Vibration and life-cycle safety equivalent test method based on bridge twin model

Abstract

To overcome the problem that existing technologies struggle to predict and reproduce actual bridge vibration phenomena through equivalent modal excitation loading tests, this invention provides a vibration and life-cycle safety equivalent test method based on a bridge twin model. This method, based on an established bridge twin mathematical model and an equivalent scaled-down verification model, presents a method for conducting equivalent modal excitation loading tests on actual bridges. It uses deconvolution to estimate the ideal input vector and, based on the obtained ideal input vector, provides an engineering implementation method for discrete loading of the input vector. The results can be directly used for bridge vibration prediction or reproduction of existing bridge vibration phenomena, predicting the reliability, availability, and maintainability of actual bridges and adjusting current safety operation management methods. By repeatedly predicting and reproducing actual bridge vibration phenomena, bridge health prediction and life-cycle safety operation management are achieved, overcoming the technical problem of difficulty in predicting and reproducing actual bridge vibration phenomena through equivalent modal excitation loading tests.

Description

Technical Field

[0001] This invention relates to bridge safety performance design and full life cycle operation safety simulation methods, and particularly to vibration and full life cycle safety equivalent test methods based on bridge twin models, belonging to the field of road infrastructure safety analysis. Background Technology

[0002] Road infrastructure is the fundamental guarantee for transportation safety. 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] However, current research urgently needs to be deepened and systematized. For example, how should bridge sensors be deployed to monitor bridge fatigue, cracks and deflection, and pier tilting and subsidence, enabling early management and maintenance measures to prevent major accidents? How can accurate life-cycle models of bridge and other road infrastructure be established to implement effective health prediction management and stress intensity limits to ensure transportation safety? How can systems engineering methods be applied to conduct equivalent experiments during the design process of bridges and other road infrastructure to ensure consistency between design and actual operation? These questions still lack a comprehensive theoretical and methodological framework for the monitoring and management of bridges and other road infrastructure.

[0004] Bridge twin mathematical models and equivalent scaled-down verification models are effective methods for predicting bridge health and managing safe operation throughout the entire life cycle. However, current research lacks effective methods for predicting and reproducing bridge vibration phenomena, such as how to use equivalent scaled-down verification models to conduct equivalent modal excitation loading tests on actual bridges and how to reproduce vibrations, especially resonances, that occur in actual bridges. Summary of the Invention

[0005] To overcome the problem that existing technologies struggle to predict and reproduce actual bridge vibration phenomena through equivalent modal excitation loading tests, this invention provides a vibration and life-cycle safety equivalent test method based on a bridge twin model. This method, based on an established bridge twin mathematical model and an equivalent scaled-down verification model built upon it, provides a method for conducting equivalent modal excitation loading tests on actual bridges. It uses deconvolution to estimate the ideal input vector and, based on the obtained ideal input vector, provides an engineering implementation method for discrete loading of the input vector. The results can be directly used to predict bridge vibration or reproduce existing bridge vibration phenomena, predicting the reliability, availability, and maintainability of actual bridges and adjusting current safety operation management methods. By repeatedly predicting and reproducing actual bridge vibration phenomena, bridge health prediction and life-cycle safety operation management are achieved, overcoming the technical problem of difficulty in predicting and reproducing actual bridge vibration phenomena through equivalent modal excitation loading tests.

