CN115358088A - Bridge influence line identification method based on high-speed train excitation power response - Google Patents
Bridge influence line identification method based on high-speed train excitation power response Download PDFInfo
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Abstract
The invention belongs to the field of structural safety detection, and discloses a bridge influence line identification method based on high-speed train excitation dynamic response. The method comprises the following steps: (1) Acquiring bridge response data containing dynamic components when a high-speed train independently runs through a bridge and acquiring train parameters 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) And (3) inverting the bridge quasi-static response into a bridge influence line by using a classical least square regularization method. The method can effectively eliminate the power effect in the bridge response under the action of the high-speed train in the operation state, further invert to obtain the quasi-static influence line of the bridge, is simple to operate, has high robustness, can be suitable for identifying the bridge influence line of any vehicle speed excitation response in the operation state, and has good engineering application prospect.
Description
Technical Field
The invention belongs to the field of structural safety detection, and particularly relates to a bridge influence line identification method based on high-speed train excitation dynamic response.
Background
The high-speed railway bridge is an important component of infrastructure, and the abnormal operation state can be found in time by the bridge state evaluation and vehicle load identification technology based on the influence line, so that great life and property loss is avoided at low cost. Because the speed of the high-speed train is far greater than that of other vehicles and is influenced by the coupling effect of the train and the bridge, the bridge power effect excited by the train is often difficult to eliminate, which brings challenges to the existing influence line identification method.
The existing method for identifying the bridge influence line from the vehicle actuating force response mainly comprises an improved influence line identification method and a method for extracting a quasi-static component from the actuating force response. The first method is generally to fit influence lines based on physical properties of bridges, such as a polynomial fitting method (Extraction of fluent line through a fit method from bridge dynamic response a passing vehicle) proposed by waning waves and the like, a B-spline fitting method (a bridge influence line identification method based on basis of basis function representation and sparse regularization) proposed by chen waves and the like, and obtains a better effect in highway bridge influence line identification. The other method is more intuitive in thinking, directly processes the response signals containing the dynamic effect, and obtains the bridge influence line by utilizing the processed quasi-static response inversion. The method has the focus on how to obtain accurate quasi-static response of the bridge, and the problem is deeply researched in the fields of bridge influence line identification, bridge dynamic weighing, power amplification factor calculation and the like. The main solving means are three, namely frequency domain high frequency component filtering, such as a low pass filtering method (scaling an inflexion line from direct measurements) adopted by Obbrien and the like; temporal smoothing, such as the moving average method employed by Gonz-a-lez et al (Testing of edge weighing-in-motion algorithm using multiple longitudinal sensor locations); and (3) an empirical mode decomposition method (a bridge influence line identification method capable of eliminating the vehicle dynamic effect) adopted by time-frequency domain decomposition reconstruction, such as Zheng Xue and the like. In the methods, the dynamic response of the bridge is regarded as a high-frequency part and is filtered, so that the low-frequency quasi-static response is reserved, and then the bridge influence line is further identified.
However, the above methods are often the research on the road bridge with low operating speed, which hardly achieves satisfactory results for the high-speed railway bridge, and thus the improvement of the existing methods is required. According to the existing research, the defects that overfitting is easy to occur, the limitation of the type of the bridge is large, the applicable vehicle speed is low and the like exist when the power effect is removed by using a fitting method. The method for removing the dynamic effect by utilizing the time domain smoothing and the time-frequency domain decomposition reconstruction has the defects of uncertain physical significance, difficult parameter setting, unstable influence line identification effect and the like. The method for filtering the high-frequency components in the frequency domain has the advantages of simple operation, small calculated amount and stable filtering performance, has certain advantages in the existing method, and is widely applied. In the existing research, the method is generally realized by a low-pass filter, but the cut-off frequency of the low-pass filter is generally directly defined as the fundamental frequency of the bridge according to experience, or the parameters of the filter are repeatedly adjusted through a large number of working conditions, so that the power effect excited by the high-speed train is difficult to accurately filter. Therefore, the patent provides a bridge influence line identification method based on high-speed train excitation dynamic response, which can directly calculate the optimal separation frequency of response static and dynamic components so as to identify and obtain the bridge influence line.
