CN107357983A - A kind of bridge mobile vehicle Load Identification Methods based on compressed sensing - Google Patents
A kind of bridge mobile vehicle Load Identification Methods based on compressed sensing Download PDFInfo
- Publication number
- CN107357983A CN107357983A CN201710524508.5A CN201710524508A CN107357983A CN 107357983 A CN107357983 A CN 107357983A CN 201710524508 A CN201710524508 A CN 201710524508A CN 107357983 A CN107357983 A CN 107357983A
- Authority
- CN
- China
- Prior art keywords
- vehicle
- carried mobile
- formula
- bridge
- msub
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Architecture (AREA)
- Civil Engineering (AREA)
- Structural Engineering (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Traffic Control Systems (AREA)
Abstract
The invention discloses a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing, comprise the following steps：Survey the translational speed of vehicle and car causes bridge response；Establish bridge physical mechanics model, derive the analytical expression that car causes bridge response, by vehicle-carried mobile it is discrete be jump function form, while cause the time-domain progress of bridge response analytical expression discrete to car；Bridge response is caused to carry out stochastical sampling in car using compressive sensing theory；Deploy unknown vehicle-carried mobile in the transform domain that discrete trigonometric function is formed, vehicle-carried mobile identification is converted into the Solve problems of decomposition coefficient；Bridge response normalized is caused to the car after stochastical sampling, and introduces L1Norm regularization establishes vehicle-carried mobile identification equation；Vehicle-carried mobile identification equation is solved with the LeastR functions in sparse optimization problem kit SLEP, and recognition result is converted to the TIME HISTORY SIGNAL of vehicle-carried mobile.Calculating cost is low when this method solves, and meets the accurate quick needs for identifying vehicle-carried mobile in scene.
Description
Technical field
The invention belongs to bridge structural health monitoring field, and in particular to a kind of bridge mobile vehicle based on compressed sensing
Load Identification Methods.
Background technology
For bridge structural health monitoring, bridge floor mobile vehicle load plays very important effect, and it is bridge clothes
One of main mobile load being subject to during labour, affect the service life of bridge.Due to Vehicle bridge action and pavement roughness
Etc. the influence of factor, vehicle-carried mobile constantly changes with time and space, and therefore, direct measurement vehicle-carried mobile is difficult to realize.Herein
Under background, the indirect identification method for studying vehicle-carried mobile just seems very necessary.Vehicle-carried mobile indirect identification method refers to pass through
Sensor in bridge structure obtains car and causes bridge response message, and response message and the dynamic characteristics of bridge are mutually tied
Close, the time history of inverting vehicle-carried mobile.
At present, the achievement in research of existing many vehicle-carried mobile recognition methods.Chinese invention patent (number of patent application：
CN201510062912.6 a kind of " bridge mobile vehicle load knowledge based on Kaczmarz algebraically iterative reconstruction approach) is disclosed
Other method ", this method needs to solve vehicle-carried mobile using Kaczmarz algebraically iterative reconstruction approach, by choosing suitable iteration
Step is iterated solution in time domain to actual measurement response.Chinese invention patent (number of patent application：CN201610876895.4 it is) public
Open " a kind of bridge moving load identification method based on concatenate dictionaries Yu sparse regularization ", this method is by using cascade word
Allusion quotation is deployed to vehicle-carried mobile, then by weighting L1Norm regularization constructs asking between dictionary atom and time domain response signal
Solve expression formula.But for Practical Project, the Modular Bridge System transfer matrix of required foundation and the response data dimension of collection are too
Greatly, it is unfavorable for data transfer and data analysis.
In Practical Project, bridge response data and system needed for most of existing vehicle-carried mobile recognition methods transmit square
The dimension of battle array is all very big, and data transfer and analysis process are both needed to higher calculating cost, is unfavorable for live quick identification vehicle-carried mobile.
Development and maturation with this new signal processing method of compressed sensing, signal will be gathered by way of stochastical sampling to be become
Increasingly popularize, how the signal collected using this new acquisition mode, be to need the problem that cracks.
