CN112461358B - Bridge modal parameter identification method based on instantaneous frequency of vehicle-bridge system - Google Patents

Abstract

The invention discloses a bridge modal parameter identification method based on the instantaneous frequency of a vehicle-bridge system, which is to make a two-axle vehicle drive on a bridge at a uniform speed, and test a small number of sensors arranged on the bridge to obtain a two-axle vehicle-bridge. The dynamic response of the bridge coupling system, and then according to the time-varying characteristics of the vehicle-bridge coupling system, the time-frequency analysis is carried out through synchronous extraction and transformation, and the instantaneous frequency related to the bridge frequency is extracted, and then the time-frequency coefficient modulus maximum value method is used to determine the time-frequency coefficient. Frequency ridge line, select the midpoint of each step section of the time-frequency ridge line as an effective data point, and then identify the bridge mode shape through the physical relationship between the instantaneous frequency and the bridge mode shape, and finally determine the dynamic force of the bridge after the vehicle leaves the bridge. The responses are Fourier transformed to identify bridge frequencies. The invention can convert mode shape identification into instantaneous frequency identification, thereby effectively solving the problems of low precision and efficiency in processing non-stationary signals in the existing calculation.

Description

Identification method of bridge modal parameters based on instantaneous frequency of vehicle-bridge system

technical field

The invention relates to the field of bridge safety detection, in particular to a bridge modal parameter identification method based on the instantaneous frequency of a vehicle-bridge system, and the identification result can be used to evaluate the safety state of the bridge structure.

Background technique

With the development of the economy and the changes of the times, more and more large bridges have been put into use. At the same time, people pay more and more attention to the safety of the structure. Modal analysis plays an important role in the safety diagnosis of large-scale structural engineering. Modal parameters can be used to monitor and detect the health status of structures, and are widely used in beam structure damage identification and health status assessment. The natural frequency and mode shape are the most important modal parameters of the bridge, so the frequency and mode shape identification has become one of the important tasks in the field of bridge engineering structure testing.

Bridge modal parameter identification is actually a process of processing various dynamic responses collected by sensors. The traditional direct measurement method is to install a large number of various types of sensors on the bridge structure, analyze the massive response signals collected by the sensors to obtain its frequency and mode shape, and use the modal parameter variation law to indirectly evaluate its health status. However, installing a large number of sensors is costly and labor-intensive; processing a large number of response signals is labor-intensive and difficult. Moreover, in practical applications, the response signal of the vehicle-bridge system is non-stationary and the modal parameters are time-varying when the quality of the vehicle-bridge is not small. The traditional method ignores the time-varying characteristics of the vehicle-bridge system, and the accuracy is low when processing the data. The accuracy of modal parameter identification directly affects its effectiveness in bridge safety diagnosis applications.

SUMMARY OF THE INVENTION

In order to avoid the defects of the above-mentioned traditional bridge modal identification method, the present invention provides a bridge modal parameter identification method based on the instantaneous frequency of the vehicle-bridge system, so as to be able to test the vehicle- The method of instantaneous frequency of bridge system converts mode shape identification into instantaneous frequency identification, which can effectively solve the traditional modal parameter identification method, which requires a large number of sensors to be arranged on the bridge, high cost, high data processing difficulty, and processing of non-stationary signals. problems such as low accuracy and efficiency.

The present invention adopts the following technical scheme in order to achieve the above-mentioned purpose of the invention:

The characteristics of a bridge modal parameter identification method based on the instantaneous frequency of the vehicle-bridge system of the present invention include the following steps:

Step 1: Determine two-axle vehicle parameters, including: total weight m _v , two wheelbases d ₁ and d ₂ and travel speed v;

Step 2: When the vehicle is driving on the bridge at the speed v, use the acceleration sensor to obtain the dynamic response s ₁ (t) of the two-axle vehicle-bridge coupling system at time t on the bridge measuring point in real time:

Step 3: perform time-frequency analysis on the dynamic response s ₁ (t) by the time-frequency processing method, and identify the instantaneous frequencies of each order of the two-axle vehicle-bridge coupling system;

Step 3.1: Perform short-time Fourier transform on the dynamic response s ₁ (t) to obtain the time-frequency coefficient matrix S _t (t, η) of the two-axle vehicle-bridge coupling system, where η is the frequency of the vehicle-bridge system ;

Step 3.2: Preliminarily estimate the two-dimensional instantaneous frequency η ₀ (t, η) of the two-axle vehicle-bridge coupling system using equation (1):

In formula (1), i is a complex unit;

Step 3.3: Use equation (2) to obtain the time-frequency coefficient ω ₀ (t, η) of the two-axle vehicle-bridge coupling system:

Step 4: Perform modulo maxima ridge extraction processing on the time-frequency coefficient ω ₀ (t, η), obtain the modulo maxima of each column and use it as a time-frequency ridge, and select the ridge of each step of the time-frequency ridge graph. The midpoint is used as a valid data point, where the k-th valid data point is denoted as (t _k ,ω _n (t _k )), where t _k is the vehicle travel time corresponding to the k-th valid data point, and n represents nth order instantaneous frequency of the bridge, ω _n (t _k ) is the nth order instantaneous frequency of the bridge when the vehicle travel time is t _k ;

Step 5: Identify Bridge Frequency:

Step 5.1: When the vehicle leaves the bridge, use the acceleration sensor to collect the acceleration response s ₂ (t) of the bridge;

Step 5.2: use Fourier transform to perform spectrum analysis on the acceleration response s ₂ (t), and identify the natural frequency ω _n of the bridge;

Step 6: Calculate Bridge Mode Shapes:

Step 6.1: Use formula (3) to calculate the distance a _{k between the position on the bridge corresponding to the vehicle traveling to the bridge and the starting point when the time is t k :}

a _k =v×t _k -d ₁ (3)

Step 6.2: Use equation (4) to calculate the bridge mode shape φ _n ( _ak ) when the distance between the vehicle and the starting point is a _k :

The natural frequency ω _n and the bridge mode shape φ _n ( _ak ) are used as the identified bridge modal parameters.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention only needs to arrange a small number (single or two) of acceleration sensors for testing by allowing the vehicle to drive across the bridge at a constant speed, and by using advanced signal processing methods to perform time-frequency analysis on the collected acceleration responses, through the obtained The high-precision mode shape can be obtained at the instantaneous frequency, which effectively solves the problems of dense arrangement of a large number of sensors, expensive and time-consuming installation of equipment, repeated operations, and heavy workload in the data processing process in the past.

2. The present invention makes good use of the physical relationship between the frequency change of the vehicle-bridge system and the bridge modal parameters at this point. The identification of the Tonghua mode shape is an instantaneous frequency identification, which can significantly improve the identification accuracy. The entire vehicle passing process adopts advanced technology. The time-frequency analysis method processes the signal, which is easy to operate and can identify the time-varying characteristics of the vehicle-bridge coupling system, and the result of processing non-stationary signals has high accuracy.

3. The present invention uses a two-axle vehicle for testing, and has stronger operability in actual bridge health monitoring and detection.

Description of drawings

Fig. 1 is the identification process schematic diagram of the method of the present invention;

Fig. 2 is the numerical simulation constant cross-section simply supported girder bridge diagram of the present invention;

3 is a typical dynamic response diagram of a simply supported beam bridge of equal section under vehicle excitation of the present invention;

4 is a time-frequency analysis diagram of a typical dynamic response of a simply supported girder bridge of equal cross-section under vehicle excitation of the present invention;

Figure 5 is a time-frequency ridge diagram of a typical dynamic response of a simply supported girder bridge with constant cross-section under vehicle excitation according to the present invention

FIG. 6 is a spectrum diagram of a typical dynamic response of a simply supported girder bridge with constant cross-section after the vehicle leaves the vehicle according to the present invention.

