A method for seismic vulnerability analysis of urban building complexes based on Poisson binomial distribution

Abstract

The present invention discloses a method for analyzing the seismic vulnerability of urban building complexes based on Poisson binomial distribution, comprising the following steps: obtaining the property parameters of the building complex in the target city and establishing a numerical model of each building; determining the site characteristics of the target city and obtaining earthquake motion records that meet the site characteristics; using a probabilistic machine learning model to predict the unsafe probability of each building in the target city under the earthquake scenario; based on the Poisson binomial distribution, deriving the functional failure probability of the building complex in the target city under a given earthquake scenario according to the unsafe probability of each building, and obtaining the seismic vulnerability model of the building complex in the target city. The present invention can efficiently and quickly construct a numerical model of a building that takes into account the variability between buildings; establish a probabilistic machine learning model that can quantify the inherent randomness of the building response, and directly provide the probability distribution parameters required for the parameterized brittle model; and strongly support the evaluation of the loss, risk and resilience of urban building complexes.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake-resistant building structures, and in particular to a method for analyzing earthquake vulnerability of urban building complexes based on Poisson binomial distribution. Background Art

[0002] With the continuous advancement of urbanization, urban populations are dense and buildings are relatively concentrated. Therefore, it is necessary to conduct seismic vulnerability analysis of building complexes at a regional scale. Urban areas are usually composed of many buildings, each of which may have different geometric shapes, materials and structural characteristics, such as lateral load resistance systems and details. Considering the differences between urban buildings, it may be challenging to develop vulnerability models for building combinations at a regional scale. On the one hand, modeling a large number of buildings in a region and performing nonlinear time history analysis (NLTHA) requires a lot of computational costs, especially when using sophisticated finite element models. In order to reduce the computational cost of NLTHA, simplified numerical models are required to simulate the nonlinear dynamic response of buildings. On the other hand, the study of building structural vulnerability is mainly aimed at individual buildings, not regional building complexes. Therefore, how to describe the probability of functional damage to building complexes under different earthquake intensities from a regional perspective is an urgent problem to be solved. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a method for analyzing seismic vulnerability of urban building complexes based on Poisson binomial distribution.

[0004] Technical solution: The present invention comprises the following steps:

[0005] S1: Obtain the building complex attribute parameters of the target city and establish a numerical model for each building;

[0006] S2: Determine the site characteristics of the target city and obtain seismic records that meet the site characteristics;

[0007] S3: Based on the seismic records and the numerical model of the building complex, a nonlinear time history analysis is performed on each building to construct an earthquake damage database for the building complex in the target city;

[0008] S4: Determine the optimal hyperparameters based on the evaluation indicators and establish a probabilistic machine learning model for predicting building damage response;

[0009] S5: Given an earthquake scenario, use a probabilistic machine learning model to predict the unsafe probability of each building in the target city under the earthquake scenario;

[0010] S6: Based on the Poisson binomial distribution, the functional failure probability of the target city building complex under a given earthquake scenario is derived according to the unsafe probability of each building. Repeatedly given different earthquake scenarios, the seismic vulnerability model of the target city building complex is obtained.

[0011] Furthermore, the building complex attribute parameters in step S1 include the building type of each building, the construction age of each building, the number of floors of each building, the total building height of each building, the number of north-south spans of each building, the number of east-west spans of each building, the north-south span of each building, and the east-west span of each building.

[0012] Furthermore, in step S1, a simplified numerical model of each building is established using OpenSees software according to the building complex attribute parameters of the target city, wherein a simplified multi-degree-of-freedom MDOF shear model is used for multi-story buildings, and a simplified multi-degree-of-freedom MDOF bending-shear coupling model is used for high-rise buildings.

[0013] Furthermore, step S2 determines the site characteristic parameters according to the fortification intensity, site conditions and design earthquake grouping of the target city, obtains the seismic records matching the site characteristics of the target city, and calculates the intensity index AvgSA corresponding to each seismic record.

[0014] Furthermore, in step S3, the acquired earthquake records are randomly input into the numerical model of each building, and nonlinear time history analysis is performed to obtain the engineering demand parameters EDPs of each building.

[0015] Furthermore, the earthquake damage database in step S3 takes the earthquake intensity index and the building attribute parameters as input, and takes the maximum inter-story displacement angle MIDR and the floor peak acceleration PFA as output.

