Structural damage measure index based on non-probabilistic reliability model

Abstract

Uncertainties in the structural model and measurement data affect structural condition assessment in practice. As the probabilistic information of these uncertainties lacks, the non-probabilistic interval analysis framework is developed to quantify the interval of the structural element stiffness parameters. According to the interval intersection of the element stiffness parameters in the undamaged and damaged states, the possibility of damage existence is defined based on the reliability theory. A damage measure index is then proposed as the product of the nominal stiffness reduction and the defined possibility of damage existence. This new index simultaneously reflects the damage severity and possibility of damage at each structural component.Numerical and experimental examples are presented to illustrate the validity and applicability of the method. The results show that the proposed method can improve the accuracy of damage diagnosis compared with the deterministic damage identification method.

The use of a non-probabilistic artificial neural network to consider uncertainties in vibration-based-damage detection

“…Therefore, this study employed the DMI parameter suggested by Wang et al [24] to provide a quantitative measure of damage severity. Moreover, in most applications of the statistical method for damage detection [10,35,36], the outcomes are given in terms of probabilities, which are unable to indicate the exact damage severity.…”

“…The existence of damage was determined by observing the load at which the structure changes from exhibiting elastic behavior to nonlinear behavior. Recently Wang et al [24] improved the method by providing a new damage measure index (DMI) that combines the stiffness reduction factors (SRFs) and the possibility of damage existence (PoDE) using a non-probabilistic interval analysis framework. In their study, both the physical and dynamic characteristics are measured using interval analysis.…”

Interval process model and non-random vibration analysis

“…9, an N-DOF spring-mass-damper model is considered. The equation of motion can be created as [56],    MZ CZ KZ F (31) where…”

“…In recent years, to deal with more complex uncertainty problems several new convex models were also developed such as the super ellipsoid model [23], the multi-ellipsoid model [24,25] and the multidimensional parallelepiped model [26], thus promoting the non-probabilistic convex model theory to a further stage. With the flourishing of convex model theory, some related structural uncertainty analysis and design techniques were also developed, such as non-probabilistic reliability analysis [25,[27][28][29][30][31], probability-interval hybrid reliability analysis [32][33][34] and uncertain optimization [35,36], etc.…”

Set-membership identification technique for structural damage based on the dynamic responses with noises

“…Therefore, choosing the middle value of the stiffness reduction or the PoDE solely may not gain an accurate damage estimate. In the literature [26], Wang combined the SRF and the PoDE as a new damage measure index (DMI), which is defined as the product of the SRF and the PoDE, as shown in (27), where β i represents the DMI of the ith element and the SRF i and PoDE i represent the SRF and the PoDE of the ith element, respectively. It simultaneously takes the middle value of the SRF and the PoDE into account.…”