1Department of Civil and Environmental Engineering, Incheon National University, Incheon 22012, Republic of Korea
2Incheon Disaster Prevention Research Center, Incheon National University, Incheon 22012, Republic of Korea
3Department of Public Works and Civil Engineering, Mansoura University, Mansoura 35516, Egypt
Received 15 November 2016; Revised 14 February 2017; Accepted 14 February 2017; Published 2 March 2017
Copyright © 2017 Mosbeh R. Kaloop and Jong Wan Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Modeling response of structures under seismic loads is an important factor in Civil Engineering as it crucially affects the design and management of structures, especially for the high-risk areas. In this study, novel applications of advanced soft computing techniques are utilized for predicting the behavior of centrically braced frame (CBF) buildings with lead-rubber bearing (LRB) isolation system under ground motion effects. These techniques include least square support vector machine (LSSVM), wavelet neural networks (WNN), and adaptive neurofuzzy inference system (ANFIS) along with wavelet denoising. The simulation of a 2D frame model and eight ground motions are considered in this study to evaluate the prediction models. The comparison results indicate that the least square support vector machine is superior to other techniques in estimating the behavior of smart structures.
Nowadays, smart structures are used widely to reduce and control the dynamic loads effects and structures response, respectively [1, 2]. Structures built on lead-rubber bearing (LRB) isolations are ones of high effectiveness of structure control system [1–3], but the application of this system is still limited to use in real construction cases. Moreover, the LRB is more effective in controlling steel and reinforced concrete buildings under seismic loads [1, 4]. However, responses of structures with base isolation under seismic loads should be modeled to predict their behavior under the changes of seismic loads effects. Despite the responses of passive and active controller structures being modeled before [5, 6], this study presents the modeling prediction systems for a building with base isolation as a first application for this type of smart structures. Therefore, the response prediction of structures with base isolation is the main aim of this study.
The dynamic response of structures with base isolation is studied in time and frequency domains previously for the steel and reinforced concrete structures [2, 7]. In addition, the design model of LRB is presented in , and the advantages and disadvantages of this system are presented in [2, 8]. The LRB model used in this study is designed based on a maximum vertical load of 15630 KN and the allowable lateral displacement of 400 mm . In general, as any controlled structure, the response of structures under seismic loads contains three components of movements: static, semistatic, and dynamic [9–11]. The dynamic response of structures is highly impacted in the seismic time effects and the periodically dynamic effects are affected by collapse of structures, so this study is focused on the dynamic behavior of structures. A nonlinear component of steel structure is simulated to study the behavior of centrically braced frame (CBF) steel building subjected to earthquake loading by using the OpenSees . Moreover, this study is limited for the simulation of full scale control system.
Applications of soft computing modeling of the response of controlled structures are still limited, and the CBF with LRB isolation system is not previously studied. Therefore, this study aims to develop a prediction model (PM) that can be used to detect the behavior of these types of structures. The advanced PMs are support vector machine (SVM), neural networks (NN), and neurofuzzy (NF) [5, 6, 13–15]. The wavelet is linked with NN and NF to improve the responses of these techniques [6, 16]. The NN and NF methods are used for modeling the performance of the controller structures; however there is no study implementing the SVM in predicting the behavior of controller structures. Furthermore, the model design is divided into two models that are input-output and output-only models. In this study, the input-output system is utilized . The input parameters (seismic effects and response of structures) are evaluated previously by [5, 6, 14] and it is found that the seismic loads with time delay response output are good parameters that can be used to predict the nonlinear behavior of controlled structures. One and two time delays for the response of controlled structures are studied and it is found that the two-time delayed input parameters are more influential on the performance of model [6, 14, 18]. In this study, novel PMs are investigated. The two-delayed responses of structure are considered with seismic loads effects and the wavelet denoising is applied.
Finally, this study aims to develop new models that can be used to detect the behavior of controlled structures using LRB system. Three advanced soft computing techniques are utilized. A simulation building is designed using OpenSees program and subjected to nonlinear dynamic loads based on Los Anglos (LA) ground motion (GM) to predict the high response of the building. This paper is organized as follows: Section 2 discusses the methodology and evaluation theories such as the strategy used to investigate the performance of the identification models. Section 3 contains the simulation and GM’s process and collection data, as well as the measurements preanalysis. The modeling results and discussions for the training and testing stages are given in Section 4. The conclusions are summarized in Section 5.
2. Models Overview and Design
In this study, three advanced models are used after input data filtration using discrete wavelet transforms (DWT) to remove the noise. The Daubechies wavelet for low frequency decomposition utilized to denoise the response data which is used as inputs to the models. To compare the results with previous studies [5, 6, 15], two levels of DWT are applied to train the responses of smart structures. The DWT is described in [6, 14]; however, this section is dedicated to summarize the models used.
The least square support vector machine (LSSVM), wavelet neural networks (WNN), and adaptive neurofuzzy inference system (ANFIS) are highly advanced models that can be used to detect the response of structures, environmental effects, and so forth [13, 14, 16, 19]. Based on previous studies [5, 6, 14, 15, 18], time-delayed models are good to predict the behavior of smart structures. It has been reported that the two-time delayed models are better than one-time delayed . Accordingly, in this study a two-time delayed model is applied.
