CN115563446A - Method for identifying mobile load by utilizing space-time adaptive shape function response matrix - Google Patents

Method for identifying mobile load by utilizing space-time adaptive shape function response matrix Download PDF

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CN115563446A
CN115563446A CN202211152322.9A CN202211152322A CN115563446A CN 115563446 A CN115563446 A CN 115563446A CN 202211152322 A CN202211152322 A CN 202211152322A CN 115563446 A CN115563446 A CN 115563446A
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顾睿
项子儒
钱王苹
王星彦
吕晓云
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Abstract

The invention provides a method for identifying a moving load by utilizing a time-space adaptive shape function response matrix, belonging to the technical field of structural health monitoring. The problem that timeliness is reduced due to the fact that a system matrix needs to be reconstructed when loads at different speeds are identified is solved. The technical scheme is as follows: the method comprises the following steps: s1: measuring a vehicle-induced response signal of the bridge; s2: analyzing and determining the step size and the number of the shape function; s3: forming a space adaptive shape function; s4: applying the shape function as an excitation on the bridge to simulate a response matrix of the bridge; s5: establishing a space-time distribution rule of the base matrix corresponding to vehicles with different speeds; s6: obtaining a shape function coefficient by inverting the vehicle-induced response at any speed with the adaptive shape function response matrix; s7: and fitting the load by using the shape function and the corresponding shape function coefficient, thereby identifying the vehicle-mounted vehicle at any speed. The invention has the beneficial effects that: the invention realizes accurate and rapid identification of loads at different speeds on bridges with different slopes.

Description

一种利用时空自适应形函数响应矩阵识别移动荷载的方法A Method for Identifying Moving Loads Using Space-Time Adaptive Shape Function Response Matrix

技术领域technical field

本发明涉及结构健康监测技术领域，尤其涉及一种利用时空自适应形函数响应矩阵识别移动荷载的方法。The invention relates to the technical field of structural health monitoring, in particular to a method for identifying moving loads using a space-time adaptive shape function response matrix.

背景技术Background technique

移动荷载是影响桥梁使用寿命的主要因素之一，对其准确的监测与识别是提供“养桥”的依据，更是预防灾难性事故的关键。传统荷载识别方法主要用动态称重系统，以某大桥为例，其动态称重系统造价为579227.92元，而以结构动力响应反演移动荷载理论监测桥梁的系统在成本上可以节约近65％，因此，基于动力反演方法与动态称重系统相比具有明显的经济优势。目前识别精度较高且研究较成熟的动力反演方法包括时域法与频时域法，其本质上是利用桥梁的系统矩阵(脉冲响应矩阵)建立系统输入(移动荷载)与输出(桥梁响应)的关系，并进行逆向求解的过程。若测量噪声大、时间长或初始条件不准则极易引起系统矩阵奇异性导致识别失败。改善该问题的技术通常由正则化方法、基函数方法等，但大部分现有方法存在以下问题：1)其抑制奇异性的措施会产生额外的运算成本；2)识别不同速度荷载时需要重构系统矩阵导致时效性下降；3)未考虑桥梁坡度变化从而限制其在不同桥梁上的推广应用。The moving load is one of the main factors affecting the service life of the bridge, and its accurate monitoring and identification is the basis for "maintaining the bridge" and the key to preventing catastrophic accidents. The traditional load identification method mainly uses the dynamic weighing system. Taking a bridge as an example, the cost of the dynamic weighing system is 579,227.92 yuan, and the system that uses the structural dynamic response to invert the moving load theory to monitor the bridge can save nearly 65% in cost. Therefore, the method based on dynamic inversion has obvious economic advantages compared with dynamic weighing system. At present, the dynamic inversion methods with high recognition accuracy and relatively mature research include time-domain method and frequency-time-domain method, which essentially use the system matrix (impulse response matrix) of the bridge to establish the system input (moving load) and output (bridge response ) relationship, and the process of reverse solution. If the measurement noise is large, the time is long, or the initial conditions are not standard, it is easy to cause the singularity of the system matrix and cause the identification failure. Techniques to improve this problem usually include regularization methods, basis function methods, etc., but most of the existing methods have the following problems: 1) the measures to suppress the singularity will generate additional computing costs; 3) It does not consider the slope change of the bridge, which limits its application on different bridges.

如何解决上述技术问题为本发明面临的课题。How to solve the above technical problems is the subject of the present invention.

发明内容Contents of the invention

本发明的目的在于提供一种利用时空自适应形函数响应矩阵识别移动荷载的方法。解决了识别不同速度荷载时需要重构系统矩阵导致时效性下降等问题。实现不同坡度桥梁上对不同速度荷载准确、快速的识别。The purpose of the present invention is to provide a method for identifying moving loads by using the space-time adaptive shape function response matrix. It solves the problem that the system matrix needs to be reconstructed when identifying different speed loads, which leads to the decrease of timeliness. Accurate and fast identification of different speed loads on bridges with different slopes.

本发明的思想为：一种时空自适应形函数，首先利用形函数拟合系统矩阵，在降低系统矩阵奇异性的同时降低其维度，实现计算效率的一次提升；其次，利用时间适应技术，在预构建的形函数数据库中快速演化不同速度荷载所需系统矩阵，避免矩阵重构，实现计算效率的二次提升；最后，利用空间适应技术，实时构造贴合桥梁坡度变化的加载方式，建立准确的输入-输出关系；从而实现不同坡度桥梁上对不同速度荷载准确、快速的识别。The idea of the present invention is: a space-time adaptive shape function, which first uses the shape function to fit the system matrix, reduces its dimension while reducing the singularity of the system matrix, and realizes an improvement in calculation efficiency; secondly, uses the time adaptation technology, in In the pre-built shape function database, the system matrix required for rapid evolution of different speed loads can be avoided, and the matrix reconstruction can be avoided, and the calculation efficiency can be improved twice; The input-output relationship; so as to realize the accurate and rapid identification of different speed loads on bridges with different slopes.