Fig. 7 is the first-order vibration shape identification result diagram of the equal-section simply supported girder bridge of the present invention;

8 is a diagram showing the identification result of the second-order mode shape of a simply supported girder bridge of equal cross-section according to the present invention;

9 is a diagram of a numerical simulation two-span continuous beam bridge of equal cross-section according to the present invention;

FIG. 10 is a diagram showing the identification result of the first-order mode shape of a two-span continuous girder bridge of constant cross-section according to the present invention;

Fig. 11 is a diagram showing the identification result of the second-order mode shape of a two-span continuous girder bridge of constant cross-section according to the present invention.

Detailed ways

In this Example 1, as shown in Figure 2, the simply supported girder bridge of equal section has a bridge span length of 30m, an elastic modulus of 27.5Gpa, and a mass per linear meter of 2000kg/m. When simulated by the finite element method, the bridge is divided into 30 plane Euler beam elements equidistantly. The dynamic response of the bridge is calculated by the Newmark-β method. The sampling frequency is 1000Hz. A method for identifying bridge modal parameters based on the instantaneous frequency of the vehicle-bridge system, as shown in Figure 1, includes the following steps:

Step 1: Determine the parameters of the two-axle vehicle, including: total weight m _v =1800kg, two wheelbases d ₁ =0.2m and d ₂ =0.2m, and travel speed v=0.5m/s;

Step 2: The position of the bridge measuring point is selected 10m from the starting position of the vehicle. When the vehicle is driving on the bridge at the driving speed v, the acceleration sensor is used to obtain the power of the two-axle vehicle-bridge coupling system at time t on the bridge measuring point in real time. The response s ₁ (t), the dynamic response s ₁ (t) of the two-axle vehicle-bridge coupling system is shown in Fig. 3;

Step 3: perform time-frequency analysis on the dynamic response s ₁ (t) by the time-frequency processing method, and identify the instantaneous frequencies of each order of the two-axle vehicle-bridge coupling system;

Step 3.1: Perform short-time Fourier transform on the dynamic response s ₁ (t) to obtain the time-frequency coefficient matrix S _t (t, η) of the two-axle vehicle-bridge coupling system, where η is the frequency of the vehicle-bridge system;

Step 3.2: Preliminarily estimate the two-dimensional instantaneous frequency η ₀ (t, η) of the two-axle vehicle-bridge coupling system using equation (1):

In formula (1), i is a complex unit;

Step 3.3: Use equation (2) to obtain the time-frequency coefficient ω ₀ (t, η) of the two-axle vehicle-bridge coupling system, and the time-frequency diagram is shown in Figure 4:

Step 4: Perform modulo maxima ridge extraction processing on the time-frequency coefficient ω ₀ (t, η), obtain the modulo maxima of each column as the time-frequency ridge, and select the middle of each step of the time-frequency ridge. point, as a valid data point, where the kth valid data point is denoted as (t _k ,ω _n (t _k )), where t _k is the vehicle travel time corresponding to the kth valid data point, and n represents the bridge The n-th order instantaneous frequency of , ω _n (t _k ) is the n-th order instantaneous frequency of the bridge when the vehicle travel time is t _k , and the time-frequency ridge line is shown in Figure 5;

Step 5: Identify Bridge Frequency:

Step 5.1: When the vehicle leaves the bridge, use the acceleration sensor to collect the acceleration response s ₂ (t) of the bridge;

Step 5.2: use Fourier transform to perform spectrum analysis on the acceleration response s ₂ (t), the spectrum is shown in Figure 6, and the natural frequency ω _n of the bridge is identified;

Step 6: Calculate Bridge Mode Shapes:

Step 6.1: Using formula (3), when the time is t _k , the distance _ak between the position on the bridge and the starting point corresponding to the vehicle traveling to the bridge can be used to convert ω _n (t _k ) into ω _n ( _ak ):

a _k =v×t _k -d ₁ (3)

Step 6.2: Use the physical relationship between the instantaneous frequency of the vehicle-bridge coupling system and the bridge mode amplitude at the corresponding point (4) to calculate the bridge mode shape φ _n ( _ak ) when the distance between the vehicle and the starting point is a _k , The comparison between the recognition results of the first and second orders and the reference values are shown in Table 1, Figure 7 and Figure 8, respectively.

