F ″') of step (32), respectivelyRFR,1 F″RFR,2 ... F″RFR,pAnd (5) after the non-peak-valley point is randomly inserted, the point is not the peak-valley point, namely the non-peak-valley point is only randomly inserted into the peak-valley half cycle containing the load value of the point, so that a random multi-parameter principal component load reconstruction history { F'RFR,1 F′RFR,2... F′RFR,p}, wherein: element F'RFR,1、F′RFR,2、F′RFR,pRespectively representing the reconstruction process of each principal component load data quantity.
Further, the specific steps of the step (5) are as follows:
(51) and (3) reconstructing a history { F 'of the random multi-parameter principal component load obtained in the step (4)'RFR,1 F′RFR,2 ... F′RFR,pLinearly resolving the principal component load process, and reversely deducing to obtain a new random multi-parameter standardized reconstruction load spectrum, wherein the calculation formula is as follows:
[fRFR,i1 fRFR,i2 ... fRFR,ip]＝[f′RFR,i1 f′RFR,i2 ... f′RFR,ip]U-1
wherein, F'RFR,i＝[f′RFR,i1 f′RFR,i2 ... f′RFR,ip]The middle elements are respectively the principal components of the ith sampling time point of the p principal component load parametersA load reconstruction value; fRFR,i＝[fRFR,i1 fRFR,i2 ... fRFR,ip]The middle elements are respectively the normalized load reconstruction values of the ith sampling time point of the p normalized load parameters;
Figure BDA0003365886090000052
an eigenvector matrix of a correlation coefficient matrix R for the normalized random multi-parameter load in step (21);
(52) and (5) normalizing the reconstructed load spectrum { F) with respect to the random multi-parameter obtained in the step (51)RFR,1 FRFR,2 ... FRFR,p}, wherein: element FRFR,1、FRFR,2、FRFR,pRespectively representing the normalized reconstruction process of each principal component load according to the average value F of j-th column data of the actually measured random multi-parameter load data matrix F in the step (11)jStandard deviation sigma of j-th column data of actually measured random multi-parameter load data matrix FjAnd (3) carrying out de-standardization processing to obtain a compiled multi-parameter load spectrum based on principal component analysis, wherein the calculation formula is as follows:
Figure BDA0003365886090000061
wherein f isRFR,ijReconstructing a normalized load reconstruction value for the ith sampling time point of the jth normalized load parameter of the load spectrum for multi-parameter normalizationF,ijLoad values at the ith sampling time point of the jth load parameter of the compiled multi-parameter load spectrum based on principal component analysis are obtained.
Based on a single-parameter load spectrum compilation idea, the invention carries out rain flow circulation and load process reconstruction aiming at the multi-parameter principal component load spectrum, thereby carrying out random multi-parameter load spectrum compilation taking load correlation and multi-axis damage information as comprehensive consideration, and compared with the traditional multi-parameter load spectrum compilation method, the invention has the following beneficial effects:
(1) the method is simple and intuitive, and has clear steps and accurate description;
the method comprises the steps of taking a random multi-parameter component load spectrum as basic spectrum data, conducting rain current cycle counting and load process reconstruction aiming at mutually independent multi-parameter main component load processes through main component analysis of the multi-parameter load processes, randomly inserting non-peak-valley points to obtain a main component load reconstruction process, conducting linear calculation and reverse thrust on the main component load to obtain a new multi-parameter random load spectrum, comprehensively considering load correlation and multi-axis damage information, and being more reasonable compared with a single-parameter load spectrum compiling method.
(2) Has wide engineering application value;
the multi-parameter load spectrum compiling method provided by the invention is simple and has strong universality, so that under the existing technical condition, the load characteristics of the complex mechanical component can be reasonably compiled to be consistent with those under the actual load condition by using the multi-parameter load spectrum compiling method, the random multi-parameter load spectrum of the correlation among multi-parameter loads is reserved, and the multi-parameter load spectrum compiling method has wide engineering application value.
(3) Researching a new multi-axis damage model and a multi-axis fatigue life analysis method;
the random multi-parameter load spectrum compilation method compiled by the invention can reflect the actual load characteristics and damage characteristics of the component, can provide a compilation basis for load spectrum for researching multi-axial damage and multi-axial fatigue life analysis methods under the actual service working condition of a specific mechanical component, and can preliminarily carry out multi-axial fatigue test at a material level according to the multi-parameter fatigue test spectrum compiled by the invention so as to reduce the design research and development cost and time.
