# Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN
## 1 Introduction  
The safe development of nuclear power is important. As one of the key components of a nuclear power unit, the main role of the planetary gearbox is to transmit the rotational power of the motor to the impeller of the pump. The gears in the nuclear power planetary gearbox are prone to cracks, pitting corrosion, and other faults [1]. Moreover, current research on the fault diagnosis and health monitoring of the planetary gearbox is relatively weak. Therefore, it is of great significance to establish a fault diagnosis method for the planetary gear train of the nuclear power planetary gearbox. The fault diagnosis methods are divided into three types [2]. (1) The mechanistic model-based approach. This method provides an in-depth system understanding with good epitaxy and reliability, but the mechanistic model needs sufficient knowledge and data support. With the increasing complexity of the system structure, some mechanism knowledge is difficult to obtain. Even if the mechanistic model is constructed, it is not possible to obtain all the information of the physical system. Especially when the system is highly coupled and has complex nonlinearities, the accuracy of the obtained mechanistic model is limited, which limits the application of this method. (2) The knowledge-based approach. This method is based on the integration of expert experience and prior knowledge, to explore the relationship between system faults, phenomena as well as causes, and to build a system diagnosis model according to certain rules. It does not require precise mathematical expressions and is suitable for many complex systems that are difficult to model. However, this method is poorly adaptable. An important prerequisite for obtaining accurate results is to have a knowledge base with a large amount of rich empirical knowledge. For unknown faults without any prior knowledge, not only there will be misdiagnoses, but also it is impossible to give accurate diagnostic information in the event of a fault. (3) The data-driven approach. This method aims to model and predict the physical system by processing and analyzing the input and output data of the physicalsystem, mining the hidden rules and patterns in the data. The main advantage of this method is that it does not require any knowledge of the internal mechanism, and it can use a large amount of actual data to improve the accuracy and generalization ability of the model, which is outstanding in the absence of accurate mathematical/physical models. The vibration signal contains the essential information about the operating status of the monitored object. Therefore, it is a commonly used signal in data-driven diagnostic methods. The empirical mode decomposition [3] and wavelet transform [4] have been proven to be effective diagnostic methods. [PERSON] [5] proposed an adaptive optimization algorithm for VMD parameters based on a differential search, combined with the relevant kurtosis index, to achieve the adaptive extraction of bearing fault features. The effectiveness of the method was verified by experiments. [PERSON] et al. [6] proposed a fault diagnosis method for rolling bearings based on singular spectrum decomposition and independent component analysis, which solved the problem that the early failure of bearings was overwhelmed by noise due to low energy. [PERSON] et al. [7] proposed a multi-band envelope extraction method based on cyclic bivariate mapping, which solved the problem of the difficulty in detecting faulty bearing noise signals using single-pass filtering. [PERSON] et al. [8] proposed a fault diagnosis method based on parameter optimization variational mode decomposition and multi-domain manifold learning to solve the problem of difficult feature extraction of planetary gearbox features, and verified that the multi-domain feature extraction method is superior to the single-domain feature extraction methods in the time domain and frequency domain. [PERSON] et al.