Constituent Modes Research Articles

VMD-BiGRU for Short-term Power Load Forecasting with Energy Valley Optimizer Enhancement

Abstract Electrical load, given context of this modern era, is recognized to have distinct characteristics: diversity, flexibility, and inherently, non-linearity and temporality. Aiming to leverage these characteristics and counteract the challenges within, we propose an electrical load forecasting method, namely EVO-VMD-BiGRU. The proposed technique initiates by utilizing Variational Mode Decomposition (VMD) for the breakdown of the load data into constituent modes, extract the principal modes, and merge them with the features of air temperature, wind speed, precipitation, electricity price and holidays. The modes are then fed to the BiGRU model for training to forecast. The Energy Valley Optimizer (EVO) is applied to search for optimal hyperparameters of the BiGRU model, with the objective of minimizing the RMSE, in order to obtain models for each mode. Finally, the method utilizes these models to forecast the values of each mode, summing them to generate the final predictions. T The efficacy of this approach was confirmed through testing on load datasets sourced from Singapore and Australia. The proposed method achieved an RMSE of 81.20 MW and 30.15 MW on the respective datasets, the MAPE of 0.79% and 0.47%, and the R-squared (R2) of 0.99 and 0.99, which are superior to the alternative methods in the experiments. Results show that the proposed method achieves superior outcomes in short-term electricity load forecasting and exhibits promising potential for practical use.

Finite-time input-to-state stability and settling-time estimation of impulsive switched systems with multiple impulses

This paper investigates finite-time input-to-state stability (FT-ISS) of impulsive switched systems with multiple impulses. Some FT-ISS conditions, using Lyapunov method and dwell-time condition, are established for impulsive switched systems involving destabilizing and stabilizing impulses simultaneously. When constituent modes regulating continuous dynamics are FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the FT-ISS is retained if impulsive-switching signal satisfies some dwell-time condition. When some constituent modes regulating continuous dynamics are not FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the impulsive-switching signal which satisfies some dwell-time conditions can achieve the FT-ISS of system. In addition, the settling time can be derived conveniently for certain impulsive-switching signal that is formalized by dwell-time condition. The estimation of settling time presents a class of uniformity with respect to the impulsive-switching signals. Two examples are finally presented for the proposed FT-ISS results.

Spatial Mode Division Multiplexing of Free-Space Optical Communications Using a Pair of Multiplane Light Converters and a Micromirror Array for Turbulence Emulation

Multi-plane light converters (MPLC) are a means of deconstructing a wavefront into constituent modes that are focused at specific spatial locations, and the reverse—that specific inputs result in controlled modal output. We have used a pair of MPLCs with 21 Hermite–Gaussian modes to represent a free-space optical connection. The effects of strong atmospheric turbulence (Cn2 = 10−13 m−2/3) are emulated using a micromirror array producing a time sequence of aberrating frames. The modal crosstalk between transmitter and receiver modes induced by the turbulence is presented by measuring the intensity in receiver channels for the same turbulence. Six receiver modes are used for optical communication channels with a rate of 137 Gbits/s displaying the benefits of single input multiple output (SIMO) operation for overcoming the deleterious effects of turbulence.

Hydrodynamic instabilities of a dual-mode air–SF6 interface induced by a cylindrically convergent shock

Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

Controlling the Coverage of Full Poincaré Beams through Second-Harmonic Generation

Ideal full Poincar\'e (FP) beams contain all possible polarization states on the surface of the Poincar\'e sphere and are readily created by linear optical techniques and, more recently, by nonlinear optical processes. An inherent limitation in the latter is the inability to achieve all polarization states, coined coverage, due to modal size, polarization, and modal weighting changes during the nonlinear conversion of the constituent modes. Here, we demonstrate a simple technique to control the coverage of FP beams, using second-harmonic generation as an example, from fully scalar (no coverage) to fully vectorial (full coverage). Our method for determining the coverage confirms the vectorial characteristics of the generated beams and reveals a balancing act between mode order, modal nonlinear efficiency, and initial relative modal weights, all in close agreement with that theoretically predicted. Our findings will hopefully be of value to the communities interested in nonlinear structured light, particularly for vectorial nonlinear modal creators and detectors and control of quantum hybrid entangled states.

