# A Size-Controlled AFGAN Model for Ship Acoustic Fault Expansion
## 1 Introduction  
Monitoring the condition of the ship structure has been a challenge for decades [1; 2]. Two general approaches are considered including the theoretical and numerical simulation method and the experimental method. Due to the complexity of the ship structure and its components inside, accurate simulation of its dynamic property is difficult and time-consuming [1; 3]. Thus, researchers try to establish the condition monitoring model based on actual experimental data [4; 5] and among all other methods, using the vibration and acoustic data provide a safe, non-invasive, and constant condition monitoring [2]. [PERSON] et al. in 2012 proposed a support vector machine model to detect the oil leakage condition of the ship. His model was built based on 300 samples of instantaneous angular speed, which achieved 94.7% accuracy [5]. He also combines independent component analysis, principal component analysis to model to the normal and fault engine conditions based on 100 samples each [6]. This model presents 90.5% accuracy. However, as shown by previous studies, practical acoustic fault identification in ships is considered as a small-sample recognition problem because of the difficulty of obtaining representative fault samples, the high experimentation cost, and so on [2]. Typical problems are increasing sound power from a vibrating source, decreasing transmission loss of the structure, and decreasing insertion loss of vibration mounts. Sample expansion is an effective way to solve the problem of incomplete samples in ship acoustic fault source identification [2]. In general, there are two main methods for constructing expanded samples. One is to obtain expanded samples by introducing the prior knowledge, which can be regarded as an effective supplement to actual fault samples. [PERSON] et al. proposed a virtual sample generation technology based on geometric transformation in an image recognition field [7]. For noise source recognition in a double-layer cylindrical shell structure, [PERSON] et al. generated virtual samples based on a system frequency response function, which demanded a deep understanding of a priori knowledge from field researchers [8]. The other method is to expand samples by employing the concept of a disturbance, such as bootstrapping [9], noise disturbance [10], and so on. The advantage of such methods is that the expanded samples can be constructed directly from the original training samples. However, bootstrapping constrains itself by picking up the same sample multiple times, which introduces no new information. Furthermore, signal augmentation like adding noise disturbance might generate poor samples due to the ignorance of the field's priori knowledge. Other common sample expansion methods like interpolation and synthetic minority over-sampling technique can present good performance when the sample is represented by a set of features, which are not applicable to time series data like acoustic data. Therefore, the lack of priori knowledge and the nature of acoustic data make the sample expansion difficult. The generative adversarial network (GAN) provides a method to directly generate the acoustic signal under a fault condition. In 2014, [PERSON] et al. proposed the GAN and successfully applied it to the field of computer vision by generating a large number of highly realistic images [11]. Instead of assuming the distribution of functions first, the real data were directly approximated by sampling in the GAN. This anti-competitive approach ensured the quality of the generated samples. The GAN approach has been applied to image recognition [12], audio [13], video [14], and other fields [15; 16; 17; 18]. However, only a small amount of work has been reported related to fault vibration signal identification [19]. This paper attempts to apply a GAN to acoustic fault sample expansion under small-sample conditions and presents an Acoustic Fault Generative Adversarial Network (AFGAN) model, which can directly expand the acoustic sample under fault condition.