最大系数多重同步挤压变换识别结构瞬时频率

Instantaneous Frequency Identification of Time⁃Varying Structures Using Maximum Coefficient Based Multi⁃synchrosqueezing Transform

针对多重同步挤压变换及其改进算法存在的未重排点问题,提出了一种基于最大系数的多重同步挤压变换(maximum coefficient based multi-synchrosqueezing transform,简称MCMSST)方法来识别时变结构非平稳响应信号的瞬时频率(instantaneous frequency,简称IF)。首先,引入傅里叶频谱来辅助多分量响应信号选取截止频率;其次,对响应信号进行短时傅里叶变换(short time fourier transform,简称STFT),针对短时傅里叶变换系数求取针对时间的偏导,从而获得估算的瞬时频率;然后,在对瞬时频率的估算值进行多次迭代的基础上,仅保留时频系数模值最大处所对应的估算瞬时频率,并将其余位置的瞬时频率值归零;最后,对时频系数模值最大处所对应的瞬时频率进行时频重排即可得到细化后的瞬时频带。由于基于MCMSST方法提取的是瞬时频带,故采用时频系数模极大值法在限定的频带范围内提取瞬时频率曲线。通过2组数值算例和1个铝合金悬臂梁质量突变试验,验证了所提方法的有效性。研究结果表明,MCMSST方法不仅彻底解决了未重排点问题,而且提高了瞬时频率的识别精度和抗噪能力。

In order to solve the problem of non-reassigned points in multi-synchrosqueezing transform and its improved algorithm,a maximum coefficient based multi-synchrosqueezing transform(MCMSST)is proposed to identify the instantaneous frequency(IF)of nonstationary response signals from time-varying structures.The Fourier spectrum is introduced at first to facilitate the selection of cut-off frequency of multi-component signals.After that,short-time Fourier transform is performed on the response signal and the estimated IF can be obtained by taking partial derivative of the Fourier coefficients with respect to time.Multiple iterations are then applied on the obtained IF and only the maximum modulus of time frequency coefficient is retained,in which extra coefficients at other positions are defined as zero.Finally,an operation of reassignment is performed on the estimated IF to get a refined IF band.Due to what the MCMSST extracts is only an IF band but not an IF curve,the maxima of time frequency coefficient modulus method is applied to extract the IF curve in the frequency band restricted by MCMSST.In addition,two numerical cases and an aluminum cantilever beam test with abrupt mass reduction are investigated to verify the effectiveness of the proposed method.The results demonstrate that the proposed MCMSST not only completely removes non-reassigned points in the refined frequency band,but also enhance the accuracy of IF identification and the robustness on noise resistance.