Multifractal detrended fluctuation analysis based on optimized empirical mode decomposition for complex signal analysis

Nonlinear Dynamics - Multifractal detrended fluctuation analysis (MFDFA) is a powerful tool to uncover nature of complex signals. However, MFDFA runs into difficulties in determining the type of...     

HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD

A novel approach of signal extraction of a harmonic component from a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition (EMD) and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted from the chaotic signals. Simulation results show the approach is satisfactory.     

An error analysis of the dynamic mode decomposition

Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and temporal dynamics of coherent structures in experimental fluid flows. To aid interpretation of experimental data, error-bars on the measured growth rates are needed. In this article, we undertake a massively parallel error analysis of the DMD algorithm using synthetic waveforms that are shown to be representative of the canonical instabilities observed in shear flows. We show that the waveform of the instability has a marked impact on the error of the measured growth rate. Sawtooth and square waves may have an order of magnitude larger error than sine waves under the same conditions. We also show that the effects of data quantity and quality are of critical importance in determining the error in the growth or decay rate, and that the effect of the key parametric variables are modulated by the growth rate itself. We further demonstrate methods by which ensemble and orthogonal data may be introduced to improve the noise response. With regard for the important variables, precise measurement of the growth rates of instabilities may be supplemented with an accurately estimated uncertainty. This opens many new possibilities for the measurement of coherent structure in shear flows.     

Determination of turbulence properties by using empirical mode decomposition on periodic and random perturbed flows

Stationary and non-stationary grid-generated turbulence was studied using a complementary technique that combines empirical mode decomposition (EMD) and triple-decomposition. Non-stationary conditions were generated by superimposing periodic and random fluctuations on the original flow. Empirical mode decomposition (EMD) was applied as a filter to separate these fluctuations from the turbulent velocity component. Triple-decomposition was then used and the turbulent intensity, the integral length scales and the Power Spectral Density of the velocity were determined. How to use EMD in order to optimize this decomposition is discussed. Finally, the properties of the turbulence are compared to those characterized without addition of fluctuations and a good agreement is found.     

Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal

In this paper, based on the Hirota bilinear method, a kind of lump solutions and two classes of interaction solutions are discussed to the \((2+1)\)-dimensional generalized KdV equation with the aid of symbolic computation system Mathematica. Analyticity is naturally guaranteed by taking special choices of the involved parameters to achieve a positive constant term. Particularly, these solutions with special values of the included parameters are plotted, as illustrative example.     

Lamb wave mode decomposition for structural health monitoring

Lamb waves propagate over large distances in plate-like thin structures and they have received great attention in the structural health monitoring (SHM) field as an efficient means to inspect a large area of a structure by using only a small number of sensors. The times-of-flight of the Lamb wave modes are useful for detecting damage generated in a structure. However, due to the dispersive and multi-mode nature of Lamb waves, it is very challenging to decompose Lamb wave modes into symmetric and anti-symmetric modes for potential applications to structural health monitoring. Thus, we propose an efficient Lamb wave mode decomposition method based on two fundamental rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of _A0$A_0$ and _S0$S_0$ modes must be constant. The mode amplitude ratio rule means that the ratio of the magnitudes of _A0$A_0$ and _S0$S_0$ modes in a measured response signal must be always greater than one once the center frequency of the input signal is determined, such that the magnitude of the _A0$A_0$ mode in the excited signal is larger than that of the _S0$S_0$ mode, and vice versa. The proposed method is verified through experiments conducted for a plate specimen.     

Probabilistic response and analysis for a vibro-impact system driven by real noise

Nonlinear Dynamics - In this paper, a new stochastic averaging method is proposed to derive the stationary probabilistic response of vibro-impact system subject to real noise excitation, and the...     

Dynamic mode decomposition based analysis of flow over a sinusoidally pitching airfoil

Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in accounting in the DMD formulation, for a body of non-zero thickness moving through the field of interest. This work presents a method for decomposing the flow on or near a moving boundary by a change of reference frame, followed by a correction to the computed modes that is determined by the frequency spectrum of the motion. The correction serves to recover the modes of the underlying flow dynamics, while removing the effect of change in reference frame. This method is applied to flow over sinusoidally pitching airfoils, and the DMD analysis is used to derive useful insights regarding flow-induced pitch oscillations of these airfoils.     

Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump

Nonlinear Dynamics - The paper treats stationary response of a stochastically excited multi-degree-of-freedom (multi-DOF) vibro-impact system undergoing Markovian jump. The vibro-impact system with...     

