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CN114459644A - Identification method of landing gear drop load based on optical fiber strain response and Gaussian process - Google Patents

Identification method of landing gear drop load based on optical fiber strain response and Gaussian process Download PDF

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CN114459644A
CN114459644A CN202111650177.2A CN202111650177A CN114459644A CN 114459644 A CN114459644 A CN 114459644A CN 202111650177 A CN202111650177 A CN 202111650177A CN 114459644 A CN114459644 A CN 114459644A
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曾捷
冯振辉
徐云涛
岳应萍
王云嵩
孟理华
綦磊
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention relates to an undercarriage drop load identification method based on optical fiber strain response and Gaussian process, which is characterized in that S FBG sensors distributed along the direction of a bearing structure at preset positions on a target undercarriage supporting arm are used for constructing drop load prediction data which respectively comprise noise at each time point in the sinking duration of a test working condition and correspond to a target undercarriage according to Gaussian process regression models f-GP (mu (-) and k (-) on the basis of S FBG sensors
Figure DDA0003446622820000011
Training under training conditions and testing conditions in each constructed sample by combining with the corresponding overflow conditions compared with the actual measured values to obtain a falling load identification model corresponding to the target undercarriage; further, in practical application, the falling shock can be passedThe load identification model realizes real-time identification of the falling load of the target undercarriage, and can effectively improve the working efficiency of health monitoring of the target undercarriage.

Description

基于光纤应变响应与高斯过程的起落架落震载荷辨识方法Identification method of landing gear drop load based on optical fiber strain response and Gaussian process

技术领域technical field

本发明涉及基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,属于起落架落震载荷辨识技术领域。The invention relates to a landing gear drop shock load identification method based on optical fiber strain response and Gaussian process, and belongs to the technical field of landing gear drop shock load identification.

背景技术Background technique

研究表明飞行事故多发阶段常出现在起飞和着陆过程,约有50%以上的安全事故出现在飞机起飞和着陆阶段,根本原因在于起落架设计中仅考虑结构的静强度,对结构疲劳强度和耐久性考虑较少。因此,开展针对起落架落震载荷实时监测,已成为飞行器健康管理重要组成部分,能够为未来多功能/一体化起落架设计提供技术支撑。Studies have shown that flight accidents often occur during take-off and landing, and more than 50% of safety accidents occur during take-off and landing. The fundamental reason is that only the static strength of the structure is considered in the design of the landing gear, and the fatigue strength and durability of the structure are not affected. Sexual consideration is less. Therefore, carrying out real-time monitoring of landing gear shock loads has become an important part of aircraft health management, which can provide technical support for future multi-functional/integrated landing gear designs.

发明内容SUMMARY OF THE INVENTION

本发明所要解决的技术问题是提供基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,采用特征表征方法,能够针对起落架,实现高效快捷的落震载荷监测。The technical problem to be solved by the present invention is to provide a landing gear drop shock load identification method based on optical fiber strain response and Gaussian process, and the characteristic characterization method can realize efficient and fast drop shock load monitoring for the landing gear.

本发明为了解决上述技术问题采用以下技术方案:本发明设计了基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,基于目标起落架支撑臂上预设位置沿承载结构方向所分布设置的S个FBG传感器,实现针对目标起落架的落震载荷辨识;按步骤A至步骤H,获得目标起落架所对应的落震载荷辨识模型;然后实时执行步骤i,实现对目标起落架落震载荷的实时辨识;In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions: the present invention designs a landing gear drop shock load identification method based on optical fiber strain response and Gaussian process, based on the preset positions on the target landing gear support arm distributed along the direction of the bearing structure. S FBG sensors to realize the shock load identification for the target landing gear; according to step A to step H, obtain the shock load identification model corresponding to the target landing gear; then execute step i in real time to realize the shock load of the target landing gear real-time identification;

步骤A.基于目标起落架支撑臂上所承载预设不同投放重量与目标起落架对应预设不同下沉速度所组成的预设数量M种工况,获得各种工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,以及测量获得各种工况下沉时长内各时间点、目标起落架落震载荷测量数据,然后进入步骤B;Step A. Based on the preset number M working conditions composed of preset different delivery weights carried on the support arm of the target landing gear and preset different sinking speeds corresponding to the target landing gear, obtain each time within the sinking duration of each working condition point, the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear, and the measurement data of the drop shock load of the target landing gear at each time point within the sinking duration of various working conditions, and then enter step B;

步骤B.基于m≤M/2,随机选择M种工况中的m种工况,构成各个训练工况,同时选择由M种工况中剩余各工况中随机选择m种工况,构成各个测试工况,并构建各训练工况与各测试工况之间的随机一对一关系,构成m个样本,然后进入步骤C;Step B. Based on m≤M/2, randomly select m working conditions among the M working conditions to form each training condition, and at the same time select m working conditions randomly from the remaining working conditions in the M working conditions to form Each test condition is constructed, and a random one-to-one relationship between each training condition and each test condition is constructed to form m samples, and then proceed to step C;

步骤C.由S个FBG传感器中随机选择的s个FBG传感器作为各目标FBG传感器,然后进入步骤D;Step C. The s FBG sensors randomly selected from the S FBG sensors are used as each target FBG sensor, and then step D is entered;

步骤D.基于以工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组为输入,以工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据为输出的高斯过程回归模型f,结合f~GP(μ(·),k(·)),以样本中训练工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Xi,该样本中训练工况下沉时长内各时间点、目标起落架落震载荷测量数据Fi,测,该样本中测试工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Yj,构建如下模型:Step D. Based on the input of the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point in the sinking duration of the working condition and the corresponding noise contained in the target landing gear at each time point in the sinking duration of the working condition and the target landing gear. The predicted data of the drop load is the output Gaussian process regression model f, combined with f ~ GP(μ( ), k( )), the target landing gear support arm at each time point in the training condition sinking duration in the sample The strain response data set X i corresponding to each FBG sensor above, the measured data F i, of the drop shock load of the target landing gear at each time point within the sinking duration of the training condition in this sample, and the measured data F i, measured under the sinking duration of the test condition in this sample, within the sinking duration of the test condition in this sample For the strain response data set Y j corresponding to each FBG sensor on the target landing gear support arm at each time point, the following model is constructed:

