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Interpretation of crack-induced rotor non-linear response using instantaneous frequency

机译：瞬时频率解释裂纹诱导的转子非线性响应

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摘要

Instantaneous frequency was introduced to describe the dependency of frequency components on time for non-stationary signals. A powerful alternative to the Fourier-based spectral analysis that provides insufficient resolution for the temporal progression of all frequency components, the concept of instantaneous frequency has rarely been applied to machine monitoring and diagnosis. The confusing fact that instantaneous frequencies determined could occasionally be negative and the associated amplitudes could be infinite for certain types of vibration signals inevitably limits the adaptability of the concept to fault detection as a result. Significant insight into the applicability of instantaneous frequency is gained through re-examining the fundamentals upon which the concept was first defined. It is found that the Hilbert-transform-based definition of instantaneous frequency is applicable only to signals of monocomponent, thus implying the need for separating a multicomponent signal into its monocomponent subsets. Misuse of the definition to multicomponent signals would result in the individual instantaneous frequency associated with each inherent monocomponent being averaged and thus obscure the underlying characteristics of the signal. A mathematically complete decomposition scheme effective in resolving a multicomponent signal into an orthogonal space spanned by its intrinsic monocomponents is explored. Several examples are considered to show that the scheme not just enables the removal of the difficulties commonly encountered in applying instantaneous frequency but also imparts valid renditions to the interpretation of fault-induced bifurcation and dynamic instability.
机译：引入瞬时频率来描述非平稳信号的频率分量对时间的依赖性。作为基于傅立叶频谱分析的强大替代方法，它无法为所有频率分量的时间进程提供足够的分辨率，因此，瞬时频率的概念很少用于机器监视和诊断。对于某些类型的振动信号来说，确定的瞬时频率有时可能为负，并且相关的振幅可能为无限，这一令人困惑的事实不可避免地限制了该概念对故障检测的适应性。通过重新检查最初定义该概念的基本原理，可以深入了解瞬时频率的适用性。发现基于希尔伯特变换的瞬时频率的定义仅适用于单分量信号，因此暗示需要将多分量信号分离为其单分量子集。对多分量信号的定义使用不当会导致与每个固有单分量相关的单个瞬时频率被平均，从而使信号的基本特征变得模糊。探索了一种数学上完整的分解方案，该方案可有效地将多分量信号解析为由其固有单分量跨越的正交空间。几个例子被认为表明该方案不仅可以消除在施加瞬时频率时通常遇到的困难，而且可以为解释故障引起的分叉和动态不稳定性提供有效的解释。

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