Three significant tuning components in structural finite element model updating including
objective function, optimization algorithm, and updating variables have a drastic influence
on the accuracy of structural damage location diagnosis and intensity prognosis. These
three components require both physical concepts and trial-and-error approaches. To assess
damage in a structure accurately, the common information of several modes of the
structure is required. The availability of higher modes data in engineering structures with a
high degree of freedom is a complex task or even not practical in real cases. This study
intends to propose a versatile objective function based only on the first vibration frequency
and mode shape data. A new hybrid criterion called “Relative Discrepancy Function (RDF)”
is proposed which is composed of relative differences of natural frequency and mode
shape vector. Hereupon, the efficiency of the proposed identification method is evaluated
through five sets including different robust objective functions and meta-heuristic optimization
algorithms. These five damage identification sets are composed of three objective
functions (Normalized Modal Strain Energy, Modified Total Modal Assurance Criterion, and
RDF) and three optimization algorithms (Imperialist Competitive Algorithm, Teaching-
Learning-Based Optimization algorithm, and the Most Valuable Player Algorithm
(MVPA)). Subsequently, three truss and frame benchmark structures are assessed by means
of five identification methods in single and multiple damage scenarios. It is observed that
MVPA has both the fastest convergence rate and the lowest computational run time.
Furthermore, the damage assessment results illustrate that when merely the first vibration
mode data are used, the proposed identification method (RDF, MVPA) not only predicts the
damage location properly, but also estimates the damage intensity successfully.