A monitoring and early warning method for vortex-induced vibration of main beams of long-span suspension bridges

Abstract

The present invention discloses a vortex-induced vibration monitoring and early warning method for a main beam of a large-span suspension bridge. The method determines the start and end times of multi-modal vortex-induced vibration of the main beam by monitoring the multi-point vibration acceleration power spectrum of the main beam, uses principal component analysis to evaluate the proportion of energy concentration coefficients corresponding to different modes, selects multi-order modal frequencies of vortex-induced vibration, and thereby determines multi-modal vortex-induced vibration results of the main beam of the suspension bridge in real time. The method solves the problem that the prior art cannot solve the multi-modal vortex-induced vibration problem in monitoring the vortex-induced vibration of the main beam, which makes it difficult to perceive the abnormal vibration state of the main beam by using the power spectrum data of the main beam.

Description

Technical Field

[0001] The invention relates to the field of bridge structure performance monitoring, and in particular to a vortex-induced vibration monitoring and early warning method for a main beam of a long-span suspension bridge. Background Art

[0002] The main beam is the most important load-bearing component of a suspension bridge. Vehicles and pedestrians travel on the main beam. Therefore, the normal service of the main beam structure of a suspension bridge is of great significance to the safety of the bridge. The service status of the bridge is relatively complex. Under the action of specific wind conditions, the main beam of the suspension bridge will produce multi-order vortex-induced vibrations, which will not only cause fatigue damage to the main beam structure, but also cause abnormal vibrations of the bridge. Because the main beam of the suspension bridge is very long, the vortex-induced vibration of the main beam of the suspension bridge is obviously different from the general single-mode vortex-induced vibration, and it manifests as multi-mode vortex-induced vibration.

[0003] In order to sense the vibration characteristics of suspension bridges, acceleration sensors are usually installed on the main beams, and the vibration frequency power spectrum of the main beams is calculated based on the acceleration time history data. The multi-peak data of the power spectrum represents the vibration characteristics of the main beams. However, the existing technology cannot solve the problem of multi-modal vortex-induced vibration in monitoring the vortex-induced vibration of the main beams, which makes it difficult to sense the abnormal vibration state of the main beams using the power spectrum data of the main beams. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a vortex-induced vibration monitoring and early warning method for the main beam of a large-span suspension bridge, which solves the problem that the existing technology cannot solve the multi-modal vortex-induced vibration problem in monitoring the vortex-induced vibration of the main beam, resulting in that it is difficult to perceive the abnormal vibration state of the main beam using the main beam power spectrum data.

[0005] Technical solution: The present invention provides a vortex-induced vibration monitoring and early warning method for a main beam of a long-span suspension bridge, comprising the following steps:

[0006] (1) Acceleration sensors are installed at the mid-span, 1 / 4 mid-span, and 1 / 8 mid-span of the main beam of the suspension bridge to collect the vertical acceleration response of the main beam, and an anemometer is installed at the mid-span position of the main beam to collect the wind speed data on the bridge deck;

[0007] (2) Perform linear regression analysis on the vertical acceleration response at the middle of the main beam span and the wind speed data, thereby establishing a linear regression model of the vertical acceleration at the middle of the main beam span and the wind speed and obtaining a regression formula; substituting the wind speed data into the regression formula to obtain the acceleration response regression value, and then using the vertical acceleration response corresponding to the wind speed data minus the acceleration response regression value to obtain the acceleration response time history data without the influence of wind speed, thereby establishing the wind speed normalized vertical acceleration response time history curve at the middle of the main beam span; using the same method as that for establishing the wind speed normalized vertical acceleration response time history curve at the middle of the main beam span to establish the wind speed normalized vertical acceleration response time history curves at the 1 / 4 and 1 / 8 middle of the main beam span;

[0008] (3) PSD is used to calculate the acceleration power spectrum of the vertical acceleration response time history curve of the main beam at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam with the preset time interval;

[0009] (4) For each acceleration power spectrum in the span of the main beam, extract the frequency f1 of the first order of the acceleration power spectrum amplitude and its corresponding amplitude A1, extract the frequency f2 of the second order of the acceleration power spectrum amplitude and its corresponding amplitude A2, extract the frequency f3 of the third order of the acceleration power spectrum amplitude and its corresponding amplitude A3, and on this basis calculate two energy concentration coefficients: A2 / A1 and (A2+A3) / A1 with a preset time as the time interval, thereby obtaining the time history data of the energy concentration coefficient A2 / A1 at the mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1; adopt the same method as that for obtaining the time history data of the energy concentration coefficient A2 / A1 at the mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1, to obtain the time history data of the energy concentration coefficient A2 / A1 at the 1 / 4 mid-span and 1 / 8 mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1;

