# Modal Strain Energy-Based Structural Damage Detection Using Convolutional Neural Networks
## 1 Introduction  
Structural damage detection is an important research field of structural health monitoring (SHM) to prevent the sudden collapse of structures and avoid casualties and heavy economic losses. The assessment of structural safety in practice generally depends on the engineering judgment of experts by visual inspections. Though promising results have been achieved in structural surface crack detection [1], visual inspections may be costly or inefficient, and the safety rating assigned by trained inspectors may be subjective [2; 3]. Vibration-based methods have increasingly become a hot research topic in structural damage detection due to their flexibility of measurement, cost-effectiveness, and non-destructiveness [4]. By collecting the vibration excitation and response data of a structure, the modal parameters can be obtained, and the potential damage of the structure can then be able to be detected by analyzing the change of its modal parameters, e.g., natural frequencies, modal shapes, or damping [4; 5; 6]. A frequency-based structural damage detection method has been used in damage detection of composite structures [7; 8]. Modal-based methods have shown that local damage causes the irregularity of mode shapes [9], which is significant for relatively large damage [10]. Nevertheless,the changes in natural frequencies and mode shapes have been unable to detect very small damage by modal experiments [11]. Modal strain energy (MSE), which is related to the second-order derivatives of the mode shapes for plate-like structures, has been proven to be much more sensitive to the damage than natural frequencies and mode shapes; thus, MSE has been defined as a damage index to successfully locate structural damage and quantify the damage level [2; 4; 12; 13; 14; 15]. In engineering practice, measuring the high order mode has been difficult due to noise [16]. There have been discrepancies between experimental and numerical results [17]. To reduce the noise effect of the measurement data, a powerful information processing tool is needed, one such as artificial neural networks (ANNs) [18], which are able to extract the features of structural damage and eliminate some interference (e.g., noise).  
The application of ANNs in damage detection provides a new method for SHM. The early application of a back-propagation (BP) neural network has achieved promising results [19; 20], but it has some inherent shortcomings, such as a low convergence, being time-consuming, and the over-fitting of data [21; 22]. The dimensions of sample data of large structures can be huge, and the training time is not affordable [23]. To overcome the limitations of ANNs, the convolutional neural network (CNN), with several convolution layers and pooling layers, has been developed to extract the features of the image [24] and been proven successful. It has a more powerful feature learning ability and feature expression ability [25] than BP neural networks. At present, the CNN has been widely used in font recognition, license plate detection, face recognition and other fields [26; 27; 28]. The CNN has also been applied to SHM for such aspects as crack detection [29; 30], damage feature extraction from low-order vibration signals [23], vibration-based damage detection [31], data anomaly detection [32], verified on benchmark frames [33], and other frames [34; 35]. It is expected that CNNs can effectively detect damage in large structures.  
In this paper, a CNN is proposed to detect damage in a steel frame. Numerical simulation data were used to train the network, and experimental data were inputted into the network to verify the damage detection capability of the CNN. Furthermore, the CNN was compared with traditional BP neural networks to demonstrate its efficiency and effectiveness.