CN110017929B - Ship-bridge collision load and damage synchronous identification method based on substructure sensitivity analysis - Google Patents

Ship-bridge collision load and damage synchronous identification method based on substructure sensitivity analysis Download PDF

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CN110017929B
CN110017929B CN201910182384.6A CN201910182384A CN110017929B CN 110017929 B CN110017929 B CN 110017929B CN 201910182384 A CN201910182384 A CN 201910182384A CN 110017929 B CN110017929 B CN 110017929B
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bridge
coefficient
structural
acceleration
ship
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CN110017929A (en
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翁顺
朱宏平
李润玲
李富年
曾敏
瞿国钊
余兴胜
殷鹏程
刘凌肖
韩贻坤
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/0052—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to impact
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
    • G01M5/0008—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings of bridges
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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    • G01M7/08—Shock-testing

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Abstract

The invention discloses a ship bridge collision load and damage synchronous identification method based on substructure sensitivity analysis, and belongs to the field of civil engineering large-scale structure detection. The method comprises the following steps: firstly, acquiring real-time data of an acceleration sensor arranged in an actual engineering structure, judging whether a ship bridge-collision event occurs in real time by using an acceleration root-mean-square control chart, and if the ship bridge-collision event occurs, positioning by using the acceleration root-mean-square; when the ship bridge collision event is judged to occur by using the root mean square acceleration, the ship bridge collision load and damage are synchronously identified by using a model correction method based on sensitivity analysis. The method synchronously identifies the load and the damage of the ship hitting the bridge through the model correction method, avoids the problem that a large amount of time is consumed by utilizing a large amount of instruments to identify the damage after an accident occurs, can greatly improve the efficiency and the precision of identifying the load and the damage of the ship hitting the bridge, has strong practicability, and plays an important role in bridge health monitoring.

Description

Ship-bridge collision load and damage synchronous identification method based on substructure sensitivity analysis
Technical Field
The invention belongs to the field of civil engineering large structure detection, relates to a ship bridge collision load and damage synchronous identification method based on substructure sensitivity analysis, and more particularly relates to a ship bridge collision load and damage synchronous identification method based on a sensitivity model correction method.
Background
With the development of the scientific technology of ships and the expansion of the world shipping volume, river-crossing bridges are more and more constructed, and meanwhile, the tonnage of the ship is sharply increased, the shipping speed is improved, and the shipping is more and more crowded. When a ship runs in a navigable river, a ship-bridge collision accident is easily caused when the ship is steered improperly or is interfered by external factors such as wind, current, wave and the like, the bridge is damaged by light persons, and the bridge collapses by heavy persons, so the ship-bridge collision is a problem which cannot be ignored. In order to guarantee the safety and the durability of a bridge body structure, ship collision monitoring and damage assessment are carried out on a bridge, and a method for timely and effectively recognizing ship and bridge collision and recognizing collision load and damage after collision is explored.
In the dynamic response test of the structure, the acceleration response signal has the advantages of convenience in acquisition, high precision, relatively mature technology and the like, so that the acceleration response signal is directly used as the damage identification index to prevent the damage information of the structure from being lost easily. In structural health monitoring, the sensors can not be arranged on all degrees of freedom according to actual conditions, so that the sensors can only be arranged at partial degrees of freedom to obtain multipoint dynamic response output of a structure, but each sensor can only describe a measured object in a certain range from one aspect, and cannot provide comprehensive, accurate and correct information. The Root Mean Square (RMS) of the structural acceleration is an important quantity value of the statistical characteristic of the structural dynamic response, reflects the vibration intensity and energy of the signal, and can be used as a characteristic value for measuring the vibration intensity of the whole structure. And combining a control map, judging that the ship bridge collision occurs to the structure when the root mean square of the acceleration of the measuring points exceeds the upper limit and the lower limit of the control map, and meanwhile, judging that the root mean square of the acceleration of each measuring point is the maximum near the collision position, so that the collision position can be obtained by judging the root mean square value of the acceleration of each measuring point.
The model correction method is a system identification method, vibration response data are obtained through tests, a stiffness matrix, a damping matrix and a mass matrix are correspondingly corrected to obtain a new matrix, the new matrix is matched with the actually measured vibration response data, and a more accurate finite element model can be obtained through analysis. Its ultimate goal is to make the vibrational response of the modified model as close as possible to the structural dynamic or static observed response data. The basic idea of model correction in the structural damage identification method is to adopt a specific vector expansion technology or a model polycondensation technology, successfully match the degree of freedom of an original model with a corrected model, and then evaluate the damage degree by comparing the difference between the degrees of freedom and the corrected model.
At present, the problem of identifying the load of a ship-bridge collision is rarely researched, and an existing method is to obtain the relation between impact force and voltage output by using an intelligent piezoelectric sensor, obtain voltage signals by using piezoelectric sensors at different positions and identify the impact force of the ship-bridge collision by using the relation between the impact force and the voltage output.
One existing approach is to propose equations that predict the loading and unloading durations based on the SDOF analytical model. And then, obtaining a bow deformation-time relation by using the SDOF analysis model and the bilinear force-deformation relation of the bow, thereby identifying the load of the ship colliding with the bridge.