In conclusion, the method provides a basis for multi-axial fatigue damage analysis of the actual complex mechanical component under random multi-parameter load, and provides a basis for multi-parameter fatigue test evaluation of the complex mechanical component.
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FIG. 1 is a technical specific roadmap according to the present invention;
FIG. 2 is a random multi-parameter load spectrum consisting of three loads of example 1;
FIG. 3 is the result of normalization of random multi-parameter load spectrum data in example 1;
FIG. 4 is the random multi-parameter principal component load history of example 1;
FIG. 5 is a random multi-parameter principal component load peak-to-valley sequence of example 1;
FIG. 6 is a random multi-parameter principal component loading local peak-to-valley sequence of example 1;
FIG. 7 is a random multi-parameter principal component loading rain flow circulation matrix of example 1;
FIG. 8 is a random multi-parameter principal component load reconstruction peak-to-valley sequence of example 1;
FIG. 9 is the random multi-parameter principal component load reconstruction history of example 1;
FIG. 10 is the random multi-parameter normalized load reconstruction history of example 1;
FIG. 11 is a stochastic multi-parameter loading spectrum based on principal component analysis of example 1.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
Example 1
Referring to fig. 1, which is a technical roadmap of the present invention, an example analysis of the present invention is now performed using a random multi-parameter loading spectrum consisting of three loads,
a multi-parameter test spectrum compiling method based on principal component analysis comprises the following steps:
(1) carrying out standardization processing and correlation analysis on a random multi-parameter load spectrum of the complex mechanical component, thereby obtaining a correlation coefficient matrix of the random multi-parameter load;
the specific steps of the step (1) are as follows:
(11) taking a multi-parameter actual measurement load spectrum of a complex mechanical component as basic spectrum data, for example, fig. 2 is a random multi-parameter load spectrum composed of three paths of loads in embodiment 1, where in embodiment 1 of the load spectrum, 3 load parameters are shared, and 3050 sampling time points, that is, p is 3, and n is 3050 in this embodiment; carrying out standardization processing on random multi-parameter load data; let p load parameters in total, n sampling time points, and let the load value of the jth load parameter at the ith sampling time point be fij3050, · i ═ 1, 2; 1,2,3, in this example, p is 3 and n is 3050, then random measurements are taken at randomMulti-parameter load data matrix F:
Figure BDA0003365886090000081
converting the measured random multi-parameter load data matrix F into a standardized random multi-parameter load data matrix F':
Figure BDA0003365886090000082
wherein,
Figure BDA0003365886090000083
Figure BDA0003365886090000084
is the average value of j-th column data of the measured random multi-parameter load data matrix F, i.e.
Figure BDA0003365886090000085
And σjFor the standard deviation of the j-th column data of the measured random multi-parameter payload data matrix F,
Figure BDA0003365886090000086
FIG. 3 shows the result of normalization of random multi-parameter load spectrum data in example 1;
(12) carrying out correlation analysis on each column of loads of a standardized random multi-parameter load data matrix F' of the complex mechanical component, thereby obtaining a correlation coefficient matrix R of the standardized random multi-parameter loads;
Figure BDA0003365886090000087
wherein r isjkThe correlation coefficient between j-th column data and k-th column data in the normalized random multi-parameter load data matrix F', that is, the correlation coefficient between j-th load parameter and k-th load parameter, where j, k is 1,2,3, and the calculation formula is as follows:
Figure BDA0003365886090000088
wherein, f'ij、f′ikThe normalized load values of the ith sampling time point of the jth load parameter and the kth load parameter are elements in a normalized random multi-parameter load data matrix F'.
