Predicting the Fundamental Period of Light-Frame Wooden Buildings by Employing Bat Algorithm-Based Artificial Neural Network

Introduction And Background

Reliable seismic analysis and design of a structure require precise knowledge about the fundamental period of the building, among other dynamic characteristics. Building codes around the world provide simplified formulas for estimating the fundamental periods of buildings constructed with different materials, structural systems and geometries (Panthi et al., 2021). The National Building Code of Canada (NBCC) provides empirical formulas to calculate the fundamental lateral period of vibration of different structural systems, such as shear walls, steel moment-resisting frames, reinforced concrete moment resisting frames, and steel braced frames (NRC/IRC, 2015). The formula for shear walls can also be applied to what is termed in the code as “other structures” and it is only a function of building height above the base, h_n, as presented in Eq. (1).

Proper estimates of the fundamental period is imperative in seismic analysis and design as it is the basis for the calculation of the design base shear and any error in estimating the fundamental period could have significant consequences in over- or under- estimating the seismic forces, leading to an overly conservative or unsafe design. An alternative method for calculating the building period, which is permitted by the NBCC is using numerical methods, such as Rayleigh’s method or eigenvalue analysis. The drawback of using such methods is their association with uncertainty in input parameters, especially pertaining to the stiffness of the structural system, as well as some limitations related to lower bound limits imposed on the base shear.

It has been well recognized that considering the building height as the only variable describing the dynamic characteristics of a building and to approximate the period based only on the height is not sufficient. Several investigations have been conducted to evaluate the adequacy of these equations on concrete, steel and wooden buildings, and several authors have suggested improved equations. The subsequent section provides the state-of-the-art knowledge on building periods established based on field measurements and using finite element analysis methods. In the present study, an ANN model employing the Bat Algorithm is developed to provide a better prediction of the fundamental period of light-frame wooden buildings including several additional parameters to the building height. While similar approaches can be found in the literature, the methodologies used in these studies are limited to mainly concrete structures (Plevris & Solorzano, 2021; Solorzano & Plevris, 2021). In the current study, the model exhibiting the best performance is selected from a set of examined ANN models and subsequently compared with other models, such as ANN-Particle Swarm Optimization, Nonlinear regression, the NBCC (NRC/IRC, 2015), as well as equations derived from the Eureqa software (Dubčáková, 2011; Schmidt & Lipson, 2009).

Literature Review

The majority of the available literature on experimental studies with aim to investigate the fundamental period of existing buildings have been focused on concrete structures, while limited studies are available for steel and wooden buildings. The proposed equations have primarily depended on the seismic force resisting system (SFRS) typology, material types which relates to the building mass, and overall building geometry. Farsi and Bard (Farsi & Bard, 2004), Lagomarsino (Lagomarsino, 1993) and Gilles (Gilles, 2011) performed ambient vibration tests (AVT) on several reinforced concrete shear wall buildings and suggested improved relationships for estimating the building periods required for the calculation of the base shear in seismic design. The proposed equations were limited to linear expressions with the height of the buildings. The period equations suggested by other authors for reinforced concrete shear wall buildings, such as Goel and Chopra (Goel Rakesh & Chopra Anil, 1997), Lee et al. (Lee et al., 2000), Morales (Dominguez Morales, 2000) provided expressions with multiple variables and were not limited to building height.