CN111832442B - Method for automatically separating temperature strain components from massive bridge dynamic strain data - Google Patents

Method for automatically separating temperature strain components from massive bridge dynamic strain data Download PDF

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CN111832442B
CN111832442B CN202010599658.4A CN202010599658A CN111832442B CN 111832442 B CN111832442 B CN 111832442B CN 202010599658 A CN202010599658 A CN 202010599658A CN 111832442 B CN111832442 B CN 111832442B
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CN111832442A (en
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曹茂森
李帅
张鑫
胡帅涛
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Hohai University HHU
Chuzhou University
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Abstract

The invention discloses a method for automatically separating temperature strain components from massive bridge dynamic strain data. According to the method, based on EMD decomposition of strain monitoring data, Gaussian mixture model clustering (GMM) is adopted, and attribute classification is carried out on IMFs according to Hilbert marginal spectrum change characteristics of the IMFs generated by EMD decomposition, so that the temperature effect is automatically separated from the monitored strain. The method overcomes the limitations that the traditional method is low in precision, does not have universality and cannot achieve automatic implementation due to the fact that the temperature effect threshold parameter is preset, can automatically separate the temperature strain component from the bridge dynamic strain data in a high-precision, self-adaptive and parameter-free mode, is good in noise resistance, meets the engineering requirements of separating the temperature strain component from massive bridge strain data in an online and instantaneous mode, and has wide engineering application potential.

Description

Method for automatically separating temperature strain components from massive bridge dynamic strain data
Technical Field
The invention relates to the technical field of bridge health monitoring, in particular to a method for separating a temperature effect from massive bridge dynamic strain data.
Background
The bridge health monitoring system collects and stores massive bridge operation state monitoring data in real time, wherein the monitoring data comprise a large amount of strain monitoring data, the dynamic strain of the bridge obtained by monitoring is a composite quantity comprising multiple factor components, and compared with factors such as shrinkage and creep, the strain component caused by vehicle load and temperature is a main control component of the composite quantity.
Temperature strain components generated by temperature changes may be larger than strain caused by vehicle loads, signal characteristics reflected by the vehicle load strain components are covered or submerged, effective judgment of bridge operation states is affected, massive bridge dynamic strain monitoring data cannot be effectively utilized, and therefore effective separation of the temperature strain components in the strain monitoring data becomes an actual engineering problem which needs to be solved urgently.
For mass bridge dynamic strain monitoring data which are collected and stored in real time, the central problem of extracting vehicle load strain from the mass bridge dynamic strain monitoring data to realize strain separation is to separate temperature strain components with high efficiency and high precision.
At present, the separation of temperature effect by using signal decomposition theory is widely applied, and a typical method for separating temperature strain components based on the signal decomposition theory is an EMD (empirical Mode decomposition) method, and one technical key of the method for separating temperature strain is to identify an IMF (Intrinsic Mode Function) sequence corresponding to strain caused by temperature and vehicle load. However, at present, the IMFs are segmented based on manual empirical judgment of the IMFs sequence characteristics or setting parameter thresholds of temperature effects, and such manual intervention segmentation is not only poor in universality, but also subjective. In addition, the existing separation method can not ensure the continuous operation of the program, can not realize the automatic implementation of the temperature strain component separation, and greatly influences the separation efficiency. Therefore, the engineering requirement of efficiently and accurately separating the temperature strain component from the massive strain data online and instantly cannot be met.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: aiming at the defect of temperature strain separation based on the EMD method in the prior art, the invention provides the method for realizing automatic attribute classification of IMFs based on GMM (Gaussian Mixture Model) clustering according to the change characteristics of Hilbert marginal spectrum of IMF sequences, automatically determining the IMF sequences corresponding to vehicle load strain and temperature strain, avoiding manual intervention and realizing automatic separation of strain components caused by vehicle load, temperature and the like.
The invention adopts the following technical means for solving the technical problems:
the invention provides a method for automatically separating temperature strain components from massive bridge dynamic strain data, which comprises the following steps:
inputting real-time strain data of a mass of bridges;
step (2), decomposing corresponding variable data through an EMD method to obtain IMF sequences and residual res with different time scales;
step (3), Hilbert transformation is carried out on the IMF sequences obtained by decomposition in the step (2) to obtain Hilbert marginal spectrums of the IMF sequences, and normalization processing is carried out;
step (4), solving a normalized Hilbert marginal spectral area through a trapezoidal method, then carrying out GMM clustering on the marginal spectral area of each IMF, and automatically separating IMFs corresponding to temperature load strain and vehicle load strain;
and (5) overlapping the IMF sequences which are separated by GMM clustering and are attributed to vehicle load strain to obtain vehicle load strain, and overlapping the IMF sequences which are attributed to temperature load strain to obtain temperature load strain, so that the automatic separation of the temperature load strain and the vehicle load strain components is realized.
