Elsevier

Expert Systems with Applications

Volume 110, 15 November 2018, Pages 335-351
Expert Systems with Applications

A hybrid computational approach for seismic energy demand prediction

https://doi.org/10.1016/j.eswa.2018.06.009Get rights and content

Highlights

  • An evolutionary method is proposed to formulate the energy-based engineering demand parameters.

  • A multi-objective genetic programming is combined with linear regression in this framework.

  • Both structural and earthquake characteristics are included in the proposed prediction models.

  • For each problem, one model with four different coefficient sets is proposed for various soil types.

  • A comparative study is performed to compare the model performance with other well-known models.

Abstract

In this paper, a hybrid genetic programming (GP) with multiple genes is implemented for developing prediction models of spectral energy demands. A multi-objective strategy is used for maximizing the accuracy and minimizing the complexity of the models. Both structural properties and earthquake characteristics are considered in prediction models of four demand parameters. Here, the earthquake records are classified based on soil type assuming that different soil classes have linear relationships in terms of GP genes. Therefore, linear regression analysis is used to connect genes for different soil types, which results in a total of sixteen prediction models. The accuracy and effectiveness of these models were assessed using different performance metrics and their performance was compared with several other models. The results indicate that not only the proposed models are simple, but also they outperform other spectral energy demand models proposed in the literature.

Introduction

The approaches currently used for the seismic analysis and design of structures could be improved through considering appropriate engineering demand parameters that would represent the characteristics of a structure and the design earthquake. In current approaches, either the structural members are designed based on satisfying the balance between the force demand and the corresponding strength supply while providing an adequate level of ductility (based on e.g. ANSI/AISC, 2010), or based on the concept whether they are force- or deformation-controlled (based on e.g. FEMA-356, 2000). Such approaches disregard the frequency content and duration of earthquake ground motion, as well as the velocity response and hysteretic behavior (Gupta, 1990). The importance of considering these factors lies in evidences suggesting that, for instance, dissipated hysteretic energy due to repeated inelastic excursions could result in a certain amount of seismic damage (Fajfar & Vidic, 1994). In fact, in addition to the force and deformation, the energy demand is of great importance in capturing the mentioned seismic factors as the inelastic behavior is expected to occur due to the design and maximum earthquakes. Housner (1956) was first to introduce these factors through defining the energy concept. This concept requires that the energy dissipation capacity be more than the input energy demand.

Both structural properties and earthquake characteristics affect the seismic energy demand. Determining the spectral values of energy demand is beneficial due to its connection to the amount of structural damage (Fajfar and Vidic, 1994, Gharehbaghi, 2018). The design codes have not explicitly implemented the energy demand parameter in predicting seismic demands yet. Moreover, the priority of the energy-based design approach compared with the conventional strength-based design approach needs further studies. Although, previous studies (e.g. Akiyama, 1985; Bertero & Uang, 1988; Decanini & Mollaioli, 2001; Fajfar & Vidic, 1994; Housner, 1956; Kalkan & Kunnath, 2007; Manfredi, 2001) have stipulated that the seismic energy parameters are of great importance in seismic design of structures. It was shown that the hystertic energy demand is directly connected to the structural damage (Akiyama, 1985, Benavent-Climent et al., 2010, Bertero and Uang, 1988, Decanini and Mollaioli, 2001, Fajfar and Vidic, 1994, Gharehbaghi, 2018, Kalkan and Kunnath, 2007, Manfredi, 2001). After more than two decades that the Housner's proposal was almost neglected, it was received considerable attention among researchers (Akiyama, 1985, Kuwamura and Galambos, 1989), and became the key issue of a conference held in Bled city of Slovenia (Fajfar & Krawinkler, 1992). It was recognized that input energy and hysteretic energy are the good indicators of ground motion and have a correlation with the structural damage, and the quantity related to cumulative damage is the hysteretic energy (Bertero and Uang, 1988, Decanini and Mollaioli, 2001, Fajfar and Vidic, 1994). Most recently, Deniz, Song, and Hajjar (2017) also found that the most appropriate and reliable intensity measure for the seismic fragility analysis of buildings is the seismic energy demand.

