Influence of Rotational Components of Mode Shapes in Damage Detection of Three Dimensional Structures

Damage in structural elements causes obvious changes in their physical properties such as stiffness and damping. These changes affect the stiffness and damping matrices of whole building so its mode shapes change. Therefore, mode shapes of existing building are widely used in damage detection methods. Since vibration test can only provide translational components of mode shapes, previous methods mostly worked with this type of data. This paper focused on considering the importance of using some rotational/translational components of the mode shapes to detect damages in structural frames. In order to analyze the frames and update them, an automatic iterative model updating program is developed in MATLAB software that works with OpenSees for conducting finite element analysis. The iterative program evaluates a set of objective functions in each step and tries to optimize them by means of nonlinear least square method. Objective functions are defined based on the combination of two criteria of these four items: comparison between frequencies and/or mode shapes of two situations, the modal assurance criteria (MAC), and the modal flexibility matrices. In each step of the analysis, based on optimization results, a new frame will be modeled in OpenSees software that its elements stiffness is changed according to new sets of data, then finite element analysis will be done and new modal data will be extracted and optimization process will be repeated by new data. To verify the effectiveness of the developed program, two three-dimensional steel structures are modeled and evaluated, one of them is a five-story moment resisting frame and the other one is a three-story brace frame. It has been considered that these frames suffered damages which are defined by three different scenarios for each of them. Damage scenarios consist of minor, severe and both minor and severe damages. Actually, in this study, damages are defined by reduction in elements’ stiffness. In fact, damage is a percentage of reduction of stiffness in damaged element in comparison with its healthy condition. Mode shape components and natural frequencies of damaged structures are the only needed input data for the program. To investigate the influence of rotational components in model updating, frames have been analyzed with three types of data in each scenario, all translational or rotational components, and all components of mode shapes. Extensive analyses show that among employed objective function, the one which compares mode shapes is the most successful one in damage detection, also modal flexibility can be effective when it works by only rotational components of mode shapes. The findings indicated that the translational components of mode shapes are not capable of detecting damages accurately. Results of model updating by use of only translational components of mode shapes indicate that not only the damages’ location and their intensities could not be predicted, but also several false damages are reported in undamaged elements. It can be concluded that using rotational data leads to more precise results in determining both damages’ locations and their intensities. Besides, the number of false damage detection has been decreased by use of rotational components. It means, when the rotational components are employed, the methods report no damage in healthy elements or the amount of detected damage is very small that can be ignored. Real data extracted from existing building are always polluted by noises due to human or machine faults or sometimes errors in numerical methods lead to inexact input data. Since the data employed in this study are exact numerical data, to consider the effects of these errors, analytical modal data has been polluted by some noises. These noises are generated by use of random function in MATLAB software. Surprisingly, the results show that even with noisy data, the proposed method can detect damages precisely.