Further, according to the method for automatically separating the temperature strain component from the massive bridge dynamic strain data, in the step (2), the bridge dynamic strain signal is decomposed into n-order IMFs and a remainder res through an EMD method, wherein the remainder res is used for representing the signal mean value change trend, is a periodic trend component in the signal and belongs to the temperature strain component.
Further, in the method for automatically separating the temperature strain component from the massive bridge dynamic strain data, in the step (3), Hilbert transformation is performed on an IMF sequence, including res, and a remainder res is recorded as an n +1 th order IMF to obtain Hilbert marginal spectrums corresponding to the IMFs, and then the marginal spectrums are normalized according to the following formula:
Figure BDA0002558167090000021
in the formula, M ij An ith amplitude value expressed as the jth term IMF marginal spectrum;
Figure BDA0002558167090000022
is the ith frequency valueCorresponding normalized amplitude values.
Further, in the method for automatically separating temperature strain components from mass bridge dynamic strain data provided by the present invention, in step (4), during GMM clustering, an initialized hybrid model parameter K is set to 2, and IMFs including res are divided into 2 classes, where class 1 is an IMFs corresponding to vehicle load strain and class 2 is an IMFs corresponding to temperature strain.
Further, the method for automatically separating the temperature strain component from the mass bridge dynamic strain data, provided by the invention, comprises the steps of (5) superposing IMF sequences classified into class 1 and separated by GMM clustering to obtain vehicle load strain, and superposing IMF sequences classified into class 2 to obtain temperature load strain.
By adopting the technical means, compared with the prior art, the invention has the following advantages:
the method overcomes the limitations that the traditional method is low in precision, does not have universality and cannot achieve automatic implementation due to the fact that the temperature effect threshold parameter is preset, can automatically separate the temperature strain component from the bridge dynamic strain data in a high-precision, self-adaptive and parameter-free mode, is good in noise resistance, meets the engineering requirements of separating the temperature strain component from massive bridge strain data in an online and instantaneous mode, and has wide engineering application potential.
Drawings
FIG. 1 is a flow chart of the Auto-EMD method of the present invention for separating temperature strain;
FIG. 2 is a graph of the total strain calculated by the finite element software SAP 2000;
FIG. 3 is an automatic classification of IMFs into 2 classes by GMM clustering;
FIG. 4 is a temperature strain curve separated by Auto-EMD method in numerical verification;
FIG. 5 is a vehicle load strain curve separated by Auto-EMD method in numerical verification
FIG. 6 is a graph of the effect of fit to the separation effect during numerical verification;
FIG. 7 is a graph of total strain in an engineering example;
FIG. 8 is an automatic classification of IMFs into 2 classes by GMM clustering;
FIG. 9 is a temperature strain curve isolated by Auto-EMD during engineering example validation;
FIG. 10 is a vehicle load strain curve isolated by Auto-EMD during engineering example validation.
Detailed Description
In order to better understand the technical scheme, the technical scheme of the invention is further described in detail in the following description with reference to the drawings and the specific embodiments:
it will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The invention provides an Auto-EMD method for automatically separating temperature strain components from massive bridge dynamic strain data, which is characterized in that an EMD method is adopted to decompose bridge dynamic strain signals into n-order IMF sequences and remainder res, IMF marginal spectrums are obtained through Hilbert transformation and are subjected to normalization processing, normalized marginal spectrum area values are obtained through a trapezoid method, further, automatic attribute classification of the IMF sequences is realized through GMM clustering according to Hilbert marginal spectrum area value change characteristics of IMFs, the IMFs are divided into 2 classes, the first class of IMFs are IMF sequences corresponding to vehicle load strain, the second class of IMFs are IMF sequences corresponding to temperature strain, corresponding strain components can be obtained through respective superposition, and the Auto-EMD method for automatically separating the temperature strain components from the massive bridge dynamic strain data is formed. The method can realize the automatic separation of the temperature strain components in the mass bridge strain monitoring data with no intervention, high efficiency and high precision.
Referring to fig. 1 for explanation, the specific implementation steps of the present invention are as follows:
step 1, inputting dynamic strain data of the bridge, and then performing EMD on the dynamic strain data of the bridge to obtain IMF components and residual res of each order.
Step 2, further solving the marginal spectrum of the IMF through Hilbert transformation, then carrying out normalization processing on each marginal spectrum through the following formula, and taking a remainder res as an (n + 1) th IMF during calculation for convenient expression:
Figure BDA0002558167090000041
in the formula, M ij The ith amplitude value expressed as the jth term IMF marginal spectrum;
Figure BDA0002558167090000042
and the normalized amplitude value corresponding to the ith frequency value is obtained.
And 3, the normalized IMF marginal spectrum has mutation from high-frequency IMF to low-frequency IMF, and the separation of the IMF component of the vehicle load strain and the IMF component of the vehicle temperature strain can be realized according to the IMF mutation order.
The temperature strain is a trend curve formed in a long time scale, is reflected on a Hilbert marginal spectrum of the IMF, is expressed from physical characteristics, has small marginal spectral area and similar size, and is different from a gradual reduction rule of the marginal spectral area corresponding to the vehicle strain.
Step 4, approximately solving the normalized marginal spectrum area by using the concept of a trapezoidal method, and defining the area of the IMF marginal spectrum of the jth order as a j Then, there are:
Figure BDA0002558167090000043
in the formula, x ij Is the ith frequency value in the IMF marginal spectrum of the jth order; x is a radical of a fluorine atom (i+1)j Expressed as the (i + 1) th frequency value.
Then, the marginal spectral area A for each IMF j And carrying out GMM clustering.
For a Gaussian Mixture Model (GMM) containing K Components, it can be described by:
Figure BDA0002558167090000044
in the formula, N (x | mu) k Σ k) is a Gaussian probability density function, w k ，μ k And Σ k is the weight, mean, covariance matrix of the kth Component in the hybrid model, respectively. The K components of the GMM actually correspond to the K cluster clusters.
When GMM clustering is adopted to cluster the marginal common area, dividing IMF sequences into 2 types, and setting an initialized mixed model parameter K to be 2; the first type is IMFs corresponding to vehicle load strain, and the second type is IMFs corresponding to temperature strain.
The GMM clustering method automatically separates IMF sequences of temperature strain and vehicle load strain according to the change characteristics of the marginal spectral area under the condition of not setting parameters.
And 5, respectively superposing the IMFs to obtain the load strain and the temperature strain of the vehicle. Thus, the automatic separation of the temperature strain component is realized by the Auto-EMD method.
The effect of the solution of the present embodiment will be explained by numerical simulation and engineering examples.
Firstly, a bridge dynamic strain signal model.
The dynamic strain of the bridge structure is influenced by the environment (temperature, humidity and the like) besides traffic loads of vehicles and the like, and the strain monitored by the bridge monitoring system is the superposition of the strain caused by various factors. If the influence of other environmental effects on the structural strain is neglected, the total strain value epsilon of a certain measuring point of the bridge structure can be expressed as:
ε＝ε l +ε w +ε s +ε c
in the formula, epsilon l Strain, epsilon, induced by loads (dead and live) w For temperature-induced strain,. epsilon s For shrinkage strain,. epsilon c Creep strain.
After the bridge is formed for three years, most of contraction and creep can be completed, the change is smooth, and the influence can be ignored. After removing the effects of shrinkage, creep, the total strain value ε can be expressed as:
ε＝ε l +ε w
and secondly, testing the effectiveness of the Auto-EMD method by numerical simulation.
1. Simulation of random vehicle loads in numerical simulation.
The total mass of two-axle (truck, bus, light bus) vehicles can be described by adopting lognormal distribution, and the probability density function is as follows:
Figure BDA0002558167090000051
wherein g is a vehicle mass random variable; i is 1,2, and 3 respectively denote a two-axle light bus, a two-axle motor bus, and a two-axle truck.
The total mass of the three-axis, four-axis, five-axis and six-axis vehicle can be described by superposition of 2 normal distributions, and the probability density function can be expressed as follows:
Figure BDA0002558167090000052
where i ═ 4,5,6, and 7 denote a three-axle truck, a four-axle truck, a five-axle truck, and a six-axle truck, respectively.
2. When random vehicle load is simulated, a vehicle is supposed to pass through a monitoring position at any monitoring moment, and the method comprises the following specific steps:
(1) determining a total number n of random vehicles;
(2) extracting n random sample values according to the vehicle type proportion, and determining the vehicle type of a random vehicle;
(3) extracting n random sample values according to a vehicle mass probability model, and determining the mass of a random vehicle;
(4) and distributing the obtained random vehicle mass to vehicles of corresponding vehicle types, so as to realize the simulation of random vehicle load.
3. Inputting simulated random vehicle load and temperature (actually measured data of the Sutong Yangtze river road bridge selected by temperature change) into a finite element model, simulating the bridge model by finite element software SAP2000, and comparing the finite element calculation result serving as a known quantity with a subsequent Auto-EMD separation result.
The total structural strain obtained through finite element calculation is shown in fig. 2, the total strain obtained through finite element calculation is subjected to EMD decomposition to obtain IMF sequences with different time scales, and further, the marginal spectrum of the IMFs is obtained through Hilbert transformation.
Normalizing the IMF marginal spectrum to obtain normalized IMF marginal spectrum, calculating the area of each marginal spectrum by a trapezoidal method, and defining the area of the jth IMF marginal spectrum as A j And then:
Figure BDA0002558167090000061
in the formula, x ij Is the ith frequency value in the IMF marginal spectrum of the jth order; x is a radical of a fluorine atom (i+1)j Expressed as the (i + 1) th frequency value.
The obtained marginal spectrum areas are subjected to GMM clustering, and the clustering result is shown in FIG. 3.
The vehicle load strain can be obtained by superposing the IMFs of the first type, the temperature load strain can be obtained by superposing the IMFs of the second type, and the automatic separation of the temperature strain component by the Auto-EMD method can be realized.
Fig. 4 and 5 show the temperature strain component and the vehicle load strain component separated by the Auto-EMD method.
And thirdly, checking the separation effect.
For the temperature and vehicle strain results obtained by the Auto-EMD method, if the results are completely consistent with the finite element calculation results, the two are in a perfect linear relationship, namely a straight line is presented in the coordinate relationship, such as a white straight line in FIG. 6; if the two data are not completely matched, the data point will deviate, such as the black scattered point in fig. 6.
In order to judge the separation effect, the goodness-of-fit test can be carried out on the separation result, and the closer the statistical result is to 1, the higher the goodness-of-fit between the separation result and the actual result is. Using determinants of regression equationsNumber R 2 Judging the fitting degree of the two, and calculating the following formula:
Figure BDA0002558167090000062
where SSR is expressed as the regression sum of squares and SST is expressed as the sum of the squares of the total deviations, ε i Expressed as strain values calculated for the finite elements,
Figure BDA0002558167090000063
expressed as the mean of the strain values calculated for the finite elements; epsilon' i Expressed as strain values from Auto-EMD decomposition.
Calculating the coefficient R of determinability when the temperature strain and the vehicle load strain are fitted by the formula 2 0.9435 and 0.9986 respectively, the fitting effect of the two is good, and the fact that the Auto-EMD method can well separate temperature strain and vehicle load strain is proved.
FIG. 6 is a graph showing the effect of fitting by the Auto-EMD method.
And fourthly, verifying the effectiveness of the Auto-EMD method by the engineering example.
Taking the Sutong Yangtze river highway bridge as an engineering background, strain and temperature data monitored by the strain gauge with the serial number YB030100 and the thermometer with the serial number WD020217 within 2017.04.01-2017.04.03 days are selected as analysis data, and the total strain time course data of the bridge measuring point positions are shown in figure 7.
EMD decomposition is carried out on strain data, Hilbert transformation is carried out on an IMF sequence obtained through decomposition, a Hilbert marginal spectrum is obtained, normalization processing is carried out on the marginal spectrum, the normalized marginal spectrum area is further obtained, and GMM clustering is carried out on the marginal spectrum area.
GMM clustering divides the IMF marginal spectrum (after normalization) area into two types, the clustering result is shown in figure 8, the vehicle load strain can be obtained by overlapping IMFs in the type 1, and the temperature strain can be obtained by overlapping IMFs in the type 2.
The above operation can realize the separation of the temperature strain in the strain signal by the Auto-EMD method, and the separation result is shown in fig. 9 and 10.
And fifthly, checking the separation effect of the engineering example.
