Abnormal phenomenon reproduction and resonance prevention fu-rie method based on bridge twin dynamic model

Abstract

To overcome the current technical problems of difficulty in analyzing the causes of bridge anomalies and the inability to actively prevent bridge resonance, this invention provides a Fourier method for anomaly reproduction and resonance prevention based on a bridge twin dynamic model. This method relies on the fact that the system matrix related to all bridge nodes and the observation coefficient matrix related to nodes are only related to the bridge parameters and do not change significantly during a single continuous bridge test. The reproduction of bridge anomalies or the simulation of bridge resonance and abnormal loading tests are relatively short. Based on the characteristics of slowly changing matrices, a singular perturbation method is used to set the slowly changing matrix as a constant matrix in a single continuous test. Fourier series approximation is used to approximate the fast-changing variable over time, obtaining the ambiguous excitation input when bridge anomalies occur. The system's reproduction of anomalies is verified through equivalent bridge simulation; thus, the artificial excitation input for simulating bridge resonance or anomalies is obtained, solving the technical problems of difficulty in analyzing the causes of bridge anomalies and the inability to actively prevent bridge resonance.

Description

Technical Field

[0001] This invention relates to methods for analyzing the stress on bridge structures, and particularly to Fourier methods for reproducing anomalies and preventing resonance based on bridge twin dynamic models, belonging to the field of road infrastructure safety analysis. Background Technology

[0002] Road infrastructure is the fundamental guarantee of transportation safety. However, major bridge collapses continue to occur, causing numerous deaths and injuries, and significant economic losses. Therefore, many research institutions both domestically and internationally attach great importance to bridge safety research. For example, Blue Road Research in the United States has independently developed a large number of temperature, stress, and strain sensors and applied them to the monitoring of the Horsetail Falls Bridge in Columbia River Canyon, Oregon. UbiPOS and the University of Nottingham in the United Kingdom have developed structural health monitoring systems for major and large bridges and put them into use on the Forth Road Bridge in Scotland, the Yichang-Zhixi Yangtze River Bridge in China, and the Wuhan-Erqi Yangtze River Bridge. In China, the integrated safety monitoring management system of China Communications Construction Company (CCCC) has been applied to the health monitoring of the Xihoumen Bridge and Jintang Bridge in the Zhoushan Island Link Project, as well as the main structure of the Hong Kong-Zhuhai-Macau Bridge. Meanwhile, scholars and institutions both domestically and internationally have published numerous national standards and books, numerous academic papers, and authorized numerous invention patents. These include the widely recognized book "Health Monitoring of Bridges" (Wiley, 2009) by Helmut Wenzel, and the numerous national standards developed based on this work.

[0003] Bridge twin models and equivalent simulation verification methods are of great significance for the design demonstration of bridges to be built, vibration analysis of bridge construction process and performance of completed bridges, fault diagnosis and health prediction management, bridge equivalent test schemes, and exploration of maintenance and operation management schemes. They have already attracted international attention and importance.

[0004] When abnormal phenomena occur on a bridge, it is necessary to find the cause in time so that effective protective measures can be taken to prevent major traffic accidents. On the other hand, in order to ensure the safe operation of the bridge, it is necessary to prevent the occurrence of other abnormal phenomena such as bridge resonance. Both of these points are necessary measures to ensure bridge safety. However, at present, there are more textual qualitative analyses of abnormal phenomena on bridges, but fewer systematic quantitative analyses. Similarly, there is even less research on proactive prevention of bridge safety events such as resonance and other abnormal phenomena. Summary of the Invention

[0005] To overcome the current technical problems of difficulty in analyzing the causes of bridge anomalies and the inability to actively prevent bridge resonance, this invention provides a Fourier method for anomaly reproduction and resonance prevention based on a bridge twin dynamic model. This method relies on the fact that the system matrix related to all bridge nodes and the observation coefficient matrix related to nodes are only related to the bridge parameters and do not change significantly during a single continuous bridge test. The reproduction of bridge anomalies or the simulation of bridge resonance and abnormal loading tests are relatively short. Based on the characteristics of slowly changing matrices, a singular perturbation method is used to set the slowly changing matrix as a constant matrix in a single continuous test. Fourier series approximation is used to approximate the fast-changing variable over time, obtaining the ambiguous excitation input when bridge anomalies occur. The system's reproduction of anomalies is verified through equivalent bridge simulation; thus, the artificial excitation input for simulating bridge resonance or anomalies is obtained, solving the technical problems of difficulty in analyzing the causes of bridge anomalies and the inability to actively prevent bridge resonance.

