54 Y. Gu and Y. Lu Table 6.1 Mode frequency comparison between selected damage scenario and intact situation – Intact (Hz) S5, S6 =0 (Hz) Percentage difference to the intact situation (%) S10, S11 =0 (Hz) Percentage difference to the intact situation (%) Section2 at 40%of intact stiffness (Hz) Percentage difference to the intact situation (%) Section5 at 40%of intact stiffness (Hz) Percentage difference to the intact situation (%) Mode 1 28.59 27.62 −2.10% 28.59 0.00% 28.33 −0.91% 27.6 −3.46% Mode 2 90.83 89.70 −0.07% 87.77 −3.37% 88.88 −2.15% 90.34 −0.54% Mode 3 184.5 184.3 −1.14% 184.3 −0.11% 179 −2.98% 179.9 −2.49% Mode 4 310.7 310.0 −1.29% 306.6 −1.32% 302.9 −2.51% 306.3 −1.42% The above numerical simulation results indicate that the effect of damage to the shear connectors on the overall structural performance is complicated, on the one hand, and, on the other hand, the effect on the modal frequencies and mode shapes is distinctively different from flexural damage. This suggests that using transverse vibration data should contain pertinent information that could allow the separation of the two groups of parameters in a composite beam. In the next section, we will demonstrate the identification of the two groups of damage parameters using the framework of finite element model updating with genetic algorithms. 6.4 Identification of Damage in Composite Beams Using Genetic Algorithm-Based Finite Element Model Updating In the FE model updating-based structural damage assessment, the main idea is to establish a residual (objective) function that represents the discrepancy of dynamic properties between the damaged structure and the finite element model and then by means of a global optimization algorithm to update the parameters of the finite element model until the dynamic properties computed from the FE model minimizes the residual function [5]. In this section, the objective function is established with the residuals of the mode frequency and mode shape information, shown by Eq. (6.11). In order to minimize the influence of the basic model error, the measured and theoretical modal information of the damaged beam is normalized with respect to its undamaged counterpart, and the objective function of the residual error is formulated by the normalized values: R= 1 Nf Nf i=1 abs f 2 dNmi f 2 0Nmi − f 2 dNci f 2 0Nci + 1 NmsNn Nms j=1 Nn i=1 abs φ j dm i φ j 0m i 2 − φ j dc i φ j 0c i 2 (6.11) where fNi represents i-th natural frequency and subscripts “c” and “m” stand for the FE calculated and the measured data, respectively. Subscripts “d” and “0” stand for the damaged and intact states of the beam, respectively. φ j mi is the j-th element in the i-th displacement normalized mode shape vector. Subscripts “c” and “m” stand for the FE calculated and measured data. Nf, Nms, andNn represent the number of the natural frequency, number of the mode shape, and number of the measured node, respectively. The stiffness parameter of each segment is used to update the model, and the genetic algorithm (GA) is employed to guide the updating process [5]. Generally speaking, GA-based model updating has several advantages. For example, the GA searching results do not depend on the initial setting of the updating parameters; thus, a global optimal result rather than a local one is generally guaranteed. Furthermore, there is no need to calculate the sensitivity matrix of the structure during the updating process, and this makes the updating more robust. In the present study, the standard GA function in MATLAB has been used to update the FE model. A random distribution of the section stiffness on each segment of the beam is assigned firstly in MATLAB. Then these stiffness parameters are imported into Abaqus to calculate the modal information. Subsequently, the calculated modal information is exported to MATLAB from Abaqus to calculate the R function. If the value of the fitness function does not meet a pre-set requirement, the GA will carry out an iteration to find a more suitable distribution of segment stiffness parameters. If the fitness meets the requirement, the iteration process stops, and the optimized distribution of segment stiffness parameters is exported. The previously introduced FE model (Sect. 6.3) is used here to demonstrate the damage identification procedure. To extract the mode shape information, 19 measurement points are uniformly arranged along the bottom of the composite beam, staring at the position of 0.1 m from the left end to the right end with an interval of 0.1 m. As previously stated, the top portion of the composite beam is separated into 10 segments, and the 20 shear connectors are similarly divided into 10 groups, each
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