[0016] Furthermore, the step S4 comprises:

[0017] S41: The damage database is randomly divided into training and test sets according to the P:Q ratio, and the probabilistic machine learning method uses the natural gradient boosting tree NGBoost;

[0018] S42: Using mean square error MSE To evaluate the indicators, we use the following formula to determine the optimal hyperparameters for the probabilistic machine learning model:

[0019] ,

[0020] in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city;

[0021] Goodness of fit using the test set and RMS error RMSE Used to demonstrate the predictive performance of machine learning models, RMSE The calculation formula is as follows:

[0022] ,

[0023] in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city.

[0024] Furthermore, step S5 includes inputting the corresponding earthquake intensity index value and the property parameters of the building into the established probabilistic machine learning model according to the given earthquake scenario, and predicting the unsafe probability of each building in the target city under the earthquake scenario. , the calculation formula is as follows:

[0025] ,

[0026] in, Indicates the threshold corresponding to the unsafe state of the building. When the building is severely damaged, it is considered to be in an unsafe state; Indicates a given earthquake intensity index; represents the natural logarithm; Represents the standard normal cumulative distribution function CDF; and Respectively represent The mean and standard deviation of the responses of the buildings are provided by the probabilistic machine learning model.

[0027] Further, the step S6 comprises:

[0028] S61: According to the unsafe probability of each building ,in , the number of unsafe buildings in the target city z It follows the following Poisson binomial distribution:

[0029] ,

[0030] in, It is The probability of a building being unsafe; Defined as all sizes z The set of subsets of ; Representing a collection A complement of; According to the Poisson binomial distribution function, the number of unsafe buildings in the target city z The mean μ and variance It is expressed as:

[0031] ,

[0032] ,

[0033] S62: The functional failure probability of the target city building complex is expressed by the proportion of unsafe buildings. The expected functional failure probability of the building complex is expressed as:

[0034] ,

[0035] in, It is The probability of a building being unsafe; N is the total number of buildings in the target city.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: by adopting a simplified multi-degree-of-freedom model based on building attribute parameters, a numerical model of a building that takes into account the variability between buildings can be constructed efficiently and quickly; a probabilistic machine learning model that can quantify the intrinsic randomness of building responses is established, and the probability distribution parameters required for the parameterized brittle model are directly provided; the regional seismic vulnerability of a building complex is evaluated using the Poisson binomial distribution, and a building complex vulnerability model that includes damage to structural and non-structural components is established, which strongly supports the assessment of losses, risks, and resilience of urban building complexes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of the present invention;

[0038] Figure 2 spectral accelerograms recorded for ground motions;

[0039] Figure 3 Predict performance graphs for machine learning models;

[0040] Figure 4 It is the probability cloud map of unsafe buildings;

[0041] Figure 5 This is the earthquake vulnerability curve of the building complex area. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0043] like Figure 1 As shown, the present invention provides a method for analyzing seismic vulnerability of urban building complexes based on Poisson binomial distribution, comprising the following steps:

[0044] S1: Obtain the attribute parameters of the building complex in the target city and establish a numerical model of each building; specifically as follows: Collect 8 attribute parameters of 1,000 buildings in the target city, namely, the building type of each building, the construction age of each building, the number of floors of each building, the total building height of each building, the number of north-south spans of each building, the number of east-west spans of each building, the north-south span of each building, and the east-west span of each building; Based on the attribute parameters of each building, a simplified multi-degree-of-freedom MDOF shear model is used in the OpenSees software to establish a numerical model of a multi-story building, and a simplified multi-degree-of-freedom MDOF bending-shear coupling model is used to establish a numerical model of a high-rise building.

[0045] S2: Determine the site characteristics of the target city and obtain earthquake motion records that meet the site characteristics; the details are as follows: According to the site characteristics of the target city (i.e., fortification intensity, site conditions, and design earthquake grouping), select 100 earthquake motion records that meet the target response spectrum from the earthquake database of the Pacific Earthquake Engineering Research Center. The spectral acceleration is as follows: Figure 2 As shown, the intensity index AvgSA corresponding to each earthquake motion record is calculated.

[0046] S3: Based on seismic motion records and numerical models of building complexes, nonlinear time-history analysis is performed on each building to construct an earthquake damage database for building complexes in the target city; specifically, the 100 seismic motion records obtained are expanded to 1,000, and they are randomly input into the numerical models of these 1,000 buildings to perform nonlinear time-history analysis to obtain the maximum inter-story displacement angle MIDR and floor peak acceleration PFA of each building; the constructed building earthquake damage database takes seismic motion intensity index and building attribute parameters as input, and takes the maximum inter-story displacement angle MIDR and floor peak acceleration PFA as output.

