CN114674511B - Bridge modal anomaly early warning method for eliminating time-varying environmental factor influence - Google Patents
Bridge modal anomaly early warning method for eliminating time-varying environmental factor influence Download PDFInfo
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Abstract
The invention belongs to the field of bridge structure health monitoring, and provides a bridge modal anomaly early warning method for eliminating the influence of time-varying environmental factors. Firstly, extracting slow features of actually measured bridge modal frequency by using a slow feature analysis technology, reducing data dimensionality and eliminating redundant information influence; secondly, automatically searching a k neighbor sample set with high similarity to the current sample from a training database by adopting a distance method on the principle that similar bridge response output is generated by similar environment load excitation, calculating a mean vector of the k neighbor sample set, and estimating slow characteristics of modal frequency; then, eliminating the influence of time-varying environmental factors by calculating a differential matrix of the slow characteristic of the actually measured and estimated modal frequency; and finally, constructing a bridge modal abnormality early warning index aiming at the difference matrix and determining a reference early warning control limit. According to the invention, environmental monitoring data is not needed, and the nonlinear and non-Gaussian distribution characteristics of the model data under the action of time-varying environmental load are considered, so that the reliable early warning of bridge performance abnormity is facilitated.
Description
Technical Field
The invention belongs to the field of bridge structure health monitoring, and particularly relates to a bridge modal anomaly early warning method for eliminating the influence of time-varying environmental factors.
Background
The bridge modal frequency is an important parameter reflecting the overall characteristic change and state evaluation of the structure. However, in the service process of the bridge, the modal frequency is significantly changed due to the continuous environmental load, and the change amplitude of the modal frequency is possibly annihilated from the change of the modal frequency caused by the real damage of the structure, so that the precision of the traditional modal frequency-based early warning method is reduced or the traditional modal frequency-based early warning method is failed. Therefore, how to eliminate or reduce the influence of various operating environment factors and obtain the real evolution law of modal frequency has become one of the key problems to be solved urgently in the bridge early warning field.
In order to eliminate potential environmental changes in bridge modal frequency, the existing rejection methods are mainly classified into two types: 1) The input-output based correlation modeling method comprises the following steps: establishing an explicit relation model between modal frequency and environmental factors to realize the prediction of the modal frequency and the separation of environmental effects; 2) The output response-based correlation modeling method comprises the following steps: environmental factors are not required to be measured, the environmental variables are regarded as potential influence variables, and the environmental influences are captured and separated by means of technical means such as machine learning. For practical engineering, the first method requires a large amount of environmental monitoring data, and it is difficult to establish an accurate relationship model between environmental factors and modal frequencies, while the second method is particularly simple and practical because it does not require environmental monitoring data. The feature extraction method based on principal component analysis is the most commonly used method at present, and performs data dimension compression according to the data projection rear variance maximization, eliminates redundant information, and effectively extracts environmental fluctuation trend components in modal variables. However, the principal component analysis only focuses on the statistical characteristics among modal variables, and changes among monitoring samples in the modal variables are ignored, so that the risk of information loss of potential environment or damage features in the extracted modal frequency is caused; in addition, the principal component analysis method is used as a linear transformation method, the problem of nonlinearity among modal variables caused by environmental factors cannot be solved, and meanwhile, the method limits the application range of the modal response data due to multivariate Gaussian distribution assumption, so that the environmental influence of the modal frequency of the bridge cannot be effectively eliminated, and the early warning precision is reduced or even fails. Therefore, under the influence of time-varying environmental factors, an early warning technology which gives consideration to both the nonlinear and non-Gaussian distribution characteristics of bridge modal response is developed, and the early warning technology has important significance for reliably evaluating the state of the bridge.
Disclosure of Invention
The invention aims to provide a bridge modal abnormality early warning method for eliminating the influence of time-varying environmental factors, and a corresponding early warning index is established based on the method. The technical scheme of the invention is as follows: firstly, extracting slow characteristics of the measured modal frequency of the bridge by using a slow characteristic analysis technology, reducing data dimension and eliminating redundant information influence; secondly, automatically searching a k neighbor sample set with high similarity to the current sample from a training database by adopting a distance method on the principle that similar bridge response output is generated by similar environment load excitation, calculating a mean vector of the k neighbor sample set, and estimating slow characteristics of modal frequency; then, eliminating the influence of time-varying environmental factors by calculating a differential matrix of the slow characteristic of the actually measured and estimated modal frequency; and finally, constructing a bridge modal abnormality early warning index aiming at the difference matrix and determining a reference early warning control limit.
