CN116698323B - Bridge health monitoring method and system based on PCA and extended Kalman filtering - Google Patents
Bridge health monitoring method and system based on PCA and extended Kalman filtering Download PDFInfo
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- 230000036541 health Effects 0.000 title claims abstract description 116
- 238000001914 filtration Methods 0.000 title claims abstract description 55
- 238000012544 monitoring process Methods 0.000 title claims abstract description 40
- 238000000034 method Methods 0.000 title claims abstract description 30
- 238000007781 pre-processing Methods 0.000 claims abstract description 27
- 239000011159 matrix material Substances 0.000 claims description 188
- 238000012545 processing Methods 0.000 claims description 22
- 238000005259 measurement Methods 0.000 claims description 21
- 238000005070 sampling Methods 0.000 claims description 19
- 230000002159 abnormal effect Effects 0.000 claims description 15
- 230000009467 reduction Effects 0.000 claims description 13
- 238000000354 decomposition reaction Methods 0.000 claims description 4
- 238000010606 normalization Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 4
- 238000009825 accumulation Methods 0.000 claims description 3
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- 238000000513 principal component analysis Methods 0.000 description 28
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
- G01K13/00—Thermometers specially adapted for specific purposes
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
- G01M5/0075—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by means of external apparatus, e.g. test benches or portable test systems
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/10—Pre-processing; Data cleansing
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
- G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
- G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis
Abstract
The invention discloses a bridge health monitoring method and system based on PCA and extended Kalman filtering, and relates to the field of bridge structure health monitoring systems, wherein the method comprises the following steps: acquiring temperature data and deflection data of a bridge; preprocessing temperature data and deflection data; PCA is adopted to separate the preprocessed temperature data and deflection data to obtain deflection components and temperature components; and monitoring the health state of the bridge by adopting extended Kalman filtering according to the deflection component and the temperature component. According to the bridge health monitoring method, the temperature component and the deflection component in the sensor data can be separated through PCA, and the bridge health state is monitored through the extended Kalman filtering by utilizing the separated temperature component and deflection component, so that the accuracy of bridge health monitoring can be effectively improved.
Description
Technical Field
The invention relates to the field of bridge structure health monitoring, in particular to a bridge health monitoring method and system based on PCA (principal component analysis) and extended Kalman filtering.
Background
Bridges are important infrastructure assets that play a critical role in traffic networks. However, they are subject to various environmental and operational loads, which over time may cause damage and degradation.
Bridge health monitoring systems are effective tools for assessing bridge condition and safety, and have found increasing use in recent years. Bridge health monitoring systems typically use sensors to monitor structural responses of the bridge, such as deflection, strain, and temperature. However, the data acquired from the sensors is often complex and contains multiple components and is therefore difficult to interpret and analyze. One of the key factors affecting the response of bridge structures is temperature. The temperature change can cause expansion and contraction, thereby influencing the deflection of the bridge. In the prior art, temperature components and deflection in sensor data are not separated, so that the accuracy of bridge structure health monitoring cannot be guaranteed.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the bridge health monitoring method and the bridge health monitoring system based on PCA and extended Kalman filtering, which can separate the temperature component and the deflection component in the sensor data, thereby improving the accuracy of bridge structure health monitoring.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
a bridge health monitoring method based on PCA and extended Kalman filtering comprises the following steps:
s1, acquiring temperature data and deflection data of a bridge;
s2, preprocessing the temperature data and the deflection data in the step S1;
s3, separating the temperature data and the deflection data which are preprocessed in the step S2 by adopting PCA to obtain a deflection component and a temperature component;
and S4, monitoring the health state of the bridge by adopting extended Kalman filtering according to the deflection component and the temperature component in the step S3.
Further, step S2 includes the following sub-steps:
s21, carrying out standardization processing on the temperature data and the deflection data in the step S1, wherein the standardization processing is expressed as follows:
wherein:the +.f. for temperature data and deflection data>Normalized values of the individual characteristic values, < >>The +.f. for temperature data and deflection data>Personal characteristic value->The +.f. for temperature data and deflection data>Average value of the individual characteristic values in the dataset, +.>The +.f. for temperature data and deflection data>Standard deviation of the individual eigenvalues in the dataset;
s22, filtering the temperature data and deflection data after the normalization processing in the bisection step S21, wherein the filtering is expressed as follows:
wherein:is the firstnFiltered outputs of the individual sampling points, +.>To find the median of the sample values in brackets, +.>Is->Values of the individual sampling points +.>For the width of the sliding window +.>Is the firstValues of the individual sampling points +.>Is->Values of the individual sampling points +.>Is->Values of the sampling points;
s23, detecting abnormal values of the temperature data and the deflection data filtered in the dividing step S22 by adopting a 3 sigma rule, wherein the abnormal values are expressed as follows:
wherein:for the value of the sample point, +.>Is the overall mean value of->Is the total standard deviation.
