Bridge damage early warning method considering modal frequency non-stationary variation

Abstract

The invention discloses a bridge damage early warning method considering modal frequency non-stationary variation, and belongs to the field of bridge service performance early warning, the method comprises the following steps: step 1, interval clustering of main beam multi-modal frequency under different environment temperature action modes; step 2, establishing a multi-modal frequency localization co-integration environmental effect implicit elimination model; 3, constructing bridge damage early warning indexes based on co-integration model errors; 4, probability distribution of early warning indexes is counted and analyzed, and a dynamic reference control limit value is set; and 5, judging the service health state of the bridge by comparing the statistical deviation between the online estimated value of the early warning index and the reference control limit value. According to the method, the nonlinear influence of the environment temperature on the non-stationary frequency sequence is eliminated, and meanwhile, the problems of large prediction error and high false alarm rate of the classical linear co-integration theory in bridge damage identification in a changing environment are solved.

Description

Technical Field

[0001] The present invention belongs to the field of bridge service performance early warning, and specifically relates to a bridge damage early warning method taking into account non-stationary variation of modal frequency. Background Art

[0002] Structural health monitoring technology is an effective means to ensure the safety of bridge operation. It is a hot topic in the field of bridge service performance early warning to establish the model of environmental and operational loads and their effects using long-term monitoring data and statistical analysis theory. Modal frequency is a commonly used sensitive feature of bridge damage, which has the advantages of easy measurement, high identification accuracy and low sensor deployment requirements. However, the frequency of real bridges under multi-source environmental interference is prone to operational variation and statistically non-stationary. Ignoring or failing to reasonably consider data non-stationarity will increase the difficulty of eliminating environmental effects and reduce the credibility of bridge damage early warning results.

[0003] The cointegration theory originated from the field of econometrics. It is a hidden variable analysis method to solve the abnormally high false alarm rate of bridge damage caused by the non-stationary characteristics of monitoring data. This method uses the long-term equilibrium relationship between multiple non-stationary variables to transform the non-stationary time series under the influence of environmental factors into a stationary series without environmental effects through linear combination, and then achieves the purpose of damage warning based on the mutation of the stationary series. The classical linear cointegration theory does not require environmental measurement information, but requires good linear correlation between monitoring variables. It has the characteristics of clear physical meaning and easy implementation.

[0004] In engineering practice, due to the complexity of the environmental conditions in which the bridge is located and the slowness of heat transfer in the temperature field of the main beam, the evolution law of the structural response is relatively complex, such as the non-Gaussian probability distribution of multi-order frequencies under seasonal temperatures, and the differences in the degree of correlation between frequency variables in different temperature ranges. If the classical linear cointegration theory is continued to be used, it will not be possible to accurately describe the true long-term equilibrium relationship between frequency variables, affecting the accuracy of eliminating environmental effects and the accuracy of damage warning. To this end, the present invention proposes a bridge damage warning method that takes into account the non-stationarity of multi-order modal frequencies, and based on this, eliminates multiple coupling influencing factors in the data, thereby improving the accuracy of bridge damage warning. Summary of the invention

[0005] The purpose of the present invention is to provide a bridge damage early warning method taking into account the non-stationary variation of modal frequency, eliminating the nonlinear influence of ambient temperature on the non-stationary frequency sequence and the non-Gaussian distribution characteristics, while overcoming the problems of large prediction error and abnormally high false alarm rate existing in the classical linear cointegration theory in bridge damage early warning under a changing environment.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A bridge damage early warning method considering non-stationary variation of modal frequency includes the following steps:

[0008] S1. Cluster analysis of multi-modal frequencies of main beams under different ambient temperature modes;

[0009] S2. Establish an implicit elimination model of environmental effects based on multimodal frequency localized cointegration;

[0010] S3, constructing a bridge damage warning indicator according to the model error in step S2;

[0011] S4. Statistically analyze the probability distribution of early warning indicators and set dynamic benchmark control limits;

[0012] S5. Damage warning of bridge online monitoring data;

[0013] S51, in the online monitoring stage, the distance from the multi-order modal frequency identified online to the center of each cluster in the offline stage is calculated, the cluster with the smallest distance is selected as the benchmark modeling data set, a multi-modal frequency localized cointegration model is constructed, and the damage warning index is calculated;

[0014] S52. Compare the statistical deviations between the online estimated values ​​of the early warning indicators and the control limits to determine whether the latest early warning indicators exceed the variation range of the normal service life of the bridge.

