## 1 Introduction
The vibrations caused by these meshing pairs are mutually coupled, superimposed, and neutralized, which greatly affects the decoupling of fault characteristics, increases the complexity of the frequency spectrum, and further increases the difficulty of fault detection [19]. Therefore, it is necessary to study the method specially used to detect faults in a planetary gearbox with multi-stage planetary rows. According to the characteristics of the vibration signal of the planetary gear transmission system, using a multi-sensor data fusion method is a feasible method. Multi-sensor fusion has always been one of the key areas of data analysis [20], and it is an effective method to solve the fault detection problem of mechanical systems [21]. Multi-sensor data fusion enhances the effectiveness and success rate of fault monitoring by providing complementary information [22]. The information collected by multiple sensors simultaneously can overcome the problems of uncertainty and low accuracy in fault recognition due to the single-sided information of a single sensor, and also overcome the complexity of environmental noise and external complicated excitation, thereby improving the robustness and reliability of fault detection [23]. Multi-sensor information fusion can be divided into three grades [24; 25], in which data level fusion directly and synchronously processes multiple sensors' data from the tested object. This level of data fusion contains the most direct and reliable information of the measured object and can provide the most accurate troubleshooting results [26]. However, in the research on fault monitoring and detection of rotating machinery based on multiple sensors, data-level fusion methods mostly rely on artificial intelligence methods such as neural networks and support vector machines [27; 28; 29], and there are few research works on multi-sensor information fusion in the field of data layers [30; 31]. The fault detection method based on multi-sensor data fusion needs to solve three problems in practical application [32]; these are: (1) how to remove noise effectively, (2) how to improve the fault feature, that is, the resolution of the signal, and (3) how to fuse the data of multiple sensors scientifically and effectively on the data layer. Next, this manuscript elaborates on the above three issues. Empirical Mode Decomposition (EMD) and Local mean decomposition (LMD) are classical signal detecting methods proposed in recent years. However, research shows that the EMD and LMD methods also have the following shortcomings in signal detection and feature extraction: (1) The robustness of anti-noise is weak [33]; (2) the inefficient ability of decoupling frequency components [34]; (3) multivariate data cannot be processed at the same time; and (4) the mode mixing problem [35]. These shortcomings greatly affect the accuracy of signal processing [36]. In 2014, [PERSON] and [PERSON] [37] proposed a new multi-resolution modal decomposition method called variational mode decomposition (VMD). Since it was published, it has been widely considered by scholars in various fields, and the method has been applied to medical treatment [38], image processing [39], financial analysis [40], electrocardiogram (ECG) [41] and other fields. The results show that VMD has an accurate mathematical model and theoretical basis in theory, and is superior to EMD and LMD [42] in signal separation and noise robustness. In the aspect of rotating machinery fault detection, researchers have carried out in-depth research. [PERSON] et al. [43] used VMD to detect defect signals in different positions of rolling bearings in multistage centrifugal pumps. [PERSON] et al. [44] proposed a new rolling bearing fault detection method based on variational mode decomposition and improved the Kernel Extremum Learning Machine. [PERSON] et al. [45] proposed an independent VMD method based on correlation analysis to adaptively extract weak fault features and compound fault features of wheelset bearings.