CN106768234A - Make the recognition methods of the bridge floor multiaxis traveling load of usage based on classical row - Google Patents
Make the recognition methods of the bridge floor multiaxis traveling load of usage based on classical row Download PDFInfo
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- CN106768234A CN106768234A CN201710061188.4A CN201710061188A CN106768234A CN 106768234 A CN106768234 A CN 106768234A CN 201710061188 A CN201710061188 A CN 201710061188A CN 106768234 A CN106768234 A CN 106768234A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01G—WEIGHING
- G01G19/00—Weighing apparatus or methods adapted for special purposes not provided for in the preceding groups
- G01G19/02—Weighing apparatus or methods adapted for special purposes not provided for in the preceding groups for weighing wheeled or rolling bodies, e.g. vehicles
- G01G19/03—Weighing apparatus or methods adapted for special purposes not provided for in the preceding groups for weighing wheeled or rolling bodies, e.g. vehicles for weighing during motion
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Abstract
The invention discloses a kind of recognition methods of the bridge floor multiaxis traveling load for making usage based on classical row, comprise the following steps:1), in bridge bottom surface correspondence position x1,x2,…xmM displacement transducer is pasted at place respectively, measures bridge floor multiaxis mobile vehicle load fkT () displacement of t at x position is v (x, t), k=1,2,3 ..., be the vehicle number of axle;2) oscillatory differential equation, is set up;3), equation (1) is solved;4) bridge, is set up under k axle Vehicle Loads, and multiaxis traveling load system equation is recognized by dynamic respond;5) exact value of multiaxis traveling load, is tried to achieve as usage using classical row.The present invention need to only measure bridge displacement response and can recognize that multiaxis traveling load, and recognition methods is simple and precision is higher, with good feasibility, can be widely applied to the moving load identification of all kinds bridge.
Description
Technical field
Bridge floor multiaxis is recognized by bridge displacement the invention belongs to bridge floor moving load identification technical field, more particularly to one kind
The method of traveling load.
Background technology
Bridges in Our Country present situation is " rebuilding light supporting ", and from 1999 to 2013, domestic media disclosed report China because various
The bridge that reason collapses up to more than 110 seats, wherein the bridge collapse not caused including Wenchuan earthquake still.Cause bridge damnification and break
Bad reason can be summarized as external factor and internal factor, wherein in external factor due to automobile overload cause bridge fatigue damage and
Durability reduction occupies leading position, and internal factor is then mainly the reduction of bridge itself bearing capacity and the strength of materials is degenerated.
With the explosive growth of highway in China traffic, the actual vehicle flowrate for bearing of many bridges increases compared with Earlier designs value
A lot, the increase of speed and car weight can have a negative impact to bridge, the multiple-axle vehicle and large-scale multiple-axle vehicle especially overloads
Appearance substantially exacerbate the risk of bridge collapse.
Highway in China transfinites to stand and make many work in control vehicle overload method, but measuring method is to use ground mostly at present
Pound technology, i.e., weigh to realize the measurement of gross combination weight by parking.Under the trend of development rapid transit, how in vehicle row
Accurate vehicle load has important practical meaning in engineering during sailing, especially to the accurate measurement of each axle load of multiaxis lorry
Security and durability to protecting bridge all have very great help.
It is identified for conventional two-axle car more than existing moving load identification technology, it is impossible to which multiple-axle vehicle load is entered
Row identification, therefore it is badly in need of a kind of method that can be identified to bridge floor multiaxis mobile vehicle load.
The content of the invention
Only need to measure the identification bridge floor multiaxis by bridge displacement is responded rapidly and efficiently it is an object of the invention to provide a kind of
Mobile vehicle load, accuracy of identification is high and does not influence bridge floor vehicle normal pass.
