利用混沌振子系统识别超声导波信号的仿真研究

Simulations of ultrasonic guided wave identification using a chaotic oscillator

提出一种基于改进型杜芬混沌振子系统的强噪声下超声导波的识别和定位方法。首先,采用(-x^3+x^5)作为杜芬方程的非线性恢复力项,提高了系统的敏感性;其次,利用Melnikov方法、并结合待检测信号频率、噪声水平设置了杜芬系统参数;再次,利用驱动力幅值变化使得杜芬系统产生间歇式混沌,并将系统由大周期态向混沌吸引子过度的临界态作为检测系统。为了说明杜芬系统对噪声信号的免疫力,分析了随机噪声对系统扰动的统计特性。最后,利用导波信号对系统相轨图的显著变化识别导波信号,并提出了二分法用于识别导波发生时刻,并对输入信号的长度影响进行了讨论。仿真算例表明,利用杜芬系统相轨图对噪声和导波信号截然不同的响应特点,可以有效地检测弱导波信号,该方法对于延长导波的检测范围、以及提高微缺陷的检测灵敏度具有重要意义。

A novel inspection method of ultrasonic guided waves was proposed here based on the improved Duffing chaotic oscillator with substitution of （ - x3 ＋ x5 ） for （ - x ＋ x3 ） of the non-linear restoring force item. Firstly, the effects of frequency and damping ratio on the chaotic systems were studied using Melnikov＇s method. Based on this, the frequency of the force and the damping ratio could be determined considering the frequency of the detected signal and noise level, respectively. The chaotic system could transfer the phase from a quasi-periodic motion to chaotic motion with double attractors by changing the amplitude of the driving force. And then, the statistical properties of the noise effect on the system were discussed in detail. It was obviously different from the non-balance phase transition of the system, inducing a chaotic motion with double attractors when inputting a guided wave signal but only inducing a disturbance when inputting a pure noise. Furthermore, a dichotomy was suggested to locate the time of the guided wave. And the effect of the guided wave length on the phase map was studied in detail. The simulations showed the higher sensitivity of the system to the guided wave and its stronger immunity to noise. It was shown that the presented method can be used to inspect weaker guided waves, to extend their detection range and to increase the sensitivity of detecting micro-defects.