Further, step S3 includes the following sub-steps:
s31, constructing a data matrix of the temperature data and the deflection data which are preprocessed in the step S2, and calculating a covariance matrix of the data matrix;
s32, calculating the eigenvalues of the covariance matrix in the step S31 by using an eigenvalue decomposition method;
s33, determining the principal components of the data matrix according to the eigenvalues of the covariance matrix in the substep S32, reducing the dimension of the data matrix in the substep S31 by utilizing the principal components of the data matrix, and determining the principal component coefficients;
s34, separating the data matrix subjected to dimension reduction in the substep S33 according to the principal component coefficients in the substep S33 to obtain a deflection component and a temperature component.
Further, step S31 includes the following sub-steps:
s311, taking the temperature data and the deflection data which are preprocessed in the step S2 as columns, and taking the sampling time of the preprocessed temperature data and the preprocessed deflection data as rows to construct a data matrix;
s312, calculating the average value vector of each column of the data matrix in the substep S311;
s313, calculating a covariance matrix of the data matrix according to the mean vector of each column of the data matrix in the substep S312, wherein the covariance matrix is expressed as follows:
wherein:covariance matrix of data matrix, +.>For the number of samples +.>Data matrix>Mean vector for each column of the data matrix, +.>To transpose the symbols.
Further, step S33 includes the following sub-steps:
s331, determining the variance contribution rate of each principal component of the data matrix according to the eigenvalue of the covariance matrix in the substep S32;
s332, determining the principal components of the data matrix according to the variance contribution rate and the principal component accumulation contribution rate threshold value of each principal component in the substep S331;
s333, performing dimension reduction on the data matrix in the dividing step S31 by using the main component of the data matrix in the dividing step S332, wherein the dimension reduction is expressed as follows:
wherein:is the data matrix after dimension reduction, namely the principal component coefficient matrix,>data matrix>For matrix multiplication, ++>A transformation matrix composed of the principal components of the data matrix;
s334, the principal component coefficients are determined using the principal component coefficient matrix in the substep S333.
Further, step S34 includes the following sub-steps:
s341, determining a principal component coefficient threshold according to the historical monitoring data;
s342, judging whether the principal component coefficient in the substep S33 is larger than a principal component coefficient threshold in the substep S341; if yes, separating into temperature components, otherwise separating into deflection components.
Further, step S4 includes the following sub-steps:
s41, constructing a bridge state space model comprising a nonlinear state equation and a nonlinear measurement equation;
s42, predicting the bridge health state and the covariance matrix of the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41;
s43, updating the bridge health state and the covariance matrix of the bridge health state according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health state predicted value in the substep S42 and the covariance matrix predicted value of the bridge health state.
Further, step S42 includes the following sub-steps:
s421, predicting the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the predicted bridge health state is expressed as follows:
wherein:for a time step equal +.>Bridge health state predictive value +.>Is a nonlinear state equation>For a time step equal +.>Bridge health state estimation value at the time +.>For a time step equal +.>Control amount at the time;
s422, predicting a covariance matrix of the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the covariance matrix is expressed as follows:
wherein:for a time step equal +.>Covariance matrix predicted values of bridge health at the time,for a time step equal +.>Covariance matrix estimate of bridge health at time,/->Is equal to the time stepState transition matrix at time,/->For transposed symbol +.>For a time step equal +.>Process noise covariance matrix at that time.
Further, step S43 includes the following sub-steps:
s431, calculating a Kalman gain according to the covariance matrix predicted value of the bridge health state in the substep S42, wherein the Kalman gain is expressed as follows:
wherein:for a time step equal +.>Kalman gain at time>For a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For a time step equal +.>Measurement matrix at time, < >>For transposed symbol +.>For a time step equal +.>Measuring a noise covariance matrix;
s432, updating the bridge health according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health predicted value in the substep S42 and the Kalman gain in the substep S431, wherein the updating is expressed as:
wherein:for a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Kalman gain at time>For a time step equal +.>Measured values at the time, i.e. deflection component, +.>Is a nonlinear measurement equation;
s433, updating the covariance matrix of the bridge health state according to the covariance matrix predicted value of the bridge health state in the substep S42 and the Kalman gain in the substep S431, wherein the covariance matrix is expressed as:
wherein:for a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->Is a matrix of units which is a matrix of units,for a time step equal +.>Kalman gain at time>For a time step equal +.>Measurement matrix at time, < >>For a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For transposed symbol +.>For a time step equal +.>The noise covariance matrix is measured.