为了实现上述发明目的，本发明采用的技术方案如下：In order to realize the foregoing invention object, the technical scheme that the present invention adopts is as follows:

一种利用时空自适应形函数响应矩阵识别移动荷载的方法，包括以下步骤：A method for identifying moving loads using a space-time adaptive shape function response matrix comprising the steps of:

S1：通过传感器测得桥梁的车致响应信号；S1: The vehicle-induced response signal of the bridge is measured by the sensor;

S2：基于响应信号的频域分析确定形函数的步长和数量；S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal;

S3：建立形函数对应不同桥梁坡度的空间分布规律，形成空间自适应形函数；S3: Establish the spatial distribution of the shape function corresponding to different bridge slopes to form a space adaptive shape function;

S4：将指定速度的空间自适应形函数作为激励施加在桥梁上模拟其响应矩阵：基矩阵；S4: Apply the space-adaptive shape function of specified speed as excitation to the bridge to simulate its response matrix: basis matrix;

S5：建立基矩阵对应不同速度车载的时空分布规律，基于基矩阵快速创建任意速度荷载的自适应形函数响应矩阵；S5: Establish the base matrix corresponding to the time-space distribution of vehicles at different speeds, and quickly create an adaptive shape function response matrix for any speed load based on the base matrix;

S6：通过任意速度车致响应与自适应形函数响应矩阵求逆获得形函数系数；S6: Obtain the shape function coefficient by inverting the vehicle-induced response at any speed and the adaptive shape function response matrix;

S7：利用形函数与相应的形函数系数拟合荷载，从而识别出任意速度下的车载。S7: Use the shape function and the corresponding shape function coefficient to fit the load, so as to identify the vehicle at any speed.

所述步骤S1中，包括以下步骤：In the step S1, the following steps are included:

S11：通过应变、加速度、动挠度等传感器测取桥梁的任意速度车致响应

Figure BDA0003856907630000031
S11: Measuring the vehicle-induced response of the bridge at any speed through sensors such as strain, acceleration, and dynamic deflection
Figure BDA0003856907630000031

所述步骤S2中，包括以下步骤：In the step S2, the following steps are included:

S21，形函数的频率可由下式计算得到：S21, the frequency of the shape function can be calculated by the following formula:

Figure BDA0003856907630000032
Figure BDA0003856907630000032

其中fLSF为形函数频率，fs为采样频率，l为截断形函数的单元步长，该步长与形函数个数m存在以下关系，其中T为总采样数：where f LSF is the shape function frequency, f s is the sampling frequency, and l is the unit step size of the truncated shape function, which has the following relationship with the number m of shape functions, where T is the total number of samples:

T＝l×m (2)。T=l×m (2).

所述步骤S3中，包括以下步骤：In the step S3, the following steps are included:

S31：对于从任意起点(x0，y0，z0),以速度v0(km/h)行驶t0(s)的移动荷载，其通过的桥梁截面(x，y，z)用如下竖曲线模型拟合，即形函数的空间分布规律：S31: For a moving load traveling t 0 (s) at speed v 0 (km/h) from any starting point (x 0 , y 0 , z 0 ), the bridge section (x, y, z) it passes through is used as follows Vertical curve model fitting, that is, the spatial distribution of shape functions:

Figure BDA0003856907630000033
Figure BDA0003856907630000033

其中α为桥梁一端纵坡度，β为桥梁另一端纵坡度，m1为桥梁竖曲线起点，m2为桥梁竖曲线终点，xm为变坡点，i为路拱横坡度，R是桥梁竖曲线半径。Where α is the longitudinal slope at one end of the bridge, β is the longitudinal slope at the other end of the bridge, m 1 is the starting point of the vertical curve of the bridge, m 2 is the end point of the vertical curve of the bridge, x m is the slope change point, i is the transverse slope of the road arch, R is the vertical slope of the bridge curve radius.

S32：利用S31中的空间分布律，形函数可施加于任何坡度的桥梁上，形成空间自适应形函数激励。S32: Utilizing the spatial distribution law in S31, the shape function can be applied to bridges with any slope to form a space-adaptive shape function excitation.

所述步骤S4中，包括以下步骤：In described step S4, comprise the following steps:

S41：将中位速度(一般为20m/s)的空间自适应形函数激励施加于桥梁上模拟其形函数响应矩阵，即基矩阵

Figure BDA0003856907630000034
S41: Apply the space-adaptive shape function excitation of the median velocity (generally 20m/s) to the bridge to simulate its shape function response matrix, namely the basis matrix
Figure BDA0003856907630000034

所述步骤S5中，包括以下步骤：In described step S5, comprise the following steps:

S51：基矩阵本质上为空间自适应形函数在不同时间点xi下对桥梁的作用效果，对于整个时间历程内fs×t+1个时间点xi，各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同，因此任意速度下的响应数据LR均可由基响应矩阵通过插值方法获得S51: The basis matrix is essentially the effect of the space-adaptive shape function on the bridge at different time points x i . For f s ×t+1 time points x i in the entire time course , the mutual independent, the influence of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L R at any speed can be obtained from the base response matrix by interpolation method

S52，由于各时间点xi之间相互独立，对于不同行驶时间t，其对于时间历程影响仅表现为包含时间点xi的多少，即需要插值的次数；S52, because each time point x i is independent of each other, for different travel times t, its influence on the time history is only shown as the number of time points x i included, that is, the number of interpolation times required;

S53，建立基矩阵的时间分布规律，定义三次样条插值过程spline()，其函数如下：S53, establish the time distribution law of the base matrix, define the cubic spline interpolation process spline (), its function is as follows:

对于fs×t+1个时间点，将整个时间历程分成fs×t＝n段，在每个区间内构造一个三次函数，共n段函数，其构造形式如下：For f s ×t+1 time point, divide the whole time course into f s ×t=n segments, construct a cubic function in each interval, a total of n segment functions, and its construction form is as follows:

Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3，i＝0，1，...，n-1 (4)S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , i=0, 1, . . . , n-1 (4)

其中：每个xi对应fs×t+1个时间点，Si(xi)为xi在三次函数上对应的因变量；ai、bi、ci、di为三次函数的拟合系数。Among them: each x i corresponds to f s ×t+1 time points, S i ( xi ) is the dependent variable corresponding to x i on the cubic function; a i , b i , c i , d i are the cubic function fit coefficient.

