A bridge safety monitoring method

By setting up a variety of sensors on the bridge for real-time data acquisition and monitoring, the problem of untimely monitoring of bridges in the existing technology is solved, and safety monitoring and early warning of bridge structures is realized, its reliability and load-bearing capacity are evaluated, and vehicle parking is avoided illegal parking is avoided. , improve the safety and service life of the bridge.

CN115762074BInactive Publication Date: 2025-01-07CHINA RAILWAY 11TH BUREAU GRP CORP LTD +1
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Patent Information

Application Number
CN202211158669.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-09-22
Publication Date
2025-01-07
Estimated Expiration
Not applicable · inactive patent

AI Technical Summary

Technical Problem

Existing bridge monitoring methods cannot respond to risks in a timely manner, especially in harsh environments, it is difficult to effectively monitor the safety status of bridges, resulting in the failure to detect and deal with potential hazards in a timely manner.

Method used

Using a real-time data acquisition method combined with multiple parameters, by setting tensile sensors, displacement sensors, weighing sensors, wind speed and direction sensors on the bridge, the tension, displacement, wind speed, wind direction and coordinate information of the bridge is monitored in real time, and three-dimensional The coordinate system combines strong wind warning and vehicle flow monitoring to generate risk reports and early warning information, triggering traffic light blockade and maintenance reminders.

Benefits of technology

Real-time non-destructive monitoring, early warning and damage diagnosis of bridge structures are realized, the reliability and load-bearing capacity of the structure are evaluated, the illegal parking of vehicles is avoided, the safety and service life of the bridge are improved, and the basis for timely decision-making is provided.

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Abstract

The present invention discloses a bridge safety monitoring method, which includes a tension sensor and a displacement sensor arranged at the connection position of two span beams, a weighing area arranged at both ends of the span beam, a wind speed and direction sensor arranged above the bridge; and a positioning sensor arranged at the upper end of the pier. The monitoring method includes steps S1-S11. The present invention constructs a set of comprehensive intelligent bridge safety detection system, and through a real-time monitoring method, realizes non-destructive monitoring of the bridge structure, early warning of expected hazards, and diagnosis of the damage location and degree of the structure, and intelligent evaluation of the reliability, durability and bearing capacity of the structure. At the same time, it also has a process of monitoring the congestion above the bridge to avoid illegal parking of vehicles on the bridge and increase the load of the bridge. Early warning and alarm signals are triggered in the event of emergencies or serious abnormalities in the use of the structure, providing timely decision-making basis and guidance for the repair, maintenance, protection and management decisions of the structure.
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Description

Technical Field

[0001] The invention relates to the technical field of bridge safety, and in particular to a bridge safety monitoring method. Background Art

[0002] Bridges generally refer to structures built on rivers, lakes and seas to enable vehicles and pedestrians to pass smoothly. In order to adapt to the modern high-speed development of the transportation industry, bridges are also extended to buildings that cross mountain streams, poor geology or meet other traffic needs to make passage more convenient. Bridges are generally composed of span beams, piers and auxiliary structures. The span beam is the main structure for crossing obstacles, and the pier is the foundation. With the rapid development of the national economy, more and more "old" bridges will appear over time. These bridges are repeatedly subjected to various loads, material fatigue and corrosion, and damage from natural factors. There are certain hidden dangers in the safety of bridges; and the losses caused by bridge damage are immeasurable, so it is extremely important to monitor the health of bridges in a timely manner. The existing means of bridge monitoring is to patrol the bridges by maintenance personnel and inspect the bridges in different time periods, but this kind of inspection is often not timely for risk monitoring of bridges, and is also restricted by environmental factors such as typhoons and heavy rains. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a bridge safety monitoring method that combines multiple parameters and performs real-time data collection and monitoring.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] Provided is a bridge safety monitoring method, which includes a tension sensor and a displacement sensor arranged at the connection position of two span beams, the tension sensor monitors the tension between the two span beams on the bridge pier, and the displacement sensor monitors the displacement between the two span beams; a weighing area is arranged at both ends of the span beam, and a weighing sensor is arranged in the weighing area to monitor the weight of the car entering each span beam; a wind speed and direction sensor is arranged above the bridge, and the wind speed and direction sensor monitors the wind speed and wind direction experienced by the bridge in real time; a positioning sensor is arranged at the upper end of the bridge pier, and the positioning sensor obtains the coordinate information and altitude information of the upper end of the bridge pier; the positioning sensor, the wind speed and direction sensor, the vibration sensor and the weighing sensor are all connected to a bridge safety monitoring center;

