Sparse Bayesian learning for damage identification using nonlinear models: Application to weld fractures of steel‐frame buildings

Abstract

Sparse Bayesian learning (SBL) is a well-established technique for tackling supervised learning problems, while taking advantage of the prior knowledge that the expected solution is sparse. Based on the premise that initial damage of a structure appears only in a limited number of locations, SBL has been explored for identifying structural damage, showing promising results. Existing SBL methods for structural damage identification use measurements related to modal properties and are thus limited to linear models. In this paper, we present a methodology that allows for application of SBL in nonlinear models, using time history measurements. We develop a two-step optimization algorithm in which the most probable values of the structural model parameters and the hyperparameters are iteratively obtained. An equivalent, single-objective, minimization problem that results in the most probable model parameter values is also derived. We consider the example problem of identifying damage in the form of weld fractures in a 15-story moment-resisting steel-frame building, using a nonlinear finite-element model and simulated acceleration data. Fiber elements and a bilinear material model are used to account for the change in local stiffness when cracks at the welds are subjected to tension, and the model parameters characterize the loss of stiffness as the cracks open under tension. The damage identification results demonstrate the effectiveness and robustness of the proposed methodology in identifying the existence, location, and severity of damage for a variety of different damage scenarios and levels of model and measurement error.

Structural nonlinear damage identification based on the information distance of GNPAX/GARCH model and its experimental study

“…After the optimal model structure of the GNPAX/ GARCH model was obtained, the K-L distance could be calculated from the acceleration time series data of the baseline state and the test state (damage scenarios). Two damage identification methods were used for comparison with the proposed method: (1) the damage identification method based on AR(30)/ARCH(5) model and SOVI proposed by Cheng et al 6 ; (2) the damage identification method based on ARX (25,15,30) model and K-L distance. In order to facilitate the comparison of the three methods, Equation (30) was used to transform the three damage indicators into the expression based on the dimensionless damage indicator…”

“…However, when the breathing crack is closed, the stiffness to bear compressive loads does not change. 30 That is, the structural components with breathing cracks exhibit bilinear stiffness characteristics due to the crack’s openness and closeness. 31 The bilinear stiffness model can be expressed as follows 32 :…”

Seismic assessment of bridges through structural health monitoring: a state-of-the-art review

“… 2019 ) and for parameter estimation for sparse spatial distribution of damage in nonlinear structures using measured response time histories (Filippitzis et al. 2022 ).…”

Probabilistic model updating of steel frame structures using strain and acceleration measurements: A multitask learning framework

“…As a more effective countermeasure for ill-posed and ill-conditioned inverse problems, the hierarchical Bayesian model (HBM) has received increasing interest in the context of model updating and structural health monitoring (SHM) [10][11][12][13][14][15][16][17]. Behmanesh et al [10] presented an HBM framework that flexibly quantified the inherent variability of structural parameters because of environmental variations (such as changing temperature) by setting hierarchical prior distributions over these parameters.…”

“…Similar formulations were made for quantifying the variability attributed to the excitation amplitude [11], time-domain model updating [12], and hysteretic model updating [13]. Sparse Bayesian learning (SBL) for model updating purposes was formulated based on the HBM [14][15][16][17], where the sparsity of damage locations in a structure was assumed in the absence of structural collapse.…”