Genetic programming for predicting aseismic abilities of school buildings

https://doi.org/10.1016/j.engappai.2012.04.002Get rights and content

Abstract

In general, the aseismic ability of buildings is analyzed using nonlinear models. To obtain aseismic abilities of buildings, numerical models are constructed based on the structural configuration and material properties of buildings, and their stress responses and behaviors are simulated. This method is complex, time-consuming, and should only be conducted by professionals. In the past, soft computing techniques have been applied in the construction field to predict the particular stress responses and behaviors; however, only a few studies have been made to predict specific properties of entire buildings. In this study, a weighted genetic programming system is developed to construct the relation models between the aseismic capacity of school buildings, and their basic design parameters. This is based on information from the database of school buildings, as well as information regarding the aseismic capacity of school buildings analyzed using complete nonlinear methods. This system can be further applied to predict the aseismic capacity of the school buildings.

Highlights

► We propose an application of weighted genetic programming on predict aseismic ability of real school buildings. ► We build prediction models to predict aseismic ability of real school buildings. ► The models have better accuracy than it proposed by ANNs and can be formed as a mathematic formulation. ► We select an attribute set which can represent the characteristic of school buildings.

Introduction

When large seismic forces impact a building, the stress behaviors generated are generally nonlinear. Hence, nonlinear structural analysis is the most common and reliable method for assessing the aseismic capacity of buildings. Aseismic capacity is defined as the capacity of a building to withstand destruction or collapse during a strong earthquake. The most suitable nonlinear analytical methods for assessing the aseismic capacity of buildings were developed by countries based on their geological situations, geographic environment, and other factors. In the United States, the aseismic capacity standard of reinforced-concrete buildings, namely, the Seismic Evaluation and Retrofit of Concrete Buildings (FEMA-273, 1997, Applied Technology Council (ATC), 1996), uses the capacity spectrum method to determine the aseismic capacity.

The capacity spectrum method is divided into two parts (Freeman, 1998). The first part is the demand spectrum, which is obtained from factors such as the intensity of the earthquake, soil profile, and seismic region coefficient. The second part is the capacity spectrum that describes the relationship between the force and the strain when buildings are impacted by seismic forces. The workflow diagram is shown in Fig. 1. The capacity spectrum of a building is obtained from the pushover analysis, which simulates the nonlinear behaviors of a structure subjected to lateral forces. Pushover analysis uses the two curves from the demand and capacity spectra to obtain the identified building performance points, as shown in Fig. 2. The collapse ground acceleration and aseismic ability index can also be obtained by analyzing the coordinates of the performance points.

However, the capacity spectrum method is not sufficient for estimating the aseismic ability of a real building. The pre-processing work needed for establishing the non-linear analysis model also takes a long time. A completed nonlinear structure model of a building must be constructed before the pushover analysis can be used. Due to the fact that ready-made models are unavailable, professional assessors often construct these models based on actual situations. The structural analysis software requires the basic framework of a building to be established; this is based on its geometrical dimensions. The blueprints of the buildings, when available, can be used as references. An assessor obtains any data that are missing for old buildings, and calculates the weight of the buildings based on the materials, and the number and weight of the equipment. These data are obtained for bearing structures such as columns and walls. Assessing the nonlinear behaviors of structural members (beams, columns, walls, etc.) from a building under stress is arguably the most important task. The relationship between the force and the strain is obtained through experiments, or analytical simulations. The numerical model for the pushover analysis is then finally constructed.

The procedures for the pushover analysis are as follows: (1) Apply an incrementally increasing external force on the structural model, as recommended by FEMA-440 (2004) and other standards; (2) Push the structure over towards one direction; (3) Conduct a structural analysis for each incremental increase in the external force; (4) Calculate the incremental stress and strain of each structural member, and add the values to the last analytical result to derive the response of each structural member; (5) Determine whether a structural member is damaged with cracks, or if the ultimate strength is reached; (6) Update the behavior of each structural member based on the extent of failure, such as change in stiffness or removal of damaged structural members from the model; (7) Repeat the analysis until the structure is unstable and collapses. The building capacity spectra are obtained by following the procedures of the pushover analysis.

The seismic demand spectrum is generated based on the environmental status quo, such as soil horizons of buildings, and regulations which define the mapping of the environment and demand spectrum. Buildings with a hard soil horizon have good aseismic capacities. Moreover, earthquakes often cause serious damage to buildings near fault lines. Hence, the distance between buildings and a fault line is also included in the reference; this is called the special effect of near-source earthquakes. With reference to the regulations, the demand spectrum suited to a building can be generated from data associated with the stratum and earthquake areas.

