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The degradation starting time is an important variable affecting the accuracy of degradation path prediction, but little work has been considered in existing studies. This article investigates the problem of predicting the performance of rolling element bearings based on early degradation analysis. Based on an improved dual linear structural support vector machine with envelope spectrum algorithm and $\mu +4\sigma$ criteria, a new health indicator is proposed to detect the degradation starting time. As well the detected time is sensitive to early anomalies. In addition, according to the degradation starting time, a convolutional neural network prediction model is established to predict the degradation path. Experiments show the effectiveness and superiority of the proposed method.

In modern industrial processes, the remaining useful life (RUL) of core manufacturing equipments is regarded as an important indicator for assessing the continuous serving ability by considering safety and reliability. Accurate RUL predictions contribute to saving maintenance costs, and can be applied to the life extension technologies. Being subjected to complicated noise environments, the fractional characteristic usually exists in the stochastic heterogeneous diffusions. Traditional methods mostly utilize the fractional Brownian motion (FBM) to describe a simple class of memory effect in the time domain, but lose sight of potential time-varying state-dependencies from historical information. In view of uncertain lagging levels, the state-dependent delay (SDD) is introduced to construct a novel nonlinear fractional degradation model in this paper. Based on a specific discretization scheme, the unknown parameters are estimated by optimizing an approximate log-likelihood function. The RUL distribution is then derived under a Markovian statistical transformation. Finally, a case study on certain hearth wall degradation processes is provided to validate the proposed prognostic method in production practice.