[0006] The technical solution adopted by this invention to solve its technical problem is: a Fourier transform method for anomaly reproduction and resonance prevention based on a bridge twin dynamic model, characterized by the following steps: Step 1: Dynamic Force Analysis of the Bridge Twin Dynamic Mathematical Model: When the bridge is subjected to external forces, the state equation and observation equation of the twin dynamic mathematical model of the comprehensive force at the bridge joints are as follows: (1) (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. For time variables, , , For the bridge under external forces, the first The node and the first The dynamic combined force coefficient of each node connector, , , This is a dynamic parameter vector of a bridge under external forces, including parameters such as temperature, pressure, tension, reaction force, plastic deformation, included angle, elastic deformation, torque, shear force, and other forces and moments of special bridge structures that change over time. The input vector for external forces includes every vehicle traveling on the bridge surface, external wind, water flow impact, and ship collisions; This includes vehicle type, vehicle weight, vehicle coordinates, vehicle speed, vehicle acceleration, external wind force, wind direction, water flow impact force and direction, and ship collision and direction. ; The input is a non-constant dynamic dimension that varies over time. , , ,for For the The contribution coefficient of each node's dynamic input; The observation vector is formed by direct observation points on the bridge, such as accelerometers placed on the bridge surface to measure bridge vibration; its dimension is... , , They are respectively the corresponding , The observation coefficient matrix; the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step 2: Method for reproducing abnormal phenomena on the bridge: For ease of analysis, equation (1) is written as: (2) (2) In the formula, for The Column vector, for The Column vector; because and It only relates to the bridge's parameters and will not change significantly during a single continuous test of the bridge. The initial comprehensive test of the bridge twin dynamic mathematical model and the subsequent comprehensive correction processes for each bridge twin dynamic mathematical model are relatively short. Based on the characteristics of the slowly changing matrix, the singular perturbation method is used to transform the slowly changing matrix... and Assuming and The constant matrix, This marks the starting time for the first and every subsequent comprehensive correction of the bridge vibration mode using the bridge twin dynamic mathematical model. , This corresponds to the start time of the first comprehensive test of the bridge twin dynamic mathematical model; When a bridge exhibits abnormal phenomena, the comprehensive stress state vector at the bridge joints under external forces is... Given and having sequence measurements, the current system matrix Given, and assuming , and Known; and , and All unknown. When abnormal phenomena occur on a bridge, it is necessary to identify the unknown inputs in order to find the cause of the abnormality and take effective protective measures to prevent major traffic accidents. Will and input-related , Approximating using Fourier series, we obtain: (3) (3) In the formula, , , , , , , , It is a constant matrix;

[0007] For Fourier orthogonal polynomials, It is the highest order; Substituting equation (3) into equation (2) yields: (4) In equation (4), in equation (4), , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the known input, and the expansion constant matrix of the input part of the observation equation corresponding to the known input, respectively. , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the unknown input and the expansion constant matrix of the input part of the observation equation corresponding to the unknown input, respectively. ; To the bridge Different external forces are applied to obtain (5) According to equation (4), we can obtain: (6) Therefore, we can conclude that: (7) Therefore, the expression for the coefficient matrix of the Fourier expansion of the unknown input is: (8) Step 3: Reproduce abnormal phenomena through the bridge equivalent simulation verification system: Based on the bridge twin dynamic mathematical model, the result of the bridge abnormal phenomenon input excitation (8) is obtained. The abnormal phenomenon of the actual bridge will be reproduced in the bridge equivalent simulation verification system. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the result of the bridge equivalent simulation verification system is consistent with the abnormal phenomenon of the actual bridge, the bridge twin dynamic mathematical model and the bridge equivalent simulation verification system are consistent with the actual bridge. Otherwise, if the bridge twin dynamic mathematical model or the bridge equivalent simulation verification system is inconsistent with the actual bridge, the bridge twin dynamic mathematical model needs to be corrected in time and the bridge equivalent simulation verification system needs to be adjusted until the verification test is consistent. Step 4: The conditions for preventing bridge resonance and other abnormal phenomena are analyzed as follows: According to equations (2) and (3), the state equation and observation equation of the bridge twin dynamic mathematical model obtained by applying the Fourier series approximation method are: (9) According to equation (9), we can obtain: (10) Therefore, the Fourier expansion coefficient matrix of the loading input required for simulating bridge resonance and other abnormal phenomena is: (11) Step 5: Test the occurrence of bridge resonance and other abnormal phenomena through the bridge equivalent simulation verification system: According to the bridge twin dynamic mathematical model, simulate the input excitation to obtain the results of bridge resonance and other abnormal phenomena (10). The bridge equivalent simulation verification system can generate bridge resonance and other abnormal phenomena. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the resonance or other abnormal phenomena in the bridge equivalent simulation verification system are consistent with the calculation results of the bridge twin dynamic mathematical model, the bridge equivalent simulation verification system is consistent with the bridge twin dynamic mathematical model. Otherwise, the bridge equivalent simulation verification system is inconsistent with the bridge twin dynamic mathematical model. It is necessary to adjust the bridge equivalent simulation verification system in time until the results of the bridge twin dynamic mathematical model can be verified.

