Suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring and diagnosing method

Abstract

The application discloses a kind of suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring diagnosis method, steps are as follows: (1) main girder longitudinal quasi-static cumulative displacement extraction based on monitoring data;(2) the establishment and extraction of equivalent traffic volume index;(3) damper oil leakage diagnosis based on the correlation modeling of equivalent traffic volume and quasi-static cumulative displacement.This application constructs an equivalent traffic volume index that can represent the characteristics of traffic flow and is not affected by the damage of beam end constraint device;Establishes damper oil leakage diagnosis method based on the correlation modeling of equivalent traffic volume and main girder longitudinal cumulative displacement, effectively eliminates the interference of traffic volume change on liquid viscous damper oil leakage degradation warning, realizes the online monitoring of liquid viscous damper.Finally, the effectiveness of the method is verified using long-term monitoring data of an in-service suspension bridge.Therefore, the application has high engineering application value in the field of suspension bridge longitudinal liquid viscous damper performance evaluation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge structure performance evaluation, and particularly relates to a suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring and diagnosing method. BACKGROUND

[0002] Under normal operating conditions, a suspension bridge will be subjected to the continuous action of temperature, vehicles, wind and other environmental loads. Frequent load excitation will cause excessive longitudinal cumulative displacement of the main girder, and further cause the expansion joint and support to wear and be destroyed prematurely. In order to suppress the longitudinal vibration of the main girder of the suspension bridge, a longitudinal restraint device is usually added between the tower and the girder. In the current practical engineering application, the liquid viscous damper is the most common restraint device in the suspension bridge. However, the long-term and frequent vibration of the main girder will cause the liquid viscous damper to leak and degrade, resulting in an increase in the cumulative displacement and weakening of the suppression effect on the longitudinal displacement of the girder end. Based on the structural response monitoring data provided by the structural health monitoring system, early diagnosis of the oil leakage and degradation of the liquid viscous damper is of great significance to ensure the stability and reliable work of the restraint system of the long-span suspension bridge.

[0003] For the research on the liquid viscous damper of the long-span suspension bridge, most of the current researches are on the comparative analysis of the vibration control effect of the structure before and after the damper is installed and the parameter optimization of the damper, and there is little research on the performance evaluation of the liquid viscous damper based on the monitoring data. Sun Zhen et al. proposed a damper malfunction diagnosis method based on the random forest algorithm and cumulative displacement (Cumulative displacement-based detection of damper malfunction in bridges using data-driven isolation forest algorithm), but the machine learning method used in this method has poor interpretability, the universality of the method is difficult to guarantee, and the method will produce false alarms for the change of cumulative displacement caused by the reduction of vehicle flow during the Spring Festival holiday.

[0004] In summary, there is little research on the state evaluation of the liquid viscous damper based on the monitoring data at present, and the existing methods will be affected by the change of traffic volume, thereby resulting in poor early warning effect, and it is urgent to establish a method that can reliably identify the oil leakage and degradation of the liquid viscous damper. Therefore, the application proposes a suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring and diagnosing method, which can effectively eliminate the interference of the change of traffic volume on the oil leakage and degradation early warning of the liquid viscous damper, and realize the online monitoring and identification of the liquid viscous damper. At the same time, the method can effectively reduce the number of sensors, and has the advantages of simplicity and easy implementation in engineering. SUMMARY

[0005] The application aims to provide a suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring and diagnosing method.

[0006] The technical scheme of the application is as follows:

[0007] A suspension bridge main girder longitudinal nonlinear liquid viscous damper oil leakage monitoring and diagnosing method, the steps are as follows:

[0008] Step 1. Main girder longitudinal quasi-static cumulative displacement extraction based on monitoring data

[0009] (1.1) Removing the dead load and temperature trend item in the main girder longitudinal displacement monitoring data: first, set the moving window length to 15 min and select the main girder longitudinal displacement monitoring data in a window length for kernel density estimation fitting, and take the main girder longitudinal displacement corresponding to the maximum probability density point in the kernel density estimation model as the main girder longitudinal static load displacement representative value in this period; then, set the moving window step to 5 min, and constantly repeat the above steps to update the main girder longitudinal static load displacement representative value in different periods; the extracted main girder longitudinal static load displacement representative value is sequentially subjected to spline interpolation, median filtering and moving average for the extraction of the main girder longitudinal static load displacement trend item, and the original displacement data is subtracted from the main girder longitudinal static load displacement trend item to remove the influence of the dead load and temperature in the main girder longitudinal displacement monitoring data; it should be noted that the longitudinal displacement monitoring data of any measuring point of the main girder can be used in this method;