[0006] Methods for monitoring bridge safety include:

[0007] S1: Establish a three-dimensional coordinate system with the sea level as the XOY plane, the vertical direction as the Z axis, the midpoint of the bridge on the Z axis, and the length direction of the bridge on the X axis;

[0008] S2: Collect the altitude and coordinate information of the bridge pier design and convert it into the coordinates A(xA0 ,y A0 , z A0 ), where A is the installation point of the upper end positioning sensor of the pier; A0 Equal to the designed elevation of the bridge pier;

[0009] S3: When the municipal environmental monitoring background issues a strong wind warning, the wind speed and direction sensor collects wind speed v and wind direction f every set time t;

[0010] S4: Calculate the wind speed component v' applied vertically to the side of the vertical bridge by the wind speed v: v' = v·tanθ, where θ is the angle between the wind direction f and the X-axis;

[0011] S5: Compare the wind speed component v' with the designed lateral wind speed threshold V of the bridge. If v'≥V, it is determined that the bridge may be damaged by strong winds, and step S6 is executed; otherwise, the bridge is safe, and the process returns to step S3;

[0012] S6: Collect the coordinate information A'(x A1 ,y A1 , z A1 );

[0013] S7: Calculate the offset of the swing at the upper end of the bridge pier And the sedimentation D: D = | z A1 -z A0 |;

[0014] S8: Compare the offset L with the swing amplitude L' allowed when the bridge pier is designed. If L ≥ L', it is determined that the bridge pier is at risk. The bridge safety monitoring center generates a bridge pier risk report information, and issues a bridge pier risk alarm. The bridge pier risk alarm information is sent to the traffic control department. The traffic control department activates the no-entry traffic light at the entry end of the span beam and blocks the bridge. Otherwise, the bridge pier is not at risk, and step S9 is executed.

[0015] S9: collect the tension f and displacement s between the two span beams, and compare the displacement s with the allowable displacement s';

[0016] If s≥s', it is determined that the span beam has risk displacement on the bridge pier, and the bridge safety monitoring center generates a span beam risk report information and issues a span beam risk alarm. The span beam risk report information is sent to the traffic control department, and the traffic control department activates the no-entry traffic signal light at the span beam entry end and blocks the bridge;

[0017] If s<s', execute step S10;

[0018] S10: subtract the tension f from the design tension value f' between the two span beams to obtain a tension fluctuation value Δf: Δf=f-f', and compare the tension fluctuation value Δf with the fluctuation allowable threshold Δf';

[0019] If Δf ≥ Δf', it is determined that the span beam may be displaced, and the bridge safety monitoring center generates a span beam risk warning report information, and sends the span beam risk warning report information to the bridge maintenance personnel to remind them to go up the bridge to inspect whether the connection structure between the span beams is safe;

[0020] If Δf<Δf', it is determined that the strong wind warning does not affect the safety of the bridge, and the process returns to step S3;

[0021] S11: The weighing sensor collects the weight of vehicles entering and leaving the two ends of the span beam and calculates the weight of the vehicles piled on the span beam;

[0022] At the entry end of the span beam, the total weight T1 of the vehicles entering the span beam within a time period of t1 is collected, and at the exit end of the span beam, the total weight T2 of the vehicles leaving the span beam within a time period of t1 is collected.

[0023] If T2<T1, it is determined that there is a traffic jam on the span or a vehicle is parked illegally during this period. The bridge safety monitoring center sends information about a large number of vehicles on the span to the traffic control department, which activates the no-entry traffic light at the entry end of the span to temporarily control the vehicles entering.

