CN109359311A - A kind of ground motion intensity indices preferred method based on canonical correlation analysis - Google Patents
A kind of ground motion intensity indices preferred method based on canonical correlation analysis Download PDFInfo
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Abstract
The invention discloses a kind of ground motion intensity indices preferred method based on canonical correlation analysis, the following steps are included: establishing the overall relevancy between ground motion intensity indices and structural elements demand parameter by Canonical Correlation Analysis, consider correlation between the correlation and component demand between ground motion intensity indices, based on ground motion intensity indices canonical correlation variable and structural elements demand parameter canonical correlation variable, ground motion intensity indices in bridge Probabilistic Seismic Demand Analysis are carried out preferred, avoid the complexity and limitation for carrying out correlation analysis one by one for single ground motion intensity indices and solid memder seismic demand parameter, preferred ground motion intensity indices are more reasonable.The present invention allows rapid screening out the optimal ground motion intensity indices for bridge structure Seismic Demand Analysis, solves the problems, such as that traditional ground motion intensity indices selection method is difficult to consider the correlation between ground motion intensity indices and correlation between structural elements seismic demand.
Description
Technical field
The present invention relates to a kind of ground motion intensity indices preferred method based on canonical correlation analysis, it is general for bridge structure
Rate Seismic Demand Analysis belongs to bridge structure earthquake resistant engineering studying technological domain.
Background technique
As a kind of sudden relatively strong, destructive biggish natural calamity, life and property to the people are caused sternly for earthquake
It threatens again.The country multiple as an earthquake of China carries out Aseismic Design ten to engineering structure especially civil infrastructure
Divide necessity.Component part of the bridge structure as lifeline engineering restores to play an important role after earthquake relief work and calamity,
It is more necessary to improve its Aseismic Design.Due to the complexity and randomness of earthquake motion, amplitude, frequency spectrum and the group strong earthquakes of earthquake motion
Etc. characteristics significant impact is all had to the seismic response of bridge structure, however influenced by communication process and site condition, i.e.,
Making earthquake motion information is recorded also in different places under same geological process has certain otherness.Therefore, it is suitable to choose
Ground motion intensity indices are accurately reflected destruction of the earthquake motion to bridge, are bridge structures with the size of quantitative description earthquake
The key of aseismic analysis.But seek the index of an energy concentrated expression Earthquake Intensity size for structural earthquake demand point
Analysis, is one of the difficult point of Construction Anti-earthquake field face, is also based on urgently to be resolved one of performance-based seismic design and asks substantially
Topic.If the ground motion intensity indices and structural earthquake demand parameter chosen are closely related, structural earthquake demand point can be effectively reduced
The discreteness of analysis.The angle of correlation between ground motion intensity indices and topology requirement parameter, can be to ground motion intensity indices
Carry out preliminary screening, but existing method is just for the correlation of single ground motion intensity indices and solid memder demand parameter,
The correlation between the correlation and component seismic demand parameter between ground motion intensity indices is had ignored, earthquake is not only resulted in
The larger workload of fatigue resistance index screening, and make the selection of ground motion intensity indices that there is certain one-sidedness.
Summary of the invention
The present invention is to carry out to solve the above-mentioned problems, and it is an object of the present invention to provide a kind of ground based on canonical correlation analysis
Shockproofness index preferred method, by establishing ground motion intensity indices canonical correlation variable and topology requirement parameter canonical correlation
Variable considers the correlation between the correlation and component seismic demand parameter between ground motion intensity indices, and then selects
Optimal ground motion intensity indices, the Probabilistic Seismic Demand Analysis for bridge structure.
To achieve the goals above, it is preferably square to provide a kind of ground motion intensity indices based on canonical correlation analysis by the present invention
Method, comprising the following steps:
It obtains existing ground motion intensity indices and is arranged, classified according to its physical significance；Wherein, existing earthquake
Characteristic strength index when fatigue resistance index includes at least amplitude Characteristics intensity index, spectrum signature intensity index and holds, classification
Physical significance includes at least acceleration, speed and displacement；
The practically vibration record of different Site Types is obtained, and calculates the earthquake intensity index for practically shaking record；
Correlation analysis is carried out to the ground motion intensity indices for practically shaking record, is filtered out for canonical correlation analysis
Basic ground motion intensity indices；
The finite element model for constructing bridge structure carries out Probabilistic Seismic Demand Analysis in conjunction with practically vibration record；
For the antidetonation key member in finite element model, the correlation analysis of seismic demand is carried out；
To the seismic demand of basic ground motion intensity indices and antidetonation key member, canonical correlation analysis is carried out, solves ground
The canonical correlation variable of shockproofness index and seismic demand；
Canonical correlation variable based on ground motion intensity indices Yu structural earthquake demand carries out ground motion intensity indices excellent
Choosing；
Using validity, applicability and adequacy interpretational criteria, test to preferred ground motion intensity indices.
Wherein, in the step of practically vibration for obtaining different Site Types records, according to the earthquake magnitude of setting, earthquake centre
Pulse characteristics away from, shear wave velocity and earthquake motion, from Pacific Ocean earthquake engineering research center a new generation strong-motion data library and state
Download the practically vibration record of a certain number of different Site Types in family's Seismological data sharing center；The earthquake motion of downloading
Acceleration time course data, speed time course data and displacement time course data in record including earthquake motion.
Wherein, it in calculating the step of practically shaking the earthquake intensity index of record, is calculated using Seismosignal
Software calculates practically vibration record, solves all kinds of ground motion intensity indices of every seismic motion record, including accelerate
Degree type intensity index, velocity profile intensity index and displacement type intensity index.
Wherein, in the step of solving all kinds of ground motion intensity indices of every seismic motion record, using rank correlation analysis
Method carries out correlation analysis, the formula of rank correlation analysis method to the ground motion intensity indices that solution obtains are as follows:
Wherein, (xi,yi) (i=1,2 ..., n) be the sample from bivariate population (x, y), use γiIndicate xiIn x1,
x2,……,xnIn order observation, θiIndicate yiIn y1,y2,……,ynIn order observation；
Due to
Then the formula of rank correlation analysis can be reduced to
When x and y are positively correlated, i.e. when an increase in x and y, another value is also inclined to increase, and then x and y has
Certain synchronism, γiWith θiAlso there is synchronism, at this time rs(x, y) > 0；
Wherein, if x1,x2,……,xnWith y1,y2,……,ynSize order it is identical, rs(x, y)=1；
With should x and y it is negatively correlated, i.e. when increases in x and y, another value tendency reduction, r at this times(x,
Y) 0 <；
If x1,x2,……,xnWith y1,y2,……,ynSize order it is completely reverse, i.e. γi+θiWhen=n+1, rs(x,y)
=-1.
Wherein, in the finite element model for establishing bridge structure the step of, consider that coagulation soil compressive stress in structure, reinforcing bar are bent
Take stress, concrete density, support modulus of shearing, Abutment stiffness, basic resistance coefficient, damping ratio and expansion joint width parameter
Uncertainty constructs bridge probability sample based on Latin Hypercube Sampling and carries out nonlinear dynamical damage.
Wherein, in the seismic demand to basic ground motion intensity indices and antidetonation key member, canonical correlation analysis is carried out
The step of in, select bridge pier, support and abutment as crucial antidetonation component, using rank correlation analysis method to crucial antidetonation component
Correlation between seismic demand is analyzed.
Wherein, in the step of solving the canonical correlation variable of ground motion intensity indices and seismic demand:
With a=(a1,a2,…,ap) ' and b=(b1,b2,…,bq) ' indicate two groups of constant value vectors, X=(X1,X2,…,Xp)′
With Y=(Y1,Y2,…,Yq) ' respectively indicate ground motion intensity indices and component demand parameter, by ground motion intensity indices and structure
Part demand parameter is respectively combined
A ' X=a1X1+a2X2+…+apXp,
B ' Y=b1Y1+b2Y2+…+bqYq,
Vector a, b appropriate are selected, keeps the correlation coefficient ρ of combination parameter a ' X and b ' Y maximum, the expression formula of correlation coefficient ρ
Are as follows:
Wherein, Cov indicates covariance；
Enable a ' D (X) a=1, b′The construction of D (X) b=1, combination parameter a ' X and b ' Y is converted into constrained optimization problem:
It enables:
It is sought into local derviation to a, b respectively, and enabling local derviation result is zero, can be obtained
Two above equation is distinguished into premultiplication a ', b ' and is based on its constraint condition, can be obtained
Due to ∑YX=∑ 'XY, therefore a ' ∑XYB=b ' ∑YX a, therefore k1=k2=a ' ∑XYB=ρ (a ' X, b ' Y),
Remember λ=k1=k2, obtain
Above formula is solved using Lagrange multiplier method, is obtained
Wherein, if A and B have r non-zero characteristics root, r is matched to combination parameter a ' X and b ' Y, according to related coefficient
Size, is referred to as first pair of canonical correlation variable, second pair of canonical correlation variable, and related coefficient between the two is known as typical case
Related coefficient, the first canonical correlation variable of ground motion intensity indices are the first combination seism fatigue resistance index, bridge structure
First canonical correlation variable of demand parameter is the first combined bridge topology requirement parameter；
Ground motion intensity indices and two groups of stochastic variable X=(X of bridge structure demand parameter1,X2,…,XP) ' and Y=(Y1,
Y2,…,Yq) ' the p+q that is unified into dimension random vectorCovariance matrixFrom totalityMiddle extraction refers to
The sample of constant volume
Wherein, X(i)=(xi1,xi2,…,xiP) ', Y(i)=(yi1,yi2,…,yiq) ', it is based on moment estimation method, is used respectively
As ∑XX、∑YY、∑XY、∑YXEstimation, replace corresponding population covariance square respectively with sample covariance matrix
Battle array carries out canonical correlation analysis；
Ground motion intensity indices have different dimensions from two groups of all components of stochastic variable of bridge structure demand parameter, by sample
Observation X(i)=(xi1,xi2,…,xiP) ' execution standardization processing beStandardization
Formula is
Wherein, n is the sample number of standardization.
Wherein, ground motion intensity indices are being carried out in preferred step, is being based on ground motion intensity indices and structural earthquake
The canonical correlation variable of demand, canonical correlation coefficient is positive value and value is bigger, then combination seism fatigue resistance index and combined member
Demand parameter positive correlation degree is higher, which is the optimal Earthquake Intensity of bridge Seismic Demand Analysis
Index；If the weight coefficient of a certain basic ground motion intensity indices is significantly greater than other indexs, show the index in earthquake motion
It occupies an leading position in intensity index canonical correlation variable, it is bridge seismic demand point which, which can be approximately considered,
The optimal ground motion intensity indices of analysis.
Wherein, it in the interpretational criteria based on validity, applicability and adequacy, tests to ground motion intensity indices
In step, the probabilistic seismic demand based on bridge structure establishes the index between ground motion intensity indices and component seismic demand
Relationship
Wherein, IM is ground motion intensity indices, and a, b are coefficient,For component seismic demand median；
Calculate the Validity Index β of ground motion intensity indicesD|IM
Wherein, diFor structural earthquake demand sample, N is sample size, and Validity Index numerical value is smaller, and ground motion parameter is got over
Effectively；
Calculate the applicability index ζ of ground motion intensity indices
ζ=βD|IM/ b,
The index can take into account the validity and feasibility of ground motion intensity indices, and ζ value is smaller, ground motion intensity indices
Applicability it is better；
Adequacy is by carrying out residual error point to seismic characteristic parameter (magnitude M or epicentral distance R) for component seismic demand model
Analysis obtains, residual epsilon | and IM is indicated by between the regression model component seismic demand predicted value being calculated and seismic demand true value
Relative error, if the adequacy of ground motion intensity indices is preferable, residual epsilon | IM is statistical iteration for seismic characteristic parameter
, which is described by the significance p value of significance test, and the p value the big, and ground motion intensity indices fill
Divide property better.
The beneficial effects of the present invention are: establishing ground motion intensity indices and structural elements by Canonical Correlation Analysis needs
Seek the overall relevancy between parameter, it is contemplated that related between the correlation and component demand between ground motion intensity indices
Property, it is based on ground motion intensity indices canonical correlation variable and structural elements demand parameter canonical correlation variable, to bridge probability
The ground motion intensity indices in demand analysis are shaken preferably, avoid for single ground motion intensity indices and solid memder
Shake demand parameter carries out the complexity and limitation of correlation analysis one by one, and preferred ground motion intensity indices are more reasonable.
Detailed description of the invention
Fig. 1 is implementation process diagram of the present invention.
Fig. 2 is that the present invention implements logical schematic.
Fig. 3 is the spectral acceleration figure of the seismic motion record of embodiment selection.
Dependency graph of the Fig. 4 between embodiment ground motion intensity indices.
Fig. 5 is embodiment bridge structure finite element analysis model.
Dependency graph of the Fig. 6 between embodiment component demand parameter.
Fig. 7 is the validity check result figure of embodiment ground motion intensity indices.
Fig. 8 is the applicability inspection result figure of embodiment ground motion intensity indices.
Fig. 9 is the adequacy inspection result figure that embodiment ground motion intensity indices are directed to earthquake magnitude.
Figure 10 is the adequacy inspection result figure that embodiment ground motion intensity indices are directed to epicentral distance.
Specific embodiment
In order to keep the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment to the present invention
It is further elaborated.
Refering to fig. 1 and Fig. 2, Fig. 1 and Fig. 2 are that a kind of Earthquake Intensity based on canonical correlation analysis provided by the invention refers to
Mark the flow diagram and logical schematic of preferred method.The step of this method includes:
S110: existing ground motion intensity indices are obtained and are arranged, are classified according to its physical significance；Wherein, existing
Characteristic strength index when thering are ground motion intensity indices to include at least amplitude Characteristics intensity index, spectrum signature intensity index and hold,
The physical significance of classification includes at least acceleration, speed and displacement.
S120: the practically vibration record of different Site Types is obtained, and calculates the earthquake intensity for practically shaking record
Index.
S130: correlation analysis is carried out to the ground motion intensity indices for practically shaking record, is filtered out for typical phase
Close the basic ground motion intensity indices of analysis.
S140: constructing the finite element model of bridge structure, carries out Probabilistic Seismic Demand Analysis in conjunction with practically vibration record.
S150: for the antidetonation key member in finite element model, the correlation analysis of seismic demand is carried out.
S160: to the seismic demand of basic ground motion intensity indices and antidetonation key member, canonical correlation analysis is carried out, is asked
Solve the canonical correlation variable of ground motion intensity indices and seismic demand.
S170: the canonical correlation variable based on ground motion intensity indices Yu structural earthquake demand, to ground motion intensity indices
It carries out preferred.
S180: validity, applicability and adequacy interpretational criteria are used, preferred ground motion intensity indices are examined
It tests.
<embodiment>
Embodiment is a common Mid and minor spans reinforced concrete hollow shear wall, is often made of across girder 4 T beams, bridge
Pier is solid circles two-columned pier, and bent cap is rectangular section, and basis uses single bored concrete pile, and geological conditions locating for bridge is
II class place, for size in addition to elevation is m, remaining is cm.
Common ground motion intensity indices are aggregated to obtain 18 kinds of ground motion intensity indices, it is strong according to earthquake motion
The physical significance for spending index, is classified as acceleration type intensity index, velocity profile intensity index and displacement type intensity index, such as
Peak acceleration, peak velocity PGV and peak displacement PGD, as a result such as table 1.
1 ground motion intensity indices summary sheet of table
According to the earthquake magnitude of setting, epicentral distance, shear wave velocity and the pulse characteristics of earthquake motion, from the Pacific Ocean, earthquake engineering is ground
Study carefully center a new generation strong-motion data library and national Seismological data sharing center and downloads a certain number of different Site Types
Practically vibration records, and includes Acceleration time course data, speed time course data and the position of earthquake motion in the seismic motion record of downloading
Move time course data；For the requirement for meeting statistical analysis, the present embodiment chooses 100 seismic motion records for meeting site condition,
Acceleration response spectrum is as shown in Figure 3.
Using Seismosignal software for calculation 100 selected in previous step are practically shaken with record to count
It calculates, solves 18 ground motion intensity indices of every seismic motion record.
Correlation analysis, rank correlation analysis are carried out to the ground motion intensity indices that solution obtains using rank correlation analysis method
Formula are as follows:
Wherein, (xi,yi) (i=1,2 ..., n) be the sample from bivariate population (x, y), use γiIndicate xiIn x1,
x2,……,xnIn order observation, θiIndicate yiIn y1,y2,……,ynIn order observation.
Further, due to
The formula of rank correlation analysis can be reduced to
When x and y are positively correlated, i.e. when increases in x and y, another value is also inclined to increase, then x andyHave
Certain synchronism,γiWith θiAlso there is certain synchronism, at this time rs(x, y) > 0.
Further, if x1,x2,……,xnWith y1,y2,……,ynSize order it is identical, rs(x, y)=1.
With should x and y it is negatively correlated, i.e. when increases in x and y, another value tendency reduction, r at this times(x,
Y) 0 <.
Further, if x1,x2,……,xnWith y1,y2,……,ynSize order it is completely reverse, i.e.,γi+θi=n+1
When, rs(x, y)=- 1.
Rank correlation coefficient between ground motion intensity indices is as shown in Figure 4.
It is highly relevant between same type of ground motion intensity indices as shown in Figure 4, and with other types Earthquake Intensity
Correlation between index is relatively weak.PGA refers to acceleration type ground motion intensity indices, PGV and velocity profile Earthquake Intensity
Related coefficient between mark, PGD and displacement type ground motion intensity indices is larger；And the related coefficient between PGA, PGV, PGD
It is smaller.Therefore, the ground motion intensity indices that 3 seed types are represented using PGA, PGV, PGD, as the basic of canonical correlation analysis
Ground motion intensity indices, can more comprehensively corresponsively vibration information.
The finite element model of bridge structure is established using OpenSees platform, girder is substantially at elasticity under geological process
State is simulated using elastic beam-column unit；Bridge pier is likely to form plastic hinge, plastic failure occurs, using nonlinear fiber beam column
Unit simulation；Support is simulated using zero-length unit, and constitutive relation uses ideal elastoplastic model；According to the base of abutment
Plinth type and platform back banket, and are simulated using simplified model；Pier footing is simulated using Hookean spring, bridge structure
Finite element model is as shown in Figure 5.
Further, consider structure in coagulation soil compressive stress, reinforcement yielding stress, concrete density, support modulus of shearing,
The uncertainty of the parameters such as Abutment stiffness, basic resistance coefficient, damping ratio and expansion joint width, is based on Latin Hypercube Sampling structure
Bridge construction beam probability sample simultaneously carries out nonlinear dynamical damage, obtains its probabilistic seismic demand.
The antidetonations key members such as bridge pier, abutment and the support in bridge structure are selected, to the correlation of component seismic demand
It is analyzed, obtains the rank correlation coefficient between component seismic demand parameter, as shown in Figure 7.
Fig. 6 shows that the rank correlation coefficient between bridge pier, support and abutment seismic demand is all larger than 0.5, shows component earthquake
It is highly relevant between demand parameter.
It is solved in conjunction with basic ground motion intensity indices and the seismic demand of key member with Canonical Correlation Analysis
The canonical correlation variable of ground motion intensity indices and structural earthquake demand, basic theories are as follows:
With a=(a1,a2,…,ap) ' and b=(b1,b2,…,bq) ' indicate two groups of constant value vectors, X=(X1,X2,…,Xp)′
With Y=(Y1,Y2,…,Yq) ' respectively indicate ground motion intensity indices and component demand parameter, by ground motion intensity indices and structure
Part demand parameter is respectively combined
A ' X=a1X1+a2X2+…+apXp,
B ' Y=b1Y1+b2Y2+…+bqYq,
Further, vector a, b appropriate are selected, the correlation coefficient ρ of combination parameter a ' X and b ' Y can be made maximum, phase relation
The expression formula of number ρ are as follows:
Wherein, Cov indicates covariance.
Further, enable the construction of a ' D (X) a=1, b ' D (Y) b=1, combination parameter a ' X and b ' Y that can be converted into constraint excellent
Change problem
Further, it enables:
It is sought into local derviation to a, b respectively, and it is enabled to be equal to zero, can be obtained
Further, two above equation is distinguished into premultiplication a', b' is simultaneously based on its constraint condition, can obtain
Further, due to ∑YX=∑ 'XY, therefore a' ∑XYB=b' ∑YXA, therefore k1=k2=a' ∑XYB=ρ (a'X,
B'Y), remember λ=k1=k2, obtain
Further, above formula is solved using Lagrange multiplier method, is obtained
From the above equation, we can see that if A and B have r non-zero characteristics root, r can be matched to combination parameter a ' X and b ' Y, according to
The size of related coefficient is referred to as first pair of canonical correlation variable, second pair of canonical correlation variable etc. respectively, between them
Related coefficient is known as canonical correlation coefficient；First canonical correlation variable of ground motion intensity indices be first in combination vibration it is strong
Index is spent, the first canonical correlation variable of bridge structure demand parameter is the first combined bridge topology requirement parameter.
Further, ground motion intensity indices and two groups of stochastic variable X=(X of bridge structure demand parameter1,X2,…,XP)'
With Y=(Y1,Y2,…,Yq) ' the p+q that is unified into dimension random vectorCovariance matrixIt is usually unknown
, it needs from totalityThe middle sample for extracting certain capacityWherein, X(i)=(xi1,xi2,…,
xiP) ', Y(i)=(yi1,yi2,…,yiq) ', it is based on moment estimation method, is used respectively
As ∑XX、∑YY、∑XY、∑YXEstimation, be based on sample
Covariance matrix replaces corresponding population covariance matrix to carry out canonical correlation analysis respectively.
Further, ground motion intensity indices and two groups of all components of stochastic variable of bridge structure demand parameter have not same amount
Guiding principle, need to be by sample observations X(i)=(xi1,xi2,…,xiP) ' execution standardization processing beMark
Standardization processing formula be
Wherein, n is the sample number of standardization.
Solution obtains the canonical correlation variable of ground motion intensity indices Yu structural earthquake demand are as follows:
X=-0.046PGA+1.133PGV-0.168PGD
Y=-0.363Y1-0.104Y2+0.189Y3+0.614Y4-0.199Y5+0.885Y6,
ρ (X, Y)=0.96
Wherein, Y1、Y2、Y3、Y4、Y5、Y6Respectively indicate the displacement of support vertical, horizontal, the vertical, horizontal displacement of bridge pier and abutment
Vertical, horizontal displacement.
Canonical correlation variable based on ground motion intensity indices Yu structural earthquake demand carries out ground motion intensity indices excellent
Choosing；Canonical correlation coefficient is positive value and value is bigger, then combination seism fatigue resistance index and combined member demand parameter are positively correlated journey
Degree is higher, which is the optimal ground motion intensity indices of bridge Seismic Demand Analysis.Earthquake Intensity refers to
Marking the canonical correlation coefficient between canonical correlation variable and topology requirement parameter canonical correlation variable is 0.96, shows combination seism
Fatigue resistance index and combined member demand parameter high-positive correlation.Combination seism fatigue resistance index is bridge probabilistic seismic demand point
Optimal ground motion intensity indices in analysis.
Further, the weight coefficient of a certain basic ground motion intensity indices is significantly greater than other indexs, then shows that this refers to
It is marked in ground motion intensity indices canonical correlation variable and occupies an leading position, it is bridge which, which can be approximately considered,
The optimal ground motion intensity indices of Seismic Demand Analysis；In ground motion intensity indices canonical correlation variable, the weight coefficient of PGV
Significantly greater than PGA and PGD shows that PGV occupies an leading position in ground motion parameter canonical correlation variable.Single shockproofness index
In, it is optimal ground motion intensity indices in bridge Probabilistic Seismic Demand Analysis that PGV, which can be approximately considered,.
Using validity, applicability and adequacy interpretational criteria, test to preferred ground motion intensity indices.It is based on
The probabilistic seismic demand of bridge structure establishes the exponential relationship between ground motion intensity indices and component seismic demand
Wherein, IM is ground motion intensity indices, and a, b are coefficient,For component seismic demand median.
Further, the Validity Index β of ground motion intensity indices is calculatedD|IM
Wherein, diFor structural earthquake demand sample, N is sample size, and result is as shown in Figure 7.
Further, the applicability index ζ of ground motion intensity indices is calculated
ζ=βD|IM/ b,
The index can take into account the validity and feasibility of ground motion intensity indices, and result is as shown in Figure 8.
Further, component seismic demand model is subjected to residual analysis to seismic characteristic parameter (magnitude M or epicentral distance R)
Obtaining, residual epsilon | IM is indicated by between the regression model component seismic demand predicted value being calculated and seismic demand true value
Relative error.If the adequacy of ground motion intensity indices is preferable, residual epsilon | IM is statistical iteration for seismic characteristic parameter,
The independence can be described by the p value of significance test, and the adequacy of the more big then ground motion intensity indices of p value is better.
Ground motion intensity indices are as shown in Figure 9 for the adequacy inspection result of earthquake magnitude.
Ground motion intensity indices are as shown in Figure 10 for the adequacy inspection result of epicentral distance.
The inspection result of validity, applicability and adequacy shows: the combination seism fatigue resistance being made of PGA, PGV, PGD
Validity, applicability and the adequacy of index are better than single ground motion intensity indices；In single ground motion intensity indices, PGV
Validity, applicability and adequacy be better than PGA and PGD.Therefore, in the Probabilistic Seismic Demand Analysis of bridge structure, PGA,
The combination seism fatigue resistance index or PGV ground motion intensity indices that PGV, PGD are constituted can be excellent in the probability demand analysis of bridge
First use.
The beneficial effects of the present invention are: establishing ground motion intensity indices and structural elements by Canonical Correlation Analysis needs
Seek the overall relevancy between parameter, it is contemplated that related between the correlation and component demand between ground motion intensity indices
Property, it is based on ground motion intensity indices canonical correlation variable and structural elements demand parameter canonical correlation variable, to bridge probability
The ground motion intensity indices in demand analysis are shaken preferably, avoid for single ground motion intensity indices and solid memder
Shake demand parameter carries out the complexity and limitation of correlation analysis one by one, and preferred ground motion intensity indices are more reasonable.
The above is only the embodiment of the present invention, are not intended to limit the scope of the invention, all to be said using the present invention
Equivalent structure or equivalent flow shift made by bright book content is applied directly or indirectly in other relevant technical fields,
Similarly it is included within the scope of the present invention.
Claims (9)
1. a kind of ground motion intensity indices preferred method based on canonical correlation analysis, for bridge structure probabilistic seismic demand point
Analysis, which comprises the following steps:
It obtains existing ground motion intensity indices and is arranged, classified according to its physical significance；Wherein, existing earthquake motion is strong
Characteristic strength index when degree index includes at least amplitude Characteristics intensity index, spectrum signature intensity index and holds, the physics of classification
Meaning includes at least acceleration, speed and displacement；
The practically vibration record of different Site Types is obtained, and calculates the earthquake intensity index for practically shaking record；
Correlation analysis is carried out to the ground motion intensity indices for practically shaking record, filters out the base for canonical correlation analysis
This ground motion intensity indices；
The finite element model for constructing bridge structure carries out Probabilistic Seismic Demand Analysis in conjunction with practically vibration record；
For the antidetonation key member in finite element model, the correlation analysis of seismic demand is carried out；
To the seismic demand of basic ground motion intensity indices and antidetonation key member, canonical correlation analysis is carried out, solves earthquake motion
The canonical correlation variable of intensity index and seismic demand；
Canonical correlation variable based on ground motion intensity indices Yu structural earthquake demand carries out ground motion intensity indices preferred；
Using validity, applicability and adequacy interpretational criteria, test to preferred ground motion intensity indices.
2. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
In the step of practically vibration for obtaining different Site Types records, according to the earthquake magnitude of setting, epicentral distance, shear wave velocity
And the pulse characteristics of earthquake motion, from Pacific Ocean earthquake engineering research center a new generation strong-motion data library and national earthquake science number
The practically vibration record of a certain number of different Site Types is downloaded according to Sharing Center；Include ground in the seismic motion record of downloading
Acceleration time course data, speed time course data and the displacement time course data of vibration.
3. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
In calculating the step of practically shaking the earthquake intensity index of record, using Seismosignal software for calculation to reality
Seismic motion record is calculated, and all kinds of ground motion intensity indices of every seismic motion record are solved, including acceleration type intensity refers to
Mark, velocity profile intensity index and displacement type intensity index.
4. the ground motion intensity indices preferred method according to claim 3 based on canonical correlation analysis, it is characterised in that:
In the step of solving all kinds of ground motion intensity indices of every seismic motion record, using rank correlation analysis method to solution
Obtained ground motion intensity indices carry out correlation analysis, the formula of rank correlation analysis method are as follows:
Wherein, (xi,yi) (i=1,2 ..., n) be the sample from bivariate population (x, y), use γiIndicate xiIn x1,x2,……,xn
In order observation, θiIndicate yiIn y1,y2,……,ynIn order observation；
Due to
Then the formula of rank correlation analysis can be reduced to
When x and y are positively correlated, i.e. when increases in x and y, another value is also inclined to increases, and then x and y is with certain
Synchronism, γiWith θiAlso there is synchronism, at this time rs(x, y) > 0；
Wherein, if x1,x2,……,xnWith y1,y2,……,ynSize order it is identical, rs(x, y)=1；It together should x and y
When increases in negative correlation, i.e. x and y, another value tendency reduction, r at this times(x, y) < 0；If x1,x2,……,
xnWith y1,y2,……,ynSize order it is completely reverse, i.e. γi+θiWhen=n+1, rs(x, y)=- 1.
5. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
In the finite element model for establishing bridge structure the step of, coagulation soil compressive stress in structure, reinforcement yielding stress, mixed is considered
Solidifying soil bulk density, support modulus of shearing, Abutment stiffness, basic resistance coefficient, damping ratio and expansion joint width parameter uncertainty,
Bridge probability sample is constructed based on Latin Hypercube Sampling and carries out nonlinear dynamical damage.
6. the ground motion intensity indices preferred method according to claim 4 based on canonical correlation analysis, it is characterised in that:
In the seismic demand to basic ground motion intensity indices and antidetonation key member, in the step of carrying out canonical correlation analysis,
Select bridge pier, support and abutment as crucial antidetonation component, using rank correlation analysis method to crucial antidetonation component seismic demand
Between correlation analyzed.
7. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
In the step of solving the canonical correlation variable of ground motion intensity indices and seismic demand:
With a=(a1,a2,…,ap) ' and b=(b1,b2,…,bq) ' indicate two groups of constant value vectors, X=(X1,X2,…,Xp) ' and Y
=(Y1,Y2,…,Yq) ' respectively indicate ground motion intensity indices and component demand parameter, by ground motion intensity indices and component
Demand parameter is respectively combined
A ' X=a1X1+a2X2+…+apXp,
B ' Y=b1Y1+b2Y2+…+bqYq,
Vector a, b appropriate are selected, keeps the correlation coefficient ρ of combination parameter a ' X and b ' Y maximum, the expression formula of correlation coefficient ρ are as follows:
Wherein, Cov indicates covariance；
The construction of a ' D (X) a=1, b ' D (X) b=1, combination parameter a ' X and b ' Y is enabled to be converted into constrained optimization problem:
It enables:
It is sought into local derviation to a, b respectively, and enabling local derviation result is zero, can be obtained
Two above equation is distinguished into premultiplication a ', b ' and is based on its constraint condition, can be obtained
Due to ∑YX=∑ 'XY, therefore a ' ∑XYB=b ' ∑YXA, therefore k1=k2=a ' ∑XYB=ρ (a ' X, b ' Y),
Remember λ=k1=k2, obtain
Above formula is solved using Lagrange multiplier method, is obtained
Wherein, if A and B have r non-zero characteristics root, r is matched to combination parameter a ' X and b ' Y, according to the big of related coefficient
It is small, it is referred to as first pair of canonical correlation variable, second pair of canonical correlation variable, related coefficient between the two is known as typical phase
Relationship number, the first canonical correlation variable of ground motion intensity indices are the first combination seism fatigue resistance index, and bridge structure needs
The the first canonical correlation variable for seeking parameter is the first combined bridge topology requirement parameter；
Ground motion intensity indices and two groups of stochastic variable X=(X of bridge structure demand parameter1,X2,…,XP) ' and Y=(Y1,
Y2,…,Yq) ' the p+q that is unified into dimension random vectorCovariance matrixFrom totalityMiddle extraction refers to
The sample of constant volume
Wherein, X(i)=(xi1,xi2,…,xiP) ', Y(i)=(yi1,yi2,…,yiq) ', it is based on moment estimation method, is used respectively
As ∑XX、∑YY、∑XY、∑YXEstimation, replaced respectively with sample covariance matrix corresponding population covariance matrix into
Row canonical correlation analysis；
Ground motion intensity indices have different dimensions from two groups of all components of stochastic variable of bridge structure demand parameter, and sample is observed
Value X(i)=(xi1,xi2,…,xiP) ' execution standardization processing beThe formula of standardization
For
Wherein, n is the sample number of standardization.
8. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
Ground motion intensity indices are being carried out in preferred step, the typical case based on ground motion intensity indices Yu structural earthquake demand
Correlated variables, canonical correlation coefficient is positive value and value is bigger, then combination seism fatigue resistance index and combined member demand parameter be just
Degree of correlation is higher, which is the optimal ground motion intensity indices of bridge Seismic Demand Analysis；If certain
The weight coefficient of one basic ground motion intensity indices is significantly greater than other indexs, then shows the index in ground motion intensity indices allusion quotation
Occupy an leading position in type correlated variables, the ground motion intensity indices can be approximately considered be bridge Seismic Demand Analysis optimally
Shockproofness index.
9. the ground motion intensity indices preferred method according to claim 1 based on canonical correlation analysis, it is characterised in that:
In the interpretational criteria based on validity, applicability and adequacy, in the step of testing to ground motion intensity indices, base
In the probabilistic seismic demand of bridge structure, the exponential relationship between ground motion intensity indices and component seismic demand is established
Wherein, IM is ground motion intensity indices, and a, b are coefficient,For component seismic demand median；
Calculate the Validity Index β of ground motion intensity indicesD|IM
Wherein, diFor structural earthquake demand sample, N is sample size, and Validity Index numerical value is smaller, and ground motion parameter is more effective；
Calculate the applicability index ζ of ground motion intensity indices
ζ=βD|IM/ b,
The index can take into account the validity and feasibility of ground motion intensity indices, and ζ value is smaller, and ground motion intensity indices are fitted
It is better with property；
Adequacy is obtained by the way that component seismic demand model is carried out residual analysis to seismic characteristic parameter (magnitude M or epicentral distance R)
Arriving, residual epsilon | IM is indicated by the phase between the regression model component seismic demand predicted value being calculated and seismic demand true value
To error, if the adequacy of ground motion intensity indices is preferable, residual epsilon | IM is statistical iteration for seismic characteristic parameter, should
Independence is described by the significance p value of significance test, the adequacy of the more big then ground motion intensity indices of p value more
It is good.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111177908A (en) * | 2019-12-22 | 2020-05-19 | 同济大学 | Model box design method for simulating seismic motion space differential effect and model box |
| CN112214722A (en) * | 2020-09-30 | 2021-01-12 | 西南交通大学 | Method for evaluating seismic oscillation strength parameters of high-speed rail short-tower cable-stayed bridge based on dominant mode |
| CN113268852A (en) * | 2021-04-14 | 2021-08-17 | 西南交通大学 | Monte Carlo simulation-based earthquake landslide probability risk analysis method |
| CN113987632A (en) * | 2021-10-19 | 2022-01-28 | 武汉大学 | Method for predicting liquefaction lateral displacement of site |
| CN117251926A (en) * | 2023-11-20 | 2023-12-19 | 东南大学 | Earthquake motion intensity index optimization method for earthquake response prediction |
| CN117271964A (en) * | 2023-09-01 | 2023-12-22 | 南昌航空大学 | Probability earthquake analysis model optimization method in subway station structure based on probability earthquake demand analysis model |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103512718A (en) * | 2013-10-09 | 2014-01-15 | 江苏交科工程检测技术有限公司 | Prediction-correction mixed testing method based on earthquake model |
| CN107657393A (en) * | 2017-10-30 | 2018-02-02 | 中铁二院工程集团有限责任公司 | The Seismic Evaluation method of the lower bridge of near-fault ground motion effect |
-
2018
- 2018-08-01 CN CN201810860531.6A patent/CN109359311A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103512718A (en) * | 2013-10-09 | 2014-01-15 | 江苏交科工程检测技术有限公司 | Prediction-correction mixed testing method based on earthquake model |
| CN107657393A (en) * | 2017-10-30 | 2018-02-02 | 中铁二院工程集团有限责任公司 | The Seismic Evaluation method of the lower bridge of near-fault ground motion effect |
Non-Patent Citations (2)
| Title |
|---|
| 宋帅: "地震动参数之间的距离分析及相关分析", 《地震工程与工程振动》 * |
| 宋帅: "考虑构件相关性的桥梁系统地震易损性分析方法研究", 《中国博士学位论文全文数据库 (工程科技Ⅱ辑)》 * |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111177908A (en) * | 2019-12-22 | 2020-05-19 | 同济大学 | Model box design method for simulating seismic motion space differential effect and model box |
| CN111177908B (en) * | 2019-12-22 | 2024-03-26 | 同济大学 | Model box design method for simulating earthquake motion space differential effect and model box |
| CN112214722A (en) * | 2020-09-30 | 2021-01-12 | 西南交通大学 | Method for evaluating seismic oscillation strength parameters of high-speed rail short-tower cable-stayed bridge based on dominant mode |
| CN113268852A (en) * | 2021-04-14 | 2021-08-17 | 西南交通大学 | Monte Carlo simulation-based earthquake landslide probability risk analysis method |
| CN113987632A (en) * | 2021-10-19 | 2022-01-28 | 武汉大学 | Method for predicting liquefaction lateral displacement of site |
| CN113987632B (en) * | 2021-10-19 | 2023-07-21 | 武汉大学 | Method for predicting field liquefaction transverse displacement |
| CN117271964A (en) * | 2023-09-01 | 2023-12-22 | 南昌航空大学 | Probability earthquake analysis model optimization method in subway station structure based on probability earthquake demand analysis model |
| CN117251926A (en) * | 2023-11-20 | 2023-12-19 | 东南大学 | Earthquake motion intensity index optimization method for earthquake response prediction |
| CN117251926B (en) * | 2023-11-20 | 2024-03-15 | 东南大学 | Earthquake motion intensity index optimization method for earthquake response prediction |
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