Unsupervised learning driven bridge support tensile function degradation grading diagnosis method

Abstract

The invention belongs to the technical field of bridge structure key restraint device performance monitoring and evaluation, and discloses an unsupervised learning driven bridge support tensile function degradation grading diagnosis method. The method comprises the following steps: (1) constructing a relationship between support tensile stiffness degradation and bridge frequency; (2) unsupervised learning driven environmental effect separation; and (3) carrying out multi-stage diagnosis on degradation of the tensile function of the support. According to the method, the mapping relation between the tensile stiffness of the support and the frequency of the bridge in different states is obtained based on the Rayleigh method. Then, a manifold learning assisted regularization Gaussian mixture model is constructed, and environmental effect separation of frequency data is realized. And taking a negative logarithm form of a model output value as a diagnosis index. And setting a hierarchical control limit by adopting an EWMA control chart based on statistical characteristics of indexes when the support is normal and locally fractured. Finally, the example research of a cable-stayed bridge shows that the method can realize hierarchical diagnosis of the degradation of the tensile function of the support, and can provide guidance for a management and maintenance department to adopt different decisions for different degradation degrees of the tensile function of the support. The method has a high engineering application value in the technical field of performance monitoring and evaluation of the key constraint device based on the bridge structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of performance monitoring and evaluation of key constraint devices of bridge structures, and particularly relates to a method for grading diagnosis of anti-tension function degradation of bridge bearings driven by unsupervised learning. BACKGROUND

[0002] As a key constraint device of a bridge, a bearing can transmit loads from an upper structure to a lower structure. According to the stress form of the bearing, it can be divided into pressure-only bearing and tension-compression bearing. The tension-compression bearing refers to a bearing capable of bearing both pressure and tension, which is usually arranged at a bridge pier where negative reaction force appears. As a vulnerable component, the tension-compression bearing will not only appear the same sliding function abnormality as the pressure-only bearing, but also appear anti-tension function degradation. This is caused by the repeated tension and compression of the bearing under external loads, which leads to the damage of the anti-tension device. The degradation of the anti-tension function of the bearing changes the boundary conditions of the structure and affects the safe operation of the bridge. However, since the anti-tension device is usually arranged inside the bearing structure, the traditional manual detection and machine vision method cannot effectively detect the damage of the anti-tension device. Therefore, it is of great engineering significance to carry out research on the diagnosis of anti-tension function degradation of the bearing based on monitoring data.

[0003] With the wide application of health monitoring technology, more and more long-span bridges are equipped with health monitoring system. It usually deploys high-precision sensors at key locations to monitor the service state of the bridge. Many scholars based on the monitoring data collected by the health monitoring system, to early warning and evaluation of the degradation of the sliding function of the bearing. Yang based on deep learning algorithm to establish the prediction model of the thermally induced displacement of the bearing, to realize the identification of the wear detection of bridge sliding bearing (Wear Detection Of Bridge Sliding Bearing Based On Temporal Variation Of Thermally Induced Daily Displacement Amplitude). Wu established the hysteresis model of temperature and displacement, and based on the cumulative and control chart to early warning of the sliding function degradation of the bearing (Friction Anomaly Alarm for Bridge Sliding Bearings Under Operating Environmental Conditions). Yang through the extraction of equivalent sliding friction coefficient index by monitoring data, to realize the multilevel diagnosis of bridge bearing wear (Multilevel Diagnosis of Bridge Bearing Wear By Monitoring Equivalent Sliding Friction Coefficient). Wei considers the wear of the sliding plate of the bearing under the action of temperature and vehicle load, to realize the prediction of the service life of the bearing (Wear Life Prediction of Sliding Bearings Based on Multitype Monitoring Data of Bridges). But the research on the degradation of the tensile function of the bearing is relatively less. Wu based on Rayleigh method to analyze the sensitivity of bridge vertical bending frequency to the degradation of tensile function of bearing (Damage Detection of Tension Pendulums in Cable-Stayed Bridges using Structural Frequency Variance). So far, although some scholars have carried out early warning on the degradation of the tensile function of the bearing. But it does not reveal the change characteristics of the bridge frequency under different damage conditions of the tensile device, and cannot realize the multilevel diagnosis of the degradation of the tensile function of the bearing. SUMMARY

[0004] In view of the defects in the prior art, the present application provides a kind of unsupervised learning driven bridge bearing tensile function degradation multilevel diagnosis method, and the specific technical solutions are as follows: Step-1: Analyze the variation law of the vertical bending frequency of the bridge structure when the tension-compression bearing changes from normal working condition to damaged working condition, and construct the relationship between the tensile stiffness degradation of the bearing and the bridge frequency. Step-2: Use Gaussian Mixture Model (GMM) to cluster the frequency data to reduce the influence of environmental factors and achieve unsupervised learning-driven separation of environmental effects; Step-3: Based on the statistical characteristics of the indicators of the bearing tensile device under different working conditions, an exponential weighted control chart is used to classify and diagnose the performance degradation of the bearing tensile device.