The technical scheme of the invention is as follows:
a bridge modal abnormality early warning method for eliminating the influence of time-varying environmental factors comprises the following steps:
the method comprises the following steps: extracting slow fluctuation trend characteristics of bridge modal frequency
(1) Order to
A bridge modal frequency data set with p variables and n samples; in practical application, a linear slow characteristic analysis technology is used for extracting a fluctuation trend component which changes slowest in the actually measured modal frequency to reflect the inherent attribute change of the structure, namely a linear mapping matrix W is searched to realize linear mapping of an original data space, and the obtained modal frequency slow characteristic s is ensured i ＝W i T x (t) (1 < i < p) has the smallest slowness, and the optimization problem is as follows:
the slow feature constraint conditions are as follows:
<s i > t ＝0
in the formula:
the first derivative of the slow characteristic s to the time t characterizes the fluctuation speed of the sample;<·> t desire to monitor samples;
(2) In order to obtain slow modal frequency characteristics, solving the optimization problem through two times of singular value decomposition; first, covariance matrix B = of original modal data<xx T > t Performing a first singular value decomposition:
B＝UΛU T
in the formula: u is a characteristic vector matrix; Λ is a diagonal matrix;
(3) Let whitening matrix Q = Λ -1/2 U, then transition variable z:
z＝Λ -1/2 Ux＝Qx
(4) Let orthogonal matrix P = WQ -1 Defining a slow characteristic matrix s of the bridge modal frequency:
s＝P T z＝Wx
in the formula: w = PA -1/2 U T Is a linear mapping matrix; x is bridge modal frequency response;
(5) Slowness of modal frequency slow features s (t) equal to singular values λ in the second singular value decomposition i I.e. by
The diagonal characteristic values meet descending order arrangement, wherein the characteristic which changes the slowest can better represent the essential fluctuation characteristic of the monitoring data, and the characteristic which changes the fastest is often a noise signal; lambda [ alpha ] i The larger the original modal variable information, the more it reflects, so the slow feature quantity can be determined by the cumulative contribution rate:
in the formula: the number r of slow features should satisfy theta more than or equal to 80%;
step two: searching a subset of neighbor samples for modal responses
(6) Based on the characteristic that similar environmental load excitation generates similar bridge response output, a distance method is used for evaluating the similarity between bridge responses, namely the distance between any similar responses is far smaller than the distance between dissimilar responses; in practical application, the training data set is taken as a reference database, and the frequency response x to any structural modal frequency is determined i And calculating Euclidean distances between the reference data base and all sample points in the reference database:
d i,j ＝||x i -x j || 2
in the formula: d i,j Is a sample x i And x j The Euclidean distance between;
(7) Searching for responses x by distance method i Using the local sample subset to characterize the local characteristics of the monitored data, wherein x i The neighbor subset of (d) represents:
n(x i )＝{x i,1 ,x i,2 ,…,x i,k }
in the formula: x is the number of i,j Is x i Of (2) neighbor samples x j ；n(x i ) Is x i A neighbor subset of (d) i,1 ≤d i,2 ≤…≤d i,k (ii) a k is the number of the neighbor subsets, the number of the subsets corresponding to the minimum false alarm rate is selected as a k value used by the method through a cross validation method by taking the false alarm rate of response data in a normal state as a target;
step three: rejecting time-varying environmental effect effects
(8) Computing an arbitrary sample x i Is n (x) i ) Mean vector of (2):
in the formula: m is a mean vector of the neighboring modal response data set; x is the number of i,j Is x i Of (2) neighbor samples x j Wherein j =1,2, …, k;
(9) By using the mean vector m, the estimation value of the slow characteristic of the modal frequency can be calculated
In the formula: w r Linear mapping matrixes corresponding to the first r slow characteristics;
(10) Calculating the measured slow feature s and the estimated slow feature
The obtained difference matrix e is an error matrix which is not influenced by time-varying environmental effects:
the calculation process of the difference matrix e can eliminate the difference of the monitored sample relative to the origin of coordinates and obtain the change information relative to the adjacent sample; according to the method, the nonlinear characteristics of the data are approximated by adopting a local linearization idea, and the local characteristics of the data can be effectively guaranteed by the searched local sample subset, so that the influence of nonlinear and non-Gaussian environmental effects in the modal frequency of the bridge can be effectively reduced in the differential process, and the early warning precision is improved;
step four: early warning index for abnormal modal of structural bridge and determining early warning control limit
(11) Calculating the Mahalanobis distance statistic of a difference matrix e which is not influenced by time-varying environmental factors in a normal state, and defining the difference matrix e as a bridge modal abnormality early warning index
In the formula:
a covariance matrix which is a difference matrix e; p is the number of modal variables in the bridge modal frequency data x (t);
(12) For abnormal early warning index in normal state
Calculating early warning control limit under given significance level alpha by using nuclear density estimation method
In the formula: f -1 (. Is an early warning index)
The inverse cumulative distribution function of; in practical application, when a plurality of continuous early warning indexes obviously exceed the early warning control limit, a bridge mode abnormity warning is sent out.