Figure BDA0003446622800000021
Figure BDA0003446622800000021

其中,1≤i≤I,I表示该样本中训练工况下沉时长内各时间点的数量;J表示相应样本中测试工况下沉时长内各时间点的数量,Fj,预表示该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据;μ(·)表示均值函数,μ(·)包括μi与μj;σ2表示起落架落震载荷历程响应对应的噪声方差,I'表示单位矩阵,K(Xi,Xi)为起落架落震历程应变响应特征对应该样本训练工况的协方差矩阵,K(Xi,Yj)为起落架落震历程应变响应特征对应该样本中训练工况与测试工况之间的协方差矩阵,K(Yj,Yj)为起落架落震历程应变响应特征对应该样本测试工况的协方差矩阵,μi、μj分别表示起落架落震历程应变响应特征对应该样本中训练工况、测试工况的均值函数;k(·)表示协方差函数;N表示联合正态分布符号;然后进入步骤E;Among them, 1≤i≤I, I represents the number of each time point in the subsidence duration of the training condition in the sample; J represents the number of each time point in the subsidence duration of the test condition in the corresponding sample, F j, predenotes the In the sample, the noise-free drop load prediction data corresponding to the target landing gear at each time point in the subsidence duration of the test condition; μ( · ) represents the mean function, μ(·) includes μ i and μ j ; The noise variance corresponding to the load history response of the landing gear drop shock, I' represents the unit matrix, K(X i , X i ) is the covariance matrix of the strain response characteristic of the landing gear drop shock history corresponding to the sample training condition, K(X i , Y j ) is the covariance matrix between the training condition and the test condition in the sample corresponding to the strain response characteristic of the landing gear drop history, K(Y j , Y j ) is the landing gear drop history strain response characteristic corresponding to the sample The covariance matrix of the test condition, μ i and μ j represent the mean function of the landing gear drop shock history strain response characteristic corresponding to the training condition and the test condition in the sample; k( ) represents the covariance function; N represents the joint Normal distribution symbol; then go to step E;

步骤E.计算获得协方差函数k(·)中所涉及的各个超参数的值,并结合步骤D中所构建的模型、以及贝叶斯原理,获得该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,然后进入步骤F;Step E. Calculate and obtain the value of each hyperparameter involved in the covariance function k( ), and combine the model constructed in step D and the Bayesian principle to obtain the subsidence duration of the test condition in the sample. The time point, the target landing gear corresponds to the noise-free drop load prediction data F j, the pre- posterior distribution, and then enter step F;

步骤F.根据该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,获得该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000031
然后进入步骤G;Step F. According to the predicted posterior distribution of the noise-free drop load Fj corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample, the subsidence duration of the test condition in the sample is obtained. Prediction data of drop shock load including noise corresponding to each time point in the target landing gear
Figure BDA0003446622800000031
Then enter step G;

步骤G.根据该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000032
以及该样本中测试工况下沉时长内各时间点、目标起落架落震载荷测量数据Fj,测,以两者之间差值与预设差值阈值的比较构成溢出条件,然后进入步骤H;Step G. According to the predicted data of the drop shock load containing noise corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample
Figure BDA0003446622800000032
And each time point in the test condition subsidence duration in this sample, the measured data Fj of the drop shock load of the target landing gear is measured , and the comparison between the difference between the two and the preset difference threshold constitutes an overflow condition, and then enters the step H;

步骤H.基于各个样本,按上述步骤D至步骤G的方式,针对高斯过程回归模型f进行训练,获得训练后的高斯过程回归模型,即为目标起落架所对应的落震载荷辨识模型;Step H. Based on each sample, according to the above-mentioned steps D to step G, training is carried out for the Gaussian process regression model f, and the Gaussian process regression model after the training is obtained, which is the shock load identification model corresponding to the target landing gear;

步骤i.获得目标起落架实时所在工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,应用目标起落架所对应的落震载荷辨识模型,获得目标起落架对应该工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据,实现对目标起落架落震载荷的实时辨识。Step i. Obtain the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point within the sinking duration of the real-time working condition of the target landing gear, and apply the shock load identification model corresponding to the target landing gear to obtain the target landing gear. The landing gear corresponds to each time point in the sinking duration of the working condition, and the target landing gear corresponds to the drop shock load prediction data containing noise, so as to realize the real-time identification of the target landing gear drop shock load.

作为本发明的一种优选技术方案:所述μi=0,μj=0,所述协方差函数k(·)如下:As a preferred technical solution of the present invention: the μ i =0, μ j =0, the covariance function k(·) is as follows:

k(a,b)=λ1kRBF(a,b)+λ2kPKF(a,b)+λ3kNoise(a,b)k(a,b)=λ 1 k RBF (a,b)+λ 2 k PKF (a,b)+λ 3 k Noise (a,b)

其中:in:

Figure BDA0003446622800000033
Figure BDA0003446622800000033

kPKF(a,b)=(a·b+1)q k PKF (a,b)=(a·b+1) q

kNoise(a,b)=σN 2δ* k Noise (a,b)=σ N 2 δ *

式中,λ1、λ2、λ3表示预设权重因子,且满足0<λ1≤0.5,0<λ2≤0.5,0<λ3≤0.5,λ123=1;σf、σl、σN表示协方差函数k(·)中所涉及的各个超参数;q表示多项式度;δ*表示Kronecker函数。In the formula, λ 1 , λ 2 , λ 3 represent preset weighting factors, and satisfy 0<λ 1 ≤0.5, 0<λ 2 ≤0.5, 0<λ 3 ≤0.5, λ 123 =1 ; σ f , σ l , σ N represent the hyperparameters involved in the covariance function k(·); q represents the polynomial degree; δ * represents the Kronecker function.