[0015] Furthermore, the specific method of performing cluster analysis in step S1 includes:

[0016] S11. Accelerometers are arranged at different positions of the bridge main beam to collect the acceleration response of the main beam structure when the bridge is intact under different ambient temperatures;

[0017] S12. The random subspace method is used to identify the modal parameters of the collected acceleration response, and the measured frequency F∈R of the bridge main beam is obtained. n×m , where f i ∈R 1×m represents the frequency sample at the i-th moment, n and m represent the number of samples and variables respectively; the main beam frequency data is divided into an offline training set, an online validation set and an online test set according to the proportion;

[0018] S13. Use the Dirichlet process mixture model hard clustering technology to cluster the main beam frequencies under different ambient temperatures in the offline stage.

[0019] Furthermore, in step S13, the method of clustering the main beam frequencies at different ambient temperatures in the offline stage using the Dirichlet process mixture model hard clustering technology is as follows:

[0020] S131, initialize the number of clusters k of the Dirichlet process mixture model hard clustering method = 1, the initial cluster l1 = {f1, f2, ..., f n} and cluster center μ1, where μ1 is the global mean of the frequency sample; initialize the clustering index z i =1 and i=1,2,…,n;

[0021] S132, calculate any sample point f i and cluster center μ c The Euclidean square distance d ic =||f i -μ c || 2 and c=1,2,…,k; if there exists min c d ic >λ, then k=k+1, z i = k and μ k =f i ; otherwise z i =argmin c d ic ; Then based on the clustering index z1,z2,…,z k Generate clusters l1,l2,…,l k , i.e. l j ={f i |z i =j},

[0022] S133, loop all sample points until the algorithm converges, and then the cluster center μ can be obtained c And the sample labels l in each cluster, the main beam frequency clusters are adaptively divided according to the sample labels to realize the piecewise linearization of the frequency sample sequence.

[0023] Furthermore, the method of establishing the model is:

[0024] S21, using the augmented Dickey-Fuller test to test the stationarity of the multi-order frequency series in different clusters in step S13; if the test result shows that the change trend of each frequency series is the same and the first-order single integral I(1), it indicates that each frequency variable is a non-stationary time series and there is a long-term equilibrium relationship between them;

[0025] S22. Establish a multimodal frequency localized cointegration model within each cluster:

[0026]

[0027] Where: f i is the i-th order modal frequency; e tis the cointegration model error after eliminating the temperature effect; β is the cointegration vector estimated by the Johansen test;

[0028] Furthermore, the method for constructing the bridge damage early warning index in step S3 is:

[0029] S31, if the frequency variable p in step S12 is greater than 2, and the model error E in step S22 is a multidimensional vector, the slow feature analysis is used to extract the frequency slow feature in the model error, and the objective function of extracting the feature is expressed as:

[0030]

[0031] Where: is the first-order derivative of the slow feature s of the i-th frequency with respect to time t; <g t is the sample expected value;

[0032] Afterwards, singular value decomposition is used to solve the objective function and define the slow frequency feature: s = WE, where W is the mapping matrix; then, the bridge damage warning index is calculated based on the robust Mahalanobis square distance: in and MCD are the mean vector and robust covariance matrix of the slow feature s, respectively;

[0033] S32. If the frequency variable p in step S12 is equal to 2, and the model error E in step S22 is a one-dimensional vector, the model error is directly defined as an early warning indicator.