The invention has the beneficial effects that: by eliminating the bridge modal variation caused by the time-varying environmental effect, the early warning index of the structure can be more reliable, and the success rate of the early warning of the abnormal performance of the bridge is obvious. In addition, the method searches the neighbor subset of the modal response by a distance method, can ensure the local characteristics of the data, and efficiently processes the problems of nonlinearity and non-Gaussian property of the modal response data under the action of time-varying environmental load; and the method does not need environment monitoring data, is suitable for the condition that a nonlinear relation exists between bridge modal variables and the modal response data has non-Gaussian distribution characteristics, and has good engineering practical value.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 shows the bridge warning result implemented by the conventional method.
Fig. 3 shows the bridge early warning result implemented by the method of the present invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings and technical solutions.
The effectiveness of the invention is verified by taking modal frequency data of 3932 hours in 10 months for a certain prestressed concrete bridge as an example. Monitoring data under a normal state for 1-3123 hours is used as a training set; the data sets to be detected under the unknown state are divided into two types, wherein the monitoring data under the normal state within 3124-3470 hours are used as a verification set, and the monitoring data under the damage state within 3471-3932 hours are used as a test set. The specific implementation mode of the invention is as follows:
(1) Analyzing the bridge modal frequency data in a normal state, establishing a slow characteristic analysis model, and extracting slow characteristics of modal frequency; determining the number of slow features by adopting a cross validation method; searching k neighbor subsets of the training samples, and calculating the mean value and the slow characteristic estimation value of the k neighbor subsets; eliminating nonlinear and non-Gaussian environmental effects in the bridge modal frequency by calculating a slow characteristic difference matrix; the modal anomaly early warning index is calculated by using a difference matrix which is not influenced by environmental factors, and the control limit of the early warning index is determined by a kernel density estimation method (as shown in figure 1).
(2) Analyzing the modal frequency data of the bridge to be detected in an unknown state: firstly, substituting data to be detected into an established slow characteristic analysis model, reducing dimensionality of original data, eliminating noise interference, and calculating a slow characteristic matrix; secondly, searching a local neighbor subset of the data to be detected from the training data set, and calculating the mean value of the local neighbor subset and the estimation value of the slow characteristic matrix; then, the elimination of the time-varying environmental effect is realized through the difference process of the slow features, the corresponding modal anomaly early warning indexes are calculated and compared with the early warning control limit, and if a plurality of continuous indexes obviously exceed the control limit, a modal anomaly alarm is sent out (as shown in fig. 1).
(3) The result shows that the early warning rate of the traditional method is 37.01% (as shown in fig. 2), while the early warning rate of the method is 95.24%, and the structural damage or performance degradation can be identified more effectively (as shown in fig. 3).
Claims (1)
1. A bridge modal abnormality early warning method for eliminating time-varying environmental factor influence is characterized by comprising the following steps:
the method comprises the following steps: extracting slow fluctuation trend characteristics of bridge modal frequency
(1) Order to
A bridge modal frequency data set with p variables and n samples; in practical application, a linear slow characteristic analysis technology is used for extracting a fluctuation trend component which changes slowest in actually measured modal frequency to reflect the inherent attribute change of the structure, namely a linear mapping matrix W is searched to realize linear mapping of an original data space, and the obtained modal frequency slow characteristic s is ensured i ＝W i T x (t) (1 < i < p) has the smallest slowness, and the optimization problem is as follows:
the slow feature constraint conditions are as follows:
<s i > t ＝0
in the formula:
the first derivative of the slow characteristic s to the time t characterizes the fluctuation speed of the sample;<·> t desire to monitor the sample;
(2) In order to obtain slow modal frequency characteristics, solving the optimization problem through two times of singular value decomposition; first, covariance matrix B = of original modal data<xx T > t Performing a first singular value decomposition:
B＝UΛU T
in the formula: u is a characteristic vector matrix; Λ is a diagonal matrix;
(3) Let whitening matrix Q = Λ -1/2 U, then transition variable z:
z＝Λ -1/2 Ux＝Qx
(4) Let orthogonal matrix P = WQ -1 Defining a slow characteristic matrix s of the bridge modal frequency:
s＝P T z＝Wx
in the formula: w = PA -1/2 U T Is a linear mapping matrix; x is bridge modal frequency response;
(5) Slowness of modal frequency slow feature s (t) is equal to singular value λ in the second singular value decomposition i I.e. by
The diagonal characteristic values meet descending order arrangement, wherein the characteristic which changes the slowest can better represent the essential fluctuation characteristic of the monitoring data, and the characteristic which changes the fastest is often a noise signal; lambda [ alpha ] i The larger the original modal variable information, the more it reflects, so the slow feature quantity can be determined by the cumulative contribution rate:
in the formula: the number r of slow features should satisfy theta is more than or equal to 80%;
step two: searching a subset of neighbor samples for modal responses
(6) Based on the characteristic that similar environmental load excitation generates similar bridge response output, a distance method is used for evaluating the similarity between bridge responses, namely the distance between any similar responses is far smaller than the distance between dissimilar responses; in practical application, the training data set is taken as a reference database, and the frequency response x to any structural modal frequency is determined i And calculating Euclidean distances between the reference data base and all sample points in the reference database:
d i,j ＝||x i -x j || 2
in the formula: d i,j Is a sample x i And x j The Euclidean distance between;
(7) Searching for responses x by distance method i Using the local sample subset to characterize the local characteristics of the monitored data, wherein x i The neighbor subset of (d) represents:
n(x i )＝{x i,1 ,x i,2 ,…,x i,k }
in the formula: x is the number of i,j Is x i Of (2) neighbor samples x j ；n(x i ) Is x i A neighbor subset of (d) i,1 ≤d i,2 ≤…≤d i,k (ii) a k is the number of the neighbor subsets, the number of the subsets corresponding to the minimum false alarm rate is selected as a k value used by the method through a cross validation method by taking the false alarm rate of response data in a normal state as a target;
step three: rejecting time-varying environmental effects
(8) Computing an arbitrary sample x i Is n (x) i ) Mean vector of (2):
in the formula: m is a mean vector of the neighboring modal response data set; x is the number of i,j Is x i Of neighbor sample x j Wherein j =1,2, …, k;
(9) By using the mean vector m, the estimation value of the slow characteristic of the modal frequency can be calculated
In the formula: w r Linear mapping matrixes corresponding to the first r slow characteristics;
(10) Calculating the measured slow feature s and the estimated slow feature
The obtained difference matrix e is an error matrix which is not influenced by the time-varying environmental effect:
the calculation process of the difference matrix e can eliminate the difference of the monitored sample relative to the origin of coordinates and obtain the change information relative to the adjacent sample;
step four: early warning index for abnormal modal of structural bridge and determining early warning control limit
(11) Calculating the Mahalanobis distance statistic of a difference matrix e which is not influenced by time-varying environmental factors in a normal state, and defining the difference matrix e as a bridge modal abnormality early warning index
In the formula:
a covariance matrix which is a difference matrix e; p is the number of modal variables in the bridge modal frequency data x (t);
(12) For abnormal early warning index in normal state
Calculating early warning control limit under given significance level alpha by using nuclear density estimation method
In the formula: f -1 (. Is an early warning index)
The inverse cumulative distribution function of; in practical application, when a plurality of continuous early warning indexes obviously exceed the early warning control limit, a bridge mode abnormity warning is sent out.
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| CN107389285A (en) * | 2017-06-16 | 2017-11-24 | 东南大学 | A kind of quick test and evaluation method of bridge changed based on temperature |
| CN112329191A (en) * | 2019-08-05 | 2021-02-05 | 华中科技大学 | Modal identification method and transition mode fault detection method in multi-mode process |
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| CN107389285A (en) * | 2017-06-16 | 2017-11-24 | 东南大学 | A kind of quick test and evaluation method of bridge changed based on temperature |
| CN112329191A (en) * | 2019-08-05 | 2021-02-05 | 华中科技大学 | Modal identification method and transition mode fault detection method in multi-mode process |
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