  The impedance/admittance measurements of a piezoelectric transducer bonded to
or embedded in a host structure can be used as damage indicator. When a
credible model of the healthy structure, such as the finite element model, is
available, using the impedance/admittance change information as input, it is
possible to identify both the location and severity of damage. The inverse
analysis, however, may be under-determined as the number of unknowns in
high-frequency analysis is usually large while available input information is
limited. The fundamental challenge thus is how to find a small set of solutions
that cover the true damage scenario. In this research we cast the damage
identification problem into a multi-objective optimization framework to tackle
this challenge. With damage locations and severities as unknown variables, one
of the objective functions is the difference between impedance-based model
prediction in the parametric space and the actual measurements. Considering
that damage occurrence generally affects only a small number of elements, we
choose the sparsity of the unknown variables as another objective function,
deliberately, the l0 norm. Subsequently, a multi-objective Dividing RECTangles
(DIRECT) algorithm is developed to facilitate the inverse analysis where the
sparsity is further emphasized by sigmoid transformation. As a deterministic
technique, this approach yields results that are repeatable and conclusive. In
addition, only one algorithmic parameter, the number of function evaluations,
is needed. Numerical and experimental case studies demonstrate that the
proposed framework is capable of obtaining high-quality damage identification
solutions with limited measurement information.
