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CN114048678A - Local tangent space reconstruction method for nonlinear correlation structural damage diagnosis index - Google Patents

Local tangent space reconstruction method for nonlinear correlation structural damage diagnosis index Download PDF

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CN114048678A
CN114048678A CN202111327346.9A CN202111327346A CN114048678A CN 114048678 A CN114048678 A CN 114048678A CN 202111327346 A CN202111327346 A CN 202111327346A CN 114048678 A CN114048678 A CN 114048678A
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刘洋
杨昌熙
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Abstract

本发明公开了一种非线性相关结构损伤诊断指标的局部切空间重构方法，所述方法采用无损伤状态下的桥梁结构响应数据构建结构损伤诊断指标，对非线性相关的结构损伤诊断指标，采用非线性窄域特征判别因子判定是否具备非线性窄域特征。对不具备非线性窄域特征的结构损伤诊断指标，采用局部切空间排列法，建立结构损伤诊断指标的主要特征坐标矩阵，利用局部切空间排列法的逆运算，建立结构损伤诊断指标的重构指标。本发明解决复杂环境影响下非线性相关的结构损伤诊断指标不具备非线性窄域特征，导致损伤诊断指标分段线性化准确性低的缺点。

Figure 202111327346

The invention discloses a local tangent space reconstruction method of nonlinear related structural damage diagnosis indexes. The non-linear narrow-domain feature discriminant factor is used to determine whether there is a nonlinear narrow-domain feature. For the structural damage diagnosis indexes that do not have nonlinear narrow domain characteristics, the local tangent space arrangement method is used to establish the main feature coordinate matrix of the structural damage diagnosis indexes, and the inverse operation of the local tangent space arrangement method is used to establish the reconstruction of the structural damage diagnosis indexes. index. The invention solves the shortcoming that the non-linear related structural damage diagnosis index under the influence of complex environment does not have the nonlinear narrow domain characteristic, resulting in low accuracy of segmental linearization of the damage diagnosis index.

Figure 202111327346

Description

Local tangent space reconstruction method for nonlinear correlation structural damage diagnosis index
Technical Field
The invention belongs to the field of bridge structure damage diagnosis, and relates to a local tangent space reconstruction method of nonlinear correlation structure damage diagnosis indexes.
Background
The strong crossing capability of the bridge structure shortens the traffic mileage, optimizes the road network construction, improves the traffic efficiency, and plays an important role in both road transport networks and railway transport networks. The safe operation of the transportation network is the key for guaranteeing the national economic development, so the operation safety of the bridge structure is very important. Due to the particularity of the construction position of the bridge, the bridge structure is usually located in a complex and severe environment, and natural environment factors such as temperature, wind speed and humidity directly influence the operation state of the bridge structure and interfere the accuracy of damage identification of the bridge structure. In order to effectively identify the damage of the bridge structure, the influence of environmental factors in the structural damage diagnosis index must be eliminated, so that the accuracy of identifying the damage of the bridge structure can be improved.
The bridge structure is often in a multiple statically indeterminate structure, and the influence of multiple environmental factors causes the response of the bridge structure to show a nonlinear correlation relationship, so that structural damage diagnosis indexes applied to damage identification also show nonlinear correlation. In the damage identification method for solving the problem that the structural damage diagnosis index is in nonlinear correlation under the influence of the environment, the bridge structural damage identification method based on the nonlinear narrow-area characteristic of the structural damage diagnosis index fully utilizes the hidden characteristic of the structural damage diagnosis index, namely the nonlinear narrow-area characteristic, and has the advantages of simple calculation, high damage identification speed and high damage identification accuracy. However, this method requires that the structural damage diagnostic index must have a nonlinear narrow-band characteristic. For different types of bridge structures, the influence degrees caused by environmental factors are inconsistent, so that the structural damage diagnosis index does not necessarily have a nonlinear characteristic, and the use of the bridge structure damage identification method based on the nonlinear narrow-area characteristic of the structural damage diagnosis index is seriously influenced. Only by further mining the distribution characteristics when the structural damage diagnosis indexes are in nonlinear correlation and constructing the structural damage diagnosis indexes with nonlinear narrow-area characteristics, the influence of environmental factors when the structural damage diagnosis indexes are in nonlinear correlation can be effectively eliminated. Therefore, the research on the reconstruction method when the bridge structure damage diagnosis index is nonlinear correlation is the key for breaking through the use condition of the bridge structure damage identification method.
Disclosure of Invention
The invention provides a local tangent space reconstruction method of a nonlinear correlation structural damage diagnosis index, aiming at solving the problem that the nonlinear correlation structural damage diagnosis index does not have the nonlinear narrow-range characteristic under the influence of a complex environment, so that the segmented linearization accuracy of the damage diagnosis index is low.
