A multi-dimensional vulnerability assessment method for bridge structures in cold regions under ice floe impact

Abstract

A multi-dimensional vulnerability assessment method for cold-region bridge structures under the impact of drift ice relates to the technical field of bridge vulnerability assessment. The method includes generating a grid format for the finite element model parameters of the bridge structure, randomizing and optimizing the parameters, statistically analyzing the observed data of drift ice loads, constructing a probability distribution model, constructing a pier damage factor matrix, constructing a probability distribution model for the bearing capacity of the piers after a disaster, obtaining a probability distribution function for the damage factor of the piers under the action of drift ice loads, constructing a probability distribution function for the bearing capacity conditions of the piers after a disaster, and conducting damage status judgment and assessment and vulnerability assessment. For double-span continuous beam bridges, by considering the random variability of the bridge structure parameters in the finite element model, the accuracy of the vulnerability assessment can be significantly improved. Combined with the multi-dimensional characteristics of drift ice impact, the complexity of the impact behavior is fully characterized, which is more efficient and systematizable, and is helpful for predicting the impact resistance of bridge structures and evaluating their overall safety performance.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge vulnerability assessment, and in particular to a multi-dimensional vulnerability assessment method for cold region bridge structures under the impact of drifting ice. Background Art

[0002] As a vital component of transportation networks in cold regions, bridges in cold regions face significant safety concerns in extreme climates and complex natural environments. This is particularly true when impacted by drifting ice, which can cause localized damage or even complete destruction, posing a serious threat to traffic safety and bridge lifespan. Ice impacts often involve high kinetic energy, are highly random, and unpredictable, posing significant challenges to the design, inspection, and maintenance of bridges in cold regions.

[0003] Assessing the vulnerability of bridge structures to ice floes is an important foundation for determining their impact resistance and developing protective strategies. Although researchers have conducted in-depth research on the physical characteristics of ice floes, the responses of bridge structures, and failure modes, traditional methods typically assume that finite element model parameters are fixed, failing to fully account for the random variability of bridge materials, geometric dimensions, and environmental conditions. This assumption can lead to biased assessments of bridge structural performance, particularly in complex cold environments, limiting their applicability. Furthermore, ice floe impact parameters (such as ice mass, velocity, and impact location) exhibit significant randomness and multidimensional characteristics. Existing assessment methods are typically based on simplified models that fail to fully reflect the complex distribution patterns of these parameters, making it difficult to accurately predict the impact of ice floes on bridge structures. Therefore, the accuracy and reliability of current vulnerability assessments of bridge structures in cold regions to ice floes remain difficult to guarantee.

[0004] In summary, existing assessment methods for evaluating the vulnerability of bridge structures to ice floes have significant flaws. This results in assessment models that cannot accurately capture the complex behavior of actual ice floes, leading to significant deviations in assessment results and making them difficult to use as a scientific basis for the design, reinforcement, and management of bridges in cold regions. Therefore, an efficient and reliable assessment method is urgently needed to achieve a more systematic and accurate vulnerability assessment of bridge structures in cold regions to ice floes. Summary of the Invention

[0005] In order to address the shortcomings of the background technology, the present invention provides a multi-dimensional vulnerability assessment method for cold-region bridge structures under the impact of drifting ice. For double-span continuous beam bridges, by considering the random variability of bridge structure parameters in the finite element model, the method can significantly improve the accuracy of vulnerability assessment. Combined with the multi-dimensional characteristics of drifting ice impact, it comprehensively depicts the complexity of the impact behavior, is more efficient and can be systematized, and is helpful for predicting the impact resistance of bridge structures and evaluating their overall safety performance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a multi-dimensional vulnerability assessment method for cold region bridge structures under the impact of drifting ice, comprising the following steps:

[0007] Step 1: Generate the grid format of bridge structure finite element model parameters

[0008] A three-dimensional finite element model of a double-span continuous beam bridge with abutment-pier-abutment arrangement is established. Considering the random variability of the four parameters, namely, the elastic modulus of steel bar, the elastic modulus of concrete, the compressive strength of concrete, and the yield strength of steel bar, N finite element models are generated. Δ j , j = 1, 2, 3, 4 represent various parameters, as follows:

[0009] Δ1~Lognormal(μ1,σ1 2 ), Δ2~Lognormal(μ2,σ2 2 )

[0010] Δ3~Lognormal(μ3,σ3 2 ), Δ4~Lognormal(μ4,σ4 2 )

