Bridge risk assessment method considering subjective and objective cross-integration weights

Abstract

The present invention discloses a bridge risk assessment method that considers subjective and objective cross-fusion weights. Exponential interval numbers are used to fuzzy process subjective data so that the fuzziness of subjective judgment and the uncertainty of data are consistent. Cluster analysis methods are used to calculate expert personal weights to reduce the impact of individual expert bias. Based on set-valued statistical theory, the shadow method is used to calculate the expert subjective comprehensive index weight set through the idea of ​​group decision-making, and the entropy weight method is used to obtain the objective comprehensive weight of the index. Then, based on the minimum cross-entropy criterion, the subjective and objective cross-fusion index weights are calculated. Finally, a fuzzy comprehensive evaluation method is used to perform comprehensive judgment layer by layer, and the bridge risk assessment result is obtained by comprehensively considering risk probability and risk loss. Compared with similar evaluation methods, the present invention better reflects the subjective will of decision makers and reflects the accuracy of objective information, fully considers the characteristics of group decision-making, and provides a scientific and reliable evaluation method and process for bridge health assessment.

Description

Technical Field

[0001] The present invention relates to the fields of bridge risk assessment, engineering project management and bridge health detection and maintenance, and in particular to a subjective and objective comprehensive risk assessment and management and maintenance method for bridge engineering based on set value and entropy weight theory. Background Art

[0002] my country is a country with a large number of bridges, and the number of new and old bridges is among the highest in the world. Therefore, efficient and scientific bridge health assessment is of great significance to prevent, control and reduce risks and losses during its life cycle. However, the existing bridge health assessment is characterized by high resource consumption, high labor consumption, low efficiency and difficult operation. Therefore, it is necessary to establish a systematic assessment method to evaluate the comprehensive status of bridges, so as to provide a basis for decision-making for bridge management departments.

[0003] At present, the data of bridge health assessment system mainly comes from manual inspection data and data collected by health monitoring system. However, due to the high cost of monitoring system, the reliability of monitoring data and the existing assessment methods, the current bridge assessment is still mainly based on manual inspection data, supplemented by monitoring data. There are many traditional manual inspection projects, and most of them rely on the subjective experience and judgment of the inspectors. In the field of assessment management, subjective assessment methods are still used as the main assessment means, which makes the final assessment results easily affected by factors such as decision makers' experience and knowledge, resulting in the decision-making process and results being highly subjective. Although objective assessment methods are rarely presented, the calculation results of objective assessment methods are often contrary to reality, and most of the methods are based on the solution of some mathematical models, which has a large amount of calculation and ignores the influence of decision makers' subjective intentions, resulting in data distortion.

[0004] Therefore, it is particularly important to invent a subjective and objective interactive bridge evaluation method, and to establish an evaluation method that is compatible with manual detection and monitoring data by constantly adjusting and correcting the subjective and objective differences. On the one hand, it can minimize the impact of subjective errors in detection data; on the other hand, it can effectively combine monitoring data and apply it to the monitoring and evaluation management system of bridges to realize automated evaluation and management of bridges, thereby improving work efficiency. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a bridge risk assessment method that takes into account the cross-integration weights of subjective and objective factors, and realizes interactive subjective and objective risk assessment management of bridges by effectively combining the opinions of subjective group decision makers and objective monitoring data.

[0006] The technical solution of the present invention is as follows: A bridge risk assessment method considering subjective and objective cross-fusion weights comprises the following steps:

[0007] 1) Based on the identification results of bridge risk sources, the risk control target is used as the target layer indicator, and the target layer is divided into intermediate layer indicators based on the factors affecting the risk control target. Then, each intermediate layer indicator is further divided according to the factors affecting the intermediate layer indicators, and so on, until the required indicator decomposition accuracy is achieved to form a bridge risk assessment indicator model, and the last layer of the model is used as the bottom layer indicator. The bottom layer indicators are judged by experts, and the exponential interval number judgment matrix A is established according to Weber's law.

[0008] 2) Construct a probability model of the index interval number and establish an approximate numerical judgment matrix B that is convenient for consistency testing. Use the characteristic root method to calculate the subjective indicator weight set of each evaluation expert.

[0009] 3) Based on the cluster analysis method, the individual preference weights of each expert are established, where the individual preference weights of experts are calculated by the inter-class weights ρ after expert cluster analysis. a and the intra-class weight ρ b The inter-class weight is the weight of each class formed by clustering, and the intra-class weight is the weight of the experts in each class.

[0010] 4) Based on the set-valued statistical theory, the shadow method is used in combination with the expert individual preference weights obtained in step 3) to perform set-valued analysis through group decision making to obtain the group decision judgment matrix C. The characteristic root method is used to calculate the group decision judgment matrix C to obtain the subjective comprehensive index weight set ω based on group decision making. s .

[0011] 5) Use the membership function to quantitatively describe the numerical indicators and obtain their membership; use expert survey method to obtain the membership of semantic indicators by statistical means. The membership of numerical indicators and semantic indicators are combined to form an evaluation membership matrix.

[0012] 6) Establish an attribute matrix D based on the index evaluation level, and use the entropy weight method to calculate the objective comprehensive weight set ω of the evaluation index attribute matrix D of group decision making o The attribute matrix is ​​an objective value assignment matrix that describes how each indicator belongs to each evaluation level.