2.1. Least Square Support Vector Machine (LSSVM)
Suykens and Vandewalle  proposed a modified version of support vector machine (SVM) classifiers, Least Squares SVM (LSSVM) classifiers. The LSSVM model uses regression technique based on statistical learning theory . It considers a Gaussian process and regularization network to design a relation between the input and output data [13, 20, 21]. Consider a given training of data points with input () and output () data, where and are and one-dimensional vectors space for the input and output data, respectively. In this study, the input parameters are the seismic loads and time delay of the structures response and the output is the prediction of the structure response. The LSSVM models for the nonlinear modeling take the following form:where is the is a nonlinear map function between the input and output data. is an adjustable weight vector, ; is a scalar threshold, . To extract the map function estimation, the minimization principal is used firstly by penalizing a regression error as follows [22, 23]: such thatwhere is the regularization parameter and is the model errors.
Secondly, the Lagrange multipliers method is applied to solve the optimization problem in (2) as follows :where is the Lagrange multiplier. By solving the above optimization [20, 21], the prediction values of the response of structure () can be presented as follows:where is the radial basis function (RBF).
The RBF is used in this study is given bywhere is the width of RBF.
2.2. Wavelet Neural Networks (WNN)
The wavelet neural network (WNN) or WAVNet is used to detect the dynamic behavior of systems . The architecture for a WNN is the same as for a NN with wavelet neuron [16, 25]. A WNN is a model that connects the NN with wavelet decomposition that leads to a nonlinear wavelet function. In this study, the structure behavior prediction model is designed using WNN model with an output () computed as follows: where ; ; and are coefficient, dilation, and translation variables, respectively; are the input data; and is a wavelet function. The WNN consists of an input vectors, layer of weighted wavelets, and output vector. The WNN parameters can be calculated by a backpropagation-learning method . The WNN training objective is to minimize the output error of the model.
The selection of wavelet function depends on the application used [16, 25]. There are many wavelet functions that can be used. In this study, the Mexican hat wavelet function is used to implement the proposed nonlinear smart structure behavior model. The wavelet function for any variable () can be presented as follows: where is the model order. The Mexican hat wavelet function is successfully applied in WNN modeling by many authors to predict different cases of structures behavior and modeling the environmental effects [16, 19, 24, 25]; however it is selected in this study.
2.3. Adaptive Neurofuzzy Inference System (ANFIS)
The adaptive neurofuzzy inference system (ANFIS) is used previously to predict the behavior of smart structures and it was found that this method is suitable to identify the displacement and acceleration measurement of structures response with passive or active controller systems [5, 6, 18]. The ANFIS model is introduced by Jang , and it has been applied on different case studies [14, 15, 27, 28]. The process of ANFIS model is presented in . The hybrid learning rule is used to estimate the ANFIS parameters based on back propagation gradient and least square methods . The Mamdani and Sugeno are the two approaches for fuzzy inference system . The differences between the two approaches arise from the consequent part where Mamdani’s approach uses fuzzy membership functions, while linear or constant functions are used in Sugeno’s approach. The neurofuzzy model used in this study implements the Sugeno’s fuzzy approach with seismic and time delay for the response of structure as input variables and response of structure as output variable.
2.4. Models Process and Evaluation
Based on the previous studies [5, 14, 16, 18, 21, 25, 27, 29, 30], the three models can be used to predict the nonlinear behavior of structures. In addition, it is worth noting that no studies have implemented the three models in predicting the behavior of smart structures based on base isolation system. Herein, the proposed model for the behavior of the simulation of smart building (centrically braced frame (CBF) steel building with LRB isolator system) was processed over five stages as shown in Figure 1. The process of these five stages was performed through design of the simulation model and response measurement under GM, denoising of the GM signal and response measurements using wavelet denoising, prediction stage, comparison and selection of the best model that can be used in our case, and validation and evaluation of the model selection for the structure behavior under different GM cases. In the first stage, the simulation design model is introduced, evaluated, and developed by Incheon Disaster Prevention Research Center (IDPRC) (see [1, 31–33]) and the response of building is obtained by OpenSees code design; in addition, the real GM is considered in this stage (see Section 3). In the second and third stages, a novel prediction modeling was developed with wavelet denoising for the behavior of CBF steel building based on LRB isolator system. Then in the fourth stages, a comparison was made between the developed models for prediction of the structure behavior. Finally, the selected model is evaluated using different cases of GM’s (see Section 3).
Figure 1: Models process.
In the comparison and validation stages, five statistical evaluation criteria are used to assess the models performances; () is the correlation coefficient ():where and denote the measured and predicted structure behavior, respectively, is the number of time steps, and and represent the mean of measured and predicted values, respectively. provides information for linear dependence between measured and predicted values. Therefore, and are mean absolute error (MAE) and root mean-square error (RMSE), respectively; and measure a linear scouring rule and describes the average magnitude of the errors by giving more weight to large errors to evaluate the performance of the models.
Because of the design and construction requirements, the nuclear structures need to maintain the structural integrity under both design state and extreme earthquake shaking. The base-isolation technology can significantly reduce the damages of structures under extreme earthquake events, and effectively protect the safeties of structures and internal equipment. This study proposes a base-isolation design for the AP1000 nuclear shield building on considering the performance requirements of the seismic isolation systems and devices of shield building. The seismic responses of isolated and nonisolated shield buildings subjected to design basis earthquake (DBE) shaking and beyond-design basis earthquake (BDBE) shaking are analyzed, and three different strategies for controlling the displacements subjected to BDBE shaking are performed. By comparing with nonisolated shield buildings, the floor acceleration spectra of isolated shield buildings, relative displacement, and base shear force are significantly reduced in high-frequency region. The results demonstrate that the base-isolation technology is an effective approach to maintain the structural integrity which subjected to both DBE and BDBE shaking. A displacement control design for isolation layers subjected to BDBE shaking, which adopts fluid dampers for controlling the horizontal displacement of isolation layer is developed. The effectiveness of this simple method is verified through numerical analysis.