The content of the invention
The purpose of the present invention is sparse representation theory and compressed sensing reason based on signal in view of the shortcomings of the prior art
By, there is provided a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing, it the method achieve to unknown locomotive
What is carried accurately identifies, and required calculating cost is low during solution, meets that scene quick and precisely identifies the needs of vehicle-carried mobile.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of bridge mobile vehicle Load Identification Methods based on compressed sensing, the described method comprises the following steps：
1) speed measuring device is evenly arranged on bridge to be used to measure the translational speed of vehicle, while is arranged on bridge some
Strain and acceleration transducer are used to record car cause bridge response；
2) according to bridge physical mechanics model inference car cause bridge respond analytical expression, by vehicle-carried mobile it is discrete be rank
Jump functional form, while causes the time-domain progress of bridge response analytical expression discrete to car；
3) stochastical sampling is carried out to strain and acceleration responsive using compressive sensing theory；
4) transform domain formed in discrete trigonometric function deploys unknown vehicle-carried mobile, and vehicle-carried mobile identification problem is converted into
The Solve problems of each decomposition coefficient；
5) the differently strained and acceleration responsive after stochastical sampling is normalized, and introduces L1Norm regularization
Method establishes vehicle-carried mobile identification equation；
6) with sparse optimization problem kit SLEP (Sparse Learning with Efficient
Projections LeastR functions in) solve vehicle-carried mobile identification equation, and by recognition result be converted to vehicle-carried mobile when
Journey signal.
Further, the specific implementation step of methods described is：
Consider under no initial condition, vehicle-carried mobile f is acted on bridge, and vehicle-carried mobile f number is nf, the sampling interval
For Δ t, measurement altogether obtains nbIndividual measuring point response data；
Consider j-th of vehicle-carried mobile fj(j=1,2 ..., nf) in period [t1,t2] in act on bridge, make the time
Length T=t2-t1, measure obtained i-th of measuring point response bi(i=1,2 ..., nb), biDimension be Ni× 1, i.e.,：
Aijfj=bi (1)
In formula, AijRepresent in j-th of vehicle-carried mobile fjIn the presence of, i-th of measuring point responds biCorresponding sytem matrix
Coefficient；
Construct Mi×NiCalculation matrix ΦciB is responded to i-th of measuring pointiCarry out stochastical sampling, calculation matrix ΦciIn it is each
Individual element obeys independent same distribution, average 0, variance 1/MiNormal distribution, respond b with i-th measuring pointiCorresponding survey
Moment matrix ΦciLine number MiIt is calculated by relationship below：
In formula, c is constant, and its value is c ≈ 4.0, and ln () represents logarithm operation, KiB is responded for the measuring point of hypothesisi
Degree of rarefication in some transform domain；
Bridge is obtained in j-th of vehicle-carried mobile fjIn the presence of, the expression formula for i-th of measuring point response that stochastical sampling obtains
For：
ΦciAijfj=Φcibi (3)
Define cosine function discrete on frequency domain respectively is with SIN function：
In formula, time t span is [t1,t2], Δ f is j-th of vehicle-carried mobile f of concernjFrequency discrimination
Rate, parameter ntBy j-th of vehicle-carried mobile f of concernjHighest frequency ftIt is determined that is,：
In formula, ceil () represents to round up；
Using above-mentioned two class functions sequence, following conversion domain matrix is constructed：
In formula,WithRepresent to use cosine function respectively And SIN functionIn [t1,t2] in be calculated with time interval Δ t
Time series；
By j-th of vehicle-carried mobile fjIt is expressed as：
In formula,Represent conversion domain matrix ΨcnKth row, αnjkRepresent j-th of vehicle-carried mobile fjK-th of resolving system
Number；Above formula is expressed as matrix form, obtained：
fj=Ψcnαnj (9)
In formula,
By decomposition coefficients alphanjCaused stochastical sampling responds ΦcibiIt is expressed as：
ΦciAijΨcnαnj=Φcibi (10)
It is abbreviated as：
Bijαnj=yi (11)
In formula, Bij=ΦciAijΨcn, yi=Φcibi；When considering that multiple vehicle-carried mobiles and multiple measuring points respond, need to
Calculating is normalized in the measuring point response that machine samples to obtain, and above-mentioned formula is expanded to：
Above formula is abbreviated as：
Bαn=by (13)
To j-th of vehicle-carried mobile fjTransform domain normalized as follows：
In formula,Represent αnIn only αnjCaused normalization when taking 1 of i-th of element
Response , ║ ║ afterwards2Represent the 2- norms of vector；
J-th of vehicle-carried mobile fjBy transform domain ΨcjIt is expressed as：
fj=Ψcjαj (15)
In formula, αjRepresent j-th of vehicle-carried mobile fjIn transform domain ΨcjIn decomposition coefficient form vector；
By decomposition coefficients alphajCaused stochastical sampling responds yiIt is expressed as：
ΦciAijΨcjαj=yi (16)
It is abbreviated as：
Cijαj=yi (17)
Consider that multiple vehicle-carried mobiles respond with multiple measuring points, above-mentioned formula can expand to：
Above-mentioned formula shows, in the presence of vehicle-carried mobile, the relation between the input and output of bridge structure can unite
One is expressed as：
C α=by (19)
In formula, C represents system transfer matrix；α represents decomposition coefficient vector, byRepresent structural response vector；Utilize L1Norm
Regularization, establish following vehicle-carried mobile identification equation：
Formula Zhong , ║ ║1Represent the 1- norms of vector, λ (λ>0) it is L1The regularization parameter of norm regularization method, use
The optimization problem of LeastR functions solution formula (20) in SLEP kits, the resolving system after being normalized in transform domain
Number, vehicle-carried mobile recognition result is calculated further combined with formula (15).
