Modal Decomposition Technique Research Articles

A novel symplectic geometry-based modal decomposition technique for accurate modal identification of tall buildings with close-spaced modes

The modal decomposition technique is of crucial importance for accurate modal parameter identification of tall buildings with close-spaced modes. However, most of the existing decomposition techniques are proposed for long-span structures, and the techniques specifically focused on tall buildings have rarely been explored. To this end, this paper proposes a novel modal decomposition technique called Symplectic Geometry Close-Spaced Mode Decomposition (SGCD) for the close-spaced modal identification of tall buildings. A numerical study conducted using a two-degree-of-freedom model is utilized to evaluate the effectiveness of the proposed approach. The results demonstrate that the SGCD method can effectively decompose close-spaced modes, and the modal parameters can be accurately identified with high robustness. Furthermore, the proposed modal decomposition technique is employed to analyze the field measurements obtained during a typhoon event on a 420-m-tall building. The results demonstrate the applicability and efficacy of the proposed modal decomposition technique to field measurement data. The main objective of this paper is to provide an effective modal decomposition technique for accurately identifying close-spaced modes of tall buildings.

Dynamics of a cantilevered pipe conveying fluid and partially subjected to a confined counter-current external axial flow of a different fluid

A linear analytical model has been developed for prediction of fluid-elastic instabilities of brine-strings during product retrieval in salt-mined caverns. These caverns are utilized for storage and subsequent retrieval of hydrocarbons, hydrogen gas or compressed air in Compressed Air Energy Storage (CAES) plants. The retrieval operation involves pumping brine downwards through a long cantilevered pipe (“brine-string”) into the cavern, causing the lighter-than-brine gaseous or liquid “product” stored in the cavern to flow upwards and out of the cavern through a shorter annular passage formed by a concentric casing surrounding the upper portion of the pipe. The presence in the cavern of two different fluids with a variable interface level is taken into account. Employing a Newtonian derivation of the equation of motion solutions were obtained via the Galerkin modal decomposition technique, demonstrating that the brine-string may develop buckling or flutter at high-enough flow rates, depending on the system parameters. Extensive computations investigated the influence of system parameters on the dynamics. It is shown that simplifying the system by considering a single fluid in the cavern, and so for the flows within and around the brine-string, leads to unrealistically high critical flow velocity predictions.

Free and forced vibrations of elastically restrained cantilever with lumped oscillator

The efficiency assessment of cantilever-based energy harvesters relies on vibrational analysis, which necessitates modifications aimed at enhancing efficiency. These modifications involve manipulating the fundamental frequency to lower values and encompassing a wider range of resonances within a specified bandwidth. Consequently, this paper introduces an original analytical-numerical exploration into the vibratory response of a cantilever with a novel boundary condition involving an elastically restrained oscillator-spring arrangement. At the microbeam's tip, an oscillator is elastically confined by a linear spring, resulting in a novel set of coupled governing equations and a distinct shearing boundary condition. Microbeam equations is derived from the modified couple stress theory to capture size dependency. During free vibration analysis, a previously unreported characteristic equation is derived. This nonlinear transcendental equation is numerically solved utilizing root-solver algorithms, such as those available in MATLAB. Significantly, it is discovered that the inclusion of a lumped oscillator with an elastic support induces a minimal (new) natural frequency. Applying the extended Hamilton's principle, the effect of the lumped oscillator emerges both on the governing equations of motion and boundary conditions of the microbeam. Novelty of the paper focuses on the both characteristic equation and transmissibility by adopting the Galerkin’s modal decomposition technique. This finding carries vital implications as the efficiency of cantilever-based energy harvesters is directly contingent upon the resonance frequency. Notably, the oscillator mass and spring constant are two parameters that directly influence the vibratory response of the microbeam. In the context of forced vibrations, harmonic base excitation is considered as the input excitation, and the mechanical frequency response function is provided. The proposed system offers two distinct advantages for energy harvester systems: the creation of minimal resonance at lower values and the potential to manipulate the system's resonance toward a desired frequency spectrum.Article HighlightsModifying the boundary conditions of a cantilever beam with lumped-parameter system, can significantly change the behavior of the vibratory response.The boundary condition directly impact the resonance frequencies; which influences the maximum amount of harvestable voltage in vibration-based energy harvesters.Spring constant and mass of the lumped oscillator, are the key factors to alter the vibratory behavior and bandwidth of frequencies. Optimizing such mentioned parameters can help reaching to the maximum harvesting of energy.