(2) Carrying out random loading on the multi-parameter into a plurality of mutually independent load processes, namely main component load processes, by using a main component analysis method, and then carrying out peak-valley value extraction processing on the main component load processes to obtain a peak-valley value sequence and a non-peak-valley value point set of the random multi-parameter main component load processes;
the specific steps of the step (2) are as follows:
(21) the standardized random multi-parameter load data matrix F 'is converted into a plurality of mutually independent load processes by using a principal component analysis method, namely a principal component load process F', and the calculation formula is as follows:
Figure BDA0003365886090000091
wherein, Fi″＝[f″i1 f″i2 f″i3]The middle elements are respectively the principal component load values of the ith sampling time point of the 3 principal component load parameters; fi′＝[f′i1 f′i2 f′i3]The middle elements are respectively the normalized load values of the ith sampling time point of the 3 normalized load parameters; u shapej＝[u1j u2j u3j]TMatrix Rjth eigenvalue lambda of correlation coefficient for normalizing random multi-parameter loadjA corresponding feature vector, wherein: element u1j、u2j、u3jAre respectively a feature vector UjT is a matrix transposition symbol; thus, the random multi-parameter principal component load course of the embodiment 1 shown in FIG. 4 can be obtained;
(22) against the product obtained in step (21)Judging peak points or valley points of each load time course of the mechanical multi-parameter principal component load course F ', if so, retaining, otherwise, moving to a non-peak-valley point set F', respectivelyR,j(j ═ 1,2,3), the data is judged by a three-point method, namely three adjacent data points f ″ "are read in sequencei-1,j、f″i,j、f″i+1,jIf the following conditions are met:
[f″i,j-f″i-1,j][f″i+1,j-f″i,j]f ≥ 0i,j-f″i-1,j≠0
f″i,jThen it is the peak or valley point; thus obtaining the main component load course non-peak-valley value point set F ″)R,j(j ═ 1,2,3) and example 1 random multiparameter principal component load history peak-to-valley value sequence { F ″', as shown in fig. 5RF,1 F″RF,2 F″RF,3}, wherein: element F ″)RF,1、F″RF,2、F″RF,3Respectively representing the peak-valley value sequence of each principal component load course, and as shown in FIG. 6, the random multi-parameter principal component load local peak-valley value sequence in the embodiment 1 is shown;
(3) carrying out rain flow cycle counting aiming at the main component load peak-valley value sequence to obtain a rain flow cycle matrix of the main component load peak-valley value sequence, and carrying out random load process reconstruction on the rain flow cycle matrix to obtain a random multi-parameter main component load reconstruction process;
the specific steps of the step (3) are as follows:
(31) and aiming at the random main component load peak-valley value sequence { F') obtained in the step (22)RF,1 F″RF,2 F″RF,3Performing rain flow circulation counting to obtain a rain flow circulation matrix (RFM) of multi-parameter principal component load history1 RFM2 RFM3}, wherein: element RFM1、RFM2、RFM3A rain flow circulation matrix respectively representing each principal component load course;
the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of a material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following steps: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely the following conditions are met:
Figure BDA0003365886090000101
thus, rain flow circulation matrixes of random multi-parameter principal component load courses in the embodiment 1 can be respectively obtained, and as shown in fig. 7, rain flow circulation matrixes of random multi-parameter principal component load partial flows in the embodiment 1 (sorted according to amplitude values) are obtained.
(32) And the rain flow circulation matrix { RFM) obtained in step (31)1 RFM2 RFM3Respectively reconstructing time histories based on rain flow statistics, namely randomly inserting and connecting cyclic loads in a rain flow cyclic 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,3As shown in fig. 8, wherein: element F ″)RFR,1、F″RFR,2、F″RFR,3Respectively representing the reconstruction process of each principal component load; wherein the peak to valley values of the inserted load cycle must be able to contain the pre-inserted load cycle peak to valley values.
(4) Randomly inserting non-peak and non-valley points to obtain a random multi-parameter principal component load reconstruction process with consistent data quantity;
the specific steps of the step (4) are as follows:
collecting the non-peak-valley value points F' obtained in the step (22)R,j(j ═ 1,2,3) the off-peak-to-valley load values were randomly inserted into the random principal component load reconstruction history { F ″) of step (32), respectivelyRFR,1 F″RFR,2 F″RFR,3And after the non-peak-valley point is randomly inserted, the point is not the peak-valley point, namely, the non-peak-valley point is only randomly inserted into the peak-valley half cycle containing the load value of the point, so that a random multi-parameter principal component load reconstruction history { F 'with consistent data quantity as shown in FIG. 9 is obtained'RFR,1 F′RFR,2F′RFR,3}, wherein: element F'RFR,1、F′RFR,2、F′RFR,3Individual watchAnd (4) showing a reconstruction process that each principal component load data quantity is consistent.
