CN110455399B - Method for carrying out global early warning on building structure vibration by using distributed optical fiber - Google Patents

Method for carrying out global early warning on building structure vibration by using distributed optical fiber Download PDF

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CN110455399B
CN110455399B CN201910738963.4A CN201910738963A CN110455399B CN 110455399 B CN110455399 B CN 110455399B CN 201910738963 A CN201910738963 A CN 201910738963A CN 110455399 B CN110455399 B CN 110455399B
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optical fiber
building structure
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CN110455399A (en
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曾滨
许庆
邵彦超
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Central Research Institute of Building and Construction Co Ltd MCC Group
China Jingye Engineering Corp Ltd
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Central Research Institute of Building and Construction Co Ltd MCC Group
China Jingye Engineering Corp Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
    • G01H9/004—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means using fibre optic sensors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
    • G01M7/02—Vibration-testing by means of a shake table
    • G01M7/025—Measuring arrangements
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention discloses a method for carrying out global early warning on building structure vibration by using a distributed optical fiber, which comprises the following steps: collecting vibration on a building structure by using a distributed optical fiber; secondly, calculating the eigenvalue and the eigenvector of the data matrix X in a high-dimensional nuclear space; (III) calculating statistic T2A control limit of (d); (IV) judging the test set xtestWhether the building structure vibration state is early-warned or not is judged, the method is used as a KPI index for representing the whole building structure vibration state, through test classification analysis of examples, the algorithm has better anti-interference performance and classification accuracy in building structure vibration monitoring compared with the traditional PCA algorithm, the dimensionality of a high-dimensional space feature matrix is effectively reduced, the calculation overhead of statistics is effectively reduced, the purpose of state whole representation is achieved, the number of high-dimensional space principal elements of the algorithm is less, the principal element contribution rate is higher, nonlinear factors in optical fiber vibration are better distinguished, and the whole monitored representation is more accurate.

Description

Method for carrying out global early warning on building structure vibration by using distributed optical fiber
Technical Field
The invention relates to a structural vibration global early warning method based on a distributed optical fiber, in particular to a method for performing global early warning by combining historical vibration data of a building structure with a kernel principal component analysis method prediction model.
Background
Monitoring and early warning are carried out on the vibration characteristics of the building structure, the traditional mode position analyzes the mode of the specified building component, a professional technician is required to use the complex mathematical model after training, the operation is very time-consuming, and the overall description and early warning are not easy to be carried out on the overall vibration situation of the building. Aiming at the problem, a building structure vibration prediction method which is easy to operate, all-area and high in calculation speed is urgently needed.
The building structure needs to perform statistical description on the vibration state of the structure under vibration conditions of machinery, environment, pipelines and the like, gives early warning on possible adverse changes, provides technical support for safety early warning and the like, introduces a kernel principal component analysis model, can effectively store nonlinear information in optical fiber signals, calculates a statistic threshold value by combining historical distributed optical fiber vibration data, and performs vibration monitoring.
Chinese patent CN201310072577 discloses a fault prediction method and system, but the above patent does not describe a sample collection and processing method, and its application scenario focuses on vibration fault identification and prediction of large machinery.
Chinese patent CN201510243981 discloses a prediction method for horizontal distribution of an ohyolite fissure water network, in the above patent, the adopted collected samples are n × 5 matrixes consisting of fault influence factors, fault dimension values, fold dimension values, abnormal change values of ohyolite temperature and 5 indexes of frightened ohyolite drilling water inflow, and the emphasis is to describe the correlation of 5 index changes in time dimension.
Chinese patent CN201510290378 discloses a KPCA-based industrial process fault diagnosis method, which is used for analyzing normal production data in the smelting production process of an electric smelting magnesium furnace, wherein the normal production data comprises an n × 4 matrix consisting of current, voltage, relative positions between electrodes and 4 indexes of the temperature of the electric smelting magnesium furnace, and the emphasis is on describing the correlation of 4 index changes in the time dimension.
The single acquisition sample is a set of 400-4000 acquisition point signals on the distributed optical fiber, and the invention creates a global description of the building structure by the global distribution of the spatial dimension.
Disclosure of Invention
The invention aims to provide a global early warning method for a vibration state of a building structure.