[0011]

[0012] Where μ j represents the mean of each parameter, σ j 2 represents the variance of each parameter, Represents the lower bound of the distribution of each parameter, Represents the upper bound of the distribution of each parameter;

[0013] The cumulative probability distribution function of each parameter is expressed as: y j =F j (x j )y j ∈[0,1];

[0014] The cumulative probability interval [0,1] is evenly divided into n probability intervals with equal probability. The probability interval matrix Λ is expressed as:

[0015]

[0016] Each row i=1,2,...,n-1, n represents a probability interval;

[0017] The probability interval passes through x j =F j -1 (y j ) is mapped to the sampling interval Get the sampling interval matrix I j for:

[0018]

[0019] Each row i=1,2,...,n-1, n represents a sampling interval;

[0020] Setting important intervals through prior knowledge Contains s sampling intervals, s+n=N;

[0021] From each sampling interval I i,j Randomly select a sample w from i,j , from the important interval I select,j An additional sample w is randomly drawn from each sampling cell i,j ′, sample w i,j With sample w i,j 'Use i as the row index and j as the column index, arrange them from small to large, and form matrices W and W'. Merge matrices W and W' to get the sample matrix W'':

[0022]

[0023] Step 2: Randomly arrange the parameters of the bridge structure finite element model

[0024] Let each column of the sample matrix W″ be W j , expressed as:

[0025]

[0026] For W j , define the set P to represent the position index, expressed as:

[0027] P={1,2,...,n-1,n,n+1,...,n+s-1,n+s}

[0028] Define the current processing position as k q , k q =N-q+1, q=1,2,...,N-1,N, for the current processing position k q Randomly select q ∈{1,2,...k q -2,k q -1} to exchange positions;

[0029] The position exchange is performed sequentially from 1 to N according to q. The expression for the qth position exchange is as follows:

[0030]

[0031] in, Indicates exchange Middle position k q With position o q The matrix after the element, represents W after exchanging the qth position j ,and

[0032] When the Nth position exchange is completed, we can get Will The initial sample matrix A is obtained by merging, which is expressed as:

[0033]

[0034] Step 3: Optimal arrangement of bridge structure finite element model parameters

[0035] Each row in the initial sample matrix A represents a sample combination. Select any two sample combinations to form a sample combination pair. Calculate the Euclidean distance between all sample combination pairs in the initial sample matrix A and keep the minimum value as Define the temperature at this moment as T0;

[0036] For each column of the initial sample matrix A, define a set R to represent the position index, expressed as:

[0037] R={1,2,...,N-1,N}

[0038] Define the rth optimization, and fix the processing position to k V =V, V = 1, 2, 3, for a fixed processing position k V Randomly select v∈{4,5,...,N-1,N} to exchange positions;

[0039] Press V to perform position swaps from 1 to 3 in sequence. The Vth position swap is expressed as follows:

[0040]

[0041] in, Indicates exchange Middle position k V with the matrix after the element at position v, Indicates that after exchanging the Vth position and

[0042] Will Merge to get the optimized sample matrix A r , expressed as:

[0043]

[0044] Calculate the optimized sample matrix A r The Euclidean distance between all sample combinations in is recorded as Define the updated temperature as λ is the cooling parameter;

[0045] like Directly accept the optimized sample matrix A r is the new matrix;

[0046] like Randomly draw a z in the interval (0,1), when Then accept the optimized sample matrix A r is the new matrix, when Then the optimized sample matrix A is not accepted r is the new matrix;

[0047] Continue until When , the optimization is stopped, the optimal sample matrix is ​​obtained, and the finite element model is optimized based on the optimal sample matrix;

[0048] Step 4: Statistics of drift ice load observation data

[0049] The relevant parameters of drift ice load are the drift ice mass π, the drift ice velocity and drift ice load position Observe N groups of drift ice load correlation numbers to obtain the drift ice mass matrix M ice , ice flow velocity matrix V ice and the drift ice load position matrix H ice , which is expressed as follows:

[0050] M ice =[Π1 Π2 ... Π N-1 Π N ] T

[0051]

[0052]

[0053] Step 5: Construction of the probability distribution model of drift ice load

[0054] The distribution type of the drift ice load correlation number is:

[0055] Π~Lognormal(μ ∏ ,σ Π 2 )

[0056]

[0057]

[0058] Constructing distribution parameters of drift ice load correlation numbers The determination formula is as follows:

[0059]

[0060] Among them, the probability density function of the drift ice load correlation number is:

[0061]

[0062]

[0063]

[0064] The probability distribution function of the drift ice load correlation number is obtained as follows:

[0065]

[0066]

[0067]

[0068] Step 6: Construction of pier damage factor matrix

[0069] Assume the damage factor of the bridge pier is u L The finite element model was used to simulate the ice flow impact. Before and after the ice flow impact simulation, a gradually increasing axial load was applied to the top of the N group of piers until the piers collapsed. The axial load at the moment of collapse was extracted to obtain the ultimate bearing capacity P of the N group of piers before ice flow impact. Lq-before and the ultimate bearing capacity after impact P Lq-after , and obtain the damage factor u of each group of piers Lq And the damage factor matrix U L , which is expressed as follows:

[0070]

[0071] U L =[u L1 u L2 ...u LN-1 u LN ] T ;

[0072] Step 7: Construction of probability distribution model of bridge pier bearing capacity after disaster

[0073] The distribution type of damage factors of bridge piers is:

[0074]

[0075] Constructing the distribution parameters of damage factors The determination formula is as follows:

[0076]

[0077]

[0078] The probability density function of the damage factor is:

[0079]

[0080] Get the distribution parameters The probability distribution function of the damage factor of the bridge pier is obtained as follows:

[0081]

[0082] Step 8: Copy Probability distribution model construction

[0083] Build a complex Probability distribution function operator λ (1) The determination formula is as follows:

[0084]

[0085] Among them The probability density function is:

[0086]

[0087] Where,

[0088]

[0089]

[0090] Get operator λ (1) , thus obtaining The probability distribution function is as follows:

[0091]

[0092] Step 9: Copy Probability distribution model construction

[0093] Constructing the probability distribution function operator λ of the complex flow ice load correlation number (2) The determination formula is as follows:

[0094]

[0095] Among them The probability density function is:

[0096]

[0097] Where,

[0098]

[0099] Get operator λ (2) , thus obtaining The probability distribution function is as follows:

[0100]

[0101] Step 10: Construction of the probability distribution function of the post-disaster bearing capacity of bridge piers

[0102] By Fu Probability distribution functions and complex The probability distribution function of the damage factor of the bridge pier under the action of drift ice load is obtained as follows:

[0103]

[0104] Step 11: Bridge damage status assessment

[0105] Establish the criterion for judging the damage state of bridges under drifting ice load: define u Lq ∈[0,0.2] is the first-level damage state SH1, u Lq ∈(0.2,0.5] is the secondary damage state SH2, u Lq ∈(0.5,0.8] is the third level damage state SH3, u Lq ∈(0.8,1] is the fourth-level damage state SH4, where the damage state of the bridge from SH1 to SH4 becomes increasingly serious;

[0106] Step 12: Bridge Vulnerability Assessment

[0107] Under the action of drifting ice load, the damage state of the bridge reaches SH δ , the probability of δ=1,2,3,4 Expressed as:

[0108]

[0109] Where, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

[0110] Compared with the existing technology, the present invention has the following advantages: it proposes an efficient and systematic vulnerability assessment method for double-span continuous beam bridges, providing scientific support for the design optimization, routine maintenance and management decision-making of bridges in cold regions, and has the following advantages:

[0111] 1. The assessment method is systematic and efficient: By conducting a batch of nonlinear dynamic time-history analyses of bridge structures at one time and obtaining bridge structure response data, a multi-dimensional vulnerability function for cold-region bridge structures under the impact of drift ice was constructed. Subsequently, by inputting drift ice load correlation coefficients and pier damage factors, the bridge structure damage probability can be quickly calculated.

[0112] 2. The assessment results are closer to reality: By analyzing the probabilistic demands of bridge structures under the action of drift ice with multi-dimensional parameters, the multi-dimensional characteristics of drift ice impact are reflected, the complexity of impact behavior is fully characterized, and the vulnerability assessment of bridge structures considering the complexity of drift ice impact behavior is realized;

[0113] 3. Intelligent evaluation method: Programming can be used to realize automatic calculation, avoiding tedious and complicated manual calculation processes, and ensuring the convenience of application of the method of the present invention through intelligent calculation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 It is a flowchart of the evaluation method of the present invention. DETAILED DESCRIPTION