(5) Carrying out linear calculation on the principal component load process, and carrying out reverse thrust to obtain a new multi-parameter random load spectrum, thereby obtaining a compiled random multi-parameter random load spectrum based on principal component analysis;
the specific steps of the step (5) are as follows:
(51) and (3) reconstructing a history { F 'of the random multi-parameter principal component load obtained in the step (4)'RFR,1 F′RFR,2 F′RFR,3Linear solution of principal component load course is carried out, and a new random multi-parameter normalized reconstructed load spectrum of the embodiment 1 shown in fig. 10 is obtained by reverse thrust, and the calculation formula is as follows:
[fRFR,i1 fRFR,i2 fRFR,i3]＝[f′RFR,i1 f′RFR,i2 f′RFR,i3]U-1，(i＝1,2,...3050；j＝1,2,3)
wherein, F'RFR,i＝[f′RFR,i1 f′RFR,i2 f′RFR,i3]The middle elements are respectively principal component load reconstruction values of the ith sampling time point of the 3 principal component load parameters; fRFR,i＝[fRFR,i1 fRFR,i2 fRFR,i3]The middle elements are respectively the normalized load reconstruction values of the ith sampling time point of the 3 normalized load parameters;
Figure BDA0003365886090000111
an eigenvector matrix of a correlation coefficient matrix R for the normalized random multi-parameter load in step (21);
(52) and (5) normalizing the reconstructed load spectrum { F) with respect to the random multi-parameter obtained in the step (51)RFR,1 FRFR,2 FRFR,3}, wherein: element FRFR,1、FRFR,2、FRFR,3Respectively representing the normalized reconstruction process of each principal component load according to the average value of j-th column data of the actually measured random multi-parameter load data matrix F in the step (11)
Figure BDA0003365886090000113
And actually measure randomlyStandard deviation sigma of j-th column data of multi-parameter load data matrix FjAnd (3) carrying out de-standardization processing to obtain a compiled multi-parameter load spectrum based on principal component analysis, wherein the calculation formula is as follows:
Figure BDA0003365886090000112
wherein f isRFR,ijReconstructing a normalized load reconstruction value for the ith sampling time point of the jth normalized load parameter of the load spectrum for multi-parameter normalizationF,ijLoad values at the ith sampling time point of the jth load parameter of the compiled multi-parameter load spectrum based on principal component analysis are obtained.
The above description is only a specific embodiment of the present invention, and further details of the object, technical solution and advantageous effects of the present invention are described. Finally, it should be noted that: the foregoing is merely a preferred embodiment of the invention and is not intended to limit the invention in any manner. For those skilled in the art, the non-innovative modifications, variations and alterations of the technical solutions of the present invention made by the above-mentioned contents should be considered as falling within the protection scope of the present invention without departing from the technical solutions of the present invention.

Claims (7)

1. A random multi-parameter load spectrum compilation method based on principal component analysis is characterized in that a member multi-parameter actual measurement load spectrum is used as basic compilation spectrum data, a principal component analysis method is utilized to randomly load multiple parameters into a plurality of mutually independent load courses, namely multi-parameter principal component load courses, then peak-valley values of the multi-parameter actual measurement load courses are extracted to obtain a peak-valley value sequence and a non-peak-valley value point set of a principal component load, rain flow circulation counting is carried out to obtain a rain flow circulation matrix of the principal component load courses, load course reconstruction is carried out on the rain flow circulation matrix, non-peak-valley value points are randomly inserted to obtain a principal component load reconstruction course, linear calculation of the principal component load courses is carried out, and new multi-parameter random load spectrums can be obtained through reverse deduction.
2. The principal component analysis-based multiparameter test spectrum compilation method according to claim 1, comprising the steps of:
(1) carrying out standardization processing and correlation analysis on a random multi-parameter load spectrum of the complex mechanical component, thereby obtaining a correlation coefficient matrix of the random multi-parameter load;
(2) carrying out random loading on the multi-parameter into a plurality of mutually independent load processes, namely main component load processes, by using a main component analysis method, and then carrying out peak-valley value extraction processing on the main component load processes to obtain a peak-valley value sequence and a non-peak-valley value point set of the random multi-parameter main component load processes;
(3) carrying out rain flow cycle counting aiming at the main component load peak-valley value sequence to obtain a rain flow cycle matrix of the main component load peak-valley value sequence, and carrying out random load process reconstruction on the rain flow cycle matrix to obtain a random multi-parameter main component load reconstruction process;
(4) randomly inserting non-peak and non-valley points to obtain a random multi-parameter principal component load reconstruction process with consistent data quantity;
(5) and carrying out linear calculation on the principal component load process, and carrying out reverse thrust to obtain a new multi-parameter random load spectrum, thereby obtaining the compiled random multi-parameter random load spectrum based on principal component analysis.