作为本发明的一种优选技术方案:所述步骤E中,按如下方式,计算获得协方差函数k(·)中所涉及的各个超参数的值;As a preferred technical solution of the present invention: in the step E, calculate and obtain the value of each hyperparameter involved in the covariance function k( ) as follows;

首先采用目标起落架震历程应变响应特征对应样本中测试工况,以及协方差函数k(·)中所涉及各未知超参数,构造极大似然函数,并根据贝叶斯原理,按似然P(fj|fi,Xi,θ)与先验P(fi|Xi,θ)的积分,即边缘似然P(fj|Xi,θ)如下:Firstly, the maximum likelihood function is constructed by using the seismic history strain response characteristics of the target landing gear corresponding to the test conditions in the sample, and the unknown hyperparameters involved in the covariance function k( ), and according to the Bayesian principle, according to the likelihood The integral of P(f j |f i ,X i ,θ) and the prior P(f i |X i ,θ), that is, the edge likelihood P(f j |X i ,θ) is as follows:

P(fj|Xi,θ)=∫P(fj|fi,Xi,θ)P(fi|Xi,θ)dfi=N(fi|0,K(Xi,Xi)+σ2I)P(f j |X i ,θ)=∫P(f j |f i ,X i ,θ)P(f i |X i ,θ)df i =N(f i |0,K(X i , X i )+σ 2 I)

其中,θ表示协方差函数k(·)中所涉及各未知超参数组成的向量;Among them, θ represents the vector composed of unknown hyperparameters involved in the covariance function k( );

然后针对边缘似然P(fj|Xi,θ),取对数获得对数边缘似然如下:Then for the edge likelihood P(f j |X i ,θ), take the logarithm to obtain the logarithmic edge likelihood as follows:

Figure BDA0003446622800000041
Figure BDA0003446622800000041

其中,N'表示工况下沉时长内各时间点的数量,即采样频率;Among them, N' represents the number of time points in the subsidence duration of the working condition, that is, the sampling frequency;

最后由矩阵微积分原理,分别针对协方差函数k(·)中所涉及各未知超参数θi,按如下公式:Finally, according to the principle of matrix calculus, for each unknown hyperparameter θ i involved in the covariance function k(·), the following formulas are used:

Figure BDA0003446622800000042
Figure BDA0003446622800000042

通过求导获取最大概率所对应的θi值,即获得协方差函数k(·)中所涉及该超参数的值,进而获得协方差函数k(·)中所涉及各未知超参数的值;其中,Tr表示矩阵的迹,

Figure BDA0003446622800000043
T表示转置。Obtain the value of θ i corresponding to the maximum probability by derivation, that is, obtain the value of the hyperparameter involved in the covariance function k( ), and then obtain the value of each unknown hyperparameter involved in the covariance function k( ); where Tr represents the trace of the matrix,
Figure BDA0003446622800000043
T stands for transpose.

作为本发明的一种优选技术方案:所述步骤F中,根据该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,按如下公式:As a preferred technical solution of the present invention: in the step F, according to each time point within the subsidence duration of the test condition in the sample and the noise-free shock load prediction data F j corresponding to the target landing gear, the predicted The test distribution, according to the following formula:

Figure BDA0003446622800000044
Figure BDA0003446622800000044

cov(Fj,预)=K(Yj,Yj)-K(Yj,Xi)[K(Xi,Xi)+σ2I']-1K(Xi,Yj)cov(F j, pre )=K(Y j ,Y j )-K(Y j ,X i )[K(X i ,X i )+σ 2 I'] -1 K(X i ,Y j )

获得该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000045
其中,cov(Fj,预)表示目标起落架落震载荷历程响应预测值的置信水平。Obtain the predicted data of the drop shock load including noise corresponding to the target landing gear at each time point in the subsidence duration of the test condition in this sample
Figure BDA0003446622800000045
Among them, cov(F j, pre ) represents the confidence level of the predicted value of the target landing gear drop shock load history response.

本发明所述基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,采用以上技术方案与现有技术相比,具有以下技术效果:The method for identifying the landing gear drop shock load based on the optical fiber strain response and the Gaussian process of the present invention adopts the above technical solution and has the following technical effects compared with the prior art:

(1)本发明所设计基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,基于目标起落架支撑臂上预设位置沿承载结构方向所分布设置的S个FBG传感器,根据高斯过程回归模型f~GP(μ(·),k(·)),构建测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000051
并结合与实际测量值之间比较所对应的溢出条件,在所构建各样本中训练工况、测试工况下进行训练,获得目标起落架所对应的落震载荷辨识模型;进而在实际应用中,即可通过该落震载荷辨识模型,对目标起落架的落震载荷实现实时辨识,能够有效提高目标起落架健康监测的工作效率。(1) The landing gear drop shock load identification method based on the optical fiber strain response and Gaussian process is designed in the present invention, based on S FBG sensors distributed at the preset position on the target landing gear support arm along the direction of the load-bearing structure, according to the Gaussian process regression Model f~GP(μ(·),k(·)), construct the prediction data of drop shock load including noise corresponding to each time point in the subsidence duration of the test condition and the target landing gear
Figure BDA0003446622800000051
Combined with the corresponding overflow conditions compared with the actual measured values, training is carried out under the training conditions and test conditions in each constructed sample to obtain the shock load identification model corresponding to the target landing gear; and then in practical applications , the drop load identification model can be used to realize real-time identification of the drop load of the target landing gear, which can effectively improve the work efficiency of the target landing gear health monitoring.

附图说明Description of drawings

图1是本发明所设计中起落架落震载荷光纤辨识应用结构示意图;1 is a schematic diagram of the application structure of the optical fiber identification of the landing gear drop shock load in the design of the present invention;

图2是基于高斯过程回归的起落架落震载荷光纤辨识流程图。Fig. 2 is a flowchart of the optical fiber identification of landing gear drop shock load based on Gaussian process regression.

具体实施方式Detailed ways

下面结合说明书附图对本发明的具体实施方式作进一步详细的说明。The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

本发明所设计基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,基于目标起落架支撑臂上预设位置沿承载结构方向所分布设置的S个FBG传感器,实现针对目标起落架的落震载荷辨识。The invention designs a landing gear drop shock load identification method based on optical fiber strain response and Gaussian process, and based on S FBG sensors distributed at preset positions on the support arm of the target landing gear along the direction of the load-bearing structure, the landing gear landing gear landing gear is designed in the present invention. Seismic load identification.