Estimation of input and hysteretic energy demands using mathematical models could be considered as one of the important steps aligned with the extension of the energy-based seismic analysis and design. As previously mentioned, both structural and earthquake characteristics need to be accounted for the issue. Some earthquake characteristics such as soil type, earthquake magnitude, peak ground acceleration (PGA), peak ground velocity (PGV), cumulative energy index, fault type, distance from the hypocenter, were used by researchers in determining the energy spectra (e.g. Fajfar, Vidic, & Fischinger, 1989; Khashaee, 2004; Sucuoğlu & Nurtuğ, 1995; Uang & Bertero, 1988; Uang & Bertero, 1990; Zahra & Hall, 1984). In addition to the earthquake characteristics, ductility ratio, damping ratio, and hysteretic behavior model (e.g. elastic-perfectly plastic, bilinear, pinching, Takeda, and Clough models) were the influential structural properties involved in the estimation of seismic energy demand spectra (e.g. Decanini & Mollaioli, 2001; Sucuoğlu and Nurtuğ, 1995, Benavent-Climent et al., 2010). Several works have been carried out on the estimation of the seismic energy demand parameters. Housner (1956) presented a model to determine input energy based on the spectral velocity of single-degree-of-freedom (SDOF) system. Kuwamura and Galambos (1989) presented energy demand spectra considering the soil type and dominant period of the earthquake. Chou and Uang (2000) estimated absorbed energy for an inelastic system by using an attenuation relation. They used nonlinear regression analysis considering both structural and earthquake variables. Manfredi (2001) proposed simple/efficient mathematical models to estimate input and hysteretic energy spectra. A dimensionless seismic index that is a function of PGA, PGV and cumulative energy was proposed to estimate the seismic energy spectra. Although the estimation models were simple and effective, the effect of soil behavior was not considered, and the number of earthquake ground motions was rather limited. Decanini and Mollaioli (2001) proposed the formulation of elastic seismic energy spectra. They also presented a comprehensive study to propose the design inelastic energy spectra by introducing the response modification factor for the input energy. Several structural variables (e.g. ductility ratio and hysteretic behavior) and earthquake characteristics such as soil type, source-to-site distance, and earthquake magnitude were considered in the proposed spectra. Arroyo and Ordaz (2007) estimated the hysteretic energy demand spectra from elastic response parameters in accordance with the earthquake events recorded in Mexico City. Their mathematical models were a function of pseudo-acceleration, velocity and displacement spectra. Elastic design input energy spectra based on Iranian earthquakes were also presented by Amiri, Darzi, and Amiri (2008). Recently, Dindar, Yalçın, Yüksel, Özkaynak, and Büyüköztürke (2015) proposed two regression-based simple mathematical models to estimate the input and hysteretic energy spectra. A database of earthquake ground motion records composed of near- and far-fault ones, PGA, soil types, earthquake magnitude, ductility ratio, and hysteretic behavior model was included in the proposed models. Using the regression analysis, Quinde, Reinoso, and Terán-Gilmore (2016) also proposed mathematical models to estimate the seismic energy spectra of inelastic systems located on the soft soil for Mexico City. They captured the effect of ductility ratio of inelastic systems and dominant period of the probable earthquakes on the presented models. More recently, Zhai et al. (2016) proposed an expression to account for the effect of after-shock on the input energy spectra using an equivalent velocity. Alıcı and Sucuoğlu (2016) carried out a regression analysis to estimate inelastic input energy spectrum. The prediction equations for the input energy spectra were expressed in terms of an equivalent velocity. Some crucial earthquake characteristics including soil type, epicentral distance, moment magnitude, and the fault type were considered in the proposed models. All the previously mentioned works use conventional regression methods to estimate their energy parameters of interest.

Based on the capability of soft computing approaches and their recent advances, it is worthwhile to use such efficient approaches for seismic demand prediction. Computational complexity of the conventional methods and their limitations has made soft computing techniques, such as evolutionary algorithms, artificial neural networks, support vector machines, and fuzzy logic, popular for solving complex engineering problems. A common application of these tools is in predictive analysis for modeling the nonlinear dependency of the input parameters to the output value(s) where the conventional approaches (e.g. regression analysis) fail or perform poorly (Gandomi and Roke, 2015, Khan et al., 2003). Despite the success of artificial neural networks (ANNs) in prediction, they are inappropriate to develop practical intelligible equations. In addition to ANNs, support vector machines (SVMs) are another primary class of soft computing methods used to discover patterns and approximate relationships when large quantities of data is available. Although both ANNs and SVMs have received significant attention (e.g. Gharehbaghi and Khatibinia, 2015, Gholizadeh and Salajegheh, 2009, Khatibinia et al., 2015, Papadopoulos et al., 2012, Salajegheh and Heidari, 2005, Yazdani et al., 2017), they require a pre-defined and initial structure for the equation and network architecture to be determined by the user. Genetic programming (GP), a learning algorithm originated from genetic algorithms, is another well-known and successful technique for developing nonlinear mathematical models for the complex problems. GP and its variants have been effectively used for solving various problems in civil engineering (e.g. Kayadelen et al., 2009, Alavi et al., 2011, Cabalar and Cevik, 2011, Gandomi et al., 2012, Mirzahosseini et al., 2011, Vardhan et al., 2016). Several variants of GP have been proposed in the literature, such as gene expression programming (Ferreira, 2006) and multi-stage genetic programming (Gandomi & Alavi, 2011). One of the robust variants of GP is multi-gene genetic programming (MGGP) that adds the capability of conventional regression to the standard GP ability in parameter estimation. The effectiveness of MGGP has been proved in the works reported by Babanajad et al. (2013), Gandomi and Alavi, 2012a, Gandomi and Alavi, 2012b), Gandomi, Roke, and Sett (2013), Gandomi, Sajedi, Kiani, and Huang (2016).

