A bridge influence line identification method based on high-speed train excitation dynamic response

Abstract

The present invention belongs to the field of structural safety detection, and discloses a method for identifying bridge influence lines based on high-speed train excitation dynamic response. The method includes: (1) collecting bridge response data containing dynamic components when a high-speed train travels alone over a bridge and obtaining train parameter and bridge parameter information; (2) calculating the optimal separation frequency range of the static and dynamic components of the response and designing a low-pass filter to filter the dynamic response; (3) using the classic least squares regularization method to invert the quasi-static response of the bridge into the bridge influence line. The present invention can effectively eliminate the dynamic effect in the bridge response under the action of a high-speed train in an operating state, and then invert the quasi-static influence line of the bridge. The method is simple to operate and has high robustness. It can be applied to the identification of bridge influence lines of any vehicle speed excitation response in an operating state, and has good engineering application prospects.

Description

Technical Field

[0001] The invention belongs to the field of structural safety detection, and in particular relates to a bridge influence line identification method based on high-speed train excitation dynamic response. Background Art

[0002] High-speed railway bridges are an important part of infrastructure. Bridge status assessment and vehicle load identification technology based on influence lines can timely detect abnormal operating conditions, thereby avoiding major losses of life and property at a relatively low cost. Since the speed of high-speed trains is much higher than that of other vehicles and is affected by vehicle-bridge coupling, the dynamic effects of train-induced bridges are often difficult to eliminate, which poses a challenge to existing influence line identification methods.

[0003] The existing methods for identifying bridge influence lines from vehicle-induced dynamic response mainly include improved influence line identification methods and extraction of quasi-static components from dynamic response. The first type of methods generally fit the influence line based on the physical properties of the bridge, such as the polynomial fitting method proposed by Wang Ningbo et al. (Extraction of influence line through a fitting method from bridge dynamic response induced by a passing vehicle) and the B-spline fitting method proposed by Chen Zhiwei et al. (a bridge influence line identification method based on basis function representation and sparse regularization), which have achieved good results in highway bridge influence line identification. The idea of ​​the other type of method is more intuitive. It directly processes the response signal containing dynamic effects and uses the processed quasi-static response to invert and obtain the bridge influence line. The focus of this type of method is how to obtain accurate quasi-static response of the bridge. This problem has been deeply studied in the fields of bridge influence line identification, bridge dynamic weighing and dynamic amplification factor calculation. There are three main solutions, namely filtering out high-frequency components in the frequency domain, such as the low-pass filtering method used by Obrien et al. (Calculating an influence line from direct measurements); time domain smoothing, such as the sliding average method used by González et al. (Testing of abridgeweigh-in-motion algorithm utilising multiple longitudinal sensor locations); and time-frequency domain decomposition and reconstruction, such as the empirical mode decomposition method used by Zheng Xu et al. (a bridge influence line identification method that can eliminate vehicle dynamic effects). All of these methods regard the dynamic response of the bridge as a high-frequency part and filter it out, thereby retaining the low-frequency quasi-static response, and then further identify the bridge influence line.

[0004] However, the above methods are often studied on highway bridges with low operating speeds, and it is difficult to obtain satisfactory results for high-speed railway bridges. Therefore, it is necessary to improve the existing methods. According to existing research, the use of fitting methods to remove dynamic effects has the disadvantages of easy overfitting, large restrictions on bridge types, and low applicable speeds. The use of time domain smoothing and time-frequency domain decomposition and reconstruction methods to remove dynamic effects has the disadvantages of unclear physical meaning, difficult parameter setting, and unstable influence line identification effect. The method of filtering out high-frequency components in the frequency domain has the advantages of simple operation, small amount of calculation, and stable filtering performance. It has certain advantages in existing methods and is therefore widely used. In existing research, this method is generally implemented through a low-pass filter, but the cutoff frequency of the low-pass filter is usually directly defined as the fundamental frequency of the bridge based on experience, or the filter parameters are repeatedly adjusted through a large number of working conditions, and it is difficult to accurately filter out the dynamic effects of high-speed train excitation. Therefore, this patent proposes a bridge influence line identification method based on the dynamic response of high-speed train excitation, which can directly calculate the optimal separation frequency of the static and dynamic components of the response, thereby identifying the bridge influence line. Summary of the invention

[0005] The purpose of the present invention is to propose a bridge influence line identification method based on high-speed train excitation dynamic response, which can directly calculate the optimal separation frequency of static and dynamic components of the response, thereby identifying the bridge influence line.

