## 1 Introduction  
Methane hydrate, also known as combustible ice, looks like ice and burns when exposed to an open flame [1; 2; 3]. Countries such as the United States, Japan, and Germany lead the world in mining combustible ice [4; 5; 6; 7]. Its combustion produces ten times more energy than coal, gasoline, and natural gas, making it the ideal energy source for a low-carbon society [8; 9; 10]. Therefore, methane sensors used to detect methane are important for the exploitation of combustible ice [11]. However, due to the impact of prolonged methane exploration engineering under the water, the methane gas sensor output signal is not only relevant to gas concentration, but also influenced by environmental factors, for example, sway, shake, temperature, and degradation of the chemical response of the sensitive materials (e.g., heating of wires or oxidation). These factors result in the gas sensor signal drifting and decreasing its detecting accuracy. Owing to the extensive use of such sensors, failures are inevitable. It is thus very necessary to distinguish the types of faults, and at the same time, to predict the occurrence time of faults in advance before they occur. Therefore, fault diagnosis and forecasting of gas sensors have become important issues for their applications [12; 13; 14]. In general, methods of fault detection for gas sensors can be grouped into 4 kinds: knowledge-based, model-based, data-driven, and hybrid/active [15; 16; 17]. As the data-driven method is fit for the task of complex data, it could accomplish the detection of fault diagnosis. A lot of professors and researchers are using this method in their papers [18; 19]. Fault prediction methods used in sensors can be separated into the following two types: time-series and deep-learning (DL) prediction methods. The first method is based on the concept of statistics. After the pre-processing of differences, recursive prediction is performed on the data from front to back. The disadvantage of this model is that the prediction time is short and the accuracy is low. The second method combines statistical time-series forecasting methods and can predict a long time series with higher accuracy, but it needs to be trained for a long time. Recently, DL [20; 21; 22] has been used to extract high dimensional features of fault diagnosis data and classify them directly, avoiding the shortcoming of requiring handcrafted features designed by engineers [23; 24]. Therefore, a significant amount of DL methods have been extensively used in fault diagnosis [25; 26]. [PERSON] et al. [27] used a convolutional neural network (CNN) for fault diagnosis. [PERSON] et al. [28] used a CNN plus random forest (RF) for sensor array diagnosis. From the work of previous researchers, we find that the algorithms used in these methods to perform fault diagnosis of sensor arrays have been less studied. The transformer is one of the most effective types of DL in the natural language processing (NLP) field. Transformer models were proposed by [PERSON] et al. (2017) [29] in the context of machine translation tasks [30; 31; 32; 33], natural language, audio, and images [34; 35; 36]. However, these tasks often need an extremely high computational and memory cost. The difficulty generally arises from the global vision of self-attention, which transforms n dimension inputs with a quadratic memory O (N\({}^{2}\)). So, transformer models are difficult to train, and their context is restricted. In this case, the model had a limited length of time series to learn and could not learn the information on the data for as long as possible [37; 38; 39; 40]. Recently, researchers have developed a number of methods to increase the context length without decreasing the results, and some of them have proposed sparse factorizations of the attention matrix which can reduce the self-attention complexity to O (N \(\sqrt{N}\)) [41]. Other researchers have also decreased the complexity to O (N log N) using locality-sensitive hashing [42]. This made the model scale to long sentences.