考虑奇点扰动问题的时间序列预测方法

目前，对于各种工业产品可靠性或者剩余寿命的预测方法通常都基于历史退化数据，这些历史数据的趋势变化可以为产品最终的维修和保障决策提供理论依据。然而，退化数据中出现的奇点扰动问题经常导致预测的准确性严重下降，这是可靠性预测领域的一个巨大挑战。为解决这个问题，该文采用样条函数方法作为数据趋势逼近模型，针对退化趋势中存在的各种奇点扰动情况，三次非多项式样条模型的二阶导数可以形成观测状态序列。引入了一种改进的结合粒子群优化算法的加权隐马尔科夫方法来外推样条函数所生成的观测序列，计算所产生的参数将更新样条函数的参数，组成一套综合完整的优化预测器。仿真和实例实验均证明了该方法的有效性。

A Comprehensive Time Series Prediction Considering Singularity Perturbation Problems

Current model for remaining useful life prognostic is usually based on the historical data, which can provide evidence for maintenance. However, singularity arising in the degradation data frequently give rise to a bad decline in prediction accuracy, this phenomenon is a great challenge for the time series prediction. To address this issue, we develop a new surrogate modeling prognostic approach based on cubic non-polynomial spline model in this paper. Meanwhile, due to the singularity perturbation in degradation tendency, the spline model's second derivative can be adopted and calculated to form a series of observation frames, and then a weighted hidden Markov model (HMM) method combined with particle swarm optimization (PSO) is used to forecast the observation sequence, then rebuild the spline function. A simulation example and a practical application involving typical singularities verified the effectiveness of the proposed method.