奇数阶累积量的计算优化及其应用

Odd-Order Cumulant Calculation Optimization and Its Application

为了用奇数阶累积量提取非线性振动系统的高次频率耦合特征,定义了四次频率耦合、二三对频率耦合等高次耦合新概念,分析了奇数阶累积量特征,研究了奇数阶累积量计算方法与计算量间的关系,提出了奇数阶累积量计算优化算法,该算法将奇数阶累积量的直接估计变为递推估计,将奇数阶累积量的多维运算转化为一维运算,大幅度减小了计算量,在工程上具有可实现性。用由计算优化算法估计的奇数阶累积量构造的自适应谱线增强器,能有效地从高斯噪声环境中恢复或提取四次频率耦合特征、二三对频率耦合特征等高次耦合特征。理论分析与仿真结果验证了算法的有效性。

For extracting higher order frequency coupling feature radiated by actual nonlinear vibration system via odd-order cumulants（OOC）, quartic frequency coupling and quadratic to cubic frequency coupling were firstly defined, OOC features analyzed, the relation between OOC calculation method and its computational load was studied. Based on these researches, OOC calculation optimization algorithm with low computation complexity, which can turn OOC direct estimation into its recursive estimation and OOC multi-dimension operation into its one dimension operation, was proposed. The OOC, which is computed by optimization algorithm, based adaptive line enhancer（OOCBALE） was developed. The OOCBALE can recover or extract quartic frequency coupling feature and quadratic-to-cubic frequency coupling feature etc. in Gaussian noise. Theoretic analysis and simulation result prove the proposed algorithm to be valid.