Bridge support displacement early warning method

Abstract

The invention provides a bridge support displacement early warning method, which comprises the following steps of: firstly, collecting early-stage bridge temperature and support displacement data, preprocessing the data, and removing abnormal values to serve as a training set; then establishing a temperature-displacement prediction model; combining the temperature sample vector and the displacement data corresponding to the time sequence, calculating the mean value and the covariance of the to-be-measured sample vector, calculating the posterior probability of the displacement data corresponding to the temperature sample to which the to-be-measured sample vector belongs, obtaining a displacement predicted value according to Gaussian distribution characteristics, and obtaining the difference between a displacement measured value and the predicted value; and then defining an early warning index by using a mahalanobis distance to obtain an early warning threshold value, and finally performing standardization processing on an upper calculation value as an early warning value. According to the invention, the service performance of the bridge support can be observed online in real time, the cost is low, the safety performance of a bridge structure can be effectively improved, the interference of a temperature factor on a monitoring result can be effectively eliminated, the early warning accuracy of displacement is extremely high, and the false alarm rate is low.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge displacement monitoring, and particularly relates to a method for early warning of bridge bearing displacement. Background Art

[0002] Bridge bearings are important components connecting the upper and lower structures of bridges. They can transfer vertical and horizontal loads, have the ability to adapt to deformations such as temperature, concrete shrinkage, creep, and settlement, and can achieve the functions of restricting displacement, ensuring structural stability and overall safety. However, with the increase of the service time of bridges, affected by environmental factors and repeated loads, the performance of bearings will degenerate to varying degrees, thus affecting the safety of bridge structures. And the on-line monitoring of bridge bearings is easily affected by environmental factors (especially temperature factors), which may lead to distorted monitoring results. Therefore, it is necessary to invent a method for early warning of bridge bearing displacement. Summary of the Invention

[0003] In view of this, the present invention aims to overcome the defects in the prior art and proposes a method for early warning of bridge bearing displacement.

[0004] To achieve the above object, the technical solution of the present invention is realized as follows:

[0005] A method for early warning of bridge bearing displacement includes the following steps:

[0006] S1. Collect the early bridge temperature and bearing displacement data, preprocess the data, and remove the outliers as the training set;

[0007] S2. Establish a temperature-displacement prediction model;

[0008]

[0009] In the formula: K is the number of Gaussian components; ω k is the combination coefficient of the k-th Gaussian component (ω k …0 and ); μ k and Σ k are the mean vector and covariance matrix of the k-th Gaussian component respectively;

[0010] S3. Define p(x|k) as the probability density function of the k-th Gaussian component, specifically:

[0011]

[0012] S4. For the temperature sample vector x t corresponding to the time series and the displacement data d tCombine them to calculate the mean μ and covariance Σ of the sample vector to be measured, and then calculate the posterior probability p(d t |x t ) of the displacement data corresponding to the temperature sample to be measured.

[0013] p(d t |x t ) = p(d t |μ d|t,k' , Σ d|t,k' )

[0014] where: μ d|t,k' and Σ d|t,k' are the corresponding mean and covariance respectively;

[0015] S5. Obtain the displacement prediction value p t according to the Gaussian distribution characteristics, and obtain the difference between the measured displacement value and the predicted value;

[0016] e = d t -p t

[0017] S6. Define the warning index using the Mahalanobis distance, and the Mahalanobis distance is expressed as follows:

[0018] D = e t (Σ d|t,k' ) -1 e

[0019] The warning threshold can be obtained:

[0020]

[0021] where: represents the chi-square distribution with degree of freedom h (the value of h is selected according to the actual monitoring situation), and α is the significance level

[0022] S7. Standardize the above calculated value as the warning value:

[0023]

[0024] When the warning value is less than 1, the bearing performance is normal; when the warning value is greater than 1, the bearing performance is abnormal.

[0025] Furthermore, in step S2, let represent the parameter set composed of all parameters in GMM. First, calculate the log-likelihood function corresponding to the data set to obtain the optimal estimate

[0026]

[0027] The problem of optimal parameter estimation of GMM is transformed into the following optimization problem:

[0028]

[0029] Furthermore, the Expectation-Maximization algorithm is used for solution. First, the initial parameters of GMM are set as Θ (0) , and then iterative calculations are carried out in two steps.