[0010] (5) The time history data of the energy concentration coefficient A2 / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis to obtain the time history curve of the first reconstructed feature P1 of the principal component analysis result of A2 / A1 of the whole bridge; The time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis to obtain the time history curve of the first reconstructed feature P2 of the principal component analysis result of (A2+A3) / A1 of the whole bridge;

[0011] (6) Judgment data: If the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 is less than 0.01, it means that the main beam has a single-mode vortex-induced vibration, and the vortex-induced vibration mode is a first-order vibration mode; if the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 satisfies 0.1>A2 / A1>0.01, and the principal component (A2+A3) / A1 in the time history curve of the first reconstructed feature P2 of the principal component analysis result of the whole bridge (A2+A3) / A1 satisfies 0.2>(A2+A3) / A1>0.02, it means that the main beam has a multi-mode vortex-induced vibration, and the vortex-induced vibration mode is a mixed vibration mode of the first, second and third orders.

[0012] Furthermore, the preset time is 1 to 30 minutes.

[0013] Furthermore, the preset time is 1 minute, which is the optimal value for comprehensive computing power and real-time performance.

[0014] Furthermore, in step (4), the same method as that used to obtain the time-history data of the energy concentration factor A2 / A1 at the mid-span position of the main beam and the time-history data of the energy concentration factor (A2+A3) / A1 are used to obtain the time-history data of the energy concentration factor A2 / A1 at the 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam and the specific process of the time-history data of the energy concentration factor (A2+A3) / A1 is as follows:

[0015] For each acceleration power spectrum in the 1 / 4 span and 1 / 8 span of the main beam, the first-order frequency f1 of the acceleration power spectrum amplitude and its corresponding amplitude A1 are extracted, the second-order frequency f2 of the acceleration power spectrum amplitude and its corresponding amplitude A2 are extracted, and the third-order frequency f3 of the acceleration power spectrum amplitude and its corresponding amplitude A3 are extracted. On this basis, two energy concentration coefficients are calculated with the preset time as the time interval: A2 / A1 and (A2+A3) / A1, so as to obtain the time-history data of the energy concentration coefficient A2 / A1 at the 1 / 4 span and 1 / 8 span of the main beam and the time-history data of the energy concentration coefficient (A2+A3) / A1.

[0016] Beneficial effects: The present invention determines the start and end times of multi-modal vortex-induced vibration of the main beam by monitoring the multi-point vibration acceleration power spectrum of the main beam, uses principal component analysis to evaluate the proportion of energy concentration coefficients corresponding to different modes, selects multi-order modal frequencies of vortex-induced vibration, and thus determines the multi-modal vortex-induced vibration results of the main beam of the suspension bridge in real time. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flowchart of the present invention;

[0018] Figure 2 is the collected wind speed data;

[0019] Figure 3 is the linear regression diagram of vertical acceleration and wind speed;

[0020] Figure 4 The normalized vertical acceleration response time history curve of each measuring point of the main beam;

[0021] Figure 5 The acceleration power spectrum of each measuring point of the main beam;

[0022] Figure 6 It is the time course curve of the first reconstructed feature P1 of the principal component analysis result of the full bridge A2 / A1;

[0023] Figure 7 It is the time course curve of the first reconstructed feature P2 of the principal component analysis result of the full bridge (A2+A3) / A1. DETAILED DESCRIPTION

[0024] The present invention will be further described below in conjunction with embodiments:

[0025] like Figure 1 As shown; the present invention provides a vortex-induced vibration monitoring and early warning method for a main beam of a long-span suspension bridge, comprising the following steps:

[0026] (1) Acceleration sensors are installed at the mid-span, 1 / 4 mid-span, and 1 / 8 mid-span of the main beam of the suspension bridge to collect the vertical acceleration response of the main beam, i.e., acceleration data, and an anemometer is installed at the mid-span position of the main beam to collect the wind speed data on the bridge deck;