Further, a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing are managed using compressed sensing
Stochastical sampling is carried out by strain and acceleration responsive, it is unknown to convert domain representation using the normalization being made up of discrete trigonometric function
Vehicle-carried mobile, introduce L1Norm regularization model establishes identification equation, is solved and known using the LeastR functions in SLEP kits
Other equation.
The present invention compared with prior art, has the following advantages that and beneficial effect：
The present invention is by combining compressive sensing theory and sparse Regularization Technique, it is proposed that a kind of bridge based on compressed sensing
Beam mobile vehicle Load Identification Methods, the method achieve and unknown vehicle-carried mobile is accurately identified, required during solution to be calculated as
This is low, meets that scene quick and precisely identifies the needs of vehicle-carried mobile.
Brief description of the drawings
Fig. 1 is a kind of implementation main flow of the bridge mobile vehicle Load Identification Methods based on compressed sensing of the embodiment of the present invention
Journey schematic diagram.
Fig. 2 is the experimental provision sketch of the embodiment of the present invention.
Fig. 3 (a) is that model vehicle front axle load carries recognition result schematic diagram in the embodiment of the present invention；Fig. 3 (b) is real for the present invention
Apply model vehicle rear axle load in example and carry recognition result schematic diagram.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are unlimited
In this.
Embodiment：
Present embodiments provide a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing, the reality of methods described
Alms giver's schematic flow sheet is as shown in figure 1, comprise the following steps：
1) speed measuring device is evenly arranged on bridge to be used to measure the translational speed of vehicle, while is arranged on bridge some
Strain and acceleration transducer are used to record car cause bridge response；
2) according to bridge physical mechanics model inference car cause bridge respond analytical expression, by vehicle-carried mobile it is discrete be rank
Jump functional form, while causes the time-domain progress of bridge response analytical expression discrete to car；
3) stochastical sampling is carried out to strain and acceleration responsive using compressive sensing theory；
4) transform domain formed in discrete trigonometric function deploys unknown vehicle-carried mobile, and vehicle-carried mobile identification problem is converted into
The Solve problems of each decomposition coefficient；
5) the differently strained and acceleration responsive after stochastical sampling is normalized, and introduces L1Norm regularization
Method establishes vehicle-carried mobile identification equation；
6) with sparse optimization problem kit SLEP (Sparse Learning with Efficient
Projections LeastR functions in) solve vehicle-carried mobile identification equation, and by recognition result be converted to vehicle-carried mobile when
Journey signal.
