Bridge twin dynamic model fliery modeling method based on test data

Abstract

In order to overcome the problem that the current technology is difficult to estimate and continuously correct the bridge twin model by obtaining a series of test and test data, the application provides a bridge twin dynamic model Fourier modeling method based on test data, which is only related to the parameters of the bridge according to the system matrix related to all nodes of the bridge and the observation coefficient matrix related to all nodes, and the first continuous test process of the bridge does not change greatly, and the first comprehensive detection of the bridge twin dynamic mathematical model and the subsequent each time of the bridge twin dynamic mathematical model comprehensive correction process is relatively short, according to the characteristics of the fast and slow change matrix, the slow change matrix is set as a constant matrix in the first continuous test, and the system matrix related to all nodes of the bridge and the observation coefficient matrix related to all nodes in the bridge twin model are established through a series of effective tests and optimal indexes, and the bridge twin model is continuously corrected in the whole life cycle of the bridge, so that the technical problem of estimating and improving the bridge vibration model by obtaining a series of test and test data is solved.

Description

Technical Field

[0001] This invention relates to methods for analyzing the stress on bridge structures, and particularly to a Fourier modeling method for bridge twin dynamic models based on experimental data, belonging to the field of road infrastructure safety analysis. Background Technology

[0002] Road infrastructure is the fundamental guarantee of transportation safety. 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] However, in bridge twin model research, there are still no effective technical methods for establishing the system matrix and observation coefficient matrix related to all nodes of the bridge in the bridge twin model through a series of effective experiments and optimal indicators, and for continuously correcting the bridge twin model throughout the entire life cycle of the bridge. Summary of the Invention

[0005] To overcome the current technical challenge of estimating and continuously refining bridge twin models through a series of experimental and test data, this invention provides a Fourier modeling method for bridge twin dynamic models based on experimental data. This method leverages the fact that the system matrix and observation coefficient matrix related to all bridge nodes are only relevant to the bridge's parameters and do not change significantly during a single continuous test. Furthermore, the initial comprehensive testing and subsequent comprehensive refinement of the bridge twin dynamic mathematical model are relatively short. Based on the characteristics of slowly changing matrices, a singular perturbation method is employed to set the slowly changing matrix as a constant matrix in a single continuous test. Through a series of effective experiments and under optimal indicators, the system matrix and observation coefficient matrix related to all bridge nodes are established in the bridge twin model. The bridge twin model is continuously refined throughout the bridge's lifespan, thus solving the technical problem of estimating and improving bridge vibration models through a series of experimental and test data.

[0006] The technical solution adopted by this invention to solve its technical problem is: a Fourier modeling method for bridge twin dynamic models based on experimental data, 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 of the twin dynamic mathematical model of the comprehensive force at the bridge joints is 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 vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters traveling on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step Two: Estimation of the State Equation System Matrix of the Bridge Twin Dynamic Mathematical Model: Typically, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments, which can be conducted by measuring the data using sensors installed at the bridge joints. However, the system matrix of the state equation It is difficult to obtain the exact value; for ease of analysis, equation (1) is written as: (2) (2) In the formula, for No. Column vector; In order to obtain the equation (2) According to a given timeframe, such as one month, a comprehensive revision of the bridge's twin dynamic mathematical model should be performed; the first comprehensive inspection of the bridge before it is put into operation should be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, This refers to the start time of the first and every subsequent comprehensive inspection of the bridge twin dynamic mathematical model. The first comprehensive inspection... And the starting time of each subsequent comprehensive correction of the bridge vibration mode. ; The process of establishing the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Will and 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), we get: (4) (4) In the formula, ; (5) To the bridge Different external forces are applied to obtain (6) Therefore, we can conclude that: (7) Therefore, we can obtain the correct answer. Two estimates: (8) (8) In the formula, It is a symmetric weighted matrix; Take a simple fusion estimate; (9) In equation (9), , for In time period The experimental estimate; Following the above method, a comprehensive revision of the bridge twin dynamic mathematical model is performed at a given time, resulting in: (10) In equation (7), These represent the maximum number of samples and the sampling period for a single continuous test corresponding to a comprehensive revision of the bridge twin dynamic mathematical model. To ensure the effectiveness of the first comprehensive test of the bridge twin dynamic mathematical model and each subsequent comprehensive correction of the bridge twin dynamic mathematical model, the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected in each of the first comprehensive test processes of the bridge twin dynamic mathematical model must be different. Step 3: Based on the result of equation (7), Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time; Step 4: The observation equations of the bridge twin dynamic mathematical model are as follows: (11) In formula (11), 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; As described in step two, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments. For example, the contribution of vehicles traveling on the bridge to vibration sensors placed on the bridge can be estimated offline. The experimental process can also be achieved by using sensors installed at the bridge joints. However, the state observation coefficient matrix of the observation equation Difficult to obtain accurately; In order to obtain the equation (8) According to a given timeframe, such as one month, a comprehensive revision will be made to the bridge's twin dynamic mathematical model, including the observation equations; the first comprehensive inspection of the bridge before it is put into operation will be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, The start time for a comprehensive revision of the bridge twin dynamic mathematical model is [time missing]. The start time for the first comprehensive test is [time missing]. The starting time for each subsequent comprehensive correction of the bridge vibration model ; The process of establishing the observation equations for the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Equation (8) can be written as: (12) In formula (12), for No. Column vector; Will , and Approximating using Fourier series, we obtain: (13) In equation (13), , , , , , It is a constant matrix. Substituting equation (13) into equation (12), we get: (14) Therefore, we can conclude that: (15) Considering , The characteristics can be obtained (16) Therefore, we can obtain the correct answer. Two estimates: (17) In equation (17), , It is a symmetric weighted matrix; Take a simple fusion estimate; (18) In equation (18), , for In time period Experimental estimates: Following the above method, a comprehensive correction is made to the observation equations of the bridge twin dynamic mathematical model at a given time, resulting in: In equation (19), The maximum number of samplings and the sampling period for a single continuous test corresponding to a comprehensive correction of the bridge twin dynamic mathematical model are determined separately. Step 5: Based on the result of equation (13), perform... Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time.