To reach above-mentioned purpose, the technical solution adopted by the present invention is:A kind of bridge floor for making usage based on classical row
The recognition methods of multiaxis traveling load, comprises the following steps:
1), in bridge bottom surface correspondence position x1,x2,…xmM displacement transducer is pasted at place respectively, measures the shifting of bridge floor multiaxis
Dynamic vehicular load fkT () displacement of t at x position is v (x, t), k=1,2,3 ..., be the vehicle number of axle;
2) vehicle-bridge system oscillatory differential equation, is set up:Bridge length is taken for L, bending rigidity is EI, bridge unit length matter
It is ρ to measure, it is considered to which viscous damping simultaneously takes damped coefficient for C, ignores detrusion and the rotary inertia of bridge, bridge floor multiaxis locomotive
Load fk (t) is moved right with speed c from beam left end supporting, then the oscillatory differential equation of vehicle-bridge system is:
Wherein δ (x-ct) is Dirac function;
The boundary condition of equation (1) is:
V (0, t)=0, v (L, t)=0,V (x, 0)=0,
3), equation (1) is solved;
4) bridge, is set up under k axle Vehicle Loads, and multiaxis traveling load system equation is recognized by dynamic respond:
v(m×1)=S(m×k)·f(k×1) (2)
v(m×1)It is traveling load fkT () is in x1,x2,…xmThe actual displacement at place, and m >=k;S(m×k)It is known system square
Battle array;f(k×1)It is required k axle traveling loads;
The discrete form of formula (2) is expressed as:
Wherein
5) exact value of multiaxis traveling load, is tried to achieve as usage using classical row;
To vehicle bridge moving load identification system equationUsage iterative is made using classical row, vehicle bridge is moved
The transposed matrix S of load identification sytem matrix STDivided by column is ST=[s1,s2,...,sn], equation v=Sf is rewritable to be:
R is one of matrix total collection and represents letter, RnIt is a matrix total collection for the row of n rows 1, si∈RnRepresent si
It is a matrix for the row of n rows one;
Classical row can be obtained and make usage Iteration, forB=0,1, if 2 ..., control sequence be taken as following
Ring is controlled, then had:
f(b+1)=f(b)+(vi-(si, f(b)))si (5)
Wherein f(0)It is iterative initial value, f(0)Can be obtained by least square method, the initial movement obtained by least square method
Load precision is not high, allows identification intensive reading to gradually step up by continuous iteration, and b is iterations, f(b)It is b number of solution of equations
Value approximate solution, f(b+1)The multiaxis traveling load for as recognizing.
Described step 3) in equation (1) is solved comprise the following steps that it is described:
Based on modal superposition principle, it is assumed that the n-th order Mode Shape function of bridge isThen equation (1)
Solution be expressed as:
Matrix form is:
Here n is mode number, qnT () (n=1,2 ... ∞) are n-th order modal displacements, equation (12) is substituted into equation (1),
And x is integrated in [0, L], using boundary condition and Dirac function characteristic, vehicle-bridge system oscillatory differential equation qn
T () is expressed as:
HereIt is qnThe second dervative of (t),It is qnThe first derivative of (t), Respectively circular frequency, damping rate and bridge floor mobile vehicle load mod table
Up to formula;
As vehicle has k axletree, and k-th axletree is to the distance of first axletreeThen equation (14)
It is written as:
Then corresponding to the modal displacement at m measuring point can be expressed as by equation (13):
X on bridge1,x2,…xmThe speed at place is tried to achieve by the once differentiation of displacement:
Further, x on bridge1,x2,…xmThe acceleration at place is tried to achieve by the second differential of displacement:
Similarly, x on beam1,x2,…xmThe moment of flexure at place can utilize relational expressionTry to achieve:
If f1,f2,…,fkIt is each axle correspondence load of known k axles vehicle, ignores the influence of damping, then the solution of equation (1) can
It is expressed as:
Wherein
The present invention can respond identification multiaxis traveling load, the method letter of measurement bridge displacement response by measuring bridge displacement
List and precision is higher, therefore identification bridge floor traveling load is responded by bridge displacement there is good feasibility and accuracy of identification energy
Guarantee is accessed, dynamic respond need to be only obtained using method proposed by the present invention and be can recognize that bridge floor multiaxis traveling load, therefore
Recognition methods proposed by the present invention has good feasibility, can be widely applied to the moving load identification of all kinds bridge.
Making usage identification multiaxis traveling load based on classical row has clear concept, it is easy to the advantages of operating, and need to only measure the position of bridge
Move the i.e. recognizable bridge floor movement multiaxis loaded vehicle load of response.By divided by column after vehicle multiple-shaft load identification sytem matrix transposition,
System identification method is converted into iteration form and is solved, and iteration is stopped by iterations meets accuracy of identification, then finally
Single-step iteration solution is the multiaxis traveling load of identification, and accuracy of identification is high.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention.
Specific embodiment
As shown in figure 1, the invention discloses a kind of identification side of the bridge floor multiaxis traveling load for making usage based on classical row
Method, comprises the following steps:
1), in bridge bottom surface correspondence position x1,x2,…xmM displacement transducer is pasted at place respectively, measures the shifting of bridge floor multiaxis
Dynamic vehicular load fk(t) at x position t displacement for v (x, t), k=1,2,3 ... be the vehicle number of axle;
2) vehicle-bridge system oscillatory differential equation, is set up:Bridge length is taken for L, bending rigidity is EI, bridge unit length matter
It is ρ to measure, it is considered to which viscous damping simultaneously takes damped coefficient for C, ignores detrusion and the rotary inertia of bridge, bridge floor multiaxis locomotive
Load fk (t) is moved right with speed c from beam left end supporting, then the oscillatory differential equation of vehicle-bridge system is:
Wherein δ (x-ct) is Dirac function;
The boundary condition of equation (1) is:
V (0, t)=0, v (L, t)=0,V (x, 0)=0,
3), equation (1) is solved;
Based on modal superposition principle, it is assumed that the n-th order Mode Shape function of beam isThen equation (1)
Solution is represented by:
Matrix form is:
Here n is mode number, qnT () (n=1,2 ... ∞) are n-th order modal displacements, equation (12) is substituted into equation (1),
And x is integrated in [0, L], using boundary condition and Dirac function characteristic, vehicle-bridge system oscillatory differential equation qn
T () is expressed as:
HereIt is qnThe second dervative of (t),It is qnThe first derivative of (t), Respectively circular frequency, damping rate and bridge floor mobile vehicle load mod table
Up to formula.
As vehicle has k axletree, and k-th axletree is to the distance of first axletreeThen equation (14)
It is written as:
Then corresponding to the modal displacement at m measuring point can be expressed as by equation (13):
X on bridge1,x2,…xmThe speed at place is tried to achieve by the once differentiation of displacement:
Further, x on bridge1,x2,…xmThe acceleration at place is tried to achieve by the second differential of displacement:
Similarly, x on beam1,x2,…xmThe moment of flexure at place can utilize relational expressionTry to achieve:
If f1,f2,…,fkIt is each axle correspondence load of known k axles vehicle, ignores the influence of damping, then the solution of equation (1) can
It is expressed as:
Wherein
4) bridge, is set up under k axle Vehicle Loads, and multiaxis traveling load system equation is recognized by dynamic respond:
v(m×1)=S(m×k)·f(k×1) (2)
v(m×1)It is traveling load fkT () is in x1,x2,…xmThe actual displacement at place (is exactly measured position in step (1)
Move), and m >=k;S(m×k)It is known sytem matrix;f(k×1)It is required k axle traveling loads;
The discrete form of formula (2) is expressed as
Wherein
5) exact value of multiaxis traveling load, is tried to achieve as usage using classical row;
, it is necessary to solving system matrix S's is inverse in solution procedure is carried out to equation (2), to avoid sytem matrix morbid state from leading
The accuracy of identification reduction of cause, spy introduces classical row and makees the accuracy of identification that usage improves multiple-axle vehicle time-histories load.
Usage iterative is made using classical row to vehicle bridge moving load identification system equation Sf=v, vehicle bridge is moved into lotus
Carry the transposed matrix S of identifying system matrix STDivided by column is ST=[s1, s2..., sn], equation v=Sf is rewritable to be:
R is one of matrix total collection and represents letter, RnIt is a matrix total collection for the row of n rows 1, si∈RnRepresent si
It is a matrix for the row of n rows one;
Classical row can be obtained and make usage Iteration, forB=0,1,2, if control sequence is taken as circulation
Control, then have:
f(b+1)=f(b)+(vi-(si, f(b)))si (5)
Wherein f(0)It is iterative initial value, f(0)Can be obtained by least square method, the initial movement obtained by least square method
Load precision is not high, allows identification intensive reading to gradually step up by continuous iteration, and b is iterations, f(b)It is b number of solution of equations
Value approximate solution, f(b+1)The multiaxis traveling load for as recognizing.