[0027] (2) Perform linear regression analysis on the vertical acceleration response at the middle of the main beam span and the wind speed data, thereby establishing a linear regression model of the vertical acceleration at the middle of the main beam span and the wind speed and obtaining a regression formula; substituting the wind speed data into the regression formula to obtain the acceleration response regression value, and then using the vertical acceleration response corresponding to the wind speed data minus the acceleration response regression value to obtain the acceleration response time history data without the influence of wind speed, thereby establishing the wind speed normalized vertical acceleration response time history curve at the middle of the main beam span; using the same method as that for establishing the wind speed normalized vertical acceleration response time history curve at the middle of the main beam span to establish the wind speed normalized vertical acceleration response time history curves at the 1 / 4 and 1 / 8 middle of the main beam span;

[0028] (3) PSD, i.e., power spectrum density analysis, is used to calculate the acceleration power spectrum of the vertical acceleration response time history curve of the main beam normalized by wind speed at the mid-span, 1 / 4 mid-span, and 1 / 8 mid-span positions of the main beam with a preset time as the time interval; the preset time can be 1 to 30 minutes, among which the preset time of 1 minute is the optimal choice for comprehensive computing power and real-time performance;

[0029] (4) For each acceleration power spectrum in the span of the main beam, extract the frequency f1 of the first order of the acceleration power spectrum amplitude and its corresponding amplitude A1, extract the frequency f2 of the second order of the acceleration power spectrum amplitude and its corresponding amplitude A2, extract the frequency f3 of the third order of the acceleration power spectrum amplitude and its corresponding amplitude A3, and on this basis calculate two energy concentration coefficients: A2 / A1 and (A2+A3) / A1 with a preset time as the time interval, thereby obtaining the time history data of the energy concentration coefficient A2 / A1 and the time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span of the main beam; adopt the same method as that for obtaining the time history data of the energy concentration coefficient A2 / A1 and the time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span of the main beam, and obtain the time history data of the energy concentration coefficient A2 / A1 and the time history data of the energy concentration coefficient (A2+A3) / A1 at the 1 / 4 mid-span and 1 / 8 mid-span of the main beam. According to the specific process, for each acceleration power spectrum in the 1 / 4 span and 1 / 8 span of the main beam, extract the frequency f1 of the first order of the acceleration power spectrum amplitude and its corresponding amplitude A1, extract the frequency f2 of the second order of the acceleration power spectrum amplitude and its corresponding amplitude A2, extract the frequency f3 of the third order of the acceleration power spectrum amplitude and its corresponding amplitude A3, and on this basis, calculate two energy concentration coefficients with a preset time as the time interval: A2 / A1, (A2+A3) / A1, so as to obtain the time history data of the energy concentration coefficient A2 / A1 at the 1 / 4 span and 1 / 8 span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1; in the acceleration power spectrum analysis, take the first three order frequencies and their corresponding power spectrum amplitudes, because the number of multi-modal participants in the vortex-induced vibration of the main beam of the suspension bridge is generally not more than 3, so the present invention selects the first three main modes for analysis, it should be understood that the selected values ​​are not limited to this;

[0030] (5) The time history data of the energy concentration coefficient A2 / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis, i.e., PCA, to obtain the time history curve of the first reconstructed feature P1 of the principal component analysis result of A2 / A1 of the whole bridge; The time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis, i.e., PCA, to obtain the time history curve of the first reconstructed feature P2 of the principal component analysis result of (A2+A3) / A1 of the whole bridge;

[0031] (6) Data judgment: If the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 is less than 0.01, it indicates that the main beam has a single-mode vortex-induced vibration, and the vortex-induced vibration mode is a first-order vibration mode; if the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 satisfies 0.1>A2 / A1>0.01, and the principal component (A2+A3) / A1 in the time history curve of the first reconstructed feature P2 of the principal component analysis result of the whole bridge (A2+A3) / A1 satisfies 0.2>(A2+A3) / A1>0.02, it indicates that the main beam has a multi-mode vortex-induced vibration, and the vortex-induced vibration mode is a mixed vibration mode of the first, second and third orders; an alarm can be issued for the above vortex-induced vibration modes. The determination interval is a numerical interval obtained by taking a 95% assurance rate for the mathematical model obtained from the measured data of the suspension bridge, which can ensure the accuracy and reliability of the determination result.

[0032] The vortex-induced vibration of the main beam of a suspension bridge is a vibration that has a great impact on driving comfort. Early identification of the vortex-induced vibration of the main beam allows timely maintenance measures to be taken. The present invention monitors the vertical vibration acceleration of the main beam, and after eliminating the influence of wind speed, the energy concentration coefficient analysis of three typical monitoring positions can quickly determine the occurrence of vortex-induced vibration of the main beam and issue an alarm, overcoming the problem of early warning lag in traditional methods of monitoring the main beam with large amplitude.

