A Multifractal Spectrum Algorithm Based on 1-Norm Minkowski Measure

doi:10.3969/j.issn.1000-1093.2012.07.010

Abstract

Abstract: A generalized multifractal spectrum algorithm based on 1-norm Minkowski measure was proposed to resolve the problem that present multifractal spectrum algorithm was too complicated to be applied in identification for early alarming, the experiment was implemented to prove the validity of the algorithm for tank-radiated noise identification as well. This algorithm reduced the numeration of the generalized multi-fractal spectrum by simplifies the measure according to the definition of generalized dimension. The experiment demonstrates that under low SNR the ability of early alarming identification by this method is higher than zero-pass analyzing method we use today.

Key words: information processing, identification for early alarming, multifractal spectrum, tank-radiated noise

CLC Number:

TJ43

ZHANG Sheng, FANG Xiang, ZHANG Wei-ping. A Multifractal Spectrum Algorithm Based on 1-Norm Minkowski Measure[J]. Acta Armamentarii, 2012, 33(7): 822-825.

References

［1］杨亦春，程翔，陈庆生．过零率分析在智能雷弹引信中的应用研究[J]．探测与控制学报, 1999，21（4）：15-18.
YANG Yi-chun，CHENG Xiang，CHENG Qing-sheng．The study on the application of zero-pass rate analyzing method in the acoustic fuze for an intelligent mine[J]．Journal of Detection & Control, 1999，21（4）：15-18. (in Chinese)
[2］丁庆海，庄志洪，祝龙石，等.混沌、分形和小波理论在被动声纳信号特征提取中的应用[J].声学学报，1999, 24(2):197-203.
DING Qing-hai, ZHUANG Zhi-hong, ZHU Long-shi, et al. Application of the chaos, fractal and wavelet theories to the feature extraction of passive acoustic signal[J]. Acta Acustica, 1999, 24(2):197-203. (in Chinese)
[3］张梅军，陈江海，侯宝科, 等.发动机故障分形诊断中噪声信号的分析和处理[J].解放军理工大学学报:自然科学版,2006,7(4):380-384.
ZHANG Mei-jun, CHEN Jiang-hai, HOU Bao-ke, et al. Analysis and processing of noise in engine fault diagnosis by fractal method [J]. Journal of PLA University of Science and Technology: Natural Science Edition, 2006,7(4):380-384. (in Chinese)
[4］关键，刘宁波，张建，等．海杂波的多重分形关联特性与微弱目标检测[J]．电子与信息学报，2010，32(1)：55-61.
GUAN Jian, LIU Ning-bo, ZHANG Jian, et al. Multifractal correlation characteristic of real sea clutter and low-observable targets detection[J]．Journal of Electronics ＆ Information Technology,2010，32(1)：55-61. (in Chinese)
[5］刘国华，黄平捷，龚翔,等. 基于分形维和独立分量分析的声发射特征提取[J]. 华南理工大学学报: 自然科学版, 2008,(1).：76-80.
LIU Guo-hua, HUANG Ping-jie, GONG Xiang， et al. Feature extraction of acoustic emission signals based on fractal dimension and independent component analysis[J]. Journal of South China University of Technology: Natural Science Edition, 2008,(1).：76-80. (in Chinese)
[6］包永强，赵力，邹采荣,等. 噪声环境下语音分形特征的提取和分析 [J]. 电子与信息学报, 2007, 29(3)：4.
BAO Yong-qiang, ZHAO Li, ZOU Cai-rong, et al. The abstraction and analysis of fractal characteristic of noisy speech [J]. Journal of Electronics & Information Technology, 2007, 29(3)：4. (in Chinese)
[7］陆扬.水中目标辐射噪声非线性特征提取研究[D].哈尔滨: 哈尔滨工程大学，2006.
LU Yang. Nonlineare feature extraction of underwater targets radiated noise[D]. Harbin: Harbin Engineering University, 2006. (in Chinese)
[8］赵健，李雷，蒲小清. 分形理论及其在信号处理中的应用[M].北京: 清华大学出版社，2008.
ZHAO Jian, LI Lei, PU Xiao-qing. Fractals theory & application on signal processing[M]. Beijing: Tsinghua University press, 2008. (in Chinese)
[9］ Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times and embedding windows[J]. Physica D, 1999, (127)：48-60.
[10］边肇祺，张学工. 模式识别[M].第2版. 北京: 清华大学出版社,2000.
BIAN Zhao-qi, ZHANG Xue-gong. Pattern recognition [M]. 2nd ed. Beijing: Tsinghua University Press, 2000. (in Chinese)
[11］ Karim Vibe, Jean-Marc Vesin. On chaos detection methods[J]. International Journal of Bifurcation and Chaos, 1996,6(3): 529-543.