Direct Measurements of Vortex-Induced Vibrations on a Horizontal Flexible Cylinder in Water

Abstract This work presents experimental results on vortex-induced vibration (VIV) of a horizontal cylinder with 2.69 m in length, 21 mm in diameter, and a mass ratio equal to 3.9. The experiments were carried out in a towing tank, where the flexible cylinder was towed under constant current profiles. Twenty reduced velocities were tested in a range of 1.75 < Vr < 15.79, corresponding to Reynolds numbers from 1000 to 10,000. The displacements were measured directly through a submerged optical system that simultaneously acquired the in-line and cross-flow movements of 18 reflective targets along the length. The extensive monitored section of the model enabled the application of a modal decomposition technique, which is a methodology that is still relatively unexplored through direct measurements. A comprehensive analysis was applied and the VIV responses related to amplitudes, frequencies, phase angles, and trajectories are shown and discussed in depth. The overall dynamics exhibits a multimodal response behavior, and the modal decomposition procedure has conclusively confirmed that the total amplitude comprises several modes vibrating at the dominant mode frequency. Root mean square values of response amplitude were up to 0.77D and 0.23D in the cross-flow and in-line directions, respectively. The cross-flow synchronization had a significant impact on the in-line excitation modes, and the trajectories showed coherence between motions.

Experimental Dataset of Tunable Mode Converter Based on Long-Period Fiber Gratings Written in Few-Mode Fiber: Impacts of Thermal, Wavelength, and Polarization Variations

Mode division multiplexing (MDM) is currently one of the most attractive multiplexing techniques in optical communications, as it allows for an increase in the number of channels available for data transmission. Optical modal converters are one of the main devices used in this technique. Therefore, the characterization and improvement of these devices are of great current interest. In this work, we present a dataset of 49,736 near-field intensity images of a modal converter based on a long-period fiber grating (LPFG) written on a few-mode fiber (FMF). This characterization was performed experimentally at various wavelengths, polarizations, and temperature conditions when the device converted from LP01 mode to LP11 mode. The results show that the modal converter can be tuned by adjusting these parameters, and that its operation is optimal under specific circumstances which have a great impact on its performance. Additionally, the potential application of the database is validated in this work. A modal decomposition technique based on the particle swarm algorithm (PSO) was employed as a tool for determining the most effective combinations of modal weights and relative phases from the spatial distributions collected in the dataset. The proposed dataset can open up new opportunities for researchers working on image segmentation, detection, and classification problems related to MDM technology. In addition, we implement novel artificial intelligence techniques that can help in finding the optimal operating conditions for this type of device.

A hybrid electricity load prediction system based on weighted fuzzy time series and multi-objective differential evolution

With advances in science and technology, the demand for electricity is increasing dramatically. Consequently, reliable short-term power load prediction is critical to ensure the safety, efficiency, and cost-effectiveness of electricity grids. However, owing to the volatility and randomness of power load time series, traditional forecasting models have struggled to meet the current power system requirements for load prediction precision and stability. In light of this, this study proposes a new hybrid short-term electricity load prediction system that combines the variational modal decomposition (VMD) technique, multi-objective differential evolutionary algorithm (MODE), and weighted fuzzy time series (WFTS) prediction model to increase load prediction precision and stability. Four Belgian datasets (spring, summer, autumn, and winter) were used for short-term power load prediction experiments and were compared with prevalent prediction methods. The experimental results indicate that the designed system obtains MAPESpring=0.6670%, MAPESummer=0.5835%, MAPEAutumn=0.7049%, MAPEWinter=0.7123% and STDSpring=60.2575, STDSpring=62.6573, STDSpring=72.7393, STDSpring=71.5549, which are obviously superior to the comparison models in terms of prediction accuracy and stability.