[0033] Example 1

[0034] Taking the Jiangyin Bridge suspension bridge as an example, the specific implementation process of the present invention is described:

[0035] (1) Acceleration sensors are installed at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam of Jiangyin Bridge to collect the vertical acceleration response of the main beam, i.e., acceleration data. An anemometer is installed at the mid-span of the main beam to collect the wind speed data on the bridge deck. These acceleration sensors and anemometers can collect acceleration data at multiple measuring points on the main beam and wind speed data at the mid-span. These acceleration data are the basis for data analysis. Figure 2 The collected wind speed data will be used for subsequent analysis.

[0036] (2) The vertical acceleration response in the middle of the main beam span and the wind speed data are subjected to linear regression analysis to establish a linear regression model of the vertical acceleration in the middle of the main beam span and the wind speed and obtain a regression formula; the wind speed data is substituted into the regression formula to obtain the acceleration response regression value, and then the vertical acceleration response corresponding to the wind speed data is subtracted from the acceleration response regression value to obtain the acceleration response time history data without the influence of wind speed, thereby establishing the vertical acceleration response time history curve in the middle of the main beam span normalized by wind speed; taking the sensor in the middle of the main span as an example, the original acceleration is a1 and the wind speed is v1, and a linear regression analysis is performed on the two to obtain a regression formula, such as Figure 3 As shown in ; the wind speed data v1 is substituted into the regression formula to obtain the acceleration response regression value, and then the acceleration response regression value is subtracted from the original acceleration data corresponding to the wind speed data, and finally the acceleration response time history data without the influence of wind speed is obtained, so as to establish the vertical acceleration response time history curve of the main beam mid-span normalized by wind speed; similarly, the vertical acceleration response time history curves of the main beam 1 / 4 mid-span and 1 / 8 mid-span normalized by wind speed are established, as shown in Figure 4 As shown;

[0037] (3) PSD (power spectrum density) analysis is used to calculate the acceleration power spectrum of the vertical acceleration response time history curve of the main beam at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam with a time interval of 1 minute, as shown in Figure 5 As shown;

[0038] (4) For the acceleration power spectrum at each monitoring position, extract the frequency f1 of the first order of the acceleration power spectrum amplitude and its corresponding amplitude A1, extract the frequency f2 of the second order of the acceleration power spectrum amplitude and its corresponding amplitude A2, extract the frequency f3 of the third order of the acceleration power spectrum amplitude and its corresponding amplitude A3, and on this basis calculate two energy concentration coefficients: A2 / A1 and (A2+A3) / A1 with a time interval of 1 min, thereby obtaining the time history data of the energy concentration coefficient A2 / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1;

[0039] (5) The time history data of the energy concentration coefficient A2 / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis (PCA) to obtain the time history curve of the first reconstructed feature P1 of the principal component analysis result of A2 / A1 of the whole bridge, as shown in Figure 6 As shown in the figure, for the time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam, principal component analysis (PCA) is used to reconstruct the time history curve of the first reconstructed feature P2 of the principal component analysis result of the whole bridge (A2+A3) / A1, as shown in the figure. Figure 7 As shown;

[0040] (6) Judgment data: If the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 is less than 0.01, it means that the main beam has a single-mode vortex-induced vibration and an alarm is triggered, and the vortex-induced vibration mode is the first-order vibration mode; if the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 satisfies 0.1>A2 / A1>0.01, and the principal component (A2+A3) / A1 in the time history curve of the first reconstructed feature P2 of the principal component analysis result of the whole bridge (A2+A3) / A1 satisfies 0.2>(A2+A3) / A1>0.02, it means that the main beam has a multi-mode vortex-induced vibration and an alarm is triggered, and the vortex-induced vibration mode is a mixed vibration mode of the first, second and third orders; the following table is the warning analysis result of a time interval (1 min):

[0041] Table 1 Final output of vortex-induced vibration mode of suspension bridge

[0042] .

