WO2022257461A1 - 基于车‐桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备 - Google Patents

基于车‐桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备 Download PDF

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WO2022257461A1
WO2022257461A1 PCT/CN2022/071663 CN2022071663W WO2022257461A1 WO 2022257461 A1 WO2022257461 A1 WO 2022257461A1 CN 2022071663 W CN2022071663 W CN 2022071663W WO 2022257461 A1 WO2022257461 A1 WO 2022257461A1
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bridge
vehicle
model
heavy
force
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PCT/CN2022/071663
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French (fr)
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丁勇
张志强
刘剑
周彤
贾献卓
常英
朱斌
陈�光
曾聪
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哈尔滨工业大学
中电建冀交高速公路投资发展有限公司
哈工大(北京)工业技术创新研究院有限公司
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Priority to US17/936,866 priority Critical patent/US20230050445A1/en
Publication of WO2022257461A1 publication Critical patent/WO2022257461A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention belongs to the technical field of engineering, in particular to a refined update method, system and equipment for a finite element model of a highway bridge
  • the purpose of the present invention is to solve the problem that there is no refined update method for the bridge model at present, resulting in low simulation accuracy.
  • a bridge model update method based on vehicle-bridge coupling force correction comprising the following steps:
  • the dynamic response of the bridge structure under the load of heavy-duty vehicles is obtained through the sensors arranged on the bridge structure;
  • the dynamic response of the bridge structure obtained by the actual measurement includes the vertical vibration acceleration and vertical deflection of the bridge;
  • a nonlinear finite element model of the bridge structure is established, the vehicle-bridge interaction force is taken as the external force, the dynamic response of the bridge structure is taken as the structural response, and the correction of the finite element model of the bridge structure is completed through the nonlinear parameter identification method.
  • the senor is arranged at a quarter point of each span of the bridge main girder.
  • the measured dynamic response of the bridge structure includes the vertical vibration acceleration and vertical deflection of the bridge. It is necessary to use an interpolation method to obtain the vertical deflection and deformation of the bridge at the center of gravity of the heavy-duty vehicle during the whole process of crossing the bridge. Vertical vibration acceleration.
  • the process of reconstructing the table response of the shaking table and obtaining the interaction force F of the vehicle-bridge coupling model includes the following steps:
  • the correction process of the finite element model of the bridge structure is completed through the nonlinear parameter identification method, and the energy conservation integral method and the UKF method are used to realize, wherein the energy conservation integral method is used to solve the structural dynamics problem, and the UKF method is used to carry out the bridge numerical model renew;
  • the specific process of using the energy conservation integral method to solve the structural dynamics problem includes the following steps:
  • M and C are the mass and damping matrix of the bridge nonlinear system
  • x is the state variable of the state space equation
  • k is the time step
  • F k is the external force of the bridge at time k
  • L is the load position matrix
  • x k are the acceleration, velocity and displacement responses of the bridge structure at time k
  • R k (x) is the nonlinear structural restoring force of the bridge nonlinear system at time k;
  • ⁇ t is the time step
  • k is the time step
  • the system speed of k+1 is the time step expression for:
  • x m , F m and R m are the mean velocity, mean external force and mean restoring force between k and k+1 time steps;
  • Formula (8) is regarded as an energy transfer process, and the energy conservation integral method is used to solve the structural dynamics problem.
  • the bridge nonlinear system damping matrix is a Rayleigh damping matrix:
  • a 1 and a 2 are the Rayleigh damping coefficients, and K is the stiffness matrix.
  • the average velocity, average external force and average restoring force x m , F m and R m between the k and k+1 time steps are as follows:
  • R m (R k+1 +R k )/2
  • a bridge model update system based on vehicle-bridge coupling force correction the system is used to implement a bridge model update method based on vehicle-bridge coupling force correction.
  • a storage medium at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement a bridge model update method based on vehicle-bridge coupling force correction.
  • a device the device includes a processor and a memory, at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by the processor to implement a bridge model based on vehicle-bridge coupling force correction update method.
  • the present invention is based on the real vehicle-shaking table hybrid test, simulates the bridge structure with a multi-degree-of-freedom shaking table, accurately picks up the vehicle-bridge interaction force, and combines the measured dynamic response of the bridge on this basis, through nonlinear parameter identification means, to complete
  • the basis of analysis is of great practical significance to solve the problem of large-scale transportation audit.
  • Fig. 1 is the updated frame diagram of the bridge model based on vehicle-bridge coupling force correction according to the present invention
  • Fig. 4 is the schematic diagram of vehicle-shaking table test
  • 1 is the heavy-duty vehicle
  • 2 is the measured dynamic response of the bridge
  • 3 is the pressure and shear force measurement version
  • 4 is the vibration table.
