CN107389285B - A kind of quick test and evaluation method of bridge changed based on temperature - Google Patents
A kind of quick test and evaluation method of bridge changed based on temperature Download PDFInfo
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- CN107389285B CN107389285B CN201710455021.6A CN201710455021A CN107389285B CN 107389285 B CN107389285 B CN 107389285B CN 201710455021 A CN201710455021 A CN 201710455021A CN 107389285 B CN107389285 B CN 107389285B
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- G—PHYSICS
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- 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
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- 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
- G01M5/0033—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining damage, crack or wear
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- 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
- G01M5/0066—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by exciting or detecting vibration or acceleration
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Abstract
The invention discloses a kind of quick test and evaluation methods of bridge changed based on temperature, structural dynamic response of the bridge structure under condition of different temperatures is acquired by the sensor being arranged on bridge, utilize basic motive characterisitic parameter of the power signal analysis method identification bridge structure under condition of different temperatures, and it is substituted into the mapping relations between vibration shape zoom factor and ambient temperature condition and kinetic parameter, obtain the vibration shape zoom factor of bridge structure and the displacement flexibility matrix deep layer subparameter under condition of different temperatures, to the deformation under pre- geodesic structure meaning static load in office, it carries out non-destructive tests and carries out the research of structure long-term behaviour, the shortcomings that needing artificial excitation's device and close traffic the present invention overcomes conventional impact vibration-testing, overcoming existing environmental vibration testing method simultaneously cannot effectively support The shortcomings that bridge structure safe is assessed has the testing time few, does not need close traffic, the advantage that precision is high and Noise Resistance Ability is strong.
Description
Technical field
The present invention relates to a kind of quick test and evaluation methods of bridge changed based on temperature, it can be achieved that bridge structure is scratched
Degree prediction and security state evaluation, belong to structural health monitoring technology field.
Background technique
The concept of structural health monitoring technology starts to be suggested in eighties of last century the '30s, and is generally considered raising
Engineering structure health and safety and realization one of structure long-life and the most effective approach of sustainable management.By the hair of decades
Exhibition, novel intelligent sensing technology such as wireless sensing, Fibre Optical Sensor, microwave radar technology etc. occur like the mushrooms after rain and obtain fast
Speed is promoted, and hardware foundation required for the health detections technology such as all types of sensors and data collection system is gradually established, and is based on
The methods of all types of structural recognition methods, damnification recognition method, Structural Behavior Evaluation prediction and the risk analysis of monitoring signals day
Become mature and is applied to more bridge blocks, such as: Gold Gate Bridge, Humber bridge, Su-Tong Brideg.
Environmental vibration testing is the main means of existing structure health monitoring, it utilizes the natural conditions such as wind load and wagon flow
Motivate bridge, relative to artificial excitation test have the advantages that it is easy to operate, it be capable of export structure basic motive characteristic join
It counts such as: frequency, damping and the vibration shape.Domestic and foreign scholars have studied various uncertain factors and external condition (temperature, wind speed and
Structural response amplitude etc.) influence to vibration characteristics.It is solid that ambient temperature conditions have been extensively studied in domestic and foreign scholars
There is the influence of frequency, such as: Los Alamos National Laboratory carries out the Alamosa Canyon bridge positioned at New Mexico
Multiple test, the variation of first three order frequency is 4.7%, 6.6% and 5.0% in one day as the result is shown.From environmental vibration testing
The modal parameters of middle identification are also studied with the relationship of ambient wind velocity and structural response amplitude.By preceding it is found that only
Dependent on environmental vibration testing method, basic modal parameter can only obtain, can not effectively support the performance of bridge structure to comment
Estimate, reason be environmental vibration testing can only export structure frequency response function shape rather than its amplitude, still, frequency response function width
It is worth most important to the identification of structure deep layer subparameter such as vibration shape zoom factor and displacement flexibility.Impact vibration test is other one
Kind be widely applied structural dynamic test and Modal Parameter Identification in test method, it can simultaneously measurement structure input impact
Power and export structure response, therefore, it has the advantages that accurately estimate structural frequency response function amplitude information, from impact vibration
In test data, the vibration shape zoom factor of structure can be accurately identified, to identify the flexibility identification and amount of deflection prediction of structure.So
And the shortcomings that impact vibration test is to need artificial excitation's device to deactivate structure, and need to close friendship during the test
Logical, this is extremely inconvenient in Practical Project test.