[0005] Preferably, Step-1 uses the Rayleigh method to analyze the variation law of the vertical bending frequency of the bridge structure from normal working condition to damaged working condition under tension-compression bearings. Based on the law of conservation of energy, if the energy absorbed by damping force is not considered, the total energy of the system during free vibration is conserved, where the maximum kinetic energy should be equal to the maximum potential energy.

[0006] (1) Support is normal Considering the direction of force on the support, the working state of tension-compression supports can be divided into two categories: compression and tension. When the support is under compression, the tensile device in the support does not function, the tension in the support is zero, and there is no potential energy in the support. The theoretical formula for the vertical bending frequency of a cable-stayed bridge can be approximately expressed as: In the formula, Indicates the number of cables; Indicates the first The axial stiffness of the cable; Indicates the bridge as the first During the free vibration of the first vertical bending mode, the first The amplitude of the cable; Indicates the first The horizontal angle of the cable; Indicates the first The length of the cable; Indicates the bridge number Vertical bending frequency; This indicates the mass per unit length of the main beam; Indicates the first Vibration shape of the main beam in the vertical bending mode; Indicates the length of the main beam; Preferably, when the support is under tension, the tensile device in the support elongates to resist the lifting tendency of the main beam, that is, the support has potential energy at this time. Based on the above assumptions and analysis, the theoretical formula for the vertical bending frequency of a cable-stayed bridge can be approximately expressed by formula (2). However, since the elongation of the tensile device of the support is small, it is a millimeter-level change. Therefore, the change in the vertical bending frequency of the bridge can be ignored.

[0007] wherein, represents the number of bearings; represents the axial stiffness of the bearing at the th bearing; represents the amplitude of the girder at the th bearing position; represents the length of the tensile device of the th bearing; (2) Bearing damage When the tensile device of the tensile-compressive bearing is partially broken, if the bearing is in a compressive state, the theoretical formula of the vertical bending frequency of the cable-stayed bridge is represented by formula (1). If a negative reaction force appears at the bearing under the action of external load, and the tensile stiffness is reduced due to the partial breakage of the tensile device. The theoretical formula of the vertical bending frequency of the bridge can be represented as: wherein, , , respectively represent the mode shape function of the girder, the amplitude at the cable position and the amplitude at the bearing position when the bearing is in a tensile state; represents the degree of partial breakage of the tensile device of the bearing, .

[0008] Preferably, when the tensile device of the tensile-compressive bearing is completely broken, the bearing loses the tensile resistance, and the boundary condition of the bridge changes. The vertical bending frequency of the bridge can be represented as: wherein, represents the mode shape function of the girder when the tensile device of the bearing is completely broken; represents the amplitude at the th cable when the tensile device of the bearing is completely broken; Preferably, the Step-2 unsupervised learning driven environmental effect separation: a Gaussian mixture model (GMM) is used to cluster the frequency data to reduce the influence of environmental factors and realize unsupervised learning driven environmental effect separation; Under variable environmental conditions, the non-stationary characteristics of the bridge modal frequency often limit its application in the field of structural health monitoring. Therefore, the present application uses a Gaussian mixture model (Gaussian mixture model, GMM) to cluster the frequency data to reduce the influence of environmental factors.

[0009] Given the training data , the probability density function of the GMM can be represented as: wherein, Indicates the parameters of GMM, ; Indicates the first The weights of each Gaussian component; This represents the total number of Gaussian distributions; , They represent the first The mean vector and covariance matrix of a Gaussian distribution; Indicates the first The probability density function of a Gaussian distribution can be expressed by the following formula: Based on formulas (5)-(6), the GMM can be characterized by the mean vector, covariance matrix, and mixed weights. Then, the maximum likelihood method can be used to evaluate the parameters. The log-likelihood function of the GMM can be expressed as: Preferably, to further constrain the clustering results of adjacent data points, this invention introduces the Local Linear Embedding (LLE) algorithm from popular learning. This invention incorporates LLE as a regularization term into the objective function of the Generative Model (GMM), using the LLE weight matrix to constrain the clustering results of the GMM, thereby improving the model's clustering performance on frequency data. Regularization term The formula can be expressed as: in, Indicates LLE-based computation right The linear reconstruction weights reflect the local geometric relationships in high-dimensional space; , These represent the known model parameters. Down, , The probability density.