  • This embodiment is a bridge model update method based on vehicle-bridge coupling force correction, including the following steps:
  • the dynamic response of the bridge structure under the load of heavy-duty vehicles is obtained through the sensors that have been deployed on the bridge structure.
  • the measured dynamic response of the bridge structure includes the vertical vibration acceleration and deflection of the bridge.
  • the sensor layout position is the main girder of each span of the bridge quarter point.
  • the heavy load in heavy-duty vehicles refers to the "Definition Method for Heavy-Duty and Heavy-Duty Traffic on Cement Concrete Pavement", as shown in Table 1:
  • Figure 2 shows the schematic diagram of the bridge field test.
  • the vertical vibration acceleration a o and vertical deflection y o of the bridge corresponding to the center of gravity o of the heavy-duty vehicle are obtained by difference processing based on adjacent sensor data.
  • Attached Figure 3 shows the acquisition process of the dynamic response of the bridge structure at the center o of the heavy-duty vehicle.
  • the actual number of spans of the bridge is j, and each bridge is divided into 4 units of equal length according to the position of the sensor.
  • the interpolation method obtains the vertical deflection deformation and vertical vibration acceleration of the bridge at the center of gravity of the heavy-duty vehicle during the whole process of the heavy-duty vehicle crossing the bridge.
  • the table response of the shaking table is reconstructed through mixed experiments, so that the reconstructed table surface
  • the vertical displacement and the vertical acceleration of the platform are consistent with y o and a o
  • the horizontal movement speed of the platform is u vehicle
  • its moving direction is opposite to that of the heavy-duty vehicle.
  • the movement of the heavy-duty vehicle is simulated through the relative motion of the vehicle-bridge.
  • the reconstruction is achieved by a hybrid experimental approach in which the experimental substructure is a full-scale heavy-duty vehicle and the numerical substructure is a finite element model of the bridge structure.
  • the bridge is divided into numerical substructures for finite element simulation.
  • the prototype and full-scale heavy-duty vehicle are selected as the test substructure, and the loading is simulated by the shaking table array.
  • the center of gravity of the vehicle is determined according to the type of the heavy-duty vehicle and the counterweight.
  • Response reconstruction is provided to the shaking table as the response quantity, so that the vibration table produces the same dynamic response of the bridge structure as the vehicle passes the bridge.
  • the interaction force of the vehicle-bridge coupling model can be obtained through the force plate; the process of obtaining the interaction force of the vehicle-bridge coupling model through the force plate includes the following steps:
  • the nonlinear finite element model of the bridge structure is established, the vehicle-bridge interaction force is taken as the external force, and the dynamic response of the bridge structure obtained from the actual measurement is taken as the structural response.
  • the correction of the finite element model of the bridge structure is completed, so that the numerical model of the bridge It can truly reflect the actual damage of the bridge and reduce the model error.
  • the vehicle-bridge interaction force F is used as the external excitation of the nonlinear finite element model of the bridge.
  • the specific model update process is as follows:
  • M and C are the mass and damping matrix of the bridge nonlinear system
  • x is the state variable of the state space equation
  • k is the time step
  • F k is the external force of the bridge at time k
  • L is the load position matrix
  • x k are the acceleration, velocity and displacement responses of the bridge structure at time k
  • R k (x) is the restoring force of the nonlinear structure of the bridge nonlinear system at time k
  • the damping of the bridge nonlinear system is Rayleigh damping:
  • a 1 and a 2 are the Rayleigh damping coefficients, and K is the stiffness matrix;
  • the parameters mainly include the physical parameters of important materials of the bridge, especially the constitutive parameters of concrete and steel structures.
  • ⁇ t is the time step length
  • k is the time step.
  • the speed of k+1 time step can be obtained expression for:
  • x m , F m and R m are the mean velocity, mean external force and mean restoring force between k and k+1 time steps;
  • R m (R k+1 +R k )/2
  • x k,m are the average acceleration, average velocity and average displacement response of the bridge structure at time k
  • R k,m (x) is the average restoring force of the nonlinear structure of the bridge nonlinear system at time k
  • F k,m is the The average external force of the axle
  • Formula (8) embodies the energy transfer process in the bridge nonlinear system.
  • the system motion equation always satisfies the principle of energy conservation. Therefore, the energy conservation integral method can be applied to solve structural dynamics problems.
  • the energy conservation integral method can be applied to solve structural dynamics problems.
  • the refined identification of parameters in the nonlinear finite element model of the bridge can be realized, and then the update process of the bridge finite element model can be completed.
  • Equation (9) can also be expressed as Equation (13) in the state space.