[0024] After setting time t2, t2 = S / V', S is the length of the span beam, V' is the minimum speed limit of the vehicle on the span beam; collect the vehicle weight T3 at the exit end of the span beam during the time period t2;

[0025] If T3 < T1-T2, it is determined that a vehicle is illegally parked on the cross beam during this period, and the traffic control department activates the camera on the cross beam to capture the illegally parked vehicle;

[0026] If T3≥T1-T2, it is determined that the bridge has been cleared, and the traffic control department activates the traffic signal light at the entrance end of the bridge to allow entry;

[0027] If T2≥T1, it is determined that the span beam is unobstructed during this period.

[0028] Furthermore, it also includes:

[0029] S12: Obtain the wind speed component v', offset L, tension fluctuation value Δf and displacement s collected over a period of time, and form wind speed component data groups (v'1, v'2, ···, v' n ), offset data group (L1, L2, ···, L n ), tension fluctuation value data group (Δf1, Δf2, ···, Δf n) and displacement data sets (s1, s2, ···, s n ), n is the number of acquisitions;

[0030] S13: Establish a multi-parameter bridge life assessment probability model:

[0031]

[0032] Among them, σ1 is the standard deviation of the wind speed component in the wind speed component data group, σ2 is the standard deviation of the offset in the offset data group, σ3 is the standard deviation of the tension fluctuation value in the tension fluctuation value data group, and σ4 is the standard deviation of the displacement in the displacement data group; is the mean value of the wind speed component in the wind speed component data set, is the mean offset value in the offset data group, is the mean value of the tension fluctuation value in the tension fluctuation value data group, is the displacement mean value within the displacement data set; P u is the reference value for the probability of lifetime assessment;

[0033] S14: Substitute the wind speed component data group, offset data group, tension fluctuation value data group and displacement data group into the bridge life assessment probability model, and establish a distribution diagram of life assessment probability and wind speed component, offset, tension fluctuation value and displacement, with the life assessment probability as the vertical coordinate, the wind speed component, offset, tension fluctuation value and displacement as the horizontal coordinate, and the reference value as the reference horizontal line to evaluate the bridge life.

[0034] The beneficial effects of the present invention are as follows: the present invention constructs a set of comprehensive intelligent detection system for bridge safety, and through a real-time monitoring method, realizes non-destructive monitoring of the bridge structure, early warning of expected hazards, and can diagnose the location and degree of damage to the structure, and intelligently evaluate the reliability, durability and bearing capacity of the structure. At the same time, it also has a process for monitoring the congestion above the bridge to avoid illegal parking of vehicles on the bridge and increase the load on the bridge. Early warning and alarm signals are triggered in the event of emergencies or serious abnormalities in the use of the structure, providing timely decision-making basis and guidance for the repair, maintenance, protection and management decisions of the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the dual-dimensional evaluation method for UAV hovering wind resistance performance based on error sorting. DETAILED DESCRIPTION

[0036] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0037] like Figure 1 As shown, the bridge safety monitoring method of this scheme includes a tension sensor and a displacement sensor arranged at the connection position of the two span beams, the tension sensor monitors the tension between the two span beams on the bridge pier, and the displacement sensor monitors the displacement between the two span beams; a weighing area is arranged at both ends of the span beam, and a weighing sensor is arranged in the weighing area to monitor the weight of the car entering each span beam; a wind speed and direction sensor is arranged above the bridge, and the wind speed and direction sensor monitors the wind speed and direction experienced by the bridge in real time; a positioning sensor is arranged at the upper end of the bridge pier, and the positioning sensor obtains the coordinate information and altitude information of the upper end of the bridge pier; the positioning sensor, the wind speed and direction sensor, the vibration sensor and the weighing sensor are all connected to the bridge safety monitoring center;

[0038] Methods for monitoring bridge safety include:

[0039] S1: Establish a three-dimensional coordinate system with the sea level as the XOY plane, the vertical direction as the Z axis, the midpoint of the bridge on the Z axis, and the length direction of the bridge on the X axis;

[0040] S2: Collect the altitude and coordinate information of the bridge pier design and convert it into the coordinates A(x A0 ,y A0 , z A0 ), where A is the installation point of the upper end positioning sensor of the pier; A0 Equal to the designed elevation of the bridge pier;

[0041] S3: When the municipal environmental monitoring background issues a strong wind warning, the wind speed and direction sensor collects wind speed v and wind direction f every set time t;

