色关联的色噪声驱动的双稳杜芬模型的稳态分析

研究了由色关联的色噪声驱动的双稳杜芬模型的稳态概率密度函数及状态变量的均值和标准方差．首先应用一致有色噪声近似方法,推导出了具有色关联的色噪声驱动的双稳杜芬模型的稳态概率密度函数的解析表达式．分析了噪声的“有色性”及关联性对稳态密度函数和状态变量的均值、标准方差的影响,发现了一些由白噪声激励的杜芬模型中不会出现的新的非线性现象：加性噪声强度、噪声之间的关联系数和关联时间都能够诱导非平衡相变．     

含时滞项的双稳系统中平均首次穿越时间的研究

研究了含时滞项的非对称双稳系统中的平均首次穿越时间问题.应用小时滞近似方法,得到了系统的Fokker-Planck方程及稳态概率密度函数,进而得到了系统的平均首次穿越时间的表达式,最后对理论结果做了数值模拟.数值计算结果表明:(1)时滞量的大小对系统的稳态概率密度函数的影响是不一样的,当0<τ<0.175时,系统的稳态概率密度函数曲线仍然为双峰形状;当τ>0.175时,系统的稳态概率密度函数曲线呈现出阱状.(2)在0<τ<0.175时,讨论了系统的乘性和加性噪声强度对系统的平均首次穿越时间的影响,发现平均首次穿越时间T -乘性噪声强度曲线上有最小值出现,而T -加性噪声强度曲线是单调的.     

Characterization of subthreshold voltage fluctuations in neuronal membranes

Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by Ornstein-Uhlenbeck processes. We derive and solve the Fokker-Planck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in Hodgkin-Huxley-type models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high-conductance states similar to in vivo conditions. Because the steady-state membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons.     

Detecting the number of 2-D harmonics in multiplicative and additive noise using enhanced matrix

This paper proposes a method for detecting the number of two-dimensional (2-D) harmonics in multiplicative and additive noise. We define an enhanced matrix using the generalized covariances of 2-D harmonics in multiplicative and additive noise and derive an inherent relation between the number of 2-D harmonics and the eigenvalues of the enhanced matrix. The number of 2-D harmonics in multiplicative and additive noise could be detected based on this special relation. The proposed method avoids the peaks searching and does not need any assumptions about the distribution and color of the multiplicative and additive noise. The computation complexity of the proposed method is analyzed. Simulations demonstrate the effectiveness of the proposed method.     

气压扰动下介电弹性体球膜的随机响应分析

研究随机扰动的压力和恒常电压联合作用下的介电弹性体球膜,发展随机响应的分析方法并总结其规律,为计及介电弹性体的应变强化现象,其力学性能由Gent应变能模型描述,压力扰动近似为高斯白噪声.引入能量相关变换并应用随机平均法导出了关于系统总能量稳态概率密度的简化Fokker-Planck-Kolmogorov方程,并解析得到方程的解,从而得到球膜伸长比及其变化率的稳态概率密度,进而得到伸长比的各阶统计量.研究针对两种典型情形进行,即球膜在伸长比为1附近的振动及球膜在材料拉伸极限附近的振动.详细讨论了激励强度、材料参数及常电压值对伸长比统计量的影响,特别强调了不同的材料参数和常电压值引起的不同振动模式.蒙特卡洛模拟证实了分析结果的有效性和精度.     

一类非线性网络系统中噪声改善信号的相关性

基于相关系数研究了在一类非线性神经网络系统中加性和乘性噪声作用下的阈上随机共振现象。仅在加性噪声或者乘性噪声的作用下,对每一个固定的系统阈值,加性噪声下的阈上随机共振比乘性噪声下的阈上随机共振更容易发生,且相关系数所达到的峰值也比在乘性噪声下的峰值大,这说明加性噪声更有利于改善信号的相关性。系统阈值的增加会降低阈上随机共振的功效;而阈值单元数目的增多,会提高阈上随机共振的功效。加性和乘性噪声共同作用下的阈上随机共振现象同样存在,对系统阈值进行恰当选取和增加系统阈值单元数目使得阈上随机共振现象更加明显;给定乘性噪声而改变加性噪声比固定加性噪声而改变乘性噪声阈上随机共振更容易发生,且功效更好。     

相关乘性和加性高斯白噪声激励下周期势系统的随机共振

研究了外加周期信号作用下,相关高斯乘性和加性白噪声激励下周期势系统的随机共振.利用线性响应理论,计算了系统输出信号的功率谱密度、振幅、相位差.研究结果表明:当加性噪声强度和关联系数不变的情况下,通过调整乘性噪声强度可以出现随机共振;关联系数的正负以及大小对随机共振的影响较小.当乘性噪声强度较小时,输出信号的振幅和相位差曲线有一个单峰出现,即出现随机共振现象,能量从噪声向信号进行转化.随着噪声强度的增大,随机共振现象消失,噪声由增大系统的有序程度渐渐变为增大系统的无序程度.     