根据三次样条函数每个分段函数之间的衔接需求，即设定求解条件如下：According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows:

Figure BDA0003856907630000041
Figure BDA0003856907630000041

其中：li表示基矩阵

Figure BDA0003856907630000042
矩阵中的各个离散数据；条件1保证三次样条函数穿过所有已知li点；条件2保证三次样条函数在所有xi节点处连续；条件3保证三次样条函数在所有xi节点处一阶导数连续；条件4保证三次样条函数在所有xi节点处二阶导数连续，Among them: l i represents the basis matrix
Figure BDA0003856907630000042
Each discrete data in the matrix; condition 1 ensures that the cubic spline function passes through all known l i points; condition 2 ensures that the cubic spline function is continuous at all x i nodes; condition 3 ensures that the cubic spline function passes through all x i nodes The first-order derivative is continuous; condition 4 ensures that the second-order derivative of the cubic spline function is continuous at all x i nodes,

并附加自由边界条件如下：And additional free boundary conditions are as follows:

S″0(x0)＝0，S″n-1(xn)＝0 (6)S″ 0 (x 0 )=0, S″ n-1 (x n )=0 (6)

其中：x0、xn为时间历程区间两端点，自由边界条件表示为曲线的摇摆最小。Among them: x 0 and x n are the two ends of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve.

S54，对于n段时间历程，每段有4个方程组，共4n个线性方程组进行求解，求得每一段区间的三次样条函数Si(x)；S54, for n sections of time history, each section has 4 equations, a total of 4n linear equations are solved, and the cubic spline function S i (x) of each interval is obtained;

S55，从起点以任意速度v(km/h)行驶t(s)，其时间历程点x′i与初始速度v0存在如下关系：S55, travel t(s) at any speed v(km/h) from the starting point, the time history point x′ i has the following relationship with the initial speed v0 :

Figure BDA0003856907630000051
Figure BDA0003856907630000051

将新时间历程点x′i代入三次样条插值过程spline()，即可求得任意速度下的基矩阵

Figure BDA0003856907630000052
Substituting the new time history point x′ i into the cubic spline interpolation process spline(), the basis matrix at any speed can be obtained
Figure BDA0003856907630000052

所述步骤S6中，包括以下步骤：In the step S6, the following steps are included:

S61，利用传感器测得任意速度的桥梁车致响应与步骤S55模拟的相应速度形函数响应矩阵

Figure BDA0003856907630000053
进行求逆，通过下式获得形函数系数
Figure BDA0003856907630000054
S61, using the sensor to measure the vehicle-induced response of the bridge at any speed and the corresponding speed shape function response matrix simulated in step S55
Figure BDA0003856907630000053
Carry out the inversion, and obtain the shape function coefficient by the following formula
Figure BDA0003856907630000054

Figure BDA0003856907630000055
Figure BDA0003856907630000055

其中：

Figure BDA0003856907630000056
表示任意速度车致响应。in:
Figure BDA0003856907630000056
Indicates the response of any speed car.

所述步骤S7中，包括以下步骤：In described step S7, comprise the following steps:

S71，形函数

Figure BDA0003856907630000057
是对桥梁脉冲激励的离散化表示，且各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同。因此任意速度下的形函数
Figure BDA0003856907630000058
均可由初始速度v0下的
Figure BDA0003856907630000059
通过spline()插值过程获得。S71, Shape functions
Figure BDA0003856907630000057
is a discretized representation of bridge impulse excitation, and each time point x i is independent of each other, so the influence of different speeds v on the time history is only the difference in the length of the unit time history. Therefore the shape function at any speed
Figure BDA0003856907630000058
can be obtained from the initial velocity v 0
Figure BDA0003856907630000059
Obtained by the spline() interpolation process.

S72，将形函数系数

Figure BDA00038569076300000510
代入下式，即可识别出未知桥梁荷载，即：S72, the shape function coefficient
Figure BDA00038569076300000510
Substituting the following formula, the unknown bridge load can be identified, namely:

Figure BDA00038569076300000511
Figure BDA00038569076300000511

其中：

Figure BDA00038569076300000512
为形函数系数、
Figure BDA00038569076300000513
为相应速度下的形函数矩阵、
Figure BDA00038569076300000514
为未知荷载。in:
Figure BDA00038569076300000512
is the shape function coefficient,
Figure BDA00038569076300000513
is the shape function matrix at the corresponding speed,
Figure BDA00038569076300000514
is an unknown load.

与现有技术相比，本发明的有益效果为：Compared with prior art, the beneficial effect of the present invention is:

1.本发明考虑了桥梁坡度变化，并针对不同速度的移动荷载，提出了自适应形函数响应矩阵，针对不同速度荷载在不同坡度桥梁上的行驶时的模拟精度，从而保障形函数响应矩阵的的准确性，可以较高的时效性识别不同类型、不同速度的桥梁荷载，为桥梁健康监测的后续分析工作提供依据。1. The present invention considers the slope change of the bridge, and proposes an adaptive shape function response matrix for moving loads of different speeds, aiming at the simulation accuracy of different speed loads when driving on bridges with different slopes, thereby ensuring the shape function response matrix It can identify different types of bridge loads at different speeds with high timeliness, and provide a basis for subsequent analysis of bridge health monitoring.