[0006] The technical solution adopted by this invention to solve its technical problem is: a vibration and full life cycle safety equivalent test method based on a bridge twin model, characterized by the following steps: Step 1: Based on the established bridge twin mathematical model and its corresponding equivalent scaled-down verification model, a series of loading tests are conducted. When the actual bridge is fully excited by external forces, the comprehensive dynamic state equation of the bridge twin mathematical model at the nodes and the observation equation formed by all observation points are as follows: (1) (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. It is a time variable; , 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 observation vector is composed of all observation points on the bridge, with dimension . , for The measured value, , They are respectively the corresponding , The observation coefficient matrix; For measuring noise; The solution to equation (1) can be expressed as: (2) The simulated vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected for the bridge equivalent scaled verification model loading test are different. The bridge equivalent scaled verification model uses a road surface layout to measure the bridge vibration and an accelerometer to measure the three-degree-of-freedom vibration magnitude. The actual measured values ​​output by the bridge twin mathematical model and the equivalent scaled verification model are compared through equation (2). The differences between them were adjusted and the equivalent scaled-down validation model was modified, while the actual measured values ​​output by the equivalent scaled-down validation model were also considered. Analyze the bridge's loading response; Step 2: For bridges exhibiting abnormal phenomena but with unclear causes, the bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used to conduct phenomenon reproduction studies in the following manner; Assuming for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to dimensionality This refers to the actual data of bridge observation vectors acquired when an anomaly occurs on a bridge but the cause is unclear, and then converted into observation data for an equivalent scaled-down verification model, assuming measurement noise. Zero-mean Gaussian white noise; definition: According to equation (2), we can obtain: , Select the weighted minimum error index (3) (3) In the formula As a weighted matrix, we can obtain: (4) (4) In the formula, for Theoretical input estimates; For each given time... Equation (4) can be obtained by iterative estimation. Step 3: In order to prevent the bridge resonance phenomenon, the bridge twin mathematical model and the corresponding equivalent scaled-down verification model can be used to conduct excitation condition prediction research in the following manner. Similar to step two, it is assumed that for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to The dimension of, according to equation (1) The bridge structure modes and natural frequencies were obtained. This is the noise-free observation vector assuming bridge resonance occurs, defined as follows: According to equation (2), we can obtain: , Select the weighted minimum error index (5) (3) In the formula As a weighted matrix, we can obtain: (6) (6) In the formula, When a bridge resonates, it corresponds to Theoretical input estimates; For each given time... Equation (6) can also be obtained by iterative estimation. Step 4: When the bridge's twin mathematical model and its corresponding equivalent scaled-down verification model are used to reproduce the phenomenon and predict bridge resonance, the results are theoretical input estimates, which are difficult to implement in engineering. Therefore, based on the specified bridge within a time period... The internal assumption is that the external forces are equivalent to the scaled-down verification model, and the number of vehicles traveling on the bridge surface is... vehicles, with Indicates the first Vehicle type, vehicle weight, vehicle coordinates, vehicle speed, and vehicle acceleration parameters are available. (7) exist During the time period, equation (1) is assumed to be: (8) For bridges exhibiting abnormal phenomena with unclear causes, a bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used for engineering reproduction of the phenomenon in the following manner; within a time period The maximum number of samples is ; definition , and The error index is set to (9) According to equation (8), we can obtain: (10) Assuming equation (8) is within the time period Internal continuity It can be obtained from equation (8), that is, according to (11) Solving this equation yields the parameter vector estimate. (12) Received This refers to the external forces that can be applied to bridges in engineering. Similarly, the time period can be obtained. External forces acting on bridges that can be realized in engineering projects can be obtained by similar methods. Based on a bridge twin mathematical model and an equivalent scaled-down verification model corresponding to the model, the external forces acting on bridges that can be realized in engineering projects can be obtained for bridge resonance prediction.

[0007] The beneficial effects of this invention are as follows: This invention provides a vibration and full life-cycle safety equivalent test method based on a bridge twin model. This method, based on an established bridge twin mathematical model and an equivalent scaled-down verification model established based on the bridge twin mathematical model, provides a method for conducting equivalent modal excitation loading tests on actual bridges. It uses deconvolution to estimate the ideal input vector, and based on the obtained ideal input vector, provides an engineering implementation method for discrete loading of the input vector. The results can be directly used for bridge vibration prediction or reproduction of existing bridge vibration phenomena, predicting the reliability, availability, and maintainability of actual bridges and adjusting current safety operation management methods. By repeatedly predicting and reproducing existing bridge vibration phenomena, bridge health prediction and full life-cycle safety operation management are achieved, overcoming the technical problem of difficulty in predicting and reproducing actual bridge vibration phenomena through equivalent modal excitation loading tests.