The specific implementation step of methods described is：
Consider under no initial condition, vehicle-carried mobile f is acted on bridge, and vehicle-carried mobile f number is nf, the sampling interval
For Δ t, measurement altogether obtains nbIndividual measuring point response data；
Consider j-th of vehicle-carried mobile fj(j=1,2 ..., nf) in period [t1,t2] in act on bridge, make the time
Length T=t2-t1, measure obtained i-th of measuring point response bi(i=1,2 ..., nb), biDimension be Ni× 1, i.e.,：
Aijfj=bi (1)
In formula, AijRepresent in j-th of vehicle-carried mobile fjIn the presence of, i-th of measuring point responds biCorresponding sytem matrix
Coefficient；
Construct Mi×NiCalculation matrix ΦciB is responded to i-th of measuring pointiCarry out stochastical sampling, calculation matrix ΦciIn it is each
Individual element obeys independent same distribution, average 0, variance 1/MiNormal distribution, respond b with i-th measuring pointiCorresponding survey
Moment matrix ΦciLine number MiIt is calculated by relationship below：
In formula, c is constant, and its value is c ≈ 4.0, and ln () represents logarithm operation, KiB is responded for the measuring point of hypothesisi
Degree of rarefication in some transform domain；
Bridge is obtained in j-th of vehicle-carried mobile fjIn the presence of, the expression formula for i-th of measuring point response that stochastical sampling obtains
For：
ΦciAijfj=Φcibi (3)
Define cosine function discrete on frequency domain respectively is with SIN function：
In formula, time t span is [t1,t2], Δ f is j-th of vehicle-carried mobile f of concernjFrequency discrimination
Rate, parameter ntBy j-th of vehicle-carried mobile f of concernjHighest frequency ftIt is determined that is,：
In formula, ceil () represents to round up；
Using above-mentioned two class functions sequence, following conversion domain matrix is constructed：
In formula,WithRepresent to use cosine function respectively And SIN functionIn [t1,t2] in be calculated with time interval Δ t
Time series；
By j-th of vehicle-carried mobile fjIt is expressed as：
In formula,Represent conversion domain matrix ΨcnKth row, αnjkRepresent j-th of vehicle-carried mobile fjK-th of resolving system
Number；Above formula is expressed as matrix form, obtained：
fj=Ψcnαnj (9)
In formula,
By decomposition coefficients alphanjCaused stochastical sampling responds ΦcibiIt is expressed as：
ΦciAijΨcnαnj=Φcibi (10)
It is abbreviated as：
Bijαnj=yi (11)
In formula, Bij=ΦciAijΨcn, yi=Φcibi；When considering that multiple vehicle-carried mobiles and multiple measuring points respond, need to
Calculating is normalized in the measuring point response that machine samples to obtain, and above-mentioned formula is expanded to：
Above formula is abbreviated as：
Bαn=by (13)
To j-th of vehicle-carried mobile fjTransform domain normalized as follows：
In formula,Represent αnIn only αnjCaused normalization when taking 1 of i-th of element
Response , ║ ║ afterwards2Represent the 2- norms of vector；
J-th of vehicle-carried mobile fjBy transform domain ΨcjIt is expressed as：
fj=Ψcjαj (15)
In formula, αjRepresent j-th of vehicle-carried mobile fjIn transform domain ΨcjIn decomposition coefficient form vector；
By decomposition coefficients alphajCaused stochastical sampling responds yiIt is expressed as：
ΦciAijΨcjαj=yi (16)
It is abbreviated as：
Cijαj=yi (17)
Consider that multiple vehicle-carried mobiles respond with multiple measuring points, above-mentioned formula can expand to：
Above-mentioned formula shows, in the presence of vehicle-carried mobile, the relation between the input and output of bridge structure can unite
One is expressed as：
C α=by (19)
In formula, C represents system transfer matrix；α represents decomposition coefficient vector, byRepresent structural response vector；Utilize L1Norm
Regularization, establish following vehicle-carried mobile identification equation：
Formula Zhong , ║ ║1Represent the 1- norms of vector, λ (λ>0) it is L1The regularization parameter of norm regularization method, use
The optimization problem of LeastR functions solution formula (20) in SLEP kits, the resolving system after being normalized in transform domain
Number, vehicle-carried mobile recognition result is calculated further combined with formula (15).
Using the hollow square tube beam in laboratory and model dolly as research object, the above-mentioned bridge based on compressed sensing of description moves
The implementation process of motor-car Load Identification Methods, experimental provision sketch is as shown in Fig. 2 experiment girder is the pin-ended of 3m length
Beam, beam section are rectangle thin wall section, width 0.14m, a height of 0.06m, thickness 0.003m；Test carriage is led by motor
Draw at the uniform velocity by testing girder.Dolly actual axial weight is：Front axle 4.5955kg, rear axle 6.0290kg, the wheelbase of dolly two from for
0.42m.The specific implementation step of vehicle-carried mobile identification is as follows：
The first, speed measuring device is installed above bridge, the speed measuring device in the present embodiment is by truss structure and photoelectric sensor
Collectively form, surveying small vehicle speed is：2.2320m/s.Should away from the soffit installation at upper bridge end 1/4,1/2 and 3/4 in bridge
Change and acceleration transducer, for measuring the moment of flexure and acceleration responsive in section.The sample frequency of response data is 1024Hz, is adopted
A length of 1.5323s during sample.