[0006] The technical solution of the present invention:

[0007] A bridge influence line identification method based on high-speed train excitation dynamic response, the steps are as follows:

[0008] Step 1: Collect bridge response data including dynamic components when a high-speed train passes over a bridge alone, and obtain train parameter and bridge parameter information

[0009] (1) Using sensors deployed on the bridge, the monitoring response data of a single high-speed train passing through the bridge is collected. Based on the bridge length l and the train speed v obtained by the speed radar, the monitoring response data intervals of the train starting to go on the bridge and completely going off the bridge are intercepted and converted in time and space so that each response sampling point corresponds to the position of the first axis of the train on the bridge;

[0010] (2) Obtain the information on the number of axles, wheelbase, and axle weight of the train, and use the monitoring data to calculate or obtain the first-order natural circular frequency ω1 and first-order damping ratio ξ1 of the bridge through historical modal test results;

[0011] Step 2: Calculate the optimal separation frequency range of the static and dynamic components of the response, and design a low-pass filter to filter the dynamic response.

[0012] (3) Calculate the theoretical spectrum analytical solution of the quasi-static and dynamic components of the bridge response based on the train and bridge parameters;

[0013] When only the first-order mode with the largest contribution is considered, the analytical solutions of the quasi-static and dynamic components of the bridge response under the action of the moving load series are shown as follows:

[0014]

[0015]

[0016] Among them, y 静 (t) and y 动 (t) represents the analytical solution of the quasi-static and dynamic components of the bridge response, respectively, and t represents the time value; G1, G2, A, and B are parameters related to the bridge modal parameters and moving load sequence information, which are calculated by traditional dynamic analysis; is the first-order load excitation circular frequency; is the first-order bridge natural circular frequency considering the damping effect;

[0017] The above equation is Fourier transformed in the time range of [0, l / v] to obtain the analytical solution of the quasi-static and dynamic component spectra of the bridge response under the action of the moving load series:

[0018]

[0019] Where X(ω) is the analytical solution of the quasi-static or dynamic component spectrum of the bridge response, ω represents the frequency value of the signal after Fourier transformation, and its value range is [0,F s / 2],F s is the sampling frequency of the bridge response;

[0020] (4) The optimal separation frequency range is solved based on the energy difference of the static and dynamic components of the bridge response. The energy of the quasi-static or dynamic components of the bridge response is calculated by the following formula:

[0021]

[0022] Where E(ω) is the energy of the quasi-static or dynamic component of the response with a frequency less than ω;

[0023] After calculating the distribution of static and dynamic component energy with frequency, the optimal separation frequency is calculated by finding the maximum difference between quasi-static and dynamic energy; after considering all the aliased parts of the response static and dynamic component energy as quasi-static or dynamic components, the range of the true static and dynamic component energy difference is given:

[0024]

[0025] in, is the direct difference between the static and dynamic component energies when energy aliasing is not considered; ΔE(ω) is the true difference between the static and dynamic component energies when energy aliasing is considered;

[0026] According to the above formula, the envelope area of ​​the response static and dynamic component energy difference is drawn. When the upper boundary of the envelope area ΔE U (ω) is greater than the lower boundary of the envelope area ΔE L When (ω) is at its maximum value, the corresponding frequency range is the optimal separation frequency range:

[0027]

[0028] (5) This optimal separation frequency range is used as the transition band range of the low-pass filter, and the minimum attenuation of the stop band of the low-pass filter is α s It is roughly determined by the following formula:

[0029]

[0030] in, and Represent the minimum and maximum values ​​of the dynamic response spectrum amplitude, respectively. The frequency interval of

[0031] According to the calculated transition band range and the minimum attenuation of the stop band, a low-pass filter is designed to filter the dynamic response of the bridge to obtain the quasi-static response of the bridge;

[0032] Step 3: Use the classic least squares regularization method to invert the quasi-static response of the bridge into the bridge influence line. After obtaining the quasi-static response of the bridge, the Tikhonov regularization method is used to invert the bridge influence line:

[0033]

[0034] Among them, Φ is the bridge influence line vector; R is the bridge quasi-static response vector; W is the vehicle information matrix, which is calculated using the classic quasi-static influence line identification model; λ is the regularization coefficient, which is selected by the L-curve method; and T is the regularization matrix.