[0008] The beneficial effects of this invention are as follows: This invention provides a Fourier method for reproducing abnormal phenomena and preventing resonance based on a bridge twin dynamic model. This method relies on the fact that the system matrix and observation coefficient matrix related to all bridge nodes are only related to the bridge parameters and do not change significantly during a single continuous bridge test. The time required for reproducing bridge anomalies or simulating bridge resonance and abnormal loading tests is relatively short. Based on the characteristics of rapidly changing matrices, a singular perturbation method is used to set the slowly changing matrix as a constant matrix in a single continuous test. Fourier series approximation is used to approximate the rapidly changing variable over time, obtaining the ambiguous excitation input when an abnormal phenomenon occurs in the bridge. The system's reproduction of the abnormal phenomenon is verified through equivalent bridge simulation. This method obtains the artificial excitation input for simulating bridge resonance or abnormal phenomena, solving the technical problems of difficulty in analyzing the causes of bridge anomalies and the inability to actively prevent bridge resonance.

[0009] The present invention will now be described in detail with reference to specific embodiments. Detailed Implementation

[0010] Step 1: Dynamic Force Analysis of the Bridge Twin Dynamic Mathematical Model: When the bridge is subjected to external forces, the state equation and observation equation of the twin dynamic mathematical model of the comprehensive force at the bridge joints are as follows: (1) (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. For time variables, For the bridge under external forces, the first The node and the first The dynamic combined force coefficient of each node connector, , , This is a dynamic parameter vector of a bridge under external forces, including parameters such as temperature, pressure, tension, reaction force, plastic deformation, included angle, elastic deformation, torque, shear force, and other forces and moments of special bridge structures that change over time. The input vector for external forces includes every vehicle traveling on the bridge surface, external wind, water flow impact, and ship collisions; This includes vehicle type, vehicle weight, vehicle coordinates, vehicle speed, vehicle acceleration, external wind force, wind direction, water flow impact force and direction, and ship collision and direction. ; The input is a non-constant dynamic dimension that varies over time. , , ,for For the The contribution coefficient of each node's dynamic input; The observation vector is formed by direct observation points on the bridge, such as accelerometers placed on the bridge surface to measure bridge vibration; its dimension is... , , They are respectively the corresponding , The observation coefficient matrix; the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step 2: Method for reproducing abnormal phenomena on the bridge: For ease of analysis, equation (1) is written as: (2) (2) In the formula, for The Column vector, for The Column vector; because and It only relates to the bridge's parameters and will not change significantly during a single continuous test of the bridge. The initial comprehensive test of the bridge twin dynamic mathematical model and the subsequent comprehensive correction processes for each bridge twin dynamic mathematical model are relatively short. Based on the characteristics of the slowly changing matrix, the singular perturbation method is used to transform the slowly changing matrix... and Assuming and The constant matrix, This marks the starting time for the first and every subsequent comprehensive correction of the bridge vibration mode using the bridge twin dynamic mathematical model. , This corresponds to the start time of the first comprehensive test of the bridge twin dynamic mathematical model; When a bridge exhibits abnormal phenomena, the comprehensive stress state vector at the bridge joints under external forces is... Given and having sequence measurements, the current system matrix Given, and assuming , and Known; and , and All unknown. When abnormal phenomena occur on a bridge, it is necessary to identify the unknown inputs in order to find the cause of the abnormality and take effective protective measures to prevent major traffic accidents. Will and input-related , Approximating using Fourier series, we obtain: (3) (3) In the formula, , , , , , , , It is a constant matrix;

