电子学报 ›› 2021, Vol. 49 ›› Issue (12): 2323-2329.DOI: 10.12263/DZXB.20201332

• 学术论文 • 上一篇    下一篇

基于EMD‑LS的非平稳时间序列多重分形去趋势波动分析方法

罗远兴1,2, 李志红1,2, 梁兴1,2, 李超1,2, 胡凤城1,2   

  1. 1.南昌工程学院机械与电气工程学院, 江西 南昌 330099
    2.南昌工程学院江西省精密驱动与控制重点实验室, 江西 南昌 330099
  • 收稿日期:2020-11-26 修回日期:2021-05-06 出版日期:2021-12-25 发布日期:2021-12-25
  • 通讯作者: 李志红
  • 作者简介:罗远兴 男,1998年6月生于重庆铜梁.现为南昌工程学院机械与电气工程学院硕士研究生.主要研究方向为故障诊断与信号处理. E‑mail:346907520@qq.com
    李志红(通信作者) 女,1963年8月生于江西南昌.现为南昌工程学院教授、硕士研究生导师.主要研究方向为水力机组故障诊断. E‑mail: 502522183@qq.com
    梁 兴 男,1980年7月生于河南南阳.现为南昌工程学院副教授、硕士研究生导师.主要研究方向为水力机组在线监测与故障诊断.E‑mail: 44562685@qq.com
  • 基金资助:
    江西省教育厅科技项目(GJJ170988);国家自然科学基金(51969017);南昌工程学院研究生创新基金项目(YJSCX202018)

Multi‑Fractal Detrended Fluctuation Analysis Method for Non‑Stationary Time Series Based on EMD‑LS

LUO Yuan-xing1,2, LI Zhi-hong1,2, LIANG Xing1,2, LI Chao1,2, HU Feng-cheng1,2   

  1. 1.School of Mechanical and Electrical Engineering,Nanchang Institute of Technology,Nanchang,Jiangxi 330099,China
    2.Jiangxi Province Key Laboratory of Precision Drive and Control,Institute of Technology,Nanchang,Jiangxi 330099,China
  • Received:2020-11-26 Revised:2021-05-06 Online:2021-12-25 Published:2021-12-25
  • Contact: LI Zhi-hong

摘要:

多重分形去趋势波动分析(Multi?Fractal Detrended Fluctuation Analysis, MFDFA)处理非平稳时间序列存在趋势项难以准确移除的问题,为此本文引入经验模态分解(Empirical Mode Decomposition, EMD)并通过趋势项自动判定方法提取趋势项,再利用最小二乘(Least Squares, LS)法对趋势项再拟合(EMD?LS),进而提出新的多重分形分析方法(EMD?LS?MFDFA),并针对具有理论值的二项式多重分形序列(Binomial Multifractal Sequence, BMS),验证了EMD?LS?MFDFA法的有效性和稳定性,然后进行仿真分析.研究表明:相较于MFDFA方法,EMD?LS?MFDFA移除趋势精度更高,计算的广义Hurst指数和质量指数的均方根误差较小,其中2阶的EMD?LS?MFDFA具有更高的计算精度,是1阶的1.8倍,分析不同参数的BMS序列,其多重标度曲线与理论曲线相吻合,证明了该算法具有较好的稳定性和精准的分析能力.

关键词: 多重分形, 去趋势波动分析, 非平稳时间序列, 经验模态分解, 最小二乘, BMS信号

Abstract:

Multi-fractal detrended fluctuation analysis(MFDFA) deals with the problem that non-stationary time series has trend items that are difficult to accurately remove. For this reason, this paper introduces empirical mode decomposition(EMD) and adopts trend items The automatic determination method extracts the trend item, and then uses the least squares(LS) method to refit the trend item(EMD-LS), and then proposes a new multi-fractal analysis method(EMD-LS-MFDFA), and the binomial multi-fractal sequence(BMS) of theoretical value verifies the validity and stability of the EMD-LS-MFDFA method, and then conducts simulation analysis. Research shows that compared with the MFDFA method, EMD-LS-MFDFA has higher precision in removing trend, and the calculated generalized Hurst index and quality index have a smaller root mean square error. The calculation accuracy of the second-order EMD-LS-MFDFA is 1.8 times higher than that of the first order. The multiple scale curve is consistent with the theoretical curve by analysis of the BMS sequence of different parameters, which proves that the algorithm has good stability and accurate analysis ability.

Key words: multi-fractal, detrended fluctuation analysis, non-stationary time series, empirical modal decomposition, least squares, BMS signal

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