[0010] (1.2) Extracting the vehicle-induced quasi-static displacement component from the main girder longitudinal displacement monitoring data which has removed the dead load and temperature trend item by using the low-pass filtering method, and the cut-off frequency of the low-pass filter is set to the generalized set excitation v / l of the vehicle, wherein v is the vehicle speed measured in m / s, and for a highway suspension bridge, it is set to 100 km / h, i.e. 28 m / s; and l is the length of the main span of the suspension bridge;

[0011] (1.3) Calculating the main girder longitudinal quasi-static cumulative displacement by superimposing the absolute value of the displacement change of the beam end displacement time history curve according to formula (1), and performing statistical analysis in units of one hour;

[0012]

[0013] In the formula, d i represents the i th main girder quasi-static longitudinal displacement data sample; n is the total number of main girder quasi-static longitudinal displacement data samples in a unit period;

[0014] (1.4) Eliminating the influence of indirect temperature effect on the main girder longitudinal quasi-static displacement: according to formula (2), a relationship model between temperature and main girder longitudinal quasi-static cumulative displacement is established, and formula (3) is used to normalize the main girder longitudinal quasi-static cumulative displacement index to the same reference temperature, so as to obtain the normalized quasi-static cumulative displacement index

[0015]

[0016] where γ1and γ0are the fitting parameters obtained by least square method; T is the average temperature of the main girder; it is noted that the relationship model is established using the longitudinal displacement data and temperature data of the main girder when the bridge damper is in normal state; D 0,T represents the measured value of the quasi-static cumulative displacement index when the structure temperature is equal to T; D T represents the estimated value of the quasi-static cumulative displacement when the structure temperature is equal to T; D 20 represents the estimated value of the quasi-static cumulative displacement when the structure temperature is equal to 20℃;

[0017] Step 2. Establishment and extraction of equivalent traffic volume index

[0018] (2.1) Extract the vertical displacement and strain monitoring data at the mid-span position of the main girder, and extract the constant load and temperature trend item and the vehicle-induced quasi-static component by using steps (1.1) and (1.2) respectively;

[0019] (2.2) Calculate the root mean square (RMS) index of displacement and strain at different transverse positions of the mid-span of the main girder according to formula (4), and further eliminate the intermediate temperature effect of the RMS index and normalize the index by using the same method in step (1.4);

[0020]

[0021] where x j represents the jth sample of the mid-span vertical displacement or strain data; m is the total number of samples of the mid-span vertical displacement or strain data set in a unit time period, and the unit time period is also set to 1 hour;

[0022] (2.3) Perform canonical correlation analysis on the normalized RMS index and the normalized longitudinal quasi-static cumulative displacement index according to formula (5) to obtain the standard orthogonal basis vector u k :

[0023]

[0024] where R VV is the covariance matrix between the RMS indexes; R DD is the covariance matrix between the beam end quasi-static cumulative displacement indexes; R VD is the cross-covariance matrix between the beam end quasi-static cumulative displacement indexes and the RMS indexes, and R VD = R DV ; U = [u1, u2,..., u kdenotes the standard orthogonal matrix composed of eigenvectors, u k denotes the kth pair of standard orthogonal basis vectors;

[0025] (2.4) The projection of the RMS index on the kth pair of standard orthogonal basis vectors u k is calculated using formula (6), that is, the equivalent traffic index is obtained;

[0026]

[0027] Step 3. Damper oil leakage diagnosis based on the correlation modeling between equivalent traffic and quasi-static cumulative displacement

[0028] (3.1) Using the monitoring data of the damper in the normal state including the main beam longitudinal displacement data, mid-span vertical displacement and strain data, and temperature data as the training set, the quasi-static cumulative displacement and equivalent traffic index are extracted according to steps 1 and 2, and then the correlation model between equivalent traffic and quasi-static cumulative displacement is established according to formula (7);

[0029]

[0030] In the formula: is the quasi-static cumulative displacement of the tth hour estimated based on the correlation model (t = 1, 2, … N), and N is the total number of quasi-static cumulative displacement indexes contained in the training set; β k is the kth regression coefficient, determined by the least squares method;

[0031] (3.2) The residual index of the measured value of the main beam longitudinal quasi-static cumulative displacement and the estimated value of the correlation model is calculated according to formula (8);

[0032]

[0033] In the formula: D h,t denotes the measured value of the tth hour quasi-static cumulative displacement; E t denotes the estimated residual of the tth hour main beam quasi-static cumulative displacement;

