Method for Analyzing Seismic Vulnerability of Urban Building Groups Based on Poisson Binomial Distribution

Abstract

Using a simple multi-degree-of-freedom model based on building attribute parameters, an efficient and rapid construction of a building numerical model considering the variation between buildings can be achieved. A probabilistic machine learning model that can quantify the essential randomness of building responses is constructed, directly providing the probability distribution parameters required for the parameterized vulnerability model. Starting from the probability of non-safety of each building in the urban area, a method for seismic vulnerability analysis of urban building groups is provided, which uses the Poisson binomial distribution to derive the regional seismic vulnerability model of the building group. 【Solution means】The method includes step (1) of constructing a simple numerical model of the building group, step (2) of selecting a set of ground motion records that satisfy the site characteristics, step (3) of obtaining a structural and non-structural damage database of the building group, step (4) of establishing a damage prediction model of probabilistic machine learning, step (5) of obtaining the probability of non-safety of the building group, and step (6) of deriving the regional vulnerability model of the building group.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic resistance of building structures, and particularly to a method for analyzing the seismic vulnerability of urban building groups based on the Poisson binomial distribution.

Background Art

[0002] With the progress of urbanization, the population density in urban areas is increasing, and buildings are becoming more and more concentrated. These urban buildings are likely to suffer large-scale structural damage and functional failures under the action of strong earthquakes, and further pose a significant threat to the safety of citizens' lives and property. Therefore, it is very necessary to conduct an analysis of the seismic vulnerability of building groups on a regional scale, which is an important support for urban disaster prevention and damage reduction. An urban area usually consists of a large number of buildings, and each building may have different geometric shapes, materials, and structural characteristics, such as systems and details for resisting horizontal loads. Considering the differences between urban buildings, it may be difficult to develop a vulnerability model of building groups on a regional scale. On the other hand, to model a large number of buildings in a region and perform time-history nonlinear analysis (NLTHA), especially when using a detailed finite element model, it requires a huge computational cost. To reduce the computational cost of NLTHA, a simple numerical model for simulating the nonlinear dynamic response of buildings is needed. On the other hand, the current research on the vulnerability of building structures mainly focuses on individual buildings and cannot directly provide the number of unsafe buildings after an earthquake in a regional scope. This information is particularly important for damage reduction. Therefore, to support scalable urban disaster resistance assessment, from a regional perspective, a seismic damage database of building groups is generated using a simple model, and a seismic vulnerability model of building groups on a regional scale is developed to describe the damage probability of building functions under different seismic intensities.

Summary of the Invention

Problems to be Solved by the Invention

[0003] The present invention aims to provide a method for analyzing the seismic vulnerability of urban building groups based on the Poisson binomial distribution, which constructs a building seismic damage database through a simplified model and establishes a seismic vulnerability model for regional building groups based on this.

Means for Solving the Problems

[0004] The method for analyzing the seismic vulnerability of urban building groups based on the Poisson binomial distribution of the present invention includes: Step S1 of obtaining the attribute parameters of the building group in the target city and establishing a numerical model for each building; Step S2 of determining the site characteristics of the target city and obtaining ground motion records that match the site characteristics; Step S3 of performing time-history nonlinear analysis on each building based on the ground motion records and the numerical model of the building group, and constructing a building seismic damage database for the building group in the target city; Step S4 of determining the optimal hyperparameters based on the evaluation index and establishing a probabilistic machine learning model for predicting the building damage response; Step S5 of giving a seismic scenario and using the probabilistic machine learning model to predict the probability of non-safety for each building in the target city in the seismic scenario, and Step S6 of deriving the functional failure probability of the building group in the target city in the given seismic scenario from the probability of non-safety of each building based on the Poisson binomial distribution, and obtaining the seismic vulnerability model of the building group in the target city by repeatedly giving different seismic scenarios. In addition, the attribute parameters of the building group in Step S1 include eight parameters: the building type of each building, the construction years of each building, the number of floors of each building, the total floor height of each building, the number of spans in the north-south direction of each building, the number of spans in the east-west direction of each building, the north-south span of each building, and the total east-west span of each building. In addition, in Step S1, according to each building attribute parameter, a simple numerical model of each building is established by using OpenSees software. For multi-story buildings, a simple multi-degree of freedom (MDOF) shear model is used, and for high-rise buildings, a simple multi-degree of freedom (MDOF) flexure-shear model is used.