[0008] The present invention will now be described in detail with reference to specific embodiments. Detailed Implementation

[0009] Step 1: Based on the established bridge twin mathematical model and its corresponding equivalent scaled-down verification model, a series of loading tests are conducted. When the actual bridge is fully excited by external forces, the comprehensive dynamic state equation of the bridge twin mathematical model at the nodes and the observation equation formed by all observation points are as follows: (1) (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. It is a time variable; , 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 observation vector is composed of all observation points on the bridge, with dimension . , for The measured value, , They are respectively the corresponding , The observation coefficient matrix; For measuring noise; The solution to equation (1) can be expressed as: (2) The simulated vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected for the bridge equivalent scaled verification model loading test are different. The bridge equivalent scaled verification model uses a road surface layout to measure the bridge vibration and an accelerometer to measure the three-degree-of-freedom vibration magnitude. The actual measured values ​​output by the bridge twin mathematical model and the equivalent scaled verification model are compared through equation (2). The differences between them were adjusted and the equivalent scaled-down validation model was modified, while the actual measured values ​​output by the equivalent scaled-down validation model were also considered. Analyze the bridge's loading response; Step 2: For bridges exhibiting abnormal phenomena but with unclear causes, the bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used to conduct phenomenon reproduction studies in the following manner; Assuming for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to dimensionality This refers to the actual data of bridge observation vectors acquired when an anomaly occurs on a bridge but the cause is unclear, and then converted into observation data for an equivalent scaled-down verification model, assuming measurement noise. Zero-mean Gaussian white noise; definition: According to equation (2), we can obtain: , Select the weighted minimum error index (3) (3) In the formula As a weighted matrix, we can obtain: (4) (4) In the formula, for Theoretical input estimates; For each given time... Equation (4) can be obtained by iterative estimation. Step 3: In order to prevent the bridge resonance phenomenon, the bridge twin mathematical model and the corresponding equivalent scaled-down verification model can be used to conduct excitation condition prediction research in the following manner. Similar to step two, it is assumed that for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to The dimension of, according to equation (1) The bridge structure modes and natural frequencies were obtained. This is the noise-free observation vector assuming bridge resonance occurs, defined as follows: According to equation (2), we can obtain: , Select the weighted minimum error index (5) (3) In the formula As a weighted matrix, we can obtain: (6) (6) In the formula, When a bridge resonates, it corresponds to Theoretical input estimates; For each given time... Equation (6) can also be obtained by iterative estimation. Step 4: When the bridge's twin mathematical model and its corresponding equivalent scaled-down verification model are used to reproduce the phenomenon and predict bridge resonance, the results are theoretical input estimates, which are difficult to implement in engineering. Therefore, based on the specified bridge within a time period... The internal assumption is that the external forces are equivalent to the scaled-down verification model, and the number of vehicles traveling on the bridge surface is... vehicles, with Indicates the first Vehicle type, vehicle weight, vehicle coordinates, vehicle speed, and vehicle acceleration parameters are available. (7) exist During the time period, equation (1) is assumed to be: (8) For bridges exhibiting abnormal phenomena with unclear causes, a bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used for engineering reproduction of the phenomenon in the following manner; within a time period The maximum number of samples is ; definition , and The error index is set to (9) According to equation (8), we can obtain: (10) Assuming equation (8) is within the time period Internal continuity It can be obtained from equation (8), that is, according to (11) Solving this equation yields the parameter vector estimate. (12) Received This refers to the external forces that can be applied to bridges in engineering. Similarly, the time period can be obtained. External forces acting on bridges that can be realized in engineering projects can be obtained by similar methods. Based on a bridge twin mathematical model and an equivalent scaled-down verification model corresponding to the model, the external forces acting on bridges that can be realized in engineering projects can be obtained for bridge resonance prediction.