[0115] The technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0116] like Figure 1 As shown, a multi-dimensional vulnerability assessment method for bridge structures in cold regions under the impact of drifting ice includes the following steps:

[0117] Step 1: Generate the grid format of bridge structure finite element model parameters

[0118] A three-dimensional finite element model of a double-span continuous beam bridge with abutment-pier-abutment arrangement is established. Considering the random variability of the four parameters, namely, the elastic modulus of steel bar, the elastic modulus of concrete, the compressive strength of concrete, and the yield strength of steel bar, N finite element models are generated. Δ j , j = 1, 2, 3, 4 represent various parameters, as follows:

[0119]

[0120]

[0121]

[0122] Where μ jrepresents the mean of each parameter, σ j 2 represents the variance of each parameter, Represents the lower bound of the distribution of each parameter, Represents the upper bound of the distribution of each parameter.

[0123] The cumulative probability distribution function of each parameter is expressed as: y j =F j (x j )y j ∈[0,1];

[0124] The cumulative probability interval [0,1] is evenly divided into n probability intervals with equal probability. The probability interval matrix Λ is expressed as:

[0125]

[0126] Each row i=1,2,...,n-1,n represents a small probability interval.

[0127] The probability interval passes through x j =F j -1 (y j ) is mapped to the sampling interval The sampling interval matrix I can be obtained j for:

[0128]

[0129] Each row i=1,2,...,n-1,n represents a sampling interval.

[0130] Setting important intervals through prior knowledge Contains s sampling intervals, s+n=N.

[0131] From each sampling interval I i,j Randomly select a sample w from i,j , w i,j ~U(I i,j ), among which, U(I i,j ) indicates that in the sampling interval I i,j Uniform random distribution within .

[0132] In addition, from the important interval An additional sample w is randomly drawn from each sampling cell i,j ′,w i,j ′~U(I select,j ), among which, U(I select,j ) indicates that in the important interval Iselect,j Uniform random distribution within .

[0133] Sample w i,j With sample w i,j ' takes i as the row index and j as the column index, arranged from small to large, to form matrices W and W' respectively:

[0134]

[0135] Combining matrices W and W′ yields the sample matrix W″:

[0136]

[0137] Step 2: Randomly arrange the parameters of the bridge structure finite element model

[0138] Let each column of the sample matrix W″ be W j , expressed as:

[0139]

[0140] For W j , define the set P to represent the position index, expressed as:

[0141] P={1,2,...,n-1,n,n+1,...,n+s-1,n+s}

[0142] Among them, each element of the set P represents W j Sequential position from top to bottom.

[0143] Define the current processing position as k q , k q =N-q+1, q=1,2,...,N-1,N, for the current processing position k q Randomly select q ∈{1,2,...k q -2,k q -1} to exchange positions,

[0144] The position exchange is performed sequentially from 1 to N according to q. The expression for the qth position exchange is as follows:

[0145]

[0146] in, Indicates exchange Middle position k q With position o q The matrix after the element, represents W after exchanging the qth position j ,and

[0147] When the Nth position exchange is completed, we can get Will The initial sample matrix A can be obtained by merging, which is expressed as:

[0148]

[0149] Step 3: Optimal arrangement of bridge structure finite element model parameters

[0150] Each row in the initial sample matrix A represents a sample combination. Select any two sample combinations in the initial sample matrix A to form a sample combination pair, and calculate their Euclidean distance d gh Expressed as:

[0151]

[0152] Among them, a gj and a hj Represent the elements of two sample combinations, g,h∈{1,2,...N-1,N} and g≠h.

[0153] Calculate the Euclidean distance between all sample combination pairs in the initial sample matrix A, and keep the minimum value as Define the temperature at this moment as T0.

[0154] For each column of the initial sample matrix A, define a set R to represent the position index, expressed as:

[0155] R={1,2,...,N-1,N}

[0156] Among them, each element of the set R represents Sequential position from top to bottom.

[0157] Define the rth optimization, and fix the processing position to k V =V, V = 1, 2, 3, for a fixed processing position k V Randomly select v∈{4,5,...,N-1,N} to exchange positions,

[0158] Press V to perform position swaps from 1 to 3 in sequence. The Vth position swap is expressed as follows:

[0159]

[0160] in, Indicates exchange Middle position k V with the matrix after the element at position v, Indicates that after exchanging the Vth position and

[0161] Will Merge to get the optimized sample matrix A r , expressed as:

[0162]

[0163] Calculate the optimized sample matrix A r The Euclidean distance between all sample combinations in is recorded as Define the updated temperature as λ is the cooling parameter.