[0005] Also, in step S2, site characteristic parameters are determined according to the design seismic intensity, site conditions, and grouping of design ground motions of the target city, ground motion records that match the site characteristics of the target city are obtained, and the intensity index AvgSA corresponding to each ground motion record is calculated.

[0006] Also, in step S3, the obtained ground motion records are randomly input into the numerical models of each building, time history nonlinear analysis is performed, and engineering response variables (Engineering Demand Parameters (EDPs)) of each building, such as the maximum inter-story drift ratio (Maximum Inter-Story Drift Ratio (MIDR)) and peak floor acceleration (Peak Floor Acceleration (PFA)), are obtained. Also, the building earthquake damage database in step S3 takes the index of ground motion intensity and building attribute parameters as inputs and outputs the maximum inter-story drift ratio (MIDR) and peak floor acceleration (PFA).

[0007] Also, step S4 includes steps S41 to S43. S41: The damage database is randomly divided into a training set and a test set according to the ratio of P to Q, and the probabilistic machine learning method uses the natural gradient boosting tree NGBoost. S42: The optimal hyperparameters of the probabilistic machine learning model are determined using the mean squared error MSE as the evaluation index, and the formula is as follows.

[0008]

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[0010] In step S5, according to the given earthquake scenario, the index value of the corresponding seismic intensity and the building attribute parameters are input into the established probabilistic machine learning model, and the probability P that each building in the target city in this earthquake scenario is not safe B,i , is predicted, and the calculation formula is as follows.

[0011]

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[0012] Moreover, step S6 is specifically as follows. First, assuming that the probability that each building is not safe is P B,i (i = 1, 2, …, N), the number z of buildings that are not safe in the target city follows the following Poisson binomial distribution.

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Advantages of the Invention

[0016] Compared with the prior art, the present invention can efficiently and rapidly construct a numerical model of a building considering the variability between buildings by using a simple multi-degree-of-freedom model based on building attribute parameters. The probabilistic machine learning model can quantify the inherent randomness of the building's response and directly provide the probability distribution parameters required for the parameterized vulnerability model. It does not focus only on the damage probability of a single building as in previous studies, but can evaluate the regional seismic vulnerability of a building group using the Poisson binomial distribution. The established vulnerability model of the building group includes damage to structural and non-structural members, and has the remarkable advantage of strongly supporting the evaluation of the losses, risks, and resilience of urban building groups.

Brief Description of the Drawings

[0017]

Figure 1

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Embodiments for Carrying Out the Invention

[0018] Hereinafter, the technical means of the present invention will be specifically described with reference to the accompanying drawings.

[0019] As shown in FIG. 1, an embodiment of the present invention provides a method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution, which includes the following steps.

[0020] Step S1: Obtain the attribute parameters of the building group in the target city and establish the numerical model of each building. Specifically, collect the eight attribute parameters of 1,000 buildings in the target city, namely, the building type of each building, the construction year of each building, the number of floors of each building, the total floor height of each building, the number of spans in the north-south direction of each building, the number of spans in the east-west direction of each building, the north-south span of each building, and the east-west span of each building. According to each building attribute parameter, use the OpenSees software to establish the numerical model of the multi-story building using a simple multi-degree-of-freedom (MDOF) shear model, and establish the numerical model of the high-rise building using a simple multi-degree-of-freedom (MDOF) flexure-shear model.

