Method for evaluating multi-dimensional vulnerability of bridge structure in cold region under action of flowing ice impact

Abstract

The invention discloses a multi-dimensional vulnerability assessment method for a bridge structure in a cold region under the impact action of flowing ice, and relates to the technical field of bridge vulnerability assessment. The method comprises the steps of bridge structure finite element model parameter grid format generation, parameter random arrangement, parameter optimal arrangement, flow ice load observation data statistics, probability distribution model construction, bridge pier damage factor matrix construction, post-disaster bridge pier bearing capacity probability distribution model construction, and bridge pier damage factor probability distribution function obtaining under the action of a flow ice load. And constructing a condition probability distribution function of the post-disaster bearing capacity of the pier, and judging and evaluating a damage state and evaluating vulnerability. For a double-span continuous beam bridge, the accuracy of vulnerability evaluation can be remarkably improved by considering the random variability of finite element model bridge structure parameters, the complexity of the impact behavior is comprehensively described in combination with the multi-dimensional characteristics of flow ice impact, and the method is more efficient and systematized; and the impact resistance prediction and the overall safety performance evaluation of the bridge structure are facilitated.

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 an important part of the transportation network in cold regions, the safety of cold region bridges in extreme climate and complex natural environment has attracted much attention. Especially under the impact of drifting ice, the bridge structure is very likely to suffer local damage or even overall destruction, posing a serious threat to traffic safety and bridge life. Drifting ice impact is often accompanied by high kinetic energy, with obvious randomness and unpredictability, which makes the design, inspection and maintenance of cold region bridges face huge challenges.

[0003] The vulnerability assessment of bridge structures under the impact of drift ice is an important basis for determining their impact resistance and formulating protection strategies. At present, although researchers have conducted in-depth research on the physical characteristics of drift ice impact, bridge structure response and failure modes, the traditional methods at this stage usually assume that the parameters of the finite element model are fixed values, and do not fully consider the random variability of bridge materials, geometric dimensions and environmental conditions. This assumption may lead to deviations in the evaluation results of bridge structure performance, especially in complex cold environment, where its applicability is limited. In addition, the parameters of drift ice impact (such as ice mass, speed, impact position, etc.) have significant randomness and multidimensional characteristics, but the existing evaluation methods are usually based on simplified models and cannot fully reflect the complex distribution laws of these parameters, making it difficult to accurately predict the impact of drift ice impact on bridge structures. Therefore, the accuracy and reliability of the vulnerability assessment of bridge structures in cold regions under the impact of drift ice is difficult to guarantee at this stage.

[0004] In summary, the existing assessment methods have significant defects in the vulnerability assessment of bridge structures under the impact of drift ice, which leads to the inability of the assessment model to accurately capture the complex behavior of actual drift ice impact, resulting in large deviations in the assessment results, making it difficult to serve 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 under the impact of drift ice. 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 accuracy of vulnerability assessment can be significantly improved. Combined with the multi-dimensional characteristics of drifting ice impact, the complexity of the impact behavior is comprehensively characterized, which is more efficient and systematizable, and is helpful for predicting the impact resistance of bridge structures and evaluating their overall safety performance.

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

[0007] Step 1: Generation of bridge structure finite element model parameter grid

[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 of steel bar elastic modulus, concrete elastic modulus, concrete compressive strength and steel bar yield strength, N finite element models are generated. j , j = 1, 2, 3, 4 represents 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] In the formula, μ j represents the mean of each parameter, σ j 2 Represents the variance of each parameter, Δ u j 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: j =F j (x j )y j ∈[0,1];

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

[0015]

[0016] Among them, each line represents a small probability interval;

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

[0018]

[0019] Among them, each line 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 selected 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, form matrices W and W', and merge matrices W and W' to get the sample matrix W':

[0022]

[0023] Step 2: Random arrangement of bridge structure finite element model parameters

[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, randomly select o for the current processing position kq 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 qth position exchange is expressed 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, a set R is defined to represent the position index, expressed as:

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

[0038] Define the rth optimization, 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 exchange from 1 to 3 in sequence. The Vth position exchange is expressed as follows:

[0040]

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

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

[0043]

[0044] Calculate the optimized sample matrix A rThe Euclidean distance between all sample combinations in is recorded as Define the update 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 ice load position Observe N groups of drift ice load correlation numbers to obtain the drift ice mass matrix M ice 、Drift ice velocity matrix V ice and the ice flow load position matrix H ice , which is expressed as follows:

