小信号混沌动力学测量研究
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摘要
利用混沌系统的初值敏感性进行小信号测量是一个很好的有应用潜力的方向，它的测量原理与现有的测量原理完全不同，其基本思想是将待测信号作为混沌系统的初值，在参数不变的条件下，利用混沌系统的初值敏感性，使混沌轨道随待测信号的变化而变化，定义轨道距离，通过测量轨道距离的变化即可测得该小信号。理论上这种测量方法的测量精度可以无限高，因此它可以用来测量极其微弱的信号。
可是混沌系统也同样对噪声非常敏感，电路中的噪声会使某一初值对应的混沌轨道偏离原来的轨道，并且噪声越大轨道的偏离就越大，这样又会否定混沌测量小信号的可能性，问题的关键是能否抑制噪声，或在受干扰的混沌轨道中把真正有用的信息提取出来，只有这样才能真正利用混沌的初值敏感性来测量小信号。
本文提出了一种消除混沌测量噪声的新方法。它是通过混沌电路的耦合，使耦合轨道相互靠拢，轨道距离减少，从而抑制电路中的噪声。两个混沌测量电路的耦合实验和计算机数值计算验证了这种方法是有效的，又进一步讨论了由N个单元电路构成的耦合实验，可得到随着N的增加它抑制噪声的能力也增强。
另外，本文在分析原有非线性电路的基础上提出一种有源积分式混沌测量电路，它克服了恒压式测量电路映射函数存在非线性失真、恒流式测量电路不宜工作在开关状态的不足，利用普通的运放也获得较好的测量精度。又由于有源电路易于级联，因此它可以推广到高阶混沌测量电路的研究。
A potentially feasible method is the use of a chaotic system's high sensitivity under condition to detect weak signals, which is quite different from all present methods. Fixing parameter of components in a nonlinear circuit, chaotic orbits change with the measured signal. A distance has been defined. By measuring the distance of orbits, very weak signal can be detected because of the sensitive dependence on initial conditions. In theory, the measuring precision is infinite.
But a chaotic system is also extremely sensitive to noise, an orbit in a circuit will exponentially drift apart the one of the map with identical initial condition. Is it impossible to measure very weak signals in a chaotic system? The key problem is whether we can reduce noise or depart the useful information from the interferential orbits or not. If we can, very weak signal can be measured based on the sensitive dependence on initial conditions.
A new method of noise reduction is proposed in this paper. By coupling of many chaotic circuits, orbits can be closed each other, distance can be shorted, and noise in measuring can be reduced. Circuit experiments consisting of two measuring units and computer analysis prove the method is effective, and circuit experiments consisting of N measuring units show noise reduction will be better as N increases.
Otherwise, an active integral chaotic measuring circuit is suggested based on the analysis of the present nonlinear circuits in this paper, which gets rid of nonlinear distortion of map function in constant-voltage mode and defect of constant-current source operating on-off state. Using a general operational amplifier, high precision can also be obtained. A nth-order chaotic measuring system can be composed of its interconnection.
可是混沌系统也同样对噪声非常敏感，电路中的噪声会使某一初值对应的混沌轨道偏离原来的轨道，并且噪声越大轨道的偏离就越大，这样又会否定混沌测量小信号的可能性，问题的关键是能否抑制噪声，或在受干扰的混沌轨道中把真正有用的信息提取出来，只有这样才能真正利用混沌的初值敏感性来测量小信号。
本文提出了一种消除混沌测量噪声的新方法。它是通过混沌电路的耦合，使耦合轨道相互靠拢，轨道距离减少，从而抑制电路中的噪声。两个混沌测量电路的耦合实验和计算机数值计算验证了这种方法是有效的，又进一步讨论了由N个单元电路构成的耦合实验，可得到随着N的增加它抑制噪声的能力也增强。
另外，本文在分析原有非线性电路的基础上提出一种有源积分式混沌测量电路，它克服了恒压式测量电路映射函数存在非线性失真、恒流式测量电路不宜工作在开关状态的不足，利用普通的运放也获得较好的测量精度。又由于有源电路易于级联，因此它可以推广到高阶混沌测量电路的研究。
A potentially feasible method is the use of a chaotic system's high sensitivity under condition to detect weak signals, which is quite different from all present methods. Fixing parameter of components in a nonlinear circuit, chaotic orbits change with the measured signal. A distance has been defined. By measuring the distance of orbits, very weak signal can be detected because of the sensitive dependence on initial conditions. In theory, the measuring precision is infinite.
But a chaotic system is also extremely sensitive to noise, an orbit in a circuit will exponentially drift apart the one of the map with identical initial condition. Is it impossible to measure very weak signals in a chaotic system? The key problem is whether we can reduce noise or depart the useful information from the interferential orbits or not. If we can, very weak signal can be measured based on the sensitive dependence on initial conditions.
A new method of noise reduction is proposed in this paper. By coupling of many chaotic circuits, orbits can be closed each other, distance can be shorted, and noise in measuring can be reduced. Circuit experiments consisting of two measuring units and computer analysis prove the method is effective, and circuit experiments consisting of N measuring units show noise reduction will be better as N increases.
Otherwise, an active integral chaotic measuring circuit is suggested based on the analysis of the present nonlinear circuits in this paper, which gets rid of nonlinear distortion of map function in constant-voltage mode and defect of constant-current source operating on-off state. Using a general operational amplifier, high precision can also be obtained. A nth-order chaotic measuring system can be composed of its interconnection.
引文
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