A reliability-based sieve technique: A novel multistage probabilistic methodology for the damage assessment of structures

A novel multistage probabilistic methodology called the “Reliability-Based Sieve Technique (RBST)” is presented in this paper for the reliable assessment of the functionality of structures. In this method, the structural damage detection problem is defined as a multistage probabilistic optimization problem. The Holistic Objective Function (HOF) based on the combination of the inherent characteristics of the structure (i.e., the vibration frequencies and mode shapes) is incorporated into the Interactive Autodidactic School (IAS) optimization algorithm, for the first time, to solve the problem. In addition, the Latin Hypercube Sampling (LHS) technique is used to simulate and analyze the probabilistic damage assessment problem. In each stage of the proposed methodology, the Probability of Damage Existence (PDE) is computed in each of the structural elements through a probabilistic damage detection analysis. According to the results of the PDE in the structural elements in each stage, the elements with low PDEs are gradually sieved in the subsequent steps. The sifted elements in each stage are considered as intact ones in the next stage. This systematic filtration of the design variables can simultaneously decrease the dimensions and increase the speed of the optimization problem. To improve the performance of the RBST, the sizes of the sieves are regularly reduced for the next stages. This multistage procedure is continued until convergence to a precise structural damage location diagnosis and intensity prognosis is achieved. Finally, to investigate the efficiency and robustness of the proposed technique, it is examined on three benchmark structures by taking the high level of uncertainties associated with both finite element modeling errors and vibration data noises into account. The obtained results confirmed that the proposed technique correctly identifies the damage indices and has consummate capability compared with the single-stage probabilistic analysis. Likewise, it is observed that the RBST accurately sieves the intact elements from the vector of the design variables in highly noisy conditions. Consequently, in the presence of both mentioned uncertainty sources, the RBST not only assesses the damage site and extent properly, but also shows a reliable performance in terms of PDE.