Claims (2)
1. a kind of recognition methods of the bridge floor multiaxis traveling load for making usage based on classical row, it is characterised in that:Including following step
Suddenly:
1), in bridge bottom surface correspondence position x1,x2,…xmM displacement transducer is pasted at place respectively, measures bridge floor multiaxis locomotive
Load fkT () displacement of t at x position is v (x, t), k=1,2,3 ..., be the vehicle number of axle;
2) vehicle-bridge system oscillatory differential equation, is set up:Bridge length is taken for L, bending rigidity is EI, and bridge linear mass is
ρ, it is considered to which viscous damping simultaneously takes damped coefficient for C, ignores detrusion and the rotary inertia of bridge, bridge floor multiaxis mobile vehicle lotus
Carry fk (t) to be moved right from beam left end supporting with speed c, then the oscillatory differential equation of vehicle-bridge system is:
Wherein δ (x-ct) is Dirac function;
The boundary condition of equation (1) is:
V (0, t)=0, v (L, t)=0,V (x, 0)=0,
3), equation (1) is solved;
4) bridge, is set up under k axle Vehicle Loads, and multiaxis traveling load system equation is recognized by dynamic respond:
v(m×1)=S(m×k)·f(k×1) (2)
v(m×1)It is traveling load fkT () is in x1,x2,…xmThe actual displacement at place, and m >=k;S(m×k)It is known sytem matrix;
f(k×1)It is required k axle traveling loads;
The discrete form of formula (2) is expressed as:
Wherein
5) exact value of multiaxis traveling load, is tried to achieve as usage using classical row;
Usage iterative is made using classical row to vehicle bridge moving load identification system equation Sf=v, by vehicle bridge traveling load
The transposed matrix S of identifying system matrix STDivided by column is ST=[s1, s2..., sn], equation v=Sf is rewritable to be:
R is one of matrix total collection and represents letter, Rn:It is a matrix total collection for the row of n rows 1, si∈RnRepresent siIt is one
The matrix of the individual row of n rows one;
Classical row can be obtained and make usage Iteration, forIf control sequence is taken as circulation control
System, then have:
f(b+1)=f(b)+(vi-(si, f (b))) si (5)
Wherein f(0)It is iterative initial value, f(0)Can be obtained by least square method, the initial traveling load obtained by least square method
Precision is not high, allows identification intensive reading to gradually step up by continuous iteration, and b is iterations, f(b)For b numerical value of solution of equations is near
Like solution, f(b+1)The multiaxis traveling load for as recognizing.
2. the recognition methods of the bridge floor multiaxis traveling load for being made usage based on classical row as claimed in claim 1, its feature is existed
In:Described step 3) in equation (1) is solved comprise the following steps that it is described:
Based on modal superposition principle, it is assumed that the n-th order Mode Shape function of bridge isThe then solution of equation (1)
It is expressed as:
Matrix form is:
Here n is mode number, qnT () (n=1,2 ... ∞) are n-th order modal displacements, by equation (12) substitution equation (1), and
X is integrated in [0, L], using boundary condition and Dirac function characteristic, vehicle-bridge system oscillatory differential equation qn(t) table
It is shown as:
HereIt is qnThe second dervative of (t),It is qnThe first derivative of (t), Respectively circular frequency, damping rate and bridge floor mobile vehicle load mod table
Up to formula;
As vehicle has k axletree, and k-th axletree is to the distance of first axletreeThen equation (14) is written as:
Then corresponding to the modal displacement at m measuring point can be expressed as by equation (13):
X on bridge1,x2,…xmThe speed at place is tried to achieve by the once differentiation of displacement:
Further, x on bridge1,x2,…xmThe acceleration at place is tried to achieve by the second differential of displacement:
Similarly, x on beam1,x2,…xmThe moment of flexure at place can utilize relational expressionTry to achieve:
If f1,f2,…,fkIt is each axle correspondence load of known k axles vehicle, ignores the influence of damping, then the solution of equation (1) can be represented
For:
Wherein
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Cited By (3)
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CN111241658A (en) * | 2019-12-30 | 2020-06-05 | 浙江大学 | Beam bridge moving load identification method based on LSTM neural network model |
CN115574906A (en) * | 2022-10-12 | 2023-01-06 | 湖南科技大学 | Bridge dynamic weighing algorithm based on iterative weighted least square |
CN115900906A (en) * | 2022-06-15 | 2023-04-04 | 东南大学 | Bridge dynamic weighing method based on mid-span boundary beam measuring point strain |
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