Urban area-oriented shock resistance toughness evaluation method and system

Abstract

The invention discloses an anti-seismic toughness evaluation method and system oriented to an urban area. The method comprises the following steps: obtaining a structure vulnerability function strength median variable under each classification; obtaining a median of a structure vulnerability function intensity median value variable; constructing an empirical vulnerability function of the single target structure, and determining damage states of all single structures in the urban area under the action of a preset earthquake; obtaining toughness levels corresponding to all the monomer structures of the urban area; and respectively calculating a region toughness index based on the individual number ratio and a region toughness index based on the building area ratio, and obtaining the seismic toughness level of the urban region. According to the scheme of the invention, two indexes of different dimensions, namely the number of the building individuals and the building area, are combined, and a comprehensive regional toughness level index is formed through weighted summation, so that the overall anti-seismic toughness condition of the urban region is reflected more comprehensively and more accurately, and the evaluation result is systematic and has operability.

Description

Technical Field

[0001] This application generally relates to the fields of civil engineering and urban disaster prevention and mitigation technology. More specifically, this application relates to a method and system for assessing the seismic resilience of urban areas. Background Technology

[0002] With the continuous advancement of global urbanization, urban areas are becoming increasingly densely populated with populations, buildings, and critical infrastructure. This high concentration makes urban systems extremely vulnerable to natural disasters such as earthquakes. A strong earthquake could lead to enormous economic losses and severe social impacts. Therefore, scientifically assessing and improving the overall earthquake resistance and disaster prevention capabilities of cities has become a core issue in the field of urban safety.

[0003] Traditional earthquake resistance and disaster reduction technologies and research typically focus on the seismic performance analysis and optimization of individual building structures or specific lifeline projects. For example, existing seismic assessments evaluate the performance or predict losses for individual structural units. While this plays a significant role in improving the safety of individual structures, it is difficult to measure the overall performance of an entire urban area under disaster impacts from a macroscopic and systemic perspective.

[0004] In recent years, the concept of "resilient cities" has gained widespread acceptance, emphasizing the ability of urban systems to resist, adapt, and recover rapidly when subjected to disturbances. However, existing technologies still have significant limitations when translating this concept into quantifiable and actionable technical methods. Specifically, there is a lack of standardized models and methods for effectively assessing the comprehensive seismic resilience of building complexes at the urban scale. Existing assessment methods often struggle to integrate the massive amounts of diverse and heterogeneous building data in cities (such as the number of buildings, building area, structural type, and construction date), and also fail to establish a scientific quantitative relationship between this data and the overall resilience level of the region.

[0005] In view of this, there is an urgent need to provide a seismic resilience assessment scheme for urban areas that can systematically and quantitatively assess the seismic resilience level at the macro scale of cities. Summary of the Invention

[0006] In order to at least address one or more of the technical problems mentioned above, this application proposes a seismic toughness assessment scheme for urban areas in several aspects.

[0007] In a first aspect, this application provides a method for assessing the seismic toughness of urban areas, comprising: classifying building structures in urban areas based on structural attributes and obtaining the median value variable of structural vulnerability function intensity under each classification; determining the optimal marginal probability distribution for the median value variable of structural vulnerability function intensity and calculating the median of the median value variable of structural vulnerability function intensity based on the optimal marginal probability distribution; constructing an empirical vulnerability function for individual target structures based on the median value of structural vulnerability function intensity and determining the damage state of all individual structures in the urban area under a preset earthquake action; obtaining the toughness level corresponding to each individual structure in the urban area according to the damage state of each individual structure in the urban area; calculating a regional toughness index based on the proportion of individual structures and a regional toughness index based on the proportion of building area based on the toughness levels corresponding to each individual structure in the urban area, and performing a weighted summation of the regional toughness index based on the proportion of individual structures and the regional toughness index based on the proportion of building area to obtain the seismic toughness level of the urban area.

[0008] In some embodiments, the structural properties include the number of structural stories and the seismic fortification intensity.

[0009] In some embodiments, during the process of determining the optimal marginal probability distribution for the positional variable in the structural vulnerability function strength, the BIC value of the positional variable in the structural vulnerability function strength under multiple candidate probability distributions is calculated based on the Bayesian information criterion, and the probability distribution with the smallest BIC value is selected as the optimal marginal probability distribution.

[0010] In some embodiments, the empirical vulnerability function of a single target structure is expressed as follows: Where x is the intensity of the ground motion, Φ[·] is the standard normal distribution function, and m R β is the median of the strength of the structural vulnerability function. R This is the preset logarithmic standard deviation.

[0011] In some embodiments, determining the damage state of all individual structures in an urban area under a preset earthquake includes: determining the ground motion intensity corresponding to the preset earthquake; substituting the ground motion intensity into the empirical vulnerability function of the constructed individual target structure to calculate the failure probability of all individual structures in the urban area reaching each level of damage state under the preset earthquake; and taking the highest damage state corresponding to the failure probability being greater than the probability threshold as the damage state of the corresponding individual structure under that ground motion intensity.