Structural and earthquake engineering has benefited from the soft computing techniques in different applications. For instance, ANNs and SVMs have been widely used for risk assessment, seismic response prediction, control and health monitoring (Tsompanakis & Topping, 2011). In this paper, MOGP is used for predicting the seismic energy demand spectra considering both typical structural and earthquake characteristics. For this purpose, eighteen set of the SDOF systems with the structural properties of different hardening ratios of bilinear hysteretic behavior model, damping ratios, and ductility ratios are used to determine the energy demand spectra mentioned. Also, four different sets of earthquake ground motion records based on their soil types (soft, firm, stiff and rock) with the source-to-site distances of more than 17.5 km and the magnitudes of greater than 5.5 were used. It was assumed that the different soil classes have linear relationships in terms of GP genes which help to find one equation with different coefficients for different soil types. The records were scaled to two PGA levels 0.5 g and 1.0 g. Finally, four mathematical models corresponding to the four engineering demand parameters (EDPs) of spectral input and hysteretic energy, spectral hysteretic to input energy ratio, and spectral energy modification factor, are proposed using MOGP. Then, the effectiveness of the models is revealed using the performance metrics compared with those of available in the literature.

In this study, Section 2 describes the seismic energy concept and its formulation. Also this section introduces the seismic energy based EDPs which can be useful in seismic design of inelastic structures. Section 3 expresses a hybrid computational approach based on genetic programming used as a predictive tool herein. Section 4 describes a framework for prediction of the EDPs. A set of mathematical models are proposed and their accuracy are examined using some performance metrics in Section 5. Finally, the developed models are discussed and compared with some other models proposed in the literature.

Section snippets

Seismic energy concept and formulation

Housner (1956) first proposed the idea of the energy-based seismic design approach. When ground motion transmits energy into a structure, some of the energy is dissipated through the damping and inelastic behavior. The remained energy of the structure is stored in the form of kinetic energy and elastic strain energy. Housner stipulated that the energy supply should be more than the energy demand during an earthquake in the form of this principle that energy supply < energy demand for

Genetic programming

There are two groups of models which can be used for modeling the complex nonlinear engineering systems: phenomenological and behavioral (Gandomi et al., 2016). Phenomenological models need a predefined structure obtained from the physical laws requiring a previous understanding about the system. Concerning the complex systems, sometimes it is hard to find such models. Unlike the phenomenological models, behavioral models can be simply generated by finding a reasonable approximate relation

Preparing exact data

Since the inelastic responses of an SDOF system highly depend on both structural and earthquake ground motion variables, the most influential ones are contributed in predicting spectral seismic energy demand. The input variables are described in the next subsections in detail.

Results and discussion

Using MOGP, all EDPs (EDP1, EDP2, EDP3, and EDP4) were predicted, and their optimal mathematical models (formulations) were determined. Four cases (S1–S4) based on different soil types of the earthquake records were considered in the prediction. Although it is quite possible that the obtained model formulations be different for different soil types, it is more practical to develop a unique mathematical model for an EDP with different coefficients. Therefore, in this paper, the complete database

Summary and conclusion

Formulation of the seismic energy demand of inelastic SDOF systems is one of the main steps of extending the energy-based seismic analysis and design approach. A comprehensive study was carried out to propose accurate and simple mathematical models for predicting seismic energy demand spectra. Multi-objective genetic programming (MOGP) was employed to formulate some main energy-based EDPs, i.e., spectral input and hysteretic energy, spectral hysteretic to input energy ratio, and spectral energy

References (65)

  • S. Gholizadeh et al.

    Optimal design of structures for time history loading by swarm intelligence and an advanced metamodel

    Computer Methods in Applied Mechanics and Engineering

    (2009)
  • C. Kayadelen et al.

