Non-Probabilistic Reliability Model for Structural Damage Identification under Uncertainty with Reduced Model

The process of identifying structural damage can be approached as an optimization challenge, where the goal is to bridge the gap between observed experimental data and theoretical model predictions. This way creates the likelihood to apply the metaheuristic algorithms for the inverse damage identification. Through experiments, we can collect vibration data such as acceleration responses, natural frequencies, mode shapes, and piezoelectric impedance, which serve as indicators of damage. However, such data may be tainted with noise or errors. Furthermore, limitations in model accuracy or a lack of comprehensive understanding of experimental boundary conditions can inject uncertainties into the damage detection process. Traditional probabilistic methods have been employed to counter these uncertainties, but they often rely on predefined statistical distributions, typically Gaussian distribution. In real-world applications, the myriad sources of uncertainty and the paucity of specific experimental data can make it difficult to exactly ascertain these distributions. In this regard, the non-probabilistic interval analysis is introduced. This method leans on the defined bounds of uncertainty in data, rather than their probabilistic nature. It assesses structural damage by measuring factors like the nominal reduction in stiffness, the likelihood of damage, and an index that combines the two, which are quantified through the non-probability reliability method. Besides, the reduced order modeling through component mode synthesis is adopted to speed up the optimization iterations. To validate this approach, vibration-based attributes are used for truss structure, ensuring a robust identification of structural damage when faced with uncertainties in data.