Analysis of High-Frequency Dynamics of a Reacting Jet in Crossflow Based on Large Eddy Simulation

Abstract Distributed combustion systems have shown the potential to reduce emissions as well as increase load and fuel flexibility. A characteristic feature of such systems is a reacting jet in crossflow, which exhibits complex vortical structures. In this paper, a generic combustion chamber with elliptic reacting jets in crossflow is examined, operating under lean-premixed conditions at elevated pressure and exhibiting high-frequency transverse mode shapes. It can be seen that depending on the orientation of the elliptical shape of the jet to the crossflow, thermoacoustic modes can be suppressed. A multidimensional fast Fourier transform shows that low aspect ratios (major axis of the jet aligned with the crossflow) result in the mixed 1L1T mode of first longitudinal and first transverse structure, while this mode disappears at high aspect ratios. To get a more detailed insight into the different vortex systems of the various aspect ratios, dynamic mode decomposition is applied. This modal decomposition technique reveals for low aspect ratios a shear layer mode that oscillates at a frequency close to the acoustic mixed mode. For this configuration, a mode representing a flapping motion is also identified. For high aspect ratios, the shear layer vortex increases its frequency and a higher-frequent mode appears in the acoustic spectrum.

Decomposition-integration-based prediction study on the development trend of film industry

Movies have the unique ability to both generate income and spread culture, thus predicting the direction of the film industry's growth has garnered a lot of interest. Given the volatility of the movie industry's entire box office revenue dataset and the peculiarities of tiny samples, this article incorporates the decomposition-integration notion to build the EEMD-PSO-LSSVM model movie box office prediction model. The historical box office data are first broken down into many components using the ensemble empirical modal decomposition technique, and then, distinct sequences are predicted using the least squares support vector machine prediction method with particle swarm optimization, and ultimately, the predictions for each sequence are combined. The experimental results demonstrate the effectiveness of the decomposition-integration technique in illustrating the data fluctuation characteristics of quarterly movie box office revenues. When compared to other models, the model proposed in this study has clear advantages in the problem of predicting the time series data of box office revenues that are non-linear, non-smooth, and non-large samples.

Wind power forecasting based on improved variational mode decomposition and permutation entropy

Abstract Due to the significant intermittent, stochastic and non-stationary nature of wind power generation, it is difficult to achieve the desired prediction accuracy. Therefore, a wind power prediction method based on improved variational modal decomposition with permutation entropy is proposed. First, based on the meteorological data of wind farms, the Spearman correlation coefficient method is used to filter the meteorological data that are strongly correlated with the wind power to establish the wind power prediction model data set; then the original wind power is decomposed using the improved variational modal decomposition technique to eliminate the noise in the data, and the decomposed wind power is reconstructed into a new subsequence by using the permutation entropy; with the meteorological data and the new subsequence as input variables, a stacking deeply integrated prediction model is developed; and finally the prediction results are obtained by optimizing the hyperparameters of the model algorithm through a genetic algorithm. The validity of the model is verified using a real data set from a wind farm in north-west China. The results show that the mean absolute error, root mean square error and mean absolute percentage error are improved by at least 33.1%, 56.1% and 54.2% compared with the autoregressive integrated moving average model, the support vector machine, long short-term memory, extreme gradient enhancement and convolutional neural networks and long short-term memory models, indicating that the method has higher prediction accuracy.

Forecasting through deep learning and modal decomposition in two-phase concentric jets

This work aims to improve fuel chamber injectors’ performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of the fuel/air mixture. However, the work carried out to date involves using experimental data (complicated to measure) or the numerical resolution of the complete problem (computationally prohibitive). The latter involves the resolution of a system of partial differential equations (PDE). These problems make difficult to develop a real-time prediction tool. Therefore, in this work, we propose using machine learning in conjunction with (complementarily cheaper) single-phase flow numerical simulations in the presence of tangential discontinuities to estimate the mixing process in two-phase flows. In this meaning we study the application of two proposed neural network (NN) models11The code of one model and two data sets are available at https://github.com/RAbadiaH/forecasting-through-deep-learning-and-modal-decomposition-in-multi-phase-concentric-jets.git. as PDE surrogate models. Where the future dynamics is predicted by the NN, given some preliminary information. We show the low computational cost required by these models, both in their training and inference phases. We also show how NN training can be improved by reducing data complexity through a modal decomposition technique called higher order dynamic mode decomposition (HODMD), which identifies the main structures inside flow dynamics and reconstructs the original flow using only these main structures. This reconstruction has the same number of samples and spatial dimension as the original flow, but with a less complex dynamics and preserving its main features. The core idea of this work is to test the limits of applicability of deep learning models to data forecasting in complex fluid dynamics problems. Generalization capabilities of the models are demonstrated by using the same NN architectures to forecast the future dynamics of four different two-phase flows.