2.传统的荷载形函数方法需计算桥梁与荷载各接触点的脉冲响应，且该脉冲响应仅适用于特定速度、行驶时间下的识别过程，例如在速度v＝50，时间t＝3s条件下，脉冲响应矩阵维度为60×151,而在速度v＝40，时间t＝2条件下，脉冲响应矩阵维度为40×101，即在不同行驶条件下脉冲响应矩阵均需重新计算，计算成本巨大。本专利分析了多个识别过程推导出荷载形函数的时空分布规律，重新构造时空自适应形函数响应矩阵，利用预构的基函数数据库的自适应变换便可得到上述两种情况的形函数矩阵，计算效率约提升80％。2. The traditional load shape function method needs to calculate the impulse response of each contact point between the bridge and the load, and the impulse response is only suitable for the identification process at a specific speed and travel time, for example, under the condition of speed v=50 and time t=3s , the dimension of the impulse response matrix is 60×151, and under the conditions of speed v=40 and time t=2, the dimension of the impulse response matrix is 40×101, that is, the impulse response matrix needs to be recalculated under different driving conditions, and the calculation cost is huge . This patent analyzes multiple identification processes to derive the space-time distribution of the load shape function, reconstructs the space-time adaptive shape function response matrix, and uses the adaptive transformation of the pre-configured basis function database to obtain the shape function matrix of the above two cases , and the calculation efficiency is increased by about 80%.

附图说明Description of drawings

附图用来提供对本发明的进一步理解，并且构成说明书的一部分，与本发明的实施例一起用于解释本发明，并不构成对本发明的限制。The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the description, and are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention.

图1为本发明实施例的不等跨连续梁桥模型示意图。Fig. 1 is a schematic diagram of a model of a continuous girder bridge with unequal spans according to an embodiment of the present invention.

图2为本发明计算识别流程示意图。Fig. 2 is a schematic diagram of the calculation and identification process of the present invention.

图3为本发明实施例的两次识别荷载结果示意图，其中：a表示：在v＝55km/h、t＝2s条件下，本方法的识别荷载结果示意图，b表示：在v＝65km/h、t＝3s条件下，本方法的识别荷载结果示意图。Fig. 3 is the schematic diagram of twice identification load results of the embodiment of the present invention, wherein: a represents: under v=55km/h, t=2s condition, the identification load result schematic diagram of this method, b represents: at v=65km/h , Under the condition of t=3s, the schematic diagram of the identification load result of this method.

其中，附图标记为：1、桥梁的第一跨；2、桥梁的第二跨；3、桥梁的第三跨；4、桥梁的第四跨。Wherein, reference signs are: 1, the first span of the bridge; 2, the second span of the bridge; 3, the third span of the bridge; 4, the fourth span of the bridge.

具体实施方式detailed description

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。当然，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

实施例1Example 1

结合图1和图2，以四跨桥为例，该桥梁由桥梁的第一跨1、桥梁的第二跨2、桥梁的第三跨3、桥梁的第四跨4顺次连接。一种利用时空自适应形函数响应矩阵识别移动荷载的方法，包括以下步骤：Combining Figures 1 and 2, taking a four-span bridge as an example, the bridge is sequentially connected by the first span 1 of the bridge, the second span 2 of the bridge, the third span 3 of the bridge, and the fourth span 4 of the bridge. A method for identifying moving loads using a space-time adaptive shape function response matrix comprising the steps of:

S1：通过传感器测得桥梁的车致响应信号；S1: The vehicle-induced response signal of the bridge is measured by the sensor;

S2：基于响应信号的频域分析确定形函数的步长和数量；S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal;

S3：建立形函数对应不同桥梁坡度的空间分布规律，形成空间自适应形函数；S3: Establish the spatial distribution of the shape function corresponding to different bridge slopes to form a space adaptive shape function;

S4：将指定速度的空间自适应形函数作为激励施加在桥梁上模拟其响应矩阵：基矩阵；S4: Apply the space-adaptive shape function of specified speed as excitation to the bridge to simulate its response matrix: basis matrix;

S5：建立基矩阵对应不同速度车载的时空分布规律，基于基矩阵快速创建任意速度荷载的自适应形函数响应矩阵；S5: Establish the base matrix corresponding to the time-space distribution of vehicles at different speeds, and quickly create an adaptive shape function response matrix for any speed load based on the base matrix;

S6：通过任意速度车致响应与自适应形函数响应矩阵求逆获得形函数系数；S6: Obtain the shape function coefficient by inverting the vehicle-induced response at any speed and the adaptive shape function response matrix;

S7：利用形函数与相应的形函数系数拟合荷载，从而识别出任意速度下的车载。S7: Use the shape function and the corresponding shape function coefficient to fit the load, so as to identify the vehicle at any speed.

所述步骤S1中，包括以下步骤：In the step S1, the following steps are included:

S11：通过应变、加速度、动挠度等传感器测取桥梁的任意速度车致响应

Figure BDA0003856907630000071
S11: Measuring the vehicle-induced response of the bridge at any speed through sensors such as strain, acceleration, and dynamic deflection
Figure BDA0003856907630000071

所述步骤S2中，包括以下步骤：In the step S2, the following steps are included:

S21，形函数的频率可由下式计算得到：S21, the frequency of the shape function can be calculated by the following formula:

Figure BDA0003856907630000081
Figure BDA0003856907630000081

其中fLSF为形函数频率，fs为采样频率，l为截断形函数的单元步长，该步长与形函数个数m存在以下关系，其中T为总采样数：where f LSF is the shape function frequency, f s is the sampling frequency, and l is the unit step size of the truncated shape function, which has the following relationship with the number m of shape functions, where T is the total number of samples:

T＝l×m (2)。T=l×m (2).

