Multi-Scale Multi-Load Federated Forecasting Method with Mode Decomposition

This paper describes the basic theory for modal decomposition and modal cluster decomposition on two-dimensional frequency domain, based on the two-dimensional Fourier transform of array sensor outputs. At first, the concept of modal cluster decomposition was introduced. Then, an objective function was derived to determine the sensor placement to place each modal cluster on any selected line in two-dimensional frequency domain. As a numerical example, the optimal sensor placement was computed for a simply supported beam in case the number of sensor is two. It is shown that this decomposition is used for suppressing several selected modal amplitudes, or placing each modal cluster on any selected line. Moreover there exists the sensor placement that is used for suppressing multiple modal cluster simultaneously.

Impact of basis, orthogonalization, and normalization on the constrained Finite Strip Method for stability solutions of open thin-walled members

Eliminations competitives lors de la decomposition basique de sels de N-alcoxypyridinium—I : Competition entre intermediaires ylure ou anhydrobase et ions hydroxydes dans l'arrachement des protons en α ou β dans la chaine alcoxyle†

Reduced-order modelling techniques can make important contributions in the control and state estimation of large systems. In hyperthermia, reduced—order modelling can provide a useful tool by which a large thermal model can be reduced to the most significant subset of its full—order modes, making real—time control and estimation possible. Two such reduction methods, one based on modal decomposition and the other on balanced realization, are compared in the context of simulated hyperthermia heat transfer problems. The results show that the modal decomposition reduction method has three significant advantages over that of balanced realization. First, modal decomposition reduced models result in less error, when compared to the full-order model, than balanced realization reduced models of similar order in problems with low or moderate advec—tive heat transfer. Second, because the balanced realization based methods require a priori knowledge of the sensor and actuator placements, the reduced-order model is not robust to changes in sensor or actuator locations, a limitation not present in modal decomposition. Third, the modal decomposition transformation is less demanding computationally. On the other hand, in thermal problems dominated by advective heat transfer, numerical instabilities make modal decomposition based reduction problematic. Modal decomposition methods are therefore recommended for reduction of models in which advection is not dominant and research continues into methods to render balanced realization based reduction more suitable for real—time clinical hyperthermia control and estimation.

The numerical method of modes analysis and decomposition of the output signal in 3D electromagnetic particle-in-cell simulation is presented. By the method, multiple modes can be resolved at one time using a set of diagnostic data, the amplitudes and the phases of the specified modes can all be given separately. Based on the method, the output signals of one X-band tri-bend mode converter used for one high power microwave device, with ionization process in the device due to the strong normal electric field, are analyzed and decomposed.

The rising interest in cislunar space as a strategic environment for easier access to the Moon and the solar system has fostered the development of several future missions. In such an environment, close-proximity operations will require innovative trajectory design and path-planning techniques. Moving toward this goal, this paper introduces an original relative motion representation with respect to a periodic chief in the circular restricted three-body problem and an original relative trajectories design methodology based on fundamental modal solutions decomposition. Specifically, a relative motion model is developed in a velocity-based orbiting frame, in which the flight-path direction is considered to define one of its primary axes. Then, modal decomposition is applied to separate the fundamental modes of motion, showing that modal coefficients, eigenvectors, and eigenvalues can be employed for a geometrical characterization of relative dynamics. The resulting relative motion model is applied to describe the relative dynamics between a chaser spacecraft and a target satellite moving onto an L2 halo orbit, and its accuracy is assessed by comparisons against numerical integration of the three-body problem equations. In addition, the use of modal decomposition coefficients as geometrically insightful relative orbital elements for trajectory design and path planning is illustrated through various applicative examples.

System identification methods for dynamic models of brain activity

There is a broad need to better understand the dynamics of neural activity in both space and time. Rigorous modeling methods are needed to improve the analysis of brain wave dynamics. Two system identification algorithms, Output-Only Modal Analysis (OMA) and Dynamic Mode Decomposition (DMD), are modified for use in neural dynamics and compared. An example application is included. The system identification methods are applied to estimate state-space models for neural dynamics. The modeling technique results in a reduced order modal decomposition of the behavior of the brain. The resultant eigenmodes can be non-orthogonal and complex, capturing the emergent space-time dynamics. We apply the modeling method to the Database for Emotion Analysis using Physiological Signals (DEAP) and the EEG Motor Movement/Imagery Dataset (EEGMMI) in a biosecurity application. It is shown that there are common modes shared among all subjects, regardless of stimuli. Further, the modal decompositions may be used to distinguish subjects from one another in a subject identification biosecurity task. The accuracy of the OMA eigenmode model is 100%, while the accuracy of the DMD eigenmode model is 96%. Output-only system identification techniques are an appropriate rigorous modeling method for EEG data. The structured modeling procedure offers new opportunities for cognitive modeling and affective computing.

