The probabilistic damage identification problem with uncertainty in the FE model parameters, external-excitations and measured acceleration responses is studied. The uncertainty in the system is concerned with normally distributed random variables with zero mean value and given covariance. Based on the theoretical model and the measured acceleration responses, the probabilistic structural models in undamaged and damaged states are obtained by two-stage model updating, and then the Probabilities of Damage Existence （PDE） of each element are calculated as the damage criterion. The influences of the location of sensors on the damage identification results are also discussed, where one of the optimal sensor placement techniques, the effective independence method, is used to choose the nodes for measurement. The damage identification results by different numbers of measured nodes and different damage criterions are compared in the numerical example.
In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.
Generally, the finite element analysis of a structure is completed under deterministic inputs.However,uncertainties corresponding to geometrical dimensions,material properties, boundary conditions cannot be neglected in engineering applications. The probabilistic methods are the most popular techniques to handle these uncertain parameters but subjective results could be obtained if insufficient information is unavailable. Non-probabilistic methods can be alternatively employed,which has led to the procedures for nonprobabilistic finite element analysis. Each non-probabilistic finite element analysis method consists of two individual parts,including the core algorithm and pre-processing procedure. In this context,three types of algorithms and two typical pre-processing procedures as well as their effectiveness are described in detail,based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.