Another existing method considers the power amplification effect and obtains a time history equation of loading time and ship deformation to identify the impact force of the bridge collision.
Structural damage identification is one of the keys of structural health monitoring, and belongs to the first category of structural dynamics inverse problem, namely, the change of inherent characteristics such as rigidity and mass of a system is acquired by knowing structural input and output information. At present, the problem of identifying damage of a ship colliding with a bridge is rarely researched.
One existing method is to utilize a static condensation method to eliminate rotational freedom to establish a mechanical model, and to provide a dynamic condensation method considering Rayleigh damping, so as to realize equivalent simplification of a finite element model of a more complex continuous beam bridge. And carrying out online damage identification on the continuous beam bridge extended Kalman filtering by using an excitation mode of generating free vibration by hammering.
Another existing method is to construct a numerical model of the bridge and obtain vibration data of the bridge before and after collision. And identifying the frequency and the vibration mode of the bridge by using a complex modal index function method, and identifying the damage by comparing the frequency and the vibration mode change of the bridge.
Loads acting on the bridge structure affect the operation process of the structure, and the health condition of the structure can be obtained in time through corresponding standard standards, so that the load identification problem is an important component of health monitoring. At present, researches on synchronous identification of load and damage of a ship-to-bridge collision are few, only one of the load and the damage can be identified in the method for identifying the load and the damage of the ship-to-bridge collision, if one of the load and the damage is known, an identification error is brought, and the method for synchronously identifying the load and the damage of the ship-to-bridge collision based on a sensitivity model correction method can effectively solve the problem.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a synchronous identification method of ship-bridge collision load and damage based on sensitivity model correction, which aims to judge the occurrence of a ship-bridge collision event in time and identify the load and the damage of the ship-bridge collision event in time when the ship-bridge collision occurs, thereby solving the technical problems of effectively judging whether the ship-bridge collision event occurs, effectively identifying the collision position and accurately identifying the collision load and the damage of a bridge body.
In order to achieve the above object, according to one aspect of the present invention, there is provided a ship bridge collision load and damage synchronous identification method based on substructure sensitivity analysis, comprising the steps of:
(1) taking bridge nodes as measuring points, obtaining real-time acceleration values at the actual bridge measuring points, calculating the root mean square of the acceleration at each measuring point, and if the root mean square of the acceleration at a certain measuring point exceeds a specified value, determining that a ship bridge collision event occurs at the measuring point;
(2) if the occurrence of the ship bridge collision event is judged, expressing unknown ship bridge collision load by using the Chebyshev orthogonal term, and expressing the overall rigidity of the structure by using the unit rigidity coefficient, thereby obtaining a structural motion equation of the bridge when the ship bridge collision event occurs, which is expressed by the Chebyshev orthogonal term and the unit rigidity coefficient;
(3) solving the structural motion equation obtained in the step (2) to obtain dynamic response including displacement, speed and acceleration at the structural node;
(4) calculating the difference between the dynamic response obtained by calculation and the actual dynamic response, and establishing a target function expression about the Chebyshev orthogonal term coefficient and the structural rigidity coefficient;
(5) calculating a sensitivity matrix of the structural dynamic response based on the Chebyshev orthogonal term coefficient and the unit stiffness coefficient, so that the target function in the step (4) is gradually reduced and converged;
(6) solving a Chebyshev orthogonal term coefficient and a structural rigidity coefficient, substituting the Chebyshev orthogonal term coefficient and the structural rigidity coefficient into the structural motion equation in the step (2) to obtain the load of the ship colliding with the bridge, and judging the damage degree of the bridge body according to the structural rigidity coefficient: the structural rigidity coefficient is less than 1, which indicates that the rigidity of the unit after collision is less than that of the unit before collision; the structural rigidity coefficient is greater than 1, which indicates that the rigidity of the unit after collision is greater than that of the unit before collision; a structural stiffness coefficient equal to 1 indicates that the post-crash cell stiffness is equal to the pre-crash cell stiffness.
Further, the step (1) further comprises the following sub-steps:
(1.1) installing an acceleration sensor on a structure, and obtaining acceleration time-course response at a node of the structure;
(1.2) calculating the root mean square of the acceleration at each measurement point, calculating the root mean square mean value mu and the standard deviation sigma of the acceleration under normal use,
(1.3) calculating the root mean square mean μ and the standard deviation σ of the acceleration using the Lauda criterion to obtain CL and the upper and lower control lines UCL, LCL, wherein,
CL＝μ
UCL＝μ+2σ
LCL＝μ-2σ
and when the root mean square of the acceleration of the measuring point exceeds the upper control line and the lower control line, judging that the ship bridge collision occurs, and obtaining the collision position when the root mean square of the acceleration at the collision position is the maximum.
Further, the step (2) further comprises the following sub-steps:
(2.1) constructing a motion equation of the bridge structure:
Figure BDA0001991684660000031
in the formula, M is a mass matrix, C is a damping matrix, K is a structural rigidity matrix, and x represents the displacement at a structural node;
Figure BDA0001991684660000041
representing the velocity at the node of the structure;
Figure BDA0001991684660000042
representing the acceleration at the structural node, F being the external load;
(2.2) expressing a certain external load F (t) by using a Chebyshev orthogonal term, which is expressed by the following formula:
Figure BDA0001991684660000043
in the formula, cmExpansion coefficient of mth orthogonal term of external load, Tm(t) is the mth orthogonal term of the external load, NmThe order is expanded for the orthogonal term of the external load;
Figure BDA0001991684660000044
in the formula, LeIs the length of the signal;
(2.3) assuming that the rigidity of the actual structure is equal to the rigidity of each unit multiplied by a rigidity coefficient, and then summing, and identifying the structural rigidity, namely converting the structural rigidity into the problem of identifying the rigidity coefficient of the unit; the overall structural stiffness K can be expressed as:
Figure BDA0001991684660000045
in the formula, ajIs the stiffness coefficient of the jth cell; n is a radical ofeIs the number of structural units;
Figure BDA0001991684660000046
represents the cell stiffness of the jth cell;
(2.4) obtaining the motion equation expressed by the Chebyshev orthogonal term according to the steps (2.1) to (2.3):
Figure BDA0001991684660000047
further, the step (3) further comprises the following sub-steps:
(3.1) setting the load acting time as t0Solving the motion equation obtained in step (2.4) to apply the load for time t0Divided into q equal parts with step length of
Figure BDA0001991684660000048
And accordingly gives a dynamic response x,
Figure BDA0001991684660000049
X (0) of,
Figure BDA00019916846600000410
And
Figure BDA00019916846600000411
(3.2) setting an integration constant:
Figure BDA00019916846600000412
Figure BDA0001991684660000051
wherein, Δ t is an integral step length, and the parameters γ and β are empirical parameters;
(3.3) construction of effective stiffness matrix
Figure BDA0001991684660000052
And calculating to obtain an inverse matrix
Figure BDA0001991684660000053
(3.4) calculating the payload for the first time step
Figure BDA0001991684660000054
Figure BDA0001991684660000055
Wherein, { F1Represents the load at the first time step;
(3.5) determining the displacement x (1) at the first time step:
Figure BDA0001991684660000056
(3.6) determining the acceleration at the first time step
Figure BDA0001991684660000057
And velocity
Figure BDA0001991684660000058
Figure BDA0001991684660000059
Figure BDA00019916846600000510
(3.7) repeating the steps (3.4) - (3.6) and calculating to the qth time step, thereby obtaining the acting time t of the whole structure0Internal dynamic response
Figure BDA00019916846600000511
Theoretical value of (Q)E。
Further, the step (4) further comprises the following sub-steps:
(4.1) calculation of the dynamic response from the actual measurement
Figure BDA00019916846600000512
Actual value of (Q)MAnd (4) calculating the theoretical value Q of the dynamic response in the step (3.7)EDifference Δ z of (a):
Δz＝QE(βu)-QM
wherein, Delta z is the difference value between the power response value obtained by actual measurement and the power response value obtained by calculation, QEFor calculated theoretical value, QMFor measuring the actual value obtained, QE(βu) Represents QETo relate to betauFunction of betau＝(cm aj) ' is a parameter vector to be identified;
(4.2) construction of the objective function g (. beta.)u)：
g(βu)＝∑(Δz)2＝∑(QE(βu)-QM)2。
Further, the step (5) further comprises the following sub-steps:
(5.1) respectively solving the coefficient c of the motion equation pair Chebyshev orthogonal term in the step (2.4)mAnd coefficient of structural stiffness ajThe partial derivatives of (A) are as follows:
Figure BDA0001991684660000061
in the formula
Figure BDA0001991684660000062
Coefficient of expansion c of orthogonal terms of structural dynamic response to external load, respectivelymThe sensitivity of (a) to (b) is,
Figure BDA0001991684660000063
respectively a structural dynamic response to a structural rigidity coefficient ajThe sensitivity of (c);
(5.2) solving the equation set in the step (5.1) to obtain a sensitivity matrix S (beta)u)：
Figure BDA0001991684660000064
(5.3) expressing the difference Δ z of step (4.1) using Taylor expansion as:
Δz＝S(βu)·Δβu
in the formula,. DELTA.beta.uIs a parameter vector beta to be identifieduThe variation of (d) can be solved by using the least square method:
Δβ＝[ST(β)S(β)]-1ST(β)Δz
updating the sensitivity matrix S (beta) by iterationu) Thus, Δ z and Δ β are updated so that the objective function g (β) of step (4.2)u) And continuously converging to obtain the objective function value.
Further, the step (6) further comprises the following sub-steps:
(6.1) obtaining the coefficient c of the Chebyshev orthogonal term at the moment according to the objective function value obtained in the step (5.3)mAnd a unit stiffness coefficient ajCoefficient c of the Chebyshev orthogonal termmSubstituting the equation in the step (2.2) to obtain the ship bridge collision load;
(6.2) coefficient of stiffness a according to structural unitjObtaining the damage ratio of the structural unit, thereby judging the damage of the pontic: a isjRepresenting the ratio of cell stiffness before and after a collision, ajLess than 1, meaning that the post-crash cell stiffness is less than the pre-crash cell stiffness; when a isjGreater than 1 indicates that the stiffness of the cell after impact is greater than the stiffness of the cell before impact, when ajEqual to 1 indicates that the post-crash cell stiffness is equal to the pre-crash cell stiffness.
Generally, compared with the prior art, the technical scheme of the invention has the advantages that the sensitivity model correction method is adopted to synchronously identify the ship bridge collision load and damage, so that the following beneficial effects can be obtained:
1. the efficiency of ship collision bridge load and damage recognition is improved: the identification method based on the sensitivity analysis of the substructure is used for synchronous identification, so that the calculation time is shortened compared with a method for respectively identifying the load and the damage;
2. the accuracy of identifying the load and damage of the ship colliding with the bridge is improved: by utilizing the synchronous load and damage identification method based on the sensitivity analysis of the substructure, the intermediate error of respectively identifying the load and the damage is effectively reduced, and the identification precision is improved;
3. according to the invention, through measuring the acceleration change of the point, whether the collision occurs or not can be accurately judged, and the collision position can be accurately identified, so that the ship bridge collision event can be effectively monitored, and the position of the ship bridge collision event can be timely positioned.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic view of a pool river bridge;
3(a) -3 (e) are schematic diagrams of finite element models of the structure of each part of the pool river bridge and the whole body;
FIG. 4 is a schematic diagram of an arrangement of acceleration sensors on a pool bridge;
FIG. 5(a) is a root-mean-square control diagram of the acceleration at the measurement point 1;
FIG. 5(b) is a root-mean-square control diagram of the acceleration at the measurement point 2;
FIG. 5(c) is a RMS control map of acceleration at point 3;
FIG. 5(d) is a RMS control map of acceleration at point 4;
FIG. 5(e) is a root mean square control diagram of the acceleration at the measurement point 5;
FIG. 5(f) is a root mean square control diagram of the acceleration at point 6;
FIG. 5(g) is a root mean square control diagram of the acceleration at point 7;
FIG. 5(h) is a root-mean-square control diagram of the acceleration at point 8;
FIG. 5(i) is a root mean square control map of the acceleration at point 9;
in fig. 5(a) -5 (i), the three straight lines are UCL, μ and LCL from top to bottom, respectively, and the curves represent the root mean square of the acceleration of the corresponding measuring point;
FIG. 6 is a hypothetical impact load time course curve;
FIG. 7 shows structural damage identified by a ship bridge collision load and damage synchronous identification method based on substructure sensitivity analysis;
FIG. 8 shows the ship-to-bridge load identified by the synchronous identification method of ship-to-bridge load and damage based on the substructure sensitivity analysis.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The method comprises the steps of monitoring whether a ship bridge collision event occurs in real time by using the root mean square acceleration, and positioning the collision position. Secondly, when a ship bridge collision event occurs, ship bridge collision load and damage are identified by using a substructure sensitivity analysis-based method. Unknown load and structural rigidity are respectively expressed by a Chebyshev orthogonal term and a structural rigidity coefficient, and the Chebyshev orthogonal term coefficient and the structural rigidity coefficient are iteratively identified by using a substructure sensitivity analysis-based method, so that the load and damage of a ship colliding with a bridge are finally solved.
In order to achieve the purpose, the invention provides a ship bridge collision load and damage synchronous identification method based on sensitivity model correction, which comprises the following steps:
(1) the method comprises the following steps of obtaining real-time acceleration values at actual bridge measuring points, calculating the root mean square of the acceleration at each measuring point, and judging whether a ship bridge collision event occurs or not by combining a control chart, wherein the specific process comprises the following steps:
(1.1) installing an acceleration sensor on a structure, and obtaining acceleration time-course response at a node of the structure;
(1.2) calculating the root mean square of the acceleration at each measuring point, calculating the mean value mu and the standard deviation of the root mean square of the acceleration under the normal use condition by utilizing the Lauda criterion to obtain a control chart center line CL and upper and lower control lines UCL and LCL, judging that a collision occurs when the root mean square of the acceleration of the measuring point exceeds the upper and lower control lines, and judging the collision position according to the principle that the root mean square of the acceleration at the collision position is maximum;
CL＝μ
UCL＝μ+2σ
LCL＝μ-2σ
(2) and judging that a ship bridge collision event occurs in the last step, and identifying load and damage. Expressing unknown ship bridge collision load by using a Chebyshev orthogonal term, expressing the integral rigidity of the structure by using a rigidity coefficient, and obtaining a motion equation expressed by the Chebyshev orthogonal term and the rigidity coefficient, wherein the specific process is as follows:
(2.1) the equation of motion of the structure can be expressed as:
Figure BDA0001991684660000081
where M is the mass matrix and C is the damping matrix (if rayleigh damping is used, C ═ w1M+w2K，w1，w2Is the rayleigh damping coefficient), K is the stiffness matrix of the structure, x represents the displacement at the node of the structure;
Figure BDA0001991684660000082
representing the velocity at the node of the structure;
Figure BDA0001991684660000083
representing the acceleration at the structural joint, F is the externally applied load.
(2.2) expressing a certain external load by using a Chebyshev orthogonal term, which is as follows:
Figure BDA0001991684660000084
in the formula cmCoefficient of expansion for the mth orthogonal term of force, Tm(t) is the orthogonal term of force (orthonormal basis), NmExpanding the order of the orthogonal terms of forceAnd (4) counting.
Tm(t) is:
Figure BDA0001991684660000091
in the formula LeIs the length of the signal; n is a radical ofmIs the order of the orthogonal function.
And (2.3) assuming that the rigidity of the actual structure is equal to the rigidity of each unit multiplied by a rigidity coefficient, and then summing, the structural rigidity coefficient is identified, namely converted into the problem of identifying the rigidity coefficient of the unit. The overall structural stiffness can be expressed as:
Figure BDA0001991684660000092
in the formula ajIs the jth cell
Figure BDA0001991684660000093
The stiffness coefficient of (a); n is a radical ofeThe number of structural units.
(2.4) equation of motion expressed in chebyshev orthogonal terms:
Figure BDA0001991684660000094
(3) solving the motion equation obtained from (2.4) by a Newmark method to obtain the dynamic response value (displacement, speed and acceleration) of the structure, wherein the solving process by the Newmark method is as follows:
(3.1) solving the motion equation obtained from (2.4) to apply the load with time LeQ is divided equally by the step length of
Figure BDA0001991684660000095
Giving an initial value x (0) of the dynamic response,
Figure BDA0001991684660000096
(3.2) setting an integration constant:
Figure BDA0001991684660000097
Figure BDA0001991684660000098
wherein, Δ t is an integral step length, and the parameters γ and β are empirical parameters;
(3.3) construction of effective stiffness matrix
Figure BDA0001991684660000099
And calculating to obtain an inverse matrix
Figure BDA00019916846600000910
(3.4) calculating the payload for the first time step
Figure BDA00019916846600000911
Figure BDA00019916846600000912
Wherein, { F1Represents the load at the first time step;
(3.5) determining the displacement x (1) at the first time step:
Figure BDA00019916846600000913
(3.6) determining the acceleration at the first time step
Figure BDA00019916846600000914
And velocity
Figure BDA00019916846600000915
Figure BDA00019916846600000916
Figure BDA0001991684660000101
And (3.7) repeating the steps (3.4) - (3.6) and calculating the time step q to obtain the response of the whole structure.
(4) Obtaining actual measured acceleration data and calculated acceleration data, obtaining a difference value of the actual measured acceleration data and the calculated acceleration data, listing an expression of a target function, and gradually reducing and converging the target function through iterative optimization, wherein the process is as follows:
(4.1) calculating the dynamic response value Q obtained by actual measurementMDynamic response Q calculated from (3.8)EDifference Δ z of (a):
Δz＝QE(βu)-QM
wherein, Delta z is the difference value between the power response value obtained by actual measurement and the power response value obtained by calculation, QEFor calculated theoretical value, QMFor measuring the actual value obtained, QE(βu) Represents QETo relate to betauFunction of betau＝(cm aj) Is the parameter vector to be identified.
(4.2) solving the objective function g (. beta.)u)：
g(βu)＝∑(QE(βu)-QM)2
And (5) converging the objective function by using the sensitivity matrix according to the step (5) to obtain an objective function value.
(5) Calculating a sensitivity matrix S (beta) of the structural dynamic response based on the Chebyshev orthogonal term coefficient and the structural rigidity coefficient, and gradually reducing and converging the target function by using the sensitivity matrix, wherein the specific process is as follows:
(5.1) respectively solving the partial derivatives of the motion equation to the coefficient of the Chebyshev orthogonal term and the structural rigidity coefficient,
Figure BDA0001991684660000102
in the formula (I), the compound is shown in the specification,
Figure BDA0001991684660000103
respectively, structural dynamic response to unknown force parameter cmThe sensitivity of (a) to (b) is,
Figure BDA0001991684660000104
Figure BDA0001991684660000105
for structural dynamic response to structural rigidity coefficient ajThe sensitivity of (2).
(5.2) solving the equation obtained in (5.1) by utilizing a dynamic explicit algorithm to obtain a sensitivity matrix S (beta)u)：
Figure BDA0001991684660000106
The dynamic explicit algorithm can be a center difference method, a linear acceleration method, a Newmark method and a wilson method, and the Newmark method is adopted in the embodiment.
(5.3) expressing the difference Δ z as:
Δz＝S(βu)·Δβu
in the formula,. DELTA.beta.uIs a parameter vector beta to be identifieduThe variation of (d) can be solved by using the least square method:
Δβ＝[ST(β)S(β)]-1ST(β)Δz
updating the sensitivity matrix S (beta) by iterationu) Thus, Δ z and Δ β are updated so that the objective function g (β) of step (4.2)u) And continuously converging to obtain the objective function value.
(6) Solving the coefficient of the Chebyshev orthogonal term and the structural rigidity coefficient to obtain the load of the ship hitting the bridge and the damage of the bridge body;
(6.1) obtaining the coefficient c of the Chebyshev orthogonal term at the moment according to the objective function value obtained in the step (5.3)mAnd a unit stiffness coefficient ajCoefficient c of the Chebyshev orthogonal termmSubstituting into step (2.2)Solving the load of the ship colliding with the bridge by an equation;
(6.2) coefficient of stiffness a according to structural unitjObtaining the damage ratio of the structural unit, thereby judging the damage of the pontic: a isjRepresenting the ratio of cell stiffness before and after a collision, ajLess than 1, meaning that the post-crash cell stiffness is less than the pre-crash cell stiffness; when a isjGreater than 1 indicates that the stiffness of the cell after impact is greater than the stiffness of the cell before impact, when ajEqual to 1 indicates that the post-crash cell stiffness is equal to the pre-crash cell stiffness.
The process of the invention is illustrated below with reference to a specific example:
as shown in fig. 2: the model of the pond river bridge is taken as an object. The Tanjiang super bridge is originated at the north station of Shenzhen city, passes through Guangzhou south sand, Zhongshan, Jiangmen and Yangjiang, is finally named as the east station, the Dongyuan deep railway, the West Zhan railway and the Hemao railway, has a main tower height of 157.1m and a main bridge length (31.885+57+130+256+63.9) m, is a large-scale cable-stayed bridge, and adopts a double-girder structure form as a main girder.
Establishing an ansys finite element model as shown in fig. 3(a) to 3(e), and dividing the whole structure into a main tower, a concrete box girder and a bridge deck, a steel box girder and a bridge deck, a stay cable and the like. The main tower, the concrete box girder and the bridge deck, and the steel box girder and the bridge deck adopt hexahedral units to divide grids. Consolidation constraint is applied to the bottom of the main tower, and transverse bridge direction constraint and vertical constraint are added at the joint of the bridge superstructure and the bridge pier.
1) The method comprises the following steps of obtaining real-time acceleration values at actual bridge measuring points, calculating the root mean square of the acceleration at each measuring point, and judging whether a ship bridge collision event occurs or not by combining a control chart, wherein the specific process comprises the following steps:
the on-bridge acceleration sensor layout is shown in fig. 4, assuming that the impact occurs between points 5, 6. Acquiring acceleration information transmitted by 9 acceleration sensors in front of and behind a ship bridge, acquiring 40 sampling data by each acceleration sensor, taking every two sampling data as a time window, acquiring 20 time windows by each acceleration sensor, judging the time when the root mean square of the acceleration at each measuring point is greatly changed by using a control chart, and considering that the root mean square of the acceleration is greatly changed when the value of the root mean square of the acceleration exceeds UCL (design rule) in the control chart or is lower than LCL (design rule)The ship bridge collides, and meanwhile, the root mean square of the acceleration near the collision position is the largest, and the collision position can be judged by finding out the position of a measuring point where the maximum value of the root mean square of the acceleration is located. The root mean square control diagrams of the acceleration of the 9 acceleration measuring points on the bridge are shown in FIGS. 5(a) -5 (i). As can be seen from FIGS. 5(a) to 5(i), the Root Mean Square (RMS) of the measuring points 3, 5, 6, 7 and 8 is greater than UCL, so that the ship bridge collision is judged to occur, and the accelerations at the measuring points 5 and 6 reach 122m/s respectively2、130m/s2And the acceleration is obviously larger than the maximum value of the acceleration at other measuring points, so that the collision position is judged to be between 5 and 6 measuring points.
The method can accurately judge whether the collision occurs and accurately identify the collision position, thereby effectively monitoring the ship bridge collision event and positioning the position of the ship bridge collision event in time.
2) And identifying load and damage. And expressing the unknown ship bridge collision load by using a Chebyshev orthogonal term, and expressing the integral rigidity of the structure by using a rigidity coefficient to obtain a motion equation expressed by the Chebyshev orthogonal term and the rigidity coefficient.
Suppose that when t is 1.25s, the bridge is struck and receives 12 × 106N impact load and load time-course curve are shown in figure 6, 20% of the units 159 of the bridge are set to be damaged, the sampling frequency is 20Hz, and the acceleration data of the 5 th measuring point and the 6 th measuring point are used for carrying out damage and load identification.
The equation of motion for a structure can be expressed as:
Figure BDA0001991684660000121
where M is the mass matrix and C is the damping matrix (if rayleigh damping is used, C ═ w1M+w2K，w1，w2Is the rayleigh damping coefficient), K is the stiffness matrix of the structure, x represents the displacement at the node of the structure;
Figure BDA0001991684660000122
representing the velocity at the node of the structure;
Figure BDA0001991684660000123
representing acceleration at a node of the structure, F being externalAnd (4) applying a load.
The impact load is expressed by a Chebyshev orthogonal term, and 20 orthogonal term coefficients are set, wherein the coefficients are as follows:
Figure BDA0001991684660000124
in the formula cmCoefficient of expansion for the mth orthogonal term of force, Tm(t) is the orthogonal term of force (orthonormal basis), NmThe order of the force expansion for the orthogonal terms is here 20.
The overall structural stiffness can be expressed as:
Figure BDA0001991684660000125
in the formula of alphajIs the jth cell
Figure BDA0001991684660000126
The stiffness coefficient of (a); n is a radical ofeThe number of structural units.
Equation of motion expressed by the chebyshev orthogonal term:
Figure BDA0001991684660000127
3) solving the motion equation obtained by the formula by a Newmark method to obtain the dynamic response value (displacement, speed and acceleration) of the structure.
4) Solving an objective function g (beta)u)：g(βu)＝∑(QE(βu)-QM)2
And obtaining actual measured acceleration data and calculated acceleration data, obtaining the difference between the actual measured acceleration data and the calculated acceleration data, listing the expression of the target function, and gradually reducing and converging the target function through the iteration of the sensitivity matrix.
5) Respectively solving partial derivatives of the motion equation to the Chebyshev orthogonal term coefficient and the structural rigidity coefficient, and solving the following formula by using a Newmark method to obtain a sensitivity matrix so as to gradually reduce and converge the target function in the step 4).
Figure BDA0001991684660000132
6) The finally obtained numerical value of the unit stiffness coefficient judges the damage degree of the unit, fig. 7 shows the damage identification result of the bridge, when the sampling frequency is 20Hz, the identified unit stiffness coefficient of the unit 159 is 0.8, namely, the damage ratio value is 20%, the maximum value of the damage ratio of the rest unit stiffness is 0.65%, the minimum value is 0, and the maximum error between the damage ratio of the unit stiffness and the theoretical damage value is 0.65%.
And substituting the finally obtained 20 Chebyshev orthogonal term coefficients into the following equation to obtain the load of the ship hitting the bridge:
Figure BDA0001991684660000133
the load identified by the sensitivity analysis method is shown in figure 8, and the identified impact load is quite consistent with a theoretical load time course curve.
In the working condition, the assumed ship-to-bridge load is the same as the load calculated by the ship-to-bridge load and damage synchronous identification method based on the substructure sensitivity analysis, and the assumed unit damage is consistent with the unit damage condition calculated by the ship-to-bridge load and damage synchronous identification method based on the substructure sensitivity analysis, which indicates that the synchronous identification method successfully judges the size of the ship-to-bridge load and the damage condition of the ship-to-bridge unit.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A ship bridge collision load and damage synchronous identification method based on substructure sensitivity analysis is characterized by comprising the following steps:
(1) taking bridge nodes as measuring points, obtaining real-time acceleration values at the actual bridge measuring points, calculating the root mean square of the acceleration at each measuring point, and if the root mean square of the acceleration at a certain measuring point exceeds a specified value, determining that a ship bridge collision event occurs at the measuring point;
the step (1) further comprises the following substeps:
(1.1) installing an acceleration sensor on a structure, and obtaining acceleration time-course response at a node of the structure;
(1.2) calculating the root mean square of the acceleration at each measurement point, calculating the root mean square mean value mu and the standard deviation sigma of the acceleration under normal use,
(1.3) calculating the root mean square mean μ and the standard deviation σ of the acceleration using the Lauda criterion to obtain CL and the upper and lower control lines UCL, LCL, wherein,
CL＝μ
UCL＝μ+2σ
LCL＝μ-2σ
when the root mean square of the acceleration of a measuring point exceeds an upper control line and a lower control line, judging that the ship bridge collision occurs, and obtaining the collision position when the root mean square of the acceleration at the collision position is the maximum;
(2) if the occurrence of the ship bridge collision event is judged, expressing unknown ship bridge collision load by using the Chebyshev orthogonal term, and expressing the overall rigidity of the structure by using the unit rigidity coefficient, thereby obtaining a structural motion equation of the bridge when the ship bridge collision event occurs, which is expressed by the Chebyshev orthogonal term and the unit rigidity coefficient;
(3) solving the structural motion equation obtained in the step (2) to obtain dynamic response including displacement, speed and acceleration at the structural node;
(4) calculating the difference between the dynamic response obtained by calculation and the actual dynamic response, and establishing a target function expression about the Chebyshev orthogonal term coefficient and the structural rigidity coefficient;
(5) calculating a sensitivity matrix of the structural dynamic response based on the Chebyshev orthogonal term coefficient and the unit stiffness coefficient, so that the target function in the step (4) is gradually reduced and converged;
(6) solving a Chebyshev orthogonal term coefficient and a structural rigidity coefficient, substituting the Chebyshev orthogonal term coefficient and the structural rigidity coefficient into the structural motion equation in the step (2) to obtain the load of the ship colliding with the bridge, and judging the damage degree of the bridge body according to the structural rigidity coefficient: the structural rigidity coefficient is less than 1, which indicates that the rigidity of the unit after collision is less than that of the unit before collision; the structural rigidity coefficient is greater than 1, which indicates that the rigidity of the unit after collision is greater than that of the unit before collision; a structural stiffness coefficient equal to 1 indicates that the post-crash cell stiffness is equal to the pre-crash cell stiffness.