  • the discrete observation function can be written as
  • V is the observation noise
  • E[X] is the expectation
  • 2n+1 sampling points can be used to construct the estimated value of the system state vector at k-1 time by the following formula:
  • i and ⁇ are the parameters in the UKF algorithm, and ⁇ is the parameter controlling the distance from each sigma point to the mean.
  • W m is the weight matrix, and there are 2n weight coefficients in total, and n is the number of elements in the state vector; I is the identity matrix, and the dimension is 2n ⁇ 2n; Q k-1 is the k-1 step process of the state equation The covariance matrix of the noise.
  • y k the observation quantity of the kth step.
  • the cyclic recursion operation is carried out to complete the estimation of the state quantity, and the bridge structural parameters are placed in the state quantity.
  • the identification of the nonlinear parameters of the bridge can be realized.
  • the parameters include the physical parameters of the important materials of the bridge, especially Constitutive parameters of concrete and steel structures, such as modulus, Poisson's ratio and other nonlinear constitutive model parameters.
  • the main parameters can be determined through the sensitivity analysis of structural response to model parameters.
  • This embodiment is a bridge model update system based on vehicle-bridge coupling force correction, and the system is used to implement a bridge model update method based on vehicle-bridge coupling force correction.
  • This embodiment is a storage medium, and at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement a bridge model update method based on vehicle-bridge coupling force correction.
  • This embodiment is a device, the device includes a processor and a memory, at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by the processor to realize a vehicle-bridge coupling force Revised bridge model update method.
  • the present invention can also have other various embodiments, without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all Should belong to the scope of protection of the appended claims of the present invention.

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  • Computer Hardware Design (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Architecture (AREA)
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Abstract

基于车‐桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备，属于工程技术领域。本发明是为了解决目前并没有针对桥梁模型的精细化更新方法，从而导致仿真精确度较低问题。本发明通过布设在桥梁结构上的传感器获得桥梁结构在重载车辆（1）荷载作用下的桥梁结构动态响应（2）；根据已重载车辆（1）重心o处桥梁竖向振动加速度a o及竖向挠度y o，以及重载车辆（1）速度u 车，重构振动台（4）台面响应，并获得车‐桥耦合模型的相互作用力；建立桥梁结构非线性有限元模型，将车‐桥相互作用力作为外力，将桥梁结构动态响应（2）作为结构响应，通过非线性参数识别方法，完成桥梁结构有限元模型的修正。本发明主要用于桥梁模型的更新。