[0012] In some embodiments, the following steps are performed in the process of obtaining the toughness levels of all individual structures in the urban area: based on the damage status of all individual structures in the urban area, determine the repair cost index, repair time index, and casualty index corresponding to each individual structure; assess the toughness level of each of the repair cost index, repair time index, and casualty index, and take the lowest toughness level as the toughness level corresponding to the corresponding individual structure.

[0013] In some embodiments, the seismic resilience level of an urban area is obtained by weighted summation of regional resilience indices based on the proportion of individual populations and the proportion of building area using the seismic resilience level calculation formula for urban areas. The formula for calculating the seismic resilience level of an urban area is: NR p =S1×NI p +S2×RI p Among them, NI p S1 is a regional resilience index based on the proportion of individuals, and RI is the weight corresponding to the regional resilience index based on the proportion of individuals. p S1 represents the regional resilience index based on the proportion of building area, and S2 represents the weight of the regional resilience index based on the proportion of building area.

[0014] In some embodiments, the formula for calculating the regional resilience index based on the proportion of individuals is as follows: Where p is the toughness level, N p The number of monomer structures with a toughness level of p.

[0015] In some embodiments, the formula for calculating the regional resilience index based on the building area ratio is as follows: Where p is the toughness level, A p Let p be the area of ​​a single-unit structure with a toughness level of p.

[0016] In a second aspect, this application provides a seismic toughness assessment system for urban areas, employing the seismic toughness assessment method for urban areas as described in any embodiment of the first aspect. The system includes: a data acquisition and classification module for classifying building structures in urban areas based on structural attributes and obtaining the median value variable of the structural vulnerability function strength under each classification; a vulnerability parameter calculation module for determining the optimal marginal probability distribution for the median value variable of the structural vulnerability function strength and calculating the median of the structural vulnerability function strength based on the optimal marginal probability distribution; and a single-structure assessment module for assessing the structural vulnerability function strength... The system uses the median of the degree median to construct an empirical vulnerability function for individual target structures and determines the damage state of all individual structures in the urban area under a preset earthquake. Based on the damage state of all individual structures in the urban area, it obtains the toughness level corresponding to each individual structure in the urban area. The regional toughness assessment module is used to calculate the regional toughness index based on the proportion of individual structures and the regional toughness index based on the proportion of building area, based on the toughness level corresponding to each individual structure in the urban area. The system then performs a weighted summation of the regional toughness index based on the proportion of individual structures and the regional toughness index based on the proportion of building area to obtain the seismic toughness level of the urban area.

[0017] Through the seismic resilience assessment scheme for urban areas provided above, this application's embodiments ensure the objectivity and scientific rigor of the assessment's fundamental parameters by classifying buildings and utilizing statistical methods to process a large amount of vulnerability data. Secondly, by constructing a vulnerability function for individual structures, it is possible to systematically assess the specific damage to each building in the city under earthquakes, realizing the transition from macro-level data to micro-level individual analysis. Thirdly, by combining two different dimensions of indicators—the number of individual buildings and their area—and using weighted summation to form a comprehensive regional resilience level index, this comprehensive assessment method reflects the overall seismic resilience of the urban area more comprehensively and accurately than single-dimensional indicators, making the assessment results both systematic and operable.

[0018] Furthermore, in some embodiments, a standardized empirical vulnerability function expression is used to directly link the intensity of ground motion with the failure probability of the structure, thereby achieving the quantification and standardization of damage assessment. By setting specific calculation steps and clear judgment criteria, namely determining the final damage state based on the failure probability exceeding a preset threshold, the assessment process becomes highly operable, ensuring the consistency and objectivity of the assessment results and avoiding the uncertainty caused by subjective judgment.

[0019] Furthermore, in some embodiments, a specific and multi-dimensional set of assessment criteria and decision-making rules is provided for accurately deriving the final toughness level from the damage state of a single structure. First, it possesses comprehensiveness in assessment, not simply equating toughness with physical damage, but comprehensively considering three key indicators directly impacting socio-economic development and people's livelihoods: repair costs, repair time, and personnel casualties. Second, it possesses rigor in assessment, ensuring the conservatism and reliability of the assessment conclusions by using the lowest toughness level among the three indicators as the final result. This effectively identifies structural weaknesses in any key dimension, making the toughness rating more prudent and safe.

