Bridge system failure probability assessment method based on improved comprehensive weighting method

Abstract

The present invention relates to the technical field related to bridges, and discloses a method for evaluating the failure probability of a bridge system based on an improved comprehensive weighting method. For bridge structural systems, the application of traditional system reliability theory to the structure of a bridge system will result in two extreme situations: being conservative and being safe. Since the relative importance of each bridge component in contributing to the normal operation of the system is different, it is difficult for traditional system reliability evaluation methods to obtain accurate and true evaluation results. The entropy weight method is an objective weighting method that uses the concept of entropy to determine the weight of an indicator, and reflects the importance of the indicator according to the degree of deviation between the observed values ​​of the same indicator. However, it still cannot avoid the subjectivity brought by expert scoring. To this end, this patent establishes an objective entropy weight evaluation index system, improves the decision matrix of the traditional expert scoring system, and aims to more accurately and reasonably determine the weights of the total components in the bridge system and calculate the failure probability of the bridge system.

Description

Technical Field

[0001] The present invention relates to the technical field related to bridges, and in particular to a method for evaluating the failure probability of a bridge system based on an improved comprehensive weighting method. Background Art

[0002] With the rapid development of the national economy, the transportation industry has gradually received attention from the country, and the intensity of investment and construction has been accelerated, especially in the construction of infrastructure. As an important hub in transportation, the safe and reliable operation of bridge structures in infrastructure is a prerequisite for ensuring development. To this end, during the "14th Five-Year Plan" period, the transportation authorities proposed a number of proposals and actions for bridge structures, such as "renovation of dangerous bridges" and "improvement of durability of long highway bridges." It can be seen that the safe operation of bridge structures has attracted great attention from the country. Reasonable and effective maintenance decisions during the operation period of bridges can not only ensure the normal use of bridges but also save national maintenance funds. However, accurate bridge status assessment structures can provide reliable advice for maintenance decisions.

[0003] Currently, bridge structural safety status assessments often use visual inspections and load tests. Both are deterministic methods that ignore the uncertainties inherent in bridge structures, such as material performance uncertainty, geometric dimension uncertainty, load uncertainty, and calculation model uncertainty. Furthermore, the assessment process is subject to significant subjectivity, making it difficult to obtain highly accurate and reasonable assessment results. Reliability, as an effective means of addressing randomness, is widely used in civil engineering, and theoretical research on reliability assessment methods for single bridge components or single cross-sections is relatively mature. However, bridge structures are complex structural systems composed of multiple components, and the assessment results of a single component cannot reflect the overall condition of the bridge system. The overall safety and reliability of the bridge system are both a focus of attention for maintenance units and an important basis for maintenance decision-making plans.

[0004] Traditional system reliability assessment methods are divided into series and parallel methods. The series method assumes that the failure of any component in the system will result in the failure of the bridge system; the parallel method assumes that the failure of all components in the system will result in the failure of the bridge system. For bridge structural systems, the application of traditional system reliability theory to bridge system architecture will result in two extreme situations: being conservative or safe. Due to the different relative importance of each bridge component in contributing to the normal operation of the system, traditional system reliability assessment methods are difficult to obtain accurate and true assessment results. The entropy weight method is an objective weighting method that uses the concept of entropy to determine the weight of an indicator. The degree of deviation between the observed values ​​of the same indicator reflects the importance of the indicator, but it still cannot avoid the subjectivity brought by expert scoring. To this end, this patent establishes an objective entropy weight evaluation index system and improves the decision matrix of the traditional expert scoring system, aiming to more accurately and reasonably determine the weight of each component in the bridge system and calculate the probability of failure of the bridge system.

[0005] Therefore, this patent proposes a bridge system failure probability evaluation method based on an improved comprehensive weighting method for bridge structures. Summary of the Invention

[0006] The purpose of the present invention is to provide a bridge system failure probability assessment method based on an improved comprehensive weighting method, so as to overcome the above-mentioned defects in the prior art.

[0007] The present invention is achieved through the following technical solutions.

[0008] The bridge system failure probability assessment method based on the improved comprehensive weighting method of the present invention comprises:

[0009] Step 1: Determine the failure modes and functional functions of each component in the bridge system

[0010] According to the stress characteristics of bridge components, determine the main failure mode of the components, such as the failure mode of the main beam structure is the bending failure mode or the shear failure mode, and determine the corresponding function Z i (X).

[0011] Z i (X) = F i (x1,x2,...,x n ),i=1,2,...,n (1)

[0012] Where: Z i (X) represents the performance function of the i-th component in the bridge structure system; X represents the random variable group in the performance function; F i (x1,x2,...,x n ) represents the specific expression of the function of the i-th component, x iare random variables in the functional function, such as structural resistance, load effect and other random variable parameters.

[0013] Step 2: Calculate the performance function Z of each component in the bridge system in step 1 i (X) corresponds to the reliability index β i and failure probability p fi .

[0014] According to the function function Z of the i-th component in the bridge system i (X), and the random variable x in the performance function i The probability distribution and statistical parameters of the first order moment method (FOSM) are used to calculate the reliability index β of the i-th component. i According to the relationship between reliability index and failure probability shown in formula (2), the failure probability p of the i-th component is calculated fi .

[0015] β i =Φ -1 (1-p fi ) (2)

[0016] Where, β i represents the reliability index of the i-th component, p fi represents the failure probability of the i-th component, Φ -1 Represents the inverse of the standard normal distribution function.

[0017] Step 3: Bridge system component weight determination method based on improved analytic hierarchy process

[0018] (1) Establishing a hierarchical analysis model for bridge system failure probability

[0019] One of the core issues in calculating the failure probability of a bridge system using the weighted method is to establish a hierarchical model for analyzing the problem and convert the failure probability of the bridge system p into fS As the target layer, the failure probability of bridge components p fi As the indicator layer, through the weight coefficient w i Connect the target layer and the indicator layer to each other.

[0020] (2) Based on the component lateral distribution coefficient m i Construct judgment matrix A

[0021] After establishing the hierarchical analysis model of the decision problem, the elements in the next level are compared pairwise based on the elements in the previous level, and the judgment matrix A is constructed.

[0022]

[0023] Where: a ijis an element in the judgment matrix A, which indicates the relative importance of the i-th indicator and the j-th indicator in the indicator layer to the target layer.

[0024] Combined with the characteristics of bridge system failure probability analysis, it is proposed to use the component lateral distribution coefficient m i As a calculation ij The failure of a bridge structure is closely related to the failure of its components. If the lateral distribution coefficient of component i is larger than that of component j, then component i distributes a greater proportion of the load than component j, making the bridge structure more likely to fail.

[0025] Transverse distribution coefficient m i The traditional hinged plate method is used for calculation. The judgment matrix element a proposed in this patent is ij The calculation formula is as follows:

[0026]

[0027] Where: m i and m j They represent the lateral distribution coefficients of components i and j respectively.

[0028] (3) Calculate the weight and maximum characteristic root of the index layer in the tomographic analysis model

[0029] According to formula (4), the weight value ω of each indicator in the indicator layer is calculated i , the weight value ω at this time i It is objective enough to meet the problem of bridge system failure probability analysis. According to formula (5), the maximum characteristic root λ of the judgment matrix A is calculated. max .

[0030]

[0031] (4) Consistency test of judgment matrix

[0032] In order to avoid the phenomenon of inconsistent judgment when judging the relative importance of each indicator, it is necessary to perform a consistency test on the judgment matrix A. According to formula (6) and formula (7), the consistency index CI and consistency ratio CR are calculated respectively. If CR is less than 0.1, the judgment matrix meets the consistency test.

[0033]

[0034] Among them, the random consistency index RI is as follows:

[0035]

[0036] Step 4: Determine component weights based on the multi-index improved entropy weight method

[0037] (1) Constructing the decision matrix M based on multiple indicators

[0038] According to the hierarchical analysis model proposed above, the entropy weight method decision matrix M is established to meet the problem of bridge system failure probability analysis. The vertical axis represents the various components in the bridge system, and the horizontal axis represents the two indicators of component failure probability and lateral distribution coefficient. The decision matrix is ​​set as M = (x ij ) m×n , x ij represents the i-th indicator of the j-th component, m and n represent the number of evaluation indicators and the number of components, respectively.

[0039] The entropy weighting method is an objective weighting method that uses the concept of entropy to determine the weights of indicators. The degree of deviation between observed values ​​for the same indicator reflects the importance of that indicator. The greater the deviation in the observed data for a particular indicator, the greater its impact on the evaluation system, and therefore the greater its weight. The entropy weighting method is used to determine the weights of each indicator layer in the AHP model for bridge system reliability assessment as follows.

[0040] (2) Standardized decision matrix

[0041] In order to eliminate the impact of different indicators on decision-making, the decision matrix needs to be standardized. According to the nature of the indicators, the standardized form corresponding to the larger the better indicator is selected.

[0042]

[0043] Where: v ij is x ij Normalized value.

[0044] (3) Calculate the characteristic weight p of the i-th index corresponding to the j-th component ij , satisfying 0≤p ij ≤1.

[0045]

[0046] (7) Calculate the entropy value of component j (e j )

[0047]

[0048] When p ij =0 or p ij =1, p ij ln(p ij )=0.

[0049] (8) Calculate the difference coefficient d of component No. j j

[0050] d j =1-e j ,j=1,2,...,n. (11)

[0051] (9) Calculate the entropy weight u of component j j

[0052]

[0053] Step 5: Calculation method of bridge system failure probability based on comprehensive weight

[0054] In order to more accurately and reasonably evaluate the system failure probability of a bridge system composed of multiple components, a comprehensive weight calculation method for each component in the bridge system is proposed by combining the characteristics of the analytic hierarchy process and the entropy weight method:

[0055]

[0056] Where: c j Represents the comprehensive weight of component No. j in the indicator layer.

[0057] Based on the failure probability of each component calculated by formula (2) and the comprehensive weight of the components calculated by formula (13), the calculation formula for the failure rate of the bridge system is shown in formula (14).

[0058] BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0060] The present invention will be further described below with reference to the accompanying drawings and examples.

[0061] Figure 1 It is a schematic diagram of the bridge system failure probability analysis hierarchy model;

[0062] Figure 2 It is a schematic diagram of the decision matrix M of the entropy weight method;

[0063] Figure 3 It is a schematic diagram of the superstructure system of a multi-component bridge; DETAILED DESCRIPTION

[0064] Step 1: Determine the failure modes and functional functions of each component in the bridge system

[0065] The bridge superstructure system consisting of five hinged components is selected as the analysis object, such as Figure 3 shown.

[0066] For bridge structures, the bending failure of components is the main failure mode, and the function function of the bending failure mode is Z i .

[0067] Z i =R i -S G1i -S G2i -S Qi

[0068] Where: Z i Represents the functional function of board i; R i 、S G1i 、S G2i and S Qi are random variables, representing the resistance of plate i, the effect of the first-phase dead load, the effect of the second-phase dead load, and the live load effect. The statistical parameters and distribution types of each random variable are shown below.

[0069] Statistical parameters of random variables

[0070]

[0071] Step 2: Use the first-order second moment method (FOSM) to calculate the reliability index β corresponding to the performance function of each component in the bridge system in step 1 i and failure probability p fi .

[0072]

[0073] Step 3: Improved analytic hierarchy process based on reliability theory

[0074] (1) Establish a failure probability analytic hierarchy model for the bridge system consisting of beams 1# to 5#, with the index layer being the failure probability p of beams 1# to 5#. fi , target layer bridge system failure probability p fS .

[0075] (2) Based on the component lateral distribution coefficient m i Construct the judgment matrix A.

[0076] Calculation of the transverse distribution coefficient m of the component using the hinged plate method i , calculate the element a in the judgment matrix according to formula (3) ij , and construct the judgment matrix A.

[0077]

[0078]

[0079] (3) Calculate the weight and maximum characteristic root of the index layer in the tomographic analysis model

[0080] Calculate the weight value ω of beam 1# to beam 5# according to formula (4): i , calculate the maximum characteristic root λ of the judgment matrix A according to formula (5) max , calculate the consistency index CI and consistency ratio CR according to formula (6) and formula (7) respectively.

[0081] The calculation results show that CI and CR are close to 0, indicating that the constructed judgment matrix has good consistency. The weights ω of beams 1# to 5# are determined by the improved hierarchical analysis method. i .

[0082]

[0083] Step 4: Determine component weights based on the multi-index improved entropy weight method

[0084] (1) Constructing the decision matrix M based on multiple indicators

[0085] According to the hierarchical analysis model proposed above, the entropy weight method decision matrix M is established to meet the problem of bridge system failure probability analysis. The vertical axis represents the various components in the bridge system, and the horizontal axis represents the two indicators of component failure probability and lateral distribution coefficient. The decision matrix is ​​set as M = (x ij ) 2×5 , x ij Represents the i-th index of the j-th component, i=1,2,j=1,2,...,5.

[0086]

[0087] (2) Standardized decision matrix

[0088] To eliminate the impact of different indicators on decision-making, the decision matrix needs to be standardized. According to the nature of the indicators, the component failure probability represents the probability that the component can complete its intended function within the specified time, and the component's lateral distribution coefficient represents the proportion of load distributed to the component. As the component failure probability and lateral distribution coefficient increase, the component's contribution to the failure of the entire bridge system increases. Therefore, the standardized form corresponding to the larger the better indicator is selected, and the indicator is standardized according to formula (8).

[0089] (3) According to formula (9), calculate the characteristic weight p of the i-th index corresponding to the j-th component ij .

[0090] (4) Calculate the entropy value (e) of the jth component according to formula (10) j ).

[0091] (5) Calculate the difference coefficient d of component No. j according to formula (11): j .

[0092] (6) Calculate the entropy weight u of component j according to formula (12): j .

[0093] According to the above steps, the calculation results of component weights determined based on the multi-index improved entropy weight method are as follows:

[0094]

[0095] Step 5: Calculation method of bridge system failure probability based on comprehensive weight

[0096] According to the above steps, the weights of slabs 1 to 5 were determined by combining the improved analytic hierarchy process based on reliability theory and the improved entropy weight method based on multiple indicators. The comprehensive weight c of each component of the bridge system was calculated according to formula (13): j , the calculation results are as follows.

[0097]

[0098] According to the failure probability p of each component fi and the component comprehensive weight c j , the failure rate of the bridge system is calculated according to formula (14) as shown below.

[0099]

[0100] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand and implement the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A bridge system failure probability assessment method based on an improved comprehensive weighting method, including: Step 1: Determine the failure modes and functional functions of each component in the bridge system; According to the stress characteristics of bridge components, determine the main failure mode of the components, such as the failure mode of the main beam structure is the bending failure mode or the shear failure mode, and determine the corresponding functional function : （1）， Where, Indicates the first The functional functions of each component; Represents the group of random variables in the functional function; Indicates the The specific expression of the component function, is the random variable in the functional function, such as the random variable parameters of structural resistance and load effect; Step 2: Calculate the performance function of each component in the bridge system in step 1 Corresponding reliability index and failure probability ; According to the bridge system component function , and the random variables in the functional function The probability distribution and statistical parameters of the first order moment method (FOSM) are used to calculate the Reliability index of each component According to the relationship between reliability index and failure probability shown in formula (2), calculate the Failure probability of a component : （2）， Where, Indicates the The reliability index of each component, Indicates the The failure probability of a component, Represents the inverse function of the standard normal distribution function; Step 3: Bridge system component weight determination method based on improved analytic hierarchy process; (1) Establishing a hierarchical analysis model for bridge system failure probability. One of the core issues in calculating the bridge system failure probability using the weighted method is to establish a hierarchical model for analyzing the problem and classify the bridge system failure probability as As the target layer, the failure probability of bridge components is used as the indicator layer, and the weight coefficient Connect the target layer and the indicator layer to each other; (2) Based on the lateral distribution coefficient of the component Constructing a judgment matrix After establishing the hierarchical analysis model of the decision problem, the elements of the previous layer are compared with the elements of the next layer from top to bottom, and the judgment matrix is ​​constructed. : ， Where: is the judgment matrix The elements in the index layer represent the The indicator and The relative importance of each indicator to the target layer; Combined with the characteristics of bridge system failure probability analysis, it is proposed to use the component lateral distribution coefficient As calculation The failure of the bridge structure system is closely related to the failure of its components. The lateral distribution coefficient of the component No. The lateral distribution coefficient of the No. component is large, then Component No. The load proportion distributed to the No. 1 component is greater, which is more likely to cause failure of the bridge structure system; Transverse distribution coefficient The traditional hinged plate method is used for calculation, and the judgment matrix elements are proposed The calculation formula is as follows: （3）， Where, and Respectively Component No. and Transverse distribution coefficient of component No. (3) Calculate the weight and maximum characteristic root of the index layer in the tomographic analysis model, and calculate the weight value of each index in the index layer according to formula (4) , the weight value at this time It is objective enough to analyze the failure probability of the bridge system. The judgment matrix is ​​calculated according to formula (5): The largest characteristic root of : (4)， (5)； (4) Consistency test of judgment matrix. In order to avoid the phenomenon of inconsistent judgment when judging the relative importance of each indicator, it is necessary to check the consistency of judgment matrix. Perform consistency test and calculate consistency index CI and consistency ratio CR according to formula (6) and formula (7) respectively. If Then the judgment matrix satisfies the consistency test: (6)， (7)， Among them, the random consistency index RI is as follows: ； Step 4: Determine component weights based on the multi-index improved entropy weight method; (1) Based on the multi-index construction of the decision matrix M, the entropy weight method decision matrix M that meets the bridge system failure probability analysis problem is established for the hierarchical analysis model proposed above. The vertical axis represents each component in the bridge system, and the horizontal axis represents the component failure probability and the lateral distribution coefficient. The decision matrix is ​​set as , represents the i-th indicator of the j-th component, m and n represent the number of evaluation indicators and the number of components, respectively; The entropy weight method is an objective weighting method that uses the concept of entropy to determine the weight of indicators. The degree of deviation between the observed values ​​of the same indicator reflects the importance of the indicator. The greater the deviation of the observed data of a certain indicator, the greater the role of the indicator in the evaluation system, that is, the greater the indicator weight should be. The method of using the entropy weight method to determine the weight of each indicator layer in the hierarchical analysis model of bridge system reliability assessment is as follows; (2) Standardized decision matrix. In order to eliminate the impact of different indicators on decision making, the decision matrix needs to be standardized. According to the nature of the indicators, the standardized form corresponding to the larger and better indicators is selected: (8)， Where: for Normalized value; (3) Calculate the characteristic weight of the i-th indicator corresponding to the j-th component ,satisfy : (9)， (4) Calculate the entropy value of component No. j ( ): (10)， when Or, ; (5) Calculate the difference coefficient of component No. j : (11)， (6) Calculate the entropy weight of component j : (12)； Step 5: A comprehensive weight-based calculation method for bridge system failure probability. To more accurately and reasonably evaluate the system failure probability of a bridge system composed of multiple components, a comprehensive weight calculation method for each component in the bridge system is proposed by combining the characteristics of the analytic hierarchy process and the entropy weight method: (12)； Step 5: A comprehensive weight-based calculation method for bridge system failure probability. To more accurately and reasonably evaluate the system failure probability of a bridge system composed of multiple components, a comprehensive weight calculation method for each component in the bridge system is proposed by combining the characteristics of the analytic hierarchy process and the entropy weight method: (13)， Where: Indicates the index layer The comprehensive weight of the components; The failure probability of each component calculated according to formula (2) and the comprehensive weight of the components calculated according to formula (13) are used to calculate the failure rate of the bridge system, as shown in formula (14): (14)。

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