[0030] Furthermore, iterative calculations are carried out in two steps, namely the E-step and the M-step. Specifically:

[0031] In the E-step, based on the current parameters Θ (i) , the posterior probability that the j-th sample vector x j belongs to the k-th Gaussian component is calculated:

[0032]

[0033] In the M-step, the parameters Θ (i+1) are iteratively updated:

[0034]

[0035] Repeat the E-step and the M-step until convergence, and the optimal parameters of GMM can be obtained. Furthermore, the joint probability density function model between temperature and displacement can be obtained.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] The method provided by the present invention can realize real-time online monitoring of the bearing displacement, saving manpower and financial resources compared with the traditional regular inspection method, and having higher safety. On the other hand, compared with the traditional online warning method, it takes into account the influence of environmental effects (temperature factor), can effectively eliminate the interference of environmental factors on the monitoring results, and achieves the effect of significantly improving the warning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0039] Figure 1 is the technical roadmap of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0040] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0041] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0042] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installed", "connected", "coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific circumstances.

[0043] The present invention will be described in detail below with reference to the drawings and in conjunction with embodiments.

[0044] In view of the fact that the performance of in-service bridge bearings will degenerate to varying degrees with the increase of service time, in order to timely grasp the working performance of bridge bearings, a bridge bearing displacement early warning method is invented. By collecting the temperature and displacement data of bridge bearings in the early stage, preprocessing the monitoring data, establishing a bearing temperature-displacement prediction model, further defining early warning indicators, and then realizing real-time early warning identification of in-service bridge bearings. Specifically, a bridge bearing displacement early warning method, as Figure 1 shown, includes the following steps:

[0045] S1. Collect the temperature and bearing displacement data of the bridge in the early stage, preprocess the data, and remove the outliers as the training set;

[0046] S2. Establish a temperature-displacement prediction model; to effectively solve the multi-peak distribution characteristics of temperature-displacement monitoring data, based on the Gaussian Mixture Model (GMM) in statistics, a linear combination of multiple Gaussian components is realized, which can fit the probability density function of multi-dimensional data, and by appropriately increasing the number of Gaussian components, the probability density function of multi-peak distribution data can be accurately fitted.

[0047]

[0048] Where: K is the number of Gaussian components; ω k is the combination coefficient of the k-th Gaussian component (ω k …0 and ); μ k and Σ k are the mean vector and covariance matrix of the k-th Gaussian component respectively;

[0049] S3. Define p(x|k) as the probability density function of the k-th Gaussian component, specifically:

[0050]

[0051] Let represent the parameter set composed of all parameters in GMM. To obtain the optimal estimate of the parameter set Θ the logarithmic likelihood function corresponding to the data set can be calculated first:

[0052]

[0053] Then, the optimal parameter estimation problem of GMM is transformed into the following optimization problem:

[0054]

[0055] To solve the above optimization problem, the Expectation-Maximization algorithm is used for solution. First, set the initial parameters of GMM as Θ (0) , and then perform iterative calculations in two steps (E step and M step).

[0056] In the E step, based on the current parameter Θ (i) , calculate the posterior probability that the j-th sample vector x j belongs to the k-th Gaussian component:

[0057]

[0058] In the M step, iteratively update the parameter Θ (i+1) :

[0059]

[0060] Repeat steps E and M until convergence to obtain the optimal parameters of the GMM. Then obtain the joint probability density function model between temperature and displacement.

