CN105760610A - Engine multi-parameter using related load spectrum simulation method based on main component analysis - Google Patents

Engine multi-parameter using related load spectrum simulation method based on main component analysis Download PDF

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CN105760610A
CN105760610A CN 201610099334 CN201610099334A CN105760610A CN 105760610 A CN105760610 A CN 105760610A CN 201610099334 CN201610099334 CN 201610099334 CN 201610099334 A CN201610099334 A CN 201610099334A CN 105760610 A CN105760610 A CN 105760610A
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spectrum
load
matrix
parameter
simulation
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CN 201610099334
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孙志刚
邢广鹏
宋迎东
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南京航空航天大学
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/50Computer-aided design
    • G06F17/5009Computer-aided design using simulation
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00Road transport of goods or passengers
    • Y02T10/80Technologies aiming to reduce greenhouse gasses emissions common to all road transportation technologies
    • Y02T10/82Elements for improving aerodynamics

Abstract

The invention discloses an engine multi-parameter using related load spectrum simulation method based on main component analysis.By the adoption of a main component analysis method, a mathematical model of an aircraft engine multi-parameter load spectrum is established and utilized for simulating and imitating normal, non-normal and actually measured aircraft engine related parameter load spectrums.Through a small number of measurement sub-samples, a multi-parameter using load spectrum at any time section is imitated, the result shows that a simulated spectrum and the original spectrum have good uniformity in level-crossing counting accumulated frequency, and it is guaranteed that correlation between all load parameters is unchanged.

Description

基于主成份分析的发动机多参数使用相关载荷谱仿真方法 Multi-parameter simulation method based on the load spectrum associated principal component analysis engine

技术领域 FIELD

[0001] 本发明设及航空发动机载荷谱技术,尤其设及一种基于主成份分析的发动机多参数使用相关载荷谱仿真方法,主要用于航空发动机应力分析、疲劳寿命可靠性预测和新机载荷谱的研究。 [0001] The present invention is provided and aviation engine load spectrum techniques, in particular, is provided, and one of the main component analysis on multiple parameters related to the engine load spectrum simulation method, mainly used in aviation engines stress analysis, fatigue life and reliability of the new machine load prediction research spectrum.

背景技术 Background technique

[0002] 航空发动机机厘、主轴、安装节等零件除了发动机本身的工作载荷之外,还受外部作用力的影响,运些载荷参数之间往往是相关的,是典型的承受多参数相关载荷的零件。 [0002] PCT aeroengine machine, spindle, mounting section and other parts in addition to the work load of the engine itself, but also by external force, the load is often some correlation between the parameters of transport, is a typical load parameters related to multiple receiving parts. 国军标中对发动机的外部作用力都有明确的规定,然而并不具体明确。 GJB are clearly defined in the external force of the engine, however, is not specific. 如何进行载荷组合W 获得极大值载荷,从而确定最危险的载荷工况是个十分复杂的问题。 How to get maximum load combinations W load, in order to determine the most dangerous load cases is a very complex issue. 航空发动机载荷谱特点为:1、获取难;2、子样少;3、参数多,相关性复杂。 Aviation engines load spectrum characteristics: 1, obtaining difficult; 2, less subsample; 3, multi-parameter correlation complexity. 因此航空发动机寿命可靠性预测和新机载荷谱的研制迫切需要载荷谱仿真方法。 Therefore, the development of aviation engine life and reliability prediction of new aircraft load spectrum of the urgent need for spectrum simulation load.

[0003] 在航空工业中,多参数载荷问题最早是在飞机上提出的。 [0003] In the aerospace industry, multi-parameter load issue was first raised on the plane. 80年代W前,由于没有找到合适的多参数处理方法,飞机的载荷谱编制也是采用的单参数编谱。 80 years ago W, due not find a suitable multi-parameter approach, a single parameter load spectrum preparation of the aircraft is also used knitting spectrum. 1977年美国的Vought公司的RRLauridia等人首次提出了根据实际测量的飞行数据编制多参数谱的方法,该方法考虑了载荷的相关性。 In 1977 the US company Vought RRLauridia, who first proposed a method based on actual flight data compiled multi-parameter measurement of the spectrum, the method takes into account the correlation between loads. 但是没有更详细的资料发布,特别是对于如何将双参数表向多参数表转换的具体方法不得而至,所W国内的飞机设计部口尚没有对上述方法进行跟踪研究和使用。 But no further details released, especially for specific methods on how to transition to the two-parameter table multi-parameter table and not to, the W domestic aircraft design portion of the mouth and yet no follow-up study using the above methods. 在航空发动机的多参数谱编制技术方面,目前尚没有见到国外的公开报导。 In terms of multi-parameter spectrum for aircraft engine technology, it is not to see foreign public reports. 所能见到的只有公开的军标]«比-6-50070、]\1比-6-50076、]\1化-510-1783、]\1化-6-87231^及MIL-E-87231A,运些军标中对发动机的多参数载荷,特别是外部载荷要求都作了类似的规定,但是并不具体和明确。 The public can see only the military standard] << than -6-50070,] \ 1 ratio -6-50076,] \ 1 of -510-1783,] \ ^ 1 of -6-87231 and MIL-E- 87231A, shipped some in military standard for multi-parameter engine load, especially external load requirements have made similar provision, but it is not specific and clear.

