CN114048678B - 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 PDFInfo
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Abstract
The invention discloses 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. The method solves the problem that under the influence of complex environment, the nonlinear related structural damage diagnosis index does not have the nonlinear narrow-range characteristic, so that the accuracy of the piecewise linearization of the damage diagnosis index is low.
Description
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.
Drawings
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 、f 2 、f 3 ) Time-course diagram of (c).
FIG. 7 shows structural damage diagnosis indicators (f) 1 、f 2 ) Distribution map in two-dimensional Euclidean space.
FIG. 8 shows a reconstruction index (f) of the structural damage diagnosis index 1 、f 2 、f 3 ) 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 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, 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
n is structural damage diagnosis index dimension, and k means clustering method is used for calculating the structural damage diagnosis index dimension
And
clustering into p and q categories, and then diagnosing the damage of the ith dimension structure
The mutual information calculation formula is as follows:
in the formula, P d (k) Is composed of
Edge probability distribution in P cluster partitions, P ind (j) Is composed of
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
The mutual information is standardized, and a structural nonlinear narrow-range feature discrimination factor rho of the damage diagnosis index is established:
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: n structural damage diagnosis indexes without nonlinear narrow-range characteristics are given as a construction index set
X＝[x 1 ,x 2 ,…,x i ,…,x N ]I belongs to (1,2, …, N), N is structural damage diagnosis index dimension, N is index number, and the ith index x is constructed i The k neighborhood point sets are used for establishing a neighborhood matrix:
Ω i ＝[x i1 ,x i2 …,x ik ] (3)；
step four and step two: taking a structural damage diagnosis index related to nonlinearity as a nonlinear manifold, representing the nonlinear manifold by using a linear manifold, and establishing a d-dimension (d < n, n is a structural damage diagnosis index dimension) linear manifold of the nonlinear manifold:
in the formula, x ij For the jth neighborhood of the ith lesion diagnostic index, 1 k Column vector of all 1, θ j Is the jth column vector in theta, and P is the conversion 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:
in the formula (I), the compound is shown in the specification,
is a neighborhood matrix omega i A 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:
in the formula, p i1 As left singular vectors, p in As left singular vector, p id In the form of the left singular vector,
in the form of the singular values of the signals,
in the form of the singular values of the signals,
is a singular value, v i1 Is the right singular vector, v ik Is the right singular vector, v id Is 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):
in the formula, P i A 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:
in the formula, T i As global coordinates, S i In order to select the matrix, the matrix is selected,
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, and arranging the eigenvalue from small to large according to the magnitude of the numerical value, and simultaneously, the eigenvector corresponding to the eigenvalue also entersLine ordering, in which the 2 nd to d +1 th eigenvectors are the global coordinates T i 。
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:
Γ i ＝T i T i + (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:
in the formula (I), the compound is shown in the specification,
is a reconstruction index of the ith structural damage diagnosis index,
neighborhood matrix omega for ith structural damage diagnosis index i Center point of (d), t i Is 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 method comprises the steps of adding 10% of white noise interference into the first 3-order natural vibration frequency of a three-span continuous rigid frame bridge structure in a non-damage state within one year, and establishing a structural damage diagnosis index of the bridge in a reference state (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 (6)
1. A local tangent space reconstruction method of a nonlinear correlation structural damage diagnosis index is characterized by comprising 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-area characteristic, reconstruction processing is not needed, wherein 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: n structural damage diagnosis indexes without nonlinear narrow-range characteristics are given as a construction index set
X＝[x 1 ,x 2 ,…,x i ,…,x N ]I belongs to (1,2, …, N), N is structural damage diagnosis index dimension, N is index number, and the ith index x is constructed i The k neighborhood point sets are used for establishing a neighborhood matrix:
Ω i ＝[x i1 ,x i2 …,x ik ]；
step four and step two: taking a structural damage diagnosis index related to nonlinearity as a nonlinear manifold, expressing the nonlinear manifold by using a linear manifold, and establishing a d-dimensional linear manifold of the nonlinear manifold:
wherein d is<n，x ij For the jth neighborhood of the ith lesion diagnostic index, 1 k Column vector of all 1, θ j Is 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 main characteristic coordinate matrixes of the structural damage diagnosis indexes are established by orderly arranging the local coordinates obtained by the neighborhood matrix of each index;
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.
2. The method for reconstructing the local tangent space of the nonlinear correlation structural damage diagnosis index according to claim 1, wherein in the step one, the specific steps of establishing the bridge structural damage diagnosis index in the reference state are as follows:
the method comprises the following steps: setting the bridge structure 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, 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.
3. The method for reconstructing a local tangent space of a structural damage diagnosis index based on nonlinear correlation according to claim 1, wherein in the second step, the specific step of determining whether the structural damage diagnosis index has nonlinear correlation is 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.
4. The method for reconstructing a local slice space of a structural damage diagnosis indicator according to claim 1, wherein in the third step, a nonlinear narrow-area feature discrimination factor of the structural damage diagnosis indicator is established, and the specific steps for determining whether the structural damage diagnosis indicator has a nonlinear narrow-area feature are as follows:
step three, firstly: given a non-linearly related structural damage diagnostic index
n is structural damage diagnosis index dimension, and k means clustering method is used for calculating the structural damage diagnosis index dimension
And
clustering into p and q categories, and then diagnosing the damage of the ith dimension structure
The mutual information calculation formula is as follows:
in the formula, P d (k) Is composed of
Edge probability distribution in P cluster partitions, P ind (j) Is composed of
Edge profile in q cluster partitions(jk) is the joint probability distribution of Φ under p × q cluster classifications;
step three: diagnosis index for i-dimensional structural damage
The mutual information is standardized, and a structural nonlinear narrow-range feature discrimination factor rho of the damage diagnosis index is established:
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.
5. The method according to claim 1, wherein in the fourth step and 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:
in the formula (I), the compound is shown in the specification,
is a neighborhood matrix omega i A 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:
in the formula, p i1 As left singular vectors, p in As left singular vectors, p id In the form of the left singular vector,
in the form of the singular values of the signals,
in the form of the singular values of the signals,
is a singular value, v i1 Is the right singular vector, v ik Is the right singular vector, v id Is 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):
in the formula, P i A 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:
in the formula, T i As global coordinates, S i In order to select the matrix, the matrix is selected,
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 T i 。
6. The method according to claim 1, wherein in the step five, 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:
Γ i ＝T i T i + ；
in the formula, T i Is a global coordinate;
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:
in the formula (I), the compound is shown in the specification,
is a reconstruction index of the ith structural damage diagnosis index,
neighborhood matrix omega for ith structural damage diagnosis index i Center point of (d), t i As global coordinate of the ith structural damage diagnostic index, P i And a matrix formed by left singular vectors corresponding to the largest d singular values.
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