Applications of the dynamic mode decomposition

The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow.     

Bispectral mode decomposition of nonlinear flows

Nonlinear Dynamics - Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow...     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Efficiency of randomised dynamic mode decomposition for reduced order modelling

ABSTRACT

The purpose of this paper is the identification of a reduced order model (ROM) from numerical code output by non-intrusive techniques (i.e. not requiring projecting of the governing equations onto the reduced basis modes). In this paper, we perform a comparison between two methods of model order reduction based on dynamic mode decomposition (DMD). The first method is a deterministic (classic) DMD technique endowed with a dynamic filtering criterion of selection of modes used in the ROM model. The second method is an adaptive randomised DMD algorithm (ARDMD) based on a randomised singular value decomposition. This produced an accelerating algorithm, which is endowed with a few additional advantages. In addition, the reduced order model is guaranteed to satisfy the boundary conditions of the full model, which is crucial for surrogate modelling. For numerical illustration, we use the shallow water equations model.     

A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm

Studies of the shallow water waves are active, possessing the applications in ocean engineering, marine environment, atmospheric science, etc. In this paper, we investigate a (3+1)-dimensional shallow water wave equation with time-dependent coefficients. Hirota method and symbolic computation help us work out (1) a bilinear form, (2) N-soliton solutions with N being a positive integer, (3) the higher-order breather solutions, (4) periodic-wave solutions and (5) hybrid solutions composed of one first-order breather and one soliton/two solitons. Moreover, we provide some nonlinear phenomena described by the associated solutions. All of the obtained results are determined via the time-dependent coefficients of that equation.

     

Optimization for vibro-impact nonlinear energy sink under random excitation

As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available for the design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effort to address this gap. Specifically, the approximate analytical solution of the system stochastic response is obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Taking advantages of this approximate solution, the variance of the system is defined and easily minimized to calculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlate with direct numeric simulations.     

Targeted energy transfers in vibro-impact oscillators for seismic mitigation

In the field of seismic protection of structures, it is crucial to be able to diminish ‘as much as possible’ and dissipate ‘as fast as possible’ the load induced by seismic (vibration-shock) energy imparted to a structure by an earthquake. In this context, the concept of passive nonlinear energy pumping appears to be natural for application to seismic mitigation. Hence, the overall problem discussed in this paper can be formulated as follows: Design a set of nonlinear energy sinks (NESs) that are locally attached to a main structure, with the purpose of passively absorbing a significant part of the applied seismic energy, locally confining it and then dissipating it in the smallest possible time. Alternatively, the overall goal will be to demonstrate that it is feasible to passively divert the applied seismic energy from the main structure (to be protected) to a set of preferential nonlinear substructures (the set of NESs), where this energy is locally dissipated at a time scale fast enough to be of practical use for seismic mitigation. It is the aim of this work to show that the concept of nonlinear energy pumping is feasible for seismic mitigation. We consider a two degree-of-freedom (DOF) primary linear system (the structure to be protected) and study seismic-induced vibration control through the use of Vibro-Impact NESs (VI NESs). Also, we account for the possibility of attaching to the primary structure additional alternative NES configurations possessing essential but smooth nonlinearities (e.g., with no discontinuities). We study the performance of the NESs through a set of evaluation criteria. The damped nonlinear transitions that occur during the operation of the VI NESs are then studied by superimposing wavelet spectra of the nonlinear responses to appropriately defined frequency – energy plots (FEPs) of branches of periodic orbits of underlying Conservative systems.     

The analysis of the spectrum of Lyapunov exponents in a two-degree-of-freedom vibro-impact system

In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an efficient tool for analyzing periodic motions and chaos. So far, different calculating methods of Lyapunov exponents have been proposed. Recently, a new method using local mappings was given to compute the Lyapunov exponents in non-smooth dynamical systems. By the help of this method and the coordinates transformation proposed in this paper, we investigate a two-degree-of-freedom vibro-impact system with two components. For this concrete model, we construct the local mappings and the Poincaré mapping which are used to describe the algorithm for calculating the spectrum of Lyapunov exponents. The spectra of Lyapunov exponents for periodic motions and chaos are computed by the presented method. Moreover, the largest Lyapunov exponents are calculated in a large parameter range for the studied system. Numerical simulations show the success of the improved method in a kind of two-degree-of-freedom vibro-impact systems.