The bridge health monitoring system based on PCA and extended Kalman filtering by applying the method comprises a data acquisition unit, a preprocessing unit, a PCA unit and an extended Kalman filtering unit;
the data acquisition unit is used for acquiring deflection data and temperature data of the bridge and transmitting the acquired deflection data and temperature data to the preprocessing unit;
the preprocessing unit is used for receiving the deflection data and the temperature data transmitted by the data acquisition unit, preprocessing the deflection data and the temperature data, and transmitting the preprocessed temperature data and the preprocessed deflection data to the PCA unit;
the PCA unit is used for receiving the preprocessed temperature data and deflection data transmitted by the preprocessing unit, separating the preprocessed temperature data and deflection data by adopting PCA to obtain a deflection component and a temperature component, and transmitting the obtained deflection component and temperature component to the extended Kalman filtering unit;
the extended Kalman filtering unit is used for receiving the deflection component and the temperature component transmitted by the PCA unit and monitoring the health state of the bridge by adopting the extended Kalman filtering according to the deflection component and the temperature component.
The invention has the following beneficial effects:
(1) According to the invention, the temperature component and the deflection component can be separated from the complex data which are obtained from the sensor through PCA and comprise a plurality of components, and then the temperature component is determined to be a main change mode;
(2) According to the bridge health monitoring method, the separated temperature component and deflection component are utilized, the deflection component is used as measurement input through the extended Kalman filtering, the temperature component is used as disturbance input, the bridge health state is monitored, and the accuracy of bridge health monitoring can be effectively improved.
Drawings
FIG. 1 is a schematic flow diagram of a bridge health monitoring method based on PCA and extended Kalman filtering;
fig. 2 is a schematic structural diagram of a bridge health monitoring system based on PCA and extended kalman filtering.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, a bridge health monitoring method based on PCA and extended kalman filtering includes steps S1-S4:
s1, acquiring temperature data and deflection data of a bridge.
In an optional embodiment of the invention, the temperature data and deflection data of the bridge are acquired through the data acquisition unit. The data acquisition unit comprises a strain gauge and a temperature sensor. The strain gauge and the temperature sensor are arranged in the bridge structure, so that the temperature data and the deflection data of the bridge can be obtained in real time, and the obtained temperature data and deflection data are transmitted to the preprocessing unit.
S2, preprocessing the temperature data and the deflection data in the step S1.
In an alternative embodiment of the invention, the invention preprocesses the temperature data and deflection data in step S1 by a preprocessing unit. The preprocessing unit comprises a standardized processing module, a filter and an abnormal value detection module. According to the invention, through the standardized processing module, the filter and the abnormal value detection module in the preprocessing unit, the received temperature data and deflection data are subjected to standardized processing, filtering and abnormal value detection.
Step S2 comprises the following sub-steps:
s21, carrying out standardization processing on the temperature data and the deflection data in the step S1, wherein the standardization processing is expressed as follows:
wherein:the +.f. for temperature data and deflection data>Normalized values of the individual characteristic values, < >>The +.f. for temperature data and deflection data>Personal characteristic value->The +.f. for temperature data and deflection data>Average value of the individual characteristic values in the dataset, +.>The +.f. for temperature data and deflection data>Standard deviation of the individual eigenvalues in the dataset.
S22, filtering the temperature data and deflection data after the normalization processing in the bisection step S21, wherein the filtering is expressed as follows:
wherein:is the firstnFiltered outputs of the individual sampling points, +.>To find the median of the sample values in brackets, +.>Is->Values of the individual sampling points +.>For the width of the sliding window +.>Is the firstValues of the individual sampling points +.>Is->Values of the individual sampling points +.>Is->The values of the sampling points.
Specifically, the invention adopts median filtering to filter the temperature data and deflection data after standardized processing, can remove burr signals and impulse noise, and has good abnormal value resistance.
S23, detecting abnormal values of the temperature data and the deflection data filtered in the dividing step S22 by adopting a 3 sigma rule, wherein the abnormal values are expressed as follows:
wherein:for the value of the sample point, +.>Is the overall mean value of->Is the total standard deviation.
S3, separating the temperature data and the deflection data which are preprocessed in the step S2 by adopting PCA to obtain deflection components and temperature components.