[0042] S4: Calculate the wind speed component v' applied vertically to the side of the vertical bridge by the wind speed v: v' = v·tanθ, where θ is the angle between the wind direction f and the X-axis;

[0043] S5: Compare the wind speed component v' with the designed lateral wind speed threshold V of the bridge. If v'≥V, it is determined that the bridge may be damaged by strong winds, and the safety risk of the bridge needs to be further confirmed, and step S6 is executed; otherwise, it is proved that the wind resistance strength of the bridge design can fully withstand the strong wind, and the bridge is safe, and the process returns to step S3, waiting for the next strong wind to start the safety monitoring mechanism;

[0044] S6: Collect the coordinate information A'(x A1 ,y A1 , z A1 );

[0045] S7: Calculate the offset of the swing at the upper end of the bridge pier And the sedimentation D: D = | z A1 -z A0 |;

[0046] S8: Compare the offset L with the swing amplitude L' allowed when the bridge pier is designed. If L ≥ L', it is determined that the bridge pier is at risk. The bridge safety monitoring center generates a bridge pier risk report information, and issues a bridge pier risk alarm. The bridge pier risk alarm information is sent to the traffic control department. The traffic control department activates the no-entry traffic light at the entry end of the span beam and blocks the bridge. Otherwise, the bridge pier is not at risk, and step S9 is executed.

[0047] S9: collect the tension f and displacement s between the two span beams, and compare the displacement s with the allowable displacement s';

[0048] If s≥s', it is determined that the span beam has risk displacement on the bridge pier, and the bridge safety monitoring center generates a span beam risk report information and issues a span beam risk alarm. The span beam risk report information is sent to the traffic control department, and the traffic control department activates the no-entry traffic signal light at the span beam entry end and blocks the bridge;

[0049] If s<s', execute step S10;

[0050] S10: subtract the tension f from the design tension value f' between the two span beams to obtain a tension fluctuation value Δf: Δf=f-f', and compare the tension fluctuation value Δf with the fluctuation allowable threshold Δf';

[0051] If Δf ≥ Δf', it is determined that the span beam may be displaced, and the bridge safety monitoring center generates a span beam risk warning report information, and sends the span beam risk warning report information to the bridge maintenance personnel to remind them to go up the bridge to inspect whether the connection structure between the span beams is safe;

[0052] If Δf<Δf', it is determined that the strong wind warning does not affect the safety of the bridge, and the process returns to step S3;

[0053] S11: The weighing sensor collects the weight of vehicles entering and leaving the two ends of the span beam and calculates the weight of the vehicles piled on the span beam;

[0054] At the entry end of the span beam, the total weight T1 of the vehicles entering the span beam within a time period of t1 is collected, and at the exit end of the span beam, the total weight T2 of the vehicles leaving the span beam within a time period of t1 is collected.

[0055] If T2<T1, it is determined that there is a traffic jam on the span or a vehicle is parked illegally during this period. The bridge safety monitoring center sends information about a large number of vehicles on the span to the traffic control department, which activates the no-entry traffic light at the entry end of the span to temporarily control the vehicles entering.

[0056] After setting time t2, t2 = S / V', S is the length of the span beam, V' is the minimum speed limit of the vehicle on the span beam; collect the vehicle weight T3 at the exit end of the span beam during the time period t2;

[0057] If T3 < T1-T2, it is determined that a vehicle is illegally parked on the cross beam during this period, and the traffic control department activates the camera on the cross beam to capture the illegally parked vehicle;

[0058] If T3≥T1-T2, it is determined that the bridge has been cleared, and the traffic control department activates the traffic signal light at the entrance end of the bridge to allow entry;

[0059] If T2≥T1, it is determined that the span beam is unobstructed during this period.