2nd, the differential equation of motion of beam is established using Euler-Bernoulli Jacob's beam theory, vehicle-carried mobile is derived by mode superposition method
With moment of flexure response, the relation between acceleration responsive, by vehicle-carried mobile it is discrete be jump function form, it is and discrete to equation progress
Change.Density p=7689kg/m of structure3, bending rigidity EI=1.41 × 105N/m.During calculating, structure first three rank mode letter is taken
Breath, wherein modal mass is obtained with Mode Shape by theoretical formula method, and modal damping is measured with modal frequency by testing.Actual measurement
First three order frequency is respectively：23.279Hz、89.519Hz、186.595Hz；Surveying first three rank damping ratio is respectively：0.0031、
0.0026、0.0058。
3rd, calculation matrix is generated at random, and each element obeys independent same distribution, average 0, variance 1/M in matrixi
Normal distribution.MiDetermined by formula (2), wherein, the degree of rarefication K of each response dataiIt is taken as 50.
4th, non-primaryload highest frequency f of concern is takent=200Hz, according to formula (3)-(6) and formula (14) point
Not Gou Zao two normalized transform domains represent two unknown vehicle-carried mobiles.Wherein, frequency resolution Δ f=1Hz, between sampling
Every Δ t=1/1024s=9.7656 × 10-4S, a length of 1.3441s during sampling；The number of decomposition coefficient is nt=ceil (ft/Δ
F)=200.
5th, different measuring points response is normalized, introduces L1Norm regularization establishes vehicle-carried mobile identification equation,
As shown in formula (20).
6th, identification equation is solved using the LeastR functions in sparse optimization problem kit SLEP, and will identification
As a result corresponding TIME HISTORY SIGNAL is converted to.1 × 10 is arranged to except parameter opts.rFlag is arranged to 1, opts.maxIter5Outside；
Other parameters use default setting.Regularization parameter λ uses bayesian information criterion (Bayesian Information
Criterion, BIC) chosen, that is, it is optimal regularization parameter λ that choosing, which makes equation below take the regularization parameter of minimum value,：
BIC=ln (P) K+Pln (RSS/P) (21)
In formula, P is vectorial α line number, and K is vectorial α degree of rarefication, and the residual error that RSS responded and rebuild response for measurement is put down
Fang He.
Shown in vehicle-carried mobile recognition result such as Fig. 3 (a) and Fig. 3 (b), it can be seen that a kind of be based on compressed sensing
Bridge mobile vehicle Load Identification Methods in this specific embodiment can inverting vehicle-carried mobile exactly, can estimate exactly
The axle weight of mobile vehicle.
On the other hand, system transfer matrix and the dimension of response data are reduced extremely by 4706 × 2750,4706 × 1 respectively
2070 × 802,2070 × 1, greatly reduce calculating cost.
It is contemplated that by the way that the method for the invention is further improved and developed, when this invention is in bridge
During the extensive use of monitoring structural health conditions field, huge engineering application value will be produced.Meanwhile when based on compressive sensing theory
Stochastical sampling method can be produced after the mature in signal acquisition field with getting the mastery among being converted in engineering technology
Raw huge economic benefit and commercial value.
It is described above, patent preferred embodiment only of the present invention, but the protection domain of patent of the present invention is not limited to
This, any one skilled in the art is in the scope disclosed in patent of the present invention, according to the skill of patent of the present invention
Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the protection domain of patent of the present invention.
Claims (3)
1. a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing, it is characterised in that methods described includes following
Step：
1) translational speed that speed measuring device is used to measure vehicle is evenly arranged on bridge, while some strains are arranged on bridge
It is used to record car cause bridge response with acceleration transducer；
2) according to bridge physical mechanics model inference car cause bridge respond analytical expression, by vehicle-carried mobile it is discrete be step letter
Number form formula, while cause the time-domain progress of bridge response analytical expression discrete to car；
3) stochastical sampling is carried out to strain and acceleration responsive using compressive sensing theory；
4) transform domain formed in discrete trigonometric function deploys unknown vehicle-carried mobile, vehicle-carried mobile identification problem is converted into each
The Solve problems of decomposition coefficient；
5) the differently strained and acceleration responsive after stochastical sampling is normalized, and introduces L1Norm regularization method
Establish vehicle-carried mobile identification equation；
6) with sparse optimization problem kit SLEP (Sparse Learning with Efficient
Projections LeastR functions in) solve vehicle-carried mobile identification equation, and by recognition result be converted to vehicle-carried mobile when
Journey signal.
