基于改进稀疏KELM的在线非平稳动态系统状态预测方法

doi:10.3969/j.issn.1001-506X.2020.09.18

Abstract

Abstract:

A new state prediction method for the problem is proposed that the kernel based incremental extreme learning machine (KB-IELM) has insufficient ability to track the time-varying state of non-stationary dynamic systems. A new objective function is constructed by integrating the forgetting factor and the adaptive time-varing regulation factor. The key nodes with the predetermined scale are selected to form the dictionary by minimizing the fast leave-one-out cross-validation (FLOO-CV) error of the dictionary. Different weights are assigned to the key nodes in the dictionary according to the sequential order via mixing the forgetting factor. Based on the FLOO-CV principle, the different regulation parameters are assigned to different nonlinear regions by utilizing the algorithm of the beetle antennae search (BAS). The online recursive update of weight vectors is realized by matrix elementary transformation and block inversion. The model is applied to the non-stationary Mackey-Glass chaotic time series prediction and the state prediction of an aircraft engine. Compared with the latest two methods of the non-stationary online sequential kernel extreme learning machine (NOS-KELM) and the online sparse kernel extreme learning machine with adaptive regulation factor (OSKELM-ARF), the training accuracy is improved by 66.67% and 50.72 %. The prediction accuracy is improved by 67.02% and 56.34%, and the maximum prediction error is reduced by 67.27% and 51.09%. Then the average relative error rate is reduced by 67.18% and 59.62% respectively. It is proved that the proposed algorithm effectively improve the accuracy of online prediction.

Key words: extreme learning machine (ELM), forgetting factor, adaptive time-varying regulation factor, state prediction

CLC Number:

V243

Xing LIU, Houqing XIONG, Jianyin ZHAO, Min ZHU. State prediction method of online non-stationary dynamic system based on improved sparse KELM[J]. Systems Engineering and Electronics, 2020, 42(9): 2022-2032.

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References 19

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算法	正则化参数C	核参数σ	其他
ReOS-ELM	2×10³	—	L=50
ALD-KOS-ELM	1×10³	10	b=0.000 01
FOKELM	2×10⁴	10	z=50
KB-IELM	10	10	—
NOS-KELM	2×10⁴	10	m=50, η=0.8
OSKELM-ARF	2×10⁵	10	m=50, η=0.8
本文算法	—	10	m=50, δ=0.95

算法	训练		测试
算法	时间/s	RMSE	时间/s	RMSE	MAPE	MRPE
ReOS-ELM	7.011 6	0.016 6	9.00E-04	0.015 2	0.036 8	0.009 8
ALD-KOS-ELM	0.102 1	0.011 2	3.61E-04	0.010 9	0.025 0	0.008 1
FOKELM	0.081 6	0.026 9	4.32E-04	0.012 3	0.031 7	0.008 3
KB-IELM	8.121 3	0.017 5	9.80E-04	0.015 3	0.042 0	0.010 8
NOS-KELM	0.421 1	0.010 2	2.32E-04	0.009 4	0.027 5	0.006 4
OSKELM-ARF	3.668 1	0.006 9	6.96E-04	0.007 1	0.018 4	0.005 2
本文算法	1.512 1	0.003 4	2.77E-04	0.003 1	0.009 2	0.002 1

算法	正则化参数	核参数	其他
ALD-KOS-ELM	1×10³	10	m=30
NOS-KELM	2×10⁴	10	b=0.000 01
OSKELM-ARF	2×10⁴	10	m=30, η=0.8
本文算法	2×10⁴	10	m=30, δ=0.95

算法	训练	测试
算法	RMSE	RMSE	MAPE	MRPE
ALD-KOS-ELM	0.062 3	0.039 0	0.062 9	0.011 7
NOS-KELM	0.077 5	0.050 4	0.075 7	0.015 2
OSKELM-ARF	0.075 2	0.045 9	0.082 4	0.082 4
本文算法	0.010 0	0.009 1	0.040 3	0.001 7

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State prediction method of online non-stationary dynamic system based on improved sparse KELM

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