所述步骤S3中，包括以下步骤：In the step S3, the following steps are included:

S31：对于从任意起点(x0，y0，z0),以速度v0(km/h)行驶t0(s)的移动荷载，其通过的桥梁截面(x，y，z)用如下竖曲线模型拟合，即形函数的空间分布规律：S31: For a moving load traveling t 0 (s) at speed v 0 (km/h) from any starting point (x 0 , y 0 , z 0 ), the bridge section (x, y, z) it passes through is used as follows Vertical curve model fitting, that is, the spatial distribution of shape functions:

Figure BDA0003856907630000082
Figure BDA0003856907630000082

其中α为桥梁一端纵坡度，β为桥梁一端纵坡度，m1为桥梁竖曲线起点，m2为桥梁竖曲线终点，xm为变坡点，i为路拱横坡度，R是桥梁竖曲线半径。Where α is the longitudinal slope at one end of the bridge, β is the longitudinal slope at one end of the bridge, m 1 is the starting point of the vertical curve of the bridge, m 2 is the end point of the vertical curve of the bridge, x m is the slope change point, i is the transverse slope of the road arch, and R is the vertical curve of the bridge radius.

S32：利用S31中的空间分布律，形函数可施加于任何坡度的桥梁上，形成空间自适应形函数激励。S32: Utilizing the spatial distribution law in S31, the shape function can be applied to bridges with any slope to form a space-adaptive shape function excitation.

所述步骤S4中，包括以下步骤：In described step S4, comprise the following steps:

S41：将中位速度(一般为20m/s)的空间自适应形函数激励施加于桥梁上模拟其形函数响应矩阵，即基矩阵

Figure BDA0003856907630000083
S41: Apply the space-adaptive shape function excitation of the median velocity (generally 20m/s) to the bridge to simulate its shape function response matrix, namely the basis matrix
Figure BDA0003856907630000083

所述步骤S5中，包括以下步骤：In described step S5, comprise the following steps:

S51：基矩阵本质上为空间自适应形函数在不同时间点xi下对桥梁的作用效果，对于整个时间历程内fs×t+1个时间点xi，各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同，因此任意速度下的响应数据LR均可由基响应矩阵通过插值方法获得S51: The basis matrix is essentially the effect of the space-adaptive shape function on the bridge at different time points x i . For f s ×t+1 time points x i in the entire time course , the mutual independent, the influence of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L R at any speed can be obtained from the base response matrix by interpolation method

S52，由于各时间点xi之间相互独立，对于不同行驶时间t，其对于时间历程影响仅表现为包含时间点xi的多少，即需要插值的次数；S52, because each time point x i is independent of each other, for different travel times t, its influence on the time history is only shown as the number of time points x i included, that is, the number of interpolation times required;

S53，建立基矩阵的时间分布规律，定义三次样条插值过程spline()，其函数如下：S53, establish the time distribution law of the base matrix, define the cubic spline interpolation process spline (), its function is as follows:

对于fs×t+1个时间点，将整个时间历程分成fs×t＝n段，在每个区间内构造一个三次函数，共n段函数，其构造形式如下：For f s ×t+1 time point, divide the whole time course into f s ×t=n segments, construct a cubic function in each interval, a total of n segment functions, and its construction form is as follows:

Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3，i＝0，1，...，n-1 (4)S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , i=0, 1, . . . , n-1 (4)

其中：每个xi对应fs×t+1个时间点，Si(xi)为xi在三次函数上对应的因变量；ai、bi、ci、di为三次函数的拟合系数。Among them: each x i corresponds to f s ×t+1 time points, S i ( xi ) is the dependent variable corresponding to x i on the cubic function; a i , b i , c i , d i are the cubic function fit coefficient.

根据三次样条函数每个分段函数之间的衔接需求，即设定求解条件如下：According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows:

Figure BDA0003856907630000091
Figure BDA0003856907630000091

其中：li表示基矩阵

Figure BDA0003856907630000092
矩阵中的各个离散数据；条件1保证三次样条函数穿过所有已知li点；条件2保证三次样条函数在所有xi节点处连续；条件3保证三次样条函数在所有xi节点处一阶导数连续；条件4保证三次样条函数在所有xi节点处二阶导数连续，Among them: l i represents the basis matrix
Figure BDA0003856907630000092
Each discrete data in the matrix; condition 1 ensures that the cubic spline function passes through all known l i points; condition 2 ensures that the cubic spline function is continuous at all x i nodes; condition 3 ensures that the cubic spline function passes through all x i nodes The first-order derivative is continuous; condition 4 ensures that the second-order derivative of the cubic spline function is continuous at all x i nodes,

并附加自由边界条件如下：And additional free boundary conditions are as follows:

S″0(x0)＝0，S″n-1(xn)＝0 (6)S″ 0 (x 0 )=0, S″ n-1 (x n )=0 (6)

其中：x0、xn为时间历程区间两端点，自由边界条件表示为曲线的摇摆最小。Among them: x 0 and x n are the two ends of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve.