[0013] 7) Based on step 4), we get the subjective comprehensive index weight set ω s and the objective comprehensive weight set ω o , and the minimum cross entropy criterion is used to establish the subjective and objective weight optimization model L(γ, ω), and after solving it, the weight set ω of the underlying subjective and objective fusion indicators is obtained.

[0014] 8) Based on the AHP-FCE method, combined with the subjective and objective fusion weight set of the bottom-level indicators and the evaluation membership matrix, the corresponding intermediate-level indicator evaluation membership is calculated, and the intermediate-level indicator subjective and objective fusion indicator weight set is obtained by experts using the method of steps 1) to 7), and the upper-level indicator evaluation membership is further calculated. The evaluation is performed layer by layer, and finally the target layer indicator membership vector R is obtained. The target indicator risk estimation result F is obtained by combining the comment set, and the relevant guidelines are queried according to the calculation results to obtain the comprehensive risk evaluation of the bridge.

[0015] Furthermore, the identification of bridge risk sources is carried out specifically through the analysis of dangerous situations and uncertain risks through bridge accidents and research data, using data method, fault tree method, expert investigation method and other methods for identification.

[0016] Furthermore, in step 1), a general formula of exponential scaling of "subjective arithmetic progression and objective geometric progression" is established according to the Weber-Fechner law:

[0017] a ij =u x , x=0, ±1, ±2,...,±8; i, j=0,1,...,n

[0018] Where: a ij It represents the importance ratio of evaluation index i to evaluation index j; u is the importance ratio constant of the comparison index, x is the subjective arithmetic difference judgment level, and n is the number of evaluation indicators.

[0019] Use exponential interval number scale a′ ij Instead of exponential scale a ij , making the fuzziness and uncertainty of experts’ subjective judgment consistent, that is, the evaluation results are more scientific.

[0020]

[0021] Furthermore, in step 2), the expert's subjective arithmetic judgment level x of the index interval between any two indicators can be considered to be subject to expectation μ and variance σ 2 According to the normal distribution probability model,

[0022]

[0023] Since the interval number comparison value a′ ij is the power function of the subjective judgment level x, so its probability density function is:

[0024]

[0025] Using the probability distribution function mean a′ ij，*Construct a numerical judgment matrix, that is, find the partial derivative of the above formula Solving for this yields:

[0026]

[0027] According to the 3σ criterion (P(|x-μ|≤3σ)≈0.997), the estimated results of the mean and variance of the random variable are: L =μ-3σ,x R =μ+3σ, we get μ=(x L +x R ) / 2,σ=(x R -x L ) / 6, substitute into the above formula and simplify to get a′ ij，* An approximate estimate of the value b ij :

[0028]

[0029] And adopt the consistency ratio CR

[0030]

[0031] where λ max is the maximum eigenvalue root, n is the matrix order; RI is the average random consistency index. When CR≤0.1, it is considered that the expert judgment matrix meets the consistency requirements, otherwise the importance judgment needs to be re-performed.

[0032] Furthermore, in step 3), based on the cluster analysis method, the indicator weight vectors of each expert are compared. The difference is recorded as Δ(q k ,q l ), q k is the indicator weight vector set of the k-th expert, q l is the indicator weight vector set of the lth expert.

[0033]

[0034] When k =q l , that is, Δ(q k ,q l )=0, it indicates that the preference among experts is completely consistent, and vice versa. Using cluster analysis method, set the threshold T≤max[Δ(q k ,q l )] / 10. When Δ(q k ,q l )≤T, that is, experts k and l are classified into the same category. Expert weight ρ k Including the inter-class expert weight ρ a and the intra-class expert weight ρb .

[0035]

[0036] Where: e is the number of expert clusters, t = 1, 2, ..., e; κ t is the number of experts in the tth category.

[0037] ρ b is the expert weight within the class, which is inversely proportional to the consistency index of the judgment matrix f(CR i ), CR i is the consistency index of the i-th expert subjective judgment matrix, which is inversely proportional to the distance from the center of gravity of the class is the inter-class centroid weight vector of the x-th class, is the i-th indicator weight in the inter-class centroid weight vector set of the x-th class.

[0038]

[0039] Where: ξ, τ, θ are proportional coefficients, which are 0.5, 10, and 10 respectively. The final weight of each expert is ρ k =ρ a ×ρ b .

[0040] Furthermore, in step 4), based on the set-valued statistical theory, considering the individual judgment preferences of group decision-making experts, a judgment index shadow function Y is constructed that can reflect the differences in the judgment levels of different experts.

[0041]

[0042] Where (a′ ij ) k is the importance judgment interval of the index i and j corresponding to the kth expert, recorded as ρ k is the individual preference weight of the kth expert.

[0043] The center of gravity of the shadow is taken as the recognized judgment value c of this indicator. ij , construct the group decision judgment matrix C = (c ij ) n×n :

[0044]

[0045] Use the eigenvalue method to solve the maximum eigenvalue λ of matrix C max , then λ max The corresponding eigenvector, after normalization, is the subjective comprehensive index weight set ω s =(ω s，1 ,ω s，2 , ..., ωs，n ).

[0046] Furthermore, in step 5), the probability of the underlying evaluation indicators belonging to each risk factor is determined in combination with the evaluation opinions of various experts on the risk factors. The indicators can be divided into semantic indicators and numerical indicators according to the nature of the indicator comments.

