The establishment of a suitable model under the limited monitoring data is the key problem to estimate RUL and an urgent need for industrial production. SVM is a machine-learning algorithm based on Vapnik-Chervonenkis theory, which is used to solve the problems of classification and prediction when the sample size is small [
123]. At present, SVM research mainly focuses on algorithm solution and model establishment. The purpose of algorithm solution is to address a constrained optimization problem by adopting the appropriate algorithm. The problem of model establishment includes optimization of model parameters, kernel function selection, feature vector extraction, and unbalanced sample. The aforementioned factors directly affect the model accuracy. Lu, et al [
124], considered the difficulty of obtaining ideal prediction results under a small sample size. Thus, they proposed a least squares SVM (LSSVM) to estimate the degradation trend of slewing bearings and used PSO to optimize LSSVM parameters. Compared with the RBFN, the LSSVM model was demonstrated to be more accurate and effective. Dong, et al [
125], used principal component analysis (PCA) to fuse the original features and reduce the dimension. Then, they used the LSSVM model to predict the bearing degradation process. Chen, et al [
126], proposed an RUL prediction method based on relative feature and multivariate SVM (MSVM). In contrast to univariate SVM, MSVM overcame the shortcomings of insufficient condition monitoring information and mined potential, and useful information from small sample size. Caesarendra, et al [
127], combined Cox proportional hazard model and SVM for failure degradation prediction of bearings. Widodo, et al [
128], proposed a prediction method based on survival analysis and SVM. Kaplan-Meier and probability density function estimators were used to generate survival probability, and the kurtosis of measured data and survival probability were used as input and output of the SVM, respectively. The trained SVM successfully predicted machine failure time. Tran, et al [
129], combined auto-regressive and moving average (ARMA) model, Cox proportional hazard model, and SVM for RUL prediction. Loutas, et al [
130], used wavelet packet nodal energies and Wiener entropy as the feature vector, and proposed ε-support vector regression method in predicting the RUL of rolling bearings. He, et al [
131], proposed a hidden Markov-SVM to predict surface roughness in hard turning. More published literature of applying SVM in RUL estimation of mechanical systems can be found in Refs. [
132‐
137]. SVM has been successfully developed rapidly in recent years, with an increasing number of studies focusing on SVM. However, SVM still has some problems to be solved, such as feature selection and large-scale training sample problem.