MIMO线性系统输入输出信号统计特征的双谱评定方法

基于高阶统计量具备处理随机信号的特性,提出了一种利用三阶谱(双谱)评定MIMO线性系统时域输入输出信号统计特征的新方法。通过建立线性系统双谱数学模型,根据系统响应、所测得的频响函数以及离散信号的双谱数值估计算法,经逆运算获得系统的双谱驱动信号,随后利用高阶谱对高斯随机信号的盲性判定其输入信号的高斯性。将上述方法与采用传统相位随机化法(对功率谱添加随机相位)所获得的驱动信号分别应用于一悬臂梁模拟控制系统中,通过对输入信号的分析及控制结果的比较,发现基于双谱所生成的时域随机驱动信号呈现出较强的非高斯性且收敛速度更快。对于输出信号统计特征的评定,提出从输入信号与系统频带接近的程度入手,再次利用高阶统计量对高斯随机信号的盲性进行定性判定,对于无法判别满足何种非高斯统计分布特征的,不管是对于输入信号还是输出信号,一律采用绘制信号的概率分布特征曲线进行定量评定。

Bispectrum evaluation method for statistical characteristics of input and output signals in MIMO linear systems

Based on the characteristics of higher-order statistics with processing random signals,a new method is proposed for estimating the statistical characteristics of time-domain input and output signals of MIMO linear systems using third-order spectrum(bispectrum).Establishing the bispectrum mathematical model of linear system,the frequency domain bispectrum driving signal of system is calculated based on the system response,the frequency response function and the bispectrum estimation algorithm of the discrete signal,and the blindness of the Gaussian random signal is used to determine the Gaussianity of the input time domain signal using higher order bispectrum.The test method is used,the generated random drive signal in the time domain and the drive signal obtained by the traditional phase randomization method(added random phase to the power spectrum)are applied in a cantilever beam simulation control system respectively,through input signal analysis and control results comparison,it finds that the random drive signal generated in the time domain based on the bispectrum presents strong non-Gaussianity and faster convergence speed.For the evaluation of the statistical characteristics of the output signal,we propose to start with the degree of closeness of the input signal to the system band,and use high-order statistics again to qualitatively determine the blindness of the Gaussian random signal.For that cannot discriminate what kind of non-Gaussian statistical distribution characteristics signals,whether the input signal or the output signal is uniformly used for the quantitative assessment of the probability distribution curve of the plotted signal.