[0008] The beneficial effects of this invention are as follows: This invention provides a Fourier modeling method for bridge twin dynamic models based on experimental data. This method is based on the fact that the system matrix and the observation coefficient matrix related to all nodes of the bridge are only related to the bridge parameters and will not change significantly during a single continuous test of the bridge. The initial comprehensive test and subsequent comprehensive correction of the bridge twin dynamic mathematical model are relatively short. Based on the characteristics of the slowly changing matrix, the singular perturbation method is used to set the slowly changing matrix as a constant matrix in a single continuous test. Through a series of effective tests and optimal indicators, the system matrix and the observation coefficient matrix related to all nodes of the bridge in the bridge twin model are established. Furthermore, the bridge twin model is continuously corrected throughout the entire life cycle of the bridge, thereby solving the technical problem of estimating and improving the bridge vibration model by obtaining a series of experimental and test data.

[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 of the twin dynamic mathematical model of the comprehensive force at the bridge joints is 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 vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters traveling on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step Two: Estimation of the State Equation System Matrix of the Bridge Twin Dynamic Mathematical Model: Typically, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments, which can be conducted by measuring the data using sensors installed at the bridge joints. However, the system matrix of the state equation It is difficult to obtain the exact value; for ease of analysis, equation (1) is written as: (2) (2) In the formula, for No. Column vector; In order to obtain the equation (2) According to a given timeframe, such as one month, a comprehensive revision of the bridge's twin dynamic mathematical model should be performed; the first comprehensive inspection of the bridge before it is put into operation should be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, This refers to the start time of the first and every subsequent comprehensive inspection of the bridge twin dynamic mathematical model. The first comprehensive inspection... And the starting time of each subsequent comprehensive correction of the bridge vibration mode. ; The process of establishing the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Will and 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), we get: (4) (4) In the formula, ; (5) To the bridge Different external forces are applied to obtain (6) Therefore, we can conclude that: (7) Therefore, we can obtain the correct answer. Two estimates: (8) (8) In the formula, It is a symmetric weighted matrix; Take a simple fusion estimate; (9) In equation (9), , for In time period The experimental estimate; Following the above method, a comprehensive revision of the bridge twin dynamic mathematical model is performed at a given time, resulting in: (10) In equation (7), These represent the maximum number of samples and the sampling period for a single continuous test corresponding to a comprehensive revision of the bridge twin dynamic mathematical model. To ensure the effectiveness of the first comprehensive test of the bridge twin dynamic mathematical model and each subsequent comprehensive correction of the bridge twin dynamic mathematical model, the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected in each of the first comprehensive test processes of the bridge twin dynamic mathematical model must be different. Step 3: Based on the result of equation (7), Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time; Step 4: The observation equations of the bridge twin dynamic mathematical model are as follows: (11) In formula (11), 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; As described in step two, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments. For example, the contribution of vehicles traveling on the bridge to vibration sensors placed on the bridge can be estimated offline. The experimental process can also be achieved by using sensors installed at the bridge joints. However, the state observation coefficient matrix of the observation equation Difficult to obtain accurately; In order to obtain the equation (8) According to a given timeframe, such as one month, a comprehensive revision will be made to the bridge's twin dynamic mathematical model, including the observation equations; the first comprehensive inspection of the bridge before it is put into operation will be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, The start time for a comprehensive revision of the bridge twin dynamic mathematical model is [time missing]. The start time for the first comprehensive test is [time missing]. The starting time for each subsequent comprehensive correction of the bridge vibration model ; The process of establishing the observation equations for the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Equation (8) can be written as: (12) In formula (12), for No. Column vector; Will , and Approximating using Fourier series, we obtain: (13) In equation (13), , , , , , It is a constant matrix. Substituting equation (13) into equation (12), we get: (14) Therefore, we can conclude that: (15) Considering , The characteristics can be obtained (16) Therefore, we can obtain the correct answer. Two estimates: (17) In equation (17), , It is a symmetric weighted matrix; Take a simple fusion estimate; (18) In equation (18), , for In time period Experimental estimates: Following the above method, a comprehensive correction is made to the observation equations of the bridge twin dynamic mathematical model at a given time, resulting in: (19) In equation (19), The maximum number of samplings and the sampling period for a single continuous test corresponding to a comprehensive correction of the bridge twin dynamic mathematical model are determined separately. Step 5: Based on the result of equation (13), perform... Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time.