发明内容 SUMMARY

[0004] 发明目的:为了弥补现有的概率分布法对子样容量需求很大的不足,进一步开展多参数组合问题的研究,本发明提供了一种基于主成份分析的多参数相关载荷谱的仿真方法,从而可W通过较小的测量子样,模拟出任意时间的多参数相关载荷,并且保证各载荷参数之间的相关性不变。 [0004] Object of the invention: prior probability distribution to compensate for lack of a large capacity like sub-method needs further study of the problem of multi-parameter combinations, the present invention provides a multi-parameter related to the load based on principal component analysis of the spectrum simulation so as to be smaller by the W sub-sample measurements, multi-parameter correlation simulated load at any time, and to ensure constant correlation between the load parameter.

[0005] 技术方案:为实现上述目的,本发明采用的技术方案为: [0005] Technical Solution: To attain the above object, the technical solution adopted by the invention is:

[0006] 本发明所述的主成份分析法是一种把原来多个指标化为少数几个相互独立的综合指标的一种统计方法。 [0006] Principal component analysis of the present invention is a plurality of the original index into a statistical method few independent comprehensive index. 如果n个载荷参数之间是相互独立的,那么,就可W对每个参数进行单独的模拟。 If the load parameter is between the n independent of each other, then W can be simulated for each separate parameter. 在数学上处理多个变量的主成份方法可W将n个相关的变量通过线性变换转换为n个相互独立的新变量,再对运n个相互独立的新变量进行仿真,在反推出原始载荷谱。 Mathematically principal component method for processing a plurality of variables may be W n variables related by a linear transformation is converted into n new variables independently of one another, and then transported to the n independent variable new simulation, the original introduction of the anti-load spectrum. 因此,可W利用主成份法将n个相关的载荷通过线性变换为n个相互独立的新载荷变量。 Accordingly, the principal component method using W n load related by a linear transformation of n independent variable new load. 用主成份分析法进行多参数相关载荷谱仿真的方法包括W下步骤。 The method of multi-parameter correlation with main component analysis simulation load spectrum comprises the steps of W.

[0007] 设总共有P个载荷参数,n个采样点,将第j个载荷参数在第i个采样点的观测值记为XU,则将原始载荷数据矩阵X记为: [0007] There are provided a P load parameter, n-sampling points, the j-th load parameter observations at the i-th sampling point is referred to as XU, then the payload data of the original matrix X referred to as:

[000引 [000 Cited

Figure CN105760610AD00051

[0009] 该方法包括如下步骤: [0009] The method comprises the steps of:

[0010] (1)将原始载荷数据矩阵X转换为标准化载荷数据矩阵X' : [0010] (1) converts the raw data matrix X is a normalized load payload data matrix X ':

[0011] [0011]

Figure CN105760610AD00052

[0012] 其中 [0012] in which

Figure CN105760610AD00053

^为原始载荷数据矩阵X的第j列数据的平均值: ^ J-th data of the original data matrix X payload average of:

Figure CN105760610AD00054

Oj为原始载荷数据矩阵X的第j列数据的标准差, Oj standard j-th data of the original payload data matrix X difference,

Figure CN105760610AD00055

[0013] (2)根据标准化载荷数据矩阵X',计算标准化载荷数据矩阵X'列之间的相关系数矩阵R: [0013] (2) The load standardized data matrix X ', calculated normalized load data matrix X' correlation coefficient matrix R between the columns:

[0014] [0014]

Figure CN105760610AD00056

[001引其中:训为标准化载荷数据矩阵X'的第巧U数据和第k列数据的相关系数, [Cited 001 wherein: the load standardized training data matrix X 'clever correlation coefficient U data and the k-th column data,

[0016] [0016]