[0034] Furthermore, the method for statistically analyzing the probability distribution of the early warning indicator and setting the dynamic benchmark control limit in step S4 is:

[0035] If the frequency variable p in step S12 is greater than 2, then step S41 is executed after step S31;

[0036] If the frequency variable p in step S12 is equal to 2, then step S42 is executed after step 32;

[0037] S41. Calculate the early warning indicator T using the kernel density estimation method 2 Benchmark control limits of

[0038] S42. Use hypothesis testing method to test whether the model error obeys normal distribution. If yes, use mean control chart to set early warning control limit. If no, use Johnson normal transformation combined with mean control chart to set early warning control limit.

[0039] S43. After completing step S41 or S42, the warning indicator vector and the control limit vector in the cluster are reordered according to the sample labels in step S13 to obtain corresponding reconstructed values ​​arranged in chronological order, thereby realizing real-time dynamic warning of bridge damage.

[0040] Beneficial effects of the present invention:

[0041] 1. The present invention considers the local strong correlation between the main beam frequencies under different environmental conditions and uses clustering technology to perform piecewise linearization on the frequency samples, so as to adapt to the non-Gaussian distribution and nonlinear correlation of the real bridge data;

[0042] 2. The present invention establishes a multi-modal frequency localized cointegration relationship model in each cluster, which greatly eliminates the influence of nonlinear environmental factors on the non-stationary frequency sequence and accurately shows the changes in the dynamic characteristics of the main beam caused by the internal factors of the structure;

[0043] 3. The present invention establishes different early warning index extraction and dynamic early warning control limit setting methods based on different modal dimensions, thereby improving the universality and early warning timeliness of the method;

[0044] 4. The present invention does not rely on environmental measurement information, overcomes the deficiency that the classical linear cointegration theory cannot timely and sensitively perceive the early damage state of the bridge main beam under a changing environment, and improves the accuracy of the damage warning results. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The present invention will be further described below in conjunction with the accompanying drawings.

[0046] Figure 1 is a flow chart of the method of the present invention;

[0047] Figure 2 is the clustering result of the first four order frequencies in the embodiment of the present invention;

[0048] Figure 3 The bridge damage warning results of the first four frequencies in the embodiment of the present invention;

[0049] Figure 4 is the clustering result of the first two order frequencies in the embodiment of the present invention;

[0050] Figure 5 It is the bridge damage warning result of the first two frequencies in the embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] The present invention discloses a bridge damage early warning method considering non-stationary variation of modal frequency, which is specifically divided into five steps: "interval clustering of multi-modal frequencies of main beams under different ambient temperature action modes", "establishment of an implicit elimination model of environmental effects based on localized cointegration of multi-modal frequencies", "construction of bridge damage early warning indicators based on cointegration model errors", "statistical analysis of the probability distribution of early warning indicators and setting of dynamic benchmark control limits" and "damage early warning of bridge online monitoring data". The implementation process of the method is as follows: Figure 1 shown.

[0053] Specifically, the steps include:

[0054] Step 1: Multi-modal frequency cluster analysis of the main beam under different ambient temperature modes

[0055] (1.1) Accelerometers are placed at different locations on the bridge girder to collect the acceleration response of the girder structure when the bridge is intact under different ambient temperatures;

[0056] (1.2) The random subspace method is used to identify the modal parameters of the collected acceleration response, and the measured frequency F∈R of the bridge main beam is obtained. n×m , where f i ∈R 1×m represents the frequency sample at the i-th moment, n and m represent the number of samples and variables respectively; the main beam frequency data is divided into an offline training set, an online validation set and an online test set according to the ratio of 80%, 10% and 10%;

[0057] (1.3) The Dirichlet process mixture model hard clustering technology is used to cluster the main beam frequencies under different ambient temperatures in the offline stage. The specific steps are as follows:

[0058] (1.3.1) Initialize the number of clusters k = 1 for the Dirichlet process mixture model hard clustering method, and the initial cluster l1 = {f1, f2, …, f n} and cluster center μ1, where μ1 is the global mean of the frequency sample; initialize the clustering index z i =1 and i=1,2,…,n;

