Interval analysis of mode shapes to identify damage in beam structures

Various damage detection methods have been proposed by several researchers in the past few decades. Amongst them, the efficiency of mode shapes in detecting damage has been demonstrated by many researchers when further processed. In most cases, the processing involves expansion or reduction of the mode shape data. However, vital information that are damage-prints are often lost during processing of the mode shape data. In addition, most of these processes involve long and complex computation, thus, leading to inaccurate damage identification. In this study, a simple and fast damage identification technique is proposed to identify damage in beam structures. Interval analysis is applied to the mode shapes of a beam structure in the damaged and undamaged states. The interval situations of each of the beam's segment via mode shape are derived to obtain the upper and lower bounds and the derived bounds are compared. To establish a relationship for identify the damaged point, a possibility of damage existence is defined for each segment of the beam structure. The mode shape increment is defined as the increase in the mode shape value. Furthermore, a damage measure index that provide enhance damage information is obtained as the product of the possibility of damage existence and mode shape increment. A numerical model of a simply supported steel beam is applied to demonstrate this method by imposing damage through thickness reduction of elements in segments. In addition, a parametric analysis is carried out to evaluate noise effect by considering varying damage severities and different noise levels. The results showed that this method is simple and provides considerable accurate results.