Claims

1. A Fourier modeling method for bridge twin dynamic models based on experimental data, 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 of the twin dynamic mathematical model of the comprehensive force at the bridge joints is 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 first The contribution coefficient of each node's dynamic input; the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration parameters traveling on the bridge are given by the on-board test system and acquired by GPS / GNSS / BeiDou and video images; Step Two: Estimation of the State Equation System Matrix of the Bridge Twin Dynamic Mathematical Model: Typically, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments, which can be conducted by measuring the data using sensors installed at the bridge joints. However, the system matrix of the state equation It is difficult to obtain the exact value; for ease of analysis, equation (1) is written as: (2) (2) In the formula, for No. Column vector; In order to obtain the equation (2) According to a given timeframe, such as one month, a comprehensive revision of the bridge's twin dynamic mathematical model should be performed; the first comprehensive inspection of the bridge before it is put into operation should be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, This refers to the start time of the first and every subsequent comprehensive inspection of the bridge twin dynamic mathematical model. The first comprehensive inspection... And the starting time of each subsequent comprehensive correction of the bridge vibration mode. ; The process of establishing the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Will and 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), we get: (4) (4) In the formula, ； (5) To the bridge Different external forces are applied to obtain (6) Therefore, we can conclude that: (7) Therefore, we can obtain the correct answer. Two estimates: （8） (8) In the formula, It is a symmetric weighted matrix; Take a simple fusion estimate; （9） In equation (9), , for In time period The experimental estimate; Following the above method, a comprehensive revision of the bridge twin dynamic mathematical model is performed at a given time, resulting in: (10) In equation (7), These represent the maximum number of samples and the sampling period for a single continuous test corresponding to a comprehensive revision of the bridge twin dynamic mathematical model. To ensure the effectiveness of the first comprehensive test of the bridge twin dynamic mathematical model and each subsequent comprehensive correction of the bridge twin dynamic mathematical model, the vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected in each of the first comprehensive test processes of the bridge twin dynamic mathematical model must be different. Step 3: Based on the result of equation (7), Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time; Step 4: The observation equations of the bridge twin dynamic mathematical model are as follows: (11) In formula (11), 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; As described in step two, when obtaining the bridge twin dynamic mathematical model through experiments, the input... It is set up in advance by personnel engaged in experimental research according to the experimental outline. It can also be estimated through offline experiments. For example, the contribution of vehicles traveling on the bridge to vibration sensors placed on the bridge can be estimated offline. The experimental process can also be achieved by using sensors installed at the bridge joints. However, the state observation coefficient matrix of the observation equation Difficult to obtain accurately; In order to obtain the equation (8) According to a given timeframe, such as one month, a comprehensive revision will be made to the bridge's twin dynamic mathematical model, including the observation equations; the first comprehensive inspection of the bridge before it is put into operation will be conducted. Secondary dynamic tests, usually It is a positive integer, because 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... Assuming The constant matrix, The start time for a comprehensive revision of the bridge twin dynamic mathematical model is [time missing]. The start time for the first comprehensive test is [time missing]. The starting time for each subsequent comprehensive correction of the bridge vibration model ; The process of establishing the observation equations for the first comprehensive test of the bridge twin dynamic mathematical model is as follows: , This represents the maximum number of samples in a single consecutive trial. The sampling period; Equation (8) can be written as: (12) In formula (12), for No. Column vector; Will , and Approximating using Fourier series, we obtain: (13) In equation (13), , , , , , It is a constant matrix. Substituting equation (13) into equation (12), we get: （14） Therefore, we can conclude that: (15) Considering , The characteristics can be obtained (16) Therefore, we can obtain the correct answer. Two estimates: (17) In equation (17), , It is a symmetric weighted matrix; Take a simple fusion estimate; (18) In equation (18), , for In time period Experimental estimates: Following the above method, a comprehensive correction is made to the observation equations of the bridge twin dynamic mathematical model at a given time, resulting in: In equation (19), The maximum number of samplings and the sampling period for a single continuous test corresponding to a comprehensive correction of the bridge twin dynamic mathematical model are determined separately. Step 5: Based on the result of equation (13), perform... Through the Each matrix element , , , , , Perform curve fitting estimation to obtain Patterns of change over time.

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