[0020] Furthermore, in some embodiments, a clear and quantitative calculation system is provided for integrating the resilience levels of individual buildings to arrive at the final overall seismic resilience level of the urban area. Firstly, through explicit mathematical formulas, the abstract concept of regional resilience is concretized into a calculable comprehensive index, enhancing the objectivity and comparability of the assessment results. Secondly, the assessment dimensions are comprehensive; it does not consider the number or area of ​​buildings in isolation, but calculates resilience indicators based on two different dimensions—the number of individual buildings and the building area—and then weights and sums them. This method can more comprehensively and accurately reflect the overall resilience of the urban area, avoiding the one-sidedness that may result from a single indicator. Attached Figure Description

[0021] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily understood by reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of this application are illustrated by way of example and not limitation, and the same or corresponding reference numerals denote the same or corresponding parts, wherein:

[0022] Figure 1 An exemplary flowchart of the seismic toughness assessment method for urban areas according to an embodiment of this application is shown;

[0023] Figure 2 The diagram illustrates the seismic vulnerability curves of individual structures as a group of reinforced concrete structures under a seismic fortification intensity of 6 degrees (0.05g) according to some embodiments of this application.

[0024] Figure 3 The diagram illustrates the seismic vulnerability curves of individual structures as a group of reinforced concrete structures under a seismic fortification intensity of 7 degrees (0.10g) according to some embodiments of this application.

[0025] Figure 4 An exemplary structural block diagram of a seismic resilience assessment system for urban areas, according to an embodiment of this application, is shown. Detailed Implementation

[0026] The technical solutions of the embodiments of this application 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 application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] It should be understood that the terms "comprising" and "including" used in the specification and claims of this application indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0028] It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this specification and claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this specification and claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations.

[0029] Figure 1 An exemplary flowchart of a seismic resilience assessment method 100 for urban areas according to an embodiment of this application is shown.

[0030] like Figure 1 As shown, in step S110, the building structures in the urban area are classified based on structural attributes, and the median value variable of the structural vulnerability function intensity under each classification is obtained.

[0031] In the embodiments of this application, structural properties include the number of structural stories and the seismic fortification intensity.

[0032] During step S110, a systematic search of literature on reinforced concrete structures is conducted in multiple publicly available databases, forming a large original literature database. From the qualified literature selected from this database, the median strength (mR) of the vulnerability function is carefully read, either manually or using tools, to find and extract the median strength. This value represents the ground motion intensity (e.g., peak ground acceleration PGA) at which the building structure has a 50% probability of reaching or exceeding a specific damage state (e.g., minor damage, moderate damage, severe damage, or collapse). While extracting the median strength, the corresponding structural attributes must be recorded. These attributes serve as the basis for subsequent classification and are the labels for the data. Each extracted median strength data point is assigned to a corresponding category based on its corresponding structural story number label and seismic fortification intensity label. After classification, each category no longer contains a single value but rather a collection of multiple median strength values ​​from various documents. These multiple median strength values ​​collected within the same category collectively constitute a statistically significant vulnerability function median strength variable. This is no longer a fixed constant, but a random variable or dataset that reflects the inherent uncertainty and research differences in the seismic resistance of this type of structure.

[0033] Specifically, in the process of assigning each extracted intensity median data point to the corresponding category, for example, when the number of structural stories is 2 and the seismic fortification intensity is 7 degrees (0.10g), the category corresponding to the intensity median data point is (2-3 stories)-7 degrees (0.10g).

[0034] Step S110 involves extensive literature collection from multiple public databases, ensuring the breadth of data sources and enabling the final variable set to more comprehensively reflect the overall picture of existing research, rather than being limited to a few isolated cases. By extracting the median strength of the vulnerability function as a core parameter and rigorously classifying it according to the two key physical attributes of structural stories and seismic fortification intensity, the data is given a clear engineering context and physical meaning. This process combines multiple strength medians within the same category into a single random variable or dataset. It scientifically acknowledges and quantifies the inherent uncertainties caused by differences in research methods and models, allowing subsequent assessments to be based on a more realistic and reliable probability foundation, rather than relying on a potentially biased single value.

[0035] After completing step S110, in step S120, the optimal marginal probability distribution is determined for the median variable of the structural vulnerability function strength, and the median of the median variable of the structural vulnerability function strength is calculated based on the optimal marginal probability distribution.

[0036] In the embodiments of this application, in the process of determining the optimal marginal probability distribution for the positional variable in the structural vulnerability function strength, the BIC value of the positional variable in the structural vulnerability function strength under multiple candidate probability distributions is calculated based on the Bayesian information criterion, and the probability distribution with the smallest BIC value is selected as the optimal marginal probability distribution.

[0037] In some embodiments of this application, various candidate probability distributions include log-normal distribution, normal distribution, and generalized extreme value distribution.

[0038] The BIC values ​​of the median value of the vulnerability function strength under log-normal, normal, and generalized extreme value distributions are shown in Table 1.

[0039] Table 1. BIC values ​​under various candidate probability distribution conditions.

[0040] probability distribution Log-normal distribution normal distribution Generalized extreme value distribution BIC value -214 -206 -32

[0041] As can be seen from the results in Table 1, the log-normal distribution is the optimal marginal probability distribution for the positional variable in the vulnerability function strength.

