微弱信号的混沌检测方法

【作者】 梁倩；

【导师】 王淑敏；

【作者基本信息】 西北工业大学 ， 电路与系统， 2007， 硕士

【摘要】 混沌现象在自然界中非常普遍，混沌运动是许多非线性系统的典型行为。混沌以其拥有的诸多天然优良特性而倍受关注，并在很多领域得到了广泛和成功的应用。当前微弱信号混沌检测技术是混沌理论在信息科学应用中的一个重要分支，由于混沌检测系统具有对小信号的敏感性及对噪声的免疫性等特征，使得混沌系统在信号检测领域具有很好的发展前景，已取得了很大的进展。目前，利用混沌振子检测微弱信号的两种方法分别是：基于系统相轨迹变化的方法和基于系统特征指数的方法。两种方法均是利用系统动力学行为从混沌状态到大尺度周期状态临界处的特性。本文将这两种方法结合起来实现对强噪声背景下微弱信号频率和幅值的检测。下面具体说一下本文的内容： 1．利用Melnikov方法和周期状态下的Lyapunov特征指数确定混沌检测系统的两个临界值。 一是基于Melnikov方法的核心思想，直接给出应用于Duffing检测方程的解析计算过程，推导出混沌状态下内策动力幅值的取值范围，进而确定检测系统进入混沌状态的临界值。第二种方法是基于临界值与结构稳定性的关系给出了利用周期状态下的Lyapunov特征指数确定检测系统临界值的基本思想，并结合具体的混沌检测模型进行了数值仿真，验证了该方法的可行性，与单纯的利用多次实验确定临界值的方法相比，该方法是一种更精确更有效的方法。 2．Duffing振子用于微弱信号混沌检测 首先对Duffing振子系统的动力学行为进行分析，并探讨这些行为在微弱信号检测中的作用。然后将处于混沌临界状态的Duffing振子作为检测模型应用到微弱正弦信号的混沌检测中，分别对单正弦信号、复合正弦信号和频率未知的正弦信号仿真实验测量其频率。还首次提出一种检测频率接近的复合正弦信号的新方法，实验结果表明，该方法具有简单、有效、易于实现等特点。 3．研究微弱信号幅值估计的方法 首先对Floquet特征指数进行分析，同时给出了Duffing振子Floquet指数的计算方法。然后根据该计算方法寻找到了系统特征指数与待测信号幅值之间的关系曲线，直接利用关系曲线的近似线性区间寻找信号幅值估计算法，并给出微弱正弦信号幅值的估计公式。与传统的周期信号参量估计的最大似然法进行数值实验比较，仿真结果表明，线性化方法同样可以很好的估计出信号幅值，而且具有更高的精度。更多还原

【Abstract】 Chaotic motion, which widely exists, can describe the very typical behavior of many nonlinear systems. Chaos has been paid wide attention because of its some good intrinsic properties, and it has been widely and successfully applied to many areas. Chaotic oscillator detection for weak signal belongs to an important application of Chaos theory in information science, chaos system is sensitive to weak signals and immune to noise, which make chaos have good prospects and a great progress in signal detection technique. There are two kinds of methods in detection for weak signals based on chaos: one is based on phase transition of the chaotic system, the other is to use some characteristic exponent of the system. Both the two weak signal detection methods are dependent on the property of the system at the critical value. In this paper, we combine these two methods together to detection weak signals under strong noise. The following gives the main work of this paper in detail.1. Melnikov method and Lyapunov characteristic exponent under period state is used to determine the critical value of the chaos detection systemOne method is that we have presented an analytical computation based on the core thought of Melnikov method, and have inferred the range of driving value under chaotic state, so we can determine the critical value of which system enters into the chaotic state.The other is that on the relation between critical value and structure stability, we have presented the basic thought of determining the critical threshold value of the detection system by the Lyapunov characteristic exponent under period state and simulation results with Duffing detector verified the feasibility. Compared with the experimental technique, the Lyapunov characteristic exponent method is more accurate and more efficient.2. Duffing oscillator in chaos detection for weak signalsFirstly, we analyze the dynamical behavior of Duffing oscillator, and study their use in weak signal detection method. Then such system which is in the critical state of chaos can be used as the detection system to detect weak sinusoid signal, including single sinusoid signal, multiple sinusoid signal and unknown frequency of sinusoid signal. First present a new measurement method of frequency when the frequencies of multiple signals are close to, the results of experiments show that above method has many merits such as simple, effective, easy to be applied.更多还原