[0050] M ice =[∏1 ∏2 ... ∏ N-1 ∏ N ] T

[0051]

[0052] Step 5: Construction of the probability distribution model of drift ice load

[0053] The distribution type of the drift ice load correlation number is:

[0054] Π~Lognormal(μ Π ,σ Π 2 )

[0055]

[0056] Constructing the distribution parameter μ of the drift ice load correlation number Π ,σ Π , The determination formula is as follows:

[0057]

[0058] Among them, the probability density function of the drift ice load correlation number is:

[0059]

[0060] The probability distribution function of the drift ice load correlation number is obtained as follows:

[0061]

[0062] Step 6: Construction of pier damage factor matrix

[0063] Assume the damage factor of the bridge pier is u L The finite element model was used to simulate the drift ice impact. Before and after the drift ice 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 the drift ice 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:

[0064]

[0065] U L =[u L1 u L2 ...u LN-1 u LN ] T ;

[0066] Step 7: Construction of probability distribution model of bridge pier bearing capacity after disaster

[0067] The distribution type of damage factors of bridge piers is:

[0068]

[0069] Constructing the distribution parameters of the damage factor The determination formula is as follows:

[0070]

[0071] The probability density function of the damage factor is:

[0072]

[0073] Get the distribution parameters The probability distribution function of the damage factor of the bridge pier is obtained as follows:

[0074]

[0075] Step 8: Copy Probability distribution model construction

[0076] Build Complex Probability distribution function operator λ (1) The determination formula is as follows:

[0077]

[0078] Among them The probability density function is:

[0079]

[0080] In the formula,

[0081]

[0082] Get operator λ (1) , thus obtaining The probability distribution function is as follows:

[0083]

[0084] Step 9: Copy Probability distribution model construction

[0085] Constructing the probability distribution function operator λ of the correlation number of complex flow ice load (2) The determination formula is as follows:

[0086]

[0087] Among them The probability density function is:

[0088]

[0089] In the formula,

[0090]

[0091] Get operator λ (2) , thus obtaining The probability distribution function is as follows:

[0092]

[0093] Step 10: Construction of the probability distribution function of the post-disaster bearing capacity of bridge piers

[0094] By Fu Probability distribution functions and complex The probability distribution function of the damage factor of the bridge pier under the action of drifting ice load is obtained as follows:

[0095]

[0096] Step 11: Determination and assessment of bridge damage status

[0097] 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 bridges from SH1 to SH4 becomes increasingly serious;

[0098] Step 12: Bridge Vulnerability Assessment

[0099] Under the action of drifting ice load, the damage state of the bridge reaches SH δ , the probability of δ=1,2,3,4 It is expressed as:

[0100]

[0101] In the formula, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

[0102] Compared with the prior art, the present invention has the following beneficial effects: the present invention proposes an efficient and systematic vulnerability assessment method for double-span continuous beam bridges, provides scientific support for the design optimization, daily maintenance and management decision-making of bridges in cold regions, and has the following advantages:

[0103] 1. The evaluation method is systematic and efficient: After carrying out nonlinear dynamic time-history analysis of a batch of bridge structures at one time and obtaining the bridge structure response data, a multi-dimensional vulnerability function of bridge structures in cold regions under the impact of drifting ice is constructed. The subsequent input of drifting ice load correlation numbers and pier damage factors can quickly obtain the bridge structure damage probability;

[0104] 2. The evaluation results are closer to reality: by analyzing the probabilistic demand of bridge structures under the impact of multi-dimensional parameters, the multi-dimensional characteristics of the impact of drift ice are reflected, the complexity of the impact behavior is fully described, and the vulnerability assessment of bridge structures considering the complexity of the impact behavior of drift ice is realized;

[0105] 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

[0106] Figure 1 It is a flowchart of the evaluation method of the present invention. DETAILED DESCRIPTION

[0107] The technical solution 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 of 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.

[0108] like Figure 1 As shown, a multi-dimensional vulnerability assessment method for cold region bridge structures under the impact of drifting ice comprises the following steps:

[0109] Step 1: Generation of bridge structure finite element model parameter grid

[0110] 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 of steel bar elastic modulus, concrete elastic modulus, concrete compressive strength and steel bar yield strength, N finite element models are generated. j , j = 1, 2, 3, 4 represents various parameters, as follows:

[0111] Δ1~Lognormal(μ1,σ1 2 ), Δ2~Lognormal(μ2,σ2 2 )

[0112] Δ3~Lognormal(μ3,σ3 2 ), Δ4~Lognormal(μ4,σ4 2 )

[0113]

[0114] In the formula, 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.

