The prediction of remaining useful life (RUL) is a critical component of prognostic and health management for industrial systems. In recent decades, there has been a surge of interest in RUL prediction based on degradation data of a well-defined degradation index (DI). However, in many real-world applications, the DI may not be readily available and must be constructed from complex source data, rendering many existing methods inapplicable. Motivated by multivariate sensor data from industrial induction motors, this paper proposes a novel prognostic framework that develops a nonlinear DI, serving as an ensemble of representative features, and employs a similarity-based method for RUL prediction. The proposed framework enables online prediction of RUL by dynamically updating information from the in-service unit. Simulation studies and a case study on three-phase industrial induction motors demonstrate that the proposed framework can effectively extract reliability information from various channels and predict RUL with high accuracy.