[0059] (1.3.2) Calculate any sample point f i and cluster center μ c The Euclidean square distance d ic =||f i -μ c || 2 and c=1,2,…,k; if there exists min c d ic >λ, then k=k+1, z i = k and μ k =f i; otherwise z i =argmin c d ic ; Then based on the clustering index z1,z2,…,z k Generate clusters l1,l2,…,l k , i.e. l j ={f i |z i =j},

[0060] (1.3.3) Loop through all sample points until the algorithm converges, and then the cluster center μ can be obtained. c and the sample labels l in each cluster, and adaptively divide the main beam frequency clusters according to the sample labels to achieve piecewise linearization of the frequency sample sequence;

[0061] Step 2: Establishment of an implicit elimination model for environmental disturbance effects based on multimodal frequency localized cointegration

[0062] (2.1) The augmented Dickey-Fuller test is used to test the stationarity of the multi-order frequency series in different clusters in step S13; if the test results show that the change trends of the frequency series are the same and the first-order single integral I(1), it indicates that the frequency variables are non-stationary time series and there is a long-term equilibrium relationship between them;

[0063] (2.2) Establish a multimodal frequency localized cointegration model within each cluster:

[0064]

[0065] Where: f i is the i-th order modal frequency; e t is the cointegration model error after eliminating the temperature effect; β is the cointegration vector estimated by the Johansen test;

[0066] Step 3: Construction of bridge damage warning indicators based on cointegration model errors

[0067] (3.1) If the frequency variable p in step (1.2) is greater than 2, then the model error E in step (2.2) is [e1, e2, …, e n ] is a multidimensional vector, which is standardized, and the slow feature analysis is used to extract the frequency slow feature in the model error E. The objective function of extracting this feature is expressed as:

[0068]

[0069] Where: is the first-order derivative of the slow feature s of the i-th frequency with respect to time t; <g> t is the sample expected value;

[0070] Afterwards, singular value decomposition is used to solve the objective function and define the slow frequency feature: s = WE, where W is the mapping matrix; then, the bridge damage warning index is calculated based on the robust Mahalanobis square distance: in and MCD are the mean vector and robust covariance matrix of the slow feature s, respectively;

[0071] (3.2) If the frequency variable p in step S12 is equal to 2, and the model error E in step S22 is a one-dimensional vector, the model error is directly defined as the early warning indicator;

[0072] Step 4: Statistically analyze the probability distribution of the early warning indicator and set the dynamic benchmark control limit (4.1) If the frequency variable p in step (1.2) is greater than 2, then step (4.1) is executed after step (3.1), that is, the dynamic early warning control limit setting based on the kernel density estimation method, specifically: the early warning indicator T is calculated using the kernel density estimation method 2 The probability density function, cumulative probability density function and inverse cumulative probability density function of the significance level α=0.003 are given as the early warning indicator T 2 Benchmark control limits for:

[0073]

[0074] Where: F -1 (g) is the early warning indicator T 2 The inverse cumulative probability density function of , 1-α is the confidence level corresponding to the significance level α;

[0075] (4.2) If the frequency variable p in step (1.2) is equal to 2, then step (4.2) is executed after step (3.2), that is, the dynamic early warning control limit setting based on the mean control chart, specifically: using the hypothesis test method to test whether the model error obeys the normal distribution, if yes, using the mean control chart to set the early warning control limit; if not, using the Johnson transformation to convert the non-normally distributed model error data into normal or approximately normal distribution data, and then using the mean control chart to set the early warning control limit;

[0076] (4.3) After completing step (4.1) or step (4.2), the warning indicator vector and the control limit vector in the cluster are reordered according to the sample labels involved in step (1.3) to obtain the corresponding reconstructed values ​​arranged in chronological order, thereby realizing real-time dynamic warning of bridge damage.

[0077] Step 5: Damage warning of bridge online monitoring data

[0078] (5.1) In the online monitoring phase, the distances from the multi-order modal frequencies identified online to the centers of each cluster in the offline phase are calculated, the cluster with the smallest distance is selected as the benchmark modeling data set, a multi-modal frequency localization cointegration model is constructed, and damage warning indicators are calculated;

[0079] (5.2) Compare the statistical deviations between the online estimated values ​​of the early warning indicators and the control limits to determine whether the latest early warning indicators exceed the variation range of the normal service life of the bridge, and finally give the judgment results of the operational health status of the bridge.