Disclosure of Invention
The invention aims to provide a bridge influence line identification method based on high-speed train excitation dynamic response, which can directly calculate the optimal separation frequency of response static and dynamic components so as to identify and obtain the bridge influence line.
The technical scheme of the invention is as follows:
a bridge influence line identification method based on high-speed train excitation power response comprises the following steps:
step 1, collecting bridge response data containing dynamic components when a high-speed train runs through a bridge independently, and acquiring train parameters and bridge parameter information
(1) The method comprises the steps that monitoring response data of a single high-speed train passing through a bridge are collected by a sensor arranged on the bridge, monitoring response data intervals of the train starting to get on the bridge and getting off the bridge are intercepted according to the length l of the bridge and the speed v of the train obtained by a speed measuring radar, and space-time conversion is carried out on the monitoring response data intervals, so that each sampling point is responded, and the position of a first shaft of the train on the bridge corresponds to each sampling point;
(2) Obtaining the axle number, the axle distance and the axle weight information of the train, and utilizing the monitoring data to calculate or obtaining the first-order natural vibration circle frequency omega of the bridge through the historical modal test result 1 And first order damping ratio ξ 1 ；
(3) Calculating theoretical spectrum analytic solutions of quasi-static and dynamic components of the bridge response according to 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 are respectively shown as the following formulas:
wherein, y Quiet (t) and y Movable part (t) respectively representing the analytical solutions of the quasi-static and dynamic components of the bridge response, wherein t represents a time value; g 1 、G 2 A and B are parameters related to bridge modal parameters and moving load column information, and are calculated through traditional dynamic analysis;
exciting the circle frequency for a first order load;
the first-order bridge natural vibration circular frequency considering damping influence;
fourier transform is carried out on the formula in the time range of [0, l/v ] to obtain an analytic solution of the bridge response quasi-static and dynamic component frequency spectrum under the following actions of moving load:
wherein X (omega) is the analytic solution of the bridge response quasi-static or dynamic component frequency spectrum, omega represents the frequency value of the signal after Fourier transform, and the value range is [0, F s /2]，F s A sampling frequency for the bridge response;
(4) Solving the optimal separation frequency range based on the energy difference value of the static and dynamic components of the bridge response, wherein the energy of the quasi-static or dynamic components of the bridge response is calculated by the following formula:
wherein E (ω) is the energy of the response quasi-static or dynamic component at a frequency less than ω;
after the distribution of static and dynamic component energy along with frequency is obtained through calculation, the optimal separation frequency is calculated by finding the maximum difference value of quasi-static and dynamic energy; and (3) after the energy aliasing part of the response static and dynamic components is completely regarded as quasi-static or dynamic components, the value range of the energy difference value of the real static and dynamic components is given:
wherein,
direct difference of static and dynamic component energy without considering energy aliasing; Δ E (ω) is energy aliasing dependentTrue difference of static and dynamic component energies;
drawing an envelope region responding to the energy difference of the static and dynamic components according to the formula, wherein when the upper boundary Delta E of the envelope region U (ω) is greater than the lower boundary Δ E of the envelope region L (ω) at the maximum, the corresponding frequency range is the optimal separation frequency range:
(5) The optimal separation frequency range is used as the transition band range of a low-pass filter, and the stopband minimum attenuation alpha of the low-pass filter s Is roughly determined by the following formula:
wherein,
and
respectively representing the minimum and maximum values of the magnitude of the dynamic response spectrum, both of which are considered only
The frequency interval of (1);
designing a low-pass filter to filter the dynamic response of the bridge according to the calculated transition band range and the stop band minimum attenuation to obtain the quasi-static response of the bridge;
step 3, inverting the quasi-static response of the bridge into a bridge influence line by using a classical least square regularization method, and after the quasi-static response of the bridge is obtained, inverting by using a Tikhonov regularization method to obtain the bridge influence line:
wherein phi is a bridge influence line vector; r is a bridge quasi-static response vector; w is a vehicle information matrix, and a classical quasi-static influence line identification model is adopted for calculation; lambda is a regularization coefficient and is selected by an L curve method; t is a regularizer.