In order to solve this problem, domestic and foreign scholars attempt by means of supplementary means directly from the only structural response of output
The vibration shape zoom factor of structure is obtained, the use of more method is the thought changed based on quality in the literature.Specifically,
Environmental structure dynamic response of the structure in no additional mass and additional mass is tested, it is basic by two kinds of situation flowering structures
The vibration shape zoom factor of dynamic parameters calculating structure.Foreign scholar has been put forward for the first time the vibration shape quality normalizing based on sensitivity
Change method, and verified with the on-the-spot test case of a laboratory example and bridge.Hereafter, many scholars are based on structure
Basic equation, derived a series of formula that the mass normalisation vibration shape is obtained from environmental vibration data.It can see
Out, the thought changed based on quality can obtain the mass normalisation vibration shape scaling system of structure from environmental vibration testing data
Number, and then identify the deep layers subparameters such as structure real displacement flexibility.But this method needs the knot under two kinds of operating conditions of measurement structure
Structure dynamic response, test process is complicated, and needs close traffic during the test, another is significant the disadvantage is that the party
Method is not directly applicable in the deep layer subparameter identification of long Loads of Long-span Bridges, this is because the introducing of additional mass is to structural dynamic
Characteristic influences very little, along with the inaccuracy of Modal Parameter Identification will lead to final recognition result serious distortion.
Play a significant role from the above it can be seen that traditional health monitors system to finding and coping with bridge emergency event, but existing
Health monitoring technique can not also really realize " health " monitoring of structure, main cause is a lack of effective data processing side
Method.Due to the presence of the challenges such as incompleteness of the complexity and observation data of civil structure, existing ambient vibration is surveyed
The main export structure basic parameter of method for testing, can not directly support the maintenance and management decision of bridge structure, then how from ring
The deep layer subparameter (such as: vibration shape zoom factor, scaling displacement flexibility and natural bow) of structure is obtained in the vibration-testing data of border
It is a urgent problem to be solved.
The invention proposes a kind of quick test and evaluation methods of bridge changed based on temperature in response to this problem.This method
The basic friction angle parameter of structure can not only be identified as traditional environmental vibration testing, and can test as impact vibration
Equally identification obtains the deep layer subparameter (vibration shape zoom factor and displacement flexibility matrix etc.) of structure, in the displacement for obtaining structure
After flexibility matrix, so that it may realize that Deformation Prediction of the bridge structure under any static load, non-destructive tests and structure are long
Phase Performance Evaluation.Artificial excitation's device is needed the present invention overcomes conventional impact vibration-testing and needs close traffic
Disadvantage, at the same overcome existing environmental vibration testing method cannot effectively support structure security evaluation the shortcomings that, have test institute
It takes time few, at low cost, precision height and the strong feature of Noise Resistance Ability, therefore be widely used in practical bridge Performance Evaluation
Good prospect.
Summary of the invention
The technical problem to be solved by the present invention is in view of the deficiency of the prior art, and provide a kind of test side
Just and the bridge structure vibration shape zoom factor with high accuracy changed based on temperature and displacement flexibility recognition methods and system.
