An integrated and adaptive prognostic framework is proposed for hiddenly degrading actuator in closed-loop system. Furthermore, the dual influence of degradation progress and operation time is considered in the established augmented model. It is important to obtain accurate and real-time distribution of degradation information under different degradation progress. Firstly, the expectation and variance of hidden index, unknown operation time parameter and degradation progress parameter are evaluated by designing a double-layer rolling optimization strategy. Then, the uncertainty distribution of degradation model is iteratively derived by employing Bayesian theorem. Finally, the distribution of remaining useful life (RUL) is calculated based on available distribution of degradation model and states. The effectiveness of proposed algorithm is demonstrated by a mold model of continuous casting driven by servo motor.