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Abstract
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The conventional modal strain energy (MSE), as a practical objective function, su®ers from the
lack of access to the damaged sti®ness matrix and uses the intact sti®ness matrix of the
structure instead. To overcome the aforementioned de¯ciency of the MSE, this study proposes a
reformed elastic strain energy-dissipation criterion called the \augmented modal strain energy"
(AMSE) which is composed of relative di®erences of natural frequency and mode shape. In the
AMSE not only the e®ects of the energy-dissipation criterion as a function of natural frequency
but also the equilibria of the elastic strain energy as a function of mode shape are considered.
Hereupon, the AMSE is implemented along with the interactive autodidactic school (IAS)
optimization algorithm to investigate the e®ectiveness of the proposed identi¯cation method. In
this regard, the AMSE is veri¯ed by assessing three benchmark truss and frame structures. The
obtained results con¯rm the reliable performance of AMSE in both terms of intensi¯cation and
diversi¯cation. Furthermore, it is observed that despite using noise-polluted modal data, the
proposed AMSE not only identi¯es the damage location accurately, but also anticipates the
extent of damage precisely. Consequently, the proposed energy-dissipation-based objective
function (AMSE) is suggested, along with the IAS optimization algorithm, as a robust technique
for the damage detection of structures.
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