Ethylene-Vinyl Acetate (EVA) copolymer was synthesized from ethylene and vinyl acetate at high temperatures and ultra-high pressures. In this condition, any reactor disturbances, such as process or mechanical faults, may trigger the run-away decomposition reaction. This paper proposes a procedure for constructing a conditional health status prediction structure that uses a virtual health index (HI) to monitor the reactor bearing’s remaining useful life (RUL). The piecewise linear remaining useful life (PL-RUL) model was constructed by machine learning regression methods trained on the vibration and distributed control system (DCS) datasets. This process consists of using Welch’s power spectrum density transformation and machine learning regression methods to fit the PL-RUL model, following a health status construction process. In this research, we search for and determine the optimum value for the remaining useful life period (T_RUL), a key parameter for the PL-RUL model for the system, as 70 days. This paper uses four-fold cross-validation to evaluate seven different regression algorithms and concludes that the Extremely randomized trees (ERTs) is the best machine learning model for predicting PL-RUL, with an average relative absolute error (RAE) of 0.307 and a Linearity of 15.064. The Gini importance of the ensemble trees is used to identify the critical frequency bands and prepare them for additional dimensionality reduction. Compared to two frequency band selection techniques, the RAE and Linearity prediction results can be further improved to 0.22 and 8.38.