S54，对于n段时间历程，每段有4个方程组，共4n个线性方程组进行求解，求得每一段区间的三次样条函数Si(x)；S54, for n sections of time history, each section has 4 equations, a total of 4n linear equations are solved, and the cubic spline function S i (x) of each interval is obtained;

S55，从起点以任意速度v(km/h)行驶t(s)，其时间历程点x′i与初始速度v0存在如下关系：S55, travel t(s) at any speed v(km/h) from the starting point, the time history point x′ i has the following relationship with the initial speed v0 :

Figure BDA0003856907630000101
Figure BDA0003856907630000101

将新时间历程点x′i代入三次样条插值过程spline()，即可求得任意速度下的基矩阵

Figure BDA0003856907630000102
Substituting the new time history point x′ i into the cubic spline interpolation process spline(), the basis matrix at any speed can be obtained
Figure BDA0003856907630000102

所述步骤S6中，包括以下步骤：In the step S6, the following steps are included:

S61，利用传感器测得任意速度的桥梁车致响应与步骤S55模拟的相应速度形函数响应矩阵

Figure BDA0003856907630000103
进行求逆，通过下式获得形函数系数
Figure BDA0003856907630000104
S61, using the sensor to measure the vehicle-induced response of the bridge at any speed and the corresponding speed shape function response matrix simulated in step S55
Figure BDA0003856907630000103
Carry out the inversion, and obtain the shape function coefficient by the following formula
Figure BDA0003856907630000104

Figure BDA0003856907630000105
Figure BDA0003856907630000105

其中：

Figure BDA0003856907630000106
表示任意速度车致响应。in:
Figure BDA0003856907630000106
Indicates the response of any speed car.

所述步骤S7中，包括以下步骤：In described step S7, comprise the following steps:

S71，形函数

Figure BDA0003856907630000107
是对桥梁脉冲激励的离散化表示，且各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同。因此任意速度下的形函数
Figure BDA0003856907630000108
均可由初始速度v0下的
Figure BDA0003856907630000109
通过spline()插值过程获得。S71, Shape functions
Figure BDA0003856907630000107
is a discretized representation of bridge impulse excitation, and each time point x i is independent of each other, so the influence of different speeds v on the time history is only the difference in the length of the unit time history. Therefore the shape function at any speed
Figure BDA0003856907630000108
can be obtained from the initial velocity v 0
Figure BDA0003856907630000109
Obtained by the spline() interpolation process.

S72，将形函数系数

Figure BDA00038569076300001010
代入下式，即可识别出未知桥梁荷载，即：S72, the shape function coefficient
Figure BDA00038569076300001010
Substituting the following formula, the unknown bridge load can be identified, namely:

Figure BDA00038569076300001011
Figure BDA00038569076300001011

其中：

Figure BDA00038569076300001012
为形函数系数、
Figure BDA00038569076300001013
为相应速度下的形函数矩阵、
Figure BDA00038569076300001014
为未知荷载in:
Figure BDA00038569076300001012
is the shape function coefficient,
Figure BDA00038569076300001013
is the shape function matrix at the corresponding speed,
Figure BDA00038569076300001014
for the unknown load

具体地，移动荷载P＝320KN，在跨长384m长的连续梁桥上以速度v＝55m/s，和v＝65m/s两次不同速度下，相同行驶时间t＝2s沿纵轴线从左至右驶过桥面。动挠度响应输出点布置于桥梁的第一跨1与桥梁的第二跨2交界处，输出频率为50Hz。Specifically, the moving load P=320KN, on a continuous girder bridge with a span length of 384m at two different speeds of v=55m/s and v=65m/s, the same travel time t=2s along the longitudinal axis from the left Go right across the bridge. The output point of the dynamic deflection response is arranged at the junction of the first span 1 of the bridge and the second span 2 of the bridge, and the output frequency is 50Hz.

本专利所述的识别移动荷载的方法具体实施方式如下：The specific implementation of the method for identifying moving loads described in this patent is as follows:

步骤1：以速度v＝55m/s v0(km/h)行驶、时间t0(s)移动荷载的反演过程作为基本数据，获得测点响应矩阵

Figure BDA0003856907630000111
Step 1: Take the inversion process of moving load at speed v=55m/sv 0 (km/h) and time t 0 (s) as the basic data to obtain the response matrix of the measuring point
Figure BDA0003856907630000111

步骤2：通过结构振动响应的频域分析确定形函数

Figure BDA0003856907630000112
的频率，从而确定形函数的步长与数量。Step 2: Determine the shape function by frequency domain analysis of the structure's vibration response
Figure BDA0003856907630000112
, so as to determine the step size and number of shape functions.

步骤3：将形函数作为脉冲矩阵施加在桥梁上获取形函数响应矩阵

Figure BDA0003856907630000113
(基矩阵)。Step 3: Apply the shape function to the bridge as an impulse matrix to obtain the shape function response matrix
Figure BDA0003856907630000113
(basis matrix).

步骤4：对测点响应矩阵

Figure BDA0003856907630000114
形函数响应矩阵
Figure BDA0003856907630000115
以及形函数矩阵
Figure BDA0003856907630000116
进行插值，获得下v＝65m/s的
Figure BDA0003856907630000117
Step 4: Response matrix to measuring points
Figure BDA0003856907630000114
shape function response matrix
Figure BDA0003856907630000115
and the shape function matrix
Figure BDA0003856907630000116
Perform interpolation to obtain the following v=65m/s
Figure BDA0003856907630000117

步骤5：通过

Figure BDA0003856907630000118
求得拟合系数
Figure BDA0003856907630000119
Step 5: Pass
Figure BDA0003856907630000118
Find the fit coefficient
Figure BDA0003856907630000119

步骤6：用形函数

Figure BDA00038569076300001110
与拟合系数
Figure BDA00038569076300001111
重构移动荷载。Step 6: Use shape functions
Figure BDA00038569076300001110
and fitting coefficient
Figure BDA00038569076300001111
Restructure moving loads.

其识别结果如图3，移动荷载为虚线所示，识别结果为实线所示，各工况识别结果与移动荷载有较高的吻合度，说明本方法能有效地识别未知荷载。The recognition results are shown in Figure 3. The moving load is shown by the dotted line, and the recognition result is shown by the solid line. The recognition results of each working condition have a high degree of agreement with the moving load, indicating that this method can effectively identify unknown loads.

