Interval analysis method for structural damage identification based on multiple load cases

Based on the measured static displacements, an improved interval analysis technique was proposed for the structural damage identification. Due to the scarcity of uncertain information, the uncertainties were considered as interval numbers in this paper. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of undamaged and damaged structures are respectively obtained. The structural damage was detected by the quantitative measure of the possibility of damage existence in elements, which was more reasonable than the probability of damage existence in the condition of less sample points for the measurement data. Furthermore, the classic interval analysis method was improved by adopting the membership-set identification and two-step model updating procedure to make identification results more accurate. An uncertain truss structure was employed for damage identification, the damage identification results obtained by interval analysis method and probabilistic method, respectively, were compared. Moreover, the effects on the detection results of the damage level and uncertainty level subjected to single or multiple load cases were studied as well. The numerical example shows that the wide intervals resulting from the interval operation can be narrowed by the improved nonprobabilistic approach, and the feasibility and effectiveness of the present method were validated.