[0042] After obtaining the optimal marginal probability distribution, the median of the median variable of the structural vulnerability function intensity is calculated using this distribution. The median of the median variable of the structural vulnerability function intensity ensures that the probability of the median variable being less than or equal to this median is exactly 0.5. Mathematically, this is expressed as: M(mR_median)≤0.5, where mR_median is the median of the median variable of the structural vulnerability function intensity, and M(·) is the optimal marginal probability distribution. When the optimal marginal probability distribution is a log-normal distribution, it is completely defined by two parameters: the logarithmic mean and the logarithmic standard deviation. By determining that the optimal distribution is a log-normal distribution, the fitting process already obtains the specific values ​​of these two parameters corresponding to each level of damage. Therefore, solving the log-normal distribution equation yields the median of the median variable of the structural vulnerability function intensity. This calculated median, based on the fitted ideal probability model, is more statistically supported and robust than directly calculating the median of the original data sample.

[0043] Specifically, the median of the median variable of the structural vulnerability function strength obtained from the above process is shown in Table 2:

[0044] Table 2 Median of the Structural Vulnerability Function Intensity Variable

[0045]

[0046]

[0047] In Table 2, LS1, LS2, LS3, and LS4 represent Level 1, Level 2, Level 3, and Level 4 damage states, respectively. Based on the number of structural stories, seismic fortification intensity, and the achieved damage state, the median of the structural vulnerability function intensity can be obtained. For example, in a structure with 1 story and a seismic fortification intensity of 6 degrees / no fortification, the median of the structural vulnerability function intensity is 0.06 when Level 1 damage is achieved.

[0048] In step S120, when determining the optimal probability distribution, a clear quantitative standard—the Bayesian Information Criterion (BIC value)—is adopted. By calculating and comparing the BIC values ​​of different candidate distributions and selecting the one with the minimum value, the objectivity and scientific nature of the model selection are ensured, avoiding biases caused by subjective judgment. Secondly, when calculating the final median, the original data sample is not used directly; instead, the determined optimal probability distribution function is used. This ensures that the obtained median is based on an ideal probability model that reflects the overall distribution pattern of the data. Therefore, it avoids the influence of sampling randomness and extreme values ​​that may exist in the original data, making the calculation results more statistically supported and more robust.

[0049] After completing step S120, in step S130, based on the median of the median value of the structural vulnerability function intensity, an empirical vulnerability function of the individual target structure is constructed, and the damage state of all individual structures in the urban area under the preset seismic action is determined.

[0050] In the embodiments of this application, the expression for the empirical vulnerability function of the single target structure is: Where x is the intensity of the ground motion, Φ[·] is the standard normal distribution function, and m R β is the median of the strength of the structural vulnerability function. R This is the preset logarithmic standard deviation.

[0051] In the embodiments of this application, β R The value is 0.5.

[0052] In the embodiments of this application, when determining the damage state of all individual structures in an urban area under a preset earthquake, firstly, the seismic intensity corresponding to the preset earthquake is determined. Next, the median of the seismic intensity and the median of the structural vulnerability function intensity corresponding to each damage state is substituted into the constructed empirical vulnerability function of the individual target structure to calculate the failure probability of all individual structures in the urban area reaching each damage state under the preset earthquake. Then, the highest damage state corresponding to a failure probability greater than a probability threshold is taken as the damage state of the corresponding individual structure under that seismic intensity.

[0053] In the embodiments of this application, the aforementioned preset earthquakes include fortified earthquakes and rare earthquakes.

[0054] In the embodiments of this application, the intensity of the design earthquake and rare earthquake action is determined according to the current "Code for Seismic Design of Buildings" and the seismic fortification intensity of the single structure.

[0055] In the embodiments of this application, the aforementioned probability threshold is 50%.

[0056] In the embodiments of this application, in calculating the failure probability of all individual structures in an urban area reaching various levels of damage under a preset earthquake, the median of the median value of the structural vulnerability function intensity corresponding to each level of damage is obtained based on the seismic fortification intensity corresponding to the seismic ground motion intensity, the number of structural stories corresponding to each individual structure, and the various levels of damage. Then, the median of the median value of the structural vulnerability function intensity corresponding to the seismic ground motion intensity and the various levels of damage is substituted into the empirical vulnerability function of the constructed individual target structure to obtain the failure probability of all individual structures in the urban area reaching various levels of damage under the preset earthquake.

[0057] In the embodiments of this application, after obtaining the failure probabilities of all individual structures in the urban area reaching various levels of damage under a preset seismic load, the highest damage state corresponding to the failure probability being greater than a probability threshold is determined and taken as the damage state of the corresponding individual structure under that seismic intensity. For example, if the probabilities of a certain individual structure reaching level one, level two, level three, and level four damage states under a preset seismic load are 0.98, 0.75, 0.40, and 0.15, respectively, then level two damage state is the highest damage state.

