## 4 Discussion
It can successfully detect damage using only a limited number of sensors and truncated modes [235]. However, the method has some limitations [235; 236; 237]. First, it is sensitive to noise in the measured data. This is because the method relies on the difference in flexibility between a damaged structure and an undamaged structure. If the measured data are noisy, the difference in flexibility may be difficult to distinguish, as shown in [PERSON]'s research, where the DLV error was around 1.5%, as shown in Figure 10[237]. Second, the scalar proves to be inconsequential for localization purposes and is only of secondary importance in quantification, as reductions in stiffness can be calculated in percentages without reference to specific values. Moreover, the method is not always able to accurately identify the location and extent of damage. This is because it is based on the assumption that damaged elements are completely stiff. In reality, damaged elements may still have some stiffness, making it difficult to identify them using the DLV method. Finally, the method can be computationally expensive. This is because it requires the calculation of the flexibility matrix of the structure. The flexibility matrix is a large matrix, and its calculation can be time-consuming. The phase diagram-based method offers several advantages including its high sensitivity to nonlinear dynamic behaviors, which are often more indicative of cracks than linear parameters [238; 239; 240; 241]. This method allows for the detailed analysis of crack characteristics such as location and depth. by using various indices like quasi-standard deviation and vertical segmentation to provide quantitative insights. It is effective under both primary and super-harmonic resonance conditions, with the latter being particularly sensitive to crack parameters [191]. Additionally, the method holds the potential for real-time monitoring, enabling continuous crack detection without interrupting the operation of the structure. However, the method has limitations including the complexity of nonlinear dynamics, which can be challenging to implement and interpret, and its sensitivity to noise and measurement errors, which may affect accuracy [242; 243]. The method also relies on achieving specific resonance conditions, which can be difficult in practical applications, and it is currently more suited to simpler structures like cantilever beams. Furthermore, it depends on accurate knowledge of the system's dynamic parameters and crack characteristics, which might not always be readily available [244; 245; 246]. Artificial neural networks (ANN) are a powerful tool in structural health monitoring, particularly for detecting cracks and other forms of damage in composite structures, due to their ability to model complex nonlinear relationships between input data such as vibration signals, and output predictions including the presence, location, and severity of cracks [247; 248; 249]. One of the significant advantages of ANN is its capacity to handle the nonlinear relationships inherent in the data, which is particularly relevant in complex materials like composites where crack severity often exhibits nonlinear patterns [250; 251]. Moreover, ANN models are robust against noise, making them effective even with noisy input data, a common scenario in real-world applications [251]. Once trained on a sufficiently diverse dataset, ANN can generalize well, enabling it to detect cracks in previously unseen structures, thus offering versatility across various applications [251]. However, challenges remain such as the need for large datasets to train the models effectively, which can be costly and time-consuming to acquire, and the difficulty in understanding the internal decision-making process of ANNs, which poses challenges in critical applications where transparency and interpretability are crucial [250]. Detecting damage in plates with VT using their DR presents several challenges.