Figure CN105760610AD00057

[0017] (3)计算相关系数矩阵R的特征值和对应每个特征值的特征向量,M = [Ai A2… Ap],、为相关系数矩阵R的第j个特征值,、> 入2 >…> Ap,Uj为第j个特征值、对应的特征向量,Uj= [Ulj U2j…UpjL由所有特征向量Uj组成的特征向量矩阵记为T: [0017] (3) calculates a correlation coefficient matrix R corresponding to each of the eigenvalues ​​and eigenvectors of the eigenvalue, M = [Ai A2 ... Ap] ,, j-th feature value of the correlation matrix R ,,> into 2 > ...> Ap, Uj is the j-th eigenvalue, the corresponding eigenvectors, Uj = [Ulj U2j ... referred UpjL eigenvectors of all feature vectors Uj consisting of T:

[001 引 [001 Cited

Figure CN105760610AD00058

[0019] 其中,I ME-Rl =0,(R-AjE) • Uj = 0;E为单位矩阵 [0019] wherein, I ME-Rl = 0, (R-AjE) • Uj = 0; E is the identity matrix

Figure CN105760610AD00061

[0020] (4)计算标准化载荷数据矩阵X'的主成分向量Y,Y=[yi y2…yp],yj为标准化载荷数据矩阵X'的第j个主成分,Y = X'T; [0020] (4) calculating normalized load data matrix X 'principal component vectors Y, Y = [yi y2 ... yp], yj standardized payload data matrix X' j-th principal component, Y = X'T;

[0021] (5)采用单参数载荷谱的仿真方法对第j个主成分yj进行单独仿真,得到第j个主成分谱y'j,将主成分谱向量记为Y',Y' = [yi' y'2…y'p]; [0021] (5) the single parameter of the load spectrum simulation j-th principal component yj separate simulation, the j-th principal component spectrum y'j, will be referred to as a main component spectrum vector Y ', Y' = [ yi 'y'2 ... y'p];

[0022] (6)根据x"j = rV'j,对主成分谱y'j进行逆变换,得到标准化载荷数据矩阵X'的仿真谱X",r=[Xl" X"2 ... X"p]; [0022] (6) The x "j = rV'j, y'j principal component spectrum inverse transform, load standardized data matrix X 'simulation spectrum X", r = [Xl "X" 2 ... X "p];

[0023] (7)根据X;=巧卢;,将标准化载荷数据矩阵X'的仿真谱r转换为原始载荷数据矩阵X 的仿真谱r',x"' = [xi"'x"'2...x"'p]。 [0023] (7) X; = Qiao Lu;, normalized load data matrix X 'simulation spectrum r converted to an analogue spectrum r original payload data matrix X', x " '= [xi"' x " '2 ... x " 'p].

[0024] 有益效果:本发明提供的基于主成份分析的发动机多参数使用相关载荷谱仿真方法,通过较小的测量子样,可W模拟出任意时间的多参数相关载荷,仿真得到的仿真谱与原谱在穿级计数累积频次曲线上具有较好的一致性,还保证了原谱与仿真谱间的相关性不变;本发明为航空发动机寿命可靠性预测和新机载荷谱的研制提供依据。 [0024] Advantageous Effects: The present invention provides a principal component analysis based on multiple parameters related to engine load spectrum simulation method, by measuring a small sub-sample, W may be simulated at any time multiple parameters associated load simulation simulation spectrum obtained original spectrum wear stage count accumulation in good agreement with the frequency curve, but also to ensure the constant correlation between the spectrum and the original spectrum simulation; Aeroengine development of this invention is a life prediction about the new machine and the load spectrum provided in accordance with.

附图说明 BRIEF DESCRIPTION

[0025] 图1五参数相关正态载荷谱; [0025] FIG five parameters related to normal load spectrum;

[00%]图2五参数相关正态载荷谱的各主成份分布的直方图; [00%] FIG five parameters related to normal load spectrum of each histogram distribution of principal component;

[0027] 图3主成份仿真的各个相关正态载荷谱的片段; [0027] fragment from each of the relevant normal load spectrum Figure 3 simulation principal component;

[0028] 图4五参数相关正态载荷谱的原谱与仿真谱的累积概率对比图; [0028] FIG. 4 five normal load parameters related to the original spectrum and the simulated spectrum spectrum cumulative probability comparison chart;

[0029] 图5两参数相关非正态载荷谱片段; [0029] FIG. 5 parameters related to two non-normal load spectrum segment;