[0164] like Directly accept the optimized sample matrix A r is the new matrix;

[0165] like Randomly draw a z in the interval (0,1), when Then accept the optimized sample matrix A r is the new matrix, when Then the optimized sample matrix A is not accepted r is the new matrix.

[0166] Continue until When , the optimization is stopped and the optimal sample matrix is ​​obtained. The finite element model is optimized based on the optimal sample matrix.

[0167] Step 4: Statistics of drift ice load observation data

[0168] The relevant parameters of drift ice load are the drift ice mass π, the drift ice velocity and drift ice load position By observing the correlation numbers of N groups of drift ice loads, the drift ice mass matrix M can be obtained. ice , ice flow velocity matrix V ice and the drift ice load position matrix H ice , which is expressed as follows:

[0169] M ice =[Π1 Π2 ... Π N-1 Π N ] T

[0170]

[0171]

[0172] Step 5: Construction of the probability distribution model of drift ice load

[0173] The distribution type of the drift ice load correlation number is:

[0174] Π~Lognormal(μ Π ,σ Π 2 )

[0175]

[0176]

[0177] Constructing distribution parameters of drift ice load correlation numbers The determination formula is as follows:

[0178]

[0179]

[0180]

[0181] Among them, the probability density function of the drift ice load correlation number is:

[0182]

[0183]

[0184]

[0185] The probability distribution function of the drift ice load correlation number can be obtained as follows:

[0186]

[0187]

[0188]

[0189] Step 6: Construction of pier damage factor matrix

[0190] Assume the damage factor of the bridge pier is u L The finite element model was used to simulate the ice flow impact. Before the ice flow impact simulation, a gradually increasing axial load was applied to the top of the N group of piers until the piers collapsed. The axial load at the moment of collapse was extracted to obtain the ultimate bearing capacity P of the N group of piers before ice flow impact. Lq-before After the ice floe impact simulation, a gradually increasing axial load is applied to the top of the N group of piers until the piers collapse. The axial load at the moment of collapse is extracted to obtain the ultimate bearing capacity P of the N group of piers after ice floe impact. Lq-after , we can get the damage factor u of each group of piers Lq And the damage factor matrix U L , which is expressed as follows:

[0191]

[0192] U L =[u L1 u L2 ...u LN-1 u LN ] T

[0193] Step 7: Construction of probability distribution model of bridge pier bearing capacity after disaster

[0194] The distribution type of damage factors of bridge piers is:

[0195]

[0196] Constructing the distribution parameters of damage factors The determination formula is as follows:

[0197]

[0198]

[0199] The probability density function of the damage factor is:

[0200]

[0201] The distribution parameters can be obtained The probability distribution function of the damage factor of the bridge pier can be obtained as follows:

[0202]

[0203] Step 8: Copy Probability distribution model construction Probability distribution function operator λ (1) The determination formula is as follows:

[0204]

[0205] Among them The probability density function is:

[0206]

[0207] Where,

[0208]

[0209] The operator λ can be obtained (1) , from this we can get The probability distribution function is as follows:

[0210]

[0211] Step 9: Copy Probability distribution model construction Constructing the probability distribution function operator λ of the complex flow ice load correlation number (2) The determination formula is as follows:

[0212]

[0213] Among them The probability density function is:

[0214]

[0215] Where,

[0216]

[0217] The operator λ can be obtained (2) , from this we can get

[0218] The probability distribution function is as follows:

[0219]

[0220] Step 10: Construction of the probability distribution function of the post-disaster bearing capacity of bridge piers

[0221] The complex obtained from step 8 Probability distribution function and the complex The probability distribution function of the damage factor of the bridge pier under the action of drift ice load is obtained as follows:

[0222]

[0223] Step 11: Bridge damage status assessment

[0224] Establish the criterion for judging the damage state of bridges under drifting ice load: define u Lq ∈[0,0.2] is the first-level damage state SH1, u Lq ∈(0.2,0.5] is the secondary damage state SH2, u Lq ∈(0.5,0.8] is the third level damage state SH3, u Lq ∈(0.8,1] is the fourth-level damage state SH4, among which the damage states of bridges from SH1 to SH4 are gradually serious.