In an alternative embodiment of the present invention, the present invention separates the temperature data and the deflection data preprocessed in step S2 by the PCA unit to obtain a deflection component and a temperature component. The PCA unit comprises a main component selection module and a temperature component separation module. The invention receives the preprocessed temperature data and deflection data transmitted by the preprocessing unit through the principal component selection module and the temperature component separation module in the PCA unit, constructs a data matrix of the preprocessed temperature data and deflection data, calculates a covariance matrix of the data matrix, calculates a characteristic value of the covariance matrix, determines the principal component of the data matrix according to the characteristic value of the covariance matrix, reduces the dimension of the data matrix by utilizing the principal component of the data matrix, determines a principal component coefficient, and separates the dimension-reduced data matrix according to the principal component coefficient to obtain a deflection component and a temperature component.
Step S3 comprises the following sub-steps:
s31, constructing a data matrix of the temperature data and the deflection data which are preprocessed in the step S2, and calculating a covariance matrix of the data matrix.
Step S31 includes the following sub-steps:
s311, taking the temperature data and the deflection data which are preprocessed in the step S2 as columns, and taking the sampling time of the preprocessed temperature data and the preprocessed deflection data as rows to construct a data matrix.
Specifically, the temperature data and the deflection data are obtained on line through the data acquisition unit, so that the sampling time when the temperature data and the deflection data are obtained on line is used as the row elements of the data matrix when the data matrix is constructed.
S312, calculating the average value vector of each column of the data matrix in the substep S311.
S313, calculating a covariance matrix of the data matrix according to the mean vector of each column of the data matrix in the substep S312, wherein the covariance matrix is expressed as follows:
wherein:covariance matrix of data matrix, +.>For the number of samples +.>Data matrix>Mean vector for each column of the data matrix, +.>To transpose the symbols.
S32, calculating eigenvalues of the covariance matrix in the step S31 by using an eigenvalue decomposition method.
Eigenvectors and eigenvalues of the covariance matrix can be solved by eigenvalue decomposition of the matrix, expressed as:
wherein:is characteristic value (I)>Is a feature vector.
The eigenvectors may be obtained by orthogonalization, expressed as:
wherein:is the first after the orthogonalization treatmentiIndividual feature vectors->Feature vector of covariance matrixiColumn vector,/->Is a feature vector +>Is a die length of the die.
S33, determining the principal component of the data matrix according to the eigenvalue of the covariance matrix in the substep S32, performing dimension reduction on the data matrix in the substep S31 by utilizing the principal component of the data matrix, and determining the principal component coefficient.
Step S33 includes the following sub-steps:
s331, determining the variance contribution rate of each principal component of the data matrix according to the eigenvalue of the covariance matrix in the substep S32.
Specifically, the present invention determines the variance contribution ratio of each principal component of the data matrix by calculating the ratio of each eigenvalue of the covariance matrix to the sum of the total eigenvalues in the substep S32.
S332, determining the principal components of the data matrix according to the variance contribution rate and the principal component accumulation contribution rate threshold value of each principal component in the substep S331.
Specifically, according to historical monitoring data, the method determines the threshold value of the total contribution rate of the main components, namely the total contribution rate of the main components reaches 80% -90%, and determines the number of the main components of the data matrix according to the threshold value of the total contribution rate of the main componentsK。
S333, performing dimension reduction on the data matrix in the dividing step S31 by using the main component of the data matrix in the dividing step S332, wherein the dimension reduction is expressed as follows:
wherein:is the data matrix after dimension reduction, namely the principal component coefficient matrix,>data matrix>For matrix multiplication, ++>A transformation matrix formed of the principal components of the data matrix.
S334, the principal component coefficients are determined using the principal component coefficient matrix in the substep S333.
S34, separating the data matrix subjected to dimension reduction in the substep S33 according to the principal component coefficients in the substep S33 to obtain a deflection component and a temperature component.
Step S34 includes the following sub-steps:
s341, determining a principal component coefficient threshold according to the historical monitoring data.
S342, judging whether the principal component coefficient in the substep S33 is larger than a principal component coefficient threshold in the substep S341; if yes, separating into temperature components, otherwise separating into deflection components.
And S4, monitoring the health state of the bridge by adopting extended Kalman filtering according to the deflection component and the temperature component in the step S3.
In an alternative embodiment of the invention, the invention monitors the health status of the bridge by means of an extended kalman filter unit. According to the invention, the bridge health state and the covariance matrix of the bridge health state are predicted by the extended Kalman filtering unit by adopting the extended Kalman filtering unit, and the bridge health state and the covariance matrix of the bridge health state are updated.
Step S4 comprises the following sub-steps:
s41, constructing a bridge state space model comprising a nonlinear state equation and a nonlinear measurement equation.