[0011] For Fourier orthogonal polynomials, It is the highest order; Substituting equation (3) into equation (2) yields: (4) In equation (4), in equation (4), , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the known input, and the expansion constant matrix of the input part of the observation equation corresponding to the known input, respectively. , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the unknown input and the expansion constant matrix of the input part of the observation equation corresponding to the unknown input, respectively. ; To the bridge Different external forces are applied to obtain (5) According to equation (4), we can obtain: (6) Therefore, we can conclude that: (7) Therefore, the expression for the coefficient matrix of the Fourier expansion of the unknown input is: (8) Step 3: Reproduce abnormal phenomena through the bridge equivalent simulation verification system: Based on the bridge twin dynamic mathematical model, the result of the bridge abnormal phenomenon input excitation (8) is obtained. The abnormal phenomenon of the actual bridge will be reproduced in the bridge equivalent simulation verification system. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the result of the bridge equivalent simulation verification system is consistent with the abnormal phenomenon of the actual bridge, the bridge twin dynamic mathematical model and the bridge equivalent simulation verification system are consistent with the actual bridge. Otherwise, if the bridge twin dynamic mathematical model or the bridge equivalent simulation verification system is inconsistent with the actual bridge, the bridge twin dynamic mathematical model needs to be corrected in time and the bridge equivalent simulation verification system needs to be adjusted until the verification test is consistent. Step 4: The conditions for preventing bridge resonance and other abnormal phenomena are analyzed as follows: According to equations (2) and (3), the state equation and observation equation of the bridge twin dynamic mathematical model obtained by applying the Fourier series approximation method are: (9) According to equation (9), we can obtain: (10) Therefore, the Fourier expansion coefficient matrix of the loading input required for simulating bridge resonance and other abnormal phenomena is: (11) Step 5: Test the occurrence of bridge resonance and other abnormal phenomena through the bridge equivalent simulation verification system: According to the bridge twin dynamic mathematical model, simulate the input excitation to obtain the results of bridge resonance and other abnormal phenomena (10). The bridge equivalent simulation verification system can generate bridge resonance and other abnormal phenomena. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the resonance or other abnormal phenomena in the bridge equivalent simulation verification system are consistent with the calculation results of the bridge twin dynamic mathematical model, the bridge equivalent simulation verification system is consistent with the bridge twin dynamic mathematical model. Otherwise, the bridge equivalent simulation verification system is inconsistent with the bridge twin dynamic mathematical model. It is necessary to adjust the bridge equivalent simulation verification system in time until the results of the bridge twin dynamic mathematical model can be verified.

