随机汇池网络中超阈值随机共振机制与应用研究

This project will introduce the class of subsystems into the stochastic pooling network, where the internal noise types and intensities in subsystems are tunable. Since these subsystems embedded in background noise can be viewed as noisy channels for transmitting the stimulus signals, the average mutual information, i.e. the difference between the network output entropy and the conditional entropy, will be explored for measuring the performance of stochastic pooling networks. Due to the positive role of internal noises that collected by the pooling functions, the maximum average mutual information at a nonzero noise level, this is the emergence phenomenon of the suprathreshold stochastic resonance, will be theoretically proved in stochastic pooling networks. Based on the relationship between the covariance matrix of arbitrary two classes of subsystems and Fisher information matrix, the determinant theorem of surpathreshold stochastic resonance will be deduced. Furthermore, the most suitable noise type and the optimal noise intensity that correspond to the maximum average mutual information will be provided. This project will also consider the practical colored noise in stochastic pooling networks, and establish the stimulus specific information quantity in terms of Fisher information. Using this information quantity, the contributions of internal noise components to the average mutual information will be clarified. Then, the theoretical framework of suprathreshold stochastic resonance based on Fisher information will be elucidated in stochastic pooling networks. Moreover, the upper bound of average mutual information will be determined by the stimulus specific information in terms of Fisher information matrix. In order to improve the balance of the aged or patients, this project will inject the suitable noise type and the optimal noise intensity into the gel tactual sensation sensor networks. Then, the experimental evidence of noise role in the human sensation enhancement of equilibrium and comfort will be investigated.

本项目将子系统类引入随机汇池网络，各子系统视为有噪信道，其内部噪声类型和强度可调谐，由汇池功能函数聚集各子系统内部噪声的积极作用，利用平均互信息-网络输出熵和条件熵的差衡量随机汇池网络性能，理论证明在非零噪声强度下随机汇池网络具有平均互信息极值的涌现规律，即超阈值随机共振；探索任意两子系统类输出的互协方差阵与Fisher信息阵的函数关系，给出随机汇池网络中超阈值随机共振判定条件以及对应互信息极值的最优噪声类型和强度；分析色噪声下基于Fisher信息的随机汇池网络刺激条件信息，利用刺激条件信息细化子系统噪声对于平均互信息的贡献，推导随机汇池网络平均互信息上限与刺激条件信息的关系，建立随机汇池网络中基于Fisher信息的超阈值随机共振机制；将提高人体舒适感的噪声优化类型和强度融入凝胶触觉感知传感网络设计中，优化人体触觉感知部位的响应，实验证实噪声对于人体触觉舒适度以及身体平衡性的积极影响。

随机汇池网络是基于随机共振理论构建的一种网络结构模型，网络的节点表示了传感器、神经元等非线性传递函数，利用节点随机噪声的有益性，网络的汇池节点能够得到的输入输出最大平均互信息大于各节点各自所贡献的信息量简单加和。随机汇池网络不仅具有逼近不易实现的高复杂度最优处理器的优点，也为理解生物神经网络信息处理中随机噪声的功能提供了一种新思路。本项目理论证明了利用超阈值随机共振方法实现随机汇池网络最优性能的Fisher信息判定条件，基于贝叶斯估计理论证明了自适应权系数的赋值与网络传递函数分类之间的关系，最优权系数向量和最优噪声分布的求解可解耦合，加权随机汇池网络的性能优化归结为人为加入噪声分布的非凸优化问题，给出了最优噪声分布的判定定理以及最优噪声分布求解方法，建立了随机汇池网络中超阈值随机共振Fisher信息理论框架；研究了更加符合实际的有色噪声模型，证实了色噪声相关时间和色噪声强度都是提高随机汇池网络性能的有利因素，引入了基于Fisher信息的刺激条件信息，细化了不同子系统类中色噪声对于随机汇池网络输入输出平均互信息的贡献；本项目还通过理论分析和电路实验证实了一束高频振荡干扰引起的随机汇池网络输出信噪比的振荡共振现象，进一步发现了弱信号检测概率的多共振峰以及峰值所对应的最优振荡幅值随背景噪声类型变化而出现的分叉现象，理论分析了高频振荡共振实质，不同的高频等价于噪声的不同样本，证实了广义高频振荡检测器的最优性能可实现性，与随机共振方法相比，研究了振荡共振机制在弱信号检测中的优势，并应用到人体触觉刺激感知增强装置设计中，制备了内嵌微电动机的人体触觉感知传感网络，实验表明该装置能够产生不同振动强度的高频刺激，并在合适的振荡幅值下使得手部运动较为稳定。研究成果不仅丰富了随机汇池网络中超阈值随机共振理论，也为振荡共振理论在人体医学功能的应用提供了实验依据，对于分布式估计、非线性系统中的噪声优化、深度随机汇池网络应用和生物医学工程具有实际应用价值。