[0030] 图6两参数相关非正态载荷谱的概率分布直方图; Probability [0030] FIG. 6 parameters related to the two non-normal load spectrum distribution histogram;

[0031 ]图7两参数相关非正态载荷谱各主成份分布的直方图; [0031] FIG 7 two non histogram normalization parameters relating to each of the main components of the load spectrum distribution;

[0032] 图8主成份仿真的各个非正态载荷谱的片段; [0032] fragment from each of the non-normal load spectrum of FIG. 8, a main component of the simulation;

[0033] 图9两参数相关非正态载荷谱的原谱与仿真谱的累积概率对比图; FIG cumulative probability comparison [0033] FIG. 9 two non-normal load parameters related to the original spectrum of the spectrum and spectrum simulation;

[0034] 图10某巧击机发动机实测多参数载荷谱; [0034] FIG 10 a clever multi-parameter Found attack aircraft engine load spectrum;

[0035] 图11实测谱的主成份概率分布图; [0035] FIG. 11 is a principal component spectra measured probability distribution;

[0036] 图12发动机实测多参数载荷谱的仿真谱片段; [0036] FIG. 12 Found multi-parameter simulation engine load spectrum fragment spectrum;

[0037] 图13实测谱与仿真谱的累积概率对比图。 [0037] Figure 13 comparison of cumulative probability FIG Found spectrum and the simulated spectrum.

具体实施方式 detailed description

[0038] 下面结合附图对本发明作更进一步的说明。 [0038] DESCRIPTION OF DRAWINGS The invention further.

[0039] (一)多参数正态载荷谱的仿真: [0039] (a) Multi-parameter simulation normal load spectrum:

[0040] 图1给出了五参数具有相关性的正态载荷谱,载荷参数的个数p = 5,总的采样点个数n = 20000,采样频率为1监。 [0040] Figure 1 shows five of the parameters associated with normal load spectrum, loading the number of parameters p = 5, the total number of sampling points n = 20000, a sampling frequency is monitored.

[0041] (I)首先将原始载荷数据矩阵X标准化,记 [0041] (I) is first normalized load raw data matrix X, denoted

Figure CN105760610AD00071

原始数据的均值和方差如下表: Mean and variance of the original data in the following table:

[0042] 表1-1各参数的均值和方差 [0042] The mean and variance of each parameter in Table 1-1

Figure CN105760610AD00072

LTO44」(2)化惦称准化载巧数惦矩阵X',计算相巧《数矩阵,具体如h表: LTO44 "(2) of said normalized carrier Dian Dian number coincidence matrix X ', is calculated with clever" of the matrix, particularly as h Table:

[0045]表1-2各参数的相关系数矩阵r004Al Correlation coefficients [0045] Table 1-2 each parameter matrix r004Al

Figure CN105760610AD00073

[004引(3)根据I ME-Rl =0、(R-AjE) • Uj = O计算相关系数矩阵R的特征值和对应每个特征值的特征向量如下表: [004 lead (3) according to I ME-Rl = 0, (R-AjE) • Uj = O correlation coefficient matrix R corresponding to each of the eigenvalues ​​and eigenvectors of the eigenvalue as follows:

[0049] 表1-3特征值 [0049] Table 1-3 eigenvalues

Figure CN105760610AD00074

[0053] (4)计算标准化载荷数据矩阵X'的主成分向量Y如下: [0053] The main component of the vector (4) is calculated normalized load data matrix X 'of Y are as follows:

[0化4] [0 of 4]

Figure CN105760610AD00081

[0化5] 通过上式即可计算出各个主成份y 1、Y2、Y3、Y4、y日。 [0 of 5] to calculate the respective main components y 1, Y2, Y3, Y4 by the above formula, y days. 每个主成份对应20000个数据。 Each principal component data corresponding to 20,000. 通过上式可W把测量出的各个时刻的参数变化变成为主成份的变化。 W by the above formula can be the parameters measured each time point becomes the main component changes. 把各主成份进行统计分析,得到各个主成份值的概率分布图(见附图2)。 The statistical analysis of each of the main components to obtain a probability distribution of the respective main component value (see FIG. 2). 通过概率密度分布直方图,可W推断各个主成份仍然和原始载荷谱保持一致均服从正态分布,各分布的均值和方差如下: By probability density histograms, W can still deduce the original components of each of the main load spectrum consistent followed a normal distribution, the mean and variance of each distribution is as follows:

[0056]表1-5各主成份的均值和方差「mwl [0056] Table 1-5 Main components of the mean and variance "mwl

Figure CN105760610AD00082

对应由原始数据经过主成份法计算出来数据(20000个)。 Shall be calculated from the raw data of the data (20000) via the main component method.