[0058] In some embodiments of this application, peak ground acceleration (PGA), which characterizes seismic intensity, is used as the abscissa, and failure probability is used as the ordinate to form a seismic vulnerability curve. Seismic vulnerability curves for reinforced concrete structures under seismic fortification intensities of 6 degrees (0.05g) and 7 degrees (0.10g) can be found in [reference needed]. Figure 2 and Figure 3 .

[0059] like Figure 2 As shown, when the seismic fortification intensity is 6 degrees (0.05g), and the PGA is 0.4g, the damage states corresponding to the failure probability greater than 0.5 include level 1 damage state, level 2 damage state, level 3 damage state, and level 4 damage state. Level 4 damage state is the highest damage state.

[0060] like Figure 3As shown, when the seismic fortification intensity is 7 degrees (0.10g), when the PGA is 0.4g, the damage states corresponding to the failure probability greater than 0.5 include first-level damage state, second-level damage state and third-level damage state, and the third-level damage state is the highest damage state.

[0061] Step S130 transforms the complex probabilistic assessment into a deterministic damage conclusion. By setting a clear probability threshold (50%), the problem of selecting a unique final state from multiple damage probabilities is solved. The source and values ​​of key parameters (such as m) are clarified. R β is determined by the median. R By using a value of 0.5, the objectivity and repeatability of the calculation process are ensured. Simultaneously, by directly linking the building's own attributes (number of stories, seismic intensity) with the seismic intensity, refined and quantitative assessments for different buildings and different earthquake scenarios are achieved, providing a solid data foundation for subsequent disaster loss analysis and emergency decision-making.

[0062] After completing step S130, in step S140, the toughness level of each individual structure in the urban area is obtained based on the damage state of each individual structure in the urban area.

[0063] In the embodiments of this application, in the process of obtaining the toughness levels corresponding to all individual structures in the urban area, firstly, based on the damage state of all individual structures in the urban area, the repair cost index, repair time index, and casualty index corresponding to each individual structure are determined. Then, the toughness level to which the repair cost index, repair time index, and casualty index belong are evaluated respectively, and the lowest toughness level is taken as the toughness level corresponding to the corresponding individual structure.

[0064] In the embodiments of this application, the formula for calculating the repair cost index is: κ=R(DS) / C T Where κ is the repair cost index, and C T R(DS) represents the construction cost of a single structure calculated according to current quotas, and R(DS) represents the repair cost of the single structure when the damage state is DS.

[0065] Specifically, Where ζ is the cost reduction factor for the repair work of structural components, and η i Let L(DS) be the repair coefficient for the i-th type of component, and L(DS) represent the economic loss when the component is in the DS damage state.

[0066] In the embodiments of this application, the formula for calculating the repair time index is: T tot =T S1 (DS)+T S2 (DS), where T S1(DS) and T S2 (DS) represents the repair time of structural and non-structural components when the structure is in the DS damage state, respectively.

[0067] In the embodiments of this application, the proportion of the number of injured and the number of dead in the total number of personnel is used as a dual evaluation index for personnel casualties, and the lower value of the two indexes is taken as the personnel casualty index.

[0068] Specifically, the formula for calculating the percentage of injured persons in the total number of people is as follows: γ H M represents the percentage of injured persons in the total number of people. H (DS) represents the number of injured persons in the structure under the DS damage state, ζ m A represents the indoor occupancy density of a building. g This refers to the total area of ​​the building.

[0069] Specifically, the formula for calculating the percentage of deaths in the total population is as follows: γ D M represents the percentage of deaths in the total population. D (DS) represents the number of deaths caused by structural damage at the DS level, ζ m A represents the indoor occupancy density of a building. g This refers to the total area of ​​the building.

[0070] Step S140 establishes a standardized process for multi-dimensional, quantitative assessment and final grading of abstract building resilience. By utilizing three indicators most directly related to socioeconomic factors and human safety—repair costs, repair time, and casualties—a comprehensive resilience evaluation system is constructed, making the assessment results more relevant to real-world situations. Clear and calculable quantitative formulas are provided for each indicator, avoiding the ambiguity of subjective assessments and ensuring the objectivity and scientific rigor of the evaluation process. It adopts the principle of taking the lowest resilience level; this conservative assessment strategy ensures that the assessment results reflect the building's weakest points, making the final resilience rating more rigorous and reliable.

[0071] After completing step S140, in step S150, based on the toughness level corresponding to each individual structure in the urban area, the regional toughness index based on the proportion of individual structures and the regional toughness index based on the proportion of building area are calculated respectively. The regional toughness index based on the proportion of individual structures and the regional toughness index based on the proportion of building area are then weighted and summed to obtain the seismic toughness level of the urban area.