Optimization of Plasma Electrolytic Oxidation Technological Parameters of Deformed Aluminum Alloy D16T in Flowing Electrolyte

The prospects of plasma electrolytic oxidation (PEO) technology applied for surface hardening of aluminum alloys are substantiated. The work aims to optimize the technological process of PEO for aluminum in flowing electrolyte. The design of the equipment and the technological process of the PEO for aluminum deformed alloy D16T in flowing silicate–alkaline electrolyte have been developed. Oxide coatings were formed according to various technological parameters of the PEO process. The properties of the oxide coatings were evaluated, respectively, by measurements of coating thickness, geometric dimensions of the samples, microhardness, wear tests, and optical and scanning electron microscopy. To study the influence of the technological parameters of the PEO process of forming oxide coatings on geometrical, physical, and mechanical properties, planning of the experiment was used. According to the results of the conducted experiments, a regression equation of the second order was obtained and the response surfaces were constructed. We determined the optimal values of the technological parameters of the PEO process: component concentration ratio (Na2SiO3/KOH), current density, flow rate, and electrolyte temperature, which provide the oxide coating with minimal wear and sufficiently high physical and mechanical properties and indicators of the accuracy of the shape of the parts. The research results showed that the properties of oxide coatings mainly depend on almost all constituent modes of the PEO process. Samples with Al2O3 oxide coating were tested during dry friction according to the “ring–ring” scheme. It was established that the temperature in the friction zone of aluminum samples with an oxide coating is lower compared to steel samples without a coating, and this indicates high frictional heat resistance of the oxide coating.

Experimental study of bubble competition and spike competition in Richtmyer–Meshkov flows

Shock-tube experiments on various two-bubble and two-spike interfaces are performed to examine the dependence of bubble competition and spike competition on the initial spectra and density ratio of the interface. The differences in the influences of bubble competition and spike competition on the Richtmyer–Meshkov instability are highlighted for the first time. The bubble-competition effect is mainly dependent on the initial spectra of the two-bubble configuration. In contrast, the spike-competition effect is determined by both the initial spectra and density ratio. The extended buoyancy–drag model is adopted to explain the variation of the drag force imposed on the long-wavelength and short-wavelength structures as the initial conditions change. Based on the spectrum analysis, it is found that the constituent modes of two-bubble and two-spike interfaces have different contributions to the long-wavelength and short-wavelength perturbation growths. A generalised, nonlinear, analytical model is then established to quantify the bubble-competition effect and spike-competition effect considering arbitrary initial spectra and density ratio. The bubble-competition effect is believed to be stronger than the spike-competition effect at a high density ratio because it suppresses the high-frequency perturbation growth more evidently.

MVME-RCMFDE framework for discerning hyper-responsivity in Autism Spectrum Disorders

BackgroundAutism Spectrum Disorder (ASD), characterized by impaired sensory processing, has a wide range of clinical heterogeneity, which handicaps effective therapeutic interventions. Therefore, it is imperative to develop potential mechanisms for delineating clinically meaningful subgroups, so as to provide individualised medical treatment. In this study, an attempt is being made to differentiate the hyper-responsive subgroup from ASD by analysing the complexity pattern of Visual Evoked Potentials (VEPs), recorded from a group of 30 ASD participants, in the presence of vertical achromatic sinewave gratings at varying contrast conditions of low (5%), medium (50%) and high (90%). MethodThis study proposes a new diagnostic framework incorporating a novel signal decomposition method termed as Modified Variational Mode Extraction (MVME) and a multiscale entropy approach. MVME segments the signal into five constituent modes with less spectral overlap in lower frequencies. Refined Composite Multiscale Fluctuation-based Dispersion entropy (RCMFDE) is extracted from these constituent modes, thereby facilitating the identification of hyper-responsive subgroup in ASD. ResultsWhen tested on both simulated and real VEPs, MVME displays appreciable performance in terms of root mean square error and minimal spectral overlap in the lower frequencies, in comparison with the other state-of-the-art techniques. Relative Complexity analysis with RCMFDE exhibits a rising trend in 43%–50% of ASD in modes 1, 2, 3 and 4. ConclusionThe proposed MVME-RCMFDE approach is efficient in discriminating the hyper-responsive subgroup in ASD in multiple modes namely mode 1, 2, 3 and 4, which correspond to delta, theta, alpha and beta frequency bands of brain signals.