In order to solve the above technical problems, technical scheme is as follows:
A kind of quick test and evaluation method of bridge changed based on temperature, which is characterized in that including sensing system, number
According to acquisition system and data analysis system, the sensing system is used to obtain bridge structure in reference temperature T0, change temperature
Spend T1And T2Under the conditions of measuring point Acceleration time course and ambient temperature condition；The data collection system is used to acquire and save
The different ambient temperature conditions for acceleration signal and the temperature sensor acquisition that acceleration transducer is got；The data point
Analysis system obtains the basic friction angle parameter of bridge structure according to the acceleration structural dynamic response under condition of different temperatures, passes through ginseng
Examine temperature T0, change temperature T1And T2Temperature load value and basic friction angle parameter under three kinds of states calculate the vibration of bridge structure
Type zoom factor can identify bridge structure not in conjunction with the basic friction angle parameter under vibration shape zoom factor and condition of different temperatures
Displacement flexibility matrix under the conditions of synthermal；Predict bridge structure in any static load based on the displacement flexibility matrix of identification
Under amount of deflection, non-destructive tests and bridge structure long-term behaviour research, and the safe condition of bridge structure is assessed.
Specific step is as follows for test and evaluation method described further:
Step 1, by one group of sensor being arranged on bridge length direction to bridge structure in reference temperature T0、
Change temperature T1And T2Under the conditions of structural dynamic response be acquired；
Step 2 is collecting bridge structure after the structural dynamic response under condition of different temperatures, is passing through mode
Parser identifies to obtain bridge structure in reference temperature T0Under the conditions of r rank natural frequency ω0rThe vibration shape is not normalized
{ψr, and change temperature T1And T2Under the conditions of r rank natural frequency ω1rAnd ω2r, to obtain about vibration shape zoom factor
Unknowm coefficientAndExpression formula are as follows:
Wherein: I is testing section the moment of inertia；CT=A α (2T0 2+T1 2+T2 2-2T0T1-2T0T2)；{ψrIt is reference temperature T0Under the conditions of r rank do not normalize the vibration shape { ψr}；
{ψr}TThe vibration shape { ψ is not normalized for r rankrTransposed matrix；A is testing section area；α is test the used material of structure
Temperature linear expansion coefficient；Matrix [B] is the constant matrices about shape function second dervative, and expression formula is
Matrix [G] is the constant matrices about shape function first derivative, and expression formula is
Wherein: N is the number of placement sensor, value range 1,2,3 ...；[Bk]=d [Nk]/dx is k-th of unit shape
The first derivative of Jacobian matrix；[Gk]=d2[Nk]/dx2For the second dervative of k-th of unit form function matrix；Form function matrix
[Nk] it is expressed as [Nk]=[0,0,0 ..., N1,N2,N3,N4..., 0,0,0], it is the shape function of k-th of unit in whole coordinate
Expression formula in system； X is any point in k-th of unit
At a distance from structural bearings end；L is the distance between adjacent sensors；
Step 3 passes through unknowm coefficientWith vibration shape zoom factor ΓrBetween relationshipAnd it is unknown
CoefficientWith vibration shape zoom factor ΓrBetween relationshipAvailable r first order mode zoom factor Γr
Expression formula are as follows:
Wherein: the proportionality coefficient between elasticity modulus and temperature knots modification of the k to test the used material of structure, for mixed
It is k=-5.4633 × 10 for solidifying soil material7Pa/℃。
Step 4, so as to obtain bridge structure in reference temperature T0, change temperature T1And T2Under the conditions of displacement flexibility
Matrix, with reference temperature T0For, expression formula are as follows:
Wherein: βrFor the constant about structural natural frequencies, value βr=1/2j ω0r, j is imaginary unit；λ0rWith reference to
Temperature T0The r rank pole of condition flowering structure, the relationship with structural natural frequencies and damping ratio are
ξ0rFor reference temperature T0Under the conditions of damping to coefficient；β* r、WithRespectively βr、ψrAnd λ0rConjugate complex number.
Equation is solved about the unknowm coefficient of vibration shape zoom factor in step 2 described further are as follows:
Reference temperature T described further0, change temperature T1And T22T need to be met0=T1+T2Equilibrium relationships.