In order to achieve the purpose of the invention, the following technical scheme is adopted in the application:
the invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: it comprises the following steps:
collecting vibration on a building structure by using a distributed optical fiber:
the optical fiber is continuously and fixedly arranged on the surface of the building structure, one end of the optical fiber is connected with the phase optical time domain reflectometer equipment,acquiring optical fiber signals, wherein n acquisition points are arranged on an optical fiber, each acquisition point is smoothly sampled by taking the frequency of H per second as the frequency, distributed optical fiber original vibration signals of n point positions are obtained, data acquired by each point position are curves changing along time, acquired signals are n-dimensional data matrixes, each sampling value of each acquisition point is spAnd carrying out averaging processing on the original signal of each acquisition point every 1 second, wherein the signal average value of the point is as follows:
Figure GDA0002440247530000021
wherein
Figure GDA0002440247530000022
For one sample of the entire fiber, i m, m > n after m seconds, resulting in an mxn data matrix X { X ═ n1，x2，x3…xn}∈Rm×n；
(II) calculating the eigenvalue and the eigenvector of the data matrix X in the high-dimensional nuclear space:
(1) for the data matrix X belongs to Rm×nPerforming normalization, wherein n is the number of samples, and m is the dimension of the samples:
composing X from the mean value of each column of the original data matrixmeanMatrix:
Figure GDA0002440247530000023
wherein XmeanIs a matrix with 1 row and n columns,
calculating the variance component X of the original data matrixstdMatrix:
Figure GDA0002440247530000024
wherein i is 1, 2, 3 … m,
Figure GDA0002440247530000025
is the average of the j columns; from XstdiM data of (2) constitute XstdMatrix, XstdIs a matrix of m rows and 1 column,
calculating a raw data matrix normalization matrix:
X0＝(X-Im×1·Xmean)./(Im×1·Xstd)
in the formula Im×1A unit vector of m × 1 dimensions; the operator is each element a in the previous matrixijWith the corresponding element b in the latter matrixijIs divided by X0A matrix of m × n;
(2) a matrix X of m × n0Conversion to mxm K matrix and centered matrix
Figure GDA0002440247530000026
Using formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) Calculating the m × n matrix X0Ith row vector X of0(i,: and j) th row vector X0(j,: wherein i is 1 to m, j is 1 to m, and σ is 1 to 20000) and calculating the obtained KijFilling the K matrix of m multiplied by m;
carrying out normalization processing on the K matrix to obtain a centralized matrix:
Figure GDA0002440247530000031
wherein, ImIs an identity matrix of dimension m x m, i.e. all elements are 1,
Figure GDA0002440247530000032
is ImThe transposed matrix of (2);
(3) and calculating to obtain a high-dimensional space characteristic value lambda and a characteristic vector P of the original data:
according to the formula:
Figure GDA0002440247530000033
to obtain
Figure GDA0002440247530000034
And will beIts characteristic value lambdaKArranged from large to small to obtain lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmWherein Λ ismIs a unit diagonal matrix of m x m dimensions, i.e., the diagonal elements of the matrix are 1, the remaining elements are 0,
respectively will be lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmξ in1，ξ2，ξ3，…，ξmSubstituting into formula
Figure GDA0002440247530000035
In (b) to obtain λKCorresponding to
Figure GDA0002440247530000036
Characteristic vector vK＝[υ1，υ2，υ3，…υm]T
Calculating to obtain the high-dimensional space characteristic value lambda of the original data as { lambda ═ lambda1，λ2，λ3…λmAnd a feature vector P ═ P1，p2，p3，…pm]Tλ is a one-dimensional matrix composed of m eigenvalue numbers; p is a feature matrix composed of m feature vectors,
Figure GDA0002440247530000037
(III) calculating statistic T2Control limit of (2):
according to λ ═ { λ1，λ2，λ3…λmSelecting the first k values of the characteristic values in the data structurek＝{λ1，λ2，λ3…λkSatisfy the conditions
Figure GDA0002440247530000038
Wherein β e (0, 1)]For the contribution ratio, a value of 0.80, 0.85, 0.90, 0.95, 0.98 or 0.99 is usually used, corresponding to Pk＝[p1，p2，p3，…pk]T
Using Hotelling T2Computing statistics using (k, m-k) degrees of freedom and a confidence level of α ∈ (0, 1)]F distribution of (d), calculating a statistic T by the following formula2Control limit of (2):
Figure GDA0002440247530000041
(IV) judging the test set xtestWhether to early warn:
collecting test set x on the building structure by using the optical fiber of the step (I)test，xtestIs a 1 Xn one-dimensional matrix, and x is calculated by using the parameters in the step (II)testIs normalized by the matrix
Figure GDA0002440247530000042
Figure GDA0002440247530000043