S42, predicting the bridge health and the covariance matrix of the bridge health by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41.
Step S42 includes the following sub-steps:
s421, predicting the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the predicted bridge health state is expressed as follows:
wherein:for a time step equal +.>Bridge health state predictive value +.>Is a nonlinear state equation>For a time step equal +.>Bridge health state estimation value at the time +.>For a time step equal +.>Control amount at the time.
S422, predicting a covariance matrix of the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the covariance matrix is expressed as follows:
wherein:for a time step equal +.>Covariance matrix predicted values of bridge health at the time,for a time step equal +.>Covariance matrix estimate of bridge health at time,/->Is equal to the time stepState transition matrix at time,/->For transposed symbol +.>For a time step equal +.>Process noise covariance matrix at that time.
S43, updating the bridge health state and the covariance matrix of the bridge health state according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health state predicted value in the substep S42 and the covariance matrix predicted value of the bridge health state.
Step S43 includes the following sub-steps:
s431, calculating a Kalman gain according to the covariance matrix predicted value of the bridge health state in the substep S42, wherein the Kalman gain is expressed as follows:
wherein:for a time step equal +.>Kalman gain at time>For a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For a time step equal +.>Measurement matrix at time, < >>For transposed symbol +.>For a time step equal +.>The noise covariance matrix is measured.
S432, updating the bridge health according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health predicted value in the substep S42 and the Kalman gain in the substep S431, wherein the updating is expressed as:
wherein:for a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Kalman gain at time>For a time step equal +.>Measured values at the time, i.e. deflection component, +.>Is a nonlinear measurement equation.
S433, updating the covariance matrix of the bridge health state according to the covariance matrix predicted value of the bridge health state in the substep S42 and the Kalman gain in the substep S431, wherein the covariance matrix is expressed as:
wherein:for a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->Is a matrix of units which is a matrix of units,for a time step equal +.>Kalman gain at time>For a time step equal +.>Measurement matrix at time, < >>For a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For transposed symbol +.>For a time step equal +.>The noise covariance matrix is measured.
As shown in fig. 2, the bridge health monitoring system based on PCA and extended kalman filter applying the above method includes a data acquisition unit, a preprocessing unit, a PCA unit and an extended kalman filter unit.
In an alternative embodiment of the invention, the data acquisition unit is configured to acquire deflection data and temperature data of the bridge, and transmit the acquired deflection data and temperature data to the preprocessing unit.
The data acquisition unit comprises a strain gauge and a temperature sensor, wherein the strain gauge is used for acquiring deflection data of the bridge and transmitting the acquired deflection data to the preprocessing unit; the temperature sensor is used for acquiring temperature data of the bridge and transmitting the acquired temperature data to the preprocessing unit.
In an optional embodiment of the present invention, the preprocessing unit is configured to receive the deflection data and the temperature data transmitted by the data acquisition unit, perform preprocessing on the deflection data and the temperature data, and transmit the preprocessed temperature data and the preprocessed deflection data to the PCA unit.
The pretreatment unit comprises a standardized processing module, a filter and an abnormal value detection module, wherein the standardized processing module is used for receiving deflection data transmitted by the strain gauge and temperature data transmitted by the temperature sensor, carrying out standardized processing on the deflection data and the temperature data, and transmitting the deflection data and the temperature data after the standardized processing to the filter; the filter is used for receiving the normalized deflection data and the temperature data transmitted by the normalization processing module, filtering the normalized temperature data and the normalized deflection data, and transmitting the filtered temperature data and deflection data to the abnormal value detection module; the abnormal value detection module is used for receiving the filtered temperature data and deflection data, detecting the abnormal value of the filtered temperature data and deflection data, and transmitting the temperature data and deflection data after the abnormal value detection to the PCA unit.
In an optional embodiment of the present invention, the PCA unit is configured to receive the preprocessed temperature data and the deflection data transmitted by the preprocessing unit, separate the preprocessed temperature data and the deflection data by using PCA to obtain a deflection component and a temperature component, and transmit the obtained deflection component and temperature component to the extended kalman filter unit.
The PCA unit comprises a main component selection module and a temperature component separation module; the main component selection module is used for receiving the preprocessed temperature data and deflection data transmitted by the preprocessing unit, constructing a data matrix of the preprocessed temperature data and deflection data, calculating a covariance matrix of the data matrix, calculating a characteristic value of the covariance matrix, determining a main component of the data matrix according to the characteristic value of the covariance matrix, reducing the dimension of the data matrix by utilizing the main component of the data matrix, determining a main component coefficient, and transmitting the determined main component coefficient to the temperature component separation module; the temperature component separation module is used for receiving the principal component coefficients transmitted by the principal component selection module, separating the dimensionality reduced data matrix according to the principal component coefficients to obtain deflection components and temperature components, and transmitting the deflection components and the temperature components to the extended Kalman filtering unit.
