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.

在现代工业过程中，核心制造设备的剩余使用寿命（RUL）被视为考虑安全性和可靠性来评估持续服务能力的重要指标。准确的 RUL 预测有助于节省维护成本，并可应用于寿命延长技术。由于受到复杂噪声环境的影响，随机异质扩散中通常存在分数特征。传统方法大多利用分数布朗运动 (FBM) 在时域中描述一类简单的记忆效应，但忽略了历史信息中潜在的时变状态依赖性。鉴于滞后水平的不确定性，本文引入状态相关延迟（SDD）来构建新的非线性分数退化模型。基于特定的离散化方案，通过优化近似对数似然函数来估计未知参数。然后在马尔可夫统计变换下导出 RUL 分布。最后，提供了有关某些炉膛壁降解过程的案例研究，以在生产实践中验证所提出的预测方法。