The further Modal Parameters Identification, including obtaining freely declining for structure by using natural excitation method
Subtract response signal, then be transformed into frequency domain with Fourier transform, finally using CMIF method identification structure under condition of different temperatures
Basic friction angle parameter.
Compared to the prior art the quick test and evaluation method of bridge changed based on temperature proposed in more of the invention
There is the difference of essence with the traditional environment method for testing vibration in bibliography.The data processing method developed makes proposed
Based under condition of different temperatures vibration signal identification structure deep layer subparameter be possibly realized, be the key that in the present invention.
The invention has the advantages that: vibration signal of the structure under condition of different temperatures is acquired by existing health monitoring systems
And temperature load, ambient temperature condition and different temperatures flowering structure basic motive characterisitic parameter are deeply excavated by theory innovation
Between mapping relations, calculate the vibration shape zoom factor of structure, and then identify the displacement flexibility matrix of structure, be based on this flexibility square
Deformation Prediction, non-destructive tests and long-term behaviour assessment of the structure under any static load may be implemented in battle array, significantly more efficient
The safe condition of bridge structure is assessed.The all types of data that the method for the present invention makes full use of health monitoring systems to acquire,
The direct parameter that assessment bridge security state can therefrom be obtained breaches in traditional health monitoring system and lacks at valid data
The bottleneck of reason method, in addition, this method has the advantages that easy to operate, result is accurate and Noise Resistance Ability is strong, it can be more
Security evaluation and maintenance management effectively are carried out to bridge, to there is the prospect applied to bridge health diagnosis and Performance Evaluation.
Detailed description of the invention
The flow diagram of Fig. 1 the method for the present invention；
Fig. 2 changes temperature T1And T2Under the conditions of the structural natural frequencies that identify；
The zoom factor and relative error analysis that Fig. 3 the method for the present invention calculates；
The change temperature T that Fig. 4 the method for the present invention calculates1Under the conditions of the preceding 4 rank mass normalisation vibration shape and theoretical value ratio
Compared with；
The change temperature T of Fig. 5 the method for the present invention identification1And T2Under the conditions of displacement flexibility matrix；
Fig. 6 changes temperature T1And T2Under the conditions of structural deflection prediction result schematic diagram.
Specific embodiment
Embodiment 1
It elaborates, but should not be limited the scope of the invention with this to the present invention below in conjunction with attached drawing.
Fig. 1 is the basic procedure of the method for the present invention.The security state evaluation of bridge passes through field investigation first and has access to knot
Composition paper determines the arrangement of acceleration transducer and temperature sensor to be familiar with tested bridge.Then, it is adopted by data
Collect equipment acquisition structure in reference temperature T0, change temperature T1And T2Under the conditions of acceleration structural dynamic response and corresponding
Ambient temperature payload values.After completing the vibration-testing under three kinds of state of temperatures, start the pretreatment of vibration-testing signal with after
Processing.Because bridge structure vibration test is inevitably influenced by factors such as transducer sensitivity and experimental enviroments, a system
Column data preconditioning technique is initially applied to vibration-testing signal to eliminate or reduce noise and improve the quality of data, such as filter,
Add average etc. in window index, time domain or frequency domain.Secondly, in such a way that natural excitation method and complex mode exp-function method combine
It identifies the bridge structure intrinsic frequency under the conditions of three kinds of temperature and does not scale the displacement vibration shape.Then, by the modal parameter of identification with
And three kinds of ambient temperature payload values substitute into the unknowm coefficient comprising bridge structure vibration shape zoom factor and solve in equation, pass through matrix
Operation obtains the value of unknowm coefficient；The complexity between unknowm coefficient and vibration shape zoom factor proposed using the method for the present invention is reflected
Penetrate relationship, the vibration shape zoom factor of available structure.Finally, in conjunction with intrinsic frequency and vibration shape contracting under condition of different temperatures
Coefficient is put, displacement flexibility matrix of the bridge structure under condition of different temperatures can be obtained.It, can be into one based on this flexibility matrix
Step is used to deformation, non-destructive tests and the assessment of structure long-term behaviour under pre- geodesic structure what static load in office, thus significantly more efficient
The safe condition of structure is assessed.