<div class="section abstract"><div class="htmlview paragraph">Numerical analysis methods are used to investigate the flow in a ported-shroud centrifugal compressor under different operating conditions, i.e. several mass flow rates at two different speed lines. A production turbocharger compressor is considered, which is widely used in the heavy automotive sector. Flow solutions obtained under steady-state and transient flow assumptions are compared with available experimental data.</div><div class="htmlview paragraph">The steady-state Reynolds Averaged Navier-Stokes method is used to assess the overall time averaged flow and the global performance parameters. Additionally, the Large Eddy Simulation (LES) approach is employed to capture the transient flow features and the developed flow instabilities at low mass flow rates near the surge line.</div><div class="htmlview paragraph">The aim of this study is to provide new insights on the flow instability phenomena in the compressor flow near surge. Comparison of flow solutions obtained for near-optimal efficiency and near-surge conditions are carried out. The unsteady features of the flow field are quantified by means of Fourier transformation analysis, Proper Orthogonal Decomposition and Dynamic Mode Decomposition. For a near optimal efficiency set-up the frequency spectra are broad-banded with no distinct instabilities. Close to the surge line, the spectra show a distinct surge cycle frequency, which is due to flow pulsation in the compressor.</div><div class="htmlview paragraph">The modal flow decomposition elucidates a mode occurring at the surge frequency. The mode explains the oscillating pumping effect occurring during surge. The surface spectra contours reveal the shape of the pressure pulsation during surge and support that a pressure gradient occurs with the oscillating modes found with the modal decomposition.</div></div>

Mode decomposition (MD) is essential to reveal the intrinsic mode properties of fiber beams. However, traditional numerical MD approaches are relatively time-consuming and sensitive to the initial values. To solve these problems, deep learning technique is introduced to perform non-iterative MD. In this paper, we focus on the real-time MD ability of the pre-trained convolutional neural network. The numerical simulation indicates that the averaged correlation between the reconstructed patterns and measured patterns is 0.9987 and the decomposing rate can reach about 125 Hz. As for the experimental case, the averaged correlation is 0.9719 and the decomposing rate is 29.9 Hz, which is restricted by the maximum frame rate of the CCD camera. The results of both simulation and experiment show the superb real-time ability of the deep learning-based MD methods.

Approaches to subgrid-scale physical parameterization in atmospheric modeling are reviewed by taking turbulent combustion flow research as a point of reference. Three major general approaches are considered for its consistent development: moment, distribution density function (DDF), and mode decomposition. The moment expansion is a standard method for describing the subgrid-scale turbulent flows both in geophysics and engineering. The DDF (commonly called PDF) approach is intuitively appealing as it deals with a distribution of variables in subgrid scale in a more direct manner. Mode decomposition was originally applied by Aubry et al (1988 J. Fluid Mech. 192 115-73) in the context of wall boundary-layer turbulence. It is specifically designed to represent coherencies in compact manner by a low-dimensional dynamical system. Their original proposal adopts the proper orthogonal decomposition (empirical orthogonal functions) as their mode-decomposition basis. However, the methodology can easily be generalized into any decomposition basis. Among those, wavelet is a particularly attractive alternative. The mass-flux formulation that is currently adopted in the majority of atmospheric models for parameterizing convection can also be considered a special case of mode decomposition, adopting segmentally constant modes for the expansion basis. This perspective further identifies a very basic but also general geometrical constraint imposed on the massflux formulation: the segmentally-constant approximation. Mode decomposition can, furthermore, be understood by analogy with a Galerkin method in numerically modeling. This analogy suggests that the subgrid parameterization may be re-interpreted as a type of mesh-refinement in numerical modeling. A link between the subgrid parameterization and downscaling problems is also pointed out.

Modal buckling analysis of thin-walled members with rounded corners by using the constrained finite strip method with elastic corner elements

In this paper modal decomposition of the deformations of thin-walled structural members are discussed. Modal decomposition is a process which separates the characteristic behavior modes. If applied in buckling analysis, modal decomposition makes it possible to analyze pure global or pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly useful in the design of thin-walled structural members, such as cold-formed steel beams or columns. Cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite element method and generalized beam theory fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. An extension to the constrained finite strip method is proposed and discussed. The proposal introduces rigid corner elements, which make it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled. The formulation of the proposal is summarized, then the rigid-corner approach is studied by an extended parametric study.

Retrieving modal contents from a multimode beam profile can provide the most detailed information of a beam. Numerical modal decomposition is a method of retrieving modal contents, and it has gained significant attention owing to its simplicity. It only requires a measured beam profile and an algorithm. Therefore, a complicated setup is not necessary. In this study, we conceived that the modal decomposition can be notably improved by data-efficiently sub-sampling the beam image instead of using full pixels of a beam profiler. By investigating the window size, the number of pixels, and algorithm for sub-sampling, the calculation time for the algorithm was faster by approximately 100 times than the case of full pixel modal decomposition. Experiments with 3-mode and 6-mode beams, which originally span 201×201 and 251×251 pixels, respectively, confirmed the remarkable improvement of calculation speed while maintaining the error function at a level of ∼10-3. This first demonstration of sub-sampling for modal decomposition is based on the modified stochastic parallel gradient descent algorithm. However, it can be applied to other numerical or artificial intelligence algorithms and can enhance real-time analysis or active control of beam characteristics.

Depicting the multimode laser beam by modal decomposition can potentially assess light field variations in the fiber, during propagation. The practical engineering conditions in the lab however could not realize ideal levels, hence further research on factors influencing this method, such as defocus, is especially necessitated. The grid spacing in observation plane by Fast Fourier Transform is fixed and unchangeable within diffraction imaging, hence possibly yielding erroneous data during obtaining light field intensities. Our research resolves these issues via a Two-step ABCD algorithm, applied in the modal decomposition to characterize various guided modes at the output of multimode fibers. A direct benefit is that the image plane size can be altered, further refining laser facula clarity. Furthermore, the quantitative expressions that analyze defocus factors impacting modal decomposition are acquired. The conclusions thereby prove the modal decomposition algorithm can keep effectiveness in the range of −0.25% to 0.25% of relative defocus for low order eigenmodes, having no suitable limited band for high order eigenmodes, with reference value in engineering applications.