## 1 Introduction
[PERSON] and [PERSON] [46] proposed a bearing fault detection method based on energy distribution variational mode decomposition. However, the above research is still based on single-sensor information collection. [PERSON] extended VMD to two-dimensional areas and proposed two-dimensional variational mode decomposition [47] in 2014, which makes simultaneous analysis and noise reduction of multivariate data possible. The application of multiple sensors inevitably brings another problem, that is, the synchronous processing of massive monitoring data. The on-line condition monitoring system of the wind turbine functions by using multiple sensors installed in different key positions of the unit to collect real-time vibration acceleration, velocity, stress and strain and other parameters synchronously. Long-cycle real-time acquisition will generate a huge amount of data [48]. The huge amounts of data used for data transmission, storage, and real-time processing pose significant challenges [49]. At the same time, big data brings problems such as noise accumulation [50]. Therefore, research on multi-sensor data noise reduction methods has attracted researchers in various fields. Compressed sensing (CS) is a new signal acquisition technology, also known as compressed sampling [51]. As a new sampling theory, it develops the sparse characteristics of the signal, obtains discrete samples of the signal by random sampling, and then reconstructs the signal perfectly by a nonlinear reconstruction algorithm [52]. The recovered signal is sparse and robust at the same time [53]. Compressed sensing technology is widely used in signal denoising and feature extraction in various professional fields. [PERSON] et al. [54] applied compressed sensing theory to wireless sensor networks, and proposed a method of data sampling compression and reconstruction based on distributed compressed sensing theory. [PERSON] [55] applied compressible sensing theory to the data recovery problem of practical sensor networks. [PERSON] et al. [56] proposed a new sparse extraction of impulses by an adaptive dictionary scheme to extract impulse components. Based on the above analysis, in order to solve the problem of planetary gearbox fault detection with multi-stage planetary rows, this paper proposes a new method of planetary gear fault detection with multi-sensor compressed sensing, 2D-VMD and full-vector spectrum theory. The paper is arranged as follows: in the preface, we review the recently proposed planetary gear fault detection method, and explain the necessity of studying the planetary gearbox fault detection method that is specially used to detect faults in a planetary gearbox with multi-stage planetary rows. In Section 2, we introduce compressed sensing, 2D-VMD, Renyi entropy and full-vector spectrum theory, and study the sparsity and noise robustness of compressed sensing in detail. A new method of planetary gear fault detection based on multi-sensor compressed sensing, 2D-VMD and full-vector spectrum is proposed. In Section 3, the synchronous acquisition of multivariate planetary gear tooth failure test data is carried out by using the planetary gear fault detection test-bed, and the spectrum characteristics of planetary gear tooth failure are studied in detail by using the proposed method. The fault features are extracted accurately, and the correctness and effectiveness of the method are proved. The conclusions are presented in Section 4.