# Fault Prediction of Mechanical Equipment Based on Hilbert-Full-Vector Spectrum and TCDAN
## 1 Introduction  
With the development of industrialization, mechanical equipment has been widely used in all walks of life. There are many parts and components of mechanical equipment, and most of the equipment is in the state of frequent startup or continuous operation in the work. Various faults inevitably occur during the use of the equipment. When faults occur, they may affect normal production or even cause safety concerns. If the occurrence of equipment failure can be accurately predicted, to take targeted measures in advance, many uncontrollable risks will be avoided [1]. Therefore, it is of great practical significance to realize the fault prediction of equipment [2].  
For equipment fault prediction, it is mainly divided into the method based on the mechanism model, the method based on data-driven, and the method combining the two [3, 4, 5, 6]. Based on the mechanism model, the degradation model is established based on an in-depth analysis of the failure mechanism of the equipment [7]. Because the specific mechanism model of the device is almost difficult to build, it is not widely used.  
The data-driven method is mainly based on the historical operational data of the equipment to mine the change rule [8], to predict the faults of the equipment. To date, it has been widely studied by many scholars, such as the autoregressive model [9], the gray prediction model [10], support vector regression (SVR) [11, 12], the artificial neural network (ANN) [13] and other methods are used in the fault-tendency prediction or the remaining useful life prediction of mechanical equipment. With the development ofartificial intelligence technology, Recurrent Neural Network (RNN) [14, 15], Long Short-Term Memory (LSTM) [16, 17], Bidirectional Long Short-term Memory (BiLSTM) [18, 19], Gate Recurrent Unit (GRU) [20, 21] and other models have been used in fault-tendency prediction and remaining useful life prediction with their powerful time-series processing ability, and have achieved better results [8]. However, LSTM, BiLSTM, and GRU are still RNN structures in essence. Although the gradient explosion and disappearance problems in RNN have been alleviated, parallel computing still cannot be carried out.  
[PERSON] et al. proposed the temporal convolutional network (TCN) model [22], which is different from the structure of RNN and does not have the problem of gradient explosion and disappearance. At the same time, due to the introduction of the shared convolution kernel, the model can carry out parallel calculation, which effectively improves the speed of model calculation. The prediction effect in multiple tasks has exceeded that of LSTM and GRU and other recurrent neural network structures, providing a new idea for the processing of time-series tasks [22, 23, 24, 25]. However, the single temporal convolutional network ignores the correlation between different dimensions of data. Since the attention mechanism has achieved good results in measuring the importance of input features, the double-layer attention mechanism [26, 27, 28] was introduced based on the temporal convolutional network model. The introduced attention layer is used to mine the correlation between different input features and data at different historical moments, respectively. By increasing the weight of the corresponding parameters, the factors that have a greater impact on the prediction value in the input of the model are highlighted.  
On the other hand, the current fault-prediction research mainly focuses on fault-tendency prediction and the remaining useful life prediction of mechanical equipment. The prediction results cannot reflect the specific information of the type of equipment fault. In this paper, based on the traditional Hilbert-envelope spectrum [11, 29, 30], combined with full-vector spectrum [31, 32] technology, the dual-channel vibration data of the equipment are fused to obtain the spectrum information that can fully reflect the running state of the equipment, which is used as the fault-prediction feature.