In  this  paper,  a  method  is  presented  for  damage  detection  of  bridges  using  the  Enhanced Colliding Bodies Optimization (ECBO)  utilizing time-domain responses. The finite element modeling of the structure is based on  the equation of motion under the moving load, and the flexural stiffness of the structure is determined by the acceleration responses obtained via sensors placed in different places. Damage detection problem presented in this research is an inverse  problem,  which  is  optimized  by  the  ECBO  algorithm,  and  the  damages  in  the structures  are  fully  detected.  Furthermore,  for  simulating  the  real  situation,  the  effect  of measured noises is considered on the structure, to obtain more accurate results.

Monte Carlo simulation (MCS) is a useful tool for computation of probability of failure in reliability analysis. However, the large number of samples, often required for acceptable accuracy, makes it time-consuming. Importance sampling is a method on the basis of MCS which has been proposed to reduce the computational time of MCS. In this paper, a new adaptive importance sampling-based algorithm applying the concepts of first-order reliability method (FORM) and using (1) a new simple technique to select an appropriate initial point as the location of design point, (2) a new criterion to update this design point in each iteration and (3) a new sampling density function, is proposed to reduce the number of deterministic analyses. Besides, although this algorithm works with the position of design point, it does not need any extra knowledge and updates this position based on previous generated results. Through illustrative examples, commonly used in the literature to test the performance of new algorithms, it will be shown that the proposed method needs fewer number of limit state function (LSF) evaluations.