Description

基于车‐桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备 技术领域
本发明属于工程技术领域，特别涉及公路桥梁有限元模型的精细化更新方法、系统及设备
背景技术
以公路桥梁为代表的基础设施的快速发展，是中国经济持续增长的重要基石。公路桥梁作为重要的交通枢纽，对促进物资运输、改善偏远地区交通状况，实现区域经济发展具有重要意义。然而，随着国内外物流业务的极速扩张，重型、超重型运载情况时有发生，这种超过桥梁常规使用设计荷载的重载车辆，极可能使桥梁产生不可逆的损伤，严重影响桥梁设计使用周期内的安全性及耐久性。
近年来，由重载车辆造成的桥梁坍塌事故频繁出现，如2015年6月赣鄂高速河源匝道桥垮塌，桥梁设计荷载110t，实际重载荷载360t；2019年10月江苏无锡高架桥垮塌，桥梁设计荷载110t，实际重载车辆荷载183t。桥梁结构的垮塌与失效，不仅造成巨额的经济损失，更会造成恶劣的社会影响，因此，聚焦重载车辆过桥的安全评估问题尤为重要。重载车辆过桥安全性评估工作，离不开桥梁数值仿真计算，因此，能够真实描述结构实际损伤的有限元模型，是桥梁安全性评估首要解决的关键问题之一。但是现有的研究中并没有考虑这方面的因素而对桥梁模型进行更新，因此仿真时精确度较低，导致了桥梁安全性可能存在隐患。
发明内容
本发明是为了解决目前并没有针对桥梁模型的精细化更新方法，从而导致仿真精确度较低问题。
一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法，包括以下步骤：
通过布设在桥梁结构上的传感器获得桥梁结构在重载车辆荷载作用下的桥梁结构动态响应；实测获得的桥梁结构动态响应包括桥梁竖向振动加速度及竖向挠度；
根据已重载车辆重心o处桥梁竖向振动加速度a o及竖向挠度y o，以及重载车辆速度u 车，重构振动台台面响应，并获得车‐桥耦合模型的相互作用力；
建立桥梁结构非线性有限元模型，将车‐桥相互作用力作为外力，将桥梁结构动态响应作为结构响应，通过非线性参数识别方法，完成桥梁结构有限元模型的修正。
优选地，所述传感器布设位置为桥梁各跨主梁四分之一分点处。
优选地，实测获得的桥梁结构动态响应包括桥梁竖向振动加速度及竖向挠度的过程中需要通过插值方法获得重载车辆在过桥全过程时间内，重载车辆重心处桥梁竖向挠度变形及竖向振动加速度。
优选地，重构振动台台面响应并获得车‐桥耦合模型的相互作用力F的过程包括以下步骤：
将重载车辆停放至振动台上，在车轮底部布设测力板，将实际测得的桥梁结构动态响应重构作为响应量提供给振动台，使振动台产生与重载车辆过桥过程中车量重心所对应的桥梁结构动态响应相一致，通过测力板获得车‐桥耦合模型的相互作用力F；
优选地，通过非线性参数识别方法，完成桥梁结构有限元模型的修正的过程，采用能量守恒积分方法与UKF方法实现，其中采用能量守恒积分方法求解结构动力学问题，采用UKF方法进行桥梁数值模型更新；
所述采用能量守恒积分方法求解结构动力学问题的具体过程包括以下步骤：
桥梁非线性系统运动方程的时间离散形式如(1)所示
Figure PCTCN2022071663-appb-000001
其中，M、C为桥梁非线性系统质量、阻尼矩阵，x表示状态空间方程的状态变量，k为时间步，F k为k时刻车桥外界作用力，L为荷载位置矩阵，
Figure PCTCN2022071663-appb-000002
和x k为桥梁结构k时刻的加速度、速度和位移响应，R k(x)为k时刻桥梁非线性系统的非线性结构恢复力；
将参数离散点幅值扩展于状态量中，采用常加速度Newmark‐β法获得相邻时刻速度及加速度之间的关系，如公式(3)所示，通过离散的运动微分方程完成对桥梁有限元模型的参数识别；
Figure PCTCN2022071663-appb-000003
其中△t为时间步长，k为时间步；
根据公式(1)得到k+1为时间步的系统速度
Figure PCTCN2022071663-appb-000004
的表达式：
Figure PCTCN2022071663-appb-000005
Figure PCTCN2022071663-appb-000006
式中x m、F m和R m是k和k+1时间步长之间的平均速度、平均外力和平均恢复力；
系统运动方程(1)写成如下形式
Figure PCTCN2022071663-appb-000007
对公式(1)右乘(x k+1-x k) T之后，得到新的运动方程：
Figure PCTCN2022071663-appb-000008
将公式(8)视为能量转移过程，利用能量守恒积分方法求解结构动力学问题。
优选地，桥桥梁非线性系统阻尼矩阵为瑞利阻尼矩阵：
C＝a 1·M+a 2·K
其中，a 1和a 2为瑞利阻尼系数，K是刚度矩阵。
优选地，所述的k和k+1时间步长之间的平均速度、平均外力和平均恢复力x m、F m和R m分别如下：
Figure PCTCN2022071663-appb-000009
Figure PCTCN2022071663-appb-000010
R m＝(R k+1+R k)/2
一种基于车‐桥梁耦合作用力修正的桥梁模型更新系统，所述系统用于执行一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
一种存储介质，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
一种设备，所述设备包括处理器和存储器，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
有益效果：