[0034] (3.3) The weighted E t statistic is constructed by formula (9) as a warning index, that is, the WE index

[0035]

[0036] In the formula: WE t denotes the tth hour warning index; λ is the smoothing constant, the smaller the value, the more sensitive to small index abnormal shifts, set to 0.05; E mean denotes the average value of E t statistic in the training set under the healthy state of the damper;

[0037] (3.4) Calculate the early warning control limit of the proposed damper oil leakage diagnosis method according to formula (10) and formula (11):

[0038]

[0039]

[0040] In the formula, LCL represents the lower limit of the early warning threshold; UCL represents the lower limit of the early warning threshold; μ0 represents the E t Mathematical expectation of statistical quantity;

[0041] (3.5) In the online monitoring stage, steps 1-2 are repeated, the WE early warning index of each new quasi-static cumulative displacement is calculated and compared with the early warning threshold set in step (3.4), so as to perform online evaluation and abnormal early warning of the liquid viscous damper.

[0042] The beneficial effects of the present application are:

[0043] 1、The damper oil leakage diagnosis method based on the correlation modeling of equivalent traffic volume and main beam longitudinal quasi-static cumulative displacement established in the present application effectively eliminates the interference of traffic volume change on the oil leakage degradation early warning of the liquid viscous damper, and realizes the online monitoring of the longitudinal liquid viscous damper of the suspension bridge.

[0044] 2、The equivalent traffic volume index which can effectively represent the change of random traffic flow characteristics is constructed in the present application, and the index is not affected by the damage of the beam end restraint device, thereby ensuring the modeling accuracy of the correlation model of equivalent traffic volume and main beam longitudinal quasi-static cumulative displacement.

[0045] 3、The present application can use the longitudinal displacement monitoring data of any measuring point of the main beam, and the requirement for sensor layout is low. In actual engineering, the performance evaluation of the longitudinal liquid viscous damper can be performed even if only the GPS spatial displacement data at the midspan is used, further simplifying the early warning process. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 The flowchart of the method of the present application;

[0047] Figure 2 The result of normalizing the main beam longitudinal quasi-static cumulative displacement index to the same reference temperature;

[0048] Figure 3 The comparison result of equivalent traffic volume and main beam quasi-static longitudinal cumulative displacement;

[0049] Figure 4 The correlation analysis result of equivalent traffic volume and main beam quasi-static longitudinal cumulative displacement;

[0050] Figure 5 a heat map related to the quasi-static cumulative displacement of different measuring points in the longitudinal direction of the main girder;

[0051] Figure 6 early warning results of the method in working condition 1;

[0052] Figure 7 early warning results of the method in working condition 2, respectively.

[0053] Figure 8 early warning results of the method in working condition 3, respectively.

[0054] Figure 9 early warning results of the method in working condition 4, respectively. DETAILED DESCRIPTION

[0055] The application will be further described in detail below in combination with the drawings and an example.

[0056] The oil leakage diagnosis method for the nonlinear longitudinal liquid viscous damper of the suspension bridge of the application is divided into three steps of "extraction of the quasi-static cumulative displacement of the longitudinal direction of the main girder based on monitoring data", "establishment of equivalent traffic volume indicators", and "establishment of the damper oil leakage diagnosis method based on the correlation modeling of the equivalent traffic volume and the quasi-static cumulative displacement", and the method implementation process is as shown in Figure 1 .

[0057] In this specific numerical example, two years of monitoring data of a certain in-service large-span suspension bridge in China are used for verification. Due to the poor quality of the actual monitoring data, there are a large number of missing and damaged sensor data, and finally only 1098 hours of GPS spatial displacement data in the span are extracted. Fortunately, the extracted data set contains relatively complete data during the Spring Festival period. Existing research shows that in addition to the obvious changes in the longitudinal movement of the beam end due to the sharp decrease in traffic flow characteristics during the Spring Festival period, the characteristics are relatively stable in the remaining period. Therefore, although the actual monitoring data is not complete, it can still be used to verify the effectiveness of the method.

[0058] Firstly, the constant load and temperature trend items of the longitudinal displacement and vertical displacement monitoring data in the GPS data are removed according to step (1.1), and then the vehicle-induced quasi-static displacement component of the longitudinal displacement and vertical displacement monitoring data in the GPS data is extracted according to step (1.2), and finally steps (1.3) and (1.4) are executed to extract the quasi-static cumulative displacement index of the longitudinal direction of the main girder and normalize it to the same reference temperature, and the extraction results are as shown in Figure 2 .

