## 1 Introduction  
Turbine blades are critical hot-section components in gas turbine engines. They can effectively convert gas energy into mechanical energy in gas turbine applications. High-performance turbine blades contribute to enhancing combustion efficiency and reducing the presence of harmful substances in exhaust emissions. However, these blades operate in extremely harsh environment conditions, such as in high temperature, high pressure, high rotational speed, and complex dynamic loading conditions [1]. The damage and failure of turbine blades will inevitably occur due to fatigue, corrosion, erosion, and oxidation, which will have a significant negative effect on the integrity and functionality of gas turbine applications [2]. Moreover, the maintenance cost of turbine blades is very high due to the much high material cost in the gas turbine applications [3]. Therefore, an accurate remaining useful life (RUL) prediction method for turbine blades could be significant in not only reducing the maintenance cost, but also in guaranteeing the operating reliability. In the past decades, several techniques have been proposed to evaluate the RUL or damage degree of gas turbine high temperature blades, mainly distinguished in physics of failure models, statistical analysis methods, and data-driven methods. [PERSON] et al. [4] developed a creep life prediction model for gas turbine first stage blades based on the finite element method and computational fluids dynamics (CFD) method. [PERSON] et al. [5] proposed a turbine blade life estimation method based on the numerical analysis of the blade conjugate heat transfer process. Furthermore, the effects of several important uncertainties were analyzed. [PERSON] et al. [6] investigated the fatigue crack formation mechanisms of an actual cooling turbine blade based on a thermal-fluid-solid coupling model. The blade's useful life under low-cycle fatigue was estimated based on the fatigue analysis results. [PERSON] et al. [7] analyzed the creep performance through the fluid-structure-interaction simulation of a three-dimensional (3D) blade, and the creep life prediction method for a single crystal blade was proposed based on the parameters at the skeletal points. Moreover, some researchers applied a statistical method for considering the uncertainties of the blade life predication. [PERSON] et al. [8] obtained the probability density functions of the turbine disc life according to the creep and fatigue testing data. [PERSON] et al. [9] proposed a Bayesian statistics-based method for the fatigue life prediction of an aircraft turbine disc. [PERSON] et al. [10] evaluated the statistical failure risk of turbine blades using the Monte Carlo simulation model of blade tip clearance data. [PERSON] et al. [11] proposed a probabilistic life assessment approach for a cooled turbine blade, which combined the Monte Carlo simulation and response surface method. In order to make full use of the monitoring histories, many researchers carried out the surrogate modeling approach based on data-driven methods for on-line blade life prediction. [PERSON] et al. [12] developed a dynamic Kriging surrogate model to efficiently and accurately evaluate the creep-fatigue life of turbine disks. [PERSON] et al. [13] applied Bayesian belief networks to predict the deterioration status of the first stage rotor blades and the second stage vanes in high pressure turbine. [PERSON] et al. [14] proposed an artificial neural network method for estimating the rotor blade life cycle of an industrial gas turbine. [PERSON] et al. [15] proposed an adaptive RUL prediction model of high-pressure turbine blades by combining long short-term memory networks and a failure mode recognizer. [PERSON] et al. [16] proposed a new RUL estimation model based on an adaptive neuro-fuzzy inference system and particle filtering approaches. From the above works in the literature, it can be seen that reliable blade data are fundament to accurately ensure the RUL prediction.