[0072] In the embodiments of this application, the seismic toughness level of the urban area is obtained by weighted summation of the regional toughness index based on the proportion of individual populations and the regional toughness index based on the proportion of building area using the seismic toughness level calculation formula for urban areas. The seismic toughness level calculation formula for urban areas is: NR p =S1×NI p +S2×RI p , among which, NI p S1 is a regional resilience index based on the proportion of individuals, and RI is the weight corresponding to the regional resilience index based on the proportion of individuals. p S1 represents the regional resilience index based on the proportion of building area, and S2 represents the weight of the regional resilience index based on the proportion of building area.

[0073] Specifically, the formula for calculating the regional resilience index based on the proportion of individuals is as follows: Where p is the toughness level, N p The number of monomer structures with a toughness level of p.

[0074] Specifically, the formula for calculating the regional resilience index based on the proportion of building area is as follows: Where p is the toughness level, A p Let p be the area of ​​a single-unit structure with a toughness level of p.

[0075] In the embodiments of this application, the weight S1 corresponding to the regional resilience index based on the proportion of individual numbers and the weight S2 corresponding to the regional resilience index based on the proportion of building area are calculated by the entropy weight method.

[0076] In the embodiments of this application, in obtaining the weight S1 of the regional resilience index based on the proportion of individual numbers and the weight S2 of the regional resilience index based on the proportion of building area, the regional resilience index based on the proportion of individual numbers and the regional resilience index based on the proportion of building area are first standardized to obtain corresponding standard matrices. Then, based on the obtained standard matrices, the difference coefficients of the regional resilience index based on the proportion of individual numbers and the regional resilience index based on the proportion of building area are calculated respectively. Finally, the weights of the regional resilience index based on the proportion of individual numbers and the regional resilience index based on the proportion of building area are obtained based on the difference coefficients.

[0077] Specifically, the following calculation formulas are used in the standardization process for the regional resilience index based on the proportion of individual numbers and the regional resilience index based on the proportion of building area: Among them, V j Let X be the new value of the j-th sample of the corresponding indicator after standardization. j X represents the original value of the j-th sample of the corresponding indicator. minX is the minimum value among all samples of the corresponding indicator. max This represents the maximum value among all samples for the corresponding indicator.

[0078] Specifically, the following calculation formula is used in obtaining the standard matrix: Where, p j V is the j-th element in the standard matrix. j Let ∑V be the new value obtained after standardization for the j-th sample of the corresponding indicator. j It is the sum of the standardized values ​​of all samples under the corresponding indicator.

[0079] Specifically, the following formula is used to calculate the difference coefficient: g k =1-e k , where g k Let e ​​be the coefficient of variation for the k-th corresponding indicator. k Let the entropy value be the k-th corresponding index. p j Let be the j-th element in the standard matrix, and m be the number of elements in the standard matrix.

[0080] Specifically, the following calculation formula is used in the process of obtaining the weights of the corresponding indicators based on the difference coefficient: Among them, g k Let Σgk be the difference coefficient of the k-th corresponding indicator, and let Σgk be the sum of the difference coefficients of all indicators.

[0081] In some embodiments of this application, the regional resilience index N is based on the proportion of individuals. Ip and the regional resilience index R based on the proportion of building area Ip The difference coefficients were 1.614 and 1.565, respectively, based on the regional resilience index N based on the proportion of individuals. Ip and the regional resilience index R based on the proportion of building area Ip The weights are 0.508 and 0.492, respectively. At this point, the seismic toughness level NR of the urban area is... p =0.508×NI p +0.492×RI p According to the regional resilience index N based on the proportion of individuals... Ip and the regional resilience index R based on the proportion of building area Ip The seismic toughness levels of the urban areas are shown in Table 3:

[0082] Table 3 Seismic toughness level of urban areas

[0083] Star rating No stars One star Two stars <![CDATA[NR p ]]> 2.66％ 13.1％ 84.1％

[0084] Step S150 avoids considering only the number or area of ​​buildings in isolation, instead taking both into account simultaneously. This resolves the potential assessment bias caused by a large number of small buildings and a small number of large-scale buildings, resulting in a more balanced and realistic assessment. The entropy weighting method is explicitly used to calculate the weights of the two core indicators. This method allocates weights based on the inherent differences in the data, eliminating the subjectivity and arbitrariness of manually setting weights and ensuring the scientific and objective nature of the final weighted result.

[0085] In summary, through the seismic resilience assessment scheme for urban areas provided above, this application's embodiments ensure the objectivity and scientific rigor of the assessment's fundamental parameters by classifying buildings and utilizing statistical methods to process a large amount of vulnerability data. Secondly, by constructing a vulnerability function for individual structures, it is possible to systematically assess the specific damage to each building in the city under earthquakes, realizing the transition from macro-level data to micro-level individual analysis. Thirdly, by combining two different dimensions of indicators—the number of individual buildings and building area—and using weighted summation to form a comprehensive regional resilience level index, this comprehensive assessment method reflects the overall seismic resilience of urban areas more comprehensively and accurately than single-dimensional indicators, making the assessment results both systematic and operable.