[0225] Step 12: Bridge Vulnerability Assessment

[0226] Under the action of drifting ice load, the damage state of the bridge reaches SH δ , the probability of δ=1,2,3,4 Expressed as:

[0227]

[0228] Where, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

[0229] Example

[0230] This example uses the Ussuri River Bridge section of the Mohe to Manchuria Expressway as an example to assess the multi-dimensional vulnerability of bridge structures in cold regions under the impact of drifting ice. The details are as follows:

[0231] (1) Generation of bridge structure finite element model parameter grid

[0232] A three-dimensional finite element model of the bridge was established. Considering the random variability of the four parameters, 120 finite element models were generated. j , j = 1, 2, 3, 4 represent various parameters, as follows:

[0233] Δ1~Lognormal(204000,2040 2 ), Δ2~Lognormal(30000,300 2 )

[0234] Δ3~Lognormal(27.68,4.44 2 ), Δ4~Lognormal(38.27,28.59 2 )

[0235] Δ1∈[197782.60,201380.79],Δ2∈[29085.68,29614.82]

[0236] Δ3∈[29085.68,29614.82],Δ4∈[16.70,22.26]

[0237] The cumulative probability interval [0,1] is evenly divided into 100 small probability intervals with equal probability as follows:

[0238]

[0239] The probability interval passes through x j =F j -1 (y j ) is mapped to the sampling interval, and the sampling interval I is obtained. i,j Some of them are shown below:

[0240]

[0241] Setting important intervals through prior knowledge Contains 20 sampling intervals, 20+100=120.

[0242] From each sampling interval I i,j Randomly select a sample w from i,j , forming the matrix W, in addition, from the important interval I select,j An additional sample w is randomly drawn from each sampling cell i,j ′, forming a matrix W′, merging matrices W and W′ to obtain the sample matrix W″ is shown as follows:

[0243]

[0244] (2) Random arrangement of finite element model parameters of bridge structure

[0245] Let each column of the sample matrix W″ be W j , for example, the W1 part is shown as follows:

[0246]

[0247] For W j , define the set P to represent the position index, expressed as:

[0248] P={1,2,...,99,100,101,...,119,120}

[0249] Define the current processing position as k q , k q =120-q+1, q=1, 2, ..., 119, 120, for the current processing position k q Randomly select q ∈{1,2,...k q -2,k q -1} to exchange positions,

[0250] Press q to perform position exchange from 1 to N. When the Nth position exchange is completed, you can get

[0251] Since there are too many exchanges, let's take an example of the first position exchange in W1, that is, q = 1, then the current processing position selected is k1 = 120, and assuming that o1 = 3 is selected, it means that the value 202257.967 at the 120th position in W1 will be exchanged with the value 199878.5089 at the 3rd position. The matrix after the exchange is

[0252] Will The initial sample matrix A obtained by merging is shown as follows:

[0253]

[0254] (3) Optimal arrangement of finite element model parameters of bridge structures

[0255] Each row in the initial sample matrix A represents a sample combination. Select any two sample combinations in the initial sample matrix A to form a sample combination pair, and calculate their Euclidean distance d gh .

[0256] Calculate the Euclidean distance between all sample combination pairs in the initial sample matrix A, and keep the minimum value as Define the temperature at this moment as T0=1.

[0257] For each column of the initial sample matrix A, define a set R to represent the position index, expressed as:

[0258] R={1,2,...,119,120}

[0259] Define the rth optimization, and fix the processing position to k V =V, V = 1, 2, 3, for a fixed processing position k V Randomly select v∈{4,5,...,N-1,N} to exchange positions,

[0260] Press V to perform position swaps from 1 to 3 in sequence. The Vth position swap is expressed as follows:

[0261]

[0262] in, Indicates exchange Middle position k V with the matrix after the element at position v, Indicates that after exchanging the Vth position and

[0263] The position exchange here is similar to the previous one, so no more examples are given.