[0035] Beneficial effects of the present invention:

[0036] 1. The bridge influence line identification method of the present invention has a complete theoretical basis. It only needs to obtain the fundamental frequency, first-order damping ratio and train speed of the bridge to effectively eliminate the dynamic effect in the bridge response under the action of the high-speed train, and then invert the quasi-static influence line of the bridge, avoiding the irrationality of selecting the cutoff frequency based on experience and the tediousness of repeatedly adjusting the filter parameters, and providing a theoretical reference for practical engineering applications.

[0037] 2. Compared with the existing influence line identification methods, the bridge influence line identification method of the present invention can reasonably set the parameters of the low-pass filter according to different train speeds. When the train speed is very high, the bridge influence line can still be inverted from the dynamic response of the bridge, and the effect is very stable.

[0038] 3. The bridge influence line identification method of the present invention has high robustness and can still accurately identify the bridge influence line under interference from large noise and track unevenness, and has good engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method of the present invention;

[0040] Figure 2 A vehicle-bridge coupling model for simulation in the implementation of the method of the present invention;

[0041] Figure 3 The method of the present invention is used to calculate the vertical displacement response of the bridge mid-span under different vehicle speeds;

[0042] Figure 4 The quasi-static response of the bridge after filtering in the calculation of the method of the present invention;

[0043] Figure 5 The influence lines of the bridges identified by quasi-static response are used in the implementation of the method of the present invention. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below with reference to the accompanying drawings and a numerical example.

[0045] The bridge influence line identification method of the present invention is divided into three steps: "collecting bridge response data containing dynamic components when a high-speed train passes over a bridge alone and obtaining train parameter and bridge parameter information", "calculating the optimal separation frequency range of static and dynamic components of the response and designing a low-pass filter to filter the dynamic response" and "using the classic least squares regularization method to invert the quasi-static response of the bridge into the bridge influence line". The specific implementation method has been given above. Next, the use method and characteristics of the invention are explained in conjunction with a calculation example.

[0046] Implementation: Identification of bridge influence lines for trains crossing the bridge at different speeds

[0047] This example uses a 10-DOF train-simply supported beam coupled vertical vibration model with 5 carriages to obtain the vertical displacement response of the bridge mid-span to verify the method. The bridge is discretized into 20 beam elements, and the US 5-level track irregularity power spectrum is used, with a time step of 0.01s. The parameters of the train and bridge coupled vibration model are shown in Table 1, and the train-bridge coupling model is shown in Figure 2 .

[0048] In this example, three train speeds of 100km / h, 200km / h and 300km / h were simulated to pass through the bridge, and the vertical displacement response of the bridge mid-span was obtained. A noise with a signal-to-noise ratio of 20 was added to the bridge response, as shown in Figure 2. Figure 3 As shown. Then according to Table 1, the number of axles of the adopted train model is calculated to be 20, and the axle weight is 1.62×10 4 kg, wheelbase information see Figure 2 Annotation.

[0049] The design parameters of the low-pass filter are calculated based on the bridge parameters and train speed, as shown in Table 2. Subsequently, a low-pass filter is designed to filter the bridge response, and the bridge influence line is obtained by inverting the filtered bridge quasi-static response through the least squares regularization method. The filtered bridge quasi-static response is shown in Figure 4 The identified bridge influence line is shown in Figure 5 .

[0050] from Figure 4 It can be seen that under different vehicle speeds, the method proposed in this patent can effectively eliminate the dynamic effect of high-speed train excitation, and can eliminate the interference of high-level noise and track unevenness. Figure 5 It can be seen that the influence line identified by the method proposed in this patent under different vehicle speeds is very close to the real influence line. This method has high robustness, very stable effect, and great engineering application prospects.