[0080] Example

[0081] The measured data analysis of a beam bridge is used for illustration. The beam bridge is a standard post-tensioned prestressed concrete double-chamber box girder bridge with a main span of 30 meters and side spans of 14 meters on both sides. The bridge was installed with a structural health monitoring system and continuously monitored on site for 10 months. The acceleration response under different ambient temperatures was collected with a sampling frequency of 100Hz. In the later stage of monitoring, bridge damage conditions such as foundation settlement and concrete spalling were gradually introduced in a human-controllable manner to obtain the acceleration response under the actual damage state.

[0082] (1) The random subspace method is used to automatically identify the first four frequency samples of 3932 hours from the bridge acceleration response in units of hours, and divide them into training set, validation set and test set. Among them, the second-order mode is nonlinearly related to the other modes.

[0083] (2) The effectiveness of the method of the present invention is verified using the first four frequencies, where the frequency variable in step (1.2) is greater than 2. Figure 2 The frequency clustering results in show that the first 4 frequencies are divided into 5 clusters, and the frequency variables in each cluster are linearly correlated. Table 1 gives the results of the augmented Dickey-Fuller test of the first 4 frequencies. It can be seen that: at the 5% significance level, the first 4 frequency series are first-order single-integrated non-stationary series, which meets the conditions for the use of cointegration theory. The error dimension of the model after cointegration analysis is equal to 3. Figure 3 The bridge damage warning results show that the damage warning control limit of the present invention has dynamic time-varying properties, can effectively eliminate the nonlinear influence of environmental factors on the bridge frequency, and can highly sensitively perceive abnormal frequency changes when the structure is damaged.

[0084] Table 1 Results of the augmented Dickey-Fuller test for the first four frequencies and their first-order difference sequences (5% confidence level)

[0085]

[0086]

[0087] (3) The effectiveness of the method of the present invention is verified using the first two measured frequencies, where the frequency variable in step (1.2) is equal to 2. Figure 4 The frequency clustering results in show that the first two frequencies are divided into four clusters, and the frequency variables within each cluster are linearly correlated; Table 2 gives the ADF unit root test results of the first two frequencies. It can be seen that: at the 5% significance level, the first two frequency sequences meet the conditions for the use of cointegration theory, and the model error dimension after cointegration analysis is equal to 1. Figure 5 The damage warning results in the paper show that the present invention can timely and effectively identify damage under the premise of low false alarm rate, and has good engineering application value.

[0088] Table 2 Results of the augmented Dickey-Fuller test of the first two frequencies and their first-order difference sequences (5% confidence level)

[0089]

[0090]

[0091] The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.< / g>

Claims

1. A bridge damage early warning method considering non-stationary variation of modal frequency, characterized in that: The steps include: S1. Cluster analysis of multi-modal frequencies of main beams under different ambient temperature modes; S2. Establish an implicit elimination model of environmental effects based on multimodal frequency localized cointegration; S3, constructing a bridge damage warning indicator according to the model error in step S2; S4. Statistically analyze the probability distribution of early warning indicators and set dynamic benchmark control limits; S5. Damage warning of bridge online monitoring data; S51, in the online monitoring stage, the distance from the multi-order modal frequency identified online to the center of each cluster in the offline stage is calculated, the cluster with the smallest distance is selected as the benchmark modeling data set, a multi-modal frequency localization cointegration model is constructed, and the damage warning index is calculated; S52. Compare the statistical deviations between the online estimated values ​​of the early warning indicators and the control limits to determine whether the latest early warning indicators exceed the variation range of the normal service life of the bridge.