Magnesium ions reversibly bind to DNA double stranded helix in thin films

Effects of magnesium (Mg2+) ions on the stability and structural properties of double-stranded DNA are vitally important for DNA folding and functional behavior. Complementing our previous study on highly hydrated thin films of DNA with sodium counterions, with no buffer (pH ≈ 6) and surrounded with Mg2+ cations, here we use Fourier transform infrared spectroscopy and band shape analysis to explore in detail the vibrational signatures of DNA-magnesium interaction in the case when DNA charges are neutralized solely by Mg2+ cations, hereafter called MgDNA. Ion atmosphere has been controlled by the magnesium to phosphate molar concentration ratio r which varied between 0.0067 and 10. For r = 0 we find that spectral features in the base region remain similar as in DNA, whereas changes in the backbone region indicate that the B conformation becomes fully stabilized. With increasing r a pronounced structural reshaping occurs in the phosphate backbone region indicating a blue shift of the asymmetric band, while the symmetric band does not show any displacement in frequency. The band shape analysis of overlapping peaks in the respective phosphate regions demonstrates that the number of constituent modes as well as their positions in frequency do not change, whereas their intensities and bandwidths display disparate changes. The results reflect a variety of local environments at the DNA backbone due to a heterogeneous ion atmosphere with randomly distributed magnesium ions and local patterns of hydrogen bonds which change with increasing r. Remarkably, after crowded r = 10 ion atmosphere is depleted, Mg induced spectral changes vanish and structural features of MgDNA (r ≈ 0) are fully restored. Overall results strongly suggest that in MgDNA on highly hydrated thin films the hydrogen-base pairing remains preserved and that Mg2+ ions, similar to sodium ions, retain their mobility and interact with double helix via water-mediated electrostatic forces.

Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF $_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

Theoretical and experimental investigation of the sources of error in stochastic parallel gradient descent-based digital modal decomposition technique

A detailed systematic investigation of the accuracy of digital modal decomposition process that uses stochastic parallel gradient descent (SPGD) algorithm is presented in this paper. Composite beams of known weights and phases corresponding to the eigenmodes of a three-mode fiber are generated theoretically and through experiments using a spatial light modulator (SLM). The weights and phases of the constituent scalar modes are extracted from the intensity profile of the composite beam using the SPGD method, for both theoretical and experimental conditions. Detailed analysis of the sources of error in such SPGD based digital modal decomposition method is carried out by generating composite beams of various modal ratios and phase combinations theoretically. Impact of the experimental errors such as effect of background noise, nonlinearity, misalignment of the camera and that due to the cumulative propagation phase, on the extracted weights and relative phase values are quantified. We find that any ambiguity at phase angles closer to 90 deg among the constituent modes especially when the modal weights are non-uniform, cannot be corrected easily and hence is a fundamental limitation of the intensity-based modal decomposition technique. The methodology used in this manuscript to identify the systemic errors in modal decomposition can be potentially extended to any digital decomposition technique.