[0060] Also includes:

[0061] S12: Obtain the wind speed component v', offset L, tension fluctuation value Δf and displacement s collected over a period of time, and form wind speed component data groups (v'1, v'2, ···, v' n ), offset data group (L1, L2, ···, L n ), tension fluctuation value data group (Δf1, Δf2, ···, Δf n ) and displacement data sets (s1, s2, ···, s n ), n is the number of acquisitions;

[0062] S13: Establish a multi-parameter bridge life assessment probability model:

[0063]

[0064] Among them, σ1 is the standard deviation of the wind speed component in the wind speed component data group, σ2 is the standard deviation of the offset in the offset data group, σ3 is the standard deviation of the tension fluctuation value in the tension fluctuation value data group, and σ4 is the standard deviation of the displacement in the displacement data group; is the mean value of the wind speed component in the wind speed component data set, is the mean offset value in the offset data group, is the mean value of the tension fluctuation value in the tension fluctuation value data group, is the displacement mean value within the displacement data set; P u is the reference value for the probability of lifetime assessment;

[0065] S14: Substitute the wind speed component data group, offset data group, tension fluctuation value data group and displacement data group into the bridge life assessment probability model, and establish a distribution diagram of life assessment probability and wind speed component, offset, tension fluctuation value and displacement, with the life assessment probability as the vertical coordinate, the wind speed component, offset, tension fluctuation value and displacement as the horizontal coordinate, and the reference value as the reference horizontal line to evaluate the bridge life.

[0066] After experiencing multiple strong winds, the higher the frequency of wind speed components, offsets, tension fluctuation values ​​and displacements exceeding the corresponding thresholds, the reference value of the life assessment probability is used as a reference value. The more curves corresponding to the wind speed components, offsets, tension fluctuation values ​​and displacement parameters are above the reference horizontal line, the shorter the service life of the bridge and the less safe the bridge is.

[0067] The present invention constructs a set of comprehensive intelligent detection system for bridge safety, and through real-time monitoring methods, it can realize non-destructive monitoring of bridge structures, early warning of expected hazards, diagnose the location and degree of structural damage, and intelligently evaluate the reliability, durability and bearing capacity of the structure. At the same time, it also has the process of monitoring the congestion above the bridge to avoid illegal parking of vehicles on the bridge and increase the load on the bridge. In the event of emergencies or serious abnormalities in the use of the structure, early warning and alarm signals are triggered, providing timely decision-making basis and guidance for the repair, maintenance, protection and management decisions of the structure.