关于上述预设位置分布设置S个FBG传感器的设计,实际应用当中,如图1所示,诸如在目标起落架支撑臂外表面选择一个沿承载结构方向的监测区域,在监测区域内布置4个FBG传感器,分别记作FBG1、FBG2、FBG3、…、FBGk,其中1≤S≤10;FBG传感器布置位置应根据支撑臂结构形式与所受载荷特点,在应变幅值较大、应变梯度较大的测量关键部位,可以适量增加FBG传感器的个数;在应变梯度较小的区域,可以减小FBG传感器的个数;S个FBG传感器之间采用波分复用技术将其串联起来,再将这些FBG传感器粘贴于支撑臂结构的外表面,以此构成FBG传感器监测网络,如图1所示,用来对目标起落架落震过程中支撑臂的应变响应信号进行采集。Regarding the above design of distributing S FBG sensors at preset positions, in practical applications, as shown in Figure 1, such as selecting a monitoring area along the direction of the bearing structure on the outer surface of the support arm of the target landing gear, and arranging 4 FBG sensors in the monitoring area FBG sensors are recorded as FBG1, FBG2, FBG3, ..., FBGk respectively, where 1≤S≤10; the arrangement position of the FBG sensor should be based on the structural form of the support arm and the load characteristics, when the strain amplitude is large and the strain gradient is large. The number of FBG sensors can be appropriately increased in the key parts of the measurement; in areas with small strain gradients, the number of FBG sensors can be reduced; wavelength division multiplexing technology is used to connect the S FBG sensors in series, and then connect the These FBG sensors are pasted on the outer surface of the support arm structure to form a FBG sensor monitoring network, as shown in Figure 1, which is used to collect the strain response signal of the support arm during the fall of the target landing gear.

之所以选择FBG传感器,是因为光纤布拉格光栅传感器(FBG)以光信号为载体,具有耐腐蚀、质量轻、抗电磁干扰等独特优势,还可实现多参量监测、分布式传感布置,对于航空航天器中大尺寸复杂结构,更能体现出其独特的优势。The reason why FBG sensors are selected is that fiber Bragg grating sensors (FBGs) use optical signals as carriers and have unique advantages such as corrosion resistance, light weight, and anti-electromagnetic interference. They can also realize multi-parameter monitoring and distributed sensing arrangements. The large-scale and complex structure in the spacecraft can better reflect its unique advantages.

基于S个FBG传感器在目标起落架支撑臂上预设位置沿承载结构方向的分布设置,实际应用当中,如图2所示,按步骤A至步骤H,获得目标起落架所对应的落震载荷辨识模型。Based on the distribution setting of the preset positions of the S FBG sensors on the support arm of the target landing gear along the direction of the bearing structure, in practical application, as shown in Figure 2, according to steps A to H, the shock load corresponding to the target landing gear is obtained Identify the model.

步骤A.基于目标起落架支撑臂上所承载预设不同投放重量与目标起落架对应预设不同下沉速度所组成的预设数量M种工况,获得各种工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,以及测量获得各种工况下沉时长内各时间点、目标起落架落震载荷测量数据,然后进入步骤B。Step A. Based on the preset number M working conditions composed of preset different delivery weights carried on the support arm of the target landing gear and preset different sinking speeds corresponding to the target landing gear, obtain each time within the sinking duration of each working condition point, the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear, and the measurement data of the drop shock load of the target landing gear at each time point within the sinking duration of various working conditions, and then go to step B.

步骤B.基于m≤M/2,随机选择S种工况中的m种工况,构成各个训练工况,同时选择由M种工况中剩余各工况中随机选择m种工况,构成各个测试工况,并构建各训练工况与各测试工况之间的随机一对一关系,构成m个样本,然后进入步骤C。Step B. Based on m≤M/2, randomly select m working conditions among the S working conditions to form each training condition, and at the same time select m working conditions randomly from the remaining working conditions in the M working conditions to form Each test condition is constructed, and a random one-to-one relationship between each training condition and each test condition is constructed to form m samples, and then step C is entered.

步骤C.由S个FBG传感器中随机选择的s个FBG传感器作为各目标FBG传感器,然后进入步骤D。Step C. The s FBG sensors randomly selected from the S FBG sensors are used as the target FBG sensors, and then step D is entered.

步骤D.基于以工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组为输入,以工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据为输出的高斯过程回归模型f,结合f~GP(μ(·),k(·)),以样本中训练工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Xi,该样本中训练工况下沉时长内各时间点、目标起落架落震载荷测量数据Fi,测,该样本中测试工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Yj,构建如下模型:Step D. Based on the input of the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point in the sinking duration of the working condition and the corresponding noise contained in the target landing gear at each time point in the sinking duration of the working condition and the target landing gear. The predicted data of the drop load is the output Gaussian process regression model f, combined with f ~ GP(μ( ), k( )), the target landing gear support arm at each time point in the training condition sinking duration in the sample The strain response data set X i corresponding to each FBG sensor above, the measured data F i, of the drop shock load of the target landing gear at each time point within the sinking duration of the training condition in this sample, and the measured data F i, measured under the sinking duration of the test condition in this sample, within the sinking duration of the test condition in this sample For the strain response data set Y j corresponding to each FBG sensor on the target landing gear support arm at each time point, the following model is constructed:

Figure BDA0003446622800000061
Figure BDA0003446622800000061

其中,1≤i≤I,I表示该样本中训练工况下沉时长内各时间点的数量;J表示相应样本中测试工况下沉时长内各时间点的数量,Fj,预表示该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据;μ(·)表示均值函数,μ(·)包括μi与μj;σ2表示起落架落震载荷历程响应对应的噪声方差,I'表示单位矩阵,K(Xi,Xi)为起落架落震历程应变响应特征对应该样本训练工况的协方差矩阵,K(Xi,Yj)为起落架落震历程应变响应特征对应该样本中训练工况与测试工况之间的协方差矩阵,K(Yj,Yj)为起落架落震历程应变响应特征对应该样本测试工况的协方差矩阵,μi、μj分别表示起落架落震历程应变响应特征对应该样本中训练工况、测试工况的均值函数;k(·)表示协方差函数;N表示联合正态分布符号;然后进入步骤E。Among them, 1≤i≤I, I represents the number of each time point in the subsidence duration of the training condition in the sample; J represents the number of each time point in the subsidence duration of the test condition in the corresponding sample, F j, predenotes the In the sample, the noise-free drop load prediction data corresponding to the target landing gear at each time point in the subsidence duration of the test condition; μ( · ) represents the mean function, μ(·) includes μ i and μ j ; The noise variance corresponding to the load history response of the landing gear drop shock, I' represents the unit matrix, K(X i , X i ) is the covariance matrix of the strain response characteristic of the landing gear drop shock history corresponding to the sample training condition, K(X i , Y j ) is the covariance matrix between the training condition and the test condition in the sample corresponding to the strain response characteristic of the landing gear drop history, K(Y j , Y j ) is the landing gear drop history strain response characteristic corresponding to the sample The covariance matrix of the test condition, μ i and μ j represent the mean function of the landing gear drop shock history strain response characteristic corresponding to the training condition and the test condition in the sample; k( ) represents the covariance function; N represents the joint Normal distribution symbol; then go to step E.

具体计算应用中,基于μi=0,μj=0,则上述协方差函数k(·)如下:In the specific calculation application, based on μ i =0, μ j =0, the above covariance function k(·) is as follows:

k(a,b)=λ1kRBF(a,b)+λ2kPKF(a,b)+λ3kNoise(a,b)k(a,b)=λ 1 k RBF (a,b)+λ 2 k PKF (a,b)+λ 3 k Noise (a,b)

其中:in:

Figure BDA0003446622800000071
Figure BDA0003446622800000071

kPKF(a,b)=(a·b+1)q k PKF (a,b)=(a·b+1) q

kNoise(a,b)=σN 2δ* k Noise (a,b)=σ N 2 δ *

式中,λ1、λ2、λ3表示预设权重因子,且满足0<λ1≤0.5,0<λ2≤0.5,0<λ3≤0.5,λ123=1;σf、σl、σN表示协方差函数k(·)中所涉及的各个超参数;q表示多项式度;δ*表示Kronecker函数。In the formula, λ 1 , λ 2 , λ 3 represent preset weighting factors, and satisfy 0<λ 1 ≤0.5, 0<λ 2 ≤0.5, 0<λ 3 ≤0.5, λ 123 =1 ; σ f , σ l , σ N represent the hyperparameters involved in the covariance function k(·); q represents the polynomial degree; δ * represents the Kronecker function.

实际应用中,根据贝叶斯原理,由步骤D中所构建的模型,可以获得目标起落架该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预分布如下:In practical applications, according to the Bayesian principle, the model constructed in step D can obtain the noise-free drop shock load prediction of the target landing gear at each time point in the subsidence duration of the test condition in this sample and the target landing gear The data Fj, predistributed as follows:

Figure BDA0003446622800000072
Figure BDA0003446622800000072

步骤E.计算获得协方差函数k(·)中所涉及的各个超参数的值,并结合步骤D中所构建的模型、以及贝叶斯原理,获得该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,然后进入步骤F。Step E. Calculate and obtain the value of each hyperparameter involved in the covariance function k( ), and combine the model constructed in step D and the Bayesian principle to obtain the subsidence duration of the test condition in the sample. The time point, the target landing gear corresponds to the noise-free shock load prediction data F j, the pre- posterior distribution, and then go to step F.

上述步骤E中,具体按如下方式,计算获得协方差函数k(·)中所涉及的各个超参数的值。In the above step E, the value of each hyperparameter involved in the covariance function k(·) is calculated and obtained in the following manner.

首先采用目标起落架震历程应变响应特征对应样本中测试工况,以及协方差函数k(·)中所涉及各未知超参数,构造极大似然函数,并根据贝叶斯原理,按似然P(fj|fi,Xi,θ)与先验P(fi|Xi,θ)的积分,即边缘似然P(fj|Xi,θ)如下:Firstly, the maximum likelihood function is constructed by using the seismic history strain response characteristics of the target landing gear corresponding to the test conditions in the sample, and the unknown hyperparameters involved in the covariance function k( ), and according to the Bayesian principle, according to the likelihood The integral of P(f j |f i ,X i ,θ) and the prior P(f i |X i ,θ), that is, the edge likelihood P(f j |X i ,θ) is as follows:

P(fj|Xi,θ)=∫P(fj|fi,Xi,θ)P(fi|Xi,θ)dfi=N(fi|0,K(Xi,Xi)+σ2I)P(f j |X i ,θ)=∫P(f j |f i ,X i ,θ)P(f i |X i ,θ)df i =N(f i |0,K(X i , X i )+σ 2 I)

其中,θ表示协方差函数k(·)中所涉及各未知超参数组成的向量。Among them, θ represents the vector of unknown hyperparameters involved in the covariance function k(·).

然后针对边缘似然P(fj|Xi,θ),取对数获得对数边缘似然如下:Then for the edge likelihood P(f j |X i ,θ), take the logarithm to obtain the logarithmic edge likelihood as follows:

Figure BDA0003446622800000081
Figure BDA0003446622800000081

其中,N'表示工况下沉时长内各时间点的数量,即采样频率。Among them, N' represents the number of each time point in the subsidence duration of the working condition, that is, the sampling frequency.

最后由矩阵微积分原理,分别针对协方差函数k(·)中所涉及各未知超参数θi,按如下公式:Finally, according to the principle of matrix calculus, for each unknown hyperparameter θ i involved in the covariance function k(·), the following formulas are used:

Figure BDA0003446622800000082
Figure BDA0003446622800000082

通过求导获取最大概率所对应的θi值,即获得协方差函数k(·)中所涉及该超参数的值,进而获得协方差函数k(·)中所涉及各未知超参数的值;其中,Tr表示矩阵的迹,

Figure BDA0003446622800000083
T表示转置。Obtain the value of θ i corresponding to the maximum probability by derivation, that is, obtain the value of the hyperparameter involved in the covariance function k( ), and then obtain the value of each unknown hyperparameter involved in the covariance function k( ); where Tr represents the trace of the matrix,
Figure BDA0003446622800000083
T stands for transpose.