[0059] (5)各个主成份yj是相互独立的,因此可W根据单参数载荷谱的仿真方法对各个主成份进行单独的仿真,从而得到仿真出来的主成分谱y'j。 [0059] (5) the respective main component yj are independent, thus W may be simulated for each separate primary components of the simulation method of a single load spectrum parameters, thereby obtaining a main component out of the simulated spectrum y'j.

[0060] (6)根据rVj,对主成分谱y'逊行逆变换,得到标准化载荷数据矩阵X'的仿真谱X",r=[Xl" X"2 ... X"p]。 [0060] (6) The RVJ, principal component spectrum y 'Johnson row inverse transformation matrix to obtain normalized load data X' simulation spectrum X ", r = [Xl" X "2 ... X" p].

[0061] (7)根据X; = a;,X;. ,将标准化载荷数据矩阵X'的仿真谱r转换为原始载荷数据矩阵X的仿真谱r',X"' = [xl"'x"/2…x"/p],如图3所示。 [0061] (7) X; = a;, X ;., normalized load data matrix X 'simulation spectrum into the original simulation spectrum r r payload data matrix X', X " '= [xl"' x "/ 2 ... x" / p], as shown in FIG.

[0062] (8)比较原谱与仿真谱的区别,分别对原谱仿真谱进行穿级计数,得到他们的累积频次曲线对比图(见附图4)。 The differences between the original spectrum and the simulated spectrum [0062] (8), respectively, of the original spectrum through simulation spectrum counting stage, they obtained a cumulative frequency curve comparison chart (see Figure 4).

[0063] 通过对比可见,本发明能够准确的仿真出原五参数具有相关性的正态载荷谱,仿真得到的仿真谱与原谱在穿级计数累积频次曲线上具有较好的一致性,保证了原谱与仿真谱的损伤是等效的,且参数之间的相关性没有发生变化。 [0063] By contrast seen, the present invention enables an accurate simulation of the original five-parameter having a correlation normal load spectrum, simulation simulation spectrum and the original spectrum obtained through count accumulation stage in good agreement with the curve of the frequency, to ensure damage the original spectrum and the simulated spectra are equivalent, and there is no correlation between the change in the parameters.

[0064] (二)多参数非正态载荷谱的仿真 [0064] (ii) multi-parameter non-normal load spectrum simulation

[0065] 附图5、6给出了两参数具有相关性的非正态载荷谱W及原始非正态载荷谱的概率分布图,载荷参数的个数P = 2,总的采样点个数n = 20000个,采样频率为1监。 [0065] figures 5 and 6 shows two parameters correlated with non-normal load W and the spectrum of the original non-normal probability distribution of load spectrum, the number of load parameter P = 2, the total number of sampling points n = 20000 th sampling frequency is a prison.

[0066] (1)首先将原始载荷数据矩阵X标准化,记 [0066] (1) First normalized raw payload data matrix X, denoted

Figure CN105760610AD00083

原始数据的均值和方差如下表: Mean and variance of the original data in the following table:

[0067] 表2-1各参数的均值和方差r00681 [0067] Table 2-1 mean and variance of each parameter r00681

Figure CN105760610AD00084

Figure CN105760610AD00091

LUUW」 恨化杯化化載何毁化巧|伴A,许算相大巧毁巧|伴,具悴yu r巧: LUUW "hate of the cup of ruin of what the carrier of clever | with A, Xu considered the most delicate phase ruin clever | partner, with haggard yu r clever:

[0070] 表2-2各参数的相关系数矩阵 [0070] TABLE 2-2 Parameters correlation coefficient matrix

[0071] [0071]

Figure CN105760610AD00092

[0073] (3)根据I ME-Rl =0、(R-AjE) • Uj = O计算相关系数矩阵R的特征值和对应每个特征值的特征向量如下表: [0073] (3) The I ME-Rl = 0, (R-AjE) • Uj = O correlation coefficient matrix R corresponding to each of the eigenvalues ​​and eigenvectors of the eigenvalue as follows:

[0074] 表2-3特征值「00751 [0074] Table 2-3 eigenvalues ​​"00751

Figure CN105760610AD00093

[0078」(4)计算标准化载荷数据矩阵X'的主成分问量Y如h : Amount of the main component Q. [0078 "(4) calculating normalized load data matrix X 'is Y as h:

[0079] [0079]