Claims

1. A bridge safety monitoring method, characterized in that: It includes a tension sensor and a displacement sensor arranged at the connection position of the two span beams, the tension sensor monitors the tension between the two span beams on the bridge pier, and the displacement sensor monitors the displacement between the two span beams; a weighing area arranged at both ends of the span beam, wherein a weighing sensor is arranged in the weighing area to monitor the weight of the car entering each span beam; a wind speed and direction sensor arranged above the bridge, wherein the wind speed and direction sensor monitors the wind speed and direction experienced by the bridge in real time; a positioning sensor arranged at the upper end of the bridge pier, wherein the positioning sensor obtains the coordinate information and altitude information of the upper end of the bridge pier; the positioning sensor, the wind speed and direction sensor, the tension sensor, the displacement sensor and the weighing sensor are all connected to the bridge safety monitoring center; Methods for monitoring bridge safety include: S1: Establish a three-dimensional coordinate system with the sea level as the XOY plane, the vertical direction as the Z axis, the midpoint of the bridge on the Z axis, and the length direction of the bridge on the X axis; S2: Collect the altitude and coordinate information of the bridge pier design and convert it into the coordinates A(x A0 ,y A0 , z A0 ), where A is the installation point of the upper end positioning sensor of the pier; A0 Equal to the designed elevation of the bridge pier; S3: When the municipal environmental monitoring background issues a strong wind warning, the wind speed and direction sensor collects wind speed v and wind direction f every set time t; S4: Calculate the wind speed component v' applied vertically to the side of the vertical bridge by the wind speed v: v' = v·tanθ, where θ is the angle between the wind direction f and the X-axis; S5: Compare the wind speed component v' with the designed lateral wind speed threshold V of the bridge. If v'≥V, it is determined that the bridge may be damaged by strong winds, and step S6 is executed; otherwise, the bridge is safe, and the process returns to step S3; S6: Collect the coordinate information A'(x A1 ,y A1 , z A1 ); S7: Calculate the offset L of the upper end of the pier: And the sedimentation D: D = | z A1 -z A0 |; S8: Compare the offset L with the swing amplitude L' allowed when the bridge pier is designed. If L≥L', it is determined that the bridge pier is at risk. The bridge safety monitoring center generates a bridge pier risk report information, issues a bridge pier risk alarm, and sends the bridge pier risk alarm information to the traffic control department. The traffic control department activates the no-entry traffic light at the entry end of the span beam and blocks the bridge. Otherwise, the bridge pier is not at risk, and step S9 is executed. S9: collect the tension f and displacement s between the two span beams, and compare the displacement s with the allowable displacement s'; If s≥s', it is determined that the span beam has risk displacement on the bridge pier, and the bridge safety monitoring center generates a span beam risk report information and issues a span beam risk alarm. The span beam risk report information is sent to the traffic control department, and the traffic control department activates the no-entry traffic signal light at the span beam entry end and blocks the bridge; If s<s', execute step S10; S10: subtract the tension f from the design tension value f' between the two span beams to obtain a tension fluctuation value Δf: Δf=f-f', and compare the tension fluctuation value Δf with the fluctuation allowable threshold Δf'; If Δf ≥ Δf', it is determined that the span beam may be displaced, and the bridge safety monitoring center generates a span beam risk warning report information, and sends the span beam risk warning report information to the bridge maintenance personnel to remind them to go up the bridge to inspect whether the connection structure between the span beams is safe; If Δf<Δf', it is determined that the strong wind warning does not affect the safety of the bridge, and the process returns to step S3; S11: The weighing sensor collects the weight of vehicles driving in and out of the two ends of the span beam and calculates the weight of the vehicles piled on the span beam; At the entry end of the span beam, the total weight T1 of the vehicles entering the span beam within a time period of t1 is collected, and at the exit end of the span beam, the total weight T2 of the vehicles leaving the span beam within a time period of t1 is collected. If T2<T1, it is determined that there is a traffic jam on the span or a vehicle is parked illegally during this period. The bridge safety monitoring center sends information about a large number of vehicles on the span to the traffic control department, which activates the no-entry traffic light at the entry end of the span to temporarily control the vehicles entering. After setting time t2, t2 = S / V', S is the length of the span beam, V' is the minimum speed limit of the vehicle on the span beam; collect the vehicle weight T3 at the exit end of the span beam during the time period t2; If T3 < T1-T2, it is determined that a vehicle is illegally parked on the cross beam during this period, and the traffic control department activates the camera on the cross beam to capture the illegally parked vehicle; If T3≥T1-T2, it is determined that the bridge has been cleared, and the traffic control department activates the traffic signal light at the entrance end of the bridge to allow entry; If T2≥T1, it is determined that the span beam is unobstructed during this period.

2. The bridge safety monitoring method according to claim 1, characterized in that: Also includes: S12: Obtain the wind speed component v', offset L, tension fluctuation value Δf and displacement s collected over a period of time, and form wind speed component data groups (v'1, v'2, ···, v' n ), offset data group (L1, L2, ···, L n ), tension fluctuation value data group (Δf1, Δf2, ···, Δf n ) and displacement data sets (s1, s2, ···, s n ), n is the number of acquisitions; S13: Establish a multi-parameter bridge life assessment probability model: Among them, σ1 is the standard deviation of the wind speed component in the wind speed component data group, σ2 is the standard deviation of the offset in the offset data group, σ3 is the standard deviation of the tension fluctuation value in the tension fluctuation value data group, and σ4 is the standard deviation of the displacement in the displacement data group; v′ is the mean value of the wind speed component in the wind speed component data set, L is the mean value of the offset in the offset data set, Δf is the mean value of the tension fluctuation value in the tension fluctuation value data set, and s is the mean value of the displacement in the displacement data set; P u is the reference value for the probability of lifetime assessment; S14: Substitute the wind speed component data group, offset data group, tension fluctuation value data group and displacement data group into the bridge life assessment probability model, and establish a distribution diagram of life assessment probability and wind speed component, offset, tension fluctuation value and displacement, with the life assessment probability as the vertical coordinate, the wind speed component, offset, tension fluctuation value and displacement as the horizontal coordinate, and the reference value as the reference horizontal line to evaluate the bridge life.

Citation Information

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