获得协方差函数k(·)中所涉及各个超参数的值后,则基于各个超参数的值,确定协方差函数k(·),并结合步骤D中所构建的模型、以及贝叶斯原理,获得该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,然后进入步骤F。After obtaining the value of each hyperparameter involved in the covariance function k( ), determine the covariance function k( ) based on the value of each hyperparameter, and combine the model constructed in step D and the Bayesian principle , obtain the pre-posterior distribution of the noise-free drop load prediction data F j corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample, and then enter step F.

步骤F.根据该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,按如下公式:Step F. According to the predicted data F j of the drop shock load without noise corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample, the pre- posterior distribution is as follows:

Figure BDA0003446622800000084
Figure BDA0003446622800000084

cov(Fj,预)=K(Yj,Yj)-K(Yj,Xi)[K(Xi,Xi)+σ2I']-1K(Xi,Yj)cov(F j, pre )=K(Y j ,Y j )-K(Y j ,X i )[K(X i ,X i )+σ 2 I'] -1 K(X i ,Y j )

获得该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000091
其中,cov(Fj,预)表示目标起落架落震载荷历程响应预测值的置信水平,然后进入步骤G。Obtain the predicted data of the drop shock load including noise corresponding to the target landing gear at each time point in the subsidence duration of the test condition in this sample
Figure BDA0003446622800000091
Among them, cov(F j, pre ) represents the confidence level of the predicted value of the target landing gear drop shock load history response, and then go to step G.

步骤G.根据该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000092
以及该样本中测试工况下沉时长内各时间点、目标起落架落震载荷测量数据Fj,测,以两者之间差值与预设差值阈值的比较构成溢出条件,然后进入步骤H。Step G. According to the predicted data of the drop shock load containing noise corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample
Figure BDA0003446622800000092
And each time point in the test condition subsidence duration in this sample, the measured data Fj of the drop shock load of the target landing gear is measured , and the comparison between the difference between the two and the preset difference threshold constitutes an overflow condition, and then enters the step H.

步骤H.基于各个样本,按上述步骤D至步骤G的方式,针对高斯过程回归模型f进行训练,获得训练后的高斯过程回归模型,即为目标起落架所对应的落震载荷辨识模型。Step H. Based on each sample, according to the above steps D to G, train the Gaussian process regression model f to obtain the trained Gaussian process regression model, which is the shock load identification model corresponding to the target landing gear.

基于上述目标起落架所对应落震载荷辨识模型的获得,进一步基于此模型,实时执行步骤i,实现对目标起落架落震载荷的实时辨识。Based on the acquisition of the drop shock load identification model corresponding to the target landing gear, and further based on this model, step i is executed in real time to realize the real-time identification of the drop shock load of the target landing gear.

步骤i.获得目标起落架实时所在工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,应用目标起落架所对应的落震载荷辨识模型,获得目标起落架对应该工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据,实现对目标起落架落震载荷的实时辨识。Step i. Obtain the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point within the sinking duration of the real-time working condition of the target landing gear, and apply the shock load identification model corresponding to the target landing gear to obtain the target landing gear. The landing gear corresponds to each time point in the sinking duration of the working condition, and the target landing gear corresponds to the drop shock load prediction data containing noise, so as to realize the real-time identification of the target landing gear drop shock load.

上述技术方案所设计基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,基于目标起落架支撑臂上预设位置沿承载结构方向所分布设置的S个FBG传感器,根据高斯过程回归模型f~GP(μ(·),k(·)),构建测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据

Figure BDA0003446622800000093
并结合与实际测量值之间比较所对应的溢出条件,在所构建各样本中训练工况、测试工况下进行训练,获得目标起落架所对应的落震载荷辨识模型;进而在实际应用中,即可通过该落震载荷辨识模型,对目标起落架的落震载荷实现实时辨识,能够有效提高目标起落架健康监测的工作效率。The above technical solution designs a landing gear drop shock load identification method based on optical fiber strain response and Gaussian process, based on S FBG sensors arranged at preset positions on the target landing gear support arm along the direction of the load-bearing structure, according to the Gaussian process regression model f ~GP(μ(·),k(·)), construct the drop shock load prediction data including noise corresponding to the target landing gear at each time point in the subsidence duration of the test condition
Figure BDA0003446622800000093
Combined with the corresponding overflow conditions compared with the actual measured values, training is carried out under the training conditions and test conditions in each constructed sample to obtain the shock load identification model corresponding to the target landing gear; and then in practical applications , the drop load identification model can be used to realize real-time identification of the drop load of the target landing gear, which can effectively improve the work efficiency of the target landing gear health monitoring.

上面结合附图对本发明的实施方式作了详细说明,但是本发明并不限于上述实施方式,在本领域普通技术人员所具备的知识范围内,还可以在不脱离本发明宗旨的前提下做出各种变化。The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned embodiments, and can also be made within the scope of knowledge possessed by those of ordinary skill in the art without departing from the purpose of the present invention. Various changes.

Claims (4)

