一种基于改进KELM的在线状态预测方法

针对核超限学习机（KELM）在线状态预测过程中，核矩阵阶数不断增长且难以跟踪时变动态特征的问题，提出了一个具有遗忘因子的稀疏KELM在线状态预测方法。通过引入遗忘因子构建新的目标函数，使稀疏字典中各元素依据时间远近具有不同权重，保证了模型对动态变化的有效跟踪；通过最小化字典的快速留一交叉验证（FLOO-CV）误差，选择具有预定规模的关键节点构成字典；基于当前字典，通过矩阵初等变换和分块求逆，实现相关参数的递推更新。某型飞机发动机的状态预测结果表明，与目前已有的3种在线序贯KELM相比，所提方法在6个监测项目上的平均训练时间分别缩短了7.5%、62.0%和81.9%，平均预测精度分别提升了44.0%、19.9%和50.9%。 

An improved KELM based online condition prediction method

In order to curb kernel matrix expansion and track the time-varying dynamic characteristics when kernel extreme learning machine (KELM) is applied to online condition prediction, a sparse KELM online prediction algorithm with forgetting factor is proposed. By introducing forgetting factor, a new objective function is constructed, which makes every element in sparse dictionary has different weights related to timestamp and ensures the effective tracking of the dynamic changes. By minimizing the fast leave-one-out cross-validation (FLOO-CV) error, key nodes with predetermined size are selected to form a dictionary. At the same time, the online recursive updating of model parameters is realized based on the elementary transformation of matrix and the inverse formula of block matrix. The proposed algorithm is compared with the recently proposed three online sequential KELM algorithms. The experimental results of aero-engine condition prediction show that the average training time of the proposed algorithm on six monitoring items is reduced by 7.5%, 62.0% and 81.9% respectively, and the average prediction accuracy is improved by 44.0%, 19.9% and 50.9% respectively.