The method of the present invention is by acquisition structure in condition of different temperatures it can be seen from the process of above-mentioned the method for the present invention
Under vibration-testing data and ambient temperature payload values, may be implemented to obtain structure from environmental vibration testing data profound
The purpose of parameter has the advantages that convenient and efficient and with high accuracy.Specifically, the data processing method proposed may be implemented
Displacement flexibility identification and corresponding Deformation Prediction of the structure under condition of different temperatures, this is unique distinction of the invention.
Specific step is as follows for the method for the present invention:
Firstly, determining sensor positioning scheme.According to specific structure type and test request, the arrangement of sensor is determined
Scheme, Specific Principles are as follows: should be taken into account that measuring point can sufficiently capture the Global Information of structure, avoid sensor arrangement in structure
Mode node.
Secondly, measurement bridge structure is in reference temperature T0Under the conditions of structural dynamic response data and record ambient temperature lotus
Load value.Before formally acquisition data, parameter required for setting acquisition data, such as: sample frequency, sampling time etc., later
Using corresponding data acquisition equipment acquisition bridge structure in reference temperature T0Under the conditions of structural dynamic response.
Then, acquisition bridge structure is changing temperature T1And T1Under the conditions of structural dynamic response data.In reference temperature T0
After measurement, and certain interval of time (such as: reference temperature is taken as the mean temperature in one day, changes temperature and is taken as respectively one day
In minimum and maximum temperature) instruction issued to data collection system start to acquire data, after guaranteeing enough data lengths
(such as: 10min), to data collection system issue instruction stop data acquisition, and save collected structural dynamic response and
Corresponding ambient temperature payload values.
Finally, carrying out the vibration shape zoom factor that analysis obtains bridge structure to the vibration-testing data under condition of different temperatures
With displacement flexibility deep layer subparameter.It is shown in detailed process is as follows:
Step 1, data prediction.Since sensor and Transmission system equipment fault, contact fault, electromagnetic interference etc. are asked
Topic often results in health monitoring systems data collected and there are a large amount of exceptions, these data are not identified, rejected or repaired
And subsequent analysis is directly applied to, huge interference necessarily is brought to the accuracy of assessment result.Common data prediction
Method has, application window function average to collected data progress Time Domain Piecewise, elimination trend term and filtering, specifically uses that
Data preprocessing method will be selected according to the characteristics of actual test data.
Step 2, bridge structure basic friction angle parameter identifies under condition of different temperatures.Structure based on structural dynamic response
Basic friction angle parameter identification method has very much, can be divided into two class of frequency domain method and time domain method, and frequency domain method has peak picking method, unusual
It is worth decomposition method, PolyMAX method and complex modal indicating function method (CMIF) etc., time domain method has Random Subspace Method (SSI), autoregression
Moving average method etc..The method of the present invention identifies the method combined using a kind of pretreatment of combination time domain and state simulation of frequency region parameter,
The free damping response signal of structure is obtained using natural excitation method (NExT), then is transformed into frequency domain with Fourier transform, benefit
With basic friction angle parameter of the CMIF method identification structure under condition of different temperatures.
Step 3 solves the unknowm coefficient about vibration shape zoom factor.Bridge structure is being obtained under condition of different temperatures
Basic friction angle parameter and ambient temperature condition value after, can substitute into about vibration shape zoom factor Wei Zhi coefficient solution
In equation:
Wherein: I is testing section the moment of inertia；CT=A α (2T0 2+T1 2+T2 2-2T0T1-2T0T2)；{ψrIt is reference temperature T0Under the conditions of r rank do not normalize the vibration shape { ψr}；
{ψr}TThe vibration shape { ψ is not normalized for r rankrTransposed matrix；A is testing section area；α is used material by test bridge structure
The temperature linear expansion coefficient of material；Matrix [B] is the constant matrices about shape function second dervative, and expression formula isMatrix [G] is the constant matrices about shape function first derivative, and expression formula isω0rFor reference temperature T0Under the conditions of r rank intrinsic frequency；ω1rAnd ω2rRespectively change temperature
Spend T1And T2Under the conditions of r rank intrinsic frequency.