Claims

1. A Fourier transform method for anomaly reproduction and resonance prevention based on a bridge twin dynamic model, characterized by the following steps: Step 1: Dynamic Force Analysis of the Bridge Twin Dynamic Mathematical Model: When the bridge is subjected to external forces, the state equation and observation equation of the twin dynamic mathematical model of the comprehensive force at the bridge joints are as follows: （1） (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. For time variables, , , For the bridge under external forces, the first The node and the first The dynamic combined force coefficient of each node connector, , , This is a dynamic parameter vector of a bridge under external forces, including parameters such as temperature, pressure, tension, reaction force, plastic deformation, included angle, elastic deformation, torque, shear force, and other forces and moments of special bridge structures that change over time. The input vector for external forces includes every vehicle traveling on the bridge surface, external wind, water flow impact, and ship collisions; This includes vehicle type, vehicle weight, vehicle coordinates, vehicle speed, vehicle acceleration, external wind force, wind direction, water flow impact force and direction, and ship collision and direction. ; The input is a non-constant dynamic dimension that varies over time. , , ,for For the The contribution coefficient of each node's dynamic input; The observation vector is formed by direct observation points on the bridge, such as accelerometers placed on the bridge surface to measure bridge vibration; its dimension is... , , They are respectively the corresponding , The observation coefficient matrix; the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step 2: Method for reproducing abnormal phenomena on the bridge: For ease of analysis, equation (1) is written as: (2) (2) In the formula, for The Column vectors for The Column vector; because and It only relates to the bridge's parameters and will not change significantly during a single continuous test of the bridge. The initial comprehensive test of the bridge twin dynamic mathematical model and the subsequent comprehensive correction processes for each bridge twin dynamic mathematical model are relatively short. Based on the characteristics of the slowly changing matrix, the singular perturbation method is used to transform the slowly changing matrix... and Assuming and The constant matrix, This marks the starting time for the first and every subsequent comprehensive correction of the bridge vibration mode using the bridge twin dynamic mathematical model. , This corresponds to the start time of the first comprehensive test of the bridge twin dynamic mathematical model; When a bridge exhibits abnormal phenomena, the comprehensive stress state vector at the bridge joints under external forces is... Given and having sequence measurements, the current system matrix Given, and assuming , and Known; and , and All unknown. When abnormal phenomena occur on a bridge, it is necessary to identify the unknown inputs in order to find the cause of the abnormality and take effective protective measures to prevent major traffic accidents. Will and input-related , Approximating using Fourier series, we obtain: (3) (3) In the formula, , , , , , , , It is a constant matrix; ， For Fourier orthogonal polynomials, It is the highest order; Substituting equation (3) into equation (2) yields: (4) In equation (4), in equation (4), , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the known input, and the expansion constant matrix of the input part of the observation equation corresponding to the known input, respectively. , , and Let represent the expansion constant matrix of the input part of the state equation corresponding to the unknown input and the expansion constant matrix of the input part of the observation equation corresponding to the unknown input, respectively. ； To the bridge Different external forces are applied to obtain (5) According to equation (4), we can obtain: （6） Therefore, we can conclude that: (7) Therefore, the expression for the coefficient matrix of the Fourier expansion of the unknown input is: （8） Step 3: Reproduce abnormal phenomena through the bridge equivalent simulation verification system: Based on the bridge twin dynamic mathematical model, the result of the bridge abnormal phenomenon input excitation (8) is obtained. The abnormal phenomenon of the actual bridge will be reproduced in the bridge equivalent simulation verification system. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the result of the bridge equivalent simulation verification system is consistent with the abnormal phenomenon of the actual bridge, the bridge twin dynamic mathematical model and the bridge equivalent simulation verification system are consistent with the actual bridge. Otherwise, if the bridge twin dynamic mathematical model or the bridge equivalent simulation verification system is inconsistent with the actual bridge, the bridge twin dynamic mathematical model needs to be corrected in time and the bridge equivalent simulation verification system needs to be adjusted until the verification test is consistent. Step 4: The conditions for preventing bridge resonance and other abnormal phenomena are analyzed as follows: According to equations (2) and (3), the state equation and observation equation of the bridge twin dynamic mathematical model obtained by applying the Fourier series approximation method are: (9) According to equation (9), we can obtain: (10) Therefore, the Fourier expansion coefficient matrix of the loading input required for simulating bridge resonance and other abnormal phenomena is: （11） Step 5: Test the occurrence of bridge resonance and other abnormal phenomena through the bridge equivalent simulation verification system: According to the bridge twin dynamic mathematical model, simulate the input excitation to obtain the results of bridge resonance and other abnormal phenomena (10). The bridge equivalent simulation verification system can generate bridge resonance and other abnormal phenomena. Since the bridge twin dynamic mathematical model is required to be highly consistent with the actual bridge model, and the bridge equivalent simulation verification system is constructed based on the bridge twin dynamic mathematical model, when the resonance or other abnormal phenomena in the bridge equivalent simulation verification system are consistent with the calculation results of the bridge twin dynamic mathematical model, the bridge equivalent simulation verification system is consistent with the bridge twin dynamic mathematical model. Otherwise, the bridge equivalent simulation verification system is inconsistent with the bridge twin dynamic mathematical model. It is necessary to adjust the bridge equivalent simulation verification system in time until the results of the bridge twin dynamic mathematical model can be verified.

Images