## 1 Introduction
It is assumed that, during the creep-fatigue interaction, damage evolution gradually processes with the ductility exhaustion of the materials and fails completely once the accumulated strain reaches a critical ductility. The strain-range partitioning method [8] isolates the overall creep-fatigue damage into the summation of the damage fraction determined by a separated strain range. According to the strain-range partitioning method, the strain range during a single cycle can be separated into subcycles, and the median cyclic fatigue life can be calculated by linear damage accumulation with partitioned strain ranges. [PERSON] [9] proposed the strain energy damage function model, which assumes that only tensile inelastic strain energy can induce the crack opening and propagation. In fact, only the deformation occurring in the tensile portion of the cycle with the crack open can contribute to the damage by propagating the crack. According to the strain energy damage function model, the fatigue life is related to the strain energy and material constants utilized in the Coffin-Manson equation. In this paper, we adopted the linear-summation rule for life prediction subjected to creep-fatigue interaction because of its conservative and robust nature among the life-prediction methods. Recently, theoretical and experimental studies have been conducted to predict fatigue [15; 16; 17; 18; 19; 20] and creep [21; 22; 23; 24] life for parts exposed to high temperatures and cyclic loads. Various evaluation methods (i.e., strain energy density, stress-based method, strain range method, linear-damage summation method, and ductility-exhaustion model) were used to evaluate the creep and fatigue life according to the loading conditions and the shape of the specimen. However, the previous studies were to prove the validity of the life-evaluation method or to predict the lifespan of the current state, and no studies were conducted to evaluate lifespan in real time. To the best of our knowledge, although deformation or displacement measurement in real time for health monitoring [25; 26; 27] have been conducted, the measured displacement-based life prediction in real time has not been studied and developed yet. There are several limitations to monitoring the life prediction in real time and utilizing it for maintenance. To evaluate life in real time, it is necessary to construct a complex model and perform analysis through various input conditions, which increases the time required for creep-fatigue life evaluation. Recently, surrogate models [28; 29; 30; 31; 32] have been used to reduce the time required for the analysis of complex models without sacrificing accuracy and detail. Surrogate modeling is widely used in engineering design loops and can be applied to various engineering problems. Surrogate models are also computationally cheaper and can approximate complex models. In this study, an efficient method for life prediction for a main steam pipe is proposed using the three-dimensional displacement measurement system (3 DDMS) and surrogate models developed by a stress-based approach. The aim of the proposed study was to develop a health-monitoring methodology for high-temperature piping to maintain the system and for periodic maintenance through life prediction of the steam pipe. The 3 DDMS was utilized to measure the displacements of the main steam pipe, and a series of pipe-stress analyses were performed to calculate the stress level within a measured displacement. Based on the stress and function of the measured displacements, we developed a surrogate model, correlating stress and displacement and life prediction under the creep-fatigue interaction. Our work implemented the stress analysis and life assessment of the piping system for the Manjung power plant in Malaysia, and it shows that the proposed method is quite a reasonable and reliable system for the stress and life assessment of high-temperature steam pipes.