The purpose of the invention is realized by the following technical scheme:
a local tangent space reconstruction method of nonlinear correlation structural damage diagnosis indexes comprises the following steps:
the method comprises the following steps: collecting structural response data of the bridge structure in a non-damage state, and establishing a bridge structure damage diagnosis index in a reference state;
step two: drawing a distribution diagram of two different indexes in a two-dimensional Euclidean space by using the structural damage diagnosis index obtained in the step one, and judging whether the structural damage diagnosis index has a nonlinear correlation relationship;
step three: if the structural damage diagnosis index determined in the second step has the nonlinear correlation relationship, establishing a nonlinear narrow-region feature discrimination factor of the structural damage diagnosis index according to the definition of the nonlinear narrow-region feature, and determining whether the structural damage diagnosis index has the nonlinear narrow-region feature; if the structural damage diagnosis index does not have the nonlinear correlation, the reconstruction processing is not needed;
step four: if the structural damage diagnosis index does not have the nonlinear narrow-area characteristic, extracting a main characteristic coordinate matrix of the structural damage diagnosis index by adopting a local tangent space arrangement method; if the structural damage diagnosis index is judged to have the nonlinear narrow-range characteristic, the reconstruction processing is not needed;
step five: establishing a reconstruction index of the structural damage diagnosis index according to the inverse operation of the local tangent space arrangement method by using the main characteristic coordinate matrix obtained in the step four;
step six: constructing a nonlinear narrow-region characteristic discrimination factor of the reconstruction index according to the definition of the nonlinear narrow-region characteristic on the reconstruction index of the structural damage diagnosis index obtained in the step five, and judging whether the reconstruction index has the nonlinear narrow-region characteristic;
step seven: and if the reconstructed index does not have the nonlinear narrow-area characteristic, repeating the fourth step to the fifth step, reconstructing the reconstructed index again, and if the reconstructed index has the nonlinear narrow-area characteristic, obtaining the reconstructed index of the structural damage diagnosis index under the action of the local tangent space reconstruction method of the nonlinear correlation structural damage diagnosis index.
Compared with the prior art, the invention has the following advantages:
1. according to the invention, the nonlinear-related structural damage diagnosis index is reconstructed, so that the reconstructed index of the structural damage diagnosis index has the nonlinear narrow-range characteristic, and the accuracy of the piecewise linearization result of the structural damage diagnosis index is improved, further the environmental factor influence in the nonlinear-related structural damage diagnosis index can be effectively eliminated by the principal component analysis method, and the accuracy of structural damage identification is finally improved.
2. The method is suitable for solving the index reconstruction problem when the structural damage diagnosis index is nonlinear correlation.
3. The invention can greatly improve the accuracy of the piecewise linearization when the structural damage diagnosis index is nonlinear correlation.
4. The method can improve the accuracy of damage identification when the structural damage diagnosis index is nonlinear correlation. The numerical simulation calculation shows that when the nonlinear-related structural damage diagnosis index does not have the nonlinear narrow-range characteristic, the piecewise linearization method cannot carry out linearization processing on the structural damage diagnosis index, and the local tangent space reconstruction method of the nonlinear-related structural damage diagnosis index is adopted to reconstruct the structural damage diagnosis index, so that the reconstruction index of the structural damage diagnosis index can be well linearized in a piecewise manner.
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Fig. 1 is a flowchart of a local tangent space reconstruction method for a nonlinear correlation structural damage diagnosis index.
Fig. 2 is a schematic structural diagram of a three-span continuous rigid frame bridge.
FIG. 3 is a graph showing the change of the concrete elastic modulus with temperature.
FIG. 4 is a graph showing the change of the modulus of elasticity of steel material with temperature.
Fig. 5 is an annual ambient temperature change curve of a bridge structure.
FIG. 6 shows structural damage diagnosis indicators (f)1、f2、f3) Time-course diagram of (c).
FIG. 7 shows structural damage diagnosis indicators (f)1、f2) Distribution map in two-dimensional Euclidean space.
FIG. 8 shows a reconstruction index (f) of the structural damage diagnosis index1、f2、f3) Time-course diagram of (c).
Fig. 9 is a distribution diagram of the structural damage diagnosis index in the three-dimensional euclidean space.
Fig. 10 is a distribution diagram of the reconstruction result of the structural damage diagnosis index in the three-dimensional euclidean space in the local tangent space reconstruction method of the nonlinear correlation structural damage diagnosis index.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a local tangent space reconstruction method of a nonlinear correlation structural damage diagnosis index, which adopts bridge structural response data in a non-damage state to construct a structural damage diagnosis index, and adopts a nonlinear narrow-region characteristic discrimination factor to judge whether the nonlinear narrow-region characteristic exists or not for the nonlinear correlation structural damage diagnosis index. For the structural damage diagnosis index without nonlinear narrow-area characteristics, a local tangent space arrangement method is adopted to establish a main characteristic coordinate matrix of the structural damage diagnosis index, and the reconstruction index of the structural damage diagnosis index is established by utilizing the inverse operation of the local tangent space arrangement method. As shown in fig. 1, the method comprises the following steps:
the method comprises the following steps: and collecting structural response data of the bridge structure in a non-damage state, and establishing a bridge structure damage diagnosis index in a reference state.