[0047] Semantic indicators can only be described in qualitative language, but not in quantitative numerical expression. They are obtained by expert survey method. Experts select from semantic evaluation levels. The evaluation result of the kth expert on the i-th indicator is z=1,2,...,h,is 0 or 1. If the evaluation result of an indicator is more important than another indicator, it takes 1, otherwise it takes 0. Perform statistical analysis:

[0048]

[0049] The evaluation results of numerical indicators can be quantitatively tested or monitored over a long period of time based on a certain physical characteristic or response, and the evaluation results are deterministic numerical results. The evaluation results of numerical indicators can be evaluated based on the corresponding membership function for a single numerical evaluation result. Transform, R is any real number;

[0050]

[0051] Where a1 and a4 are the upper and lower limits of the fuzzy evaluation value interval of the indicator, and [a2, a3] is the most likely value range of the evaluation indicator.

[0052] Furthermore, in step 6), based on the entropy weight method, the information entropy E i Calculate the objective weight ω o，i , avoid interference from subjective factors.

[0053]

[0054] in

[0055]

[0056] Furthermore, in step 7), the influence of subjective and objective factors on the weight is fully considered, the influence of subjective and objective factors on the weight is integrated, and a subjective and objective fusion weight optimization function model based on the minimum cross entropy principle is established:

[0057]

[0058] Construct the subjective and objective weight optimization model L(γ, ω) to estimate the subjective and objective fusion weight optimization function model to obtain the subjective and objective fusion weight set ω:

[0059]

[0060] The subjective comprehensive index weight set ω s ={ω s，1 ,ω s，2 , ..., ω s，i , ..., ω s，n}, objective comprehensive weight set ω o ={ω o，1 ,ω o，2 , ..., ω o，i , ..., ω o，n}, assuming that the subjective and objective comprehensive weight is ω=(ω1,ω2,...,ω n ), r is the level number of the indicator; λ is the proportion of subjective weight distribution, which is 0.3; γ-1 is the Lagrange multiplier.

[0061] Take partial derivatives of ω and γ respectively, and obtain ω jointly:

[0062]

[0063] Furthermore, in step 8), based on fuzzy theory, the underlying index interval number judgment matrix And the underlying indicator evaluation results Solve the individual preference weight ρ of the kth expert k , the underlying indicator evaluation membership matrix D 0 And the subjective and objective fusion weight of the underlying indicators ω 0 , calculate the intermediate layer index evaluation set d i , the superscript 0 indicates the underlying indicator of the indicator,

[0064]

[0065] Where: is a fuzzy operator. The Zadeh operator is used, which is determined by the main factors, that is, M (∧, ∨) highlights the influence of the main factors and ignores other minor factors. Solving multiple indicators of the middle layer in turn, the middle layer indicator evaluation membership matrix D i =(d i 1,d i 2, ..., d i n′ ), n′ is the number of intermediate layer indicators, where i is the intermediate layer at each level. i And the intermediate index interval number judgment matrix A′ k , according to the above patent content, solve the subjective and objective fusion weight ω of the intermediate layer index i .

[0066] According to the above steps, the evaluation is carried out layer by layer from the bottom layer indicators to the target layer indicators, and finally the target indicator evaluation membership vector R is obtained:

[0067]

[0068] The scoring set G = (g1, g2...g k ), the risk estimation result F of the target layer indicator can be obtained as:

[0069] F=(g1,g2...g h )·(R1, R2...R h ) T .

[0070] The beneficial effects of the present invention are:

[0071] 1) The influence of individual preferences of different experts on indicator evaluation is taken into account. By increasing the individual weights of experts, the subjective differences caused by individual reasons of experts are mitigated.

[0072] 2) The group judgment of experts is introduced, and the shadow function in the concept of set-valued statistics is adopted to eliminate the possible deviations that may occur in the judgment process of a single expert, and finally a consistent judgment matrix that satisfies the group decision-making opinions is obtained.

[0073] 3) Introduce the entropy weight theory, determine the indicator attribute evaluation matrix between different decision makers according to the membership function, and calculate the entropy value of the indicator attribute through the entropy weight concept, thereby determining the objective weight of the attribute. Reduce the subjective interference of the data and explore the objective connection of the data.

[0074] 4) Based on the minimum cross entropy criterion, an optimization model is constructed, which fully considers the objective information of indicators and the subjective opinions of decision makers, and obtains the interactive optimal coordination indicator weights through continuous adjustment and correction.

[0075] 5) The present invention can effectively reduce the subjective interference of decision makers, improve the objective validity of data information, and provide a reliable and practical reference for the health assessment system of bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the subjective and objective comprehensive risk assessment method of bridges based on set value and entropy weight theory of the present invention;

[0077] Figure 2 It is a flow chart of the weight calculation of subjective comprehensive indexes in group decision-making of the present invention.

[0078] Figure 3 It is a risk assessment hierarchical model for a suspension bridge scheme for a cross-sea bridge. DETAILED DESCRIPTION

[0079] The present invention will be further described below in conjunction with the accompanying drawings.

[0080] like Figure 1 and Figure 2 As shown, the present invention provides a bridge risk assessment method considering subjective and objective cross-fusion weights, comprising the following steps:

[0081] 1) Bridge risk assessment First, identify dangerous situations and uncertain risks through bridge accidents and research data analysis. Through the results of bridge risk source identification, use data method, fault tree method, expert investigation method and other methods. According to different classification standards, the risk control target is used as the target layer indicator. The target layer is divided into intermediate layer indicators based on the factors affecting the risk control target. The intermediate layer indicators should be included in the target layer indicators. Then, each intermediate layer indicator is further divided according to the factors affecting the intermediate layer indicators. And so on, until the required indicator decomposition accuracy is achieved to form a bridge risk assessment indicator model. The last layer of the model is used as the bottom layer indicator. Then, based on the indicator model, expert judgment and bottom layer indicator evaluation can be carried out to conduct risk assessment research on each stage of the bridge life cycle and analyze the internal connection between each stage. According to the Weber-Fechner law, the exponential interval number judgment matrix A is established. The specific process is as follows:

[0082] According to the Weber-Fechner law:

[0083] Or S = k·logR

[0084] Establish the general formula of exponential scale of "subjective arithmetic difference and objective geometric ratio":

[0085] a ij =u x , x=0, ±1, ±2,...,±8; i, j=0,1,...,n

[0086] Where: a ij It represents the importance ratio of evaluation index i to evaluation index j; u is the importance ratio constant of the comparison index, x is the subjective arithmetic difference judgment level, and n is the number of evaluation indicators.

[0087] Use exponential interval number scale a′ ij Instead of exponential scale a ij , so that the ambiguity and uncertainty of the expert's subjective judgment are consistent, that is, the evaluation result is more scientific.

[0088]

[0089] 2) Since the calculation of interval number matrix is ​​very cumbersome, in order to improve the calculation efficiency, the probability model of exponential interval number is constructed, and the approximate numerical judgment matrix B is established to facilitate consistency test. The characteristic root method is used to calculate the subjective index weight set of each evaluation expert as follows:

[0090] The expert's subjective judgment level x can be considered to obey the normal distribution. According to the normal distribution probability model,

[0091]

[0092] Since the exponential interval number scale a′ ij is the power function of the subjective judgment level x. According to the functional relationship, we can get

[0093]

[0094] Using the probability distribution function mean a′ ij，* Construct a numerical judgment matrix, that is, find the partial derivative of the above formula Solving for this yields:

[0095]

[0096] According to the 3σ criterion (P(|x-μ|≤3σ)≈0.997), the estimated results of the mean and variance of the random variable are: L =μ-3σ,x R =μ+3σ, we get μ=(x L +x R ) / 2,σ=(x R -x L ) / 6, and then substitute into formula (4) to obtain a′ ij，* An approximate estimate of the value b ij , and are combined to form an approximate numerical judgment matrix B:

[0097]

[0098] Using the characteristic root method to calculate the approximate numerical judgment matrix B

[0099] Bω=λω

[0100] Find λ max is the eigenvector ω corresponding to the maximum eigenvalue k =(ω k1 ,ω k2 ... kn ),ω k is the individual indicator weight of the k-th expert.

[0101] The consistency ratio CR is used to test the accuracy of each expert judgment matrix.

[0102]

[0103] Where RI is the average random consistency index, which can be obtained by looking up Table 1. When CR < 0.1, it is considered that the expert judgment matrix meets the consistency requirements, otherwise the importance judgment needs to be re-performed.

[0104] Table 1 Average random consistency index RI of n-order matrices

[0105] n 2 3 4 5 6 7 8 9 RI 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45

[0106] 3) Since each expert has his own unique judgment preference, based on the cluster analysis method, the correlation degree of the subjective indicator weight set of each evaluation expert is explored and analyzed, and the individual preference weight of each expert is established, and the indicator weight vector of each expert is compared. The difference is recorded as:

[0107]

[0108] When k =q l , that is, Δ(q k ,q l )=0, it indicates that the preference among experts is completely consistent, and vice versa. Using cluster analysis method, set the threshold T≤max[Δ(q k ,q l )] / 10. When Δ(q k ,q l )≤T, that is, experts k and l are classified into the same category. Expert weight ρ k Including the inter-class expert weight ρ a and the intra-class expert weight ρ b The inter-class weight is the weight of each class formed by clustering, and the intra-class weight is the weight of the experts in each class.

[0109]

[0110] Where: e is the number of expert clusters, t = 1, 2, ..., e; κ t is the number of experts in the tth category.

[0111] ρ b is the expert weight within the class, which is inversely proportional to the consistency index of the judgment matrix f(CR i )(CR i is the consistency index of the i-th expert subjective judgment matrix), which is inversely proportional to the distance from the center of gravity of the class is the inter-class centroid weight vector of the x-th class, is the i-th indicator weight in the inter-class centroid weight vector set of the x-th class.

[0112]

[0113] Where: ξ, τ, θ are proportional coefficients, which are 0.5, 10, and 10 respectively. The final weight of each expert is ρ k =ρ a ×ρ b .

[0114] 4) Based on the set-valued statistical theory, considering the individual judgment preferences of group decision-making experts, a shadow function Y of the evaluation index is constructed to reflect the differences in the evaluation levels of different experts.

[0115]

[0116] Where (a′ ij ) k is the importance judgment interval of the index i and j corresponding to the kth expert, recorded as ρ k is the individual preference weight of the kth expert.

[0117] The center of gravity of the shadow is taken as the recognized judgment value c of this indicator. ij , construct the group decision judgment matrix C = (c ij ) n×n :

[0118]

[0119] Use the eigenvalue method to solve the maximum eigenvalue λ of matrix C max , then λ max The corresponding eigenvector, after normalization, is the subjective comprehensive index weight set ω s =(ω s，1 ,ω s，2 , ..., ω s，n ):

[0120] 5) Based on expert opinions, the probability of the underlying evaluation indicators belonging to each risk factor is clarified. The indicators can be divided into semantic indicators and numerical indicators according to the nature of the indicator comments, and the membership degrees of numerical indicators and semantic indicators are combined to form an evaluation membership matrix.

[0121] Semantic indicators can only be described in qualitative language, but not in quantitative numerical expression. They are generally obtained by expert survey method. Experts select from h semantic evaluation levels. The evaluation result of the kth expert on the i-th indicator is z=1,2,...,h, is 0 or 1. The evaluation results can be Perform statistical analysis:

[0122]

[0123] The evaluation results of numerical indicators can be quantitatively tested or monitored over a long period of time based on a certain physical characteristic or response, and the evaluation results are deterministic numerical results. Evaluation results for a single value Transform, R is any real number;

[0124]

[0125] Where a1 and a4 are the upper and lower limits of the fuzzy evaluation value interval of the indicator, and [a2, a3] is the most likely value range of the evaluation indicator.

[0126] According to the membership function, construct the evaluation index attribute matrix D

[0127]

[0128] 6) Based on the entropy weight method, using information entropy E j Calculate the objective weight ω o，i , avoid interference from subjective factors.

[0129]

[0130] in

[0131]

[0132] Fully consider the influence of subjective and objective factors on weights, integrate the influence of subjective and objective factors on weights, and establish a subjective and objective fusion weight optimization function model based on the minimum cross entropy principle:

[0133]

[0134] Construct the subjective and objective weight optimization model L(γ, ω), and estimate the subjective and objective fusion weight optimization function model through continuous adjustment and correction to obtain the subjective and objective fusion weight set ω of the indicator:

[0135]

[0136] The subjective comprehensive index weight set ω s ={ω s，1 ,ω s，2 , ..., ω s，i , ..., ω s，n}, objective comprehensive weight set ω o ={ω o，1 ,ω o，2 , ..., ω o，i , ..., ω o，n}, assuming that the subjective and objective comprehensive weight is ω=(ω1,ω2,...,ωn ), r is the level number of the indicator; λ is the proportion of subjective weight distribution, which is 0.3; γ-1 is the Lagrange multiplier.

[0137] Take partial derivatives of ω and γ respectively, and obtain ω jointly:

[0138]

[0139] 7) Based on the AHP-FCE method, combined with the subjective and objective fusion weight set of the bottom-level indicators and the evaluation membership matrix, the corresponding intermediate-level indicator evaluation membership is calculated, and the intermediate-level indicator subjective and objective fusion indicator weight set is obtained by experts through the method of steps 1) to 6), and the upper-level indicator evaluation membership is further calculated. The evaluation is carried out layer by layer, and finally the target layer indicator membership vector R is obtained. The target indicator risk estimation result F is obtained by combining the comment set. According to the calculation results, the "Guidelines for Safety Risk Assessment of Highway Bridge and Tunnel Engineering Design" is queried to obtain the comprehensive risk evaluation of the bridge. The specific process is as follows:

[0140] Based on fuzzy theory, the underlying index interval number judgment matrix And the underlying indicator evaluation results Solve the individual preference weight ρ of the kth expert k , the underlying indicator evaluation membership matrix D 0 And the subjective and objective fusion weight of the underlying indicators ω 0 , the intermediate layer indicator evaluation set d′ is calculated. The superscript 0 indicates the bottom layer indicator.

[0141]

[0142] Where: is a fuzzy operator. The Zadeh operator is used, which is determined by the main factors, that is, M (∧, ∨), which highlights the influence of the main factors and ignores other minor factors. Solving multiple indicators of the middle layer in turn, the middle layer indicator evaluation membership matrix D′=(d′1,d′2,...,d′ n′ ), n′ is the number of intermediate layer indicators. The matrix A′ is determined by D′ and the number of intermediate layer indicator intervals. k , based on the above patent content, solve the subjective and objective fusion weight ω′ of the intermediate layer indicators.

[0143] In the process of risk assessment for some complex bridges, there may be multiple intermediate layers in the hierarchical model. According to the above steps, the evaluation is carried out layer by layer from the bottom layer indicators to the target layer indicators, and the evaluation is carried out layer by layer from the bottom layer indicators to the target layer, and finally the target indicator evaluation membership vector R is obtained:

[0144]

[0145] From the comment set V = (v1, v2...v k ) The middle value of the scoring interval establishes a scoring set G = (g1, g2...g k ) For example, G = (0.1, 0.3, 0.5, 0.6, 0.9), the risk estimation result F of the target layer indicator can be obtained as:

[0146] F=(g1,g2...g h )·(R1, R2...R h ) T

[0147] 8) Application Examples

[0148] A cross-sea bridge project crosses the Pearl River Estuary. The cross-sea section is about 24 km long. A 6720-meter long tunnel is used to cross the airport branch channel and the alum stone waterway. An artificial island for tunnel-bridge conversion is set up in the middle beach. A large-span bridge solution is used to cross the Lingding Waterway and the Hengmen East Waterway. The crossing section has a wide river surface, a large project scale, and complex technology. It is a super-large bridge (tunnel) project with construction characteristics different from general cross-river projects. In order to clarify the severity of the risks faced by this super project, a detailed qualitative and quantitative risk assessment study is required for the project.

[0149] Step 1: Construct a risk assessment hierarchy model

[0150] By investigating past cases and analyzing the construction data of the project, we can obtain a corresponding risk list, screen and classify indicators based on different attributes and sources, and construct a risk list such as Figure 3 Model shown:

[0151] Step 2: Invite multiple experts to make pairwise judgments on the corresponding indicators to obtain the underlying indicator interval number judgment matrix This embodiment takes the result of the 4th order judgment matrix of the structural scheme as an example for explanation. The subsequent calculations are also mainly centered around the structural scheme risk factor set U2=(U 21 , U 22 , U 23 , U 24 ) to expand.

[0152]

[0153] Step 3: Convert the subjective judgment matrix of importance into an approximate estimated numerical judgment matrix, and calculate the importance weights and rankings of indicators by the characteristic root method. The results are shown in Table 2, and the consistency of each expert is tested by the consistency ratio CR.

[0154] Table 2 Expert individual preference index weight set and index ranking

[0155]

[0156] Step 4: According to the cluster analysis method, determine the expert individual preference weights, as shown in Table 3. The clustering threshold

[0157] Table 3 Expert individual preference weights

[0158]

[0159] Step 5: Based on the cluster analysis method, the opinions of multiple experts are integrated, and the number of evaluation intervals of m experts on the same indicator is accumulated and superimposed on the number axis using the shadow method, presenting a coverage model similar to the normal probability distribution, and the group decision judgment matrix C considering the expert weights is constructed by the centroid value method.

[0160] Group decision judgment matrix C:

[0161]

[0162] Get the subjective weight set ω s ={0.2802, 0.3695, 0.2204, 0.1298}. The trend analysis of the subjective comprehensive weight set considering the individual preferences of experts and the weight sets of each expert shows that the subjective weight set of group decision-making obeys the majority opinion, while also considering the opinions of a minority of experts, so as to achieve the purpose of weighing the opinions of each expert, effectively avoid extreme value deviation, and make the data more credible.

[0163] Step 6: Construct the dimensionless evaluation index attribute matrix D based on the concept of membership

[0164]

[0165] Step 7: According to the indicator type, evaluate the risk probability of the indicator, and calculate the structural scheme indicator set evaluation membership matrix D2 by the evaluation indicator attribute matrix D and the membership function.

[0166]

[0167] Step 8: From information entropy E i , the entropy weight method is used to calculate the objective weight set of indicators ω o =(0.237, 0.245, 0.244, 0.274).

[0168] Step 9: Based on the subjective and objective fusion weight optimization function model, the subjective and objective fusion weights of the underlying indicators of the structural scheme are obtained based on the minimum cross entropy principle. The same steps can be used to obtain the fusion weights of the construction conditions and construction technology indicator sets, respectively:

[0169] ω1=(0.146, 0.183, 0.202, 0.164, 0.071, 0.127, 0.108)

[0170] ω3=(0.135, 0.163, 0.210, 0.098, 0.165, 0.229).

[0171] Step 10: From ω2, D2 and formula (21), we can get the secondary index evaluation set of the structural scheme:

[0172] d′2=(0.1560, 0.374, 0.367, 0.093, 0.014)

[0173] The same steps can be used to obtain the secondary index evaluation set of construction conditions and construction technology.

[0174] d′1=(0.160, 0.456, 0.281, 0.064, 0.040)

[0175] d′3=(0.104, 0.391, 0.388, 0.103, 0.012)

[0176] Step 11: Combined with the expert opinions, to simplify the calculation, the weight of the intermediate layer index is taken as ω′=(0.333, 0.333, 0.333). According to the fuzzy operation method, the occurrence probability evaluation membership vector R=ω·(d′1, d′2, d′3) of the target index “U=risk during the construction period of a waterway suspension bridge” is calculated. T =(0.140, 0.407, 0.345, 0.088, 0.022)

[0177] Step 12: Take the score set G = (0.1, 0.3, 0.5, 0.7, 0.9) and calculate the risk probability score F of the suspension bridge scheme. p =0.390. The same steps can be used to obtain the risk loss rating F l =0.399.

[0178] Step 13: According to Tables 4 to 6, the risk probability level of the bridge scheme is II, the risk loss level is II, and the comprehensive risk level is II. These are acceptable risks, but corresponding emergency measures must be taken or further preventive measures must be implemented to improve safety.

[0179] Table 4 Risk probability level judgment criteria

[0180] grade Quantitative judgment criteria score Qualitative judgment criteria 1 <![CDATA[P f <0.0003]]> 0.0～0.2 Almost impossible 2 <![CDATA[0.0003≤P f <0.003]]> 0.2～0.4 Rarely occurs 3 <![CDATA[0.003≤P f <0.03]]> 0.4～0.6 Occurrence 4 <![CDATA[0.03≤P f <0.3]]> 0.6～0.8 May occur 5 <![CDATA[P f ≥0.3]]> 0.8～1.0 Frequent occurrence

[0181] Table 5 Economic loss level judgment criteria

[0182] grade score Judgment criteria 1 0.0～0.2 Economic loss less than 5 million 2 0.2～0.4 Economic losses of more than 5 million yuan but less than 10 million yuan 3 0.4～0.6 Economic losses of more than 10 million yuan but less than 50 million yuan 4 0.6～0.8 Economic losses of more than 50 million yuan but less than 100 million yuan 5 0.8～1.0 Economic losses of more than 100 million

[0183] Table 6 Risk level table

[0184]

[0185] The above embodiments are used to illustrate the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A bridge risk assessment method considering subjective and objective cross-integration weights, characterized in that: The steps include: 1) Based on the identification results of bridge risk sources, the risk control target is used as the target layer indicator, and the target layer is divided into intermediate layer indicators based on the factors affecting the risk control target. Then, each intermediate layer indicator is further divided according to the factors affecting the intermediate layer indicators, and so on, until the required indicator decomposition accuracy is achieved to form a bridge risk assessment indicator model, and the last layer of the model is used as the bottom layer indicator; the bottom layer indicators are judged by experts, and the exponential interval number judgment matrix A is established according to Weber's law; 2) Construct a probability model of the index interval number and establish an approximate numerical judgment matrix B that is convenient for consistency testing; use the characteristic root method to calculate the subjective indicator weight set of each evaluation expert; 3) Based on the cluster analysis method, the individual preference weights of each expert are established, where the individual preference weights of experts are calculated by the inter-class weights ρ after expert cluster analysis. a and the intra-class weight ρ b The inter-class weight is the weight of each class after clustering, and the intra-class weight is the weight of the experts in each class. 4) Based on the set-valued statistical theory, the shadow method is used in combination with the expert individual preference weights obtained in step 3) to perform set-valued analysis through group decision making to obtain the group decision judgment matrix C; the characteristic root method is used to calculate the group decision judgment matrix C to obtain the subjective comprehensive index weight set ω based on group decision making. s ; 5) Using the membership function to quantitatively describe the numerical indicators and obtain their membership; The semantic indicators use expert survey method to obtain their membership by statistical means; The membership of numerical indicators and the membership of semantic indicators are combined to form an evaluation membership matrix; 6) Establish an evaluation index attribute matrix D based on the index evaluation level, and use the entropy weight method to calculate the objective comprehensive weight set ω of the evaluation index attribute matrix D for group decision making o ; The attribute matrix is ​​an objective value assignment matrix that describes each indicator belonging to each evaluation level; Based on the entropy weight method, using information entropy E i Calculate the objective weight ω o,i , avoid interference from subjective factors; in 7) Based on step 4), we get the subjective comprehensive index weight set ω s and the objective comprehensive weight set ω o , and use the minimum cross entropy criterion to establish the subjective and objective weight optimization model L(γ, ω), λ is the subjective weight distribution ratio, and the underlying indicator subjective and objective fusion indicator weight set ω is obtained after solving; specifically: fully consider the influence of subjective and objective factors on the weight, integrate the influence of subjective and objective factors on the weight, and establish the subjective and objective fusion weight optimization function model based on the minimum cross entropy principle: Construct the subjective and objective weight optimization model L(γ, ω) to estimate the subjective and objective fusion weight optimization function model to obtain the subjective and objective fusion weight set ω: The subjective comprehensive index weight set ω s ={ω s，1 ,ω s，2 , ..., ω s，i , ..., ω s，n }, objective comprehensive weight set ω o ={ω o，1 ,ω o，2 , ..., ω o，i , ..., ω o，n }, assuming that the subjective and objective comprehensive weight is ω=(ω1,ω2,...,ω n ), r is the level number of the indicator; λ is the subjective weight distribution ratio, which is 0.3; γ-1 is the Lagrange multiplier; Take partial derivatives of ω and γ respectively, and obtain ω jointly: 8) Based on the AHP-FCE method, combined with the subjective and objective fusion weight set of the bottom-level indicators and the evaluation membership matrix, the corresponding intermediate-level indicator evaluation membership is calculated, and the intermediate-level indicator subjective and objective fusion indicator weight set is obtained by experts using the method of steps 1) to 7), and the upper-level indicator evaluation membership is further calculated. The evaluation is performed layer by layer, and finally the target layer indicator membership vector R is obtained. The target indicator risk estimation result F is obtained by combining the comment set, and the relevant guidelines are queried according to the calculation results to obtain the comprehensive risk evaluation of the bridge.

2. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: The identification of bridge risk sources is specifically carried out through the analysis of bridge accidents and research data on dangerous situations and the identification of uncertain risks, using data method, fault tree method and expert investigation method for identification.

3. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: In step 1), the general formula of exponential scaling of "subjective arithmetic progression and objective geometric progression" is established according to the Weber-Fechner law: a ij =u x ,x=0,±1,±2,...,±8; i, j = 0, 1, ..., n Where: a ij It represents the importance ratio of evaluation index i to evaluation index j; u is the importance ratio constant of the comparison index, x is the subjective arithmetic difference judgment level, and n is the number of evaluation indicators; Use exponential interval number scale a′ ij Instead of exponential scale a ij , making the fuzziness and uncertainty of the expert's subjective judgment consistent, that is, the evaluation results are more scientific; in, is the importance judgment interval comparing indicators i and j.

4. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 3, characterized in that: In step 2), the expert's subjective arithmetic judgment level x on the index interval between any two indicators can be considered to be subject to expectation μ and variance σ 2 According to the normal distribution probability model, Since the exponential interval number scale a′ ij is the power function of the subjective judgment level x, so its probability density function is: Using the probability distribution function mean a′ ij，* Construct a numerical judgment matrix, that is, find the partial derivative of the above formula Solving for this yields: The estimation result of the mean and variance of random variables according to the 3σ criterion, that is, x L =μ-3σ,x R =μ+3σ, we get μ=(x L +x R ) / 2,σ=(x R -x L ) / 6, substitute into the above formula and simplify to get a′ ij，* An approximate estimate of the value b ij : And adopt the consistency ratio CR where λ max is the maximum eigenvalue root, n is the matrix order; RI is the average random consistency index. When CR≤0.1, it is considered that the expert judgment matrix meets the consistency requirements, otherwise the importance judgment needs to be re-performed.

5. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: In step 3), based on cluster analysis, the indicator weight vectors of each expert are compared. The difference is recorded as Δ(q k ,q l ), q k is the indicator weight vector set of the k-th expert, q l is the indicator weight vector set of the lth expert; When k =q l , that is, Δ(q k ,q l )=0, indicating that the preference among experts is completely consistent, and vice versa; using cluster analysis method, set the threshold T≤max[Δ(q k ,q l )] / 10; when Δ(q k ,q l )≤T, that is, experts k and l are classified into the same category; expert weight ρ k Including the inter-class expert weight ρ a and the intra-class expert weight ρ b ; Where: e is the number of expert clusters, t = 1, 2, ..., e; κ t is the number of experts in the tth category; ρ b is the expert weight within the class, which is inversely proportional to the consistency index of the judgment matrix f(CR i ), CR i is the consistency index of the subjective judgment matrix of the ith expert, which is inversely proportional to the distance from the center of gravity of the category to which the ith expert belongs. q x* is the inter-class centroid weight vector of the x-th class, is the i-th indicator weight in the inter-class centroid weight vector set of the x-th class; Where: ξ, τ, θ are proportional coefficients, which are 0.5, 10, and 10 respectively; the final weight of each expert is ρ k =ρ a ×ρ b .

6. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: In step 4), based on the set-valued statistical theory, considering the individual judgment preferences of group decision-making experts, a shadow function Y of the evaluation index is constructed to reflect the differences in the evaluation levels of different experts. Where (a′ ij ) k is the importance judgment interval of the index i and j corresponding to the kth expert, recorded as ρ k is the individual preference weight of the k-th expert; Take the center of gravity of the shadow as the recognized judgment value c of the importance judgment interval ij , construct the group decision judgment matrix C = (c ij ) n×n : Use the eigenvalue method to solve the maximum eigenvalue λ of matrix C max , then λ max The corresponding eigenvector, after normalization, is the subjective comprehensive index weight set ω s =(ω s，1 ,ω s，2 , ..., ω s，n ).

7. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: In step 5), the probability of the underlying evaluation indicators belonging to each risk factor is determined by combining the evaluation opinions of various experts on the risk factors. The indicators can be divided into semantic indicators and numerical indicators according to the nature of the indicator comments; Semantic indicators can only be described in qualitative language, but not in quantitative numerical expression. They are obtained by expert survey method. Experts select from semantic evaluation levels. The evaluation result of the kth expert on the i-th indicator is It is 0 or 1. If the evaluation result of an indicator is more important than another indicator, it takes 1, otherwise it takes 0. Perform statistical analysis: Among them, ρ k is the individual preference weight of the k-th expert; The evaluation results of numerical indicators can be quantitatively tested or monitored for a long time based on a certain physical characteristic or response, and the evaluation results are deterministic numerical results; the evaluation results of numerical indicators can be evaluated based on the corresponding membership function for a single numerical evaluation result. To transform; Where a1 and a4 are the upper and lower limits of the fuzzy evaluation value interval of the indicator, and [a2, a3] is the most likely value range of the evaluation indicator.

8. A bridge risk assessment method considering subjective and objective cross-fusion weights according to claim 1, characterized in that: In step 8), based on fuzzy theory, the underlying index interval number judgment matrix And the evaluation results of the underlying indicators Solve the individual preference weight ρ of the kth expert k , the underlying indicator evaluation membership matrix D 0 And the subjective and objective fusion weight of the underlying indicators ω 0 , calculate the intermediate layer index evaluation set d i , the superscript 0 indicates the underlying indicator of the indicator, In the formula, "ο" is a fuzzy operator; Zadeh operator is used, which is determined by the main factors, that is, M (∧, ∨) highlights the influence of the main factors and ignores other minor factors; multiple indicators of the middle layer are solved in turn, and the middle layer indicator evaluation membership matrix D is obtained. i =(d i 1,d i 2, ..., d i n′ ), n′ is the number of intermediate layer indicators, where i is the intermediate layer at each level; i And the intermediate index interval number judgment matrix A′ k , solve the subjective and objective fusion weight ω of the intermediate layer indicators i ; According to the above steps, the evaluation is carried out layer by layer from the bottom layer indicators to the target layer indicators, and finally the target indicator evaluation membership vector R is obtained: The scoring set G = (g1, g2...g k ), the risk estimation result F of the target layer indicator can be obtained as: F=(g1,g2...g h )·(R1,R2...R h ) T 。

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