[0115] The cumulative probability distribution function of each parameter is expressed as: j =Fj (x j )y j ∈[0,1];

[0116] The cumulative probability interval [0,1] is evenly divided into n probability intervals with equal probability. The probability interval matrix Λ is expressed as:

[0117]

[0118] Among them, each line Represents a small probability interval.

[0119] 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:

[0120]

[0121] Among them, each line Represents a sampling interval.

[0122] Setting important intervals through prior knowledge Contains s sampling intervals, s+n=N.

[0123] 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.

[0124] In addition, from the important interval An additional sample w is randomly selected 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 I select,j Uniform random distribution within.

[0125] Sample w i,j With sample w i,j ′Use i as the row index and j as the column index, arranging them from small to large, and constructing matrices W and W′ respectively:

[0126]

[0127] Combining matrices W and W′, we can get the sample matrix W″:

[0128]

[0129] Step 2: Random arrangement of bridge structure finite element model parameters

[0130] Let each column of the sample matrix W″ be W j , expressed as:

[0131]

[0132] For W j , define the set P to represent the position index, expressed as:

[0133] P={1,2,...,n-1,n,n+1,...,n+s-1,n+s}

[0134] Among them, each element of the set P represents W j Ordinal position from top to bottom.

[0135] 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, o q ~U([1,k q -1]).

[0136] The position exchange is performed sequentially from 1 to N according to q. The qth position exchange is expressed as follows:

[0137]

[0138] 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

[0139] 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:

[0140]

[0141] Step 3: Optimal arrangement of bridge structure finite element model parameters

[0142] 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 It is expressed as:

[0143]

[0144] Among them, agj and ahj represent the elements of two sample combinations respectively, g,h∈{1,2,...N-1,N} and g≠h.

[0145] 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.

[0146] For each column of the initial sample matrix A, a set R is defined to represent the position index, expressed as:

[0147] R={1,2,...,N-1,N}

[0148] Each element of the set R represents Ordinal position from top to bottom.

[0149] Define the rth optimization, 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} for position exchange, v~U([4,N]).

[0150] Press V to perform position exchange from 1 to 3 in sequence. The Vth position exchange is expressed as follows:

[0151]

[0152] in, Indicates exchange Middle position k V The matrix after the element at position v, Indicates that after the Vth position exchange and

[0153] Will Merge to get the optimized sample matrix A r , expressed as:

[0154]

[0155] Calculate the optimized sample matrix A rThe Euclidean distance between all sample combinations in is recorded as Define the update temperature as λ is the cooling parameter.

[0156] like Directly accept the optimized sample matrix A r is the new matrix;

[0157] like Randomly select a z in the interval (0,1), z~U(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.

[0158] 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.

[0159] Step 4: Statistics of drift ice load observation data

[0160] The relevant parameters of drift ice load are the drift ice mass Π, the drift ice velocity and 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 、Drift ice velocity matrix V ice and the ice flow load position matrix H ice , which is expressed as follows:

[0161] M ice =[∏1 ∏2 ... ∏ N-1 Π N ] T

[0162]

[0163] Step 5: Construction of the probability distribution model of drift ice load

[0164] The distribution type of the drift ice load correlation number is:

[0165] Π~Lognormal(μ Π ,σ Π 2 )

[0166]

[0167] Constructing the distribution parameter μ of the drift ice load correlation number Π ,σ Π , The determination formula is as follows:

[0168]

[0169] Among them, the probability density function of the drift ice load correlation number is:

[0170]

[0171] The probability distribution function of the drift ice load correlation number can be obtained as follows:

[0172]

[0173] Step 6: Construction of pier damage factor matrix

[0174] 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 drift ice impact simulation, a gradually increasing axial load is applied to the top of the N group of bridge 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 bridge piers after the drift ice 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:

[0175]

[0176] U L =[u L1 u L2 ...u LN-1 u LN ] T

[0177] Step 7: Construction of probability distribution model of bridge pier bearing capacity after disaster

[0178] The distribution type of damage factors of bridge piers is:

[0179]

[0180] Constructing the distribution parameters of the damage factor The determination formula is as follows:

[0181]

[0182] The probability density function of the damage factor is:

[0183]

[0184] The distribution parameters can be obtained The probability distribution function of the damage factor of the pier can be obtained as follows:

[0185]

[0186] Step 8: Copy Probability distribution model construction

[0187] Build Complex Probability distribution function operator λ (1) The determination formula is as follows:

[0188]

[0189] Among them The probability density function is:

[0190]

[0191] In the formula,

[0192]

[0193] We can get the operator λ (1) , from which we can get The probability distribution function is as follows:

[0194]

[0195] Step 9: Copy Probability distribution model construction

[0196] Constructing the probability distribution function operator λ of the correlation number of complex flow ice load (2) The determination formula is as follows:

[0197]

[0198] Among them The probability density function is:

[0199]

[0200] In the formula,

[0201]

[0202] We can get the operator λ (2) , from which we can get The probability distribution function is as follows:

[0203]

[0204] Step 10: Construction of the probability distribution function of the post-disaster bearing capacity of bridge piers

[0205] The complex obtained from step eight The probability distribution function and the complex The probability distribution function of the damage factor of the bridge pier under the action of drifting ice load is obtained as follows:

[0206]

[0207] Step 11: Determination and assessment of bridge damage status

[0208] 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.

[0209] Step 12: Bridge Vulnerability Assessment

[0210] Under the action of drifting ice load, the damage state of the bridge reaches SH δ , the probability of δ=1,2,3,4 It is expressed as:

[0211]

[0212] In the formula, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

[0213] Example

[0214] This embodiment takes the Wusuli River super-large bridge section of the Mohe-Manzhouli Expressway as an example to evaluate the multi-dimensional vulnerability of bridge structures in cold regions under the impact of drifting ice, as follows:

[0215] (1) Generation of bridge structure finite element model parameter grid

[0216] 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 represents various parameters, as follows:

[0217] Δ1~Lognormal(204000,2040 2), Δ2~Lognormal(30000,300 2 )

[0218] Δ3~Lognormal(27.68,4.44 2 ), Δ4~Lognormal(38.27,28.59 2 )

[0219] Δ1∈[197782.60,201380.79],Δ2∈[29085.68,29614.82]

[0220] Δ3∈[29085.68,29614.82],Δ4∈[16.70,22.26]

[0221] Divide the cumulative probability interval [0,1] into 100 small probability intervals with equal probability as follows:

[0222]

[0223] The probability interval passes through x j =F j -1 (y j ) is mapped to the sampling interval, and the sampling interval Ii,j is shown as follows:

[0224]

[0225] Setting important intervals through prior knowledge Contains 20 sampling intervals, 20+100=120.

[0226] 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 selected from each sampling cell i,j ′, forming a matrix W′, merging the matrix W and W′ to obtain the sample matrix W″ is shown as follows:

[0227]

[0228]

[0229] (2) Random arrangement of finite element model parameters of bridge structure

[0230] Let each column of the sample matrix W″ be W j , for example, the W1 part is shown as follows:

[0231]

[0232] For W j , define the set P to represent the position index, expressed as:

[0233] P={1,2,...,99,100,101,...,119,120}

[0234] 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, o q ~U([1,k q -1]).

[0235] Press q to perform position exchange from 1 to N in sequence. When the Nth position exchange is completed, we can get

[0236] Since there are too many exchanges, here is an example of the first position exchange in W1, that is, q = 1, then the selected current processing position is k1 = 120, assuming that o1 = 3 is selected, which 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

[0237] Will The initial sample matrix A obtained by merging is shown as follows:

[0238]

[0239] (3) Optimal arrangement of finite element model parameters of bridge structures

[0240] 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 .

[0241] 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.

[0242] For each column of the initial sample matrix A, a set R is defined to represent the position index, expressed as:

[0243] R={1,2,…,119,120}

[0244] Define the rth optimization, 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} for position exchange, v~U([4,N]).

[0245] Press V to perform position exchange from 1 to 3 in sequence. The Vth position exchange is expressed as follows:

[0246]

[0247] in, Indicates exchange Middle position k V The matrix after the element at position v, Indicates that after the Vth position exchange and

[0248] The position exchange here is similar to the previous one, so no more examples are given.