[0264] The optimal sample matrix obtained through optimization is shown as follows:

[0265]

[0266] (4) Statistics of drift ice load observation data

[0267] The relevant parameters of drift ice load are the drift ice mass π, the drift ice velocity and drift ice load position The ice mass matrix M can be obtained by observing 120 sets of ice load correlation numbers. ice, ice flow velocity matrix V ice and the drift ice load position matrix H ice , part of which is shown below:

[0268]

[0269] (5) Construction of probability distribution model of drift ice load

[0270] Distribution parameters of drift ice load correlation numbers The calculation results are as follows:

[0271]

[0272] The probability distribution function of the drift ice load correlation number can be obtained as follows:

[0273]

[0274]

[0275]

[0276] (6) Construction of pier damage factor matrix

[0277] The damage factor matrix U of the bridge pier was extracted by conducting drift ice impact simulation test using finite element model. L , part of which is shown below:

[0278]

[0279] (7) Construction of a probability distribution model for the bearing capacity of bridge piers after disasters

[0280] Distribution parameters of damage factors The calculation results are as follows:

[0281]

[0282] The probability distribution function of the damage factor of the bridge pier can be obtained as follows:

[0283]

[0284] (8) Repetition Probability distribution model construction

[0285] Calculate the operator λ (1) =3.7717, from this we can get The probability distribution function is as follows:

[0286]

[0287] (9) Repetition Probability distribution model construction

[0288] Calculate the operator λ (2) =0.2657, from this we can get

[0289] The probability distribution function is as follows:

[0290]

[0291] (10) Construction of the probability distribution function of the bearing capacity of bridge piers after disasters

[0292] The probability distribution function of the damage factor of the bridge pier under the action of drifting ice load is:

[0293]

[0294] Here is an example, when M ice =100,V ice =2,H ice =4.5,u L =0.3, we can get:

[0295]

[0296] (11) Assessment of bridge damage status

[0297] Define u Lq ∈[0,0.2] is the first-level damage state SH1, u Lq ∈(0.2,0.5] is the secondary damage state SH2, u Lq ∈(0.5,0.8] is the third level damage state SH3, u Lq ∈(0.8,1] is the fourth level damage state SH4.

[0298] (12) Bridge vulnerability assessment

[0299]

[0300] Here we give an example again, assuming that when M ice =100,V ice =2,H ice =4.5, When , the probability of the bridge reaching the second-level damage state is:

[0301]

