# Predicting the Life of Varistors via a Nonlinear Coefficient Based on a Small-Scale Data Model
## 1 Introduction  
The metal oxide varistor (MOV) is a nonlinear resistance element with zinc oxide (ZnO) as the main component. Due to its high surge current tolerance and very large current absorption capacity, it is the key component in surge protective devices (SPD). At present, it has been widely used in systems to protect railway communication from. Its performance directly affects the safety of the whole system [1]. In their applications, due to the influence of environmental factors such as high voltage and high temperature, varistors are more likely to deteriorate and often fail to reach their calibrated working life. At present, the operation and maintenance of SPD is generally periodic maintenance, which is mainly conducted by staff on a regular basis to observe whether the appearance is damaged or whether the thermal fuse device is fused. The efficiency is relatively low, and only SPDs that have completely failed can be detected; the SPDs that are about to fail or have just failed are often unable to respond. With the advancement of intelligent railways, it is necessary to conduct effective and accurate online evaluations of lifetime surge capacity to prevent disasters caused by SPDs and improve the level of lightning protection operation and maintenance. With the development of electronic technology, monitoring methods have become increasingly mature and advanced. It is feasible to carry out online life predictions for surge protective devices under the existing technical conditions [2; 3; 4; 5; 6]. At present, the breakdown voltage U\({}_{\text{1 mA}}\) and leakage current I\({}_{\text{Leakage}}\) are often used to judge the degree of deterioration in varistors. However, these two indicators can only reflect the working state of the varistor and cannot reflect the degree of deterioration, and there will be a certain amount of lag in their judgment on the failure of the varistor [7; 8]. The nonlinear coefficient is an important index reflecting the working performance of the varistor. The nonlinear coefficient is a calculated parameter that reflects the ratio ofthe current to the voltage after the voltage exceeds a threshold. The greater the value, the more effective the protection of the varistor on the circuit. At present, it has been shown that there is a strong correlation between the nonlinear coefficient and the degree of deterioration in a varistor. When the varistor works normally, its range is generally 20-100 [9]. [PERSON] et al. [10] found that the nonlinear coefficient of a varistor changes regularly under the impact current. Through a varistor impact experiment, [PERSON] et al. [11] found that the nonlinear coefficient of the varistor would decrease with its degradation. In recent years, some research work has explored the factors affecting the nonlinear coefficient. [PERSON] et al. [12] found that the formation of a liquid phase during sintering has a significant influence on the nonlinear coefficient, which is related to the chemical reaction between the liquid phase and the mixed elements at the grain boundary. [PERSON] et al. [13] found that the nonlinear coefficient has a great relationship with the morphology of the grain boundary. At the same time, there are many researchers and scholars committed to improving the nonlinear coefficient of varistors [14; 15; 16; 17; 18], but there are few studies that have applied the nonlinear coefficient as the main parameter to construct the lifetime model. In practice in engineering, there is often a need for a way to make automatic and accurate judgments on the deterioration of varistors. Nowadays, with the continuous development of the computer industry and the maturity of artificial neural network technology, this goal has become possible. At present, the trend of development in neural networks is deeper and more complex structures, which have a good fitting effect in the face of big data.