本发明以实车‐振动台混合试验为基础，以多自由度振动台模拟桥梁结构，准确拾取车‐桥相互作用力，在此基础上结合桥梁实测动态响应，通过非线性参数识别手段，完成桥梁有限元模型的精确修正，考虑桥梁真实情况，使桥梁数值模型与真实结构情况相吻合，桥梁数值模型的精确模拟，为桥梁后期运营与维护，特别是重在车辆 过桥的安全性评估提供分析基础，对解决大件运输审核问题具有重要实际意义。
附图说明
图1为本发明所述的基于车‐桥梁耦合作用力修正的桥梁模型更新框架图；
图2为桥梁现场试验示意图；其中，j为桥梁第j跨，i为桥梁单元数，i＝1…4，Aji为桥梁第j跨第i个单元的实测动态响应，Lj为桥梁第j跨长度；
图3重载车辆重心o处桥梁结构动态响应获取过程；
图4为车—振动台试验示意图；
其中，1为重载车辆，2为桥梁实测动态响应，3为压力、剪力测力版，4为振动台。
具体实施方式
具体实施方式一：结合图1说明本实施方式，
本实施方式为一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法，包括以下步骤：
通过已经布设在桥梁结构上的传感器获得桥梁结构在重载车辆荷载作用下的桥梁结构动态响应，实测获得的桥梁结构动态响应包括桥梁竖向振动加速度及挠度，传感器布设位置为桥梁各跨主梁四分之一分点处。
重载车辆中的重载参照《水泥混凝土路面重载与重载交通的界定方法》，如表1所示：
表1重载界限
Figure PCTCN2022071663-appb-000011
附图2给出了桥梁现场试验示意图。当重载车辆1以速度u 车沿桥长方向匀速行驶时，重载车辆重心o处所对应的桥梁竖向振动加速度a o及竖向挠度y o，根据相邻传感器数据进行差值处理获得。附图3给出了重载车辆中心o处桥梁结构动态响应获取过程，桥梁实际跨数为j,每跨桥梁根据传感器位置将其划分为4个等长度单元，根据重载车辆实际运行位置，判断重载车辆所处桥梁第j跨第i个单元，然后利用第i个单元两端A ji和A ji+1的实测数据线性插值，获得重载车辆中心o处桥梁结构动态响应；即通过插值方法获得重载车辆在过桥全过程时间内，移动重载车辆重心处桥梁竖 向挠度变形及竖向振动加速度。
根据已经获得的重载车辆重心o处桥梁竖向振动加速度a o及竖向挠度y o，以及重载水平行驶的速度u 车，通过混合实验重构振动台台面响应，使台面重构后的竖向位移、台面竖向加速度与y o及a o相一致，台面水平向运动速度为u 车，其运动方向与重载车辆行进方向相反，通过车‐桥相对运动模拟重载车辆运动，此时，测得测力的竖向数据及水平向数据，获得车‐振动台竖向及水平向车‐桥相互作用力F。
重构是通过混合实验方法实现的，混合实验中，实验子结构为足尺重载车辆，数值子结构为桥梁结构的有限元模型。
混合实验模拟实施过程中，将桥梁划分为数值子结构，进行有限元模拟。选取原型、足尺重载车辆作为试验子结构，并通过振动台台阵模拟加载。
①确定初始时间步t＝0时刻的系统初始值；②计算初始时刻桥梁模型运动量；③考虑路面平整度，并将耦合界面运动量传于振动台台阵加载控制系统，对所选重载车辆模型加载，并通过测力装置实时获得重载车辆对界面作用力；④恢复重载车辆状态量至初始状态；⑤考虑车速，在计算机中根据车辆作用力，通过数值积分方法计算t+Δt步桥梁反应，将本步的车桥耦合截面运动状态和之前所有恢复力组成向量F，传给振动台台阵加载系统；⑥振动台台阵加载系统对重载车辆从初始时刻加载至下一时间步，并将重载车辆对界面作用力传于计算机的多尺度模型计算结构反应，重复④‐⑥直至计算完成。
如图4所示，重构过程中根据重载车辆类型及配重确定车辆重心，将重载车辆停放至振动台台阵上，在车轮底部布设测力板，将实际测得的桥梁结构动态响应重构作为响应量提供给振动台，使振动台产生与车辆过桥过程中的桥梁结构动态响应相一致。此时，通过测力板可以获得车‐桥耦合模型的相互作用力；通过测力板可以获得车‐桥耦合模型的相互作用力的过程包括以下步骤：
控制振动台台面，使台面重构后的竖向位移及台面竖向加速度与车辆重心所对应位置处桥梁竖向位移与竖向加速度相一致，此时，通过测力版测得车‐振动台接触点的竖向力及水平剪力，从而获得车‐振动台相互作用力F。
建立桥梁结构非线性有限元模型，将车‐桥相互作用力作为外力，实测获得的桥梁结构动态响应作为结构响应，通过非线性参数识别方法，完成桥梁结构有限元模型的修正，使桥梁数值模型能够真实反映桥梁实际损伤，减小模型误差。
在桥梁结构有限元模型的修正的具体过程中，将车‐桥相互作用力F作为桥梁非线性有限元模型的外界激励，通过能量守恒积分方法与UKF方法的联合应用，完成桥梁数值模型中桥梁参数的反演，具体模型更新过程如下：
桥梁非线性系统运动方程的时间离散形式如(1)所示
Figure PCTCN2022071663-appb-000012
其中，M、C为桥梁非线性系统质量、阻尼矩阵，x表示状态空间方程的状态变量，k为时间步，F k为k时刻车桥外界作用力，L为荷载位置矩阵，
Figure PCTCN2022071663-appb-000013
和x k为桥梁结构k时刻的加速度、速度和位移响应，R k(x)为k时刻桥梁非线性系统的非线性结构恢复力；桥梁非线性系统阻尼为瑞利阻尼：
C＝a 1·M+a 2·K       (2)
其中，a 1和a 2为瑞利阻尼系数，K是刚度矩阵；
将参数离散点幅值扩展于状态量中，采用常加速度Newmark‐β法可以获得相邻时刻速度及加速度之间的关系，如公式(3)所示，此时可以通过离散的运动微分方程完成对桥梁有限元模型的参数识别，所述的参数主要包括桥梁重要材料的物理参数，特别是混凝土、钢结构本构参数。
Figure PCTCN2022071663-appb-000014
其中△t为时间步长，k为时间步。
根据公式(1)可以得到k+1时间步的速度
Figure PCTCN2022071663-appb-000015
的表达式：
Figure PCTCN2022071663-appb-000016
Figure PCTCN2022071663-appb-000017
式中x m、F m和R m是k和k+1时间步长之间的平均速度、平均外力和平均恢复力；其中
Figure PCTCN2022071663-appb-000018