Figure CN105760610AD00094

[0080] 通过上式即可计算出各个主成份yi、y2。 [0080] The respective main components can be calculated by the equation yi, y2. 每个主成份对应20000个数据。 Each principal component data corresponding to 20,000. 原谱经过主成分变换后可W得到主成份谱,其概率分布直方图(见附图7)。 After the original spectrum principal component W may be a main component spectrum obtained, the probability distribution histogram (see Figure 7). 把其累计概率作为数据表如下表,求满足该分布数据时,采用反函数法,查表求出随机数。 When the cumulative probability as a data table in the following table, seeking to satisfy the distribution data, using the inverse function method, a look-up table to obtain the random number. 在两个数据之间用线性插值。 Between the two data by linear interpolation.

[0081] 表2-巧正态分布的主成份累积概率表 [0081] Table 2 - Main ingredient clever cumulative normal probability table

[0082] [0082]

Figure CN105760610AD00101

[0083] (5)通过W上步骤得到各个主成份的数学模型即每个主成份yi、y2对应20000个由原始数据经过主成份法计算出来数据,各个主成份yj是相互独立的,因此可W根据单参数载荷谱的仿真方法对各个主成份进行单独的仿真,从而得到仿真出来的主成分谱y'j。 [0083] (5) a mathematical model obtained by the respective main component i.e. step W each main component yi, y2 corresponding to 20,000 data calculated from the original data through principal component method, each of the main components is yj independent of each other, thus W is simulated for each separate component of the main parameters of the simulation method of a single load spectrum, to thereby obtain a main component out of the simulated spectrum y'j.

[0084] (6)根据rVj,对主成分谱y'逊行逆变换,得到标准化载荷数据矩阵X'的仿真谱X",r=[Xl" X"2 ... X"p]。 [0084] (6) The RVJ, principal component spectrum y 'Johnson row inverse transformation matrix to obtain normalized load data X' simulation spectrum X ", r = [Xl" X "2 ... X" p].

[0085] (7)根据為,将标准化载荷数据矩阵X'的仿真谱r转换为原始载荷数据矩阵X的仿真谱r',X"' = [xl"'x"/2…x"/p],如图8所示。 [0085] (7) According to the normalized load data matrix X 'simulation spectrum r converted to an analogue spectrum r original payload data matrix X', X " '= [xl"' x "/ 2 ... x" / p ], as shown in FIG.

[0086] (8)比较原谱与仿真谱的区别,分别对原谱仿真谱进行穿级计数,得到他们的累积频次曲线对比图(见附图9)。 The differences between the original spectrum and the simulated spectrum [0086] (8), respectively, of the original spectrum through simulation spectrum counting stage, they obtained a cumulative frequency curve comparison chart (see Figure 9).

[0087] 通过对比可见,本发明能够准确的仿真出原两参数具有相关性的非正态载荷谱, 仿真得到的仿真谱与原谱在穿级计数累积频次曲线上具有较好的一致性,保证了原谱与仿真谱的损伤是等效的,且参数之间的相关性没有发生变化。 [0087] By contrast seen, the present invention enables an accurate simulation of the original two parameters correlated with non-normal load spectrum, obtained by simulation simulation spectrum and the original spectrum wearing stage count accumulation in good agreement with the frequency curve, damage to ensure the original spectrum and the simulated spectra are equivalent, and there is no correlation between the change in the parameters.

[0088] (S)实测载荷谱的仿真 Simulation [0088] (S) of the load spectrum Found

[0089] 附图10给出了某航空发动机8种机动飞行任务的发动机重屯、法向过载系数、X向的角速度和Z向的角速度谱,载荷参数的个数p = 3,总的采样点个数n=17330个,采样频率为1监。 [0089] Figure 10 shows the engine restart Tun Aeroengine eight kinds mission maneuver, the normal overload factor, the angular velocity of the X and Z-direction angular spectrum, loading the number of parameters p = 3, the total sample The number n = 17330 th point, the sampling frequency is a prison.

