二次频率耦合的对角切片谱分析

Diagonal slice spectrum analysis of quadratic frequency coupling

三阶累积量对角切片谱可以识别二次相位耦合关系,抑制不存在耦合的频率成分,由于此优良的性质,对角切片谱在信号分析领域得到了广泛的应用。然而,二次相位耦合的定义要求原始信号同时满足频率耦合和相位耦合的关系,这样的信号在实际中几乎不存在,很多文献把取得较好分析效果的原因归结于对角切片谱具有识别二次相位耦合的能力,这是不严谨的。提出的二次频率耦合的概念,相比于二次相位耦合,二次频率耦合对信号的相位没有要求。通过理论推导证明了对角切片谱能够识别仅存在频率耦合关系的信号,从而提升了二次相位耦合理论的实用性。最后,通过分析具有内圈故障的滚动轴承振动信号,对提出的二次频率耦合理论进行了验证。

The diagonal slice spectrum（DSP）of third-order cumulant can detect the relationship of quadratic phase coupling（QPC）and inhibit the non-coupling frequency components.Due to this excellent property,DSP is widely utilized in signal processing.QPC requires the raw signal to satisfy frequency coupling and phase coupling relationship at the same time.However,to meet the condition of QPC is virtually impossible in practice.Many references attribute the reason of getting nice analysis results to the detection ability of DSP for QPC,but this conclusion is not rigorous.In this paper,a novel concept of quadratic frequency coupling（QFC）is proposed.Comparing with QPC,QFC does not has any requirements on the phases of a signal.The ability of using DSP to identify the signal with frequency coupling is proved according to theoretical deduction.As a consequence,the practicability of QPC theory is improved.Finally,QFC is verified by analyzing the vibration signal of a rolling element bearing with an inner race fault.