Figure PCTCN2022071663-appb-000019
Figure PCTCN2022071663-appb-000020
R m＝(R k+1+R k)/2
此时，桥梁非线性系统运动方程(1)可以写成如下形式
Figure PCTCN2022071663-appb-000021
Figure PCTCN2022071663-appb-000022
和x k,m为桥梁结构k时刻的平均加速度、平均速度和平均位移响应，R k，m(x)为k时刻桥梁非线性系统的非线性结构平均恢复力，F k,m为k时刻车桥外界平均作用力；
对公式(1)右乘(x k+1-x k) T之后，可以得到新的运动方程：
Figure PCTCN2022071663-appb-000023
公式(8)体现了桥梁非线性系统中的能量转移过程，在考虑系统外界输入的情况下，系统运动方程始终满足能量守恒原理。因此，能量守恒积分方法可应用于求解结构动力学问题。将能量守恒积分方法与UKF方法联合应用，即可实现桥梁非线性有限元模型中参数的精细化识别，进而完成桥梁有限元模型的更新过程。
所述的UKF方法的桥梁数值模型更新过程如下：
桥梁非线性系统的离散状态空间方程可以写成：
X k＝F(X k-1,u k-1,w k-1)        (9)
X k为k时刻桥梁非线性系统状态向量，
Figure PCTCN2022071663-appb-000024
u k-1为k‐1时刻桥梁非线性系统输入，w k-1为k‐1时刻系统过程噪声向量，F为状态向量X的非线性函数。式(9)在状态空间中也可以表示为式(13)。
离散观测函数可以写成
y k＝h(X k,u k,v k)        (10)
式中，V为观测噪声，初始值定义为X 0＝E[X],
Figure PCTCN2022071663-appb-000025
其中
Figure PCTCN2022071663-appb-000026
表示X 0的估计，E[X]为期望；对于第k‐1时间步，2n+1个采样点可通过下面 公式构造k‐1时刻系统状态向量预估值：
Figure PCTCN2022071663-appb-000027
其中，i、λ为UKF算法中的参数，其中λ为控制每个sigma点到均值的距离的参数。
预测2n+1个采样点先验估计的均值
Figure PCTCN2022071663-appb-000028
和协方差
Figure PCTCN2022071663-appb-000029
可以通过每个点的权重矩阵获得：
Figure PCTCN2022071663-appb-000030
Figure PCTCN2022071663-appb-000031
Figure PCTCN2022071663-appb-000032
Figure PCTCN2022071663-appb-000033
式中，W m为权重矩阵，权重系数一共有2n个，n为状态向量中元素的个数；I是单位矩阵，维度是2n×2n；Q k‐1为状态方程第k‐1步过程噪声的协方差矩阵。
利用UKF滤波算法，递推更新经过UT变换后的观测量预估值
Figure PCTCN2022071663-appb-000034
观测量预估值加权均值μ k以及过程参数S k和C k如下：
Figure PCTCN2022071663-appb-000035
Figure PCTCN2022071663-appb-000036
Figure PCTCN2022071663-appb-000037
Figure PCTCN2022071663-appb-000038
进一步地，计算滤波增益K，更新状态量均值估计值
Figure PCTCN2022071663-appb-000039
以及协方差矩阵P。
Figure PCTCN2022071663-appb-000040
Figure PCTCN2022071663-appb-000041
Figure PCTCN2022071663-appb-000042
式中y k——第k步的观测量。通过以上步骤进行循环递推运算，完成状态量的估计工作，将桥梁结构参数置于状态量中，通过上述过程可以实现桥梁非线性参数的识别，所述参数括桥梁重要材料的物理参数，特别是混凝土、钢结构本构参数，如模量、泊松比等非线性本构模型参数，具体可通过结构反应对模型参数敏感性分析确定主要参数。
具体实施方式二：
本实施方式为一种基于车‐桥梁耦合作用力修正的桥梁模型更新系统，所述系统用于执行一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
具体实施方式三：
本实施方式为一种存储介质，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
具体实施方式四：
本实施方式为一种设备，所述设备包括处理器和存储器，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现一种基于车‐桥梁耦合作用力修正的桥梁模型更新方法。
本发明还可有其它多种实施例，在不背离本发明精神及其实质的情况下，本领域技术人员当可根据本发明作出各种相应的改变和变形，但这些相应的改变和变形都应属于本发明所附的权利要求的保护范围。

Claims (10)

  1. 一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，包括以下步骤：
    通过布设在桥梁结构上的传感器获得桥梁结构在重载车辆荷载作用下的桥梁结构动态响应；实测获得的桥梁结构动态响应包括桥梁竖向振动加速度及竖向挠度；
    根据已重载车辆重心o处桥梁竖向振动加速度a o及竖向挠度y o，以及重载车辆速度u 车，重构振动台台面响应，并获得车-桥耦合模型的相互作用力；
    建立桥梁结构非线性有限元模型，将车-桥相互作用力作为外力，将桥梁结构动态响应作为结构响应，通过非线性参数识别方法，完成桥梁结构有限元模型的修正。
  2. 根据权利要求1所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，所述传感器布设位置为桥梁各跨主梁四分之一分点处。