The invention has the beneficial effects that:
1. the bridge influence line identification method has a complete theoretical basis, can effectively eliminate the dynamic effect in bridge response under the action of a high-speed train only by obtaining the fundamental frequency, the first-order damping ratio and the train speed of the bridge, further obtains the quasi-static influence line of the bridge through inversion, avoids the irrationality of selecting the cutoff frequency only by depending on experience and the complexity of repeatedly adjusting the parameters of the filter, and provides theoretical reference for practical engineering application.
2. Compared with the existing influence line identification method, the method for identifying the bridge influence line can reasonably set the parameters of the low-pass filter aiming at different vehicle speeds, can still obtain the bridge influence line by inversion from the dynamic response of the bridge when the train speed is very high, and has very stable effect.
3. The method for identifying the bridge influence line has high robustness, can accurately identify the bridge influence line under the condition of high noise and track irregularity interference, and has good engineering application prospect.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a simulated axle coupling model implemented in a method of the present invention;
FIG. 3 shows the bridge span vertical displacement response under different vehicle speeds during the implementation of the method of the present invention;
FIG. 4 is a diagram illustrating a filtered quasi-static bridge response in a process of implementing the method of the present invention;
FIG. 5 is a diagram of bridge influence lines identified using quasi-static response in the implementation of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and a numerical example.
The bridge influence line identification method comprises three steps of collecting bridge response data containing dynamic components when a high-speed train independently runs through a bridge, obtaining train parameters and bridge parameter information, calculating the optimal separation frequency range of static and dynamic components of the response, designing a low-pass filter to filter dynamic response, and inverting the quasi-static response of the bridge into the bridge influence line by using a classical least square regularization method, wherein the specific implementation mode is given above, and the using method and the characteristics of the method are explained by combining with an operator.
Carrying out calculation: bridge influence line identification of different-speed train passing bridge
The method for obtaining the bridge mid-span vertical displacement response is verified by adopting a 10-degree-of-freedom train-simply supported beam coupling vertical vibration model with 5-section carriage marshalling, wherein the bridge is dispersed into 20 beam units, an American 5-grade rail irregularity power spectrum is adopted, and the time step length is 0.01s. The parameters of the train and bridge coupling vibration model are shown in a table 1, and the parameters of the axle coupling model are shown in a table 2.
In the present embodiment, three speed train bridge crossings of 100km/h, 200km/h and 300km/h are simulated respectively, bridge span vertical displacement response is obtained, and noise with a signal-to-noise ratio of 20 is added to the bridge response, as shown in fig. 3. Then, the number of axles of the adopted train model is 20 and the axle weight is 1.62 multiplied by 10 according to the calculation of the table 1 4 kg, wheelbase information is labeled in figure 2.
And calculating to obtain the design parameters of the low-pass filter according to the bridge parameters and the train speed, and referring to table 2. And then, designing a low-pass filter to filter the bridge response, and utilizing the filtered quasi-static bridge response to obtain a bridge influence line through inversion by a least square regularization method. The filtered quasi-static response of the bridge is shown in figure 4, and the identified influence line of the bridge is shown in figure 5.
As can be seen from the figure 4, under the action of different vehicle speeds, the method provided by the patent can effectively eliminate the power effect excited by the high-speed train and can eliminate the interference of high-level noise and track irregularity. As can be seen from the graph 5, the influence lines recognized by the method under the action of different vehicle speeds are very close to the real influence lines, the method is high in robustness, very stable in effect and wide in engineering application prospect.
