Model updating for timber-framed construction using the full-scale test

Highlights

• Failure modes of wood-framed construction under cyclic loading.

• The CKF is employed to update the finite element.

• The lateral performance of wood-framed construction.

Abstract

An accurate and reliable numerical model is vital for the structural design and performance assessment of timber-framed construction (TFC). This study executed a full-scale TFC under cyclic loading to investigate the lateral-force resisting performance. The experimental results evidenced that the adjacent sheathing panels had a relative displacement, as well as the uplift of studs. The timber shear wall itself had no damage, and nails exhibited four typical failure modes. A numerical model whose nonlinearity is governed by the spring element is created. This simplified model can capture the stiffness and strength degradation, as well as the pinching effect. To update the simplified model, the cubature Kalman filter (CKF) is proposed that is capable of characterizing the model uncertainties accounting for the modeling error. The updated result indicates the test response is enclosed by the predicted curves generated by all the cubature points. The updated model is also evaluated in term of the mechanical properties, where the ultimate load, yield load and the maximum load obtained from the updated model are consistent with the test results. The calibrated model has a good agreement with the test result, providing an efficient and accurate analysis for the structural performance under various loading conditions. The proposed CKF method serves a useful model-updating technique to warrant the reliability of numerical models.

Introduction

Timber-framed construction (TFC) is a type of residential construction commonly used in North America because of its aesthetics and constructability. In recent earthquakes, however, this type of structures suffered from severe and quantifiable property damages [1], [2]. These unexpected destructions drove some researchers to study the behavior of TFC. Filiatrault [3] analyzed the seismic performance of TFC under different levels of input intensities and the influence of finish materials to the failure modes was concluded. Pei et al. [4] conducted full-scale wood shear wall tests to study the failure modes and ultimate drift at the collapse limit. Germano et al. [5] performed shear wall tests to explore the behavior of hysteresis characteristics and energy dissipation. These abovementioned test results provided valuable first-hand experimental data to investigate the performance of TFC. Some efforts were also placed in numerical analysis. Kim and Rosowsky [6] developed the fragility curves of wood shear walls under various earthquakes, taking the peak wall displacement and ultimate uplift force into account. Pang et al. [7] proposed a framework of direct displacement design and applied this procedure to the design of shear walls used in a wood-frame building. Although these numerical studies have made significant progress and set the development of building codes for TFC, their numerical models are either according to the design blueprint without considering the model uncertainties or focused on the analysis of components that cannot fully reflect the structural system response.

Obtaining an affordable and robust numerical model is necessary for analyzing the structural behavior, such as the limit state performance, or dynamic responses due to earthquakes. To achieve this goal, model updating constitutes a powerful technique for dealing with structural reliability. Model updating is a process of adjusting model parameters to narrow the gap between the model prediction and experimental result using optimization algorithms. The Bayesian method has gained popularity because it does not only treat the model updating process as a probabilistic framework [8], [9] but also characterizes modeling uncertainties following the underlying structural system [10]. For the nonlinear filtering problems within the Bayesian framework, several Gaussian approximation filters have been developed. These frameworks include the Gauss–Hermite quadrature filter (GHQF), unscented Kalman filter (UKF), and the cubature Kalman filter (CKF).

The UKF estimates the mean vector and covariance matrix of the state vector by defining a collection of sample points. Astroza et al. [11] proposed a novel framework for updating a finite element model using the UKF and validated it with two simulation cases. Cao et al. [12] identified the model parameters of timber connections using the UKF and assessed the mechanical properties between test and model. However, the UKF may not converge with a high-dimensional state-space model because of the non-positive definite covariance[13]. In contrast, the GHQF exploits the properties of Gauss–Hermite quadrature (GHQ) for those multi-dimensional integrals. The GHQF has been applied to spacecraft attitude estimation [14] and battery charge-state estimation [15] with chances of achieving high accuracy. If the dimension of state vector increases, the GHQF is also associated with a high computational cost as the quadrature points increase exponentially.

Recently, the CKF method has become popular as it has better numerical stability than UKF and requires less computational effort than GHQF. The critical concept of CKF is to compute multidimensional integrals through several deterministic cubature points. The transferred points infer the mean and covariance through the nonlinear functions. The CKF method has been applied in many practical applications, such as bearing-only tracking [16] and navigation [17]. However, few papers have been reported the use in timber community. To address these issues, the objective of this paper is to investigate the mechanical properties of TFC and employ the CKF to update the simplified model using the test data. The rest work is organized herein. Section 2 reports the test result of TFC under cyclic loading. Section 3 develops the procedure of CKF to update the simplified model. Section 4 evaluates the updated results. Section 5 presents some conclusions.