任意均值复杂噪声下三次非线性耦合谐波分析

针对零均值乘性噪声和加性噪声共存,并且乘性噪声之间独立、乘性噪声和加性噪声之间也独立的噪声背景下谐波的三次非线性耦合问题,提出了一种特殊定义的四阶时间平均多矩谱方法.此方法能够有效地估计出观测信号中参与耦合的谐波频率,文中给出了详细的理论分析和证明.由于该方法也同样适合于非零均值噪声下的谐波耦合问题,因此不再需要对噪声的均值、颜色和分布作任何限制,从而对噪声的统计特性及分布的限制降到了最低,仿真结果表明了该方法的有效性.     

Finite element method analysis of Fokker–Plank equation in stationary and evolutionary versions

The problems that often arise in stochastic dynamics can be investigated using the Fokker–Planck (FP) equation. The response of a such systems being subjected to additive and/or multiplicative random noise is represented by probability density function (PDF) that gives the full information about a response random character. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful alternative. In particular the Finite Element Method (FEM) seems to be very effective. A couple of single dynamic linear/non-linear (Duffing and Van Der Pol type) systems under additive and multiplicative random excitations are discussed using FEM as a solution tool of the FP equation. The resulting PDFs are analyzed and if the analytic results exist mutually compared.     

Capacity of orthogonal space-time block codes in MISO fading channels with co-channel interference and noise

Orthogonal space-time block codes(OSTBCs) are an efficient mean in order to exploit the diversity offered by the wireless multiple-input multiple-output(MIMO) channel. This paper considers capacity problems of OSTBCs over spatially correlated multiple-input single-out(MISO) Rayleigh fading channels in the presence of spatially correlated Rayleigh co-channel interference and additive Gaussian noise,and derives exact expressions of the ergodic capacity and outage probability(capacity distribution) for such OS...     

色噪声激励下三势阱系统逻辑随机共振研究

本文利用基于Simulink的数值模拟方法研究了高斯色噪声激励下三势阱系统的逻辑随机共振现象.首先对于独立的加性和乘性高斯色噪声激励下的三势阱系统,发现仅有加性噪声作用不能实现可靠的逻辑操作,但加性噪声和乘性噪声共同作用可诱导良好的逻辑随机共振现象.和高斯白噪声相比较,高斯色噪声激励下能产生可靠逻辑随机共振的（D,Q）平面上的区域范围更大.进一步讨论了加性和乘性噪声之间的关联对于逻辑随机共振现象的影响,发现噪声关联对逻辑随机共振现象起着破坏性的作用.     

Despeckling SAR-type multiplicative noise

Despeckling multiplicative noise is important in processing coherent radar images. Assuming that measurements are corrupted by multiplicative noise and that a priori values are contaminated by either multiplicative or additive noise, we have obtained Bayesian, maximum likelihood and weighted least-squares (LS) estimators, based on gamma and normal distributions. These estimators have been shown to be biased if the noise in measurements is multiplicative. A technique of bias-correction to remove biases from the estimated parameters is proposed. The bias-correction technique requires no distributions about the measurements and the a priori mean, and can be applied to eliminate bias from Bayesian, maximum likelihood and weighted LS estimators in multiplicative noise models. It theoretically provides a solid foundation for, and thus justifies some of current practice in, despeckling multiplicative noise, such as Lee's local statistics and Kuan's adaptive smoothing filter. Some despeckling measures are also proposed and simulated experiment results are reported.     

Improved integral equation solution for the first passage time of leaky integrate-and-fire neurons

An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.     

A comparison between non-gaussian closure and statistical linearization techniques for random vibration of a nonlinear oscillator

The non-Gaussian closure technique is applied to a nonlinear single degree of freedom oscillator subjected to a stationary white noise excitation. The nonlinear restoring force in this system is a softening spring with a hyperbolic tangent behavior. This type of nonlinear system has practical applications in package cushioning. The governing differential equation of motion is used to generate relations between stationary response statistics. These relations are then employed to evaluate a corresponding number of unknown coefficients in a non-Gaussian probability distribution function. A truncated Gram-Charlier expansion is chosen for the probability density function. Up to the sixth order moments of the response process are obtained. The probability density functions predicted by this technique are then compared with density functions constructed by exact solution via the Fokker-Plank-Kolmogorov equation. A comparison is also made with the density function evaluated by statistical linearization for this system. Limitations of this non-Gaussian closure method are discussed.     