2. a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing according to claim 1, its feature exist
In the specific implementation step of methods described is：
Consider under no initial condition, vehicle-carried mobile f is acted on bridge, and vehicle-carried mobile f number is nf, the sampling interval is Δ
T, altogether measurement obtain nbIndividual measuring point response data；
Consider j-th of vehicle-carried mobile fj(j=1,2 ..., nf) in period [t1,t2] in act on bridge, make time span T
=t2-t1, measure obtained i-th of measuring point response bi(i=1,2 ..., nb), biDimension be Ni× 1, i.e.,：
Aijfj=bi (1)
In formula, AijRepresent in j-th of vehicle-carried mobile fjIn the presence of, i-th of measuring point responds biCorresponding sytem matrix coefficient；
Construct Mi×NiCalculation matrix ΦciB is responded to i-th of measuring pointiCarry out stochastical sampling, calculation matrix ΦciIn each element
Obey independent same distribution, average 0, variance 1/MiNormal distribution, respond b with i-th measuring pointiCorresponding calculation matrix
ΦciLine number MiIt is calculated by relationship below：
<mrow>
<msub>
<mi>M</mi>
<mi>i</mi>
</msub>
<mo>&GreaterEqual;</mo>
<msub>
<mi>cK</mi>
<mi>i</mi>
</msub>
<mi>l</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>N</mi>
<mi>i</mi>
</msub>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, c is constant, and its value is c ≈ 4.0, and ln () represents logarithm operation, KiB is responded for the measuring point of hypothesisiAt some
Degree of rarefication in transform domain；
Bridge is obtained in j-th of vehicle-carried mobile fjIn the presence of, the expression formula for i-th of measuring point response that stochastical sampling obtains is：
ΦciAijfj=Φcibi (3)
Define cosine function discrete on frequency domain respectively is with SIN function：
In formula, time t span is [t1,t2], Δ f is j-th of vehicle-carried mobile f of concernjFrequency resolution, ginseng
Number ntBy j-th of vehicle-carried mobile f of concernjHighest frequency ftIt is determined that is,：
<mrow>
<msub>
<mi>n</mi>
<mi>t</mi>
</msub>
<mo>=</mo>
<mi>c</mi>
<mi>e</mi>
<mi>i</mi>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>f</mi>
<mi>t</mi>
</msub>
<mrow>
<mi>&Delta;</mi>
<mi>f</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, ceil () represents to round up；
Using above-mentioned two class functions sequence, following conversion domain matrix is constructed：
In formula,WithRepresent to use cosine function respectively And SIN functionIn [t1,t2] in the time series that is calculated with time interval Δ t；
By j-th of vehicle-carried mobile fjIt is expressed as：
In formula,Represent conversion domain matrix ΨcnKth row, αnjkRepresent j-th of vehicle-carried mobile fjK-th of decomposition coefficient；Will
Above formula is expressed as matrix form, obtains：
fj=Ψcnαnj (9)
In formula,
By decomposition coefficients alphanjCaused stochastical sampling responds ΦcibiIt is expressed as：
ΦciAijΨcnαnj=Φcibi (10)
It is abbreviated as：
Bijαnj=yi (11)
In formula, Bij=ΦciAijΨcn, yi=Φcibi；, need to be to adopting at random when considering that multiple vehicle-carried mobiles respond with multiple measuring points
Calculating is normalized in the measuring point response that sample obtains, and above-mentioned formula is expanded to：
Above formula is abbreviated as：
Bαn=by (13)
To j-th of vehicle-carried mobile fjTransform domain normalized as follows：
In formula,Represent αnIn only αnjI-th of element when taking 1 after caused normalization
Respond , ║ ║2Represent the 2- norms of vector；
J-th of vehicle-carried mobile fjBy transform domain ΨcjIt is expressed as：
fj=Ψcjαj (15)
In formula, αjRepresent j-th of vehicle-carried mobile fjIn transform domain ΨcjIn decomposition coefficient form vector；
By decomposition coefficients alphajCaused stochastical sampling responds yiIt is expressed as：
ΦciAijΨcjαj=yi (16)
It is abbreviated as：
Cijαj=yi (17)
Consider that multiple vehicle-carried mobiles respond with multiple measuring points, above-mentioned formula can expand to：
Above-mentioned formula shows, in the presence of vehicle-carried mobile, the relation between the input and output of bridge structure can unify table
It is shown as：
C α=by (19)
In formula, C represents system transfer matrix；α represents decomposition coefficient vector, byRepresent structural response vector；Utilize L1Norm canonical
Change, establish following vehicle-carried mobile identification equation：