In this step, the concrete steps of establishing the bridge structure damage diagnosis index in the reference state are as follows:
the method comprises the following steps: setting the bridge structure response data matrix as W1＝[ω1,ω2,…,ωk](ω1,ω2,…,ωk∈Rm ×1) K is the number of monitoring data samples, m is the number of measuring points, and omega is a structural response data vector at each monitoring moment, wherein the structural response data matrix comprises structural acceleration data, strain data and displacement data;
the first step is: performing modal analysis on acceleration data of the bridge structure by using a random subspace method, and using the obtained frequency data as a structural damage diagnosis index of modal parameters;
step one is three: analyzing the strain data by using a low-pass filter and a resampling technology, and establishing a structural damage diagnosis index of strain response;
step one is: and analyzing the displacement data by using a low-pass filter and a resampling technology, and establishing a structural damage diagnosis index of displacement response.
Step two: and D, drawing a distribution diagram of two different indexes in a two-dimensional Euclidean space by using the structural damage diagnosis index obtained in the step one, and judging whether the structural damage diagnosis index has a nonlinear correlation relationship.
The influence of environmental factors causes the structural damage diagnosis index to show two types of correlation relationships, namely linear correlation and nonlinear correlation. The method comprises the following steps of judging the type of the correlation relationship of the structural damage diagnosis index by utilizing the distribution characteristics of the structural damage diagnosis index in a two-dimensional Euclidean space.
In this step, the specific steps of determining whether the structural damage diagnosis index has a nonlinear correlation relationship are as follows:
step two, firstly: combining the different dimensions of the index pairwise by using the same type of structural damage diagnosis index, and drawing a distribution map of the two different dimension structural damage diagnosis indexes in a two-dimensional European space;
step two: and judging whether the distribution characteristics distributed along the curve trend exist in the graphs or not according to the distribution graph of the structural damage diagnosis indexes obtained in the step two, wherein if the distribution characteristics distributed along the curve trend exist, the structural damage diagnosis indexes are in a nonlinear correlation relationship, and if the distribution characteristics distributed along the curve trend do not exist, the structural damage diagnosis indexes are in a linear correlation relationship.
Step three: if the structural damage diagnosis index determined in the second step has the nonlinear correlation relationship, establishing a nonlinear narrow-region feature discrimination factor of the structural damage diagnosis index according to the definition of the nonlinear narrow-region feature, and determining whether the structural damage diagnosis index has the nonlinear narrow-region feature; if it is determined that the structural damage diagnosis index does not have the nonlinear correlation, the reconstruction process is not necessary.
The nonlinear narrow-area characteristic of the structural damage diagnosis index is the correlation when the structural damage diagnosis index is nonlinear correlation under environmental influence. The nonlinear narrow-area characteristic is used for measuring the correlation degree between damage diagnosis indexes when the structure is influenced by time-varying environmental factors. The nonlinear narrow-area characteristic is used for judging whether the nonlinear-related structural damage diagnosis index is suitable for the bridge structural damage identification method based on the nonlinear narrow-area characteristic of the structural damage diagnosis index.
In this step, the specific steps of establishing a nonlinear narrow-band feature discrimination factor of the structural damage diagnosis index and judging whether the structural damage diagnosis index has the nonlinear narrow-band feature are as follows:
step three, firstly: given a non-linearly related structural damage diagnostic index
Figure BDA0003347667450000071
n is structural damage diagnosis index dimension, and k means clustering method is used for calculating the structural damage diagnosis index dimension
Figure BDA0003347667450000072
And
Figure BDA0003347667450000073
clustering into p and q categories, and then diagnosing the damage of the ith dimension structure
Figure BDA0003347667450000074
The mutual information calculation formula is as follows:
Figure BDA0003347667450000075
in the formula, Pd(k) Is composed of
Figure BDA0003347667450000076
Edge probability distribution in P cluster partitions, Pind(j) Is composed of
Figure BDA0003347667450000077
Edge probability distribution in q cluster partitions, p (jk) is joint probability distribution of Φ under p × q cluster partitions;
step three: diagnosis index for i-dimensional structural damage
Figure BDA0003347667450000078
The mutual information is standardized, and a structural nonlinear narrow-range feature discrimination factor rho of the damage diagnosis index is established:
Figure BDA0003347667450000079
step three: judging the nonlinear narrow-area characteristic of the structural damage diagnosis index, and if rho is more than or equal to 0.7, judging that the structural damage diagnosis index has the nonlinear narrow-area characteristic; and if rho is less than 0.7, judging that the structural damage diagnosis index does not have the nonlinear narrow-range characteristic.
Step four: if the structural damage diagnosis index does not have the nonlinear narrow-area characteristic, extracting a main characteristic coordinate matrix of the structural damage diagnosis index by adopting a local tangent space arrangement method; if the structural damage diagnosis index is judged to have the nonlinear narrow-band characteristic, the reconstruction processing is not required.