General theory and observation of Cherenkov radiation induced by multimode solitons

Advancements in computational capabilities along with the possibility of accessing high power levels have stimulated a reconsideration of multimode fibers. Multimode fibers are nowadays intensely pursued in terms of addressing longstanding issues related to information bandwidth and implementing new classes of high-power laser sources. In addition, the multifaceted nature of this platform, arising from the complexity associated with hundreds and thousands of interacting modes, has provided a fertile ground for observing novel physical effects. However, this same complexity has introduced a formidable challenge in understanding these newly emerging physical phenomena. Here, we provide a comprehensive theory capable of explaining the distinct Cherenkov radiation lines produced during multimode soliton fission events taking place in nonlinear multimode optical fibers. Our analysis reveals that this broadband dispersive wave emission is a direct byproduct of the nonlinear merging of the constituent modes comprising the resulting multimode soliton entities, and is possible in both the normal and anomalous dispersive regions. These theoretical predictions are experimentally and numerically corroborated in both parabolic and step-index multimode silica waveguides. Effects arising from different soliton modal compositions can also be accounted for, using this model. At a more fundamental level, our results are expected to further facilitate our understanding of the underlying physics associated with these complex “many-body” nonlinear processes.

Scattering of Higher Order Mode Clusters (HOMC) from surface breaking notches in plates with application to higher temperature gradients

The potential of higher frequency ultrasonic guided wave mode cluster (HOMC) waves to be used for remote inspection of notch defects in plate-like structures is investigated, at room and elevated temperatures. Quantitative studies of HOMC interaction with notch defects ranging from 5% to 50% of plate thickness are performed using 2D finite element simulations, and are validated by controlled experiments performed, firstly at room temperature. Analysis using reciprocity-based relations is used to uncover for the first time, how the constituent modes of HOMC play a vital role in their scattering processes. Further experiments are used to show that the results are stable up to 300 ̊C, thereby demonstrating the feasibility of short range higher-resolution remote inspection of notch defects using non-dispersive higher frequency mode clusters in industrial conditions.

Modelling hollow pultruded FRP profiles under axial compression: Local buckling and progressive failure

Pultruded Fibre-Reinforced Polymer (PFRP) profiles are widely used as structural elements in many civil infrastructure applications. However, the anisotropic elasticity and the application-driven slenderness make these profiles prone to local buckling failure, well below their ultimate load capacity. In this paper, a numerical study was undertaken to characterise the local buckling and compressive failure of hollow PFRP profiles under axial compression. The Newton method were used along with the adaptive automatic stabilisation scheme and a controlled increment size in Abaqus 2019, to overcome the numerical difficulties in simulating local buckling. The numerical predictions were validated by experiments. The energy parameters and the constituent failure modes of the FEM models were used to explain the effect of dimension, layup, and slenderness ratio on the post-peak behaviour and failure modes of the PFRP profiles. Moreover, the reliance of the strain energy restoration after buckling and the axial and transverse deformations on these parameters was explained.

Configurational complexity of nonautonomous discrete one-soliton and rogue waves in Ablowitz-Ladik-Hirota waveguide

We compute the configurational complexity (CC) for discrete soliton and rogue waves traveling along an Ablowitz-Ladik-Hirota (ALH) waveguide and modeled by a discrete nonlinear Schrödinger equation. We show that for a specific range of the soliton transverse direction κ propagating along the parametric time ζ(t), CC reaches an evolving series of global minima. These minima represent maximum compressibility of information in the momentum modes along the Ablowitz-Ladik-Hirota waveguide. Computing the CC for rogue waves as a function of background amplitude modulation μ, we show that it displays two essential features: a maximum representing the optimal value for the rogue wave inception (the “gradient catastrophe”) and saturation representing the rogue wave dispersion into constituent wave modes. We show that saturation is achieved earlier for higher values of modulation amplitude as the discrete rogue wave evolves along time ζ(t).

The polarisation method and the method of equivalent nodal forces: A comparison with other modal decomposition methods in the analysis of coupled instabilities

