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. Likewis