# Fault Diagnosis Method Based on Time Series in Autonomous Unmanned System
## 2 Related Work  
As a source of information, sensors play an essential role in automatic control systems, and the accuracy of measurement results directly affects the entire system's operation. Faulty sensor signals can lead to incorrect decisions that affect system safety and productivity. Researchers have designed many methods for the fault diagnosis of sensors, such as the diagnosis method based on signal analysis [9; 10; 11; 12; 13], and the diagnosis method based on fault pattern recognition [14; 15; 16; 17; 18]. The approach adopted in this paper is to treat the sensor data as a time series. Time series classification has been widely used in all aspects of life such as pattern recognition, industrial control, anomaly detection, etc. Time series data have high dimensions and are difficult to classify. Symbolic representation of time series refers to the representation of high-dimensional and noisy continuous real-valued data into low-dimensional and intuitive symbolic sequence data on the premise of maintaining and reflecting the basic characteristics of time series data. There are many studies on the characterization of time series. [PERSON] et al. presented piecewise approximate polymerization (PAA) [19]. This method is a way to reduce the dimension of time series data, which can effectively improve computing efficiency and reduce the cost of data storage. [PERSON] et al. first proposed SAX, a symbol approximation representation method based on the piecework approximation aggregation method [20]. The value is mapped to the corresponding coincident space according to the segmentation points of the sequence under the Gaussian curve for symbolic representation. [PERSON] proposes an improved method for traditional symbolic approximate representation to solve the problem of distance measurement. This method uses UMD distance to update the lookup table, making it more advantageous in lower bound tightness and time complexity compared with the original method [21]. Random shifting-based SAX is an improved method proposed by [PERSON], which can significantly improve the tightness of the lower bound without increasing the corresponding representation granularity [22]. [PERSON] put forward a way that adds trend information based on traditional symbol approximation aggregation. The central idea is to use linear regression for each segment to find the mean and slope and convert the time series into a binary string, the fitting error and classification effect are better than the good traditional symbol approximate aggregation method [23]. [PERSON] et al. put forward a new kind of long-time series symbol representation method based on the trends. The difference from other methods is to focus on retaining most of the trend features and patterns of the original series [24]. The above techniques are all based on the assumption that the standardized time series obeys Gaussian distribution, which is often difficult to be established in the natural environment. Especially in autonomous unmanned systems, data do not follow normal distribution due to sampling and other reasons, so the method often leads to large errors in the subsequent process. [PERSON], [PERSON] et al. proposed an adaptive time series representation aSAX (adaptive SAX), which combines the traditional symbol approximation representation method with the k-means clustering method to find adaptive symbol segmentation points. This method is superior to the classical time series representation method in all kinds of data sets with or without Gaussian distribution, but the time complexity increases [25]. In 2016, [PERSON], [PERSON] proposed an enhanced time series representation method; this method is built on the basis of extended SAX. The maximum, minimum, and average values of each time series are constructed as vectors, the cosine similarity of the vector is used to measure the similarity of the vector, and k-means clustering method is used to divide the symbol region.