The objective of this paper is to validate the newly proposed polarization method (PM) and the method of the equivalent nodal forces (NFM) and to highlight their distinctive features by comparing them with some more established modal decomposition methods, including mainly the generalized beam theory (GBT) and the constrained finite strip method (cFSM). Modal decomposition methods analyse the deformed shapes of a buckled thin-walled structural member by decomposing them into a linear combination of constituent modes (classical local, distortional and global buckling) augmented with shear and transverse extension modes. An overall comparison of the methods is provided, including practical aspects such as how the buckling modes are generated, and the versatility of these methods when applied to various cross-sectional shapes. Specific technical details are discussed for each method, along with numerical examples focusing on the buckling behaviour of thin-walled structural members under compression. Moreover, considerable attention is paid to the discrepancies between the results yielded by different methods, namely the critical stresses associated with pure local, distortional and global buckling. The numerical examples demonstrate that, in spite of the fact that these four methods stem from different theories, they provide essentially the same extended capabilities for examining and understanding thin-walled member stability. Reasons for the discrepancies between the results are discussed and the conclusion is reached that they are attributed to the differences in the criteria adopted in the various methods of mode generation, particularly in the handling of the membrane strains and stresses. In addition, through this comparison features of the newly proposed methods are unveiled such as greater mesh sensitivity, significantly lower critical stress at extremely short half-wavelengths, and different output regarding distortional buckling of hollow-flange sections.

Nonclassicality and entanglement for wave packets

Mode-entanglement based criteria and measures become insufficient for broadband emission, e.g. from spasers (plasmonic nano-lasers). We introduce criteria and measures for the (i) total entanglement of two wavepackets, (ii) entanglement of a wavepacket with an ensemble and (iii) total nonclassicality of a wavepacket~(WP). We discuss these criteria in the context of (i) entanglement of two WPs emitted from two initially entangled cavities (or two initially entangled atoms) and (ii) entanglement of an emitted WP with the ensemble/atom for the spontaneous emission and the single-photon superradiance. We also show that, (iii) when the two constituent modes of a WP are entangled, this creates nonclassicality in the WP as a noise reduction below the standard quantum limit. The criteria we introduce are, all, compatible with near-field detectors.

Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition

For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-autonomous Schrödinger equation is solved here as the wave function evolves through the attraction-repulsion transition and ceases to oscillate.

Successive variational mode decomposition

Variational mode decomposition (VMD) is a powerful technique for concurrently decomposing a signal into its constituent intrinsic modes. However, the performance of VMD will be degraded if the number of modes available in the signal is not precisely known. In this paper, we introduce a new method, namely successive variational mode decomposition (SVMD), which extracts the modes successively and does not need to know the number of modes. The method considers the mode as a signal with maximally compact spectrum, as VMD does. It achieves the mode decomposition by adding some criteria to the optimization problem of VMD: the mode of interest has no or less spectral overlap to the other modes and to the residual signal. Our simulations on some artificial and real world data have demonstrated that the new method without knowing the number of modes converges to the same modes as VMD does with knowing the precise number of modes. Moreover, the computational complexity of SVMD is much lower than that of VMD. Another advantage of SVMD over VMD is more robustness against the initial values of the center frequencies of modes.

Physiological Time Series Processing via Empirical Wavelet Transform

This paper presents the efficacy of empirical wavelet transform (EWT) for physiological time series processing. At first, EWT is applied to multivariate heterogeneous physiological time series. Secondly, EWT is used for the removal of fast temporal scales in multiscale entropy analysis. Empirical mode decomposition is an adaptive data analysis method in the sense that it does not require prior information about the signal statistics and tend to decompose a signal into various constituent modes. The utility of Standard EMD algorithm is however limited to single channel data as it suffers from the problems of mode alignment and mode mixing when applied channel wise for multivariate data. The standard EMD algorithm was extended to multivariate Empirical mode decomposition (MEMD) that can be used analyze a multivariate data. The MEMD can only be applied to multivariate data in which all the channels have equal data length. EWT is another adaptive technique for mode extraction in a signal using empirical scaling and wavelet functions. The multiscale entropy (MSE) algorithm is generally used to quantify the complexity of a time series. The original MSE approach utilizes a coarse-graining process for the removal of fast temporal scales in a time series which is equivalent to applying a finite impulse response (FIR) moving average filter. In Refined Multiscale entropy (RMSE), the FIR filter was replaced with a low pass Butterworth filter which exhibits a better frequency response than that of a FIR filter. In this paper we have presented a new approach for the removal of fast temporal scales based on empirical wavelet transform. The empirical wavelet transform is also used as an innovative filtering approach in multiscale entropy analysis.