The capacity spectrum method transforms the format of the demand and capacity spectra, and determines the performance points of buildings. Physically, a performance point refers to the maximum strain and shear force that a building can withstand under a specific earthquake scale. When a structure has a nonlinear behavior due to seismic forces, its damping effect dissipates this energy. Hence, the demand curve is reduced based on the actual situation, which is shown in Fig. 2(d). As this is an iterative process, the demand curve may need to be continuously reduced, and the accuracy of the performance points verified. Once all the analysis is completed, the true performance points of buildings can be obtained. The performance point position can be converted into the AC (collapse ground acceleration) of the building, and the capacity demand ratio (CDR) is used to present the aseismic capacity. The equation is defined as (NCREE, 2009)CDR=AC/ADwhere AC is the minimum collapse ground acceleration of buildings obtained through the pushover analysis; AD is the ground acceleration based on the position of building, and the greatest earthquake that the building can withstand in a 475 year cycle according to reference standards; and CDR, if greater than 1, indicates that the building can withstand the greatest earthquake in a cycle of 475 years in this area. Upon completion of the above analyses, a detailed assessment of a building is now complete. The whole process takes one month and the steps involved are (1) measurement of the building's geometric dimensions, (2) testing of the building material properties, (3) creation of non-linear analysis model by technicians, (4) analysis of the building's aseismic ability using the capacity spectrum method. Thus it takes a long time to estimate a building's aseismic ability. Therefore, it is always difficult to obtain a detailed analysis of a building's aseismic ability, limiting the scope of applications that require such analysis. If simpler methods developed to obtain some reliable information about the aseismic capacity of buildings, the budget allocation and priority in building aseismic capacity reinforcement can be determined. This information also can be very useful during disasters. The aim of this study is to estimate the aseismic ability of existing school buildings, which is a highly complex and highly nonlinear problem. A few studies have used soft computing to model the aseismic ability of buildings. Most of them focused on prediction problems with low system complexity, e.g. predicting properties of materials. Due to the complexity involved, naïve GP is inadequate for constructing the relation model. Only artificial neural network based methods are able to construct models of acceptable quality, however they generate complex and hard-to-reuse models. In our paper, we used an improved GP method called WGP to estimate the aseismic ability of real school buildings. The results obtained were of acceptable quality. The relation model is expressed as an equation, which can be reused easily.

Most school buildings are similar in design, for example as an I-shape with external corridors and partitions. Hence, information such as complex and varied designs and dimensions can be changed into typical properties of a school building and thus, a prediction model can be constructed using heuristic computing technology, based on its overall features. In Taiwan, the National Center for Research on Earthquake Engineering (NCREE) has constructed a comprehensive database of aseismic information for school buildings. The data was collected from twenty thousand school buildings, including information on structure, design (e.g. beam column design), quantity of structure elements, design patterns, number of floors, and distribution of classrooms. The floor layout, usage of buildings, and number of occupants are also included. From this database, the aseismic capacities of roughly one thousand school buildings have been assessed by professionals. Due to the complexity of the detailed evaluation based on numerical model, these aseismic capabilities information for school buildings are not easy to be collected in a large number, thus are quite valuable. Based on this database, the current study builds a novel prediction model to determine the aseismic capacities of school buildings using data-mining technology.

It is relatively difficult to find exact linear relationships for these types of engineering problems, and computers cannot directly obtain analytical solutions. Therefore, soft computing is generally adopted where methods such as approximation and randomly searching in a high-dimensional space are used in order to obtain the optimum solution. Common methods include artificial neural network, support vector machine, and genetic algorithm (GA); the latter two being the most popular methods. Both of these methods have a long history, and can be applied to a wide range of fields, for example. Maru and Nagpal (2004) developed a model for estimating creep and shrinkage deflections in reinforced concrete frames using the artificial neural network. Gupta et al. (2006) used the artificial neural network to predict concrete intensity, and also to set up an expert system that enables the prediction model to be applied more easily. Sarıdemir (2009) predicted the compressive strength of concrete to which silica and metakaolin was added, using the artificial neural network. Topçu and Sarıdemir (2008) adopted the artificial neural network and formula ratio of rubberized concrete to predict the mobility of concrete (unit neutral fluidity). Ince (2004) applied the artificial neural network to the prediction of concrete fracture parameters. Tsai (2009) mainly used the hybrid high order neutral network to predict the shear strength of squat walls. Arslan (2010) created several hundred virtual RC buildings, used their parameters to create nonlinear analysis model, and performed pushover analysis to estimate their aseismic ability. They then used an artificial neural network to build the aseismic ability prediction model. Our study instead uses data from real buildings. However, the use of artificial neural network has always been controversial because the network core is a black box. As a result, the output relational model cannot be further processed. Likewise, the results derived from many other software computing methods cannot be easily converted into mathematical formulas. Genetic programming (GP), which was developed from GA, was first introduced in 1992 (Koza, 1992). The strongest feature of GP is the capability to convert the output model into a mathematical formula. This guarantees subsequent analysis and application to be much easier, and makes up for the shortcoming of the artificial neutral network black box (i.e. inability to convert the output into a mathematical formula).