3. The principal component analysis-based multiparameter test spectrum compilation method according to claim 2, wherein the specific steps of step (1) are:
(11) taking a multi-parameter actual measurement load spectrum of the complex mechanical component as basic spectrum data, and carrying out standardization processing on random multi-parameter load data; let p load parameters in total, n sampling time points, and let the load value of the jth load parameter at the ith sampling time point be fijN, · i ═ 1, 2; 1,2, p, then the measured random multi-parameter load data matrix F:
Figure FDA0003365886080000011
converting the measured random multi-parameter load data matrix F into a standardized random multi-parameter load data matrix F':
Figure FDA0003365886080000021
wherein,
Figure FDA0003365886080000022
Figure FDA0003365886080000023
is the average value of j-th column data of the measured random multi-parameter load data matrix F, i.e.
Figure FDA0003365886080000024
And σjFor the standard deviation of the j-th column data of the measured random multi-parameter payload data matrix F,
Figure FDA0003365886080000025
(12) carrying out correlation analysis on each column of loads of a standardized random multi-parameter load data matrix F' of the complex mechanical component, thereby obtaining a correlation coefficient matrix R of the standardized random multi-parameter loads;
Figure FDA0003365886080000026
wherein r isjkThe correlation coefficient between the jth column data and the kth column data in the normalized random multi-parameter load data matrix F', namely the correlation coefficient between the jth load parameter and the kth load parameter, is as follows:
Figure FDA0003365886080000027
wherein, f'ij、f′ikThe normalized load values of the ith sampling time point of the jth load parameter and the kth load parameter are elements in a normalized random multi-parameter load data matrix F'.
4. The principal component analysis-based multiparameter test spectrum compilation method according to claim 3, wherein the specific steps of the step (2) are as follows:
(21) the standardized random multi-parameter load data matrix F 'is converted into a plurality of mutually independent load processes by using a principal component analysis method, namely a principal component load process F', and the calculation formula is as follows:
Figure FDA0003365886080000028
wherein, F ″)i＝[f″i1 f″i2 ... f″ip]The middle elements are respectively the principal component load values of the ith sampling time point of the p principal component load parameters; fi′＝[f′i1 f′i2 ... f′ip]The middle elements are respectively the normalized load values of the ith sampling time point of the p normalized load parameters; u shapej＝[u1j u2j ... upj]TMatrix Rjth eigenvalue lambda of correlation coefficient for normalizing random multi-parameter loadjA corresponding feature vector, wherein: element u1j、u2j、upjAre respectively a feature vector UjT is a matrix transposition symbol;
(22) respectively judging peak points or valley points aiming at each path of load time history of the random multi-parameter principal component load history F 'obtained in the step (21), if so, keeping, otherwise, moving to a non-peak-valley point set F', and otherwise, moving to a non-peak-valley point setR,j(j ═ 1,2,. and p), and three-point method judgment is carried out on the data, namely three adjacent data points f ″ "are read in sequencei-1,j、f″i,j、f″i+1,jIf the following conditions are met:
[f″i,j-f″i-1,j][f″i+1,j-f″i,j]f ≥ 0i,j-f″i-1,j≠0
Wherein: f ″)i,jThen it is the peak or valley point; thus obtaining the main component load course non-peak-valley value point set F ″)R,j(j ═ 1,2,. said., p) and a sequence of multi-parameter principal component load history peak-to-valley values { F ″ "RF,1 F″RF,2 ... F″RF,p}, wherein: element F ″)RF,1、F″RF,2、F″RF,pRespectively representing the peak-to-valley sequence of each principal component load course.