1.基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,基于目标起落架支撑臂上预设位置沿承载结构方向所分布设置的S个FBG传感器,实现针对目标起落架的落震载荷辨识;其特征在于:按步骤A至步骤H,获得目标起落架所对应的落震载荷辨识模型;然后实时执行步骤i,实现对目标起落架落震载荷的实时辨识;1. The landing gear drop load identification method based on optical fiber strain response and Gaussian process, based on S FBG sensors distributed at the preset position on the target landing gear support arm along the direction of the bearing structure, to achieve the target landing gear drop load identification; it is characterized in that: according to step A to step H, obtain the shock load identification model corresponding to the target landing gear; then perform step i in real time to realize the real-time identification of the target landing gear shock load; 步骤A.基于目标起落架支撑臂上所承载预设不同投放重量与目标起落架对应预设不同下沉速度所组成的预设数量M种工况,获得各种工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,以及测量获得各种工况下沉时长内各时间点、目标起落架落震载荷测量数据,然后进入步骤B;Step A. Based on the preset number M working conditions composed of preset different delivery weights carried on the support arm of the target landing gear and preset different sinking speeds corresponding to the target landing gear, obtain each time within the sinking duration of each working condition point, the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear, and the measurement data of the drop shock load of the target landing gear at each time point within the sinking duration of various working conditions, and then enter step B; 步骤B.基于m≤M/2,随机选择M种工况中的m种工况,构成各个训练工况,同时选择由M种工况中剩余各工况中随机选择m种工况,构成各个测试工况,并构建各训练工况与各测试工况之间的随机一对一关系,构成m个样本,然后进入步骤C;Step B. Based on m≤M/2, randomly select m working conditions among the M working conditions to form each training condition, and at the same time select m working conditions randomly from the remaining working conditions in the M working conditions to form Each test condition is constructed, and a random one-to-one relationship between each training condition and each test condition is constructed to form m samples, and then proceed to step C; 步骤C.由S个FBG传感器中随机选择的s个FBG传感器作为各目标FBG传感器,然后进入步骤D;Step C. The s FBG sensors randomly selected from the S FBG sensors are used as each target FBG sensor, and then step D is entered; 步骤D.基于以工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组为输入,以工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据为输出的高斯过程回归模型f,结合f~GP(μ(·),k(·)),以样本中训练工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Xi,该样本中训练工况下沉时长内各时间点、目标起落架落震载荷测量数据Fi,测,该样本中测试工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组Yj,构建如下模型:Step D. Based on the input of the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point in the sinking duration of the working condition and the corresponding noise contained in the target landing gear at each time point in the sinking duration of the working condition and the target landing gear. The predicted data of the drop load is the output Gaussian process regression model f, combined with f ~ GP(μ( ), k( )), the target landing gear support arm at each time point in the training condition sinking duration in the sample The strain response data set X i corresponding to each FBG sensor above, the measured data F i of the drop shock load of the target landing gear at each time point within the subsidence duration of the training condition in this sample, the measured data F i of the drop shock load of the target landing gear in this sample, the subsidence duration of the test condition in this sample is For the strain response data set Y j corresponding to each FBG sensor on the target landing gear support arm at each time point, the following model is constructed:
Figure FDA0003446622790000021
Figure FDA0003446622790000021
其中,1≤i≤I,I表示该样本中训练工况下沉时长内各时间点的数量;J表示相应样本中测试工况下沉时长内各时间点的数量,Fj,预表示该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据;μ(·)表示均值函数,μ(·)包括μi与μj;σ2表示起落架落震载荷历程响应对应的噪声方差,I′表示单位矩阵,K(Xi,Xi)为起落架落震历程应变响应特征对应该样本训练工况的协方差矩阵,K(Xi,Yj)为起落架落震历程应变响应特征对应该样本中训练工况与测试工况之间的协方差矩阵,K(Yj,Yj)为起落架落震历程应变响应特征对应该样本测试工况的协方差矩阵,μi、μj分别表示起落架落震历程应变响应特征对应该样本中训练工况、测试工况的均值函数;k(·)表示协方差函数;N表示联合正态分布符号;然后进入步骤E;Among them, 1≤i≤I, I represents the number of each time point in the subsidence duration of the training condition in the sample; J represents the number of each time point in the subsidence duration of the test condition in the corresponding sample, F j, pre- represents the In the sample, the noise-free drop load prediction data corresponding to the target landing gear at each time point in the subsidence duration of the test condition; μ( · ) represents the mean function, μ(·) includes μ i and μ j ; The noise variance corresponding to the load history response of the landing gear drop shock, I′ represents the unit matrix, K(X i , X i ) is the covariance matrix of the strain response characteristic of the landing gear drop shock history corresponding to the sample training condition, K(X i , Y j ) is the covariance matrix between the training condition and the test condition in the sample corresponding to the strain response characteristics of the landing gear drop history, K(Y j , Y j ) is the landing gear drop history strain response characteristic corresponding to the sample The covariance matrix of the test condition, μ i and μ j represent the mean function of the landing gear drop shock history strain response characteristic corresponding to the training condition and the test condition in the sample; k( ) represents the covariance function; N represents the joint Normal distribution symbol; then go to step E; 步骤E.计算获得协方差函数k(·)中所涉及的各个超参数的值,并结合步骤D中所构建的模型、以及贝叶斯原理,获得该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,然后进入步骤F;Step E. Calculate and obtain the value of each hyperparameter involved in the covariance function k( ), and combine the model constructed in step D and the Bayesian principle to obtain the subsidence duration of the test condition in the sample. Time point, the target landing gear corresponds to the noise-free shock load prediction data F j, the pre- posterior distribution, and then enter step F; 步骤F.根据该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,获得该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据
Figure FDA0003446622790000022
然后进入步骤G;
Step F. According to the pre-posterior distribution of the noise-free drop load prediction data F j corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample, the subsidence duration of the test condition in the sample is obtained. Prediction data of drop shock load including noise corresponding to each time point in the target landing gear
Figure FDA0003446622790000022
