Summary This paper presents an extended constitutive relation error (ECRE)‐based method for detecting damage in structural systems. Although most ECRE‐based methods for damage detection have relied on an iterative model calibration process, the approach advocated in this study uses residual energy to identify structural damage. Residual energy represents the spatial distribution of discrepancies between model predictions of the undamaged system and experimental measurements obtained from the damaged system. The current study calculates this residual energy by tightly linking experimentally measured vibration data to an associated numerical model. The approach implemented in this paper, referred to as the M‐K ECRE‐based approach, differs from previous ECRE‐based damage detection methods in that it incorporates both unbalanced elastic and unbalanced inertial forces in the calculation of residual energy. The rationale for including unbalanced inertial forces is that damage can also alter the mass distribution of a structure in addition to its influence on the distribution of structural stiffness. By considering unbalanced inertial forces, the proposed approach improves the calculation of residual energy, which in turn leads to an improvement in the method's ability to identify damage. At the end of this study, the efficiency of the M‐K ECRE‐based approach to identify damage is demonstrated on a scaled two‐story steel frame that is subjected to varying types and severities of structural damage.
Partitioned analysis enables numerical representation of complex systems through the coupling of smaller, simpler constituent models, each representing a different phenomenon, domain, scale, or functional component. Through this coupling, inputs and outputs of constituent models are exchanged in an iterative manner until a converged solution satisfies all constituents. In practical applications, numerical models may not be available for all constituents due to lack of understanding of the behavior of a constituent and the inability to conduct separate-effect experiments to investigate the behavior of the constituent in an isolated manner. In such cases, empirical representations of missing constituents have the opportunity to be inferred using integral-effect experiments, which capture the behavior of the system as a whole. Herein, we propose a Bayesian inference-based approach to estimate missing constituent models from available integral-effect experiments. Significance of this novel approach is demonstrated through the inference of a material plasticity constituent integrated with a finite element model to enable efficient multiscale elasto-plastic simulations.
Purpose This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process. Design/methodology/approach The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters. Findings When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system. Originality/value This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.
The creation of computer models is often driven by the need to make predictions in regions where there is no data (i.e. extrapolations). This makes validation challenging as it is difficult to ensure that a model will be suitable when it is applied in a region where there are no observations of the system of interest. The current paper proposes a method that can reveal flaws in a model which may be difficult to identify using traditional approaches for model calibration and validation. The method specifically targets the situation where one is attempting to model a dynamical system that is believed to possess time-invariant calibration parameters. The proposed approach allows these parameters to vary with time, even though it is believed that they are time-invariant. The of such an analysis is to identify key discrepancies - indications that a model has inherent flaws and, as a result, should not be used to influence decisions in regions where there is no data. The proposed method isn't necessarily a predictor of extrapolation performance, rather, it is a stringent test that, the authors believe, should be applied before extrapolation is attempted. The approach could therefore form a useful part of wider validation frameworks in the future.
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