  3. 根据权利要求2所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，实测获得的桥梁结构动态响应包括桥梁竖向振动加速度及竖向挠度的过程中需要通过插值方法获得重载车辆在过桥全过程时间内，重载车辆重心处桥梁竖向挠度变形及竖向振动加速度。
  4. 根据权利要求1、2或3所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，重构振动台台面响应并获得车-桥耦合模型的相互作用力F的过程包括以下步骤：
    将重载车辆停放至振动台上，在车轮底部布设测力板，将实际测得的桥梁结构动态响应重构作为响应量提供给振动台，使振动台产生与重载车辆过桥过程中车量重心所对应的桥梁结构动态响应相一致，通过测力板获得车-桥耦合模型的相互作用力F。
  5. 根据权利要求4所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，通过非线性参数识别方法，完成桥梁结构有限元模型的修正的过程，采用能量守恒积分方法与UKF方法实现，其中采用能量守恒积分方法求解结构动力学问题，采用UKF方法进行桥梁数值模型更新；
    所述采用能量守恒积分方法求解结构动力学问题的具体过程包括以下步骤：
    桥梁非线性系统运动方程的时间离散形式如(1)所示
    Figure PCTCN2022071663-appb-100001
    其中，M、C为桥梁非线性系统质量、阻尼矩阵，x表示状态空间方程的状态变 量，k为时间步，F k为k时刻车桥外界作用力，L为荷载位置矩阵，
    Figure PCTCN2022071663-appb-100002
    和x k为桥梁结构k时刻的加速度、速度和位移响应，R k(x)为k时刻桥梁非线性系统的非线性结构恢复力；
    将参数离散点幅值扩展于状态量中，采用常加速度Newmark-β法获得相邻时刻速度及加速度之间的关系，如公式(3)所示，通过离散的运动微分方程完成对桥梁有限元模型的参数识别；
    Figure PCTCN2022071663-appb-100003
    其中△t为时间步长，k为时间步；
    根据公式(1)得到k+1为时间步的系统速度
    Figure PCTCN2022071663-appb-100004
    的表达式：
    Figure PCTCN2022071663-appb-100005
    Figure PCTCN2022071663-appb-100006
    式中x m、F m和R m是k和k+1时间步长之间的平均速度、平均外力和平均恢复力；
    系统运动方程(1)写成如下形式
    Figure PCTCN2022071663-appb-100007
    对公式(1)右乘(x k+1-x k) T之后，得到新的运动方程：
    Figure PCTCN2022071663-appb-100008
    将公式(8)视为能量转移过程，利用能量守恒积分方法求解结构动力学问题。
  6. 根据权利要求5所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，桥桥梁非线性系统阻尼矩阵为瑞利阻尼矩阵：
    C＝a 1·M+a 2·K
    其中，a 1和a 2为瑞利阻尼系数，K是刚度矩阵。
  7. 根据权利要求5所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法，其特征在于，所述的k和k+1时间步长之间的平均速度、平均外力和平均恢复力x m、F m和R m分别如下：
    Figure PCTCN2022071663-appb-100009
    Figure PCTCN2022071663-appb-100010
    R m＝(R k+1+R k)/2
  8. 一种基于车-桥梁耦合作用力修正的桥梁模型更新系统，其特征在于，所述系统用于执行权利要求1至7之一所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法。
  9. 一种存储介质，其特征在于，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现如权利要求1至7之一所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法。
  10. 一种设备，其特征在于，所述设备包括处理器和存储器，所述存储介质中存储有至少一条指令，所述至少一条指令由处理器加载并执行以实现如权利要求1至7之一所述的一种基于车-桥梁耦合作用力修正的桥梁模型更新方法。
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CN116842348B (zh) * 2023-08-31 2023-12-01 安徽省云鹏工程项目管理有限公司 基于人工智能的桥梁健康监测系统
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CN117592382B (zh) * 2024-01-18 2024-04-26 高速铁路建造技术国家工程研究中心 一种铁路车轨桥系统动态响应预测方法、系统及介质
CN117669389B (zh) * 2024-01-31 2024-04-05 西华大学 基于深度学习的地震-车-桥系统随机振动分析方法

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103150458A (zh) * 2013-04-01 2013-06-12 中南大学 车辆-轨道-桥梁-地基基础耦合系统及其动力分析方法
CN104573274A (zh) * 2015-01-27 2015-04-29 南京工业大学 车辆荷载下基于位移时程面积的结构有限元模型修正方法
