scholarly journals Decomposing non-stationary signals with time-varying wave-shape functions

2021 ◽  
pp. 1-1
Author(s):  
Marcelo Alejandro Alejandro Colominas ◽  
Hau-Tieng Wu
Keyword(s):  
Time Varying ◽  
Shape Functions ◽  
Wave Shape ◽  
Stationary Signals

scholarly journals A Time–Frequency Correlation Analysis Method of Time Series Decomposition Derived from Synchrosqueezed S Transform

2019 ◽  
Vol 9 (4) ◽  
pp. 777 ◽  
Author(s):  
Gaoyuan Pan ◽  
Shunming Li ◽  
Yanqi Zhu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Time Varying ◽  
Analysis Method ◽  
Frequency Correlation ◽  
Time Frequency ◽  
Time Series Decomposition ◽  
S Transform ◽  
Stationary Signals ◽  
Correlation Analysis Method

Traditional correlation analysis is analyzed separately in the time domain or the frequency domain, which cannot reflect the time-varying and frequency-varying characteristics of non-stationary signals. Therefore, a time–frequency (TF) correlation analysis method of time series decomposition (TD) derived from synchrosqueezed S transform (SSST) is proposed in this paper. First, the two-dimensional time–frequency matrices of the signals is obtained by synchrosqueezed S transform. Second, time series decomposition is used to transform the matrices into the two-dimensional time–time matrices. Third, a correlation analysis of the local time characteristics is carried out, thus attaining the time–frequency correlation between the signals. Finally, the proposed method is validated by stationary and non-stationary signals simulation and is compared with the traditional correlation analysis method. The simulation results show that the traditional method can obtain the overall correlation between the signals but cannot reflect the local time and frequency correlations. In particular, the correlations of non-stationary signals cannot be accurately identified. The proposed method not only obtains the overall correlations between the signals, but can also accurately identifies the correlations between non-stationary signals, thus showing the time-varying and frequency-varying correlation characteristics. The proposed method is applied to the acoustic signal processing of an engine–gearbox test bench. The results show that the proposed method can effectively identify the time–frequency correlation between the signals.

Finite Amplitude Dynamics of a Flexible Spinning Disc

1995 ◽  
Author(s):  
N. Malhotra ◽  
N. Sri Namachchivaya ◽  
T. Whalen
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Dominant Mode ◽  
Transverse Motion ◽  
Power Series Solution ◽  
Time Varying ◽  
Bending Rigidity ◽  
Shape Functions ◽  
Spinning Disc

Abstract The transverse dynamics of a high speed spinning disc which is clamped at the inner radius and rotating with a time-varying spin rate is examined in a space fixed frame of reference. The general nonlinear equations of motion governing the disc dynamics are systematically derived using displacement as well as stress function formulations. These equations of motion include the effects due to inherent bending rigidity, membrane stresses arising from centrifugal forces, non-axisymmetry of the in-plane and transverse displacements, geometric nonlinearities, aerodynamic damping arising from air stationary and moving with respect to the disc, parametric excitation due to time varying spin rate, etc. For the constant rotation case, the linearized equations of motion are solved by taking both membrane as well as flexural stiffness effects into account. This leads to a power series solution for the radial shape functions and harmonic solutions for the circumferential shape functions. The two-dimensional eigen-functions thus obtained can describe a disc mode with any number of nodal diameters and nodal circles, and the resulting eigen-frequencies match very well with the numerical results. The nonlinear and non-axisymmetric in-plane response is also determined, and a 2-DOF system of ODEs is obtained which governs the dynamic variation of the amplitudes of traveling waves associated with the dominant mode of the transverse motion.

scholarly journals Message Passing-Based Inference for Time-Varying Autoregressive Models

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 683
Author(s):  
Albert Podusenko ◽  
Wouter M. Kouw ◽  
Bert de Vries
Keyword(s):  
Message Passing ◽  
Synthetic Data ◽  
Model Performance ◽  
Ar Model ◽  
Factor Graph ◽  
Time Varying ◽  
Real World Data ◽  
Data Set ◽  
Inference Problem ◽  
Stationary Signals

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.

scholarly journals Instantaneous Frequency Estimation of Multi-Component Non- Stationary Signals using Fourier Bessel series and Time-Varying Auto Regressive Model

2015 ◽  
Vol 61 (4) ◽  
pp. 365-376
Author(s):  
G. Ravi Shankar Reddy ◽  
Rameshwar Rao
Keyword(s):  
Instantaneous Frequency ◽  
Estimation Error ◽  
Basis Functions ◽  
Time Varying ◽  
Instantaneous Frequency Estimation ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Stationary Signals ◽  
Auto Regressive ◽  
Non Stationary Signal

Abstract In this paper, we propose a novel technique for Instantaneous Frequency (IF) estimation of multi component non stationary signals using Fourier Bessel Series and Time- Varying Auto Regressive (FB-TVAR) model. In the proposed technique, the Fourier-Bessel (FB) expansion decomposes the multi-component non stationary signal into a number of monocomponent signals and TVAR model is used to model each mono-component signal. In TVAR modeling approach the time varying parameters are expanded as a linear combination of basis functions. In this paper, the TVAR parameters are expanded by a discrete cosine basis functions. The maximum likelihood estimation algorithm for model order selection in TVAR models is also discussed. The Instantaneous Frequency (IF) is extracted from the time-varying parameters by calculating the angles of the estimation error filter polynomial roots. The estimation of the TVAR parameters of a multicomponent signal requires the inversion of a large covariance matrix, while the projected technique (FB-TVAR) requires the inversion of a number of comparatively small covariance matrices with better numerical stability properties. Simulation results are presented for Multi component discrete Amplitude and Frequency modulated (AM-FM) signal

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