2. The ship bridge-collision load and damage synchronous identification method based on substructure sensitivity analysis as claimed in claim 1, wherein said step (2) further comprises the following sub-steps:
(2.1) constructing a motion equation of the bridge structure:
Figure FDA0002713957990000021
in the formula, M is a mass matrix, C is a damping matrix, K is a structural rigidity matrix, and x represents the displacement at a structural node;
Figure FDA0002713957990000022
representing the velocity at the node of the structure;
Figure FDA0002713957990000023
representing the acceleration at the structural node, F being the external load;
(2.2) expressing a certain external load F (t) by using a Chebyshev orthogonal term, which is expressed by the following formula:
Figure FDA0002713957990000024
in the formula, cmExpansion coefficient of mth orthogonal term of external load, Tm(t) is the mth orthogonal term of the external load, NmThe order is expanded for the orthogonal term of the external load;
Figure FDA0002713957990000025
in the formula, LeIs the length of the signal;
(2.3) assuming that the rigidity of the actual structure is equal to the rigidity of each unit multiplied by a rigidity coefficient, and then summing, and identifying the structural rigidity, namely converting the structural rigidity into the problem of identifying the rigidity coefficient of the unit; the overall structural stiffness K is expressed as:
Figure FDA0002713957990000031
in the formula, ajIs the stiffness coefficient of the jth cell; n is a radical ofeIs the number of structural units;
Figure FDA00027139579900000312
represents the cell stiffness of the jth cell;
(2.4) obtaining the motion equation expressed by the Chebyshev orthogonal term according to the steps (2.1) to (2.3):
Figure FDA0002713957990000032
3. the ship bridge-collision load and damage synchronous identification method based on substructure sensitivity analysis as claimed in claim 2, wherein said step (3) further comprises the following sub-steps:
(3.1) setting the load acting time as t0Solving the motion equation obtained in step (2.4) to apply the load for time t0Divided into q equal parts with step length of
Figure FDA0002713957990000033
According to the combinationThis gives the dynamic response x,
Figure FDA0002713957990000034
X (0) of,
Figure FDA0002713957990000035
And
Figure FDA0002713957990000036
(3.2) setting an integration constant:
Figure FDA0002713957990000037
Figure FDA0002713957990000038
wherein, Δ t is an integral step length, and the parameters γ and β are empirical parameters;
(3.3) construction of effective stiffness matrix
Figure FDA00027139579900000313
And calculating to obtain an inverse matrix
Figure FDA0002713957990000039
(3.4) calculating the payload for the first time step
Figure FDA00027139579900000310
Figure FDA00027139579900000311
Wherein, { F1Represents the load at the first time step;
(3.5) determining the displacement x (1) at the first time step:
Figure FDA0002713957990000041
(3.6) determining the acceleration at the first time step
Figure FDA0002713957990000042
And velocity
Figure FDA0002713957990000043
Figure FDA0002713957990000044
Figure FDA0002713957990000045
(3.7) repeating the steps (3.4) - (3.6) and calculating to the qth time step, thereby obtaining the acting time t of the whole structure0Internal dynamic response
Figure FDA0002713957990000046
Theoretical value of (Q)E。
4. The ship bridge-collision load and damage synchronous identification method based on substructure sensitivity analysis as claimed in claim 3, wherein said step (4) further comprises the following sub-steps:
(4.1) calculation of the dynamic response from the actual measurement
Figure FDA0002713957990000047
Actual value of (Q)MAnd (4) calculating the theoretical value Q of the dynamic response in the step (3.7)EDifference Δ z of (a):
Δz＝QE(βu)-QM
wherein, Delta z is the difference value between the dynamic response value obtained by actual measurement and the dynamic response value obtained by calculation,QEfor calculated theoretical value, QMFor measuring the actual value, QE(βu) Represents QETo relate to betauFunction of betau＝(cm aj) ' is a parameter vector to be identified;
(4.2) construction of the objective function g (. beta.)u)：
g(βu)＝∑(Δz)2＝∑(QE(βu)-QM)2。
5. The ship bridge-collision load and damage synchronous identification method based on substructure sensitivity analysis according to claim 4, wherein said step (5) further comprises the following sub-steps:
(5.1) respectively solving the coefficient c of the motion equation pair Chebyshev orthogonal term in the step (2.4)mAnd coefficient of structural stiffness ajThe partial derivatives of (A) are as follows:
Figure FDA0002713957990000048
in the formula (I), the compound is shown in the specification,
Figure FDA0002713957990000051
coefficient of expansion c of orthogonal terms of structural dynamic response to external load, respectivelymThe sensitivity of (a) to (b) is,
Figure FDA0002713957990000052
respectively a structural dynamic response to a structural rigidity coefficient ajThe sensitivity of (c);
(5.2) solving the equation set in the step (5.1) to obtain a sensitivity matrix S (beta)u)：
Figure FDA0002713957990000053
(5.3) expressing the difference Δ z of step (4.1) using Taylor expansion as:
Δz＝S(βu)·Δβu
in the formula,. DELTA.beta.uIs a parameter vector beta to be identifieduThe variation of (2) is solved by a least square method to obtain:
Δβ＝[ST(β)S(β)]-1ST(β)Δz
updating the sensitivity matrix S (beta) by iterationu) Thus, Δ z and Δ β are updated so that the objective function g (β) of step (4.2)u) And continuously converging to obtain the objective function value.
6. The ship bridge-collision load and damage synchronous identification method based on substructure sensitivity analysis according to claim 5, wherein said step (6) further comprises the following sub-steps:
(6.1) obtaining the coefficient c of the Chebyshev orthogonal term at the moment according to the objective function value obtained in the step (5.3)mAnd a unit stiffness coefficient ajCoefficient c of the Chebyshev orthogonal termmSubstituting the equation in the step (2.2) to obtain the ship bridge collision load;
(6.2) coefficient of stiffness a according to structural unitjObtaining the damage ratio of the structural unit, thereby judging the damage of the pontic: a isjRepresenting the ratio of cell stiffness before and after a collision, ajLess than 1, meaning that the post-crash cell stiffness is less than the pre-crash cell stiffness; when a isjGreater than 1 indicates that the stiffness of the cell after impact is greater than the stiffness of the cell before impact, when ajEqual to 1 indicates that the post-crash cell stiffness is equal to the pre-crash cell stiffness.
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