一种基于超声共振谱的低Q值材料共振频率提取方法

超声共振谱技术通过测量样本在超声激励下产生的固有共振频率来计算弹性参数,而共振频率的提取是整个测量过程的关键.低$Q$值(品质因数)材料由于其衰减特性,导致共振谱平缓并无法直观地从谱图上观察得到共振频率,为从中提取更为有效的共振频率, 本文提出了一种新的共振频率提取方法.采用经验模态分解法将材料频率响应自适应分解为有限个具有特殊振荡特性的固有模态函数分量,根据材料的超声共振谱先验信息选择具有共振频率特性的固有模态函数分量,并从中提取共振频率. 以短切纤维环氧树脂材料(仿骨材料, $Q \approx$25)为例, 通过实验与传统线性预测方法进行对比,计算弹性系数和工程模量. 实验结果表明新方法的计算效率高,对弱激发模态更为敏感,共振频率的匹配数量(26)多于传统方法(21)且满足5倍于弹性系数的估计要求,优化后的弹性模量更接近标准值.新方法可从低$Q$值材料平缓的频谱中提取数量足够且有效的共振频率,不仅有效提升了力学参数估计的可靠性,而且拓展了超声共振谱技术的应用范围. 

A RESONANCE FREQUENCY EXTRACTION METHOD FROM LOW Q-FACTOR MATERIALS BASED ON RESONANT ULTRASOUND SPECTROSCOPY1)

Resonant ultrasound spectroscopy (RUS) allows identification of the elastic coefficients of solid materials vibrating under an ultrasonic excitation from the measurement of their inherent frequencies. Retrieving the resonant frequencies is therefore a key signal processing step in RUS. However, according to the attenuation characteristics of low $Q$-factor (quality factor) materials, the resonance spectrum obtained by the experiment is flat and the resonance frequencies can not be directly observed from the spectrum. Therefore, in order to retrieve more effective resonance frequencies than traditional approach from the low $Q$-factor materials, a new extraction method of resonance frequencies was proposed to solve the limitation in this paper. The empirical mode decomposition method was used to decompose the frequency response of the specimen into finite Intrinsic Mode Function (IMF) components with special oscillation characteristics. According to the prior information of resonant ultrasound spectroscopy (RUS),the relevant IMF component was selected to retrieve reliable resonance frequencies from the resonance spectrum. The short fiber filled epoxy (a kind of bone-like materials, $Q \approx $25) was adopted as the specimen to calculate the elastic coefficients and engineering moduli compared with the traditional linear prediction method. The experimental results show that the new method has high computational efficiency and is more sensitive to the weak excitation modes of low $Q$-factor materials. The number of effective resonance frequencies (26) are more than traditional linear prediction methods (21), which also satisfied 5 times estimation requirement of elastic constants. In addition, the optimized elastic moduli are closer to the standard values of the short fiber filled epoxy. In conclusion, the EMD-based method can retrieve a sufficient quantity and effective resonance frequencies from the flat spectrum of low $Q$-factor materials, which can not only improve the reliability of the estimation of mechanical parameters, but also extend the application range of resonant ultrasound spectroscopy.