[0051] Table 1 Parameters of the train and bridge coupled vibration model

[0052]

[0053] Table 2 Filter parameters under different vehicle speeds

[0054]

Claims

1. A bridge influence line identification method based on high-speed train excitation dynamic response, characterized in that: Here are the steps: Step 1: Collect bridge response data including dynamic components when a high-speed train passes over a bridge alone, and obtain train parameter and bridge parameter information (1) Using sensors deployed on the bridge, the monitoring response data of a single high-speed train passing through the bridge is collected. Based on the bridge length l and the train speed v obtained by the speed radar, the monitoring response data intervals of the train starting to go on the bridge and completely going off the bridge are intercepted and converted in time and space so that each response sampling point corresponds to the position of the first axis of the train on the bridge; (2) Obtain the information on the number of axles, wheelbase, and axle weight of the train, and use the monitoring data to calculate or obtain the first-order natural circular frequency ω1 and first-order damping ratio ξ1 of the bridge through historical modal test results; Step 2: Calculate the optimal separation frequency range of the static and dynamic components of the response, and design a low-pass filter to filter the dynamic response. (3) Calculate the theoretical spectrum analytical solution of the quasi-static and dynamic components of the bridge response based on the train and bridge parameters; When only the first-order mode with the largest contribution is considered, the analytical solutions of the quasi-static and dynamic components of the bridge response under the action of the moving load series are shown as follows: Among them, y 静 (t) and y 动 (t) represents the analytical solution of the quasi-static and dynamic components of the bridge response, respectively, and t represents the time value; G1, G2, A, and B are parameters related to the bridge modal parameters and moving load sequence information, which are calculated by traditional dynamic analysis; is the first-order load excitation circular frequency; is the first-order bridge natural circular frequency considering the damping effect; The above equation is Fourier transformed in the time range of [0, l / v] to obtain the analytical solution of the quasi-static and dynamic component spectra of the bridge response under the action of the moving load series: Where X(ω) is the analytical solution of the quasi-static or dynamic component spectrum of the bridge response, ω represents the frequency value of the signal after Fourier transformation, and its value range is [0,F s / 2],F s is the sampling frequency of the bridge response; (4) The optimal separation frequency range is solved based on the energy difference of the static and dynamic components of the bridge response. The energy of the quasi-static or dynamic components of the bridge response is calculated by the following formula: Where E(ω) is the energy of the quasi-static or dynamic component of the response with a frequency less than ω; After calculating the distribution of static and dynamic component energy with frequency, the optimal separation frequency is calculated by finding the maximum difference between quasi-static and dynamic energy; after considering all the aliased parts of the response static and dynamic component energy as quasi-static or dynamic components, the range of the true static and dynamic component energy difference is given: in, is the direct difference between the static and dynamic component energies when energy aliasing is not considered; ΔE(ω) is the true difference between the static and dynamic component energies when energy aliasing is considered; According to the above formula, the envelope area of ​​the response static and dynamic component energy difference is drawn. When the upper boundary of the envelope area ΔE U (ω) is greater than the lower boundary of the envelope area ΔE L When (ω) is at its maximum value, the corresponding frequency range is the optimal separation frequency range: (5) This optimal separation frequency range is used as the transition band range of the low-pass filter, and the minimum attenuation of the stop band of the low-pass filter is α s It is roughly determined by the following formula: in, and Represent the minimum and maximum values ​​of the dynamic response spectrum amplitude, respectively. The frequency interval of According to the calculated transition band range and the minimum attenuation of the stop band, a low-pass filter is designed to filter the dynamic response of the bridge to obtain the quasi-static response of the bridge; Step 3: Use the classic least squares regularization method to invert the quasi-static response of the bridge into the bridge influence line. After obtaining the quasi-static response of the bridge, the Tikhonov regularization method is used to invert the bridge influence line: Among them, Φ is the bridge influence line vector; R is the bridge quasi-static response vector; W is the vehicle information matrix, which is calculated using the classic quasi-static influence line identification model; λ is the regularization coefficient, which is selected by the L-curve method; and T is the regularization matrix.

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