[0061] S4. For the temperature sample vector x corresponding to the time series t and the displacement data d t combine them, calculate the mean μ and covariance Σ for the sample vector to be measured, and then calculate the posterior probability p(d t |x t ) of the displacement data corresponding to the temperature sample. Thus, the marginal probability density p(x t ) of x can be obtained. Furthermore, the posterior probability p(k|x t ) of x for the k-th Gaussian model can be obtained. Assign the temperature sample to the Gaussian model k' corresponding to the maximum posterior probability. t For the k-th Gaussian model, t ) of the displacement data corresponding to the temperature sample. Thus, the marginal probability density p(x

[0062] Furthermore, it can be obtained that:

[0063] p(d t |x t ) = p(d t |μ d|t,k' , Σ d|t,k' )

[0064] Where: μ d|t,k' and Σ d|t,k' are the corresponding mean and covariance respectively;

[0065] S5. Based on the characteristics of the Gaussian distribution, obtain the displacement prediction value p t , and obtain the difference between the measured displacement value and the predicted value;

[0066] e = d t -p t

[0067] S6. Define the warning index using the Mahalanobis distance. The Mahalanobis distance is expressed as follows:

[0068] D = e t (Σ d|t,k' ) -1 e

[0069] The warning threshold can be obtained:

[0070]

[0071] Where: represents the chi-square distribution with degree of freedom h (the value of h is selected according to the actual monitoring situation), and α is the significance level

[0072] S7. Standardize the above calculated value as the warning value:

[0073]

[0074] When the warning value is less than 1, the bearing performance is normal; when the warning value is greater than 1, the bearing performance is abnormal.

[0075] The present invention can observe the service performance of bridge bearings in real time and online by establishing a temperature-displacement prediction model. It has a low cost and can effectively improve the safety performance of bridge structures. Compared with traditional monitoring methods, this method can effectively eliminate the interference of temperature factors on the monitoring results, has a very high early warning accuracy rate for displacement, a low false alarm rate, can accurately judge the service performance of the bearings, has great popularization value and good social benefits, and provides a new reference method for online early warning of bridge bearing displacement.

[0076] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A bridge support displacement early warning method, characterized in that: The steps include: S1. Collect the early bridge temperature and support displacement data, pre-process the data, and remove the abnormal values ​​as a training set; S2, establishing a temperature-displacement prediction model; Where: K is the number of Gaussian components; ω k is the combination coefficient of the kth Gaussian component (ω k …0 and ); μ k and Σ k are the mean vector and covariance matrix of the kth Gaussian component respectively; S3. Define p(x|k) as the probability density function of the kth Gaussian component, specifically: S4, the temperature sample vector x corresponding to the time series t and displacement data d t Combine them, calculate the mean μ and covariance Σ of the sample vector to be tested, and then calculate the posterior probability p(d t |x t ), p(d t |x t )=p(d t |µ d|t,k' ,Σ d|t,k' ) Where: μ d|t,k' and Σ d|t,k' are the corresponding means and covariances respectively; S5. Determine the displacement prediction value p based on Gaussian distribution characteristics t , the difference between the measured displacement and the predicted displacement is obtained; e=d t -p t S6. Use Mahalanobis distance to define early warning indicators. The Mahalanobis distance is expressed as follows: D=e t (Σ d|t,k' ) -1 And Available warning thresholds: Where: represents the chi-square distribution with h degrees of freedom, and α is the significance level S7. Standardize the above calculated value as the warning value: When the warning value is less than 1, the bearing performance is normal; When the warning value is greater than 1, the bearing performance is abnormal.

2. A bridge support displacement early warning method according to claim 1, characterized in that: In step S2, let Represents the parameter set composed of all parameters in GMM. First, calculate the log-likelihood function corresponding to the data set to obtain the optimal estimate of the parameter set Θ The optimal parameter estimation problem of GMM is transformed into the following optimization problem:

3. A bridge support displacement early warning method according to claim 2, characterized in that: The expected maximum algorithm is used to solve the problem. First, the initial parameters of GMM are set to Θ (0) , and then iterative calculation is performed in two steps.

4. A bridge support displacement early warning method according to claim 3, characterized in that: The iterative calculation is divided into two steps: E step and M step, specifically: Step E is based on the current parameter Θ (i) , calculate the jth sample vector x j The posterior probability of belonging to the kth Gaussian component is: Iterate the update parameters Θ in M ​​steps (i+1) : Repeat steps E and M until convergence, and the optimal parameters of GMM can be obtained. Then the joint probability density function model between temperature and displacement can be obtained.

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