Nonlinear attitude maneuvering of a flexible spacecraft for space debris tracking and collision avoidance

This work addresses the problem of attitude maneuvering of a spacecraft equipped with two flexible solar panels, in response to an alert in two distinct operational scenarios: (a) detection of an approaching debris, and (b) collision avoidance of an impacting debris. In scenario (a) the approaching debris is assumed to be off a collision course with the satellite. As a result, the latter can track the debris, to provide supplementary observations (in addition to those given by ground stations) that allow improving the estimation of its trajectory. Instead, in scenario (b) an impact is predicted, therefore the satellite shall perform a collision avoidance maneuver. This is designed with the objective of minimizing propellant consumption, while ensuring a miss distance greater than a specified threshold value. This research considers the overall dynamics by modeling the spacecraft as a multibody structure, with the use of the Kane's method, which simplifies the process of deriving all the governing equations, while identifying their minimum number. Flexibility is introduced using a modal decomposition technique, under the assumption of small amplitude oscillations. In the two scenarios of interest, efficient strategies are introduced to rotate the solar panels, for the purpose of either maximizing their irradiation or minimizing their oscillations. A new nonlinear reduced-attitude control law, which enjoys global stability properties, is proposed, and is shown to improve the performance of attitude maneuvers when only a single axis must be driven toward a desired direction. Actuation is modeled as well, by assuming the use of a pyramidal array of four single-gimbal control momentum gyroscopes. Their steering law includes singularity avoidance, based on the singular value decomposition of the actuation matrix. Numerical simulations demonstrate that the agile attitude maneuvering strategies proposed in this study allow achieving the operational objectives in the two scenarios of interest, with limited elastic oscillations.

A response band-based method for time-dependent reliability-based robust design optimization

In this paper, a response band-based method for time-dependent reliability-based robust design optimization is proposed. The proposed method provides a novel alternative framework, consist of a two-step transformation stage and a solving stage, to solve the time-dependent reliability-based robust design optimization problem. The original time-dependent reliability-based robust design optimization problem is transformed into an equivalent deterministic robust design optimization problem in the transformation stage, and the equivalent problem is settled in the solving stage. In the transformation stage, the dynamic modal decomposition technique and the kriging technique are combined to overcome the problem that there is no standard for both time division and observation sampling in the commonly used transformation methods. In the solving stage, an approach for constructing the response band of the objective function is presented, which significantly reduces the computational consumption of the variation evaluation of the objective function. Five cases are employed to verify the effectiveness of the proposed method.

Numerical Study of Unstable Shock-Induced Combustion with Different Chemical Kinetics and Investigation of the Instability Using Modal Decomposition Technique

An unstable shock-induced combustion (SIC) case around a hemispherical projectile has been numerically studied which experimentally produced a regular oscillation. Comparison of detailed H2/O2 reaction mechanisms is made for the numerical simulation of SIC with higher-order numerical schemes intended for the use of the code for the hypersonic propulsion and supersonic combustion applications. The simulations show that specific reaction mechanisms are grid-sensitive and produce spurious reactions in the high-temperature region, which trigger artificial instability in the oscillating flow field. The simulations also show that specific reaction mechanisms develop such spurious oscillations only at very fine grid resolutions. The instability mechanism is investigated using the dynamic mode decomposition (DMD) technique and the spatial structure of the decomposed modes are further analyzed. It is found that the instability triggered by the high-temperature reactions strengthens the reflecting compression wave and pushes the shock wave further and disrupts the regularly oscillating mechanism. The spatial coherent structure from the DMD analysis shows the effect of this instability in different regions in the regularly oscillating flow field.

