加权超阈值随机共振的信号重构方法研究

发布时间：2018-11-27 19:53

【摘要】：超阈值随机共振是随机共振一种新的形式,它发生在多种阈值子系统所构成的并联阵列。超阈值随机共振是对随机共振的重要扩展,它的产生对信号的幅度没有要求,不局限于弱信号或亚阈值信号,极大地拓展了传统随机共振的应用范围,其理论和模型对随机共振在信息领域和生物医学工程的应用研究具有实际意义。超阈值随机共振模型可视为随机量化器,本文从随机量化的角度研究信号的重构方法及性能,主要的成果和创新之处体现在:1.基于超阈值随机共振模型,提出了一种新的重构方法最优加权的随机量化信号重构,构建了阈值子系统加权求和阵列模型,推导了最优权系数及信号重构表达式,并通过三种阈值设置方案——阈值相同、阈值等间隔及阈值分组研究了该重构方法的均方误差失真性能。研究结果表明:阈值分组时的重构性能最好,即均方误差失真值最小。在阈值分组情形,我们又将最优加权重构与维纳线性重构方法相比较,结果表明,在一定的分组参数设置时,我们提出的最优加权重构方法优于维纳线性重构。2.将最优加权信号重构方案由阈值子系统构成的阵列推广到任意静态非线性子系统,提出了分组加权的随机量化信号重构方法。以饱和传感器为例,研究了多组参数设置时均方误差失真性能,并与维纳线性重构方法进行比较。研究结果表明:当分组数大于2、偏移量参数等间隔设置时,最优加权重构方法的性能优于维纳线性重构。而且,随着分组数的增长,均方误差失真性能显著地提高。当分组数等于阵列尺寸时,均方误差达到最小。另外,对于饱和传感器的斜率值,除了很小的值外,最优加权重构方法的性能也优于维纳线性重构方法。3.将自适应滤波理论应用到信号重构方法中,提出了自适应加权的随机量化信号重构方法,将最优加权信号重构方法扩展到能处理具有一般特性的输入信号的情形中。我们应用这个重构方法到阈值子系统构成的并联阵列,在高斯白噪声、有色噪声环境下研究输入特性是平稳、非平稳时的重构性能。研究表明:使用自适应加权的信号重构方法,无需输入信号的先验知识,不但能处理平稳信号这种简单的情形,而且能处理非平稳信号和有色噪声这些比较复杂的情况。另外,超阈值随机共振模型也可视为信号传输的通道,本文研究了信号为广义高斯分布,噪声为高斯分布和均匀分布时的信息传输特性,重点分析与讨论了广义高斯分布指数参数对最大信息传输量的影响。研究表明:指数参数是决定系统传输特性的重要因素,它影响互信息量的最大值及该值所对应的位置。本文提出的加权重构方法,对超阈值随机共振理论的发展和完善、指导其工程应用具有重要的意义。
[Abstract]:Super-threshold stochastic resonance is a new form of stochastic resonance, which occurs in parallel arrays composed of multiple threshold subsystems. Super-threshold stochastic resonance is an important extension of stochastic resonance. It does not require the amplitude of signal and is not limited to weak signal or sub-threshold signal, which greatly expands the application of traditional stochastic resonance. Its theory and model have practical significance for the application of stochastic resonance in the field of information and biomedical engineering. The super-threshold stochastic resonance model can be regarded as a stochastic quantizer. This paper studies the signal reconstruction method and performance from the perspective of stochastic quantization. The main achievements and innovations are as follows: 1. Based on the super-threshold stochastic resonance model, a new reconstruction method is proposed. The weighted summation array model of threshold subsystem is constructed, and the optimal weight coefficient and signal reconstruction expressions are derived. The mean square error distortion performance of the reconstruction method is studied by three threshold setting schemes: the same threshold, the equal threshold interval and the threshold grouping. The results show that the reconstruction performance of threshold grouping is the best, that is, the mean square error distortion is the least. In the case of threshold grouping, we compare the optimal weighted reconstruction with the Wiener linear reconstruction method. The results show that the optimal weighted reconstruction method is better than the Wiener linear reconstruction method under certain grouping parameters. 2. The optimal weighted signal reconstruction scheme is extended from an array of threshold subsystems to an arbitrary static nonlinear subsystem, and a grouping weighted stochastic quantization signal reconstruction method is proposed. Taking saturation sensor as an example, the mean square error distortion performance of multiple sets of parameters is studied and compared with Wiener linear reconstruction method. The results show that the performance of the optimal weighted reconstruction method is better than that of Wiener linear reconstruction when the number of blocks is greater than 2 and the offset parameters are set at equal intervals. Moreover, with the increase of the number of groups, the distortion performance of mean square error is improved significantly. When the number of packets is equal to the array size, the mean square error is minimized. In addition, for the slope value of saturated sensor, the performance of the optimal weighted reconstruction method is better than that of Wiener linear reconstruction method. The adaptive filtering theory is applied to the signal reconstruction method. An adaptive weighted stochastic quantization signal reconstruction method is proposed. The optimal weighted signal reconstruction method is extended to the case where the input signal with general characteristics can be processed. We apply this reconstruction method to the parallel array composed of threshold subsystem. We study the reconstruction performance of the input in the environment of Gao Si white noise and colored noise when the input characteristic is stationary and non-stationary. The results show that the adaptive weighted signal reconstruction method can not only deal with the simple case of stationary signal, but also deal with the complex cases of non-stationary signal and colored noise without the prior knowledge of input signal. In addition, the super-threshold stochastic resonance model can also be regarded as the channel of signal transmission. In this paper, we study the information transmission characteristics when the signal is generalized Gao Si distribution, and the noise is Gao Si distribution and uniform distribution. The influence of the generalized Gao Si distribution index parameters on the maximum information transmission is analyzed and discussed. It is shown that the exponential parameter is an important factor in determining the transmission characteristics of the system, and it affects the maximum value of mutual information and the corresponding position of the value. The weighted reconstruction method proposed in this paper is of great significance for the development and improvement of the theory of super-threshold stochastic resonance and for guiding its engineering application.
【学位授予单位】：青岛大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TN911.7

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