[0010] GMM objective function with LLE regularization term As shown in formula (9), compared with the traditional GMM objective function, it can guarantee that the probability distribution of nearest neighbors is similar, thus improving the clustering effect of the model on frequency data.

[0011] In the formula, Represents the regularization parameter; After the unknown parameters in formula (9) are determined, the GMM-LLE model of the frequency data in normal state can be obtained.

[0012] Preferably, the Step-3 support anti-tension function degradation multi-stage diagnosis: based on the statistical characteristics of the indexes of the support anti-tension device under different working conditions, the performance degradation of the support anti-tension device is diagnosed by using an exponential weighted control chart.

[0013] The present application takes the negative logarithmic form of the Gaussian mixture model as the diagnosis index of the support anti-tension function degradation , as shown in formula (10).

[0014] In the formula, represents the frequency data obtained by real-time monitoring data, . The present application is based on the statistical characteristics of the indexes of the support anti-tension device under different working conditions, and the performance degradation of the support anti-tension device is diagnosed by using an exponential weighted control chart. The exponential weighted control chart can apply different weights to the historical indexes and real-time indexes in the identification process, and then realize the identification of the index deviation. The EWMA control chart can be expressed as: In the formula, represents a smoothing parameter, . represents the weighted cumulative sum of the index; In order to realize the multi-stage diagnosis of the local fracture and complete fracture of the support anti-tension device, the present application sets different control limits based on the EWMA control chart. The control limit of the EWMA control chart can be expressed as: In the formula, , respectively represent the control limits of the local fracture and complete fracture of the support anti-tension device; , respectively represent the mean of the index when the support anti-tension device is normal and locally fractured; is a constant, used to define the width of the control limit; , respectively represent the standard deviation of the index when the support anti-tension device is normal and locally fractured.

[0015] Compared with the prior art, the present application has the following beneficial effects: 1. The mapping relationship between the support tensile stiffness and the bridge frequency constructed in the application can provide theoretical support for the grading diagnosis of the tensile function degradation of the cable-stayed bridge support.

[0016] 2. The unsupervised learning driven environmental effect separation method proposed in the application can realize the environmental effect separation of the bridge frequency data under unknown temperature data.

[0017] 3. The support tensile function degradation grading diagnosis method proposed in the application can provide guidance for the bridge management and maintenance department to formulate different repair and replacement strategies according to different degradation degrees of the support. DETAILED DESCRIPTION

[0018] Figure 1 The flowchart of the method of the application is shown in the figure. Figure 2 The environmental effect separation diagram is shown in the figure. Figure 3 The support tensile function degradation grading diagnosis diagram is shown in the figure. DETAILED DESCRIPTION

[0019] The application will be further described in detail in combination with specific implementation manners.

[0020] The support tensile function degradation grading diagnosis method of the application is divided into two steps of "unsupervised learning driven environmental effect separation" and "support tensile function degradation grading diagnosis", and the method implementation flow is shown in the figure. Figure 1

[0021] In a specific numerical example, the monitoring data of a cable-stayed bridge in service in China is used for verification. First, the frequency data is extracted based on the bridge vertical acceleration data. Then, the environmental effect in the frequency data is separated according to step 2, as shown in the figure. Figure 2

[0022] Finally, the support tensile function degradation is graded and diagnosed according to step 3 of the application, as shown in the figure. Figure 3

[0023] ​​​Those skilled in the art should understand that the above description is only the preferred embodiment of the present application, and does not constitute a limitation to the present application. Any modification, equivalent replacement or improvement made in the spirit and principle of the present application should be considered as part of the protection scope of the present application.