By the operation of matrix, the unknowm coefficient about vibration shape zoom factor can be obtainedAndExpression formula
Are as follows:
Step 4, mass normalisation mode factor calculate.Pass through unknowm coefficientWith vibration shape zoom factor ΓrBetween pass
SystemAnd unknowm coefficientWith vibration shape zoom factor ΓrBetween relationshipIt can be with
Obtain r first order mode zoom factor ΓrExpression formula are as follows:
Wherein: the proportionality coefficient between elasticity modulus and temperature knots modification of the k to test the used material of bridge structure, it is right
It is k=-5.4633 × 10 for concrete material7Pa/℃。
Step 5, displacement flexibility identification.In conjunction with the basic friction angle parameter under condition of different temperatures, so as to obtain bridge
Structure is in reference temperature T0, change temperature T1And T2Under the conditions of displacement flexibility matrix, with reference temperature T0For, expression formula
Are as follows:
Wherein: βrFor the constant about structural natural frequencies, value βr=1/2j ω0r, j is imaginary unit；λ0rWith reference to
Temperature T0The r rank pole of condition flowering structure, the relationship with bridge structure intrinsic frequency and damping ratio areξ0rFor reference temperature T0Under the conditions of damping to coefficient；β* r、WithRespectively βr、ψrWith
λ0rConjugate complex number.For the displacement flexibility matrix under the conditions of other temperature, it is only necessary to by the system pole and coefficient in above formula
βrThe value being changed under current state.
Step 6, amount of deflection prediction and Performance Evaluation.After identifying bridge structure flexibility matrix, it can be used to predict bridge
Deformation, non-destructive tests and bridge structure long-term behaviour assessment of the structure under any static load.Bridge structure is displaced flexibility
Matrix is considered as the key parameter of evaluation structure safe condition, it is real by the method that is changed based on temperature in the process of the present invention
Flexibility identification and amount of deflection prediction of the existing structure under condition of different temperatures, overcome traditional environment vibration data processing method without
Method obtains structure deep layer subparameter and carries out the problem that structure safe condition is effectively assessed, thus in the Gernral Check-up of practical bridge
It has a wide range of applications in Performance Evaluation.
Embodiment 2
Illustrate that the proposed bridge changed based on temperature is quickly tested and commented below with a typical bridge case
Estimate the implementation steps of method.
Step 1 first has to the arrangement that sensor is determined according to bridge structure feature.In the implementation case, whole
It is equally spaced 12 acceleration transducers in a bridge structure and arranges 1 temperature sensor.
Step 2, reference temperature T0With change temperature T1And T2Under the conditions of structural dynamic response data and ambient temperature
Payload values.Typical acceleration responsive of the clamped beam under condition of different temperatures is as shown in Fig. 1 flow chart, in this case, ginseng
Examine temperature T0=20 DEG C, change temperature T1And T2Value is respectively 10 DEG C and is 20 DEG C.