In an alternative embodiment of the invention, the extended kalman filter unit is used for receiving the deflection component and the temperature component transmitted by the PCA unit, and monitoring the health status of the bridge by adopting the extended kalman filter according to the deflection component and the temperature component.
The extended Kalman filtering unit builds a bridge state space model comprising a nonlinear state equation and a nonlinear measurement equation, and predicts the bridge health state and a covariance matrix of the bridge health state by adopting the extended Kalman filtering according to the temperature component and the nonlinear state equation. And updating the bridge health state and the covariance matrix of the bridge health state by the extended Kalman filtering unit according to the deflection component, the nonlinear measurement equation, the bridge health state predicted value and the covariance matrix predicted value of the bridge health state.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (7)
1. The bridge health monitoring method based on PCA and extended Kalman filtering is characterized by comprising the following steps of:
s1, acquiring temperature data and deflection data of a bridge;
s2, preprocessing the temperature data and the deflection data in the step S1;
s3, separating the temperature data and the deflection data which are preprocessed in the step S2 by adopting PCA to obtain a deflection component and a temperature component;
s4, monitoring the health state of the bridge by adopting extended Kalman filtering according to the deflection component and the temperature component in the step S3;
step S4 comprises the following sub-steps:
s41, constructing a bridge state space model comprising a nonlinear state equation and a nonlinear measurement equation;
s42, predicting the bridge health state and the covariance matrix of the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41;
step S42 includes the following sub-steps:
s421, predicting the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the predicted bridge health state is expressed as follows:
wherein:for a time step equal +.>Bridge health state predictive value +.>In the form of a non-linear equation of state,for a time step equal +.>Bridge health state estimation value at the time +.>For a time step equal +.>Control amount at the time;
s422, predicting a covariance matrix of the bridge health state by adopting extended Kalman filtering according to the temperature component in the step S3 and the nonlinear state equation in the substep S41, wherein the covariance matrix is expressed as follows:
wherein:for a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For a time step equal +.>Covariance matrix estimate of bridge health at time,/->For a time step equal +.>State transition matrix at time,/->For transposed symbol +.>For a time step equal +.>A process noise covariance matrix;
s43, updating the bridge health state and the covariance matrix of the bridge health state according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health state predicted value in the substep S42 and the covariance matrix predicted value of the bridge health state;
step S43 includes the following sub-steps:
s431, calculating a Kalman gain according to the covariance matrix predicted value of the bridge health state in the substep S42, wherein the Kalman gain is expressed as follows:
wherein:for a time step equal +.>Kalman gain at time>For a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->For a time step equal +.>Measurement matrix at time, < >>For transposed symbol +.>For a time step equal +.>Measuring a noise covariance matrix;
s432, updating the bridge health according to the deflection component in the step S3, the nonlinear measurement equation in the substep S41, the bridge health predicted value in the substep S42 and the Kalman gain in the substep S431, wherein the updating is expressed as:
wherein:for a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Bridge health state predictive value +.>For a time step equal +.>Kalman gain at time>For a time step equal +.>Measured values at the time, i.e. deflection component, +.>Is a nonlinear measurement equation;
s433, updating the covariance matrix of the bridge health state according to the covariance matrix predicted value of the bridge health state in the substep S42 and the Kalman gain in the substep S431, wherein the covariance matrix is expressed as:
wherein:for a time step equal +.>Covariance matrix predictive value of bridge health at the time,/->Is a unitary matrix->For a time step equal +.>Kalman gain at time>For a time step equal +.>Measurement matrix at time, < >>Is equal to the time stepCovariance matrix predictive value of bridge health at the time,/->For transposed symbol +.>For a time step equal +.>The noise covariance matrix is measured.