5. The principal component analysis-based multiparameter test spectrum compilation method according to claim 4, wherein the specific steps of the step (3) are as follows:
(31) aiming at the random main component load peak-valley value sequence { ", obtained in the step (22)RF,1 F″RF,2 ... F″RF,pPerforming rain flow circulation counting to obtain a rain flow circulation matrix (RFM) of multi-parameter principal component load history1 RFM2 ... RFMp}, wherein: element RFM1、RFM2、RFMpA rain flow circulation matrix respectively representing each principal component load course;
the rain flow cycle counting is to extract the load full cycle of the load process based on the principle of a material stress-strain hysteresis loop, continuously read four points, namely two peak values and two valley values, in the load process, and the full cycle is selected according to the following steps: the absolute value of the difference between the two middle points is smaller than the absolute value of the difference between the two front points and the absolute value of the difference between the two rear points, namely the following conditions are met:
Figure FDA0003365886080000031
(32) and the rain flow circulation matrix { RFM) obtained in step (31)1 RFM2 ... RFMpRespectively reconstructing time histories based on rain flow statistics, namely randomly inserting cyclic loads in a rain flow cyclic matrixForming a new random load spectrum by connecting, thereby obtaining a multi-parameter principal component load reconstruction process { F ″)RFR,1 F″RFR,2 ... F″RFR,p}, wherein: element F ″)RFR,1、F″RFR,2、F″RFR,pRespectively representing the reconstruction process of each principal component load; wherein the peak to valley values of the inserted load cycle must be able to contain the pre-inserted load cycle peak to valley values.
6. The principal component analysis-based multiparameter test spectrum compilation method according to claim 5, wherein the specific steps of the step (4) are as follows:
collecting the non-peak-valley value points F' obtained in the step (22)R,j(j ═ 1, 2.. said., p) in which the off-peak-to-valley load values were randomly inserted into the random principal component load reconstruction history { F ″') of step (32), respectivelyRFR,1 F″RFR,2 ... F″RFR,pAnd (5) after the non-peak-valley point is randomly inserted, the point is not the peak-valley point, namely the non-peak-valley point is only randomly inserted into the peak-valley half cycle containing the load value of the point, so that a random multi-parameter principal component load reconstruction history { F'RFR,1 F′RFR,2 ... F′RFR,p}, wherein: element F'RFR,1、F′RFR,2、F′RFR,pRespectively representing the reconstruction process of each principal component load data quantity.
7. The principal component analysis-based multiparameter test spectrum compilation method according to claim 6, wherein the specific steps of the step (5) are:
(51) and (3) reconstructing a history { F 'of the random multi-parameter principal component load obtained in the step (4)'RFR,1 F′RFR,2 ... F′RFR,pLinearly resolving the principal component load process, and reversely deducing to obtain a new random multi-parameter standardized reconstruction load spectrum, wherein the calculation formula is as follows:
[fRFR,i1 fRFR,i2 ... fRFR,ip]＝[f′RFR,i1 f′RFR,i2 ... f′RFR,ip]U-1
wherein, F'RFR,i＝[f′RFR,i1 f′RFR,i2 ... f′RFR,ip]The middle elements are respectively principal component load reconstruction values of the ith sampling time point of the p principal component load parameters; fRFR,i＝[fRFR,i1 fRFR,i2 ... fRFR,ip]The middle elements are respectively the normalized load reconstruction values of the ith sampling time point of the p normalized load parameters;
Figure FDA0003365886080000041
an eigenvector matrix of a correlation coefficient matrix R for the normalized random multi-parameter load in step (21);
(52) and (5) normalizing the reconstructed load spectrum { F) with respect to the random multi-parameter obtained in the step (51)RFR,1FRFR,2...FRFR p}, wherein: element FRFR,1、FRFR,2、FRFR,pRespectively representing the normalized reconstruction process of each principal component load according to the average value of j-th column data of the actually measured random multi-parameter load data matrix F in the step (11)
Figure FDA0003365886080000051
Standard deviation sigma of j-th column data of actually measured random multi-parameter load data matrix FjAnd (3) carrying out de-standardization processing to obtain a compiled multi-parameter load spectrum based on principal component analysis, wherein the calculation formula is as follows:
Figure FDA0003365886080000052
wherein f isRFR,ijReconstructing a normalized load reconstruction value for the ith sampling time point of the jth normalized load parameter of the load spectrum for multi-parameter normalizationF,ijLoad values at the ith sampling time point of the jth load parameter of the compiled multi-parameter load spectrum based on principal component analysis are obtained.
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* Cited by examiner, † Cited by third party
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CN116595654A (en) * 2023-02-28 2023-08-15 南京航空航天大学 Multi-axis fatigue test spectrum compiling method based on genetic algorithm
CN116595654B (en) * 2023-02-28 2024-01-23 南京航空航天大学 Multi-axis fatigue test spectrum compiling method based on genetic algorithm

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