In the step, the specific steps of extracting the main characteristic coordinate matrix of the structural damage diagnosis index by adopting a local tangent space arrangement method are as follows:
step four, firstly: given N structures without nonlinear narrow-region characteristicsThe damage diagnosis index constitutes an index set of
Figure BDA0003347667450000081
X＝[x1,x2,…,xi,…,xN]I belongs to (1,2, …, N), N is structural damage diagnosis index dimension, N is index number, and the ith index x is constructediThe k neighborhood point sets are used for establishing a neighborhood matrix:
Ωi＝[xi1,xi2…,xik] (3)；
step four and step two: taking a nonlinear-related structural damage diagnosis index as a nonlinear manifold, expressing the nonlinear manifold by using a linear manifold, and establishing a d-dimensional (d < n, n is a structural damage diagnosis index dimension) linear manifold of the nonlinear manifold:
Figure BDA0003347667450000082
in the formula, xijFor the jth neighborhood of the ith lesion diagnostic index, 1kColumn vector of all 1, θjIs the jth column vector in theta, and P is the transformation matrix;
step four and step three: according to the singular value component theory, local coordinates of the neighborhood matrix of the ith index in the linear manifold are established, and the main characteristic coordinate matrix of the structural damage diagnosis index is established by orderly arranging the local coordinates obtained by the neighborhood matrix of each index.
In the third step, the specific steps of establishing the local coordinates of the neighborhood matrix of the ith index in the linear manifold and the main characteristic coordinate matrix of the structural damage diagnosis index are as follows:
(1): establishing a centralized neighborhood matrix according to the neighborhood matrix obtained in the step four:
Figure BDA0003347667450000091
in the formula (I), the compound is shown in the specification,
Figure BDA0003347667450000092
is a neighborhood matrix omegaiA center point of (a);
(2): according to the singular value component theory, performing singular value decomposition on the centered neighborhood matrix, and establishing a singular vector matrix of the neighborhood matrix:
Figure BDA0003347667450000093
in the formula, pi1As left singular vectors, pinAs left singular vectors, pidIn the form of the left singular vector,
Figure BDA0003347667450000094
in the form of the singular values of the signals,
Figure BDA0003347667450000095
in the form of the singular values of the signals,
Figure BDA0003347667450000096
is a singular value, vi1Is the right singular vector, vikIs the right singular vector, vidIs the right singular vector;
(3): establishing local coordinates of a neighborhood matrix of the ith index on the linear manifold according to the singular vector matrix obtained in the step (2):
Figure BDA0003347667450000097
in the formula, PiA matrix formed by left singular vectors corresponding to the largest d singular values;
(4): and (3) adopting a minimization error mode to furthest save the nonlinear manifold characteristics contained in the neighborhood matrix of the ith index, and establishing a minimization error equation:
Figure BDA0003347667450000101
Figure BDA0003347667450000102
Figure BDA0003347667450000103
in the formula, TiAs global coordinates, SiIn order to select the matrix, the matrix is selected,
Figure BDA0003347667450000104
selecting k neighborhood points of the ith structural damage diagnosis index from the N index sets;
(5): solving the eigenvalue and eigenvector of the matrix psi, arranging the eigenvalues from small to large according to the numerical value, and sequencing the eigenvectors corresponding to the eigenvalues, wherein the 2 nd to the d +1 th eigenvectors are the global coordinate Ti。
Step five: and D, establishing a reconstruction index of the structural damage diagnosis index according to the inverse operation of the local tangent space arrangement method by using the main characteristic coordinate matrix obtained in the step four.
In this step, the specific steps of establishing the reconstruction index of the structural damage diagnosis index are as follows:
step five, first: establishing a local affine transformation matrix according to the main characteristic coordinate matrix of the structural damage diagnosis index obtained in the step four:
Γi＝TiTi + (9)；
step five two: according to the inverse operation of the local tangent space arrangement method, establishing a reconstruction index of the structural damage diagnosis index:
Figure BDA0003347667450000105
in the formula (I), the compound is shown in the specification,
Figure BDA0003347667450000106
for the ith structural damageA reconstructed index of the injury diagnosis index,
Figure BDA0003347667450000107
neighborhood matrix omega for ith structural damage diagnosis indexiCenter point of (d), tiIs the global coordinate of the ith structural damage diagnosis index.
Step six: and e, constructing a nonlinear narrow-region characteristic discrimination factor of the reconstruction index according to the definition of the nonlinear narrow-region characteristic on the reconstruction index of the structural damage diagnosis index obtained in the step five, and judging whether the reconstruction index has the nonlinear narrow-region characteristic.
Step seven: and if the reconstructed index does not have the nonlinear narrow-area characteristic, repeating the fourth step to the fifth step, reconstructing the reconstructed index again, and if the reconstructed index has the nonlinear narrow-area characteristic, obtaining the reconstructed index of the structural damage diagnosis index under the action of the local tangent space reconstruction method of the nonlinear correlation structural damage diagnosis index.