2. The bridge health monitoring method based on PCA and extended kalman filtering according to claim 1, wherein step S2 comprises the following sub-steps:
s21, carrying out standardization processing on the temperature data and the deflection data in the step S1, wherein the standardization processing is expressed as follows:
wherein:the +.f. for temperature data and deflection data>Normalized values of the individual characteristic values, < >>The +.f. for temperature data and deflection data>Personal characteristic value->The +.f. for temperature data and deflection data>Average value of the individual characteristic values in the dataset, +.>The +.f. for temperature data and deflection data>Standard deviation of the individual eigenvalues in the dataset;
s22, filtering the temperature data and deflection data after the normalization processing in the bisection step S21, wherein the filtering is expressed as follows:
wherein:is the firstnFiltered outputs of the individual sampling points, +.>To find the median of the sample values in brackets,is->Values of the individual sampling points +.>For the width of the sliding window +.>Is the firstValues of the individual sampling points +.>Is->Values of the individual sampling points +.>Is->Values of the sampling points;
s23, detecting abnormal values of the temperature data and the deflection data filtered in the dividing step S22 by adopting a 3 sigma rule, wherein the abnormal values are expressed as follows:
wherein:for the value of the sample point, +.>Is the overall mean value of->Is the total standard deviation.
3. The bridge health monitoring method based on PCA and extended kalman filtering according to claim 1, wherein step S3 comprises the following sub-steps:
s31, constructing a data matrix of the temperature data and the deflection data which are preprocessed in the step S2, and calculating a covariance matrix of the data matrix;
s32, calculating the eigenvalues of the covariance matrix in the step S31 by using an eigenvalue decomposition method;
s33, determining the principal components of the data matrix according to the eigenvalues of the covariance matrix in the substep S32, reducing the dimension of the data matrix in the substep S31 by utilizing the principal components of the data matrix, and determining the principal component coefficients;
s34, separating the data matrix subjected to dimension reduction in the substep S33 according to the principal component coefficients in the substep S33 to obtain a deflection component and a temperature component.
4. A bridge health monitoring method based on PCA and extended kalman filtering according to claim 3, wherein step S31 comprises the following sub-steps:
s311, taking the temperature data and the deflection data which are preprocessed in the step S2 as columns, and taking the sampling time of the preprocessed temperature data and the preprocessed deflection data as rows to construct a data matrix;
s312, calculating the average value vector of each column of the data matrix in the substep S311;
s313, calculating a covariance matrix of the data matrix according to the mean vector of each column of the data matrix in the substep S312, wherein the covariance matrix is expressed as follows:
wherein:covariance matrix of data matrix, +.>For the number of samples +.>Data matrix>Mean vector for each column of the data matrix, +.>To transpose the symbols.
5. The bridge health monitoring method based on PCA and extended kalman filtering according to claim 1, wherein step S33 comprises the following sub-steps:
s331, determining the variance contribution rate of each principal component of the data matrix according to the eigenvalue of the covariance matrix in the substep S32;
s332, determining the principal components of the data matrix according to the variance contribution rate and the principal component accumulation contribution rate threshold value of each principal component in the substep S331;
s333, performing dimension reduction on the data matrix in the dividing step S31 by using the main component of the data matrix in the dividing step S332, wherein the dimension reduction is expressed as follows:
wherein:is the data matrix after dimension reduction, namely the principal component coefficient matrix,>data matrix>For matrix multiplication，/>A transformation matrix composed of the principal components of the data matrix;
s334, the principal component coefficients are determined using the principal component coefficient matrix in the substep S333.
6. The bridge health monitoring method based on PCA and extended kalman filtering according to claim 1, wherein step S34 comprises the following sub-steps:
s341, determining a principal component coefficient threshold according to the historical monitoring data;
s342, judging whether the principal component coefficient in the substep S33 is larger than a principal component coefficient threshold in the substep S341; if yes, separating into temperature components, otherwise separating into deflection components.
7. A bridge health monitoring system based on PCA and extended kalman filtering applying the method of any of claims 1-6, characterized by comprising a data acquisition unit, a preprocessing unit, a PCA unit and an extended kalman filtering unit;
the data acquisition unit is used for acquiring deflection data and temperature data of the bridge and transmitting the acquired deflection data and temperature data to the preprocessing unit;
the preprocessing unit is used for receiving the deflection data and the temperature data transmitted by the data acquisition unit, preprocessing the deflection data and the temperature data, and transmitting the preprocessed temperature data and the preprocessed deflection data to the PCA unit;
the PCA unit is used for receiving the preprocessed temperature data and deflection data transmitted by the preprocessing unit, separating the preprocessed temperature data and deflection data by adopting PCA to obtain a deflection component and a temperature component, and transmitting the obtained deflection component and temperature component to the extended Kalman filtering unit;
the extended Kalman filtering unit is used for receiving the deflection component and the temperature component transmitted by the PCA unit and monitoring the health state of the bridge by adopting the extended Kalman filtering according to the deflection component and the temperature component.