以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (8)

1.一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，包括以下步骤：1. A method utilizing a space-time adaptive shape function response matrix to identify a moving load, characterized in that, comprising the following steps: S1：通过传感器测得桥梁的车致响应信号；S1: The vehicle-induced response signal of the bridge is measured by the sensor; S2：基于响应信号的频域分析确定形函数的步长和数量；S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal; S3：建立形函数对应不同桥梁坡度的空间分布规律，形成空间自适应形函数；S3: Establish the spatial distribution of the shape function corresponding to different bridge slopes to form a space adaptive shape function; S4：将指定速度的空间自适应形函数作为激励施加在桥梁上模拟其响应矩阵；S4: Apply the space-adaptive shape function of specified velocity as excitation to the bridge to simulate its response matrix; S5：建立基矩阵对应不同速度车载的时空分布规律，基于基矩阵快速创建任意速度荷载的自适应形函数响应矩阵；S5: Establish the base matrix corresponding to the time-space distribution of vehicles at different speeds, and quickly create an adaptive shape function response matrix for any speed load based on the base matrix; S6：通过任意速度车致响应与自适应形函数响应矩阵求逆获得形函数系数；S6: Obtain the shape function coefficient by inverting the vehicle-induced response at any speed and the adaptive shape function response matrix; S7：利用形函数与相应的形函数系数拟合荷载，从而识别出任意速度下的车载。S7: Use the shape function and the corresponding shape function coefficient to fit the load, so as to identify the vehicle at any speed. 2.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S1中，包括以下步骤：2. A method for identifying moving loads utilizing a space-time adaptive shape function response matrix according to claim 1, characterized in that, in the step S1, comprising the following steps: S11：通过应变、加速度、动挠度传感器测取桥梁的任意速度车致响应
Figure FDA0003856907620000011
S11: Measuring the vehicle-induced response of the bridge at any speed through strain, acceleration, and dynamic deflection sensors
Figure FDA0003856907620000011
 3.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S2中，包括以下步骤：3. A method of utilizing a space-time adaptive shape function response matrix to identify moving loads according to claim 1, characterized in that, in the step S2, comprising the following steps: S21，形函数的频率可由下式计算得到：S21, the frequency of the shape function can be calculated by the following formula:
Figure FDA0003856907620000012
Figure FDA0003856907620000012
 其中fLSF为形函数频率，fs为采样频率，l为截断形函数的单元步长，该步长与形函数个数m存在以下关系，其中T为总采样数：where f LSF is the shape function frequency, f s is the sampling frequency, and l is the unit step size of the truncated shape function, which has the following relationship with the number m of shape functions, where T is the total number of samples: T＝l×m (2)。T=l×m (2). 4.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S3中，包括以下步骤：4. A method of utilizing a space-time adaptive shape function response matrix to identify a moving load according to claim 1, characterized in that, in the step S3, comprising the following steps: S31：对于从任意起点(x0，y0，z0),以速度v0(km/h)行驶t0(s)的移动荷载，其通过的桥梁截面(x，y，z)用如下竖曲线模型拟合，即形函数的空间分布规律：S31: For a moving load traveling t 0 (s) at speed v 0 (km/h) from any starting point (x 0 , y 0 , z 0 ), the bridge section (x, y, z) it passes through is used as follows Vertical curve model fitting, that is, the spatial distribution of shape functions:
Figure FDA0003856907620000021
Figure FDA0003856907620000021
 其中α为桥梁一端纵坡度，β为桥梁另一端纵坡度，m1为桥梁竖曲线起点，m2为桥梁竖曲线终点，xm为变坡点，i为路拱横坡度，R是桥梁竖曲线半径；Where α is the longitudinal slope at one end of the bridge, β is the longitudinal slope at the other end of the bridge, m 1 is the starting point of the vertical curve of the bridge, m 2 is the end point of the vertical curve of the bridge, x m is the slope change point, i is the transverse slope of the road arch, R is the vertical slope of the bridge curve radius; S32：利用S31中的空间分布律，形函数可施加于任何坡度的桥梁上，形成空间自适应形函数激励。S32: Utilizing the spatial distribution law in S31, the shape function can be applied to bridges with any slope to form a space-adaptive shape function excitation. 5.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S4中，包括以下步骤：5. A method of utilizing a space-time adaptive shape function response matrix to identify moving loads according to claim 1, characterized in that, in the step S4, comprising the following steps: S41：将中位速度的空间自适应形函数激励施加于桥梁上模拟其形函数响应矩阵，即基矩阵
Figure FDA0003856907620000022
S41: Apply the space-adaptive shape function excitation of the median velocity to the bridge to simulate its shape function response matrix, namely the basis matrix
Figure FDA0003856907620000022
 6.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S5中，包括以下步骤：6. A method of utilizing a space-time adaptive shape function response matrix to identify moving loads according to claim 1, characterized in that, in the step S5, comprising the following steps: S51：基矩阵本质上为空间自适应形函数在不同时间点xi下对桥梁的作用效果，对于整个时间历程内fs×t+1个时间点xi，各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同，因此任意速度下的响应数据LR均可由基响应矩阵通过插值方法获得；S51: The basis matrix is essentially the effect of the space-adaptive shape function on the bridge at different time points x i . For f s ×t+1 time points x i in the entire time course , the mutual independent, the influence of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L R at any speed can be obtained from the base response matrix by interpolation method; S52，由于各时间点xi之间相互独立，对于不同行驶时间t，其对于时间历程影响仅表现为包含时间点xi的多少，即需要插值的次数；S52, because each time point x i is independent of each other, for different travel times t, its influence on the time history is only shown as the number of time points x i included, that is, the number of interpolation times required; S53，建立基矩阵的时间分布规律，定义三次样条插值过程spline()，其函数如下：S53, establish the time distribution law of the base matrix, define the cubic spline interpolation process spline (), its function is as follows: 对于fs×t+1个时间点，将整个时间历程分成fs×t＝n段，在每个区间内构造一个三次函数，共n段函数，其构造形式如下：For f s ×t+1 time point, divide the whole time course into f s ×t=n segments, construct a cubic function in each interval, a total of n segment functions, and its construction form is as follows: Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3，i＝0，1，...