[0090] (1)首先将原始载荷数据矩阵X标准化,记 [0090] (1) First normalized raw payload data matrix X, denoted

Figure CN105760610AD00102

原始数据的均值和方差如下表: Mean and variance of the original data in the following table:

[0091] 表3-1实测谱的均值和方差 [0091] Table 3-1 mean and variance of the measured spectrum

[0092] [0092]

Figure CN105760610AD00111

[0093] (2)根据标准化载荷数据矩阵X',计算相关系数矩阵,具体如下表: [0093] (2) The load standardized data matrix X ', calculates a correlation coefficient matrix in the following table:

[0094] 表3-2各参数的相关系数矩阵 [0094] Table 3-2 correlation coefficient matrix of parameters

[0095] [0095]

Figure CN105760610AD00112

[0097] (3)根据I ME-Rl =0、(R-AjE) . Uj = O计算相关系数矩阵R的特征值和对应每个特征值的特征向量如下表: . [0097] (3) The I ME-Rl = 0, (R-AjE) Uj = O correlation coefficient matrix R corresponding to each of the eigenvalues ​​and eigenvectors of the eigenvalue as follows:

[0098] 表3-3特征值「00991 [0098] Table 3-3 feature value "00991

Figure CN105760610AD00113

[0104] 通过上式即可计算出各个主成份71、72、73。 [0104] can be calculated by the respective main components 71-73 formula. 每个主成份对应17330个数据。 Each principal component data corresponding to 17,330. 原谱经过主成分变换后可W得到主成份谱,其概率分布直方图(见附图11)。 After the original spectrum principal component W may be a main component spectrum obtained, the probability distribution histogram (see Figure 11). 把其累计概率作为数据表,求满足该分布数据时,采用反函数法,查表求出随机数。 When the cumulative probability as a data table, seeking to satisfy the distribution data, using the inverse function method, a look-up table to obtain the random number. 在两个数据之间用线性插值。 Between the two data by linear interpolation.

[0105] 表3-5实测谱的主成份累积概率表 [0105] Table 3-5 principal component spectra measured cumulative probability table

[0106] [0106]

[0107] (5)通过W上步骤得到各个主成份的数学模型即各个主成份所对应的数据,各个主成份yj是相互独立的,因此可W根据单参数载荷谱的仿真方法对各个主成份进行单独的仿真,从而得到仿真出来的主成分谱y ' J。 [0107] (5) the mathematical model of the respective main component by the W step i.e. the respective main component data corresponding to each principal component yj are independent, thus W load spectrum The single parameter of simulation for each principal component separate simulations, simulation out to obtain a main component spectrum y 'J.

[0108] (6)根据T-iy'j,对主成分谱y'逊行逆变换,得到标准化载荷数据矩阵X'的仿真谱X",r=[Xl" X"2 ... X"p]。 [0108] (6) The T-iy'j, principal component spectrum y 'Johnson row inverse transformation matrix to obtain normalized load data X' simulation spectrum X ", r = [Xl" X "2 ... X" p].

[0109] (7)根据^ = ,将标准化载荷数据矩阵X'的仿真谱r转换为原始载荷数据矩阵X的仿真谱r',X"' = [xl"'x"/2…x"/p],如图12所示。 [0109] (7) ^ = the normalized load data matrix X 'simulation spectrum r converted to an analogue spectrum r original payload data matrix X', X " '= [xl"' x "/ 2 ... x" / p], as shown in Figure 12.

[0110] (8)比较原谱与仿真谱的区别,分别对原谱仿真谱进行穿级计数,得到他们的累积频次曲线对比图(见附图13)。 The differences between the original spectrum and the simulated spectrum [0110] (8), respectively, of the original spectrum through simulation spectrum counting stage, they obtained a cumulative frequency curve comparison chart (see Figure 13).

[0111] 通过对比可见,本发明能够准确的仿真出原两参数具有相关性的非正态载荷谱, 仿真得到的仿真谱与原谱在穿级计数累积频次曲线上具有较好的一致性,保证了原谱与仿真谱的损伤是等效的,且参数之间的相关性没有发生变化。 [0111] By contrast seen, the present invention enables an accurate simulation of the original two parameters correlated with non-normal load spectrum, obtained by simulation simulation spectrum and the original spectrum wearing stage count accumulation in good agreement with the frequency curve, damage to ensure the original spectrum and the simulated spectra are equivalent, and there is no correlation between the change in the parameters.

[0112] W上所述仅是本发明的优选实施方式,应当指出:对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下,还可W做出若干改进和润饰,运些改进和润饰也应视为本发明的保护范围。 [0112] W a only preferred embodiment of the present invention, it should be noted: to those of ordinary skill in the art who, without departing from the principles of the invention, may make various improvements and modifications W, these transport improvements and modifications should also be regarded as the protection scope of the present invention.