<mrow>
<msub>
<mi>&alpha;</mi>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
</msub>
<mo>=</mo>
<mi>arg</mi>
<munder>
<mi>min</mi>
<mi>&alpha;</mi>
</munder>
<mo>{</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>|</mo>
<mo>|</mo>
<mi>C</mi>
<mi>&alpha;</mi>
<mo>-</mo>
<msub>
<mi>b</mi>
<mi>y</mi>
</msub>
<mo>|</mo>
<msubsup>
<mo>|</mo>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mi>&lambda;</mi>
<mo>|</mo>
<mo>|</mo>
<mi>&alpha;</mi>
<mo>|</mo>
<msub>
<mo>|</mo>
<mn>1</mn>
</msub>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula Zhong , ║ ║1Represent the 1- norms of vector, λ (λ>0) it is L1The regularization parameter of norm regularization method, using SLEP works
The optimization problem of LeastR functions solution formula (20) in tool bag, the decomposition coefficient after being normalized in transform domain, enters one
Step combines formula (15) and calculates vehicle-carried mobile recognition result.
3. a kind of bridge mobile vehicle Load Identification Methods based on compressed sensing according to claim 1, its feature exist
In：Methods described carries out stochastical sampling using compressive sensing theory to strain and acceleration responsive, using by discrete trigonometric function
The normalization conversion unknown vehicle-carried mobile of domain representation of composition, introduces L1Norm regularization model establishes identification equation, using SLEP
LeastR functions in kit solve identification equation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710524508.5A CN107357983B (en) | 2017-06-30 | 2017-06-30 | Bridge moving vehicle load identification method based on compressed sensing |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710524508.5A CN107357983B (en) | 2017-06-30 | 2017-06-30 | Bridge moving vehicle load identification method based on compressed sensing |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107357983A true CN107357983A (en) | 2017-11-17 |
| CN107357983B CN107357983B (en) | 2020-10-27 |
Family
ID=60272522
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710524508.5A Active CN107357983B (en) | 2017-06-30 | 2017-06-30 | Bridge moving vehicle load identification method based on compressed sensing |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107357983B (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108846200A (en) * | 2018-06-07 | 2018-11-20 | 大连理工大学 | A kind of quasi-static Bridge Influence Line recognition methods based on iterative method |
| CN109084943A (en) * | 2018-07-09 | 2018-12-25 | 暨南大学 | A kind of Structural Damage Identification based on subspace projection Yu sparse regularization |
| CN113408030A (en) * | 2021-06-22 | 2021-09-17 | 南通大学 | Method for rapidly inverting bridge load by using finite vibration response |
| CN115344819A (en) * | 2022-08-16 | 2022-11-15 | 哈尔滨工业大学 | State equation-based explicit Euler method symbolic network ordinary differential equation identification method |
| JP7396139B2 (en) | 2020-03-18 | 2023-12-12 | セイコーエプソン株式会社 | Measurement method, measurement device, measurement system and measurement program |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103323276A (en) * | 2013-05-28 | 2013-09-25 | 山西省交通科学研究院 | Method for fast detection and evaluation of cross-section characteristic of concrete bridge |
| CN106202789A (en) * | 2016-07-20 | 2016-12-07 | 暨南大学 | A kind of based on L1/2the recognition methods collaborative with damage of the beam bridge traveling load of regularization |
| CN106503730A (en) * | 2016-09-30 | 2017-03-15 | 暨南大学 | A kind of bridge moving load identification method based on concatenate dictionaries and sparse regularization |
-
2017
- 2017-06-30 CN CN201710524508.5A patent/CN107357983B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103323276A (en) * | 2013-05-28 | 2013-09-25 | 山西省交通科学研究院 | Method for fast detection and evaluation of cross-section characteristic of concrete bridge |
| CN106202789A (en) * | 2016-07-20 | 2016-12-07 | 暨南大学 | A kind of based on L1/2the recognition methods collaborative with damage of the beam bridge traveling load of regularization |
| CN106503730A (en) * | 2016-09-30 | 2017-03-15 | 暨南大学 | A kind of bridge moving load identification method based on concatenate dictionaries and sparse regularization |
Non-Patent Citations (5)
| Title |
|---|
| DAVID MASCAREÑAS 等: "Compressed sensing techniques for detecting damage in structures", 《STRUCTURAL HEALTH MONITORING》 * |