[0249] The optimal sample matrix obtained through optimization is shown as follows:

[0250]

[0251] (4) Statistics of drift ice load observation data

[0252] The relevant parameters of drift ice load are the drift ice mass Π, the drift ice velocity and ice load position By observing 120 sets of drift ice load correlation numbers, the drift ice mass matrix M can be obtained. ice 、Drift ice velocity matrix V ice and the ice flow load position matrix H ice , part of which is shown below:

[0253]

[0254] (5) Construction of probability distribution model of drift ice load

[0255] Distribution parameter μ of the correlation number of drift ice load Π ,σ Π , The calculation results are as follows:

[0256] μ Π =0.3862,σ Π =4.4462,

[0257] The probability distribution function of the drift ice load correlation number can be obtained as follows:

[0258]

[0259] (6) Construction of pier damage factor matrix

[0260] The damage factor matrix U of the bridge pier was extracted by conducting a drift ice impact simulation test using a finite element model. L , part of which is shown below:

[0261]

[0262] (7) Construction of probability distribution model of bridge pier bearing capacity after disaster

[0263] Distribution parameters of damage factors The calculation results are as follows:

[0264]

[0265] The probability distribution function of the damage factor of the pier can be obtained as follows:

[0266]

[0267] (8) Repetition Probability distribution model construction

[0268] The operator λ is calculated (1) =3.7717, from which we can get The probability distribution function is as follows:

[0269]

[0270] (9) Repetition Probability distribution model construction

[0271] The operator λ is calculated (2) =0.2657, so we can get The probability distribution function is as follows:

[0272]

[0273] (10) Construction of probability distribution function of bridge pier post-disaster bearing capacity condition

[0274] The probability distribution function of the damage factor of the bridge pier under the action of drifting ice load is:

[0275]

[0276] Here is an example, when M ice =100,V ice =2,H ice =4.5,u L =0.3, we can get:

[0277]

[0278] (11) Evaluation of bridge damage status

[0279] 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.

[0280] (12) Bridge vulnerability assessment

[0281]

[0282] Here we still give an example, 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:

[0283]

[0284] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0285] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description 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 may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A multi-dimensional vulnerability assessment method for cold region bridge structures under the impact of drifting ice, characterized by: The following steps are involved: Step 1: Generation of bridge structure finite element model parameter grid 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 of steel bar elastic modulus, concrete elastic modulus, concrete compressive strength and steel bar yield strength, N finite element models are generated. j , j = 1, 2, 3, 4 represents various parameters, as follows: Δ1~Lognormal(μ1,σ1 2 ), Δ2~Lognormal(μ2,σ2 2 ) Δ3~Lognormal(μ3,σ3 2 ), Δ4~Lognormal(μ4,σ4 2 ) In the formula, 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: j =F j (x j )y j ∈[0,1]; The cumulative probability interval [0,1] is evenly divided into n probability intervals, and the probability interval matrix Λ is expressed as: Among them, each line n 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 cell matrix I j for: Among them, each line n 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 selected 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, form matrices W and W', and merge matrices W and W' to get the sample matrix W': Step 2: Random arrangement of bridge structure finite element model parameters 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, randomly select o for the current processing position kq 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 qth position exchange is expressed 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, a set R is defined to represent the position index, expressed as: R={1,2,...,N-1,N} Define the rth optimization, 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 exchange from 1 to 3 in sequence. The Vth position exchange is expressed as follows: in, Indicates exchange Middle position k V The matrix after the element at position v, Indicates that after the Vth position exchange 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 update 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 ice load position Observe N groups of drift ice load correlation numbers to obtain the drift ice mass matrix M ice 、Drift ice velocity matrix V ice and the ice flow load position matrix H ice , which is expressed as follows: M ice =[∏1 ∏2 ... ∏ N-1 P N ] T Step 5: Construction of probability distribution model of drift ice load The distribution type of the drift ice load correlation number is: P~Lognormal(μ Π ,s Π 2 ) Constructing the distribution parameter μ of the drift ice load correlation number Π ,σ Π , 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 drift ice impact. Before and after the drift ice 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 the drift ice 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 the damage factor 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 Complex Probability distribution function operator λ (1) The determination formula is as follows: Among them The probability density function is: In the formula, 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 correlation number of complex flow ice load (2) The determination formula is as follows: Among them The probability density function is: In the formula, 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 drifting ice load is obtained as follows: Step 11: Determination and assessment of bridge damage status 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 bridges 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 It is expressed as: In the formula, Indicates damage status SH δ The infimum of the median value of the damage factor of the lower pier.

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