Step 3 identifies the basic friction angle parameter of condition of different temperatures flowering structure.Structure is being measured in condition of different temperatures
Under vibration signal after, first using fitting of a polynomial method eliminate measurement data trend term, band then is carried out to it
Pass filter, the frequency range selected are 0.2Hz~200Hz, and the response data for selecting sensor 1~6 to measure is as a reference point, meter
The cross-correlation function for calculating response and the reference point response of all the sensors, to obtain the free damping curve of bridge structure；For
The influence that cross-correlation function non-complete attenuation causes spectrum leakage to frequency response function required by subsequent is eliminated, is needed to free damping
Curve applies exponential window function, and the index of the exponential window function applied in present case is 0.01%；Later, to application window letter
Free damping curve after number carries out Fourier transform (Fourier transform length is 262144), obtains not contracting for bridge structure
Put frequency response function；Finally, utilizing the basic mould of complex mode exponential function (CMIF) Modal Parameters Identification identification bridge structure
State parameter, value is as shown in Fig. 2, reference temperature T0Under the conditions of preceding 4 rank intrinsic frequency be respectively 6.85Hz, 27.37Hz,
61.43Hz and 108.44Hz, reference temperature T1Under the conditions of preceding 4 rank intrinsic frequency be respectively 7.88Hz, 28.65Hz, 63.16Hz
And 111.39Hz, reference temperature T2Under the conditions of preceding 4 rank intrinsic frequency be respectively 5.68Hz, 26.19Hz, 59.94Hz and
106.61Hz does not specifically give the vibration shape of identification for simplicity herein.
Step 4 solves the unknowm coefficient about vibration shape zoom factor.Bridge structure is being obtained under condition of different temperatures
Basic friction angle parameter and ambient temperature condition value after, can substitute into about vibration shape zoom factor Wei Zhi coefficient solution
In equation, the unknowm coefficient of not same order, the 1st rank unknowm coefficient can be obtained2nd rank is not
Know coefficient3rd rank unknowm coefficient4th rank unknowm coefficient
Step 5, mass normalisation mode factor calculate.Pass through unknowm coefficientWith vibration shape zoom factor ΓrBetween pass
SystemAnd unknowm coefficientWith vibration shape zoom factor ΓrBetween relationshipIt can obtain
It is 0.3136,0.3144,0.3128 and 0.3172 to preceding 4 rank mass normalisation mode factor.
Step 6, displacement flexibility identification.In conjunction with the basic friction angle parameter under condition of different temperatures, so as to obtain bridge
Displacement flexibility matrix of the structure under condition of different temperatures, to change temperature T1For, value are as follows:
For the typical bridge, using the displacement flexibility matrix diagram of block of the method for the present invention identification as shown in fig. 6, square
Battle array dimension is 11 × 11.It, can the deformation in office anticipated under static load of pre- geodesic structure, progress using the displacement flexibility matrix of identification
Non-destructive tests and long-term behaviour assessment.In present case, for predicting bridge structure in the deformation under any static load
Son, illustrate identification displacement flexibility matrix uses figure.Using identification displacement flexibility matrix multiplied by the equivalent force under any static load
Vector can obtain bridge structure vertical deflection under this equivalent nodal force.In the present embodiment, it is applied simultaneously in all measuring points
The static load for adding 100N, the comparison of each node deflection value predicted and static test test data is as shown in fig. 6, from figure
As can be seen that the maximum value under acted on static load betides span centre measuring point, predicted using identification displacement flexibility matrix perpendicular
It is 4.996mm to amount of deflection, the direct test value of static loading experiment is 5.07mm, and the relative error of the two is 1.46%, is less than engineering and misses
Poor 5%, it was demonstrated that the validity of amount of deflection of the flexibility recognition methods prediction bridge structure proposed under any static load and quasi-
True property.