Claims (4)

  1. 1. 一种基于主成份分析的发动机多参数使用相关载荷谱仿真方法,其特征在于:设总共有P个载荷参数,η个采样点,将第j个载荷参数在第i个采样点的观测值记为则将原始载荷数据矩阵记为X, A principal component analysis based on multiple parameters related to the engine load spectrum simulation method, comprising: setting a total load parameter P, [eta] sampling points, the observed load parameter in the j-th sampling point of the i-th value will be referred to as the original data matrix payload referred to as X,
    Figure CN105760610AC00021
    该方法包括如下步骤: (1) 将原始载荷数据矩阵X转换为标准化载荷数据矩阵 The method comprises the steps of: (1) converting the raw data matrix X is a normalized load payload data matrix
    Figure CN105760610AC00022
    (2) 根据标准化载荷数据矩阵X',计算标准化载荷数据矩阵X'列之间的相关系数矩阵 (2) The load standardized data matrix X ', calculated normalized load data matrix X' between correlation coefficient matrix column
    Figure CN105760610AC00023
    (3) 计算相关系数矩阵R的特征值和对应每个特征值的特征向量,将所有特征向量组成的特征向量矩阵记为T, (3) calculate the correlation matrix R corresponding to each of the eigenvalues ​​and eigenvectors of the eigenvalues, the eigenvectors of a matrix consisting of all eigenvectors denoted as T,
    Figure CN105760610AC00024
    (4) 计算标准化载荷数据矩阵X'的主成分向量Y,Y=[yi y2…yP],yj为标准化载荷数据矩阵V的第j个主成分,YifT; (5) 采用单参数载荷谱的仿真方法对第j个主成分η进行单独仿真,得到第j个主成分谱7/」,将主成分谱向量记为¥ /,¥/=[7/17/2."7/1)]; (6) 根据χ、= ΤΛ、,对主成分谱A进行逆变换,得到标准化载荷数据矩阵f的仿真谱X'XHx' x"2 …x"P]; (7) 根据4 = σ:/< +ΐ;,将标准化载荷数据矩阵X'的仿真谱X"转换为原始载荷数据矩阵X的仿真谱…为原始载荷数据矩阵X的第j列数据的平均 The principal component vector (4) is calculated normalized load data matrix X 'is Y, Y = [yi y2 ... yP], yj standardized payload data matrix V j-th principal component, YifT; (5) the single parameter load spectrum simulation of the j-th principal component η separate simulation, the j-th principal component spectra 7 / "will be referred to as a main component vector of spectral ¥ /,¥/=[7/17/2."7/1)] ; (6) according to χ, = ΤΛ ,, a principal component spectrum inverse transform matrix to obtain normalized data payload simulated spectrum f X'XHx 'x "2 ... x" P]; (7) the 4 = σ: / <+ ΐ ;, normalized load data matrix X 'simulation spectrum X "is converted to spectral simulation of the original payload data matrix X ... j-th data is the raw data matrix X payload average
    Figure CN105760610AC00025
    value
    Figure CN105760610AC00026
    为原始载荷数据矩阵X的第j列数据的标准差, Standard j-th data of the original payload data matrix X difference,
  2. 2. 根据权利要求1所述的基于主成份分析的发动机多参数使用相关载荷谱仿真方法, 其特征在于:所述标准化载荷数据矩阵中, The principal component analysis based on the engine according to claim 1 related to the use of multi-parameter simulation load spectrum, characterized in that: said payload data normalized matrix,
    Figure CN105760610AC00027
  3. 3. 根据权利要求1所述的基于主成份分析的发动机多参数使用相关载荷谱仿真方法, 其特征在于:所述相关系数矩阵R中,rjk为标准化载荷数据矩阵f的第j列数据和第k列数据 The principal component analysis based on the engine according to claim 1 related to the use of multi-parameter simulation load spectrum, wherein: the correlation coefficient matrix R, RJK j-th column of data and the normalized data matrix payload of f k column data
    Figure CN105760610AC00031
  4. 4.根据权利要求1所述的基于主成份分析的发动机多参数使用相关载荷谱仿真方法, 其特征在于:M = [h λ2…λρ],\为相关系数矩阵R的第j个特征值,… 第j个特征值\对应的特征向量,Uj = [uij U2j…11[^];|1^-1?|=0,(1^疋)《11」=0$为单 The principal component analysis based on the engine according to claim 1 related to the use of multi-parameter simulation load spectrum, wherein: M = [h λ2 ... λρ], \ j-th feature value of the correlation matrix R, ... j-th eigenvalues ​​\ corresponding feature vector, Uj = [uij U2j ... 11 [^]; |? 1 ^ -1 | = 0, (1 ^ Cloth) "11" = 0 $ single
    Figure CN105760610AC00032
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