A method for analyzing the seismic vulnerability of urban building complexes based on the Poisson binomial distribution.
The method addresses the challenge of analyzing urban building group seismic vulnerability by constructing a database and using probabilistic machine learning to predict seismic damage, enabling efficient and accurate assessment of regional building safety.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-04-07
- Publication Date
- 2026-03-26
Smart Images
Figure 2026054420000001_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of earthquake resistance technology for 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 analyze the vulnerability of building groups to earthquakes 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 for building groups on a regional scale. On the other hand, modeling a large number of buildings in a region and performing time-history nonlinear analysis (NLTHA) requires a great deal of computational cost, especially when using a detailed finite element model. To reduce the computational cost of NLTHA, a simple numerical model for simulating the nonlinear dynamic response of buildings is required. 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 for building groups is generated using a simple model, and a seismic vulnerability model for 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 a Poisson binomial distribution, which involves constructing a building seismic damage database through a simplified model and establishing a regional building group seismic vulnerability model based on this database. [Means for solving the problem]
[0004] The present invention provides a method for analyzing the seismic vulnerability of urban building complexes based on the Poisson binomial distribution, Step S1 involves obtaining attribute parameters of the building complex in the target city and establishing a numerical model for each building. Step S2 involves determining the site characteristics of the target city and obtaining seismic motion records that match the site characteristics. Step S3 involves performing a time-history nonlinear analysis of each building based on seismic motion records and numerical models of the building complex, and constructing a seismic damage database for the building complex in the target city. Step S4 involves determining the optimal hyperparameters based on evaluation indicators and establishing a probabilistic machine learning model to predict building damage response. Step S5: Provide an earthquake scenario and use a probabilistic machine learning model to predict the probability that each building in the target city is unsafe in the earthquake scenario, and Step S6 includes deriving the probability of functional failure of the buildings in the target city under a given earthquake scenario from the probability of each building being unsafe based on the Poisson binomial distribution, and obtaining an earthquake vulnerability model of the buildings in the target city by repeatedly applying different earthquake scenarios. Furthermore, the attribute parameters of the building group in step S1 include a total of eight parameters: the building type of each building, the year of construction of each building, the number of floors of each building, the total floor 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. Furthermore, in step S1, a simplified numerical model of each building is established in OpenSees software according to each building attribute parameter. For multi-story buildings, a simplified multi-degree-of-freedom (MDOF) shear model is used, while for high-rise buildings, a simplified multi-degree-of-freedom (MDOF) bending shear model is used.
[0005] Furthermore, in step S2, site characteristic parameters are determined according to the design seismic intensity of the target city, site conditions, and grouping of design ground motions. Ground motion records that match the site characteristics of the target city are obtained, and the strength index AvgSA corresponding to each ground motion record is calculated.
[0006] Furthermore, in step S3, the obtained seismic motion records are randomly input into the numerical model of each building, and a time-history nonlinear analysis is performed to obtain the engineering demand parameters (EDPs) for each building, such as the maximum inter-story drift ratio (MIDR) and peak floor acceleration (PFA). Furthermore, the building seismic damage database in step S3 takes an index of seismic motion intensity and building attribute parameters as inputs and outputs the maximum inter-story drift angle (MIDR) and peak floor acceleration (PFA).
[0007] Furthermore, step S4 includes steps S41 to S43, S41: The damage database is randomly split into training and test sets according to the ratio of P and Q, and the probabilistic machine learning method used is the natural gradient boosting tree NGBoost. S42: The optimal hyperparameters for a stochastic machine learning model are determined using the mean squared error (MSE) as an evaluation metric, and the formula is as follows:
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[0010] Also, 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 is not safe in this earthquake scenario ,
[0013] , is predicted, and the calculation formula is as follows.
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[0012] Also, step S6 is specifically as follows. First, when the probability that each building is not safe is set as 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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Effect of the Invention
[0017] [Figure 1] This is a flowchart of the present invention. [Figure 2] This is a spectral acceleration diagram of the seismic motion record according to the present invention. [Figure 3] This figure shows the predictive performance of the machine learning model of the present invention. [Figure 4] This is a cloud diagram showing the probability of an unsafe group of buildings according to the present invention. [Figure 5] This graph shows the earthquake vulnerability of the building complex area according to the present invention. [Modes for carrying out the invention]
[0018] The technical means of the present invention will be described in detail below with reference to the attached drawings.