Claims (3)
1. a kind of quick test and evaluation method of bridge changed based on temperature, which is characterized in that including sensing system, data
Acquisition system and data analysis system, the sensing system are used to obtain bridge structure in reference temperature T0, change temperature T1
And T2Under the conditions of measuring point Acceleration time course and ambient temperature condition；The data collection system is used to acquire and save acceleration
The different ambient temperature conditions of acceleration signal and temperature sensor acquisition that degree sensor is got；Data analysis system
System obtains the basic friction angle parameter of bridge structure according to the acceleration structural dynamic response under condition of different temperatures, by reference to temperature
Spend T0, change temperature T1And T2Temperature load value and basic friction angle parameter under three kinds of states calculate the vibration shape contracting of bridge structure
Coefficient is put, bridge structure can be identified in not equality of temperature in conjunction with the basic friction angle parameter under vibration shape zoom factor and condition of different temperatures
Displacement flexibility matrix under the conditions of degree；Specific steps include:
Step 1, by one group of sensor being arranged on bridge length direction to bridge structure in reference temperature T0, change temperature
Spend T1And T2Under the conditions of structural dynamic response be acquired；
Step 2 is collecting bridge structure after the structural dynamic response under condition of different temperatures, is passing through model analysis
Algorithm identifies to obtain bridge structure in reference temperature T0Under the conditions of r rank natural frequency ω0rThe vibration shape { ψ is not normalizedr, with
And change temperature T1And T2Under the conditions of r rank natural frequency ω1rAnd ω2r, to obtain about the unknown of vibration shape zoom factor
CoefficientAndExpression formula are as follows:
Wherein: I is testing section the moment of inertia；CT=A α (2T0 2+T1 2+T2 2-2T0T1-2T0T2)； {ψrIt is reference temperature T0Under the conditions of r rank do not normalize the vibration shape { ψr}；{ψr}TFor the non-normalizing of r rank
Change the vibration shape { ψrTransposed matrix；A is testing section area；α for test the used material of structure temperature linear expansion coefficient；Square
Battle array [B] is the constant matrices about shape function first derivative, and expression formula is
Matrix [G] is the constant matrices about shape function second dervative, and expression formula is
Wherein: N is the number of placement sensor, value range 1,2,3 ...；[Bk]=d [Nk]/dx is k-th of unit shape function
The first derivative of matrix；[Gk]=d2[Nk]/dx2For the second dervative of k-th of unit form function matrix；Form function matrix [Nk] table
It is shown as [Nk]=[0,0,0 ..., N1,N2,N3,N4..., 0,0,0], it is the shape function of k-th of unit in global coordinate system
Expression formula； X is k-th of unit
Middle any point is at a distance from structural bearings end；L is the distance between adjacent sensors；
Step 3 passes through unknowm coefficientWith vibration shape zoom factor ΓrBetween relationshipAnd unknowm coefficientWith vibration shape zoom factor ΓrBetween relationshipAvailable r first order mode zoom factor ΓrExpression
Formula are as follows:
Wherein: the proportionality coefficient between elasticity modulus and temperature knots modification of the c to test the used material of structure, for concrete
It is c=-5.4633 × 10 for material7Pa/℃；
Step 4, so as to obtain bridge structure in reference temperature T0, change temperature T1And T2Under the conditions of displacement flexibility square
Battle array, reference temperature T0Under expression formula are as follows:
Wherein: βrFor the constant about structural natural frequencies, value βr=1/2j ω0r, j is imaginary unit；λ0rReference temperature T0
The r rank pole of condition flowering structure, the relationship with structural natural frequencies and damping ratio are
ξ0rFor reference temperature T0Under the conditions of damping to coefficient；β* r、WithRespectively βr、{ψrAnd λ0rConjugate complex number；{ψr}TRespectively{ ψrTransposed matrix；
Finally, predicting amount of deflection of the bridge structure under any static load, non-destructive tests based on the displacement flexibility matrix of identification
And bridge structure long-term behaviour research, and the safe condition of bridge structure is assessed.
2. a kind of quick test and evaluation method of bridge changed based on temperature according to claim 1, which is characterized in that
Equation is solved about the unknowm coefficient of vibration shape zoom factor in the step 2 are as follows:
3. a kind of quick test and evaluation method of bridge changed based on temperature according to claim 1, which is characterized in that
The reference temperature T0, change temperature T1And T22T need to be met0=T1+T2Equilibrium relationships.
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| CN113884258B (en) * | 2021-11-18 | 2023-04-18 | 郑州大学 | Inspection coefficient correction method considering influence of temperature on bridge rigidity |
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