[0059] Secondly, based on step 2, the equivalent traffic volume index was established and extracted using the quasi-static vertical displacement data at the mid-span of the main girder. Using the datasets extracted in steps 1 and 2, the datasets from the last three months were set as the test set, and the remaining datasets as the training set. Then, using the training set, a correlation model between the equivalent traffic volume and the quasi-static longitudinal cumulative displacement of the main girder was established according to the process in step 3, and the warning threshold was determined. Furthermore, since the monitoring data used were all obtained when the bridge was in normal operation, the beam end displacement data during both the training and testing phases can be considered healthy data. To further examine the effectiveness of the proposed method, a positive offset was added to the longitudinal quasi-static cumulative displacement index in the test set to simulate the degradation of the liquid viscous damper's oil leakage performance. A total of four operating conditions were simulated, namely conditions 1-4, with corresponding reduction factors of 0%, 5%, 10%, and 15%, respectively. 0% indicates that the liquid viscous damper did not experience any abnormalities, used to verify the warning stability of the proposed method under normal liquid viscous damper conditions.

[0060] Depend on Figure 3 and Figure 4 It can be seen that the established equivalent traffic volume can effectively characterize changes in traffic flow and has a good linear correlation with the quasi-static longitudinal cumulative displacement of the main girder. Furthermore, correlation analysis was conducted on the longitudinal quasi-static cumulative displacement of the main girder at different measuring points (i.e., 1 / 4, 1 / 2, and 3 / 4 spans). Figure 5 The correlation coefficients indicate a strong correlation between the quasi-static cumulative displacements at different measuring points, with all correlation coefficients greater than 0.98. This proves that the proposed method can utilize longitudinal displacement monitoring data from any measuring point along the main beam. Furthermore, from... Figure 6 The early warning effect shows that the method proposed in this invention only has a few data points exceeding the threshold when the liquid viscous damper is in normal working condition, with a false alarm rate of only 1.02%, indicating that the proposed method has good stability. Figures 7-9 It can be seen that when the longitudinal quasi-static cumulative displacement index is abnormally reduced, as the leakage degree of the liquid viscous damper increases, that is, the reduction factor of the longitudinal quasi-static cumulative displacement index increases, the early warning rate also gradually increases. When the abnormal increment of the longitudinal quasi-static cumulative displacement index reaches 15%, the early warning rate reaches 93.88%, which verifies the effectiveness of the method proposed in this invention.

