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Echo state kernel recursive least squares algorithm for machine condition prediction

机译：机器状态预测的回波状态核递推最小二乘算法

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摘要

Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and convexity. Nevertheless, KAF’s ability to handle temporal tasks is limited, because it is essentially a feed-forward neural network that lacks dynamic characteristics. Traditionally, a sliding widow that contains consecutive data points is constructed to deal with the temporal dependency between data points at neighboring time steps, but the restricted widow length may be incapable of capturing temporal patterns on a larger time scale. To manage this issue, a novel sequential learning approach called echo state KRLS (ES-KRLS) algorithm is proposed by incorporating a dynamic reservoir into kernel recursive least squares (KRLS) algorithm. The reservoir, consisting of a large number of sparsely interconnected hidden units, is treated as a temporal function that transforms the history of the time series into a high-dimensional reservoir state space. Subsequently, the spatial relationship between the reservoir state and the target output is effectively approximated by KRLS algorithm. With the utilization of the fixed reservoir, our novel method not only maintains the simplicity of the learning process but also leads to a significant improvement in the capability of modeling dynamic systems. Numerical results on benchmark tasks demonstrate the excellent performance of the novel method with respect to long-term prediction. Finally, an online prognostic method that combines ES-KRLS and a Bayesian technique is developed for tracking the health status of a degraded system and predicting remaining useful life (RUL). This prognostic method is applied to a turbofan engine degradation dataset to demonstrate its effectiveness.
机译：核自适应滤波器（KAF）由于其在线自适应方案，通用逼近能力和凸性而被广泛用于时间序列预测。尽管如此，KAF处理临时任务的能力是有限的，因为它本质上是一个缺乏动态特性的前馈神经网络。传统上，包含连续数据点的滑动寡妇被构造为处理相邻时间步长的数据点之间的时间依赖性，但是受限制的寡妇长度可能无法在较大的时间尺度上捕获时间模式。为了解决此问题，通过将动态库合并到内核递归最小二乘（KRLS）算法中，提出了一种称为回波状态KRLS（ES-KRLS）算法的新颖顺序学习方法。由大量稀疏互连的隐藏单元组成的储层被视为将时间序列的历史转换为高维储层状态空间的时间函数。随后，通过KRLS算法有效地近似了储层状态与目标产出之间的空间关系。利用固定水库，我们的新方法不仅保持了学习过程的简单性，而且还大大改善了动态系统建模的能力。在基准任务上的数值结果证明了该新方法在长期预测方面的出色性能。最终，开发了一种结合了ES-KRLS和贝叶斯技术的在线预测方法，用于跟踪退化系统的健康状况并预测剩余使用寿命（RUL）。该预测方法应用于涡轮风扇发动机退化数据集，以证明其有效性。

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