Is a 1 Xn one-dimensional matrix, and further obtains a mapping matrix of a high-dimensional kernel space
Figure GDA0002440247530000044
For 1 × n matrix
Figure GDA0002440247530000045
Vector and matrix X of0Ith row vector X of0(i,: the difference is calculated, i is selected from 1 to m, xK_testA one-dimensional matrix of 1 × m, formed by matrix xK_testCalculating a centralized mapping matrix
Figure GDA0002440247530000046
Figure GDA0002440247530000047
Wherein, ImIs an identity matrix of m x m dimensions, ItestIs a one-dimensional unit matrix of 1 × m dimensions, i.e., all elements are 1, and is calculated according to the following formula
Figure GDA0002440247530000048
Figure GDA0002440247530000049
Lambda is a one-dimensional matrix consisting of m eigenvalue numbers; p is a feature matrix consisting of m eigenvectors, ΛmIs an m x m dimensional unit diagonal matrix,
Figure GDA00024402475300000410
is composed of
Figure GDA00024402475300000411
Transposing a matrix; when in use
Figure GDA00024402475300000412
And judging the occurrence of abnormity and alarming.
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: in the fiber, there is one collection point every 0.05-1 meter.
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: the number of the n acquisition points is 400-4000.
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: the transpose matrix is the column that transforms the rows in the original matrix into the transpose matrix.
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: said formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) Is a matrix X of m × n0Ith row vector X of0(i,: and j) th row vector X0(j, wherein j is 1 to m) and calculating the calculated KijFilling the K matrix of m multiplied by m; then selecting i from 1 to m, repeating the operation, and calculating the calculated KijFilling into an m × m K matrix.
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps: the same characters represent the same meanings, and the values of σ are the same in the steps (one) to (four).
The method for carrying out global early warning on the vibration of the building structure by using the distributed optical fiber is used as a KPI (Key performance indicator) for representing the whole vibration state of the building structure. Through test classification analysis of the example, compared with the traditional PCA algorithm, the algorithm has better anti-interference performance and classification accuracy in building structure vibration monitoring, the dimension of a high-dimensional space characteristic matrix is effectively reduced, the calculation cost of statistics is effectively reduced, the purpose of state integral representation is achieved, the number of high-dimensional space principal elements of the algorithm is less, the principal element contribution rate is higher, nonlinear factors in optical fiber vibration are better distinguished, and the integral representation of the whole monitoring is more accurate.
Drawings
FIG. 1 is a graph obtained by a conventional method.
FIG. 2 is a graph of the global warning of building structure vibrations using a distributed optical fiber according to the present invention;
Detailed Description
The invention discloses a method for carrying out global early warning on building structure vibration by using distributed optical fibers, which comprises the following steps:
collecting vibration on a building structure by using a distributed optical fiber:
the optical fiber is continuously and fixedly placed on the surface of a building structure, one end of the optical fiber is connected with phase light time domain reflectometer equipment to collect optical fiber signals, n collection points are arranged on the optical fiber, one collection point is arranged every 0.05-1 meter, and 400-4000 collection points are selected. Smoothly sampling each acquisition point by taking the frequency of H per second to obtain distributed optical fiber original vibration signals of n point positions, wherein the data acquired by each point position is a curve which changes along with time, the acquired signals are n-dimensional data matrixes, and each sampling value of each acquisition point is spAnd carrying out averaging processing on the original signal of each acquisition point every 1 second, wherein the signal average value of the point is as follows:
Figure GDA0002440247530000051
wherein
Figure GDA0002440247530000052
For one sample of the entire fiber, i m, m > n after m seconds, resulting in an mxn data matrix X { X ═ n1，x2，x3…xn}∈Rm×n；
(II) calculating the eigenvalue and the eigenvector of the data matrix X in the high-dimensional nuclear space:
(1) for the data matrix X belongs to Rm×nPerforming normalization, wherein n is the number of samples, and m is the dimension of the samples:
composing X from the mean value of each column of the original data matrixmeanMatrix:
Figure GDA0002440247530000053
wherein XmeanIs a matrix of 1 row and n columns
Calculating the variance component X of the original data matrixstdMatrix:
Figure GDA0002440247530000061
wherein i is 1, 2, 3 … m,
Figure GDA0002440247530000062
is the average of the j columns; from XstdiM data of (2) constitute XstdMatrix, XstdIs a matrix of m rows and 1 column,
calculating a raw data matrix normalization matrix:
X0＝(X-Im×1·Xmean)./(Im×1·Xstd)
in the formula Im×1A unit vector of m × 1 dimensions; the operator is each element a in the previous matrixijWith the corresponding element b in the latter matrixijIs divided by X0A matrix of m × n;
(2) mixing m × nMatrix X0Conversion to mxm K matrix and centered matrix
Figure GDA0002440247530000063
Using formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) For m × n matrix X0Ith row vector X of0(i,: and j) th row vector X0(j,: wherein i is selected from 1 to m, j is selected from 1 to m, and σ is between 1 and 20000, for example, σ is 2000, formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) Is a matrix X of m × n0Ith row vector X of0(i,: and j) th row vector X0(j, wherein j is 1 to m) and calculating the calculated KijFilling the K matrix of m multiplied by m; then selecting i from 1 to m, repeating the operation, and calculating the calculated KijFilling the K matrix of m multiplied by m;
carrying out normalization processing on the K matrix to obtain a centralized matrix:
Figure GDA0002440247530000064
wherein, ImIs an identity matrix of dimension m x m, i.e. all elements are 1,
Figure GDA0002440247530000065
is ImThe transposed matrix of (2) is a matrix obtained by converting rows in the original matrix into columns of the transposed matrix;
(3) and calculating to obtain a high-dimensional space characteristic value lambda and a characteristic vector P of the original data:
according to the formula:
Figure GDA0002440247530000066
to obtain
Figure GDA0002440247530000067
And the characteristic value thereof is calculatedλKArranged from large to small to obtain lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmWherein Λ ismIs a unit diagonal matrix of m x m dimensions, i.e., the diagonal elements of the matrix are 1, the remaining elements are 0,
respectively will be lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmξ in1，ξ2，ξ3，…，ξmSubstituting into formula
Figure GDA0002440247530000068
In (b) to obtain λKCorresponding to
Figure GDA0002440247530000069
Characteristic vector vK＝[υ1，υ2，υ3，…υm]T
Calculating to obtain the high-dimensional space characteristic value lambda of the original data as { lambda ═ lambda1，λ2，λ3…λmAnd a feature vector P ═ P1，p2，p3，…pm]Tλ is a one-dimensional matrix composed of m eigenvalue numbers; p is a feature matrix composed of m feature vectors,
Figure GDA0002440247530000071
(III) calculating statistic T2Control limit of
According to λ ═ { λ1，λ2，λ3…λmSelecting the first k values of the characteristic values in the data structurek＝{λ1，λ2，λ3…λkSatisfy the conditions
Figure GDA0002440247530000072
Wherein β e (0, 1)]For the contribution ratio, a value of 0.80, 0.85, 0.90, 0.95, 0.98 or 0.99 is usually used, corresponding to Pk＝[p1，p2，p3，…pk]T
Using Hotelling T2Computing statistics using (k, m-k) degrees of freedom and a confidence level of α ∈ (0, 1)]F distribution of (d), calculating a statistic T by the following formula2Control limit of (2):
Figure GDA0002440247530000073
wherein FαWhich can be obtained by table look-up, resulting in the dashed line in figure 2,
(IV) judging the test set xtestWhether to give an early warning
Collecting test set x on the building structure by using the optical fiber of the step (I)test，xtestIs a 1 Xn one-dimensional matrix, and x is calculated by using the parameters in the step (II)testIs normalized by the matrix
Figure GDA0002440247530000074
Figure GDA0002440247530000075
Is a 1 Xn one-dimensional matrix, and further obtains a mapping matrix of a high-dimensional kernel space
Figure GDA0002440247530000076
For 1 × n matrix
Figure GDA0002440247530000077
Vector and matrix X of0Ith row vector X of0(i) the difference is calculated, i is selected from 1 to m, x is definedK_testA one-dimensional matrix of 1 × m, formed by matrix xK_testCalculating a centralized mapping matrix
Figure GDA0002440247530000078
Figure GDA0002440247530000079
Wherein, ImIs an identity matrix of m x m dimensions, ItestIs a one-dimensional unit matrix of 1 × m dimensions, i.e., all elements are 1, and is calculated according to the following formula
Figure GDA00024402475300000710
Figure GDA00024402475300000711
Lambda is a one-dimensional matrix consisting of m eigenvalue numbers; p is a feature matrix consisting of m eigenvectors, ΛmIs an m x m dimensional unit diagonal matrix,
Figure GDA0002440247530000081
is composed of
Figure GDA0002440247530000082
Transposing a matrix; when in use
Figure GDA0002440247530000083
And judging the occurrence of abnormity and alarming.
It should be noted that, in the above steps, the same characters represent the same meanings, and the values of σ are the same in the steps (one) to (four).
Calculating T of 1-755 seconds by using the method of the step (four)2Obtaining the curve of 1-755 seconds in figure 2, wherein the point of the curve 1-755 seconds is in the normal working interval, the detection value is after 756 points, and when the curve of the detection value after 756 seconds point is abnormal and exceeds the threshold Line (T)2) And when so, giving an alarm. The 755 seconds mentioned above is used as an example only, and in practice the number of seconds of sample acquisition is much greater than 755 seconds. FIG. 1 shows the T calculated by the conventional PCA method2Curves with false alarm times of 6 in 1-755 seconds, FIG. 2 shows T obtained by the method of the present invention2Curves with 2 false positives from 1-755 seconds. It is thus seen that: the method has obvious advantages in the aspects of preventing false alarm times under normal monitoring conditions, removing nonlinear influence and the like.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.

Claims (6)

1. A method for carrying out global early warning on building structure vibration by using a distributed optical fiber is characterized by comprising the following steps: it comprises the following steps:
collecting vibration on a building structure by using a distributed optical fiber:
the optical fiber is continuously and fixedly placed on the surface of a building structure, one end of the optical fiber is connected with phase optical time domain reflectometer equipment to collect optical fiber signals, n collection points are arranged on the optical fiber, smooth sampling is carried out on each collection point by taking the frequency of every second as H frequency to obtain distributed optical fiber original vibration signals of n point positions, data collected by each point position is a curve which changes along with time, the collected signals are n-dimensional data matrixes, and each sampling value of each collection point is spAnd carrying out averaging processing on the original signal of each acquisition point every 1 second, wherein the signal average value of the point is as follows:
Figure FDA0002440247520000011
wherein
Figure FDA0002440247520000012
For one sample of the entire fiber, i m, m > n after m seconds, resulting in an mxn data matrix X { X ═ n1，x2，x3…xn}∈Rm×n；
(II) calculating the eigenvalue and the eigenvector of the data matrix X in the high-dimensional nuclear space:
(1) for the data matrix X belongs to Rm×nPerforming normalization, wherein n is the number of samples, and m is the dimension of the samples:
composing X from the mean value of each column of the original data matrixmeanMatrix:
Figure FDA0002440247520000013
wherein XmeanIs a matrix with 1 row and n columns,
calculating the variance component X of the original data matrixstdMatrix:
Figure FDA0002440247520000014
wherein i is 1, 2, 3 … m,
Figure FDA0002440247520000015
is the average of the j columns; from XstdiM data of (2) constitute XstdMatrix, XstdIs a matrix of m rows and 1 column,
calculating a raw data matrix normalization matrix:
X0＝(X-Im×1·Xmean)./(Im×1·Xstd)
in the formula Im×1A unit vector of m × 1 dimensions; the operator is each element a in the previous matrixijWith the corresponding element b in the latter matrixijIs divided by X0A matrix of m × n;
(2) a matrix X of m × n0Conversion to mxm K matrix and centered matrix
Figure FDA0002440247520000021
Using formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) For m × n matrix X0Ith row vector X of0(i,: and j) th row vector X0(j,: wherein i is selected from 1 to m, j is selected from 1 to m, and σ is 1 to 20000) and calculating KijFilling the K matrix of m multiplied by m;
carrying out normalization processing on the K matrix to obtain a centralized matrix:
Figure FDA0002440247520000022
wherein, ImIs m x m dimensionI.e., all elements are 1,
Figure FDA0002440247520000023
is ImThe transposed matrix of (2);
(3) and calculating to obtain a high-dimensional space characteristic value lambda and a characteristic vector P of the original data:
according to the formula:
Figure FDA0002440247520000024
to obtain
Figure FDA0002440247520000025
And its eigenvalue λKArranged from large to small to obtain lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmWherein Λ ismIs a unit diagonal matrix of m x m dimensions, i.e., the diagonal elements of the matrix are 1, the remaining elements are 0,
respectively will be lambdaK＝{ξ1≥ξ2≥ξ3≥…≥ξmξ in1，ξ2，ξ3，…，ξmSubstituting into formula
Figure FDA0002440247520000026
In (b) to obtain λKCorresponding to
Figure FDA0002440247520000027
Characteristic vector vK＝[υ1，υ2，υ3，…υm]T，
Calculating to obtain the high-dimensional space characteristic value lambda of the original data as { lambda ═ lambda1，λ2，λ3…λmAnd a feature vector P ═ P1，p2，p3，…pm]Tλ is a one-dimensional matrix composed of m eigenvalue numbers; p is a feature matrix composed of m feature vectors,
Figure FDA0002440247520000028
(III) calculating statistic T2Control limit of (2):
according to λ ═ { λ1，λ2，λ3…λmSelecting the first k values of the characteristic values in the data structurek＝{λ1，λ2，λ3…λkSatisfy the conditions
Figure FDA0002440247520000029
Wherein β e (0, 1)]For the contribution ratio, a value of 0.80, 0.85, 0.90, 0.95, 0.98 or 0.99 is usually used, corresponding to Pk＝[p1，p2，p3，…pk]T
Using HotellingT2Computing statistics using (k, m-k) degrees of freedom and a confidence level of α ∈ (0, 1)]F distribution of (d), calculating a statistic T by the following formula2Control limit of (2):
Figure FDA0002440247520000031
(IV) judging the test set xtestWhether to early warn:
collecting test set x on the building structure by using the optical fiber of the step (I)test，xtestIs a 1 Xn one-dimensional matrix, and x is calculated by using the parameters in the step (II)testIs normalized by the matrix
Figure FDA0002440247520000032
Figure FDA0002440247520000033
Is a 1 Xn one-dimensional matrix, and further obtains a mapping matrix of a high-dimensional kernel space
Figure FDA0002440247520000034
For 1 × n matrix
Figure FDA0002440247520000035
Vector and matrix X of0Ith row vector X of0(i,: the difference is calculated, i is selected from 1 to m, xK_testA one-dimensional matrix of 1 × m, formed by matrix xK_testCalculating a centralized mapping matrix
Figure FDA0002440247520000036
Figure FDA0002440247520000037
Wherein, ImIs an identity matrix of m x m dimensions, ItestIs a one-dimensional unit matrix of 1 × m dimensions, i.e., all elements are 1, and is calculated according to the following formula
Figure FDA0002440247520000038
Figure FDA0002440247520000039
Lambda is a one-dimensional matrix consisting of m eigenvalue numbers; p is a feature matrix consisting of m eigenvectors, ΛmIs an m x m dimensional unit diagonal matrix,
Figure FDA00024402475200000310
is composed of
Figure FDA00024402475200000311
Transposing a matrix; when in use
Figure FDA00024402475200000312
And judging the occurrence of abnormity and alarming.
2. The method for global warning of building structure vibrations using distributed optical fiber according to claim 1, wherein: in the fiber, there is one collection point every 0.05-1 meter.
3. The method for global warning of building structure vibrations using distributed optical fiber according to claim 2, wherein: the number of the n acquisition points is 400-4000.
4. A method for global warning of building structure vibrations using distributed optical fiber as claimed in claim 3, characterized in that: the transpose matrix is the column that transforms the rows in the original matrix into the transpose matrix.
5. The method for global warning of building structure vibrations using distributed optical fiber according to claim 4, wherein: said formula Kij＝exp(-||X0(i，：)-X0(j，：)||2/2σ2) Is a matrix X of m × n0Ith row vector X of0(i,: and j) th row vector X0(j, wherein j is 1 to m) and calculating the calculated KijFilling the K matrix of m multiplied by m; then selecting i from 1 to m, repeating the operation, and calculating the calculated KijFilling into an m × m K matrix.
6. The method for global warning of building structure vibrations using distributed optical fiber according to claim 5, wherein: the same characters represent the same meanings, and the values of σ are the same in the steps (one) to (four).
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