| MADHUKA JAYAWARDHANA 等: "Compressive sensing for efficient health monitoring and effective damage detection of structures", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》 * |
| YONGCHAO YANG 等: "Output-only modal identification by compressed sensing:Non-uniform low-rate random sampling", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》 * |
| 余岭 等: "基于矩量法的桥梁移动车载识别试验研究", 《振动与冲击》 * |
| 季赛 等: "面向无线传感结构健康监测的压缩感知方法研究", 《传感技术学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108846200A (en) * | 2018-06-07 | 2018-11-20 | 大连理工大学 | A kind of quasi-static Bridge Influence Line recognition methods based on iterative method |
| CN109084943A (en) * | 2018-07-09 | 2018-12-25 | 暨南大学 | A kind of Structural Damage Identification based on subspace projection Yu sparse regularization |
| JP7396139B2 (en) | 2020-03-18 | 2023-12-12 | セイコーエプソン株式会社 | Measurement method, measurement device, measurement system and measurement program |
| CN113408030A (en) * | 2021-06-22 | 2021-09-17 | 南通大学 | Method for rapidly inverting bridge load by using finite vibration response |
| CN115344819A (en) * | 2022-08-16 | 2022-11-15 | 哈尔滨工业大学 | State equation-based explicit Euler method symbolic network ordinary differential equation identification method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107357983B (en) | 2020-10-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107357983A (en) | A kind of bridge mobile vehicle Load Identification Methods based on compressed sensing | |
| CN109682561B (en) | Method for automatically detecting free vibration response of high-speed railway bridge to identify mode | |
| CN106503730B (en) | A kind of bridge moving load identification method based on concatenate dictionaries Yu sparse regularization | |
| CN106197970B (en) | A kind of bridge rope monitoring method and system based on optimization tensioning string model | |
| CN109855823B (en) | Method for identifying damage of bridge structure by using test vehicle | |
| CN104598753B (en) | Bridge moving vehicle load recognition method based on Brakhage V method | |
| CN104819846B (en) | Rolling bearing sound signal fault diagnosis method based on short-time Fourier transform and sparse laminated automatic encoder | |
| CN104123463A (en) | Time domain identification method of random dynamic loads | |
| CN105912504B (en) | A kind of compression sensing method of mechanical structure multi-source shock loading identification | |
| CN104132791A (en) | Operation mode analysis experiment method and device based on pulse excitation | |
| CN103364170A (en) | Ground simulation predicting method and system for aeroelasticity stability | |
| CN104792364B (en) | Dynamic bridge parameter extracting system and dynamic bridge parameter extracting method based on laser Doppler | |
| CN108844702A (en) | The measuring method of Bridge Influence Line when vehicle at the uniform velocity passes through | |
| CN107271127A (en) | Based on the operational modal parameter recognition methods and device extracted from iteration pivot | |
| CN101587007A (en) | Output-only wavelet analytical method for recognizing flexible bridge structure kinetic parameter | |
| CN104990721A (en) | EMD (empirical mode decomposition)-based stress-strain reconstruction method | |
| CN108846200A (en) | A kind of quasi-static Bridge Influence Line recognition methods based on iterative method | |
| CN115101147A (en) | Road bearing capacity monitoring method | |
| CN112326787B (en) | Beam bridge identification method based on dedicated test vehicle multipoint rapid static acquisition | |
| Xiang et al. | Vibration-based structural damage identification using P-CNN and time-frequency hybrid index under the conditions of uncertainties and incomplete measurements | |
| CN103630588A (en) | Rapid response method of electrochemical gas sensor | |
| CN105651537B (en) | A kind of truss structure damage real-time monitoring system of high susceptibility to damage | |
| CN110231403B (en) | Long-span bridge online real-time damage identification method supported by mobile load response wavelet packet analysis | |
| CN105139025B (en) | Gas-solid fluidized bed flow pattern online intelligent recognition method based on nonlinear analysis method | |
| CN115524086A (en) | Statistical moment-curvature beam type bridge damage identification method based on axle coupling vibration |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |