A method for calculating the toughness level of an engineering structure based on fuzzy evaluation

Abstract

The application belongs to the technical field of data processing, and provides a kind of engineering structure flexibility level calculation method based on fuzzy evaluation method, comprising: establishing the finite element model of target engineering structure, according to finite element model and historical earthquake record, nonlinear time history analysis is carried out on target engineering structure, and seismic vulnerability curve is established;According to the seismic vulnerability curve, determine a plurality of loss variables, assign each loss variable to its own triangular fuzzy number, and obtain the standardized fuzzy decision matrix after standardization processing;Based on the standardized fuzzy decision matrix, combined with importance judgment and fuzzy solution, the weight coefficient of each loss variable is determined;Based on the standardized fuzzy decision matrix and weight coefficient, combined with the approximation of ideal solution sorting algorithm, the structure flexibility level index is obtained.The scheme provided by the application can not only comprehensively integrate multidimensional loss variables, but also process the fuzziness and uncertainty of the whole evaluation process.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method for calculating the toughness level of engineering structures based on fuzzy evaluation. Background Technology

[0002] Structural toughness, as a key indicator for measuring the comprehensive performance of engineering structures throughout their entire life cycle under extreme disasters, has gradually become a research hotspot in the fields of civil engineering and disaster prevention and mitigation in recent years. The assessment of structural toughness requires comprehensive consideration of multiple interrelated loss variables. However, these loss variables exhibit significant complexity and uncertainty. On the one hand, earthquakes themselves are highly random, and the damage evolution process of structures under seismic loading and the quantitative results of loss variables are difficult to predict accurately using deterministic methods. On the other hand, the physical dimensions of different loss variables differ significantly, and the importance of each variable in toughness assessment is influenced by factors such as the engineering scenario and urban planning requirements, making it difficult to achieve objective quantification through subjective judgment or simple weighting.

[0003] In related technologies, existing methods for assessing the toughness of engineering structures are mainly divided into two categories: single-index assessment methods and multi-index comprehensive evaluation methods. Single-index assessment methods select only one representative variable as the toughness measurement standard. Although the calculation process is simple, it has obvious limitations and cannot comprehensively characterize the multidimensional characteristics of structural toughness, resulting in insufficient scientific rigor and comprehensiveness of the assessment results.

[0004] Multi-indicator comprehensive evaluation methods integrate multiple loss variables for comprehensive assessment, which can improve the rationality of the results to a certain extent. However, in terms of determining the weight of indicators, existing methods mostly adopt the analytic hierarchy process, entropy weight method, or simple subjective weighting. These methods either rely too much on expert experience, resulting in strong subjectivity, or fail to fully reflect the relative importance differences of each loss variable. They are also less adaptable to fuzzy or incomplete assessment information. In addition, existing multi-indicator methods generally suffer from complex calculation processes, insufficient comparability of indicators, and a lack of intuitive interpretation of assessment results, which limits their promotion and application in practical engineering scenarios such as urban-scale seismic planning, structural reinforcement and renovation decisions, and rapid post-earthquake assessment.

[0005] It is evident that existing methods for assessing the toughness of engineering structures suffer from technical problems such as low accuracy, poor reliability, and lack of simplicity and efficiency. Summary of the Invention

[0006] This invention provides a method for calculating the toughness level of engineering structures based on fuzzy evaluation, which addresses the shortcomings of existing engineering structure toughness assessment methods, such as low accuracy, poor reliability, and lack of simplicity and efficiency.

[0007] This invention provides a method for calculating the toughness level of engineering structures based on fuzzy evaluation, comprising: A finite element model of the target engineering structure is established. Based on the finite element model and the previously obtained historical earthquake records, a nonlinear time history analysis is performed on the target engineering structure to establish an earthquake vulnerability curve. Based on the earthquake vulnerability curve, multiple loss variables are determined, each loss variable is assigned a triangular fuzzy number, and a standardized fuzzy decision matrix is ​​obtained after standardization. Based on the standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, the weight coefficient of each loss variable is determined; Based on the standardized fuzzy decision matrix and the weight coefficients, the structural resilience level index is obtained by combining the algorithm for ranking the approximate ideal solution.

[0008] According to the engineering structure toughness level calculation method based on fuzzy evaluation method provided by the present invention, based on the finite element model and pre-obtained historical earthquake records, nonlinear time history analysis is performed on the target engineering structure to establish an earthquake vulnerability curve, including: Based on the finite element model and pre-obtained historical earthquake records, damage data of the target engineering structure are determined; Based on the damage data, the vulnerability probability of the target engineering structure under different earthquake intensities is determined, and multiple theoretical data points corresponding to earthquake intensities and vulnerability probabilities are obtained. By fitting multiple theoretical data points, an earthquake vulnerability curve is obtained.

[0009] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by the present invention, the damage data includes: the spectral acceleration value, damage state, seismic demand parameters, and seismic resistance parameters of the target engineering structure corresponding to the first natural vibration period; The formula for calculating the vulnerability probability is:

[0010] in, This indicates that the earthquake intensity is Sa ( T 1) The target engineering structure reaches a damaged state. LS The probability of fragility; D E Indicates the seismic demand parameters of the structure; C E Indicates seismic resistance parameters; This indicates that the earthquake intensity is Sa ( T 1) Seismic demand parameters of the target engineering structure D E Exceeding seismic resistance parameters C E The probability of; Sa (T 1) Represents the spectral acceleration value corresponding to the first-order natural vibration period of the target engineering structure, used to characterize earthquake intensity; λ DE Represents the earthquake demand function. λ CE Represents the seismic resistance function; β tot Φ[ ] represents the uncertainty parameter; Φ[ ] represents the cumulative distribution function of the standard normal distribution.

[0011] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by this invention, each loss variable is assigned a triangular fuzzy number, and a standardized fuzzy decision matrix is ​​obtained after standardization processing, including: The initial lower limit, initial median, and initial upper limit of each loss variable are determined respectively, and the triangular fuzzy number in matrix form corresponding to each loss variable is obtained based on the initial lower limit, initial median, and initial upper limit of each loss variable. The triangular fuzzy numbers of each loss variable are standardized to transform each value in the triangular fuzzy number into a set range, thus obtaining the standardized fuzzy decision matrix.

[0012] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by the present invention, the triangular fuzzy number of each loss variable is standardized, and each value in the triangular fuzzy number is transformed into a set value range to obtain a standardized fuzzy decision matrix, including: Determine the measured minimum value of the initial lower limit for each loss variable as the data baseline value; The ratio of the data baseline value to the initial upper limit value is used as the standardized lower limit value; The ratio of the data baseline value to the initial median is used as the standardized median; The ratio of the data baseline value to the initial lower limit value is used as the standardized upper limit value; Based on the standardized lower bound, standardized median, and standardized upper bound, the standardized fuzzy decision matrix for each loss variable is obtained.

[0013] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by the present invention, based on the standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, the weight coefficient of each loss variable is determined, including: Perform pairwise comparisons of multiple loss variables to determine the semantic description of the importance of each loss variable; Based on the pre-constructed semantic and numerical comparison relationship, the semantic description of importance is transformed into quantitative values, and a judgment matrix is ​​constructed. Based on the judgment matrix, the importance fuzzy number corresponding to each loss variable is calculated by fuzzy solution; Based on the aforementioned importance fuzzy number, the weight coefficient of each loss variable is determined.

[0014] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by the present invention, the weight coefficient of each loss variable is determined based on the importance fuzzy number, including: Determine the probability that the importance fuzzy number of each loss variable is greater than or equal to the importance fuzzy number of any other loss variable, and obtain the probability coefficient of each loss variable; Sum the probability coefficients of all loss variables to obtain the probability summation value; The ratio of the probability coefficient of each loss variable to the sum of the probabilities is used as the weight coefficient of each loss variable.

[0015] The method for calculating the toughness level of engineering structures based on fuzzy evaluation provided by the present invention obtains a structural toughness level index based on the standardized fuzzy decision matrix and the weight coefficients, combined with an algorithm for ranking approximate ideal solutions, including: Multiplying the standardized fuzzy decision matrix by the weight coefficients yields the weighted fuzzy decision matrix; Based on the algorithm for ranking the approximating ideal solutions, the fuzzy positive ideal solution and the fuzzy negative ideal solution of each element in the weighted fuzzy decision matrix are extracted; Calculate the Euclidean distances between the target engineering structure and the fuzzy positive ideal solution and the fuzzy negative ideal solution, respectively; Based on the Euclidean distance, the structural toughness level index of the target engineering structure is calculated.

[0016] According to the engineering structure toughness level calculation method based on fuzzy evaluation provided by the present invention, the structural toughness level index of the target engineering structure is calculated based on the Euclidean distance, including: Add the Euclidean distance between the target engineering structure and the fuzzy positive ideal solution to the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to obtain the distance summation value; The ratio of the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to the sum of the distances is used as the structural toughness level index of the target engineering structure.

[0017] According to the method for calculating the toughness level of engineering structures based on fuzzy evaluation method provided by the present invention, the method further includes: Based on the structural toughness level index, the seismic toughness of the target engineering structure is assessed, and the seismic toughness assessment results are obtained.

[0018] This invention provides a method for calculating the resilience level of engineering structures based on fuzzy evaluation. It constructs seismic vulnerability curves using a finite element model and nonlinear time history analysis, accurately characterizes the uncertainty of loss variables using triangular fuzzy numbers, and eliminates dimensional differences through standardization to ensure comparability of indicators. Weighting coefficients are determined based on importance judgment and fuzzy solution, balancing subjective experience and objective logic to reduce the subjective bias of traditional weighting. A ranking algorithm approximating ideal solutions outputs a quantified structural resilience level index, providing intuitive results with clear physical meaning, facilitating resilience comparisons across different structures and scenarios. The entire method is clear and highly applicable to engineering, comprehensively integrating multi-dimensional loss variables while effectively handling the fuzziness and uncertainty of the entire evaluation process. This provides scientific and reliable quantitative support for seismic design optimization, reinforcement and retrofit decisions, and post-earthquake emergency planning for engineering structures. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the method for calculating the toughness level of engineering structures based on fuzzy evaluation, as provided in an embodiment of the present invention. Figure 2 This is the seismic vulnerability curve for structure 1; Figure 3 This is the seismic vulnerability curve for structure 2; Figure 4 These are the histogram and cumulative distribution curve of the loss variable corresponding to Structure 1; Figure 5 This is a pie chart showing the percentage of the loss variables corresponding to Structure 1 across different intervals; Figure 6 This is a statistical bar chart of casualty indicators for Structure 1 under earthquake loading; Figure 7 These are the histogram and cumulative distribution curve of the loss variable corresponding to Structure 2; Figure 8 This is a pie chart showing the interval proportions of the loss variables corresponding to Structure 2; Figure 9 This is a bar chart showing the statistical indicators of casualties in Structure 2 under earthquake conditions; Figure 10 This is a diagram illustrating the relationship between semantics and numerical values. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] The following is combined Figures 1 to 10 This invention describes the detailed scheme of the method for calculating the toughness level of engineering structures based on fuzzy evaluation, provided in the embodiments of the present invention.

[0023] like Figure 1 As shown in the figure, the method for calculating the toughness level of engineering structures based on fuzzy evaluation method provided in this embodiment of the invention mainly includes the following steps: Step 110: Establish a finite element model of the target engineering structure. Based on the finite element model and the previously obtained historical earthquake records, perform nonlinear time history analysis on the target engineering structure and establish an earthquake vulnerability curve.

[0024] This embodiment establishes a refined finite element model of the target engineering structure, which can accurately simulate the geometric shape, material constitutive relationship, and component connection characteristics of the structure. Then, historical earthquake records that conform to the characteristics of the engineering site are selected as input loads to carry out nonlinear time history analysis, obtain the seismic demand and damage evolution data of the target engineering structure under earthquakes of different intensities, i.e., the damage data of the target engineering structure, and construct seismic vulnerability curves. This realizes the transformation from mechanical response analysis to probabilistic damage assessment, thus providing a core basis for the subsequent quantification of loss variables.

[0025] Step 120: Based on the seismic vulnerability curve, determine multiple loss variables, assign each loss variable its own triangular fuzzy number, and obtain the standardized fuzzy decision matrix after standardization.

[0026] In practical applications, multiple loss variables such as direct economic loss, repair time, and casualties can be extracted based on the damage data and seismic vulnerability curve of the target engineering structure. Combined with engineering specifications and statistical data, triangular fuzzy numbers are assigned to each loss variable to depict the randomness and fuzziness of the loss variables under seismic action. Subsequently, standardization processing is used to eliminate the dimensional differences between different loss variables, and finally a standardized fuzzy decision matrix is ​​formed, which can provide unified and comparable basic data for subsequent weight calculation and comprehensive evaluation.

[0027] Step 130: Based on the standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, determine the weight coefficient of each loss variable.

[0028] In this embodiment, based on a standardized fuzzy decision matrix, the importance of each loss variable is judged pairwise and fuzzy solved through expert experience or engineering requirements, and finally the weight coefficients of each loss variable are obtained. This approach takes into account the rationality of subjective experience and reduces the bias of traditional subjective weighting through fuzzy computation, thereby achieving objective quantification of the importance of loss variables.

[0029] Step 140: Based on the standardized fuzzy decision matrix and weight coefficients, and combined with the algorithm for ranking the approximate ideal solution, obtain the structural resilience level index.

[0030] It is understandable that the structural toughness level index obtained in this embodiment can intuitively reflect the seismic toughness of the target engineering structure, thereby enabling quantitative comparison and evaluation of toughness levels under different structures and scenarios.

[0031] In one embodiment, based on a finite element model and pre-obtained historical earthquake records, a nonlinear time history analysis is performed on the target engineering structure to establish an earthquake vulnerability curve, specifically including: First, based on the finite element model and previously obtained historical earthquake records, the damage data of the target engineering structure is determined.

[0032] In practical applications, a refined finite element model can be constructed based on the design drawings, material performance parameters, and geometric dimensions of the target engineering structure. This model accurately simulates the component connection methods, material constitutive relations, and structural boundary conditions, ensuring that the finite element model can truly reflect the mechanical response characteristics of the structure. Subsequently, historical earthquake records matching the ground motion parameters of the target engineering site are selected, and the earthquake acceleration time history curve is extracted as the input load. This earthquake time history curve is imported into structural analysis software, and nonlinear time history analysis is performed on the finite element model to simulate the entire process of the structure under earthquake loading, from elastic deformation to plastic damage, and finally to a specific damage state. The software calculates and outputs mechanical response data such as displacement, internal force, and strain of key structural components. Finally, the mechanical response data is analyzed and processed in conjunction with structural damage judgment criteria to identify the degree and distribution characteristics of damage to each structural component. Ultimately, the complete damage data of the target engineering structure under the corresponding earthquake loading is obtained.

[0033] In this embodiment, the damage data specifically includes: the spectral acceleration value, damage state, seismic demand parameters, and seismic resistance parameters of the target engineering structure corresponding to the first natural vibration period.

[0034] Then, based on the damage data, the vulnerability probability of the target engineering structure under different earthquake intensities is determined, and multiple theoretical data points corresponding to earthquake intensities and vulnerability probabilities are obtained.

[0035] In this embodiment, the formula for calculating the vulnerability probability is: (1) in, This indicates that the earthquake intensity is Sa ( T 1) The target engineering structure reaches a damaged state. LS The probability of fragility; D E Indicates the seismic demand parameters of the structure; C E Indicates seismic resistance parameters; This indicates that the earthquake intensity is Sa ( T 1) Seismic demand parameters of the target engineering structure D E Exceeding seismic resistance parameters C E The probability of; Sa ( T 1) Represents the spectral acceleration value corresponding to the first-order natural vibration period of the target engineering structure, used to characterize earthquake intensity; λ DE Represents the earthquake demand function. λ CE Represents the seismic resistance function; β tot Φ[ ] represents the uncertainty parameter; Φ[ ] represents the cumulative distribution function of the standard normal distribution.

[0036] Finally, multiple theoretical data points are fitted to obtain the seismic vulnerability curve.

[0037] In practical applications, seismic vulnerability curves can be constructed, with spectral acceleration (characterizing earthquake intensity) as the independent variable and the probability of the target engineering structure reaching various damage states as the dependent variable. For example, for two reinforced concrete structures, namely Structure 1 and Structure 2, finite element models of the two structures can be established, the required historical earthquake records can be selected, and nonlinear time history analysis of the structures can be performed to obtain damage data. The resulting seismic vulnerability curves for Structure 1 and Structure 2 are shown below. Figure 2 and Figure 3 As shown.

[0038] Figure 2 and Figure 3 middle LS 1. LS 2. LS 3. LS4 represents four extreme damage states: minor damage, moderate damage, severe damage, and collapse. The corresponding regions represent the probability distribution range of each damage state. As can be seen from the curve distribution characteristics, the probability of the structure experiencing each level of damage gradually increases with the increase of earthquake intensity. Under the same earthquake intensity, there are significant differences in the probability distribution of each damage state between structure 1 and structure 2. The overall damage resistance and earthquake robustness of the structure can be intuitively reflected by the shape, regional distribution, and probability change trend of the vulnerability curve.

[0039] This set of seismic vulnerability curves can quantitatively reflect the evolution of damage probability of different structures under earthquakes of various levels, providing direct data support and probabilistic basis for subsequent extraction of loss variables such as economic losses, repair time, and casualties.

[0040] In one embodiment, a triangular fuzzy number is assigned to each loss variable, and a standardized fuzzy decision matrix is ​​obtained through standardization, specifically including: First, determine the initial lower bound, initial median, and initial upper bound for each loss variable. Then, based on the initial lower bound, initial median, and initial upper bound for each loss variable, obtain the triangular fuzzy number in matrix form for each loss variable.

[0041] In this embodiment, the triangular fuzzy number can be a Fuzzy triangular fuzzy number, specifically represented as follows: (2) in, For the first M The first target engineering structure N The triangular fuzzy number of the loss variable. M The number of target engineering structures to be evaluated. N The number of loss variables; l , m and u These represent the 16th percentile, 50th percentile, and 84th percentile, respectively.

[0042] Taking direct economic loss, repair time, and casualties as examples, for the two reinforced concrete structures mentioned above, for structure 1, the 16th, 50th, and 84th percentile values ​​of the three loss variables are as follows: Figure 4 , Figure 5 and Figure 6 As shown; for structure 2, the 16th, 50th, and 84th percentiles of the three loss variables are respectively as follows: Figure 7 , Figure 8 and Figure 9 As shown.

[0043] in, Figure 4The histogram and cumulative distribution curve of the loss variables corresponding to Structure 1 are shown. The horizontal axis represents the loss value of the structure under seismic action, the left vertical axis represents the statistical frequency of the corresponding loss interval, and the right vertical axis represents the cumulative distribution probability of the loss value. The bar chart reflects the sample distribution frequency of each loss interval. Figure 4 The curve in the middle is the cumulative distribution function curve of the loss data. Figure 4 The 5.5×10 marked in the middle 5 1.9×10 6 3.7×10 6 The quantile values ​​corresponding to the cumulative probabilities of 16%, 50%, and 84% are used as the basis for determining the lower limit, median, and upper limit of the triangular fuzzy number of the loss variable, respectively. By using the statistical frequency distribution and cumulative probability characteristics, the discrete interval and central trend of the loss variable can be quantitatively determined. This provides a statistically consistent original numerical basis for the subsequent construction of the triangular fuzzy number, standardization processing, and fuzzy comprehensive evaluation, ensuring the objectivity and rationality of the fuzzification processing of the loss variable.

[0044] Figure 5 This shows a pie chart illustrating the interval proportions of the loss variables corresponding to Structure 1. Figure 5 The data is divided into four loss value intervals: [0,10], (10,60], (60,100], and (100,+∞) using different fill patterns. The proportions of each interval are 21.06%, 20%, 3.33%, and 55.61%, respectively, visually demonstrating the distribution characteristics of structural loss values ​​in different intervals under seismic action. Meanwhile... Figure 5 The 16th, 50th, and 84th percentile values ​​of the loss data are labeled as 14.2, 122.6, and 146.6, respectively. These three percentile values ​​are used as the lower limit, median, and upper limit of the triangular fuzzy number corresponding to the loss variable, respectively.

[0045] It can be seen that by combining statistical distribution proportions with probability quantiles, the fuzzy range and core feature values ​​of the loss variable can be scientifically determined, providing real and reliable statistical data support for the subsequent construction of triangular fuzzy numbers, standardization processing, and fuzzy comprehensive evaluation, and ensuring the rationality and accuracy of loss variable quantification and fuzzification processing.

[0046] Figure 6The chart shows the statistical histogram of casualty indicators for Structure 1 under seismic loading. The vertical axis uses a logarithmic scale to represent the casualty values, while the horizontal axis is marked with the three cumulative probability quantiles of 16%, 50%, and 84%. The corresponding bar heights represent the quantitative results of casualties at each quantile. These quantile values ​​serve as the lower, median, and upper limits of the triangular fuzzy numbers corresponding to loss variables such as casualties. The logarithmic scale clearly presents the order-of-magnitude differences and discrete characteristics of casualties at different probability levels, intuitively reflecting the probability distribution law of casualty indicators in earthquake risk. This provides a quantitative basis for constructing triangular fuzzy numbers related to casualties and conducting fuzzy comprehensive assessments that integrate multiple loss variables, ensuring the statistical rationality and engineering authenticity of the personnel safety dimension indicators in resilience evaluation.

[0047] Figure 7 , Figure 8 and Figure 9 Aside from the numerical differences, the meanings expressed in the content shown are the same as... Figure 4 , Figure 5 and Figure 6 They are basically the same, so I won't go into too much detail here.

[0048] Then, the triangular fuzzy numbers of each loss variable are standardized to transform each value in the triangular fuzzy numbers into a set range of values, thus obtaining the standardized fuzzy decision matrix.

[0049] In one specific implementation, the triangular fuzzy number of each loss variable is standardized, transforming each value in the triangular fuzzy number to a predetermined range to obtain a standardized fuzzy decision matrix. This process specifically includes: The first step is to determine the measured minimum value of the initial lower limit for each loss variable, which will serve as the data baseline.

[0050] The second step is to use the ratio of the data baseline value to the initial upper limit value as the standardization lower limit value.

[0051] The third step is to use the ratio of the baseline value to the initial median as the standardized median.

[0052] The fourth step is to use the ratio of the data baseline value to the initial lower limit value as the standardized upper limit value.

[0053] The fifth step is to obtain the standardized fuzzy decision matrix for each loss variable based on the standardized lower limit, standardized median, and standardized upper limit.

[0054] In this embodiment, through standardization, the values ​​in the triangular fuzzy numbers can be made to fall within the interval [0,1]. The standardized fuzzy decision matrix can be represented as: (3) in, For the first M The first target engineering structure N The standardized fuzzy decision matrix of the loss variables. For all target engineering structures, the first N The measured minimum value of the initial lower bound of the loss variable. , This is the initial lower limit value. The initial median, This is the initial upper limit value.

[0055] In one embodiment, based on a standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, the weight coefficient of each loss variable is determined, specifically including: First, pairwise comparisons are performed on multiple loss variables to determine the semantic description of the importance of each loss variable.

[0056] Then, based on the pre-constructed semantic-numerical comparison relationship, the semantic description of importance is transformed into quantitative values, and a judgment matrix is ​​constructed.

[0057] In this embodiment, taking direct economic loss, repair time, and casualties as three loss variables as examples, the importance of the three loss variables can be ranked by comparing them pairwise, thereby obtaining the semantic description of importance.

[0058] In practical applications, the semantic and numerical correspondence can be found in [reference needed]. Figure 10 ,like Figure 10 As shown, the semantic-numerical correspondence can include five core semantic variables: equally important, relatively important, important, very important, and absolutely important, as well as three transitional semantic variables between the core semantic variables, totaling eight semantic levels. Each semantic level corresponds to a unique set of triangular fuzzy numbers consisting of a lower limit, a median, and an upper limit, forming a one-to-one correspondence between semantic descriptions and triangular fuzzy numbers. Specifically, the triangular fuzzy number corresponding to equally important semantic variables is (1,1,1); the triangular fuzzy number corresponding to relatively important semantic variables is (1,3,5); the triangular fuzzy number corresponding to important semantic variables is (3,5,7); the triangular fuzzy number corresponding to very important semantic variables is (5,7,9); the triangular fuzzy number for absolutely important semantic variables can be completed by combining the logic of transitional semantic variables. The transitional semantic variables and their corresponding triangular fuzzy numbers are as follows: The triangular fuzzy number for semantic variables between relatively important and important is (2,4,6); the triangular fuzzy number for semantic variables between important and very important is (4,6,8); and the triangular fuzzy number for semantic variables between very important and absolutely important is (6,8,9).

[0059] at the same time, Figure 10 The numerical axis can be used to help illustrate the value range of each triangular fuzzy number, thereby further clarifying the quantification boundaries of different semantic levels. This ensures that when making pairwise importance judgments on the three loss variables of direct economic loss, repair time, and casualties, qualitative descriptions such as repair time being more important than economic loss can be accurately transformed into standardized triangular fuzzy numbers. This provides a unified numerical input standard for subsequent construction of judgment matrices, calculation of probability coefficients and weight coefficients, effectively reducing the fuzziness and randomness of subjective judgments and improving the standardization and reliability of weight calculations.

[0060] Furthermore, based on the semantic-numerical comparison relationship and fuzzy summation and fuzzy inversion algorithms, weight coefficients can be calculated for the loss variables. The judgment matrix can be represented as: (4) (5) (6) in, for N The judgment matrix of order fuzzy complementarity. K and N Subscript number K ≤ N The elements on the main diagonal of the judgment matrix are all triangular fuzzy numbers (1,1,1), indicating that a certain loss variable is judged to be equally important when compared with itself in terms of importance; any off-diagonal element in the judgment matrix... Indicates the first K The loss variable relative to the first N The importance of each loss variable is represented using triangular fuzzy numbers. These represent the lower limit, median, and upper limit of the triangular fuzzy number, respectively. To satisfy the consistency and reciprocity requirements of the judgment matrix, the elements in the judgment matrix satisfy the reciprocity operation rule. N Line number K Column elements For the first K Line number N Column elements The reciprocal of.

[0061] This embodiment constructs inverse triangular fuzzy numbers by taking the reciprocals of the lower limit, median, and upper limit of the original triangular fuzzy number and rearranging them. This ensures the completeness and consistency of the judgment matrix in a mathematical sense, providing a standardized and unified matrix foundation for subsequent fuzzy summation, probability coefficient calculation, and weight coefficient solution.

[0062] For example, assuming that repair time is more important than direct economic loss, repair time is more important than casualties, and direct economic loss is equally important as casualties, based on the semantic and numerical comparison, weighting coefficients are calculated for the loss variables, resulting in the following judgment matrix: (7) Furthermore, based on the fuzzy summation and fuzzy inversion algorithm, the weight coefficients of the three loss variables are obtained as [economic loss, repair time, casualties] = [0.21, 0.58, 0.21].

[0063] Next, based on the judgment matrix, the importance fuzzy number corresponding to each loss variable is calculated through fuzzy solution.

[0064] Based on the judgment matrix and fuzzy operations, the importance fuzzy number can be represented as follows: (8) Among them, S N No. N The importance fuzzy number corresponding to the loss variable, This indicates the judgment matrix for the first... N All triangular fuzzy number elements of the column along K Perform fuzzy summation on the direction. This represents fuzzy multiplication operations. This indicates a global double fuzzy summation operation on all elements in the judgment matrix.

[0065] Finally, based on the importance fuzzy number, the weight coefficient of each loss variable is determined.

[0066] In a specific implementation, the weight coefficient of each loss variable is determined based on the importance fuzzy number, specifically including: The first step is to determine the probability that the importance fuzzy number of each loss variable is greater than or equal to the importance fuzzy number of any other loss variable, and to obtain the probability coefficient of each loss variable.

[0067] In this embodiment, the probability coefficient can be expressed as follows: (9) in, Indicates the first N Importance of loss variables fuzzy numbers S N Greater than or equal to the K Importance of loss variables fuzzy numbers S K The probability coefficient, with a value range of [0,1]; , , These are the fuzzy numbers of importance. S K The lower limit, median, and upper limit values, , , These are the fuzzy numbers of importance. S N The lower limit, median, and upper limit.

[0068] The second step is to sum the probability coefficients of all loss variables to obtain the probability sum value.

[0069] The third step is to use the ratio of the probability coefficient of each loss variable to the sum of its probabilities as the weight coefficient of each loss variable.

[0070] In this embodiment, the first K Taking the weighting coefficients of a loss variable as an example, it can be represented as follows: (10) in, For the first K The weighting coefficients of the loss variable, No. K The probability coefficient of a loss variable can be obtained by comprehensively calculating all probability coefficients related to that loss variable. This represents the sum of the probability values ​​of all loss variables, i.e., the sum of probability values.

[0071] In one embodiment, a structural resilience level index is obtained based on a standardized fuzzy decision matrix and weight coefficients, combined with an algorithm for ranking the approximate ideal solution. Specifically, this includes: First, the standardized fuzzy decision matrix is ​​multiplied by the weight coefficients to obtain the weighted fuzzy decision matrix.

[0072] In this embodiment, each variable in the weighted fuzzy decision matrix can be represented as follows: (11) in, For the weighted processing of the first M The first target engineering structure N The weighted fuzzy decision value corresponding to each loss variable. For the first M The first target engineering structure N The triangular fuzzy number of the loss variable after standardization. For the first N The weighting coefficients of the loss variables.

[0073] Then, based on the algorithm for ranking the approximating ideal solutions, the fuzzy positive ideal solution and the fuzzy negative ideal solution of each element in the weighted fuzzy decision matrix are extracted.

[0074] In this embodiment, based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), the fuzzy positive ideal solution and fuzzy negative ideal solution for each element can be determined, which can be specifically represented as follows: (12) (13) in, It is a fuzzy positive ideal solution, specifically composed of the positive ideal fuzzy numbers of each element; For the first N The positive ideal fuzzy number corresponding to the loss variable is specifically represented in the form of triangular fuzzy number. It can be constructed by taking the extreme values ​​of the components of the weighted fuzzy value of the target engineering structure under the loss variable. When calculating the positive ideal fuzzy number, each component needs to take the maximum value of the lower limit, median and upper limit of all triangular fuzzy numbers. For fuzzy negative ideal solutions, For the first N The negative ideal fuzzy number corresponding to the loss variable is calculated by taking the minimum value of the lower limit, median and upper limit of all triangular fuzzy numbers for each component.

[0075] It is understandable that by clearly defining the two types of reference benchmarks, namely the optimal and the worst, this embodiment can provide a core evaluation reference for subsequently calculating the fuzzy distance between each target engineering structure and the ideal solution, and thus solving the structural toughness level index.

[0076] For example, the fuzzy positive ideal solution and fuzzy negative ideal solution for the three loss variables—direct economic loss, repair time, and casualties—are shown in Table 1 below.

[0077] Table 1. Fuzzy positive ideal solutions and fuzzy negative ideal solutions for the three loss variables.

[0078] Next, the Euclidean distances between the target engineering structure and the fuzzy positive ideal solution and the fuzzy negative ideal solution are calculated respectively.

[0079] In practical applications, after determining the fuzzy positive ideal solution and the fuzzy negative ideal solution, the Euclidean distance between the weighted fuzzy decision matrix of the target engineering structure and the fuzzy positive ideal solution and the fuzzy negative ideal solution can be calculated. For the three components of the triangular fuzzy number—lower limit, median, and upper limit—the sum of squares of the differences between the corresponding components is calculated, and then the square root of the sum of squares is taken. Finally, the Euclidean distance between the target engineering structure and the fuzzy positive ideal solution and the fuzzy negative ideal solution can be obtained. This Euclidean distance can quantitatively reflect the degree of closeness between the comprehensive toughness state of the structure and the optimal reference state and the worst reference state, thus providing a key quantitative basis for the subsequent calculation of the structural toughness level index.

[0080] Finally, based on the Euclidean distance, the structural toughness index of the target engineering structure is calculated.

[0081] In a specific implementation, the structural toughness index of the target engineering structure is calculated based on the Euclidean distance, specifically including: The first step is to add the Euclidean distance between the target engineering structure and the fuzzy positive ideal solution and the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to obtain the sum of distances.

[0082] The second step is to use the ratio of the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to the sum of the distances as the structural toughness index of the target engineering structure.

[0083] In this embodiment, the structural toughness level index can be expressed as follows: (14) in, For the first M The structural toughness level index of the target engineering structure. For the first M The Euclidean distance between the target engineering structure and the fuzzy negative ideal solution. For the first M The Euclidean distance between each target engineering structure and the fuzzy positive ideal solution is given in this embodiment, where the sum of the structural toughness level indices of all target engineering structures is 1.

[0084] Understandably, the higher the structural toughness level index, the closer the structure is to its optimal toughness state and the further it is from its worst toughness state, indicating better overall seismic toughness performance. This embodiment uses the above formula to achieve quantitative calculation, intuitive comparison, and scientific ranking of the toughness levels of different engineering structures.

[0085] In practical applications, the Euclidean distance between the fuzzy positive ideal solution and the fuzzy negative ideal solution can be calculated and the proximity coefficient can be obtained. This proximity coefficient is the structural toughness level index. Taking the two reinforced concrete structures mentioned above as examples, the structural toughness level indices of structure 1 and structure 2 are 0.4 and 0.6, respectively.

[0086] In one embodiment, the above-mentioned method for calculating the toughness level of engineering structures based on fuzzy evaluation may further include: Based on the structural toughness level index, the seismic toughness of the target engineering structure is assessed, and the seismic toughness assessment results are obtained.

[0087] In practical applications, after calculating the structural toughness level index of the target engineering structure using the algorithm for approximating ideal solutions, this index serves as the core quantitative basis. Combined with preset toughness level classification standards, industry standard thresholds, and engineering application requirements, the numerical value of the structural toughness level index is analyzed and judged. The relative proximity of the target engineering structure to the fuzzy positive and fuzzy negative ideal solutions is analyzed to clarify its seismic toughness, performance shortcomings, and key risks. Simultaneously, the structural toughness level index of the target engineering structure can be compared horizontally with similar structures, design benchmark structures, or regional average levels to comprehensively assess its resistance capacity, damage control level, and functional recovery performance under seismic loading. Ultimately, a complete seismic toughness assessment result is formed, including toughness level, performance evaluation, weak points, and optimization suggestions. This provides scientific and reliable quantitative support for structural seismic strengthening, optimized design, operation and maintenance management, and post-earthquake emergency decision-making.

[0088] In summary, the embodiments of the present invention, compared with existing solutions, have at least the following beneficial effects: First, it has a strong ability to handle uncertainty. By introducing fuzzy triangular fuzzy numbers to describe loss variables, it effectively characterizes the objective uncertainty and fuzziness in the earthquake loss assessment process, and improves the rationality and stability of the resilience assessment results.

[0089] Second, the weight determination is more reasonable. The weight calculation method based on fuzzy judgment is adopted, which fully considers the relative importance of different loss variables in resilience assessment and reduces the sensitivity of traditional deterministic weighting methods to subjective judgment.

[0090] Third, the evaluation results are intuitive and comparable. The structural toughness index obtained based on TOPSIS has a clear physical meaning and numerical range, which facilitates the comparative analysis of toughness levels of different engineering structures or different earthquake scenarios.

[0091] Fourth, it has strong engineering applicability. The calculation process of the method of this invention is clear and can be combined with existing structural analysis software and earthquake loss assessment methods. It is applicable to the seismic toughness assessment of single structures and regional-scale engineering structures, and can provide scientific reference for urban managers to formulate structural reinforcement and renovation plans and carry out post-earthquake assessment work.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the toughness level of engineering structures based on fuzzy evaluation, characterized in that, include: A finite element model of the target engineering structure is established. Based on the finite element model and the previously obtained historical earthquake records, a nonlinear time history analysis is performed on the target engineering structure to establish an earthquake vulnerability curve. Based on the earthquake vulnerability curve, multiple loss variables are determined, each loss variable is assigned a triangular fuzzy number, and a standardized fuzzy decision matrix is ​​obtained after standardization. Based on the standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, the weight coefficient of each loss variable is determined; Based on the standardized fuzzy decision matrix and the weight coefficients, the structural resilience level index is obtained by combining the algorithm for ranking the approximate ideal solution.

2. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 1, characterized in that, Based on the aforementioned finite element model and pre-obtained historical earthquake records, a nonlinear time history analysis is performed on the target engineering structure to establish an earthquake vulnerability curve, including: Based on the finite element model and pre-obtained historical earthquake records, damage data of the target engineering structure are determined; Based on the damage data, the vulnerability probability of the target engineering structure under different earthquake intensities is determined, and multiple theoretical data points corresponding to earthquake intensities and vulnerability probabilities are obtained. By fitting multiple theoretical data points, an earthquake vulnerability curve is obtained.

3. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 2, characterized in that, The damage data includes: the spectral acceleration value, damage state, seismic demand parameters, and seismic resistance parameters of the target engineering structure corresponding to the first natural vibration period; The formula for calculating the vulnerability probability is: in, This indicates that the earthquake intensity is Sa ( T 1) The target engineering structure reaches a damaged state. LS The probability of fragility; D E Indicates the seismic demand parameters of the structure; C E Indicates seismic resistance parameters; This indicates that the earthquake intensity is Sa ( T 1) Seismic demand parameters of the target engineering structure D E Exceeding seismic resistance parameters C E The probability of; Sa ( T 1) Represents the spectral acceleration value corresponding to the first-order natural vibration period of the target engineering structure, used to characterize earthquake intensity; λ DE Represents the earthquake demand function. λ CE Represents the seismic resistance function; β tot Φ[ ] represents the uncertainty parameter; Φ[ ] represents the cumulative distribution function of the standard normal distribution.

4. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 1, characterized in that, Each loss variable is assigned a triangular fuzzy number, and after standardization, a standardized fuzzy decision matrix is ​​obtained, including: The initial lower limit, initial median, and initial upper limit of each loss variable are determined respectively, and the triangular fuzzy number in matrix form corresponding to each loss variable is obtained based on the initial lower limit, initial median, and initial upper limit of each loss variable. The triangular fuzzy numbers of each loss variable are standardized to transform each value in the triangular fuzzy number into a set range, thus obtaining the standardized fuzzy decision matrix.

5. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 4, characterized in that, The triangular fuzzy numbers of each loss variable are standardized, transforming each value within a predetermined range to obtain the standardized fuzzy decision matrix, which includes: Determine the measured minimum value of the initial lower limit for each loss variable as the data baseline value; The ratio of the data baseline value to the initial upper limit value is used as the standardized lower limit value; The ratio of the data baseline value to the initial median is used as the standardized median; The ratio of the data baseline value to the initial lower limit value is used as the standardized upper limit value; Based on the standardized lower bound, standardized median, and standardized upper bound, the standardized fuzzy decision matrix for each loss variable is obtained.

6. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 1, characterized in that, Based on the standardized fuzzy decision matrix, and combining importance judgment and fuzzy solution, the weight coefficients of each loss variable are determined, including: Perform pairwise comparisons of multiple loss variables to determine the semantic description of the importance of each loss variable; Based on the pre-constructed semantic and numerical comparison relationship, the semantic description of importance is transformed into quantitative values, and a judgment matrix is ​​constructed. Based on the judgment matrix, the importance fuzzy number corresponding to each loss variable is calculated by fuzzy solution; Based on the aforementioned importance fuzzy number, the weight coefficient of each loss variable is determined.

7. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 6, characterized in that, Based on the aforementioned importance fuzzy number, determine the weight coefficient for each loss variable, including: Determine the probability that the importance fuzzy number of each loss variable is greater than or equal to the importance fuzzy number of any other loss variable, and obtain the probability coefficient of each loss variable; Sum the probability coefficients of all loss variables to obtain the probability summation value; The ratio of the probability coefficient of each loss variable to the sum of the probabilities is used as the weight coefficient of each loss variable.

8. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 1, characterized in that, Based on the standardized fuzzy decision matrix and the weight coefficients, and combined with the algorithm for ranking the approximate ideal solution, the structural resilience level index is obtained, including: Multiplying the standardized fuzzy decision matrix by the weight coefficients yields the weighted fuzzy decision matrix; Based on the algorithm for ranking the approximating ideal solutions, the fuzzy positive ideal solution and the fuzzy negative ideal solution of each element in the weighted fuzzy decision matrix are extracted; Calculate the Euclidean distances between the target engineering structure and the fuzzy positive ideal solution and the fuzzy negative ideal solution, respectively; Based on the Euclidean distance, the structural toughness level index of the target engineering structure is calculated.

9. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 8, characterized in that, Based on the Euclidean distance, the structural toughness index of the target engineering structure is calculated, including: Add the Euclidean distance between the target engineering structure and the fuzzy positive ideal solution to the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to obtain the distance summation value; The ratio of the Euclidean distance between the target engineering structure and the fuzzy negative ideal solution to the sum of the distances is used as the structural toughness level index of the target engineering structure.

10. The method for calculating the toughness level of engineering structures based on fuzzy evaluation method according to claim 1, characterized in that, The method further includes: Based on the structural toughness level index, the seismic toughness of the target engineering structure is assessed, and the seismic toughness assessment results are obtained.

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