3. Modal Curvature Based Damage Detection

In the present chapter, a finite element model of a cantilever beam is used to develop a fuzzy logic system (FLS) for damage detection in structures using modal curvature vectors. A new sliding window defuzzifier proposed for fault isolation in Chap. 2 for frequency damage indicators is now extended to modal curvature. The proposed FLS is tested for noisy data as well as for the case when some of the measurements are missing or faulty. Section 3.1 provides a background on modal methods for damage detection and motivates the use of modal curvature as a damage indicator. Section 3.2 presents the beam model and defines the mode shape curvature. Section 3.3 presents the fuzzy logic system based on inputs from modal curvatures and outputs involving damage size and location. Section 3.4 presents damage detection results using modal curvature for the case where no material uncertainty is present. Section 3.5 then moves from a uniform beam model to a tapered beam model and considers multiple damages in the beam. Section 3.6 introduces the curvature damage factor as an indicator of damage. Section 3.7 presents the material uncertainty model for the isotropic steel tapered beam and Sect. 3.8 discusses the uncertainty quantification method. Section 3.9 presents a fuzzy logic system for the uncertain tapered beam and Sect. 3.10 presents damage detection results. Finally, Sect. 3.10 presents the main ideas from the chapter. The content of this chapter is adapted from [1, 2].