TABLE 1 train and bridge coupled vibration model parameters
TABLE 2 Filter parameters under different vehicle speeds
Claims (1)
1. A bridge influence line identification method based on high-speed train excitation power response is characterized by comprising the following steps:
step 1, collecting bridge response data containing dynamic components when a high-speed train runs through a bridge independently, and acquiring train parameters and bridge parameter information
(1) The method comprises the steps that monitoring response data of a single high-speed train passing through a bridge are collected by a sensor arranged on the bridge, monitoring response data intervals of the train starting to get on the bridge and getting off the bridge are intercepted according to the length l of the bridge and the speed v of the train obtained by a speed measuring radar, and space-time conversion is carried out on the monitoring response data intervals, so that each sampling point is responded, and the position of a first shaft of the train on the bridge corresponds to each sampling point;
(2) Obtaining the axle number, the axle distance and the axle weight information of the train, and utilizing the monitoring data to calculate or obtaining the first-order natural vibration circle frequency omega of the bridge through the historical modal test result 1 And first order damping ratio xi 1 ；
Step 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) Calculating theoretical spectrum analytical solutions of quasi-static and dynamic components of the bridge response according to 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 are respectively shown as the following formulas:
wherein, y Quiet (t) and y Movable part (t) respectively representing the analytical solutions of the quasi-static and dynamic components of the bridge response, wherein t represents a time value; g 1 、G 2 A and B are parameters related to bridge modal parameters and moving load column information, and are calculated through traditional dynamic analysis;
exciting the circular frequency for a first order load;
the first-order bridge natural vibration circle frequency considering damping influence;
fourier transform is carried out on the formula in the time range of [0, l/v ] to obtain an analytic solution of the bridge response quasi-static and dynamic component frequency spectrum under the following action of the moving load:
wherein X (omega) is the analytic solution of the bridge response quasi-static or dynamic component frequency spectrum, omega represents the frequency value of the signal after Fourier transform, and the value range is [0, F ] s /2]，F s A sampling frequency for the bridge response;
(4) Solving the optimal separation frequency range based on the energy difference value of the static and dynamic components of the bridge response, wherein the energy of the quasi-static or dynamic components of the bridge response is calculated by the following formula:
wherein E (ω) is the energy of the response quasi-static or dynamic component with frequency less than ω;
after the distribution of static and dynamic component energy along with frequency is obtained through calculation, the optimal separation frequency is calculated by finding the maximum difference value of quasi-static and dynamic energy; and (3) after the energy aliasing part of the response static and dynamic components is completely regarded as quasi-static or dynamic components, the value range of the energy difference value of the real static and dynamic components is given:
wherein,
is the direct difference of the energy of the static and dynamic components when the energy aliasing is not considered; Δ E (ω) is the true difference of the energy of the static and dynamic components considering the energy aliasing;
according to the formula, an envelope region responding to the energy difference of the static and dynamic components is drawn, and when the upper boundary Delta E of the envelope region is U (ω) is greater than the lower boundary Δ E of the envelope region L (ω) at the maximum, the corresponding frequency range is the optimal separation frequency range:
(5) The optimal separation frequency range is used as the transition band range of the low-pass filter, and the stop band minimum attenuation alpha of the low-pass filter s Is roughly determined by the following formula:
wherein,
and
respectively representing the minimum and maximum values of the magnitude of the dynamic response spectrum, both of which are considered only
The frequency interval of (1);
designing a low-pass filter to filter the dynamic response of the bridge according to the calculated transition band range and the stop band minimum attenuation to obtain the quasi-static response of the bridge;
step 3, inverting the quasi-static response of the bridge into a bridge influence line by using a classical least square regularization method, and after the quasi-static response of the bridge is obtained, inverting by using a Tikhonov regularization method to obtain the bridge influence line:
wherein phi is a bridge influence line vector; r is a bridge quasi-static response vector; w is a vehicle information matrix, and a classical quasi-static influence line identification model is adopted for calculation; lambda is a regularization coefficient and is selected by an L curve method; t is a regularization matrix.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115876413A (en) * | 2023-02-14 | 2023-03-31 | 济南城建集团有限公司 | Bridge displacement estimation method under action of moving vehicle based on acceleration |
| CN116358679A (en) * | 2023-05-16 | 2023-06-30 | 中铁大桥局集团有限公司 | Dynamic weighing method for urban rail transit train bridge |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115876413A (en) * | 2023-02-14 | 2023-03-31 | 济南城建集团有限公司 | Bridge displacement estimation method under action of moving vehicle based on acceleration |
| CN116358679A (en) * | 2023-05-16 | 2023-06-30 | 中铁大桥局集团有限公司 | Dynamic weighing method for urban rail transit train bridge |
| CN116358679B (en) * | 2023-05-16 | 2024-04-23 | 中铁大桥局集团有限公司 | Dynamic weighing method for urban rail transit train bridge |
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