[0047] S4: Determine the optimal hyperparameters based on the evaluation indicators and establish a probabilistic machine learning model for predicting building damage response; the details are as follows: randomly divide the damage database into training set and test set in a ratio of 7:3, use natural gradient boosting tree NGBoost for model training; use mean square error MSE The mean square error is used as an evaluation indicator to determine the optimal value of the model hyperparameter and obtain the probabilistic machine learning prediction model. MSE The formula is as follows:

[0048] ,

[0049] in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city;

[0050] Goodness of fit using the test set and RMS error RMSE Used to demonstrate the predictive performance of machine learning models, RMSE The calculation formula is as follows:

[0051] ,

[0052] in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city.

[0053] like Figure 3 The figure shows the prediction performance of the machine learning model, which shows the average prediction accuracy of the NGBoost model for the maximum inter-story displacement angle MIDR through the test set and the training set. Figure 3 As can be seen from (a) in the figure, the actual data points and the predicted data points are along The lines fit closely and the RMSE value is almost zero. The value is 0.853. Figure 3 (b) shows the average prediction accuracy of the NGBoost model for the floor peak acceleration PFA. The actual data points and the predicted data points are very consistent, and the RMSE on both the training set and the test set is close to 0. It is close to 1. The results show that the NGBoost model has high accuracy and can effectively predict the damage response of structural and non-structural components of buildings.

[0054] S5: Given an earthquake scenario, use the probabilistic machine learning model to predict the unsafe probability of each building in the target city under the earthquake scenario; specifically: add the given earthquake scenario AvgSA=0.5g and the attribute parameters of each building to the established probabilistic machine learning model to predict the unsafe probability of each building in the target city under the earthquake scenario The calculation formula is as follows:

[0055] ,

[0056] in, Indicates the threshold corresponding to the unsafe state of the building. When the building is severely damaged, it is considered to be in an unsafe state; Indicates a given seismic intensity index; represents the natural logarithm; Represents the standard normal cumulative distribution function CDF; and Respectively represent The mean and standard deviation of the building responses are provided by the probabilistic machine learning NGBoost model.

[0057] According to the damage state thresholds recommended by the code, a building is considered unsafe when it is severely damaged: the maximum inter-story displacement angle MIDR of the building's structural components is unsafe in the range of 0.02-0.04; the peak floor acceleration PFA of the building's non-structural components is unsafe in the range of 0.40-0.80 g, such as Figure 4 The figure shows the unsafe probability cloud map of the building complex, which can evaluate the unsafe probability of the structural components and non-structural components of each building in the target city under a given earthquake intensity AvgSA=0.5g. Figure 4 (a) in the equation is the unsafe probability of the structural component. Figure 4 (b) in the figure is the unsafe probability of non-structural components.

[0058] S6: Based on the Poisson binomial distribution, the functional failure probability of the target city building complex under a given earthquake scenario is derived from the unsafe probability of each building. The earthquake vulnerability model of the target city building complex is obtained by repeating the given different earthquake scenarios. The details are as follows:

[0059] First, according to the unsafe probability of each building ,in , the number of unsafe buildings in the target city z It follows the following Poisson binomial distribution:

[0060] ,

[0061] in, It is The probability of a building being unsafe; Defined as all sizes z The set of subsets of ; Representing a collection A complement of; According to the Poisson binomial distribution function, the number of unsafe buildings in the target city z The mean μ and variance It is expressed as:

[0062] ,

[0063] ,

[0064] Then, the functional failure probability of the target city building complex is expressed by the proportion of the number of unsafe buildings, and the expected functional failure probability of the building complex can be calculated as follows:

[0065] ,

[0066] in, It is The probability of a building being unsafe; Nis the total number of buildings in the target city.

[0067] like Figure 5 As shown, it shows the proportion of unsafe buildings under different earthquake intensities, among which, Figure 5 (a) is the building structural damage vulnerability curve based on the maximum inter-story drift angle MIDR. Figure 5 (b) is the vulnerability curve of non-structural damage of buildings based on the peak floor acceleration PFA. Since the number of unsafe buildings is uncertain, the vulnerability curve of the target city building group is fluctuating. Figure 5 The fluctuation range of seismic vulnerability of regional-scale building groups shown in is relatively small, which suggests that the expectation of using the proportion of unsafe buildings is acceptable.