[0021] Step S2: Determine the site characteristics of the target city and obtain the ground motion records that match the site characteristics. Specifically, based on the site characteristics of the target city (i.e., the design seismic intensity, site conditions, and grouping of the design ground motion), select 100 ground motion records that match the target response spectrum from the earthquake database of the Pacific Earthquake Engineering Research Center. The acceleration response spectrum and the mean response spectrum are shown in Figure 2, and the strength index AvgSA corresponding to each ground motion record is calculated.

[0022] Step S3: Based on the ground motion records and the numerical model of the building group, perform the time-history nonlinear analysis of each building and construct the earthquake damage database of the building group in the target city. Specifically, expand the 100 ground motion records to 1,000, randomly input them into the numerical models of these 1,000 buildings to perform the time-history nonlinear analysis, obtain the maximum inter-story drift ratio (MIDR) and the peak floor acceleration (PFA) of each building. The constructed building earthquake damage database takes the ground motion intensity index and the building attribute parameters as inputs and the maximum inter-story drift ratio (MIDR) and the peak floor acceleration (PFA) as outputs.

[0023] Step S4: Determine the optimal hyperparameters based on the evaluation index and establish a probabilistic machine learning model for predicting the building damage response. Specifically, divide the damage database into a training set and a test set at a ratio of 7:3, and train the model with the natural gradient boosting tree NGBoost. The optimal values of the model hyperparameters are determined using the mean squared error MSE as the evaluation metric, and a predictive model of probabilistic machine learning is obtained. The formula for the mean squared error MSE is as follows.

[0024] [Number]

[0025] [Number]

[0026] The average prediction accuracy of the NGBoost model for the maximum inter-story deformation angle (MIDR) is shown for the test set and the training set. As shown in Figure 3(a), the actual data points and the predicted data points coincide along the line y = x, the RMSE value is almost zero, and the 2 R value is 0.853. At the same time, Figure 3(a) shows the average prediction accuracy of the NGBoost model for the peak floor acceleration (PFA). The actual data points and the predicted data points are in very good agreement, and the RMSEs on both the training set and the test set are close to 0, and the 2 R is close to 1. This result shows that the NGBoost model has very high accuracy and can effectively predict the damage responses of the structural and non-structural members of buildings.

[0027] Step S5: Provide an earthquake scenario and use the probabilistic machine learning model to predict the probability of non-safety of each building in the target city in the earthquake scenario. Specifically, the given earthquake scenario AvgSA = 0.5g and the established probabilistic machine learning model of each building attribute parameter are input, and the probability P B,i , of non-safety of each building in the target city in the earthquake scenario is predicted, and the calculation formula is as follows.

[0028] [Number]

[0029] According to the damage state threshold recommended by the standard, when a building suffers serious damage, the building is considered unsafe, that is, the building is not safe when the maximum inter-story drift ratio (MIDR) of the building's structural members is within the range of 0.02 - 0.04, and the building is not safe when the peak floor acceleration (PFA) of the building's non-structural members is within the range of 0.40 - 0.80g. The probability of non-safety of the structural and non-structural members of each building in the target city under the given seismic intensity AvgSA = 0.5g can be estimated, as shown in Figures 4(a) and 4(b) respectively.

[0030] Step S6: Based on the probability of non-safety of each building according to the Poisson binomial distribution, derive the probability of functional failure of the building group in the target city under the given seismic scenario, and by repeatedly giving different seismic scenarios, obtain the seismic vulnerability model of the building group in the target city. Specifically, it is as follows.

[0031] First, let the probability of non-safety of each building be P B,i (i = 1, 2, …, N), then the number z of non-safe buildings in the target city follows the following Poisson binomial distribution.

[0032]

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[0033]

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[0034] Next, the probability of functional loss of the building group in the target city is represented by the ratio of the number of non-safe buildings, and the expected value of the probability of functional loss of the building group can be calculated. The formula is as follows.