[0019] As shown in Figure 1, embodiments of the present invention provide a method for analyzing the seismic vulnerability of urban building complexes based on a Poisson binomial distribution, which includes the following steps.
[0020] Step S1: Obtain attribute parameters for the buildings in the target city and establish numerical models for each building. Specifically, collect eight attribute parameters for 1,000 buildings in the target city: building type, age of each building, number of floors, total floor height, number of north-south spans, number of east-west spans, north-south span, and east-west span. Then, according to each building attribute parameter, establish numerical models for multi-story buildings using a simple multi-degree-of-freedom (MDOF) shear model in OpenSees software, and establish numerical models for high-rise buildings using a simple multi-degree-of-freedom (MDOF) bending shear model.
[0021] Step S2: Determine the site characteristics of the target city and obtain seismic motion records that match the site characteristics. Specifically, based on the site characteristics of the target city (i.e., design seismic intensity, site conditions, and grouping of design seismic motion), 100 seismic motion records that match the target response spectrum are selected from the Pacific Earthquake Engineering Research Center's earthquake database. The acceleration response spectrum and mean response spectrum are shown in Figure 2, and the strength index AvgSA corresponding to each seismic motion record is calculated.
[0022] Step S3: Based on seismic motion records and numerical models of the building complex, perform time-history nonlinear analysis on each building to construct a seismic damage database for the building complex in the target city. Specifically, expand the 100 seismic motion records to 1000, randomly input these 1000 building data into numerical models, and perform time-history nonlinear analysis to obtain the maximum inter-story drift angle (MIDR) and peak floor acceleration (PFA) for each building. The constructed building seismic damage database will take seismic motion intensity indices and building attribute parameters as inputs and output the maximum inter-story drift angle (MIDR) and peak floor acceleration (PFA).
[0023] Step S4: Determine the optimal hyperparameters based on the evaluation metrics and establish a probabilistic machine learning model to predict building damage response. Specifically, the damage database is split into a training set and a test set in a 7:3 ratio, and the model is trained using Natural Gradient Boosting Tree NGBoost. The mean squared error (MSE) is used as an evaluation metric to determine the optimal values of the model hyperparameters and obtain a probabilistic machine learning predictive model. The formula for the mean squared error (MSE) is as follows:
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[0026] The average prediction accuracy of the NGBoost model for the maximum inter-story drift angle (MIDR) is shown for the test and training sets. As shown in Figure 3(a), the actual data points and predicted data points coincide along the y=x line, and the RMSE value is approximately zero. 2 The value was 0.853. Simultaneously, Figure 3(a) shows the average predictive accuracy of the NGBoost model for peak floor acceleration (PFA), where the actual data points and predicted data points are in very good agreement, and the RMSE on both the training and test sets is close to 0. 2 The value is close to 1. This result indicates that the NGBoost model is highly accurate and can effectively predict the damage response of structural and non-structural components of buildings.
[0027] Step S5: A seismic scenario is given, and a probabilistic machine learning model is used to predict the probability of each building in the target city being unsafe under the seismic scenario. Specifically, the given seismic scenario AvgSA=0.5g and each building attribute parameter are input into the established probabilistic machine learning model, and the probability P of each building in the target city being unsafe under the seismic scenario is calculated. B,i The prediction is as follows, and the calculation formula is as follows:
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[0029] According to the damage thresholds recommended by the standard, a building is considered unsafe if it has suffered significant damage. Specifically, it is unsafe if the maximum inter-story drift angle (MIDR) of the building's structural members is in the range of 0.02 to 0.04, or if the peak floor acceleration (PFA) of the building's non-structural members is in the range of 0.40 to 0.80 g. The probability of unsafety for the structural and non-structural members of each building in the target city at a given seismic intensity AvgSA = 0.5 g can be estimated and is shown in Figures 4(a) and 4(b), respectively.
[0030] Step S6: Based on the probability of each building being unsafe using the Poisson binomial distribution, the probability of functional failure of the buildings in the target city under a given earthquake scenario is derived. By repeatedly applying different earthquake scenarios, an earthquake vulnerability model of the buildings in the target city is obtained. Specifically, this is done as follows:
[0031] First, P is the probability that each building is unsafe. B,i If we set (i=1,2,…,N), the number of unsafe buildings z in the target city follows the following Poisson binomial distribution.