，n-1 (4)S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 , i=0, 1, . . . , n-1 (4) 其中：每个xi对应fs×t+1个时间点，Si(xi)为xi在三次函数上对应的因变量；ai、bi、ci、di为三次函数的拟合系数；Among them: each x i corresponds to f s ×t+1 time points, S i ( xi ) is the dependent variable corresponding to x i on the cubic function; a i , b i , c i , d i are the cubic function fit coefficient; 根据三次样条函数每个分段函数之间的衔接需求，即设定求解条件如下：According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows:
Figure FDA0003856907620000031
Figure FDA0003856907620000031
 其中：li表示基矩阵
Figure FDA0003856907620000032
矩阵中的各个离散数据；条件1保证三次样条函数穿过所有已知li点；条件2保证三次样条函数在所有xi节点处连续；条件3保证三次样条函数在所有xi节点处一阶导数连续；条件4保证三次样条函数在所有xi节点处二阶导数连续，Among them: l i represents the basis matrix
Figure FDA0003856907620000032
Each discrete data in the matrix; condition 1 ensures that the cubic spline function passes through all known l i points; condition 2 ensures that the cubic spline function is continuous at all x i nodes; condition 3 ensures that the cubic spline function passes through all x i nodes The first-order derivative is continuous; condition 4 ensures that the second-order derivative of the cubic spline function is continuous at all x i nodes, 并附加自由边界条件如下：And additional free boundary conditions are as follows: S″0(x0)＝0，S″n-1(xn)＝0 (6)S″ 0 (x0) = 0, S″ n-1 (x n ) = 0 (6) 其中：x0、xn为时间历程区间两端点，自由边界条件表示为曲线的摇摆最小；Among them: x 0 and x n are the two ends of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve; S54，对于n段时间历程，每段有4个方程组，共4n个线性方程组进行求解，求得每一段区间的三次样条函数Si(x)；S54, for n sections of time history, each section has 4 equations, a total of 4n linear equations are solved, and the cubic spline function S i (x) of each interval is obtained; S55，从起点以任意速度v(km/h)行驶t(s)，其时间历程点x′i与初始速度v0存在如下关系：S55, travel t(s) at any speed v(km/h) from the starting point, the time history point x′ i has the following relationship with the initial speed v0 :
Figure FDA0003856907620000041
Figure FDA0003856907620000041
 将新时间历程点x′i代入三次样条插值过程spline()，即可求得任意速度下的基矩阵
Figure FDA0003856907620000042
Substituting the new time history point x′ i into the cubic spline interpolation process spline(), the basis matrix at any speed can be obtained
Figure FDA0003856907620000042
 7.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移动荷载的方法，其特征在于，所述步骤S6中，包括以下步骤：7. A method of utilizing a space-time adaptive shape function response matrix to identify moving loads according to claim 1, characterized in that, in the step S6, comprising the following steps: S61，利用传感器测得任意速度的桥梁车致响应与步骤S55模拟的相应速度形函数响应矩阵
Figure FDA0003856907620000043
进行求逆，通过下式获得形函数系数
Figure FDA0003856907620000044
S61, using the sensor to measure the vehicle-induced response of the bridge at any speed and the corresponding speed shape function response matrix simulated in step S55
Figure FDA0003856907620000043
Carry out the inversion, and obtain the shape function coefficient by the following formula
Figure FDA0003856907620000044
Figure FDA0003856907620000045
Figure FDA0003856907620000045
 其中：
Figure FDA0003856907620000046
表示任意速度车致响应。in:
Figure FDA0003856907620000046
Indicates the response of any speed car. 8.根据权利要求1所述的一种利用时空自适应形函数响应矩阵识别移荷载的方法，其特征在于，所述步骤S7中，包括以下步骤：8. A method of utilizing the space-time adaptive shape function response matrix to identify shifting loads according to claim 1, characterized in that, in the step S7, comprising the following steps: S71，形函数
Figure FDA0003856907620000047
是对桥梁脉冲激励的离散化表示，且各时间点xi之间相互独立，则不同速度v对时间历程的影响仅为单位时间历程长度的不同；因此任意速度下的形函数
Figure FDA0003856907620000048
均可由初始速度v0下的
Figure FDA0003856907620000049
通过spline()插值过程获得；S71, Shape functions
Figure FDA0003856907620000047
is the discretized representation of bridge impulse excitation, and each time point x i is independent of each other, then the influence of different speeds v on the time history is only the difference in the length of the unit time history; therefore, the shape function at any speed
Figure FDA0003856907620000048
can be obtained from the initial velocity v 0
Figure FDA0003856907620000049
Obtained through the spline() interpolation process; S82，将形函数系数
Figure FDA00038569076200000410
代入下式，即可识别出未知桥梁荷载，即：S82, the shape function coefficient
Figure FDA00038569076200000410
Substituting the following formula, the unknown bridge load can be identified, namely:
Figure FDA00038569076200000411
Figure FDA00038569076200000411
 其中：
Figure FDA00038569076200000412
为形函数系数、
Figure FDA00038569076200000413
为相应速度下的形函数矩阵、
Figure FDA00038569076200000414
为未知荷载。in:
Figure FDA00038569076200000412
is the shape function coefficient,
Figure FDA00038569076200000413
is the shape function matrix at the corresponding speed,
Figure FDA00038569076200000414
is an unknown load.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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