Example (b):
the present embodiment takes the three-span continuous rigid frame bridge structure shown in fig. 2 as an example. The bridge span is 24m +48m +24 m. The bridge abutment is hinged with the main beam in the horizontal direction, the beam is rigidly connected with the bridge pier, and the bridge pier is rigidly connected with the ground. The additional main beam of the fulcrum is made of concrete material, and the midspan part is made of steel. The bridge piers are made of concrete materials, the height of the bridge piers is 12m, and the size of the rectangular piers is 1.5m multiplied by 0.8 m. The full bridge was simulated using 32 beam elements each 3m in length. Assuming that concrete and steel in the structure are related to the ambient temperature, the change relationship of the elastic modulus of concrete with the temperature is shown in fig. 3, the change relationship of the elastic modulus of steel with the temperature is shown in fig. 4, and the annual change rule of the ambient temperature of the bridge structure is shown in fig. 5.
The structural damage diagnosis index of the bridge under the reference state is established by adding 10% of white noise interference by utilizing the first 3-order natural vibration frequency of the three-span continuous rigid frame bridge structure in the non-damage state within one year (figure 6).
And drawing a distribution diagram of the structural damage diagnosis index in a two-dimensional Euclidean space, and judging the structural damage diagnosis index to be in a nonlinear correlation relationship according to the distribution trend (figure 7) of the structural damage diagnosis index in the distribution diagram.
And establishing a nonlinear narrow-area characteristic discrimination factor by using the bridge structure damage diagnosis index in the reference state, and determining that the established structure damage diagnosis index does not have the nonlinear narrow-area characteristic according to the nonlinear discrimination factor.
And extracting a main characteristic coordinate matrix of the structural damage diagnosis index by using a local tangent space arrangement method, and establishing a reconstruction index of the structural damage diagnosis index according to the inverse operation of the local tangent space arrangement method (figure 8).
And establishing a nonlinear narrow-area characteristic discrimination factor of the reconstruction index, and determining that the reconstruction index of the structural damage diagnosis index has nonlinear narrow-area characteristics according to the nonlinear discrimination factor.
The distribution map of the structural damage diagnosis index before reconstruction in the three-dimensional european space is shown in fig. 9, and the distribution map of the structural damage diagnosis index after reconstruction in the three-dimensional european space is shown in fig. 10, and it is understood from the results of fig. 6 and 8, and fig. 9 and 10 that: compared with the structural damage diagnosis index which is not reconstructed, the amplitude fluctuation of the reconstruction index is smaller, the distribution trend of the reconstruction index in the three-dimensional Euclidean space is more obvious, and the distribution of the structural damage diagnosis index is more concentrated.

Claims (7)

1.一种非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述方法包括如下步骤：1. A method for reconstructing a local tangent space of a non-linear correlation structural damage diagnosis index, characterized in that the method comprises the following steps: 步骤一：采集桥梁结构在无损伤状态下的结构响应数据，建立参考状态的桥梁结构损伤诊断指标；Step 1: Collect the structural response data of the bridge structure in the non-damaged state, and establish the bridge structure damage diagnosis index in the reference state; 步骤二：利用步骤一所得的结构损伤诊断指标，绘制两个不同指标在二维欧式空间的分布图，判断结构损伤诊断指标是否存在非线性相关关系；Step 2: Using the structural damage diagnosis index obtained in step 1, draw a distribution diagram of two different indexes in the two-dimensional Euclidean space, and determine whether there is a nonlinear correlation between the structural damage diagnosis indexes; 步骤三：若对步骤二判定结构损伤诊断指标具备非线性相关关系，则根据非线性窄域特征的定义，建立结构损伤诊断指标的非线性窄域特征判别因子，判断结构损伤诊断指标是否具备非线性窄域特征；若判定结构损伤诊断指标不具备非线性相关关系，则不需要进行重构处理；Step 3: If the structural damage diagnosis index determined in step 2 has a nonlinear correlation, then according to the definition of the nonlinear narrow-area characteristic, the nonlinear narrow-area characteristic discriminant factor of the structural damage diagnosis index is established to determine whether the structural damage diagnosis index has a non-linear characteristic. Linear narrow