电阻点焊位移信号的混沌与分形特性试验
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摘要
以混沌理论为基础对电阻点焊位移信号进行分析与研究,通过对7种不同工作状态下时间序列的最大Lyapunov指数计算,发现点焊位移信号的值均大于0,证明位移信号中存在混沌现象,应采用混沌的方法研究与分析点焊位移信号,该研究为点焊质量的判断和预测开辟有效的途径。由于用经典欧式几何方法描述位移信号误差较大,提出用分形维数作为特征值来量化具有混沌特性的点焊质量,点焊位移检测试验结果表明此方法能反映点焊质量微小变化,可提高质量检验的准确性。
Based on chaos time series and fractal theory,electrode displacement signals are studied in the process of spot welding. Seven states of electrode displacement signals are studied to determine the largest Lyapunov exponents from acquired time series data.According to the calculating results using phase space reconstruction,the largest Lyapunov exponents are positive number in the seven states of electrode displacement signals,and chaos characteristics are discovered in electrode displacement signals of spot welding.Therefore,the result shows a new state in the process of the spot welding and electrode displacement signals should be analysed by chaos method.In order to research electrode displacement signal,box counting dimension is put forward to analyze and calculate chaos characteristics.The experiment and calculation results indicate that the box counting dimension of electrode displacement signals is clearly distinguishable in the welding process with different welding parameters.A new method of judging and forecasting the quality of spot welding is provided.
Based on chaos time series and fractal theory,electrode displacement signals are studied in the process of spot welding. Seven states of electrode displacement signals are studied to determine the largest Lyapunov exponents from acquired time series data.According to the calculating results using phase space reconstruction,the largest Lyapunov exponents are positive number in the seven states of electrode displacement signals,and chaos characteristics are discovered in electrode displacement signals of spot welding.Therefore,the result shows a new state in the process of the spot welding and electrode displacement signals should be analysed by chaos method.In order to research electrode displacement signal,box counting dimension is put forward to analyze and calculate chaos characteristics.The experiment and calculation results indicate that the box counting dimension of electrode displacement signals is clearly distinguishable in the welding process with different welding parameters.A new method of judging and forecasting the quality of spot welding is provided.
引文
[1]赵熹华，冯吉才．压焊方法及设备[M]．北京：机械工业出版社，2005．ZHAO Xihua,FENG Jicai.Pressure welding method and equipment[M].Beijing:China Machine Press,2005.
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[6]蔡聪波．混沌系统最大LyapIlllOV指数的计算及其在脑电数据分析中的应用[D]．厦门：厦门大学，2001．CA]Congbo.Chaos system of calculating the largest Lyapunov exponent and application on EEG analysis[D]. Xiamen:Xiamen University,2001.
[7]WOLF A,SWIFT J B,SWINNEY H L.Determining Lyapunov exponents from a time series[J].Physica D, 1985,16(9):285-317.
[8]ZHANG Jun,LAM K C,YAN W J.Time series predic, tion using Lyaptmov exponents in embedding phase space[J].Computers and Electrical Engineering,2004, 30(3):1-15.
[9]MARTIN J,BUNNER R.Estimation of Lyapunov spectra from space-time data[J].Physics Letters A,1999,258: 25-30.
[10]娄建武，龙源，徐全军．爆破地震信号分形维数计算的矩形盒模型[J]．振动与冲击，2005，24(1)：81-84．LOU Jianwu,LONG Yuan,XU Quanjun.A study on the fractal dimension of blasting seismic waves[J].Journal of Vibration and Shock,2005,24(1):81-84.
[11]樊福梅，梁平．基于分形盒维数的汽轮机转子振动故障诊断的实验研究[J]．核动力工程，2006，27(2)：85-89．FAN Fumei,LIANG Ping.Experimental research on steam-turbine rotor vibration fault diagnosis based on the fractal box counting dimension[J].Nuclear Power Engineering,2006,27(2):85-89.
[2]罗震，单平．铝合金点焊过程中电极振动信号的建模[J]．天津大学学报，2006，39(4)：496-500．LUO Zhen,SHAN Ping.Modeling of electrode vibration signal in the process of aluminum alloy spot welding[J]. Journal of Tianjin University,2006,39(4):496-500.
[3]吕金虎，张锁春．Lyapunov指数的数值计算方法[J]．非线性动力学报，2001，3(8)：84-90．LJinhu,ZHANG Suochun.The numerical calculating method of Lyapunov exponent[J].Journal of Nonlinear Dynamics in Science and Technology,2001,3(8):84-90.
[4]吴祥兴，陈忠．混沌学导论[M]．上海：上海科学技术文献出版社，1996．WU Xiangxing,CHEN Zhong.Introduce chaos[M]. Shanghai:Shanghai Science Technology Literature Press, 1996.
[5]陈国华，盛昭瀚．基于Lyapunov指数的混沌时间序列识别[J]．系统工程理论方法应用，2003，12(12)：317-320．CHEN Guohua,SHENG Zhaohan.Identification of chaotic time series based on Lyapunov exponents[J]. Systems Engineering Theory Methodology Applications, 2003,12(12):317-320.
[6]蔡聪波．混沌系统最大LyapIlllOV指数的计算及其在脑电数据分析中的应用[D]．厦门：厦门大学，2001．CA]Congbo.Chaos system of calculating the largest Lyapunov exponent and application on EEG analysis[D]. Xiamen:Xiamen University,2001.
[7]WOLF A,SWIFT J B,SWINNEY H L.Determining Lyapunov exponents from a time series[J].Physica D, 1985,16(9):285-317.
[8]ZHANG Jun,LAM K C,YAN W J.Time series predic, tion using Lyaptmov exponents in embedding phase space[J].Computers and Electrical Engineering,2004, 30(3):1-15.
[9]MARTIN J,BUNNER R.Estimation of Lyapunov spectra from space-time data[J].Physics Letters A,1999,258: 25-30.
[10]娄建武，龙源，徐全军．爆破地震信号分形维数计算的矩形盒模型[J]．振动与冲击，2005，24(1)：81-84．LOU Jianwu,LONG Yuan,XU Quanjun.A study on the fractal dimension of blasting seismic waves[J].Journal of Vibration and Shock,2005,24(1):81-84.
[11]樊福梅，梁平．基于分形盒维数的汽轮机转子振动故障诊断的实验研究[J]．核动力工程，2006，27(2)：85-89．FAN Fumei,LIANG Ping.Experimental research on steam-turbine rotor vibration fault diagnosis based on the fractal box counting dimension[J].Nuclear Power Engineering,2006,27(2):85-89.
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