[0302] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other configurations without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations coming within the meaning and range of equivalents of the claims are intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0303] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A multi-dimensional vulnerability assessment method for bridge structures in cold regions under the impact of drift ice, characterized by: The following steps are involved: Step 1: Generate the grid format of bridge structure finite element model parameters A three-dimensional finite element model of a double-span continuous beam bridge with abutment-pier-abutment arrangement is established. Considering the random variability of the four parameters, namely, the elastic modulus of steel bar, the elastic modulus of concrete, the compressive strength of concrete, and the yield strength of steel bar, N finite element models are generated. Δ j , j = 1, 2, 3, 4 represent various parameters, as follows: Δ1~Lognormal(μ1,σ1 2 ), Δ2~Lognormal(μ2,σ2 2 ) Δ3~Lognormal(μ3,σ3 2 ), Δ4~Lognormal(μ4,σ4 2 ) Where μ j represents the mean of each parameter, σ j 2 represents the variance of each parameter, Represents the lower bound of the distribution of each parameter, Represents the upper bound of the distribution of each parameter; The cumulative probability distribution function of each parameter is expressed as: y j =F j (x j )y j ∈[0,1]; The cumulative probability interval [0,1] is evenly divided into n probability intervals with equal probability. The probability interval matrix Λ is expressed as: Each row Represents a small probability interval; The probability interval passes through x j =F j -1 (y j ) is mapped to the sampling interval Get the sampling interval matrix I j for: Each row Represents a sampling interval; Setting important intervals through prior knowledge Contains s sampling intervals, s+n=N; From each sampling interval I i,j Randomly select a sample w from i,j , from the important interval I select,j An additional sample w is randomly drawn from each sampling cell i,j ′, sample w i,j With sample w i,j 'Use i as the row index and j as the column index, arrange them from small to large, to form matrices W and W'. Merge matrices W and W' to get the sample matrix W'': Step 2: Randomly arrange the parameters of the bridge structure finite element model Let each column of the sample matrix W″ be W j , expressed as: For W j , define the set P to represent the position index, expressed as: P={1,2,...,n-1,n,n+1,...,n+s-1,n+s} Define the current processing position as k q , k q =N-q+1, q=1,2,...,N-1,N, for the current processing position k q Randomly select q ∈{1,2,...k q -2,k q -1} to exchange positions; The position exchange is performed sequentially from 1 to N according to q. The expression for the qth position exchange is as follows: in, Indicates exchange Middle position k q With position o q The matrix after the element, represents W after exchanging the qth position j ,and When the Nth position exchange is completed, we can get Will The initial sample matrix A is obtained by merging, which is expressed as: Step 3: Optimal arrangement of bridge structure finite element model parameters Each row in the initial sample matrix A represents a sample combination. Select any two sample combinations to form a sample combination pair. Calculate the Euclidean distance between all sample combination pairs in the initial sample matrix A and keep the minimum value as Define the temperature at this moment as T0; For each column of the initial sample matrix A, define a set R to represent the position index, expressed as: R={1,2,...,N-1,N} Define the rth optimization, and fix the processing position to k V =V, V = 1, 2, 3, for a fixed processing position k V Randomly select v∈{4,5,...,N-1,N} to exchange positions; Press V to perform position swaps from 1 to 3 in sequence. The Vth position swap is expressed as follows: in, Indicates exchange Middle position k V with the matrix after the element at position v, Indicates that after exchanging the Vth position and Will Merge to get the optimized sample matrix A r , expressed as: Calculate the optimized sample matrix A r The Euclidean distance between all sample combinations in is recorded as Define the updated temperature as λ is the cooling parameter; like Directly accept the optimized sample matrix A r is the new matrix; like Randomly draw a z in the interval (0,1), when Then accept the optimized sample matrix A r is the new matrix, when Then the optimized sample matrix A is not accepted r is the new matrix; Continue until When , the optimization is stopped, the optimal sample matrix is ​​obtained, and the finite element model is optimized based on the optimal sample matrix; Step 4: Statistics of drift ice load observation data The relevant parameters of drift ice load are the drift ice mass π, the drift ice velocity and drift ice load position Observe N groups of drift ice load correlation numbers to obtain the drift ice mass matrix M ice , ice flow velocity matrix V ice and the drift ice load position matrix H ice , which is expressed as follows: M ice =[Π1 Π2...∏ N-1 ∏ N ] T Step 5: Construction of the probability distribution model of drift ice load The distribution type of the drift ice load correlation number is: ∏~Lognormal(μ ∏ ,s Π 2 ) Constructing the distribution parameter μ of the drift ice load correlation number Π ,σ ∏ , The determination formula is as follows: Among them, the probability density function of the drift ice load correlation number is: The probability distribution function of the drift ice load correlation number is obtained as follows: Step 6: Construction of pier damage factor matrix Assume the damage factor of the bridge pier is u L The finite element model was used to simulate the ice flow impact. Before and after the ice flow impact simulation, a gradually increasing axial load was applied to the top of the N group of piers until the piers collapsed. The axial load at the moment of collapse was extracted to obtain the ultimate bearing capacity P of the N group of piers before ice flow impact. Lq-before and the ultimate bearing capacity after impact P Lq-after , and obtain the damage factor u of each group of piers Lq And the damage factor matrix U L , which is expressed as follows: IN L =[in L1 in L2 ...in LN-1 in LN ] T ; Step 7: Construction of probability distribution model of bridge pier bearing capacity after disaster The distribution type of damage factors of bridge piers is: Constructing the distribution parameters of damage factors The determination formula is as follows: The probability density function of the damage factor is: Get the distribution parameters The probability distribution function of the damage factor of the bridge pier is obtained as follows: Step 8: Copy Probability distribution model construction Build a complex Probability distribution function operator λ (1) The determination formula is as follows: Among them The probability density function is: Where, Get operator λ (1) , thus obtaining The probability distribution function is as follows: Step 9: Copy Probability distribution model construction Constructing the probability distribution function operator λ of the complex flow ice load correlation number (2) The determination formula is as follows: Among them The probability density function is: Where, Get operator λ (2) , thus obtaining The probability distribution function is as follows: Step 10: Construction of the probability distribution function of the post-disaster bearing capacity of bridge piers By Fu Probability distribution functions and complex The probability distribution function of the damage factor of the bridge pier under the action of drift ice load is obtained as follows: Step 11: Bridge damage status assessment Establish the criterion for judging the damage state of bridges under drifting ice load: define u Lq ∈[0,0.2] is the first-level damage state SH1, u Lq ∈(0.2,0.5] is the secondary damage state SH2, u Lq ∈(0.5,0.8] is the third level damage state SH3, u Lq ∈(0.8,1] is the fourth-level damage state SH4, where the damage state of the bridge from SH1 to SH4 becomes increasingly serious; Step 12: Bridge Vulnerability Assessment Under the action of drifting ice load, the damage state of the bridge reaches SH δ , the probability of δ=1,2,3,4 Expressed as: Where, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

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