Claims

1. A method for monitoring and early warning of vortex-induced vibration of a main beam of a long-span suspension bridge, characterized in that: The following steps are involved: (1) Acceleration sensors are installed at the mid-span, 1 / 4 mid-span, and 1 / 8 mid-span of the main beam of the suspension bridge to collect the vertical acceleration response of the main beam, and an anemometer is installed at the mid-span position of the main beam to collect the wind speed data on the bridge deck; (2) Performing linear regression analysis on the vertical acceleration response in the span of the main beam and the wind speed data, thereby establishing a linear regression model of the vertical acceleration in the span of the main beam and the wind speed and obtaining a regression formula; Substitute the wind speed data into the regression formula to obtain the acceleration response regression value, and then use the vertical acceleration response corresponding to the wind speed data minus the acceleration response regression value to obtain the acceleration response time-history data without the influence of wind speed, so as to establish the wind speed normalized vertical acceleration response time-history curve of the main beam mid-span; the wind speed normalized vertical acceleration response time-history curves of the main beam 1 / 4 mid-span and 1 / 8 mid-span are established by the same method as that of establishing the wind speed normalized vertical acceleration response time-history curve of the main beam mid-span; (3) PSD is used to calculate the acceleration power spectrum of the vertical acceleration response time history curve of the main beam at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam with the preset time interval; (4) For each acceleration power spectrum in the span of the main beam, extract the frequency f1 of the first order of the acceleration power spectrum amplitude and its corresponding amplitude A1, extract the frequency f2 of the second order of the acceleration power spectrum amplitude and its corresponding amplitude A2, extract the frequency f3 of the third order of the acceleration power spectrum amplitude and its corresponding amplitude A3, and on this basis calculate two energy concentration coefficients: A2 / A1 and (A2+A3) / A1 with a preset time as the time interval, thereby obtaining the time history data of the energy concentration coefficient A2 / A1 at the mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1; adopt the same method as that for obtaining the time history data of the energy concentration coefficient A2 / A1 at the mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1, to obtain the time history data of the energy concentration coefficient A2 / A1 at the 1 / 4 mid-span and 1 / 8 mid-span of the main beam and the time history data of the energy concentration coefficient (A2+A3) / A1; (5) The time history data of the energy concentration coefficient A2 / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis to obtain the time history curve of the first reconstructed feature P1 of the principal component analysis result of A2 / A1 of the whole bridge; The time history data of the energy concentration coefficient (A2+A3) / A1 at the mid-span, 1 / 4 mid-span and 1 / 8 mid-span of the main beam are reconstructed using principal component analysis to obtain the time history curve of the first reconstructed feature P2 of the principal component analysis result of (A2+A3) / A1 of the whole bridge; (6) Judgment data: If the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 is less than 0.01, it means that the main beam has a single-mode vortex-induced vibration, and the vortex-induced vibration mode is a first-order vibration mode; if the principal component A2 / A1 in the time history curve of the first reconstructed feature P1 of the principal component analysis result of the whole bridge A2 / A1 satisfies 0.1>A2 / A1>0.01, and the principal component (A2+A3) / A1 in the time history curve of the first reconstructed feature P2 of the principal component analysis result of the whole bridge (A2+A3) / A1 satisfies 0.2>(A2+A3) / A1>0.02, it means that the main beam has a multi-mode vortex-induced vibration, and the vortex-induced vibration mode is a mixed vibration mode of the first, second and third orders.

2. The method for monitoring and early warning of vortex-induced vibration of a main beam of a long-span suspension bridge according to claim 1 is characterized in that: The preset time is 1 to 30 minutes.

3. The method for monitoring and early warning of vortex-induced vibration of main beam of a long-span suspension bridge according to claim 2 is characterized in that: The preset time is 1 minute.

4. The method for monitoring and early warning of vortex-induced vibration of a main beam of a long-span suspension bridge according to claim 1 is characterized in that: In step (4), the same method as that used to obtain the time history data of the energy concentration factor A2 / A1 at the mid-span position of the main beam and the time history data of the energy concentration factor (A2+A3) / A1 are used to obtain the time history data of the energy concentration factor A2 / A1 at the 1 / 4 mid-span and 1 / 8 mid-span positions of the main beam and the specific process of the time history data of the energy concentration factor (A2+A3) / A1 is as follows: For each acceleration power spectrum in the 1 / 4 span and 1 / 8 span of the main beam, the first-order frequency f1 of the acceleration power spectrum amplitude and its corresponding amplitude A1 are extracted, the second-order frequency f2 of the acceleration power spectrum amplitude and its corresponding amplitude A2 are extracted, and the third-order frequency f3 of the acceleration power spectrum amplitude and its corresponding amplitude A3 are extracted. On this basis, two energy concentration coefficients are calculated with the preset time as the time interval: A2 / A1 and (A2+A3) / A1, so as to obtain the time-history data of the energy concentration coefficient A2 / A1 at the 1 / 4 span and 1 / 8 span of the main beam and the time-history data of the energy concentration coefficient (A2+A3) / A1.

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