Abstract
Generally, the damage of the structure will lead to the discontinuity of the local mode shape, which can be well reflected by the modal curvature of the structure, and the local information entropy of the beam structure will also change with the discontinuity of the mode. In this paper, based on the information entropy theory and combining the advantages of modal curvature index in damage identification of beam structure, the modal curvature utility information entropy index is proposed. The modal curvature curves of nondestructive structures were obtained by fitting the modal curvature curves of damage structures with the gapped smoothing technique to avoid dependence on the baseline data of nondestructive structures. The index comprehensively reflects the damage state of the structure by calculating mutual weight change matrix and the weight‐probability coefficient. The performance of the new index was verified by the finite element simulation and model test of simply supported beam, respectively. The results show that the modal curvature utility information entropy index takes advantage of the modal curvature index which is sensitive to damage and can overcome its shortcomings effectively. The index proposed can identify the damage location and damage degree accurately and has certain noise immunity, which provides an effective damage identification indicator for beam structures.
Highlights
High requirements on the integrity and performance of civil engineering structures is increasingly needed, which is reflected in the increasing complexity of civil structures, bridge structures, large stadiums, and tunnels, as well as the increasing service performance and construction scale. e safety of the beam structure is inevitably reduced due to the natural environment, material deterioration, construction defects, overload, and other factors, which may cause serious consequences. erefore, it is of great practical significance to study the structural health monitoring (SHM) technology [1, 2]
E identification results of damage cases 1–3 under the modal curvature difference (MCD) are shown in Figures 11(a) and 11(b); the value of MCD index shows an obvious peak at the set damage position, so the damage position of the structure can be located
Because the modal curvature at the second-order modal nodes is positive and negative offset, which negatively influences the identification of the relative damage degree of the structure
Summary
High requirements on the integrity and performance of civil engineering structures is increasingly needed, which is reflected in the increasing complexity of civil structures, bridge structures, large stadiums, and tunnels, as well as the increasing service performance and construction scale. e safety of the beam structure is inevitably reduced due to the natural environment, material deterioration, construction defects, overload, and other factors, which may cause serious consequences. erefore, it is of great practical significance to study the structural health monitoring (SHM) technology [1, 2].With the use of an advanced and reliable sensor, the SHM technology has been rapid developed [3,4,5]. e most fashionable approaches in SHM are based on the structure vibration characteristics. ese methods depend on the stiffness change on the influence of the dynamic characteristics of structure [6], which get the extensive attention of scholars because it is simple and easy. In view of the insufficient sensitivity of early damage identification indexes such as natural frequency and modal displacement, Pandey [10] firstly proposed a damage identification method for beam structure based on modal curvature (MC) in 1991, which has been widely applied and extended. In order to improve the damage identification ability of MC index, some scholars obtained the analytical expression of the modal curvature change of the beam damage state by using the perturbation solution of the Euler beam motion equation, and introduced the filtering technology of the modal curvature change to establish the inverse problem of damage positioning based on the modal curvature only [16, 17]. MC index has been popularized and applied to damage identification of plate structures based on two-dimensional mode curvature [18]. Yang et al [19] proposed a curvature correction method incorporating bending and torsion effects into damage assessment
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