domain features; if it is determined that the structural damage diagnosis index does not have a nonlinear correlation, reconstruction processing is not required; 步骤四：若对步骤三判定结构损伤诊断指标不具备非线性窄域特征，则采用局部切空间排列法提取结构损伤诊断指标的主要特征坐标矩阵；若判定结构损伤诊断指标具备非线性窄域特征，则不需要进行重构处理；Step 4: If it is determined in step 3 that the structural damage diagnosis index does not have nonlinear narrow-domain characteristics, the local tangent space arrangement method is used to extract the main feature coordinate matrix of the structural damage diagnosis index; if it is determined that the structural damage diagnosis index has nonlinear narrow-domain characteristics , no refactoring is required; 步骤五：利用步骤四所得的主要特征坐标矩阵，根据局部切空间排列法的逆运算，建立结构损伤诊断指标的重构指标；Step 5: Using the main feature coordinate matrix obtained in Step 4, according to the inverse operation of the local tangent space arrangement method, the reconstruction index of the structural damage diagnosis index is established; 步骤六：对步骤五所得的结构损伤诊断指标的重构指标，根据非线性窄域特征的定义，构建重构指标的非线性窄域特征判别因子，并判断重构指标是否具备非线性窄域特征；Step 6: For the reconstruction index of the structural damage diagnosis index obtained in Step 5, according to the definition of the nonlinear narrow domain feature, construct the nonlinear narrow domain feature discriminant factor of the reconstruction index, and judge whether the reconstruction index has the nonlinear narrow domain feature; 步骤七：若步骤六判定重构指标不具备非线性窄域特征，则重复步骤四至步骤五，再次对重构指标进行重构，若判定重构指标具备非线性窄域特征，则得到非线性相关结构损伤诊断指标的局部切空间重构方法作用下结构损伤诊断指标的重构指标。Step 7: If it is determined in step 6 that the reconstruction index does not have nonlinear narrow-domain characteristics, repeat steps 4 to 5, and reconstruct the reconstruction index again. If it is determined that the reconstruction index has nonlinear narrow-domain characteristics, the nonlinear Reconstruction index of structural damage diagnosis index under the action of local tangent space reconstruction method of relevant structural damage diagnosis index. 2.根据权利要求1所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤一中，建立参考状态的桥梁结构损伤诊断指标的具体步骤如下：2. The local tangent space reconstruction method of nonlinear correlation structural damage diagnosis index according to claim 1, it is characterized in that in described step 1, the concrete steps of establishing the bridge structure damage diagnosis index of reference state are as follows: 步骤一一：设桥梁结构响应数据矩阵为W1＝[ω1,ω2,…,ωk](ω1,ω2,…,ωk∈Rm×1)，k为监测数据样本数，m为测点数，ω为每个监测时刻下的结构响应数据向量，该结构响应数据矩阵包含结构加速度数据、应变数据、位移数据；Step 11: Set the bridge structural response data matrix as W 1 =[ω 1 ,ω 2 ,…,ω k ](ω 1 ,ω 2 ,…,ω k ∈R m×1 ), k is the number of monitoring data samples , m is the number of measuring points, ω is the structural response data vector at each monitoring time, and the structural response data matrix contains structural acceleration data, strain data, and displacement data; 步骤一二：利用随机子空间法对桥梁结构的加速度数据进行模态分析，利用所得的频率数据作为模态参数的结构损伤诊断指标；Step 1 and 2: use the random subspace method to carry out modal analysis on the acceleration data of the bridge structure, and use the obtained frequency data as the structural damage diagnosis index of the modal parameters; 步骤一三：利用低通滤波器和重采样技术对应变数据进行分析，建立应变响应的结构损伤诊断指标；Step 1 and 3: Use low-pass filter and resampling technology to analyze the strain data, and establish the structural damage diagnosis index of strain response; 步骤一四：利用低通滤波器和重采样技术对位移数据进行分析，建立位移响应的结构损伤诊断指标。Step 14: Use low-pass filter and resampling technology to analyze the displacement data, and establish the structural damage diagnosis index of displacement response. 3.根据权利要求1所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤二中，判断结构损伤诊断指标是否存在非线性相关关系的具体步骤如下：3. The method for reconstructing the local tangent space of the non-linear correlation structural damage diagnosis index according to claim 1, wherein in the step 2, the concrete steps of judging whether the structural damage diagnosis index has a non-linear correlation is as follows: 步骤二一：利用同一种类的结构损伤诊断指标，将该指标的不同维度间进行两两组合，在二维欧式空间内绘制两个不同维度结构损伤诊断指标的分布图；Step 21: Using the same type of structural damage diagnosis index, combine the different dimensions of the index in pairs, and draw a distribution map of the structural damage diagnosis indexes in two different dimensions in a two-dimensional Euclidean space; 步骤二二：根据步骤二一所得的结构损伤诊断指标的分布图，判断这些图中是否存在沿曲线趋势分布的分布特征，若存在沿曲线趋势分布的分布特征，则结构损伤诊断指标为非线性相关关系，若不存在沿曲线趋势分布的分布特征，则结构损伤诊断指标为线性相关关系。Step 22: According to the distribution diagrams of the structural damage diagnosis indicators obtained in Step 21, determine whether there are distribution characteristics along the curve trend distribution in these diagrams. If there are distribution characteristics along the curve trend distribution, the structural damage diagnosis indicators are nonlinear If there is no distribution characteristic along the trend distribution of the curve, the structural damage diagnosis index is a linear correlation. 