New inverse wavelet transform method with broad application in dynamics
New inverse wavelet transform method with broad application in dynamics
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DOI：
10.1016/j.ymssp.2021.107691
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发表时间：
2021-02-06
影响因子：
8.4
通讯作者：
Vakakis, Alexander F.
中科院分区：
文献类型：
--
作者：
Mojahed, Alireza;Bergman, Lawrence A.;Vakakis, Alexander F.
从平稳或非平稳测量信号(如时间序列)的系统辨识中提取多尺度模型在工程和应用科学中具有重要意义。提出了一种新的基于小波逆变换的信号谐波分析与分解的计算方法，并在动力学的多个领域中验证了其有效性。小波变换是在时间/空间域中测量的信号到时间-频率/空间-波数域的线性变换，适用于平稳和非平稳测量。该方法基于数值小波逆变换，根据主次谐波分量对测量信号进行分解。首先，我们以一种适合于计算实现的方式来表示解析的连续小波逆变换。然后以一个一般的测量信号为例，(I)数值计算了它的数值小波变换谱，(Ii)定义了一组谐波区域？在包含待逆研究的主次谐波的小波谱中，(Iii)对每个谐波区域分别进行数值逆小波变换，得到各自在时间域中的分解后的谐波。注意，通过构造，所有分解的谐波的叠加重建原始信号。接下来，我们用一些例子说明了该方法的有效性。我们从含有规定的谐波分量的人工信号开始，以突出该方法及其准确性。然后，将该方法应用于具有密集振型的线性耦合振子系统的模态分析，证明了该方法在系统辨识中的适用性。最后，我们展示了新方法如何能够量化由强非线性系统响应中的每个分解分量(谐波)捕获的能量。为此，考虑了单自由度几何非线性振子，并用该方法对非线性能量散射？在它的频域里。这些例子表明，新方法在信号处理和动力学的不同领域具有广泛的适用性，包括具有强(甚至非光滑)非线性的离散和连续动力系统。？2021爱思唯尔有限公司。版权所有。
Extracting multi-scale models from system identification of stationary or nonstationary measured signals (e.g., time series) is of great importance in engineering and the applied sciences. We propose a new computational method for harmonic analysis and decomposition of signals based on the inverse wavelet transform and demonstrate its efficacy in diverse areas in dynamics. The wavelet transform is a linear transformation of a signal measured in the temporal/spatial domain to the time?frequency/space-wavenumber domain and applies to stationary and nonstationary measurements. The new method is based on a numerical inverse wavelet transform and yields decomposition of the measured signal in terms of its dominant harmonic components. First, we formulate the analytical continuous inverse wavelet transform in a way that is suitable for computational implementation. Then, taking as example a general measured signal in the time domain, (i) we numerically compute its numerical wavelet transform spectrum, (ii) define a set of ?harmonic regions? in the wavelet spectrum containing the dominant harmonics to be inverted and studied, and (iii) by numerically inverse wavelet transforming each of the harmonic regions separately, obtain the respective decomposed harmonics in the time domain. Note that, by construction, the superposition of all decomposed harmonics reconstructs the original signal. Next, we demonstrate the efficacy of the method with some examples. We start with an artificial signal with prescribed harmonic components to highlight the method and its accuracy. Then, we show applicability of the method to system identification, by applying it to the modal analysis of a system of linearly coupled oscillators with closely spaced modes. Lastly, we show how the new method enables quantification of the energy captured by each of the decomposed components (harmonics) in the response of a strongly nonlinear system. To this end, a single degree of freedom geometrically nonlinear oscillator is considered, and the method is used to quantify nonlinear energy ?scattering? in its frequency domain. These examples hint at the broad applicability of the new method to diverse areas of signal processing and dynamics, including discrete and continuous dynamical systems with strongly (and even non-smooth) nonlinearities. ? 2021 Elsevier Ltd. All rights reserved.