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[0034] Next, the probability of a group of buildings in the target city losing functionality can be expressed as the proportion of unsafe buildings, and the expected value of the probability of a group of buildings losing functionality can be calculated using the following formula.
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[0036] Figure 5 shows the proportion of unsafe buildings under different seismic intensities. Figure 5(a) is the structural damage vulnerability curve of buildings based on the maximum inter-story drift angle (MIDR), and Figure 5(b) is the non-structural damage vulnerability curve of buildings based on the peak floor acceleration (PFA). Because the number of unsafe buildings is uncertain, the vulnerability curves for the buildings in the target city fluctuate as shown in the shaded area of Figure 5. The range of variation in seismic vulnerability for the regional-scale building groups shown in the figure is relatively small, suggesting that the expectation of using the proportion of unsafe buildings is acceptable.
Claims
1. A method for analyzing the seismic vulnerability of urban building groups based on the Poisson binomial distribution, Step S1 involves obtaining attribute parameters of the building complex in the target city and establishing a numerical model for each building. Step S2: Determine the site characteristics of the target city and obtain seismic motion records that match the site characteristics. Step S3 involves performing a time-history nonlinear analysis on each building based on the aforementioned seismic motion records and a numerical model of the building group, thereby constructing a seismic damage database for the building group in the target city. Step S4 involves determining the optimal hyperparameters based on evaluation indicators and establishing a probabilistic machine learning model to predict building damage response. Step S5: Provide an earthquake scenario and use the probabilistic machine learning model to predict the probability that each building in the target city is unsafe in the earthquake scenario, and Step S6 includes deriving the probability of functional failure of the buildings in the target city under a given earthquake scenario from the probability of each building being unsafe based on the Poisson binomial distribution, and obtaining an earthquake vulnerability model of the buildings in the target city by repeatedly applying different earthquake scenarios. In step S1, a simplified numerical model of each building is established in the OpenSees software according to each building attribute parameter. For multi-story buildings, a simplified multi-degree-of-freedom (MDOF) shear model is used, and for high-rise buildings, a simplified multi-degree-of-freedom (MDOF) bending shear model is used. In step S3, the obtained seismic motion records are randomly input into numerical models of each building, and time history nonlinear analysis is performed to obtain the engineering response variables (EDPs) of each building. The building earthquake damage database in step S3 takes the seismic motion intensity index and building attribute parameters as inputs and outputs the maximum inter-story drift angle (MIDR) and peak floor acceleration (PFA). A method for analyzing the seismic vulnerability of urban building complexes based on a Poisson binomial distribution, characterized by the above.
2. The method for analyzing the seismic vulnerability of a group of urban buildings based on a Poisson binomial distribution according to claim 1, characterized in that the attribute parameters of the group of buildings in step S1 include the building type of each building, the year of construction of each building, the number of floors of each building, the total floor 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 method for analyzing the seismic vulnerability of urban building groups based on a Poisson binomial distribution according to claim 1, characterized in that in step S2, site characteristic parameters are determined according to the design seismic intensity of the target city, site conditions, and grouping of design seismic motions, seismic motion records that match the site characteristics of the target city are obtained, and strength index AvgSA corresponding to each seismic motion record is calculated.
4. The method for analyzing the seismic vulnerability of urban building groups based on a Poisson binomial distribution according to claim 1, wherein step S4 includes the following steps. S41: The damage database is randomly divided into a training set and a test set according to the ratio of P and Q, and the probabilistic machine learning method uses a natural gradient boosting tree NGBoost. S42: A step in which the optimal hyperparameters of the stochastic machine learning model are determined using the mean squared error (MSE) as an evaluation index, formula: [Math 1] [Math 2]
5. In step S5, the corresponding seismic intensity index value and the building attribute parameters are input into the established probabilistic machine learning model according to the given earthquake scenario, and the probability P of each building in the target city being unsafe in the earthquake scenario is calculated. Ｂ，ｉ A method for analyzing the seismic vulnerability of urban building groups based on a Poisson binomial distribution according to claim 1, characterized by predicting . Calculation formula: [Math 3]
6. Step S6 includes steps S61 to S62, S61: The probability that each building is unsafe is P Ｂ，ｉ If we let (i = 1, 2, ..., N), the number of unsafe buildings z in the target city follows the following Poisson binomial distribution: [Math 4] [Math 5] [Math 6]