# Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation
## 1 Introduction  
During service life, structures are subjected to different loads, external factors, and unpredictable influences that can cause considerable structural damage. Regular inspections of structures are essential for early damage detection, analysis, and repair of damaged structures in order to extend the service life while assuring safety and reliability. Due to the lack of regular inspections and poor maintenance of structures, the damage can decrease the bearing capacity and endanger safety. The widely accepted structure inspection is based on visual inspections or locally limited nondestructive testing methods for damage assessment such as acoustic or ultrasonic methods, magnet field methods, radiography, eddy current methods, thermal field methods, and X-rays [1]. The mentioned methods have numerous limitations, such as the small inspection area and the location of damage needing to be known in advance. The problem is that the part of the structure where the inspection is carried out has to be accessible. The difficulties in damage detection can be overcome by analyzing the dynamic response of structures obtained using the vibration-based monitoring system [2]. Global behavior of the structure is defined by its dynamic properties that can be determined using relatively simple measurement methods at a single or several locations in the structure. The main reason for using vibration-based monitoring is that structural damages such as changes in boundary conditions and bending cracks cause the loss of stiffness and consequently a change in dynamic properties (natural frequencies, mode shapes, and damping ratios). Four levels of damage detection in structures are defined as follows [3]: detecting the presence of damage, detecting the damage location, determining the severity of the damage, and predicting the remaining service life. Different methods have been proposed on thebasis of the change in natural frequencies [4; 5; 6; 7; 8; 9]; mode shapes [10; 11]; and their derivatives such as the change in modal flexibility [12; 13], the change in modal curvature [14; 15], the change in modal strain energy [16; 17; 18], and other modal methods used for damage detection on plate-like structures [19]. Furthermore, a number of non-modal methods are used for damage detection on plate-like structures, such as the frequency response function (FRF) method [20] and guided waves approach [21]. They are mainly used with some other algorithms (artificial neural networks, genetic algorithm, Bayesian approach, etc. ), requiring additional effort to detect damage. Mentioned methods are primarily used for the first two levels of damage assessment, i.e., damage detection and localization. Some of them can even be used to quantify the severity of the damage but mostly to identify the difference between lower and higher levels of damage [7; 16; 18]. When multiple structural damages are considered, determining damage severity becomes a challenge [22]. Most of the methods are applied to numerical and experimental models of rods, plates [23], and beams with simulated damages or real-life structures such as bridges [10; 24]. Modal assurance criterion (MAC) [25; 26; 27], among other indicators, is used for damage detection based on mode shape changes. The MAC is a scalar quantity related to the degree of consistency between two mode shapes, and it can be used for the direct comparison of mode shapes in the undamaged and damaged condition. This criterion is not sensitive to small differences between mode shapes and cannot be used for the damage localization, but it can serve as an indicator of damage in the structure [28; 29]. In order to detect and localize damages in structures, researchers proposed the mode shape damage index (MSDI) algorithm on the basis of a modified MAC matrix (\(\Delta\)MAC), which considers mode shapes that are almost identical and excludes dissimilar mode shapes [30].