US20150198502A1 (en) * 2014-01-14 2015-07-16 Iowa State University Research Foundation, Inc. Methods and systems for automated bridge structural health monitoring
US20190234834A1 (en) * 2016-08-03 2019-08-01 Southeast University Method and system for measuring vertical wheel impact force in real-time based on tire pressure monitoring
CN110132515A (zh) * 2019-05-10 2019-08-16 哈尔滨工业大学 一种基于模型更新的时程级迭代实时混合试验方法
CN111027256A (zh) * 2020-03-09 2020-04-17 杭州鲁尔物联科技有限公司 一种基于车辆荷载空间分布的桥梁风险预测方法及系统
CN113392451A (zh) * 2021-06-09 2021-09-14 哈尔滨工业大学 基于车-桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备

Family Cites Families (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101739816B (zh) * 2009-11-26 2011-08-24 西北工业大学 交通车辆道路行驶安全分析方法
CN105825014A (zh) * 2016-03-17 2016-08-03 中铁大桥勘测设计院集团有限公司 一种基于车桥耦合分析的车桥安全健康评估系统及方法
CN106197910B (zh) * 2016-07-01 2017-04-26 东南大学 一种基于车桥耦合振动分析的桥梁检测方法与检测系统
CN106097819A (zh) * 2016-07-31 2016-11-09 重庆交通大学 用于实验教学的桥梁仿真检测方法及系统
KR101938352B1 (ko) * 2018-04-30 2019-01-14 김도빈 상시진동실험 데이터로 교량의 강성계수의 산출이 가능한 것을 특징으로 하는 교량의 강성계수 산출 방법 및 프로그램
CN110334371A (zh) * 2019-04-18 2019-10-15 朱思宇 一种基于有限元模型的车-桥耦合系统振动计算方法
CN110543706B (zh) * 2019-08-21 2023-03-24 哈尔滨工业大学 一种基于车辆刹车作用的在役桥梁支座损伤诊断方法
CN110795780B (zh) * 2019-09-09 2023-02-10 杭州鲁尔物联科技有限公司 一种基于XGBoost算法的斜拉桥有限元修正方法
CN110909405B (zh) * 2019-11-19 2023-11-14 广州大学 基于车辆载荷的桥梁结构优化方法、系统及智能设备
CN111353252B (zh) * 2020-03-25 2024-03-22 山东高速集团有限公司 一种基于环境激励的桥梁静载试验方法
CN111832099A (zh) * 2020-05-28 2020-10-27 东南大学 基于fbg和有限元模型修正的桥梁结构损伤识别方法
CN111898304B (zh) * 2020-08-06 2021-05-07 西南交通大学 风车流桥耦合振动分析方法及系统

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103150458A (zh) * 2013-04-01 2013-06-12 中南大学 车辆-轨道-桥梁-地基基础耦合系统及其动力分析方法
US20150198502A1 (en) * 2014-01-14 2015-07-16 Iowa State University Research Foundation, Inc. Methods and systems for automated bridge structural health monitoring
CN104573274A (zh) * 2015-01-27 2015-04-29 南京工业大学 车辆荷载下基于位移时程面积的结构有限元模型修正方法
US20190234834A1 (en) * 2016-08-03 2019-08-01 Southeast University Method and system for measuring vertical wheel impact force in real-time based on tire pressure monitoring
CN110132515A (zh) * 2019-05-10 2019-08-16 哈尔滨工业大学 一种基于模型更新的时程级迭代实时混合试验方法
CN111027256A (zh) * 2020-03-09 2020-04-17 杭州鲁尔物联科技有限公司 一种基于车辆荷载空间分布的桥梁风险预测方法及系统
CN113392451A (zh) * 2021-06-09 2021-09-14 哈尔滨工业大学 基于车-桥梁耦合作用力修正的桥梁模型更新方法、系统、存储介质及设备

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117610307A (zh) * 2023-12-15 2024-02-27 大连海事大学 一种移动质量作用下简支梁的数字孪生构建方法
CN117610307B (zh) * 2023-12-15 2024-05-17 大连海事大学 一种移动质量作用下简支梁的数字孪生构建方法

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