[1]	LIU Yong-qing， JIANG Shuo， YU Dong， SHAO Xiao-tian. Effect of Narrowband Interference Suppression on Pseudorandom Code Zero Value [J]. Acta Armamentarii, 2016, 37(2): 293-298.
[2]	GUAN Si-hai， LI Zhi, HUANG Hui, WANG Zhe. Modified Zero-Attracting l₀-NLMS Algorithm [J]. Acta Armamentarii, 2016, 37(11): 2170-2176.
[3]	JIAO Chuan-hai, LI Yong-cheng, XIE Kai, YANG Yun-fu. Wideband Compressed Blind Sensing without Reconstruction Based on Expectation Deviation and Generalized Likelihood RatioTest [J]. Acta Armamentarii, 2016, 37(10): 1837-1843.
[4]	GUO Ye-cai, WU Hua-peng, WANG Hui, ZHANG Miao-qing. DNA Genetic Bat Algorithm Based Fractionally Spaced Multi-modulus Algorithm [J]. Acta Armamentarii, 2015, 36(8): 1502-1507.
[5]	ZHU Ming-qiang， HOU Jian-jun, LIU Ying ， LI Xu, TIAN Hong-juan. An Time Delay Difference Estimation Algorithm Based on Improved Unscented Particle Filter Suitable for Target Tracking inWireless Sensor Network [J]. Acta Armamentarii, 2015, 36(7): 1266-1272.
[6]	LI Zheng-zhou, HOU Qian, DAI Zhen, FU Hong-xia, GE Feng-zeng, JIN Gang. Dim Moving Target Detection Algorithm Based on Spatial-temporal Sparse Representation [J]. Acta Armamentarii, 2015, 36(7): 1273-1279.
[7]	GUO Ye-cai， ZHANG Miao-qing. A Multi-modulus Blind Equalization Algorithm Based on Shuffled Frog Leaping Algorithm [J]. Acta Armamentarii, 2015, 36(7): 1280-1287.
[8]	LIU Kun, MA Wen-ping, LIU Hong-ying. Speckle Suppression of Polarimetric Synthetic Aperture Radar Images Based on Sublook Data Correlation [J]. Acta Armamentarii, 2015, 36(7): 1288-1294.
[9]	ZHU Xia, CHEN Ren-wen, XIA Hua-kang, ZHANG Piao-yan. A Novel Image Registration Based on Cultural Particle Swarm Optimization Algorithm [J]. Acta Armamentarii, 2015, 36(6): 1033-1039.
[10]	DENG Bing, LUAN Jun-bao. Study of Reconnaissance Reception Algorithm of Wide-band Channelization in the Fractional Fourier Domain [J]. Acta Armamentarii, 2015, 36(6): 1040-1045.
[11]	WU Yi-quan， SONG Yu. Background Suppression of Small Infrared Target Image Based on Nonsubsampled Complex Contourlet Transform and GaussianWavelet Support Vector Regression [J]. Acta Armamentarii, 2015, 36(4): 687-695.
[12]	ZHANG Liang-jun, YANG Jie, LU Kai-wang, SUN Ya-dong. Underdetermined Blind Source Separation Based on Time-frequency Method Using Cyclostationary Characteristic [J]. Acta Armamentarii, 2015, 36(4): 703-709.
[13]	JIANG Run-xiang， LIN Chun-sheng， GONG Shen-guang. Electrostatic Electric Field Inversion Method for Ship Based on Point Charge Source Model [J]. Acta Armamentarii, 2015, 36(3): 545-551.
[14]	WU Zhen， DAI Ji-sheng， ZHU Xiang-lin， ZHAO De-an. A Real-valued Sparse Representation Method for DOA Estimation with Unknown Mutual Coupling [J]. Acta Armamentarii, 2015, 36(2): 294-298.
[15]	ZHANG Peng-fei, LIU Wei, JIANG Ze-lin, LIU Ji-yuan, ZHANG Chun-hua. Research on Shadow Enhancement for Synthetic Aperture Sonar Images [J]. Acta Armamentarii, 2015, 36(2): 305-312.