    Modeling of the angle of shearing resistance of soils using soft computing systems

    Expert Systems with Applications

    (2009)
  • S.A. Khan et al.

    Sensor calibration and compensation using artificial neural network

    ISA Transactions

    (2003)
  • M.R. Mirzahosseini et al.

    Permanent deformation analysis of asphalt mixtures using soft computing techniques

    Expert Systems with Applications

    (2011)
  • V. Papadopoulos et al.

    Accelerated subset simulation with neural networks for reliability analysis

    Computer Methods in Applied Mechanics and Engineering

    (2012)
  • P. Quinde et al.

    Inelastic seismic energy spectra for soft soils: Application to Mexico city

    Soil Dynamics and Earthquake Engineering

    (2016)
  • S. Sajjadi et al.

    Extreme learning machine for prediction of heat load in district heating systems

    Energy and Buildings

    (2016)
  • H. Vardhan et al.

    Measurement of stress dependent permeability of unsaturated clay

    Measurement

    (2016)
  • H. Akiyama

    Earthquake-resistant limit-state design for buildings

    (1985)
  • F.S. Alıcı et al.

    Prediction of input energy spectrum: Attenuation models and velocity spectrum scaling

    Earthquake Engineering and Structural Dynamics

    (2016)
  • G.G. Amiri et al.

    Design elastic input energy spectra based on Iranian earthquakes

    Canadian Journal of Civil Engineering

    (2008)
  • Specification for structural steel buildings

    (2010)
  • D. Arroyo et al.

    On the estimation of hysteretic energy demands for SDOF systems

    Earthquake Engineering and Structural Dynamics

    (2007)
  • A. Bakhshi et al.

    Energy-based design spectra for seismic resistant design

    Proceedings of the 7th international conference on civil eng., Tehran, Iran

    (2006)
  • V.V. Bertero et al.

    Implications of recorded earthquake ground motions on seismic design of building structures

    (1988)
  • A.K. Chopra

    Dynamics of structures: Theory and applications to earthquake engineering

    (2012)
  • ChouC.C. et al.

    Establishing absorbed energy spectra – an attenuation approach

    Earthquake Engineering and Structural Dynamics

    (2000)
  • K. Deb et al.

    A fast and elitist multi objective genetic algorithm: NSGA-II

    IEEE Transactions on Evolutionary Computation

    (2002)
  • A.A. Dindar et al.

    Development of earthquake energy demand spectra

    Earthquake Spectra

    (2015)
  • P. Fajfar et al.

    Consistent inelastic design spectra: Hysteretic and input energy

    Earthquake Engineering and Structural Dynamics

    (1994)
  • P. Fajfar et al.

    Seismic demand in medium- and long-period structures

    Earthquake Engineering and Structural Dynamics

    (1989)
  • P. Fajfar et al.

    Nonlinear seismic analysis and design of reinforced concrete buildings

    (1992)
  • Cited by (13)

    • Seismic fragility analysis of RC box-girder bridges based on symbolic regression method

      2022, Structures
      Citation Excerpt :

      Step 3 – Creation of the new population: A new population is formed using elitism, selection, mutation, and crossover operators. These operators have been explained in previous studies ([32,35]). Step 4 – Evaluation of the termination criteria: steps 2 and 3 are repeated until termination conditions are met.

    • Prediction of seismic damage spectra using computational intelligence methods

      2021, Computers and Structures
      Citation Excerpt :

      A detailed description of the process can be found in [58]. It is worth noting that two sources of complexity affect the accuracy of the models: Firstly, the behavior of the structures under consideration as they experience inelastic deformations with high nonlinearity, and secondly, the nature of earthquake excitations includes some effective characteristics, such as frequency content, which make a structure experience different cyclic excursions associated with complex behavior [25]. The parameter settings used for the MOGP are listed in Table 3.

    • Estimation of inelastic seismic input energy

      2021, Soil Dynamics and Earthquake Engineering
      Citation Excerpt :

      In this respect, input energy estimation is subjected to investigation in many studies. It is found that be EI spectrum is a function of ground motion features as well as structural properties [3–5,32]. Summarizing the previous attempts, several approaches can be mentioned.

    • Hysteretic energy demand for self-centering SDOF systems

      2019, Soil Dynamics and Earthquake Engineering
      Citation Excerpt :

      Previous studies have proposed various methodologies for input energy spectra and EH/EI spectra. They have indicated that structural characteristics play an important role in this respect [3,4,8–10,23–41]. However, few of these studies consider the influential parameters comprehensively.

    View all citing articles on Scopus
    View full text