[0086] Furthermore, in some embodiments, a standardized empirical vulnerability function expression is used to directly link the intensity of ground motion with the failure probability of the structure, thereby achieving the quantification and standardization of damage assessment. By setting specific calculation steps and clear judgment criteria, namely determining the final damage state based on the failure probability exceeding a preset threshold, the assessment process becomes highly operable, ensuring the consistency and objectivity of the assessment results and avoiding the uncertainty caused by subjective judgment.

[0087] Furthermore, in some embodiments, a specific and multi-dimensional set of assessment criteria and decision-making rules is provided for accurately deriving the final toughness level from the damage state of a single structure. First, it possesses comprehensiveness in assessment, not simply equating toughness with physical damage, but comprehensively considering three key indicators directly impacting socio-economic development and people's livelihoods: repair costs, repair time, and personnel casualties. Second, it possesses rigor in assessment, ensuring the conservatism and reliability of the assessment conclusions by using the lowest toughness level among the three indicators as the final result. This effectively identifies structural weaknesses in any key dimension, making the toughness rating more prudent and safe.

[0088] Furthermore, in some embodiments, a clear and quantitative calculation system is provided for integrating the resilience levels of individual buildings to arrive at the final overall seismic resilience level of the urban area. Firstly, through explicit mathematical formulas, the abstract concept of regional resilience is concretized into a calculable comprehensive index, enhancing the objectivity and comparability of the assessment results. Secondly, the assessment dimensions are comprehensive; it does not consider the number or area of ​​buildings in isolation, but calculates resilience indicators based on two different dimensions—the number of individual buildings and the building area—and then weights and sums them. This method can more comprehensively and accurately reflect the overall resilience of the urban area, avoiding the one-sidedness that may result from a single indicator.

[0089] This application also provides a seismic toughness assessment system for urban areas, which can be used to conduct seismic toughness assessment using the aforementioned seismic toughness assessment method 100 for urban areas, or other methods can be used for seismic toughness assessment, and this application does not limit it here.

[0090] Figure 4 An exemplary structural block diagram of a seismic resilience assessment system for urban areas, according to an embodiment of this application, is shown.

[0091] like Figure 4 As shown, the system 400 includes a data acquisition and classification module 410, a vulnerability parameter calculation module 420, a single-unit structure evaluation module 430, and a regional toughness evaluation module 440. In the embodiments of this application, the data acquisition and classification module 410, the vulnerability parameter calculation module 420, the single-unit structure evaluation module 430, and the regional toughness evaluation module 440 may be separate units or integrated into the same controller; this application does not impose any restrictions here.

[0092] Specifically, the data acquisition and classification module 410 is used to classify the building structures in urban areas based on structural attributes and obtain the median value variable of the structural vulnerability function strength under each classification.

[0093] Specifically, the vulnerability parameter calculation module 420 is used to determine the optimal marginal probability distribution for the median variable of the structural vulnerability function strength, and to calculate the median of the median variable of the structural vulnerability function strength based on the optimal marginal probability distribution.

[0094] Specifically, the single-structure assessment module 430 is used to construct an empirical vulnerability function for the single target structure based on the median of the strength median of the structural vulnerability function, determine the damage state of all single structures in the urban area under the preset earthquake action, and obtain the toughness level corresponding to each single structure in the urban area based on the damage state of all single structures in the urban area.

[0095] Specifically, the regional resilience assessment module 440 is used to calculate the regional resilience index based on the proportion of individual structures and the regional resilience index based on the proportion of building area, respectively, based on the resilience level corresponding to all individual structures in the urban area. The regional resilience index based on the proportion of individual structures and the regional resilience index based on the proportion of building area are then weighted and summed to obtain the seismic resilience level of the urban area.

[0096] When system 400 performs seismic toughness assessment using the aforementioned seismic toughness assessment method 100 for urban areas, the data acquisition and classification module 410 executes step S110, the vulnerability parameter calculation module 420 executes step S120, the individual structure assessment module 430 executes steps S130 and S140, and the regional toughness assessment module 440 executes step S150. The specific execution process can be found above and will not be repeated here.

[0097] While numerous embodiments of this application have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will arise for those skilled in the art without departing from the spirit and intent of this application. It should be understood that various alternatives to the embodiments of this application described herein may be employed in the practice of this application. The appended claims are intended to define the scope of protection of this application and therefore cover equivalents or alternatives within the scope of these claims.