The WGP method used in this paper has also been used in related applications (Tsai, 2011, Tsai and Lin, 2011). The topic of this paper, i.e. the estimation of the aseismic ability of real school buildings is a highly complex problem. The relationship between the aseismic ability of school buildings and the design parameters is very non-linear. It is also not easy to obtain all the required data. Since all these factors make this a challenging topic, we focus on dealing with this special prediction problem. In our previous study (Kao et al., 2011), we dealt with the same problem of estimating the aseismic ability of school buildings using design parameters. The modeling methods used in the previous study was Artificial Neural Networks and the Generalized Linear Model. In that study, we built an aseismic ability prediction model that provided results of acceptable accuracy. However, using such a model is inconvenient as it is simpler to apply GP to optimize the operation tree. Due to the complexity of the aseismic ability estimation problem, ordinary GP optimization cannot build a usable prediction model. By implementing WGP with variable weights, we are able to build an easy-to-use model with similar accuracy to artificial neural network models.

The existing applications of soft computing on behavioral predictions of building structures mostly are at the levels of building materials and building components. Current results on the predictions of overall structural behaviors by soft computing are limited in relatively simple behaviors, such as long-term creep. Compared to building materials and building components, the amount and type of factors that affect the seismic behavior of an overall structure are numerous. Besides, the seismic behavior of an overall structure possesses highly nonlinearity, thus is difficult to predict. In addition, structural seismic assessment information, which requires professional analysis using numerical model, would not be easy to collect in a large number. However, establish prediction model for aseismic abilities of school buildings could be feasible, because regularity does exist in the structural format of typical school building. Supported by the seismic assessment data of about one thousand school buildings collected by a nationwide project in Taiwan, this study proposes data processing model base on the expertise of structural engineering, and then establishes aseismic prediction model with the application of soft computing method, for typical school buildings. It should be a unique, challenging and contributing application case of soft computing. Based on the database of school buildings and their aseismic capacity analyzed using the complete nonlinear method, a GP system is developed in order to construct the relation model between the aseismic capacity of the school buildings and their basic design parameters. This system can be further applied to predict the aseismic capacity of the school buildings.

Section snippets

School building aseismic ability prediction

The NCREE (2005) in Taiwan has constructed a School Building Aseismic Database in response to the needs of aseismic studies of school buildings. It incorporates a range of information, including geographical locations, structural form, and geometric dimensions. Storing massive volumes of geometric and design information for different buildings in a database was previously deemed difficult because buildings have varying forms, and cannot be expressed using a limited number of symbolic

Genetic programming system

The genetic programming system developed in this study is composed of two modes: the long-history genetic programming (GP), and the weighted genetic programming (WGP). GP is based on the method proposed by Koza (1992), and the original concept is derived from the GA. Conversely, WGP is proposed by Tsai (2011), and adds the idea of a weight balance to the GP. The latter not only enables the equation constructed by the system to vary freely, but also reveals the importance of different inputs in

Genetic programming system for school building aseismic ability prediction

In addition to basic GP, this study also adopts WGP to build the model. As well as the analysis of the relational model, data pre-processing is also important because its pattern and quality affect reliability of the final model. This section describes this in detail.

Conclusions

In order to estimate the aseismic ability of a building, we need to obtained detailed information about its geometric dimensions, the properties of materials used, etc. and we may need to perform sampling and other experiments to obtain certain information e.g. the properties of materials used. Based on this information, a structural model of the building has to be constructed and then non-linear pushover analysis is used to perform estimation. This process is time-consuming, and technicians

References (27)

  • FEMA-273, 1997. NEHRP Guidelines for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency....
  • FEMA-440, 2004. Improvement of Nonlinear Static Seismic Analysis Procedures. Federal Emergency Management Agency....
  • Freeman, S.A., 1998. Development and Use of Capacity Spectrum Method. The 6th US National Conference on Earthquake...
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