Claims

1. The working steps of the unsupervised learning-driven graded diagnosis method for the degradation of tensile function of bridge bearings are as follows: Step-1: Analyze the variation law of the vertical bending frequency of the bridge structure when the tension-compression bearing changes from normal working condition to damaged working condition, and construct the relationship between the tensile stiffness degradation of the bearing and the bridge frequency. Step-2: Use Gaussian Mixture Model (GMM) to cluster the frequency data to reduce the influence of environmental factors and achieve unsupervised learning-driven separation of environmental effects; Step-3: Based on the statistical characteristics of the indicators of the bearing tensile device under different working conditions, an exponential weighted control chart is used to classify and diagnose the performance degradation of the bearing tensile device.

2. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 1, characterized in that: Under normal operating conditions, considering the force direction of the support, the working state of the tension-compression support is divided into two categories: compression and tension. Under the compression state, the formula for the vertical bending frequency of the cable-stayed bridge is as follows: ； In the formula, Indicates the bridge number Vertical bending frequency; Indicates the number of cables; Indicates the first The axial stiffness of the cable; Indicates the bridge as the first During free vibration of the first vertical bending mode, the first... The amplitude of the cable; Indicates the first The horizontal angle of the cable; Indicates the first The length of the cable; This indicates the mass per unit length of the main beam; Indicates the first Vibration shape of the main beam in the vertical bending mode; Indicates the length of the main beam; The formula for the vertical bending frequency of a cable-stayed bridge when the support is under tension is as follows: ； In the formula, Indicates the number of supports; Indicates the first Axial stiffness of each support; Indicates the first The amplitude of the main beam at each support location; Indicates the first The length of each support tensile device.

3. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 1, characterized in that: The formula for the vertical bending frequency of the cable-stayed bridge under the condition of bearing damage and under compression is consistent with that under the normal condition of bearing under compression.

4. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 3, characterized in that: Under the aforementioned bearing damage condition, and under compression and external load, a negative reaction force occurs at the bearing; the tensile stiffness decreases due to localized fracture of the tensile device; the formula for the bridge's vertical bending frequency can be expressed as: ； In the formula, , , These represent the mode shape function of the main beam, the amplitude at the cable location, and the amplitude at the support location, respectively, when the support is in tension. This indicates the degree of localized fracture in the tensile support device. .

5. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 3, characterized in that: Under the aforementioned bearing damage condition, when the tensile device of the tension-compression bearing completely breaks under compression, the bearing loses its tensile strength, the bridge boundary conditions change, and the bridge's vertical bending frequency can be expressed as: ； In the formula, This represents the mode shape function of the main beam when the tensile support device completely breaks. This indicates that when the tensile support device completely breaks, the first The amplitude at each cable.

6. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 1, characterized in that: The specific process of clustering frequency data using the Gaussian Mixture Model (GMM) is as follows: Given training data The probability density function of a GMM can be expressed as: ； In the formula, Indicates the parameters of GMM, ; Indicates the first The weights of each Gaussian component; This represents the total number of Gaussian distributions; , They represent the first The mean vector and covariance matrix of a Gaussian distribution; Indicates the first The probability density function of a Gaussian distribution can be expressed by the following formula: ； The log-likelihood function of the GMM can be expressed as: ； Furthermore, LLE is added as a regularization term to the objective function of GMM. The formula can be expressed as: ； in, Indicates LLE-based computation right The linear reconstruction weights reflect the local geometric relationships in high-dimensional space; , These represent the known model parameters. Down, , The probability density; GMM objective function with LLE regularization term The formula is as follows: ； In the formula, The regularization parameter is represented; the GMM-LLE model of frequency data under normal conditions is obtained; the environmental effects can be separated by inverting the GMM-LLE model.

7. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 1, characterized in that: The negative logarithmic form of the Gaussian mixture model serves as a diagnostic indicator of the degradation of the tensile strength of the support. The calculation formula is as follows: ； In the formula, This indicates frequency data obtained through real-time monitoring. ; An EWMA control chart can be represented as: ； In the formula, Indicates the smoothing parameter. ; This represents the weighted cumulative sum of the indicators.

8. The unsupervised learning-driven graded diagnosis method for bridge bearing tensile function degradation according to claim 7, characterized in that: Different control limits are set based on the EWMA control chart. The control limits of the EWMA control chart can be expressed as follows: ； ； In the formula, , These represent the control limits for partial and complete fracture of the tensile support device, respectively. , These represent the average values ​​of the indicators when the tensile support device is functioning normally and when there is partial fracture, respectively. It is a constant used to define the control limit width; , These represent the standard deviations of the indicators when the tensile support device is functioning normally and when there is partial fracture, respectively.

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