Claims

1. A method for assessing the seismic toughness of urban areas, characterized in that, include: The building structures in urban areas are classified based on structural attributes, and the median value of the structural vulnerability function strength under each classification is obtained. The optimal marginal probability distribution is determined for the median variable of the structural vulnerability function strength, and the median of the median variable of the structural vulnerability function strength is calculated based on the optimal marginal probability distribution. Based on the median of the strength median of the structural vulnerability function, an empirical vulnerability function for a single target structure is constructed, and the damage state of all single structures in the urban area under a preset seismic action is determined. Based on the damage state of all individual structures in the urban area, obtain the toughness level of each individual structure in the urban area. Based on the resilience levels corresponding to all individual structures in the urban area, regional resilience indices based on the proportion of individual structures and the proportion of building area are calculated separately. The seismic resilience level of the urban area is obtained by weighted summation of the regional resilience indices based on the proportion of individual structures and the proportion of building area.

2. The seismic toughness assessment method for urban areas according to claim 1, characterized in that, The structural properties include the number of structural stories and the seismic fortification intensity.

3. The seismic toughness assessment method for urban areas according to claim 1, characterized in that, In determining the optimal marginal probability distribution for the positional variable in the structural vulnerability function strength, based on the Bayesian information criterion, the BIC value of the positional variable in the structural vulnerability function strength under multiple candidate probability distributions is calculated, and the probability distribution with the smallest BIC value is selected as the optimal marginal probability distribution.

4. The seismic toughness assessment method for urban areas according to claim 1, characterized in that, The expression for the empirical vulnerability function of a single target structure is: Where x is the intensity of the ground motion, Φ[·] is the standard normal distribution function, and m R β is the median of the strength of the structural vulnerability function. R This is the preset logarithmic standard deviation.

5. The seismic toughness assessment method for urban areas according to claim 4, characterized in that, Determining the damage state of all individual structures in the urban area under the preset seismic load includes: Determine the intensity of the ground motion corresponding to the preset earthquake; Substitute the earthquake intensity into the empirical vulnerability function of the constructed single target structure to calculate the failure probability of all single structures in the urban area reaching various levels of damage under the preset earthquake action. The highest damage state corresponding to the failure probability being greater than the probability threshold is taken as the damage state of the corresponding single structure under that earthquake intensity.

6. The seismic toughness assessment method for urban areas according to claim 1, characterized in that, In obtaining the toughness levels of all individual structures in the urban area, the following steps are performed: Based on the damage status of all individual structures in the urban area, determine the repair cost index, repair time index, and casualty index for each individual structure. The toughness levels of the repair cost, repair time, and casualty indicators were assessed separately, and the lowest toughness level was taken as the toughness level of the corresponding single structure.

7. The seismic toughness assessment method for urban areas according to claim 1, characterized in that, The seismic toughness level of urban areas is obtained by weighted summation of regional toughness indices based on the proportion of individual populations and the proportion of building area, using the formula for calculating the seismic toughness level of urban areas. The formula for calculating the seismic toughness level of urban areas is as follows: No. p =S1×NI p +S2×RI p ; Among them, NI p S1 is a regional resilience index based on the proportion of individuals, and RI is the weight corresponding to the regional resilience index based on the proportion of individuals. p S1 is a regional resilience index based on the proportion of building area, and S2 is the weight of the regional resilience index based on the proportion of building area.

8. The seismic toughness assessment method for urban areas according to claim 7, characterized in that, The formula for calculating the regional resilience index based on the proportion of individuals is as follows: Where p is the toughness level, N p The number of monomer structures with a toughness level of p.

9. The seismic toughness assessment method for urban areas according to claim 7 or 8, characterized in that, The formula for calculating the regional resilience index based on the building area ratio is as follows: Where p is the toughness level, A p Let p be the area of ​​a single-unit structure with a toughness level of p.

10. A seismic toughness assessment system for urban areas, characterized in that, The seismic toughness assessment is performed using the seismic toughness assessment method for urban areas as described in any one of claims 1-9, wherein the system comprises: The data acquisition and classification module is used to classify building structures in urban areas based on structural attributes and obtain the median value variable of structural vulnerability function strength under each classification. The vulnerability parameter calculation module is used to determine the optimal marginal probability distribution for the median variable of the structural vulnerability function strength, and to calculate the median of the median variable of the structural vulnerability function strength based on the optimal marginal probability distribution. The single-structure assessment module is used to construct the empirical vulnerability function of the single target structure based on the median of the strength median of the structural vulnerability function, determine the damage state of all single structures in the urban area under the preset earthquake action, and obtain the toughness level of each single structure in the urban area based on the damage state of each single structure in the urban area. The regional resilience assessment module is used to calculate regional resilience indices based on the proportion of individual structures and the proportion of building area, respectively, based on the resilience levels corresponding to all individual structures in the urban area. The regional resilience indices based on the proportion of individual structures and the proportion of building area are then weighted and summed to obtain the seismic resilience level of the urban area.

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