[0035]

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[0036] Figure 5 shows the percentage of unsafe buildings under the action of different seismic intensities. Figure 5(a) is the structural damage vulnerability curve of buildings based on the maximum inter-story drift ratio (MIDR), and Figure 5(b) is the non-structural damage vulnerability curve of buildings based on the peak floor acceleration (PFA). Since the number of unsafe buildings is uncertain, the vulnerability curves of the building groups in the target cities vary as shown in the shaded part of Figure 5. The variation range of the seismic vulnerability of the building groups at the regional scale shown in the figure is relatively small, suggesting that the use of the percentage of unsafe buildings is acceptable.

Claims

1. A method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution, comprising: Step S1 of obtaining the attribute parameters of the building group in the target city and establishing a numerical model for each building; Step S2 of determining the site characteristics of the target city and obtaining ground motion records that match the site characteristics; Step S3 of performing time-history nonlinear analysis on each building based on the ground motion records and the numerical model of the building group, and constructing a seismic damage database for the building group in the target city; Step S4 of determining optimal hyperparameters based on evaluation indicators and establishing a probabilistic machine learning model for predicting building damage responses; Step S5 of giving a seismic scenario and using the probabilistic machine learning model to predict the probability of non-safety for each building in the target city in the seismic scenario; and Step S6 of deriving the functional failure probability of the building group in the target city in the given seismic scenario from the probability of non-safety for each building based on the Poisson binomial distribution, and repeating the giving of different seismic scenarios to obtain a seismic vulnerability model for the building group in the target city. In step S1, according to each building attribute parameter, a simple numerical model of each building is established using OpenSees software. For multi-story buildings, a simple multi-degree-of-freedom (MDOF) shear model is used, and for high-rise buildings, a simple multi-degree-of-freedom (MDOF) flexure-shear model is used. In step S3, the obtained ground motion records are randomly input into the numerical model of each building, and time-history nonlinear analysis is performed to obtain the engineering response variables (EDPs) of each building. The building seismic damage database in step S3 takes the ground motion intensity index and building attribute parameters as inputs and outputs the maximum inter-story drift ratio (MIDR) and peak floor acceleration (PFA). A method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution, characterized in that.

2. The attribute parameters of the building group 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 floor height of each building, the number of spans in the north-south direction of each building, the number of spans in the east-west direction of each building, the north-south span of each building, and the east-west span of each building. The method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution according to claim 1, characterized in that.

3. In step S2, a site characteristic parameter is determined according to the design seismic intensity, site conditions, and grouping of design ground motions of the target city, a ground motion record that matches the site characteristics of the target city is obtained, and a strength index AvgSA corresponding to each ground motion record is calculated. The method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution according to claim 1 is characterized in that.

4. The step S4 includes the following steps. The method for analyzing the seismic vulnerability of an urban building group based on the Poisson binomial distribution according to claim 1 is characterized in that. S41: Randomly divide the damage database into a training set and a test set according to the ratio of P to Q. The step of using the natural gradient boosting tree NGBoost as the probabilistic machine learning method. S42: The step of determining the optimal hyperparameters of the probabilistic machine learning model using the mean squared error MSE as an evaluation index. Equation: 【Number 1】 【Number 2】

5. In the step S5, according to the given earthquake scenario, the index value of the corresponding seismic intensity and the building attribute parameters are input into the established probabilistic machine learning model, and the probability P that each building in the target city in the earthquake scenario is not safe is predicted. Ｂ，ｉ , which is characterized by predicting the seismic vulnerability analysis method of urban building groups based on the Poisson binomial distribution according to claim 1. Calculation formula: 【Number 3】

6. The step S6 includes steps S61 to S62. S61: Let the probability that each building is not safe be P Ｂ，ｉ (i = 1, 2,..., N), then the number z of buildings that are not safe in the target city follows the following Poisson binomial distribution 【Number 4】 【Number 5】 【Number 6】

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