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Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103439070A (en) * | 2013-08-01 | 2013-12-11 | 广州大学 | Separation method for long-term deflection effect of bridge |
| CN104880217A (en) * | 2015-06-17 | 2015-09-02 | 卢伟 | Fault sensor information reconstruction method based on measured value association degree |
| CN106202781A (en) * | 2016-07-19 | 2016-12-07 | 广州大学 | A kind of deflection of bridge span temperature effects and the separation method of Long-term Deflection |
| CN106897505A (en) * | 2017-02-13 | 2017-06-27 | 大连理工大学 | A kind of structure monitoring data exception recognition methods for considering temporal correlation |
| JP2017151497A (en) * | 2016-02-22 | 2017-08-31 | 東京電力ホールディングス株式会社 | Time-sequential model parameter estimation method |
| CN109959493A (en) * | 2019-04-29 | 2019-07-02 | 中国矿业大学 | A kind of cable-stayed bridge cable damage real-time quantitative appraisal procedure based on natural bow modeling |
| CN111829738A (en) * | 2020-07-20 | 2020-10-27 | 唐堂 | Impact load-based bridge bearing capacity lightweight evaluation method |
| CN112066724A (en) * | 2020-08-18 | 2020-12-11 | 广东工业大学 | Roller kiln energy consumption abnormity detection method based on self-adaptive principal component analysis |
| KR102397107B1 (en) * | 2021-08-19 | 2022-05-12 | 한국건설기술연구원 | Apparatus for Monitoring Damage of Structure with Unscented Kalman Filter based on Global Optimization |
| CN114692465A (en) * | 2022-04-15 | 2022-07-01 | 石家庄铁道大学 | Nondestructive identification method of bridge damage position, storage medium and equipment |
| CN115964603A (en) * | 2023-02-10 | 2023-04-14 | 成都理工大学 | Maneuvering target tracking method based on improved Kalman filtering |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7209938B2 (en) * | 2001-12-17 | 2007-04-24 | Lockheed Martin Corporation | Kalman filter with adaptive measurement variance estimator |
| CN107169241B (en) * | 2017-06-26 | 2019-09-13 | 大连三维土木监测技术有限公司 | It is a kind of based on temperature-displacement relation model bridge expanssion joint performance method for early warning |
-
2023
- 2023-08-07 CN CN202310983327.4A patent/CN116698323B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103439070A (en) * | 2013-08-01 | 2013-12-11 | 广州大学 | Separation method for long-term deflection effect of bridge |
| CN104880217A (en) * | 2015-06-17 | 2015-09-02 | 卢伟 | Fault sensor information reconstruction method based on measured value association degree |
| JP2017151497A (en) * | 2016-02-22 | 2017-08-31 | 東京電力ホールディングス株式会社 | Time-sequential model parameter estimation method |
| CN106202781A (en) * | 2016-07-19 | 2016-12-07 | 广州大学 | A kind of deflection of bridge span temperature effects and the separation method of Long-term Deflection |
| CN106897505A (en) * | 2017-02-13 | 2017-06-27 | 大连理工大学 | A kind of structure monitoring data exception recognition methods for considering temporal correlation |
| CN109959493A (en) * | 2019-04-29 | 2019-07-02 | 中国矿业大学 | A kind of cable-stayed bridge cable damage real-time quantitative appraisal procedure based on natural bow modeling |
| CN111829738A (en) * | 2020-07-20 | 2020-10-27 | 唐堂 | Impact load-based bridge bearing capacity lightweight evaluation method |
| CN112066724A (en) * | 2020-08-18 | 2020-12-11 | 广东工业大学 | Roller kiln energy consumption abnormity detection method based on self-adaptive principal component analysis |
| KR102397107B1 (en) * | 2021-08-19 | 2022-05-12 | 한국건설기술연구원 | Apparatus for Monitoring Damage of Structure with Unscented Kalman Filter based on Global Optimization |
| CN114692465A (en) * | 2022-04-15 | 2022-07-01 | 石家庄铁道大学 | Nondestructive identification method of bridge damage position, storage medium and equipment |
| CN115964603A (en) * | 2023-02-10 | 2023-04-14 | 成都理工大学 | Maneuvering target tracking method based on improved Kalman filtering |
Non-Patent Citations (3)
| Title |
|---|
| "基于卡尔曼滤波和统计分析的简支梁桥损伤识别研究";王志宇;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》;C034-187 * |
| Z. He et al. .Integrated structural health monitoring in bridge engineering.《Automation in Construction》.2022,1-16. * |
| 自适应卡尔曼滤波在桥梁健康监测系统中的应用;强明辉;谭政贵;于波;;噪声与振动控制(05);144-146+181 * |
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