Take the natural frequency ω _n and the bridge mode shape φ _n ( _ak ) as the identified bridge modal parameters.

Table 1

In this embodiment 2, as shown in Figure 9, the two-span continuous girder bridge of equal cross-section is 15m long, the elastic modulus is 27.5Gpa, and the mass per linear meter is 2000kg/m. When simulated by the finite element method, the bridge is divided into 30 plane Euler beam elements equidistantly. The acceleration response of the bridge is calculated by the Newmark-β method. The sampling frequency is 1000 Hz, and the parameters of the vehicle are the same as those in Example 1. The solution method and identification process are the same as those in Example 1. The comparison of the identification results of the first and second order frequencies and mode shapes with the reference values are shown in Table 2, Figure 10 and Figure 11, respectively.

Table 2

It can be seen from Table 1 and Table 2 that a bridge modal parameter identification method based on the instantaneous frequency of the vehicle-bridge system proposed by the present invention can more accurately identify the modal parameters of different types of bridges, with small errors, and is applicable and practical. Strong sex.

Claims (1)

1. a bridge modal parameter identification method based on vehicle-bridge system instantaneous frequency is characterized in that comprising the following steps: Step 1: Determine two-axle vehicle parameters, including: total weight m _v , two wheelbases d ₁ and d ₂ and travel speed v; Step 2: When the vehicle is driving on the bridge at the speed v, use the acceleration sensor to obtain the dynamic response s ₁ (t) of the two-axle vehicle-bridge coupling system at time t on the bridge measuring point in real time: Step 3: perform time-frequency analysis on the dynamic response s ₁ (t) by the time-frequency processing method, and identify the instantaneous frequencies of each order of the two-axle vehicle-bridge coupling system; Step 3.1: Perform short-time Fourier transform on the dynamic response s ₁ (t) to obtain the time-frequency coefficient matrix S _t (t, η) of the two-axle vehicle-bridge coupling system, where η is the frequency of the vehicle-bridge system ; Step 3.2: Preliminarily estimate the two-dimensional instantaneous frequency η ₀ (t, η) of the two-axle vehicle-bridge coupling system using equation (1):

In formula (1), i is a complex unit; Step 3.3: Use equation (2) to obtain the time-frequency coefficient ω ₀ (t, η) of the two-axle vehicle-bridge coupling system:

Step 4: Perform modulo maxima ridge extraction processing on the time-frequency coefficient ω ₀ (t, η), obtain the modulo maxima of each column and use it as a time-frequency ridge, and select the ridge of each step of the time-frequency ridge graph. The midpoint is used as a valid data point, where the k-th valid data point is denoted as (t _k ,ω _n (t _k )), where t _k is the vehicle travel time corresponding to the k-th valid data point, and n represents nth order instantaneous frequency of the bridge, ω _n (t _k ) is the nth order instantaneous frequency of the bridge when the vehicle travel time is t _k ; Step 5: Identify Bridge Frequency: Step 5.1: When the vehicle leaves the bridge, use the acceleration sensor to collect the acceleration response s ₂ (t) of the bridge; Step 5.2: use Fourier transform to perform spectrum analysis on the acceleration response s ₂ (t), and identify the natural frequency ω _n of the bridge; Step 6: Calculate Bridge Mode Shapes: Step 6.1: Use formula (3) to calculate the distance a _{k between the position on the bridge corresponding to the vehicle traveling to the bridge and the starting point when the time is t k :} a _k =v×t _k -d ₁ (3) Step 6.2: Use equation (4) to calculate the bridge mode shape φ _n ( _ak ) when the distance the vehicle travels from the starting point is a _k :

The natural frequency ω _n and the bridge mode shape φ _n ( _ak ) are used as the identified bridge modal parameters.

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