Then enter step G;
步骤G.根据该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据
Figure FDA0003446622790000031
以及该样本中测试工况下沉时长内各时间点、目标起落架落震载荷测量数据Fj,测,以两者之间差值与预设差值阈值的比较构成溢出条件,然后进入步骤H;
Step G. According to the predicted data of the drop shock load containing noise corresponding to the target landing gear at each time point within the subsidence duration of the test condition in the sample
Figure FDA0003446622790000031
and the measured data Fj of the drop shock load of the target landing gear at each time point in the subsidence duration of the test condition in the sample, and the comparison between the difference between the two and the preset difference threshold constitutes an overflow condition, and then enters the step H;
步骤H.基于各个样本,按上述步骤D至步骤G的方式,针对高斯过程回归模型f进行训练,获得训练后的高斯过程回归模型,即为目标起落架所对应的落震载荷辨识模型;Step H. Based on each sample, according to the above-mentioned steps D to step G, training is carried out for the Gaussian process regression model f, and the Gaussian process regression model after the training is obtained, which is the shock load identification model corresponding to the target landing gear; 步骤i.获得目标起落架实时所在工况下沉时长内各时间点、目标起落架支撑臂上各FBG传感器对应的应变响应数据组,应用目标起落架所对应的落震载荷辨识模型,获得目标起落架对应该工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据,实现对目标起落架落震载荷的实时辨识。Step i. Obtain the strain response data set corresponding to each FBG sensor on the support arm of the target landing gear at each time point within the sinking duration of the real-time working condition of the target landing gear, and apply the shock load identification model corresponding to the target landing gear to obtain the target landing gear. The landing gear corresponds to each time point in the sinking duration of the working condition, and the target landing gear corresponds to the drop shock load prediction data containing noise, so as to realize the real-time identification of the target landing gear drop shock load.
2.根据权利要求1所述基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,其特征在于:所述μi=0,μj=0,所述协方差函数k(·)如下:2. The method for identifying the landing gear drop shock load based on optical fiber strain response and Gaussian process according to claim 1, characterized in that: the μ i =0, μ j =0, and the covariance function k(·) is as follows : k(a,b)=λ1kRBF(a,b)+λ2kPKF(a,b)+λ3kNoise(a,b)k(a, b)=λ 1 k RBF (a, b)+λ 2 k PKF (a, b)+λ 3 k Noise (a, b) 其中:in:
Figure FDA0003446622790000032
Figure FDA0003446622790000032
kPKF(a,b)=(a·b+1)q k PKF (a, b)=(a·b+1) q kNoise(a,b)=σN 2δ* k Noise (a, b)=σ N 2 δ * 式中,λ1、λ2、λ3表示预设权重因子,且满足0<λ1≤0.5,0<λ2≤0.5,0<λ3≤0.5,λ123=1;σf、σl、σN表示协方差函数k(·)中所涉及的各个超参数;q表示多项式度;δ*表示Kronecker函数。In the formula, λ 1 , λ 2 , λ 3 represent preset weighting factors, and satisfy 0<λ 1 ≤0.5, 0<λ 2 ≤0.5, 0<λ 3 ≤0.5, λ 123 =1 ; σ f , σ l , σ N represent the hyperparameters involved in the covariance function k(·); q represents the polynomial degree; δ * represents the Kronecker function.
3.根据权利要求2所述基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,其特征在于:所述步骤E中,按如下方式,计算获得协方差函数k(·)中所涉及的各个超参数的值;首先采用目标起落架震历程应变响应特征对应样本中测试工况,以及协方差函数k(·)中所涉及各未知超参数,构造极大似然函数,并根据贝叶斯原理,按似然P(fj|fi,Xi,θ)与先验P(fi|Xi,θ)的积分,即边缘似然P(fj|Xi,θ)如下:3. The landing gear drop shock load identification method based on optical fiber strain response and Gaussian process according to claim 2, characterized in that: in the step E, in the following manner, calculate and obtain the covariance function k ( ) involved in value of each hyperparameter; first, the maximum likelihood function is constructed by using the seismic history strain response characteristics of the target landing gear corresponding to the test conditions in the sample, and the unknown hyperparameters involved in the covariance function k( ). Yeas's principle, according to the integral of the likelihood P(f j |f i , X i , θ) and the prior P(f i |X i , θ), that is, the edge likelihood P(f j |X i , θ) as follows: P(fj|Xi,θ)=∫P(fj|fi,Xi,θ)P(fi|Xi,θ)dfi=N(fi|0,K(Xi,Xi)+σ2I)P(f j |X i , θ)=∫P(f j |f i ,X i ,θ)P(f i |X i ,θ)df i =N(f i |0,K(X i , X i )+σ 2 I) 其中,θ表示协方差函数k(·)中所涉及各未知超参数组成的向量;Among them, θ represents the vector composed of unknown hyperparameters involved in the covariance function k( ); 然后针对边缘似然P(fj|Xi,θ),取对数获得对数边缘似然如下:Then for the edge likelihood P(f j |X i ,θ), take the logarithm to obtain the logarithmic edge likelihood as follows:
Figure FDA0003446622790000041
Figure FDA0003446622790000041
其中,N'表示工况下沉时长内各时间点的数量,即采样频率;Among them, N' represents the number of time points in the subsidence duration of the working condition, that is, the sampling frequency; 最后由矩阵微积分原理,分别针对协方差函数k(·)中所涉及各未知超参数θi,按如下公式:Finally, according to the principle of matrix calculus, for each unknown hyperparameter θ i involved in the covariance function k(·), the following formulas are used:
Figure FDA0003446622790000042
Figure FDA0003446622790000042
通过求导获取最大概率所对应的θi值,即获得协方差函数k(·)中所涉及该超参数的值,进而获得协方差函数k(·)中所涉及各未知超参数的值;其中,Tr表示矩阵的迹,
Figure FDA0003446622790000043
T表示转置。
Obtain the value of θ i corresponding to the maximum probability by derivation, that is, obtain the value of the hyperparameter involved in the covariance function k( ), and then obtain the value of each unknown hyperparameter involved in the covariance function k( ); where Tr represents the trace of the matrix,
Figure FDA0003446622790000043
T stands for transpose.
4.根据权利要求1所述基于光纤应变响应与高斯过程的起落架落震载荷辨识方法,其特征在于:所述步骤F中,根据该样本中测试工况下沉时长内各时间点、目标起落架对应不含噪声的落震载荷预测数据Fj,预的后验分布,按如下公式:4. The method for identifying the landing gear drop shock load based on optical fiber strain response and Gaussian process according to claim 1, characterized in that: in the step F, according to each time point and target in the subsidence duration of the test condition in the sample The pre-posterior distribution of the landing gear corresponding to the noise-free drop load prediction data F j, is as follows:
Figure FDA0003446622790000044
Figure FDA0003446622790000044
cov(Fj,预)=K(Yj,Yj)-K(Yj,Xi)[K(Xi,Xi)+σ2I']-1K(Xi,Yj)cov(F j, pre )=K(Y j ,Y j )-K(Y j ,X i )[K(X i ,X i )+σ 2 I'] -1 K(X i ,Y j ) 获得该样本中测试工况下沉时长内各时间点、目标起落架对应包含噪声的落震载荷预测数据
Figure FDA0003446622790000045
其中,cov(Fj,预)表示目标起落架落震载荷历程响应预测值的置信水平。
Obtain the predicted data of the drop shock load including noise corresponding to the target landing gear at each time point in the subsidence duration of the test condition in this sample
Figure FDA0003446622790000045
Among them, cov(F j, pre ) represents the confidence level of the predicted value of the target landing gear drop shock load history response.
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