4.根据权利要求1所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤三中，建立结构损伤诊断指标的非线性窄域特征判别因子，判断结构损伤诊断指标是否具备非线性窄域特征的具体步骤如下：4 . The method for reconstructing the local tangent space of the non-linear correlation structural damage diagnosis index according to claim 1 , wherein in the third step, a nonlinear narrow-domain characteristic discriminant factor of the structural damage diagnosis index is established to determine the structural damage. 5 . The specific steps for diagnosing whether the index has nonlinear narrow-domain characteristics are as follows: 步骤三一：给定非线性相关的结构损伤诊断指标
Figure FDA0003347667440000031
n为结构损伤诊断指标维数，利用k均值聚类方法将
Figure FDA0003347667440000032
与
Figure FDA0003347667440000033
聚类为p、q个类别，则第i维结构损伤诊断指标
Figure FDA0003347667440000034
的互信息计算公式为：Step 31: Given nonlinear correlation structural damage diagnosis index
Figure FDA0003347667440000031
n is the dimension of the structural damage diagnosis index, and the k-means clustering method is used to
Figure FDA0003347667440000032
and
Figure FDA0003347667440000033
Clustering into p and q categories, the i-th dimension structural damage diagnostic index
Figure FDA0003347667440000034
The formula for calculating mutual information is:
Figure FDA0003347667440000035
Figure FDA0003347667440000035
 式中，Pd(k)为
Figure FDA0003347667440000036
在p个聚类划分中的边缘概率分布，Pind(j)为
Figure FDA0003347667440000037
在q个聚类划分中的边缘概率分布，P(jk)为Φ在p×q个聚类分类下的联合概率分布；In the formula, P d (k) is
Figure FDA0003347667440000036
The marginal probability distribution in p cluster partitions, Pind (j) is
Figure FDA0003347667440000037
Marginal probability distribution in q clustering divisions, P(jk) is the joint probability distribution of Φ under p×q clustering classifications; 步骤三二：对第i维结构损伤诊断指标
Figure FDA0003347667440000038
的互信息进行标准化处理，建立损伤诊断指标的结构非线性窄域特征判别因子ρ：Step 32: Diagnosing the damage of the i-th dimensional structure
Figure FDA0003347667440000038
The mutual information is standardized, and the structural nonlinear narrow-domain characteristic discriminant factor ρ of the damage diagnosis index is established:
Figure FDA0003347667440000039
Figure FDA0003347667440000039
 步骤三三：判定结构损伤诊断指标的非线性窄域特征，若ρ≥0.7，则判定该结构损伤诊断指标具有非线性窄域特征；若ρ＜0.7，则判定该结构损伤诊断指标不具有非线性窄域特征。Step 33: Determine the nonlinear narrow-domain feature of the structural damage diagnosis index. If ρ≥0.7, it is determined that the structural damage diagnosis index has nonlinear narrow-domain characteristics; if ρ<0.7, it is determined that the structural damage diagnosis index does not have non-linear characteristics. Linear narrow domain features. 5.根据权利要求1所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤四中，采用局部切空间排列法提取结构损伤诊断指标的主要特征坐标矩阵的具体步骤如下：5. The method for reconstructing the local tangent space of the non-linear correlation structural damage diagnosis index according to claim 1, wherein in the step 4, the local tangent space arrangement method is used to extract the main characteristic coordinate matrix of the structural damage diagnosis index. Specific steps are as follows: 步骤四一：给定N个不具备非线性窄域特征的结构损伤诊断指标构成指标集合为
Figure FDA0003347667440000041
X＝[x1,x2,…,xi,…,xN],i∈(1,2,…,N)，n为结构损伤诊断指标维数，N为指标数量，构建第i个指标xi的k个邻域点集合，建立邻域矩阵：Step 41: Given N structural damage diagnosis indicators that do not have nonlinear narrow domain characteristics, the index set is:
Figure FDA0003347667440000041
X=[x 1 ,x 2 ,…,x i ,…,x N ],i∈(1,2,…,N), n is the dimension of structural damage diagnosis indicators, N is the number of indicators, construct the i-th Sets of k neighborhood points of index x i to establish neighborhood matrix: Ωi＝[xi1,xi2…,xik]；Ω i =[x i1 ,x i2 …,x ik ]; 步骤四二：将非线性相关的结构损伤诊断指标作为非线性流形，利用线性流形表示非线性流形，建立该非线性流形的d维线性流形：Step 42: Take the nonlinear related structural damage diagnosis index as the nonlinear manifold, use the linear manifold to represent the nonlinear manifold, and establish the d-dimensional linear manifold of the nonlinear manifold:
Figure FDA0003347667440000042
Figure FDA0003347667440000042