Claims

1. A method for monitoring and diagnosing oil leakage in a longitudinal nonlinear liquid viscous damper of a suspension bridge main girder, characterized in that, The steps are as follows: Step 1. Extraction of longitudinal quasi-static cumulative displacement of the main beam based on monitoring data (1.1) Remove the dead load and temperature trend terms from the longitudinal displacement monitoring data of the main beam: First, set the moving window length to 15 min and select the longitudinal displacement monitoring data of the main beam within a window length for kernel density estimation fitting. The longitudinal displacement of the main beam corresponding to the maximum probability density point extracted from the kernel density estimation model is taken as the representative value of the longitudinal static load displacement of the main beam in this period. Then set the moving window length to 5 minutes and repeat the above steps to update the representative value of the longitudinal static load displacement of the main beam under different time periods. The extracted representative value of the longitudinal static load displacement of the main beam is then processed by spline interpolation, median filtering and moving average to extract the trend term of the longitudinal static load displacement of the main beam. The influence of dead load and temperature in the longitudinal displacement monitoring data of the main beam is removed by subtracting the trend term of the longitudinal static load displacement of the main beam from the original displacement data. (1.2) The vehicle-induced quasi-static displacement component was extracted from the longitudinal displacement monitoring data of the main beam after the dead load and temperature trend terms were removed using a low-pass filtering method. The cutoff frequency of the low-pass filter was set to the generalized set excitation of the vehicle. ,in This refers to vehicle speed measured in m / s. For highway suspension bridges, it is set to 100 km / h, which is 28 m / s. This refers to the length of the main span of a suspension bridge; (1.3) By superimposing the absolute value of the displacement change of the beam end displacement time history curve by formula (1), the longitudinal quasi-static cumulative displacement of the main beam is calculated and statistical analysis is performed in one-hour units; (1) In the formula: Representing the i Sample longitudinal quasi-static displacement data of one main beam; The total number of samples in the longitudinal quasi-static displacement dataset of the main beam within a unit time period; (1.4) Eliminating the influence of indirect temperature effect on the longitudinal quasi-static displacement of the main beam: Establish the relationship model between temperature and longitudinal quasi-static cumulative displacement of the main beam according to equation (2), and use equation (3) to normalize the longitudinal quasi-static cumulative displacement index of the main beam to the same reference temperature to obtain the normalized longitudinal quasi-static cumulative displacement index of the main beam. : (2) (3) In the formula: and These are the fitting parameters obtained using the least squares method; T The average temperature of the main girder; the relationship model is established using the longitudinal displacement data and temperature data of the main girder when the bridge damper is in normal condition; Indicates that the structural temperature is equal to T The measured value of the longitudinal quasi-static cumulative displacement index of the main beam at that time; Indicates that the structural temperature is equal to T Estimated longitudinal quasi-static cumulative displacement of the main beam at that time; This represents the estimated longitudinal quasi-static cumulative displacement of the main beam when the structural temperature is equal to 20℃. Step 2. Establishment and extraction of equivalent traffic volume indicators (2.1) Extract the vertical displacement and strain monitoring data at the mid-span of the main beam, and extract the dead load and temperature trend terms and the vehicle-induced quasi-static displacement components using steps (1.1) and (1.2) respectively; (2.2) Calculate the root mean square index of displacement and strain at different transverse positions at the mid-span of the main beam according to formula (4), and further use the same method in step (1.4) to remove the indirect temperature effect in the root mean square index and normalize the index. (4) In the formula: Representing the j A sample of vertical displacement or strain data at mid-span; This represents the total number of samples in the dataset of vertical displacement or strain at mid-span of the main beam within a unit time period, which is also set to 1 hour. (2.3) Based on equation (5), a canonical correlation analysis was performed on the normalized RMS index and the normalized longitudinal quasi-static cumulative displacement index of the main beam to obtain the standard orthogonal basis vector of the canonical correlation model. : (5) In the formula, The covariance matrix among the RMS indices; The covariance matrix between the quasi-static cumulative displacement indices at the beam ends; Let be the cross-covariance matrix between the quasi-static cumulative displacement index and the RMS index at the beam end, and ; This represents an orthogonal matrix composed of eigenvectors. Indicates the first k For orthogonal basis vectors; (2.4) The RMS index is calculated using formula (6) in the first quarter. k For orthogonal basis vectors The equivalent traffic volume index is obtained by projecting it onto the surface. (6) Step 3. Damper oil leakage diagnosis based on the correlation model between equivalent traffic volume and longitudinal quasi-static cumulative displacement of the main beam. (3.1) The monitoring data including the longitudinal displacement data of the main beam, the vertical displacement and strain data at mid-span, and the temperature data when the damper is in normal condition are used as the training set. The longitudinal quasi-static cumulative displacement and equivalent traffic volume index of the main beam are extracted according to steps 1 and 2. Then, the correlation model between the equivalent traffic volume and the longitudinal quasi-static cumulative displacement of the main beam is established according to equation (7). (7) In the formula: For the first estimated based on the correlation model t Longitudinal quasi-static cumulative displacement of the main beam over hours ( ), The total number of longitudinal quasi-static cumulative displacement indices of the main beam contained in the training set; For the first k The regression coefficients are determined using the least squares method; (3.2) Calculate the residual index between the measured value and the estimated value of the longitudinal quasi-static cumulative displacement of the main beam according to formula (8); (8) In the formula: Indicates the first t Measured value of longitudinal quasi-static cumulative displacement of the main beam over 24 hours; Indicates the first t The estimated residual of the longitudinal quasi-static cumulative displacement of the main beam over 1 hour; (3.3) Construct the weighted average using equation (9). Statistics are used as early warning indicators, that is... index (9) In the formula: Indicates the first t Hourly warning indicators; It is a smoothing constant. The smaller its value, the more sensitive it is to small abnormal deviations in indicators. It is set to 0.

05. Indicating the training set under the healthy state of the damper The average of the statistics; (3.4) Calculate the warning threshold of the proposed damper oil leakage diagnosis method according to equations (10) and (11): (10) (11) In the formula, Indicates the lower limit of the warning threshold; Indicates the upper limit of the warning threshold; This indicates that the computation is based on the training set. The mathematical expectation of a statistic; (3.5) During the online monitoring phase, repeat steps 1-2 to calculate the longitudinal quasi-static cumulative displacement of each new main beam. The warning indicators are compared with the warning thresholds set in step (3.4) to conduct online evaluation and abnormal warning of the liquid viscous damper.

Images