Claims

1. A method for analyzing seismic vulnerability of urban buildings based on Poisson binomial distribution. It is characterized in that The steps include: S1: Obtain the building complex attribute parameters of the target city and establish a numerical model for each building; S2: Determine the site characteristics of the target city and obtain seismic records that meet the site characteristics; S3: Based on the seismic records and the numerical model of the building complex, a nonlinear time history analysis is performed on each building to construct an earthquake damage database for the building complex in the target city; S4: Determine the optimal hyperparameters based on the evaluation indicators and establish a probabilistic machine learning model for predicting building damage response; S5: Given an earthquake scenario, use a probabilistic machine learning model to predict the unsafe probability of each building in the target city under the earthquake scenario; S6: Based on the Poisson binomial distribution, the functional failure probability of the target city building complex under a given earthquake scenario is derived according to the unsafe probability of each building. Repeatedly given different earthquake scenarios, the earthquake vulnerability model of the target city building complex is obtained; In step S1, a simplified numerical model of each building is established using OpenSees software according to the building complex attribute parameters of the target city, wherein a simplified multi-degree-of-freedom MDOF shear model is used for multi-story buildings, and a simplified multi-degree-of-freedom MDOF bending-shear coupling model is used for high-rise buildings. The step S3 randomly inputs the acquired earthquake records into the numerical model of each building, performs nonlinear time history analysis, and obtains the engineering demand parameters EDPs of each building. The earthquake damage database in step S3 takes the earthquake intensity index and the building attribute parameters as input, and takes the maximum inter-story displacement angle MIDR and the floor peak acceleration PFA as output.

2. The urban building complex seismic vulnerability analysis method based on Poisson binomial distribution according to claim 1, It is characterized in that The building complex attribute parameters in step S1 include the building type of each building, the construction age of each building, the number of floors of each building, the total building height of each building, the number of north-south spans of each building, the number of east-west spans of each building, the north-south span of each building, and the east-west span of each building.

3. The urban building complex seismic vulnerability analysis method based on Poisson binomial distribution according to claim 1, It is characterized in that The step S2 determines the site characteristic parameters according to the fortification intensity, site conditions and design earthquake grouping of the target city, obtains the seismic records matching the site characteristics of the target city, and calculates the intensity index AvgSA corresponding to each seismic record.

4. The urban building complex seismic vulnerability analysis method based on Poisson binomial distribution according to claim 1, It is characterized in that The step S4 comprises: S41: The damage database is randomly divided into training and test sets according to the P:Q ratio, and the probabilistic machine learning method uses the natural gradient boosting tree NGBoost; S42: Using mean square error MSE To evaluate the indicators, we use the following formula to determine the optimal hyperparameters for the probabilistic machine learning model: ， in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city; Goodness of fit using the test set and RMS error RMSE Used to demonstrate the predictive performance of machine learning models, RMSE The calculation formula is as follows: ， in, and are the true value and the predicted value respectively; N is the total number of buildings in the target city.

5. The method for analyzing seismic vulnerability of urban buildings based on Poisson binomial distribution according to claim 1, It is characterized in that The step S5 includes inputting the corresponding earthquake intensity index value and the property parameters of the building into the established probabilistic machine learning model according to the given earthquake scenario, and predicting the unsafe probability of each building in the target city under the earthquake scenario. , the calculation formula is as follows: ， in, Indicates the threshold corresponding to the unsafe state of the building. When the building is severely damaged, it is considered to be in an unsafe state; Indicates a given earthquake intensity index; represents the natural logarithm; Represents the standard normal cumulative distribution function CDF; and Respectively represent The mean and standard deviation of the building responses are provided by the probabilistic machine learning model. Represents the true value.

6. The method for analyzing seismic vulnerability of urban buildings based on Poisson binomial distribution according to claim 1, It is characterized in that The step S6 comprises: S61: According to the unsafe probability of each building ,in , the number of unsafe buildings in the target city z It follows the following Poisson binomial distribution: ， in, It is The probability of a building being unsafe; Defined as all sizes z The set of subsets of ; Representing a collection A The complement of Represents a given earthquake intensity index; according to the Poisson binomial distribution function, the number of unsafe buildings in the target city z The mean μ and variance It is expressed as: ， ， S62: The functional failure probability of the target city building complex is expressed by the proportion of unsafe buildings. The expected functional failure probability of the building complex is expressed as: ， in, It is The probability of a building being unsafe; N is the total number of buildings in the target city.

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