 其中，d<n，xij为第i个损伤诊断指标的第j个邻域，1k为全1的列向量，θj为Θ中的第j个列向量，P为转换矩阵；Among them, d<n, x ij is the j-th neighborhood of the i-th damage diagnosis index, 1 k is the column vector of all 1s, θ j is the j-th column vector in Θ, and P is the transformation matrix; 步骤四三：根据奇异值分量理论，建立第i个指标的邻域矩阵在线性流形的局部坐标，通过对每个指标的邻域矩阵所得局部坐标进行有序排列，建立结构损伤诊断指标的主要特征坐标矩阵。Step 43: According to the singular value component theory, establish the local coordinates of the neighborhood matrix of the ith index on the linear manifold, and establish the structural damage diagnosis index by orderly arranging the local coordinates obtained by the neighborhood matrix of each index. The main eigencoordinate matrix. 6.根据权利要求5所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤四三中，建立第i个指标的邻域矩阵在线性流形的局部坐标和结构损伤诊断指标的主要特征坐标矩阵的具体步骤如下：6. The method for reconstructing the local tangent space of a non-linear correlation structural damage diagnosis index according to claim 5, wherein in the step 4 and 3, the neighborhood matrix of the ith index is established at the local coordinates of the linear manifold The specific steps of the main characteristic coordinate matrix of the structural damage diagnosis index are as follows: (1)：根据步骤四一所得的邻域矩阵，建立中心化的邻域矩阵：(1): According to the neighborhood matrix obtained in step 41, establish a centralized neighborhood matrix:
Figure FDA0003347667440000051
Figure FDA0003347667440000051
 式中，
Figure FDA0003347667440000052
为邻域矩阵Ωi的中心点；In the formula,
Figure FDA0003347667440000052
is the center point of the neighborhood matrix Ω i ; (2)：根据奇异值分量理论，对中心化的邻域矩阵进行奇异值分解，建立该邻域矩阵的奇异向量矩阵：(2): According to the singular value component theory, perform singular value decomposition on the centralized neighborhood matrix, and establish the singular vector matrix of the neighborhood matrix:
Figure FDA0003347667440000053
Figure FDA0003347667440000053
 式中，pi1为左奇异向量，pin为左奇异向量，pid为左奇异向量，
Figure FDA0003347667440000054
为奇异值，
Figure FDA0003347667440000055
为奇异值，
Figure FDA0003347667440000056
为奇异值，vi1为右奇异向量，vik为右奇异向量，vid为右奇异向量；where p i1 is the left singular vector, p in is the left singular vector, p id is the left singular vector,
Figure FDA0003347667440000054
is a singular value,
Figure FDA0003347667440000055
is a singular value,
Figure FDA0003347667440000056
is a singular value, v i1 is a right singular vector, v ik is a right singular vector, and v id is a right singular vector; (3)：根据(2)所得的奇异向量矩阵，建立第i指标的邻域矩阵在线性流形的局部坐标：(3): According to the singular vector matrix obtained in (2), establish the local coordinates of the neighborhood matrix of the i-th index on the linear manifold:
Figure FDA0003347667440000057
Figure FDA0003347667440000057
 式中，Pi为最大的d个奇异值对应的左奇异向量构成的矩阵；In the formula, P i is the matrix formed by the left singular vectors corresponding to the largest d singular values; (4)：采用极小化误差方式最大程度保存第i个指标的邻域矩阵所包含的非线性流形特征，建立极小化误差方程：(4): The nonlinear manifold feature contained in the neighborhood matrix of the ith index is preserved to the greatest extent by the method of minimizing error, and the minimizing error equation is established:
Figure FDA0003347667440000061
Figure FDA0003347667440000061
Figure FDA0003347667440000062
Figure FDA0003347667440000062
Figure FDA0003347667440000063
Figure FDA0003347667440000063
 式中，Ti为全局坐标，Si为选择矩阵，
Figure FDA0003347667440000064
从N个指标集合中选择出第i个结构损伤诊断指标的k个邻域点；where T i is the global coordinate, S i is the selection matrix,
Figure FDA0003347667440000064
Select k neighborhood points of the i-th structural damage diagnosis index from the N index sets; (5)：求解矩阵Ψ的特征值与特征向量，并根据数值大小，对特征值进行从小到大排列，同时特征值所对应的特征向量也进行排序，其中的第2到第d+1个特征向量即是全局坐标Ti。(5): Solve the eigenvalues and eigenvectors of the matrix Ψ, and arrange the eigenvalues from small to large according to the size of the values. At the same time, the eigenvectors corresponding to the eigenvalues are also sorted, among which the 2nd to the d+1th The eigenvectors are the global coordinates T i . 7.根据权利要求1所述的非线性相关结构损伤诊断指标的局部切空间重构方法，其特征在于所述步骤五中，建立结构损伤诊断指标的重构指标的具体步骤如下：7. The method for reconstructing the local tangent space of the non-linear correlation structural damage diagnosis index according to claim 1, wherein in the step 5, the specific steps of establishing the reconstruction index of the structural damage diagnosis index are as follows: 步骤五一：根据步骤四所得的结构损伤诊断指标的主要特征坐标矩阵，建立局部仿射变换矩阵：Step 51: According to the main feature coordinate matrix of the structural damage diagnosis index obtained in step 4, establish a local affine transformation matrix: Γi＝TiTi +；Γ i =T i T i + ; 步骤五二：根据局部切空间排列法的逆运算，建立结构损伤诊断指标的重构指标：Step 52: According to the inverse operation of the local tangent space arrangement method, the reconstruction index of the structural damage diagnosis index is established:
Figure FDA0003347667440000065
Figure FDA0003347667440000065
 式中，
Figure FDA0003347667440000066
为第i个结构损伤诊断指标的重构指标，
Figure FDA0003347667440000067
为第i个结构损伤诊断指标邻域矩阵Ωi的中心点，ti为第i个结构损伤诊断指标的全局坐标。In the formula,
Figure FDA0003347667440000066
is the reconstruction index of the ith structural damage diagnosis index,
Figure FDA0003347667440000067
is the center point of the neighborhood matrix Ω i of the ith structural damage diagnosis index, and t i is the global coordinate of the ith structural damage diagnosis index.
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