2. A bridge damage early warning method considering non-stationary variation of modal frequency according to claim 1, characterized in that: The specific method of performing cluster analysis in step S1 includes: S11. Accelerometers are arranged at different positions of the bridge main beam to collect the acceleration response of the main beam structure when the bridge is intact under different ambient temperatures; S12. The random subspace method is used to identify the modal parameters of the collected acceleration response, and the measured frequency F∈R of the bridge main beam is obtained. n×m , where f i ∈R 1×m represents the frequency sample at the i-th moment, n and m represent the number of samples and variables respectively; the main beam frequency data is divided into an offline training set, an online validation set and an online test set according to the proportion; S13. Use the Dirichlet process mixture model hard clustering technology to cluster the main beam frequencies under different ambient temperatures in the offline stage.

3. A bridge damage early warning method considering non-stationary variation of modal frequency according to claim 2, characterized in that: In step S13, the method of clustering the main beam frequencies at different ambient temperatures in the offline stage using the Dirichlet process mixture model hard clustering technology is as follows: S131, initialize the number of clusters k of the Dirichlet process mixture model hard clustering method = 1, the initial cluster l1 = {f1, f2, ..., f n } and cluster center μ1, where μ1 is the global mean of the frequency sample; initialize the clustering index z i =1 and i=1,2,…,n; S132, calculate any sample point f i and cluster center μ c The Euclidean square distance d ic =||f i -μ c || 2 and c=1,2,…,k; if there exists min c d ic >λ, then k=k+1, z i = k and μ k =f i ; otherwise z i =argmin c d ic ; Then based on the clustering index z1,z2,…,z k Generate clusters l1,l2,…,l k , i.e. l j ={f i |z i =j}, S133, loop all sample points until the algorithm converges, and then the cluster center μ can be obtained c And the sample labels l in each cluster, the main beam frequency clusters are adaptively divided according to the sample labels to realize the piecewise linearization of the frequency sample sequence.

4. A bridge damage early warning method considering non-stationary variation of modal frequency according to claim 3, characterized in that: The method to build the model is: S21, using the augmented Dickey-Fuller test to test the stationarity of the multi-order frequency series in different clusters in step S13; if the test result shows that the change trend of each frequency series is the same and the first-order single integral I(1), it indicates that each frequency variable is a non-stationary time series and there is a long-term equilibrium relationship between them; S22. Establish a localized cointegration model of multiple frequencies within each cluster: Where: f i is the i-th order modal frequency; e t is the cointegration model error after eliminating the temperature effect; β is the cointegration vector estimated by the Johansen test.

5. The bridge damage early warning method considering non-stationary variation of modal frequency according to claim 4 is characterized in that: The method for constructing the bridge damage early warning index in step S3 is: S31, if the frequency variable p in step S12 is greater than 2, and the model error E in step S22 is a multidimensional vector, the slow feature analysis is used to extract the frequency slow feature in the model error, and the objective function of extracting the feature is expressed as: Where: is the first-order derivative of the slow feature s of the i-th frequency with respect to time t; <g t is the sample expected value; After that, singular value decomposition is used to solve the objective function and define the slow frequency feature: s = WE, where W is the mapping matrix; then, the bridge damage warning index is calculated based on the robust Mahalanobis square distance: in and MCD are the mean vector and robust covariance matrix of the slow feature s, respectively; S32. If the frequency variable p in step S12 is equal to 2, and the model error E in step S22 is a one-dimensional vector, the model error is directly defined as an early warning indicator.

6. A bridge damage early warning method considering non-stationary variation of modal frequency according to claim 5, characterized in that: The method for statistically analyzing the probability distribution of the early warning indicator and setting the dynamic benchmark control limit in step S4 is: If the frequency variable p in step S12 is greater than 2, then step S41 is executed after step S31; If the frequency variable p in step S12 is equal to 2, then step S42 is executed after step 32; S41. Calculate the early warning indicator T using the kernel density estimation method 2 Benchmark control limits of S42. Use hypothesis testing method to test whether the model error obeys normal distribution. If yes, use mean control chart to set early warning control limit; If not, the Johnson normal transformation combined with the mean control chart is used to set the early warning control limit; S43. After completing step S41 or S42, the warning indicator vector and the control limit vector in the cluster are reordered according to the sample labels in step S13 to obtain corresponding reconstructed values ​​arranged in chronological order, thereby realizing real-time dynamic warning of bridge damage.

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