Statics-Based Model-Free Damage Detection under Uncertainties Using Modal Interval Analysis

Deterministic damage detection methods often fail in practical applications due to ever-present uncertainties. Moreover, vibration-based model updating strategies are easily affected by measurement noises and could encounter ill-conditioning problems during inverse solutions. On this account, a model-free method has been proposed combining modal interval analyses with static measurements. Structural geometrical dimensions, material parameters and external loads are expressed by interval variables representing uncertainties. Mechanical formulas for static responses are then extended to their interval forms, which are subsequently solved using classic interval and modal interval analyses. The analytical interval envelopes of static responses such as deflections and strains are defined by the interval solutions, and damage can be detected when the measured responses intersect the envelopes. By this approach, potential damage can be found in a fast and rough way without any inverse solution process such as model updating. The proposed method has been verified against both numerical and experimental reinforced concrete beams whose strains were taken as the desirable responses. It was found that the strain envelopes provided by modal interval analysis were narrower than those by classic interval analysis. Modal interval analysis effectively avoids the phenomenon of interval overestimation. In addition, the intersection point also identifies the current external load, providing a loading alarm for structures.