According to the strong linear relation between the temperature and the temperature strain generated by the temperature, the separation effect of the separation temperature effect of the Auto-EMD method can be judged based on the linear correlation coefficient of the temperature and the temperature strain, and therefore an evaluation index of the separation effect of the Auto-EMD method is established. The correlation coefficient is determined by:
Figure BDA0002558167090000071
in the formula, T i For each measurement time, temperature, S i In order to respond to the strain,
Figure BDA0002558167090000072
the average values for temperature and strain, respectively.
The closer the correlation coefficient R is to 1, the better the linear relation between the temperature and the temperature strain is, the more thoroughly the temperature strain and the vehicle strain are separated, and the better the effect of the Auto-EMD method on separating the temperature effect is.
The correlation coefficient of the two is calculated to be 0.9475, which shows that the two have strong linear relation and the effect of decomposing temperature strain and vehicle strain based on the Auto-EMD method is still better in practical engineering application.
In conclusion, the invention establishes the evaluation index of the temperature strain component separation effect of the Auto-EMD method and discusses the influence of noise on the temperature strain component separation effect. And by numerical analysis, the separation temperature effect component of the Auto-EMD method is checked, and the engineering practicability of the Auto-EMD method is verified by taking the Sutong Yangtze river road bridge as an engineering example.
When the EMD method is applied to separating the temperature strain in the strain signal in the actual engineering, the separation effect of the EMD method cannot be quantitatively evaluated, and only the smoothness degree of the separated temperature strain is used for preliminary judgment. Aiming at the deficiency of the research of the problem, the invention judges the separation effect of the separation temperature effect of the Auto-EMD method according to the linear correlation coefficient of the temperature and the temperature strain generated by the temperature based on the stronger linear relationship between the temperature and the temperature strain, thereby establishing the evaluation index of the separation effect of the Auto-EMD method.
The above description is provided to explain in detail embodiments of the present invention by referring to the figures. Furthermore, it should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to examples, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (5)

1. A method for automatically separating temperature strain components from massive bridge dynamic strain data is characterized by comprising the following steps:
inputting real-time strain data of a mass of bridges;
step (2), decomposing corresponding variable data through an EMD method to obtain IMF sequences and residual res with different time scales;
step (3), Hilbert transformation is carried out on the IMF sequences obtained by decomposition in the step (2) to obtain Hilbert marginal spectrums of the IMF sequences, and normalization processing is carried out;
step (4), solving a normalized Hilbert marginal spectral area by a trapezoidal method, then performing GMM clustering on the marginal spectral area of each IMF, and automatically separating IMFs corresponding to temperature load strain and vehicle load strain;
and (5) overlapping the IMF sequences which are separated by GMM clustering and are attributed to vehicle load strain to obtain vehicle load strain, and overlapping the IMF sequences which are attributed to temperature load strain to obtain temperature load strain, so that the automatic separation of the temperature load strain and the vehicle load strain components is realized.
2. The method for automatically separating the temperature strain component from the mass bridge dynamic strain data as claimed in claim 1, wherein in the step (2), the bridge dynamic strain signal is decomposed into n-order IMFs and a remainder res by an EMD method, wherein the remainder res is used for representing a signal mean value variation trend, is a periodic trend component in the signal, and belongs to the temperature strain component.
3. The method for automatically separating temperature strain components from mass bridge dynamic strain data according to claim 1, wherein in step (3), Hilbert transform is performed on the IMF sequence, including res, and the remainder res is recorded as IMF of order n +1, so as to obtain Hilbert marginal spectrum corresponding to each IMF, and then normalization processing is performed on the marginal spectrum according to the following formula:
Figure FDA0003705913520000011
in the formula, M ij The ith amplitude value expressed as the jth term IMF marginal spectrum;
Figure FDA0003705913520000012
and the normalized amplitude value corresponding to the ith frequency value is obtained.
4. The method for automatically separating temperature strain components from mass bridge dynamic strain data according to claim 1, wherein in step (4), during GMM clustering, an initialized hybrid model parameter K is set to 2, and the IMFs including res are divided into 2 classes, where class 1 is the IMFs corresponding to vehicle load strain and class 2 is the IMFs corresponding to temperature strain.
5. The method for automatically separating the temperature strain component from the dynamic strain data of the mass bridge according to claim 4, wherein in the step (5), IMF sequences classified as class 1 and separated from GMM clustering are superposed to obtain the vehicle load strain, and IMF sequences classified as class 2 are superposed to obtain the temperature load strain.
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