非加性噪声情形下卡尔曼滤波器的推广

在数字信号处理中,得到的信号总是或多或少伴随着噪声。如何去除噪声,恢复真实的信号,是信号处理面临的首要问题。一般情形下我们都假定噪声是加性的,即噪声是不依赖于信号的,此时,卡尔曼滤波器是一种非常简便的降噪方法,它是一个最优化自回归数据处理算法,是用前一个估计值和最近一个观察数据来估计信号的当前值,是用状态方程和递推的方法进行估计的,而且它在均方误差意义下是最优的。本文将噪声推广到一般的乘性噪声的情形,利用卡尔曼滤波的基本思想,同样可以得到均方误差意义下的最优滤波,最后通过一个模拟的例子验证了该方法的有效性。     

高阶统计量方法在谐波恢复中的应用

谐波恢复是信号处理中的重要问题,谐波恢复就是在噪声中分析组成信号的各次谐波.噪声分为加性噪声和乘性噪声,本文分析加性噪声和乘性噪声的特点,提出采用高阶统计量的方法抑制噪声,恢复谐波.通过四阶统计量的切片抑制乘性噪声,采用二阶累积量谱抑制加性噪声.仿真结果表明,本方法具有很好的抑制噪声效果.     

一种平稳化短时交通流预测方法

支持向量机回归模型是以预测噪声具有对称性概率分布为假设条件,而实际的短时交通流数据序列具有非平稳特征,这就使得在采用支持向量机回归模型进行短时交通流预测时,难以保证预测噪声的对称性概率分布,从而会影响到预测精度.针对上述问题,在证明支持向量机回归模型对平稳时间序列的预测噪声具有对称性概率分布的基础上,分别针对平稳化和未平稳化的短时交通流观测序列进行了仿真预测,并对预测结果进行了比对分析.分析结果表明,采用平稳化短时交通流预测方法可将预测的均方根误差降低约21.6％,绝对值误差降低约21.3％,相对误差降低约17.3％,仿真结果验证了所提方法的有效性.     

Stochastic analysis of the Least Mean Kurtosis algorithm for Gaussian inputs

The Least Mean Kurtosis (LMK) algorithm was initially proposed as an adaptive algorithm that is robust to the observation noise distribution. Good performances of this algorithm have been shown for non-Gaussian additive measurement noise. However, the complexity of the algorithm imposes difficulties for the development of a reasonably complete theoretical stochastic model for its behavior. The purpose of this paper is to contribute to the development of such a model. We study the stochastic behavior of Least Mean Kurtosis (LMK) algorithm for Gaussian inputs and for additive noises with even probability density functions. Deterministic recursions are derived for the adaptive weight error covariance matrix in a very novel manner, leading to a recursive model for the excess mean square error (EMSE) behavior that is shown to be accurate for Gaussian, uniform and binary noise distributions. The analysis results are then used to compare the performances of LMK with the least mean squares (LMS) and least mean fourth (LMF) algorithms under different circumstances.     

受多随机噪声和多随机脉冲干扰的非线性系统稳定性分析

针对一类受多有色噪声和多随机脉冲干扰的非线性系统(其中系统连续动态中的多随机噪声包含乘性和加性有色噪声且离散动态中多随机脉冲幅值的类型由一个齐次不可约非周期Markov链决定),分别提出概率意义和矩意义下的噪声-状态稳定性、概率意义下的全局渐近稳定性、矩意义下的指数稳定性判据.在脉冲数量受模态依赖平均脉冲区间约束下,首先基于乘性随机噪声的估计和Lyapunov函数方法,分别研究系统在矩意义下的噪声到状态稳定性和指数稳定性判据;然后基于乘性随机噪声满足大数定律的假设和Lyapunov函数方法,分别给出系统在概率意义下的噪声-状态稳定和全局渐近稳定的充分条件;最后通过仿真结果验证所提出稳定性判别准则的有效性.     

Assessing the Noise Immunity and Generalization of Radial Basis Function Networks

In previous work we have derived a magnitude termed the 'Mean Squared Sensitivity' (MSS) to predict the performance degradation of a MLP affected by perturbations in different parameters. The present Letter continues the same line of researching, applying a similar methodology to deal with RBF networks and to study the implications when they are affected by input noise. We obtain the corresponding analytical expression for MSS in RBF networks and validate it experimentally, using two different models for perturbations: an additive and a multiplicative model. We discuss the relationship between MSS and the generalization ability. MSS is proposed as a quantitative measurement to evaluate the noise immunity and generalization ability of a RBFN configuration, giving even more generalization to our approach.