Claims

1. A vibration and life-cycle safety equivalent test method based on a bridge twin model, characterized by the following steps: Step 1: Based on the established bridge twin mathematical model and its corresponding equivalent scaled-down verification model, a series of loading tests are conducted. When the actual bridge is fully excited by external forces, the comprehensive dynamic state equation of the bridge twin mathematical model at the nodes and the observation equation formed by all observation points are as follows: (1) (1) In the formula, This is the combined stress state vector at the bridge joint under external forces. It is a time variable; , 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 observation vector is composed of all observation points on the bridge, with dimension . , for The measured value, , They are respectively the corresponding , The observation coefficient matrix; For measuring noise; The solution to equation (1) can be expressed as: （2） The simulated vehicle type, vehicle weight, vehicle coordinate position, vehicle speed, and vehicle acceleration selected for the bridge equivalent scaled verification model loading test are different. The bridge equivalent scaled verification model uses a road surface layout to measure the bridge vibration and an accelerometer to measure the three-degree-of-freedom vibration magnitude. The actual measured values ​​output by the bridge twin mathematical model and the equivalent scaled verification model are compared through equation (2). The differences between them were adjusted and the equivalent scaled-down validation model was modified, while the actual measured values ​​output by the equivalent scaled-down validation model were also considered. Analyze the bridge's loading response; Step 2: For bridges exhibiting abnormal phenomena but with unclear causes, the bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used to conduct phenomenon reproduction studies in the following manner; Assuming for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to dimensionality This refers to the actual data of bridge observation vectors acquired when an anomaly occurs on a bridge but the cause is unclear, and then converted into observation data for an equivalent scaled-down verification model, assuming measurement noise. Zero-mean Gaussian white noise; definition: According to equation (2), we can obtain: ， Select the weighted minimum error index （3） (3) In the formula As a weighted matrix, we can obtain: （4） (4) In the formula, for Theoretical input estimates; For each given time... Equation (4) can be obtained by iterative estimation. Step 3: In order to prevent the bridge resonance phenomenon, the bridge twin mathematical model and the corresponding equivalent scaled-down verification model can be used to conduct excitation condition prediction research in the following manner. Similar to step two, it is assumed that for the sampling time , The sampling period is The maximum number of samples is calculated according to equation (2). The dimension is greater than or equal to The dimension of, according to equation (1) The bridge structure modes and natural frequencies were obtained. This is the noise-free observation vector assuming bridge resonance occurs, defined as follows: According to equation (2), we can obtain: ， Select the weighted minimum error index （5） (3) In the formula As a weighted matrix, we can obtain: (6) (6) In the formula, When a bridge resonates, it corresponds to Theoretical input estimates; For each given time... Equation (6) can also be obtained by iterative estimation. Step 4: When the bridge's twin mathematical model and its corresponding equivalent scaled-down verification model are used to reproduce the phenomenon and predict bridge resonance, the results are theoretical input estimates, which are difficult to implement in engineering. Therefore, based on the specified bridge within a time period... The internal assumption is that the external forces are equivalent to the scaled-down verification model, and the number of vehicles traveling on the bridge surface is... vehicles, with Indicates the first Vehicle type, vehicle weight, vehicle coordinates, vehicle speed, and vehicle acceleration parameters are available. （7） exist During the time period, equation (1) is assumed to be: (8) For bridges exhibiting abnormal phenomena with unclear causes, a bridge twin mathematical model and its corresponding equivalent scaled-down verification model can be used for engineering reproduction of the phenomenon in the following manner; within a time period The maximum number of samples is ; definition , and The error index is set to （9） According to equation (8), we can obtain: (10) Assuming equation (8) is within the time period Internal continuity, It can be obtained from equation (8), that is, according to (11) Solving this equation yields the parameter vector estimate. (12) Received This refers to the external forces acting on the bridge that can be implemented in the engineering process. Similarly, the time period can be obtained. External forces that can be applied to bridges in other engineering projects; Following a similar approach, it is possible to obtain engineering-achievable external excitations for bridge resonance prediction based on a bridge twin mathematical model and a corresponding equivalent scaled-down verification model.

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