# Planetary-Gearbox Fault Classification by Convolutional Neural Network and Recurrence Plot
## 1 Introduction  
Due to their power capability in a compact, lightweight form and variable transmission ratio, planetary-gear trains are key units of rotating machinery that are widely used in helicopters, wind turbines, and other mechanical transmission systems. However, harsh operating conditions make components in planetary gearboxes, such as gears and bearings, prone to failure. Therefore, it is urgent to develop effective diagnostic approaches to detect the operating conditions of a mechanical transmission system.  
Compared with conventional fixed-axis gear sets, the structures of planetary gearboxes are more complicated and generally composed of a planet carrier, a sun gear, a ring gear, and several planets. Planet gears not only spin around their own shaft, but also revolve around the center of the sun gear. Thus, the perceived vibration from the planetary gear set characterizes heavy amplitude, frequency, and phase demodulation caused by gears or bearing faults, gear meshing motion, and time-varying transfer paths.  
Currently, popular approaches for extracting fault features caused by planetary gear sets are vibration-based methods, which include the vibration-separation technique [1], amplitude and frequency demodulation [2, 3]. However, these conventional signal-processing approaches have some disadvantages. First, when we use these approaches, the operational characteristics and failuremechanisms of planetary-gear trains should be considered. Second, it is difficult to recognize fault features form various faults.  
On the other hand, AI techniques have recently been used in the field of condition monitoring and fault diagnosis. AI techniques could be employed in the condition monitoring and fault diagnosis of rotating machinery by taking expert knowledge into consideration. In fact, some convolutional-neural-network (CNN) studies reported on the fault identification of complex machinery transmission systems. For example, the spectrum of bearing housing vibration is processed by fast Fourier transform to identify faults with the CNN [4]. The time- and frequency-domain indicators were combined with the CNN for fault classification of a fixed shaft gearbox in [5,6].  
The main deep-learning schemes generally have the advantage of taking 2D images as inputs. The perceived vibration is converted into time-frequency [7] or time-scale images by continuous wavelet transform (CWT), short-time Fourier transform (STFT), and Fourier transform (FT), which aim to be combined with the CNN for intelligent fault diagnosis [8]. Recurrence-plot (RP) analysis [9] is a powerful tool to locate nonstationary structural changes and transitions occurring in the dynamic system. It can be employed to study the response of a planetary-gear set and visualize the recurrence behavior of a faulty system [10,11]. RP results are 2D images that make the RP and CNN combination convenient. In this paper, a combination scheme of a CNN and angular-domain recurrence-plot analysis is proposed. The validity of the proposed scheme is experimentally demonstrated on a planetary-gear test rig.  
This paper is arranged as follows. Angular-domain recurrence-plot analysis is introduced in Section 2. Subsequently, the CNN principle is briefly described in Section 3. The proposed approach is discussed in Section 4. The experiment on the planetary-gear test rig and the corresponding analysis results are presented in Section 5. Finally, conclusions are drawn in Section 6.