## 1 Introduction  
A mine's hoisting system is the only way to connect the underground with the ground and is known as the \"throat\" of the mine [1; 2]. It is a mechatronics-hydraulics-integrated system (comprising a driving friction pulley, hoisting ropes, head sheaves, containers, balancing tail ropes, etc.) [3], including complex dynamic characteristics like inertia, flexibility, and damping in its operation. The tail rope is an important component of the hoisting system. It is set up to balance the gravity of the hoisting rope and to obtain equal moments in the mine hoisting system [3]. Hence, the working state and mechanical properties of the tail rope directly affect the safety of mine production [4]. The balancing tail ropes (BTRs) are located at the bottom of the hoisting container, which is in the dark shaft all (or most) the time [5]. Research and production experience show that the causes of the BTR faults (disproportional spacing, twisted rope, broken strand, broken rope, etc.) include operational vibration, the impact of the falling ore, wind in the shaft, corrosion, etc. Faults and accidents give rise to many problems, such as influencing the system stability, breaking shaft equipment, threatening the lives of mine workers and causing production to stop. However, the traditional maintenance of BTRs only depends on workers with handheld flashlights, which is difficult, inefficient, and unsafe. The frequent fault occurrences of BTRs pose a serious threat to the safe operation of the hoisting system. For example, in the main shaft hoisting system of the Tong-ting Coal Mine Enterprise, tail ropes were broken or damaged five times during 1989-1998. Its tail ropes have been replaced ten times because of faults, resulting in a serious loss of manpower, material resources, and financial resources. The tail ropes in the main shaft of the Bei-ming-he Iron Mine Enterprise broke and fell on 14 February 2011, causing shaft damage, and resulting in substantial economic losses. Therefore, health monitoring for identifying faults in BTRs and taking appropriate measures to eliminate the faults would be beneficial to the safety and efficiency of hoisting systems. A variety of research focusing on health monitoring and fault diagnosis methods in hoisting systems has already been conducted. For instance, [PERSON] et al. [6] proposed a condition-monitoring method based on variational mode decomposition and support vector machine via vibration signal analysis to facilitate accurate fault monitoring of the abnormal lifting load of a mine hoist. [PERSON] et al. [7] also proposed a mine hoist fault diagnosis method using a support vector machine. [PERSON] et al. [8] theoretically and experimentally analyzed the stator current and load torque of a three-phase induction machine in a hoisting winch system and realized the fault detection of the wire rope. In addition, an application of a probabilistic causal-effect model based on the artificial fish-swarm algorithm for fault diagnosis in mine hoists was proposed by [PERSON] [9]. However, there are few studies on the health monitoring and fault diagnosis of hoisting system BTRs. [PERSON] [5] designed an online monitoring and early warning system for the hoist balance tail ropes based on machine vision. The system extracts the image feature parameters with integral projection and Hu invariant moment, and the pattern recognition is ultimately used to identify the fault information. The method used by [PERSON] needs complex image processing and manual feature extraction in the early stage, which has the disadvantages of low efficiency and poor accuracy when handling big data, and is difficult to meet the requirements of real time and accuracy. At the same time, it is unable to cover the entire feature space because there are so few samples in the dataset, meaning that the model's generalization performance is poor.