Transonic Shock Buffet Flowfield Assessment Using Various Dynamic Mode Decomposition Techniques

Dynamic mode decomposition (DMD) is a powerful data-driven modal decomposition technique that extracts spatiotemporal coherent structures: a useful process in flow diagnostics and future state estimation of complex nonlinear flow phenomena. Transonic shock buffet is a complicated phenomenon, and modal decomposition techniques such as DMD provide significant insight into its complicated flow physics; but, often, flowfield data are corrupted because of various sources of noise due to the presence of outliers or the absence of critical data components. Therefore, noise corruption renders the modal decomposition inaccurate, and thereby not useful. In this paper, two sources of noise have been considered: simple white noise, and complex salt-and-pepper-type spurious noise. Various DMD techniques including standard DMD, forward–backward DMD, total-least-squares DMD, higher-order DMD, and robust DMD have been implemented. Their effectiveness and limitations in countering noise corruption have been investigated systematically. In the case of white noise corruption, forward–backward DMD, total-least-squares DMD, and higher-order DMD capture the buffet frequency and growth rate with sufficient accuracy, whereas the latter outperforms the other two when the noise variance level is above 5%. In the case of spurious noise, robust DMD handles noise corruption efficiently, with surprisingly high values of pixel corruption of up to 30%.

Vibrations of axially travelling CNT reinforced beams with clamped-clamped boundary condition and an elastic support

Vibrational analysis in engineering systems of axially travelling beams has attracted noticeable attention due to the many applications, such as in robotic manipulators, cable tramways, textile fibres, and in general when there is the axial mass transport of a continuous structure. This article studies the vibrational response of axially-travelling, functionally-graded, carbon nanotube-(CNT)-reinforced beam structures, by investigating linear gyroscopic aspects, such as Argand diagrams. The distribution of CNT fibres is assumed to vary along the thickness of the beam. The Hamilton principle is employed to obtain the coupled axial and transverse behaviour of the beam, subjected to clamped-clamped boundary condition and additionally supported by a spring. These equations of motion are then solved using the modal decomposition technique for the Coriolis-dependent axial and transverse frequencies. For verification, the results are compared to the simplified case in the literature for CNT strengthened beams with zero axial velocity, the dynamics of axially travelling beams, studies of the clamped-clamped boundary condition, and the effects on the Argand diagrams, which have been performed. The Argand diagrams are plotted to examine the effects of varying axial speed on the different linear characteristics of vibration. Variation of the volume fraction of the CNT and the spring support, has also been considered, to understand its effects on the vibration characteristics. Results produced in this article are important in assisting in the future design of engineering devices involving axially travelling systems.

On Alternative Algorithms for Computing Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a data-driven, modal decomposition technique that describes spatiotemporal features of high-dimensional dynamic data. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations. The main purpose of this article is to introduce new alternatives to the currently accepted algorithm for calculating the dynamic mode decomposition. We present two new algorithms which are more economical from a computational point of view, which is an advantage when working with large data. With a few illustrative examples, we demonstrate the applicability of the introduced algorithms.

Short-Term Electricity Price Forecasting Based on the Two-Layer VMD Decomposition Technique and SSA-LSTM

Accurate electricity price forecasting (EPF) can provide a necessary basis for market decision making by power market participants to reduce the operating cost of the power system and ensure the system’s stable operation. To address the characteristics of high frequency, strong nonlinearity, and high volatility of electricity prices, this paper proposes a short-term electricity price forecasting model based on a two-layer variational modal decomposition (VMD) technique, using the sparrow search algorithm (SSA) to optimize the long and short-term memory network (LSTM). The original electricity price sequence is decomposed into multiple modal components using VMD. Then, each piece is predicted separately using an SSA-optimized LSTM. For the element with the worst prediction accuracy, IMF-worst is decomposed for a second time using VMD to explore the price characteristics further. Finally, the prediction results of each modal component are reconstructed to obtain the final prediction results. To verify the validity and accuracy of the proposed model, this paper uses data from three electricity markets, Australia, Spain, and France, for validation analysis. The experimental results show that the proposed model has MAPE of 0.39%, 1.58%, and 0.95%, RMSE of 0.25, 0.9, and 0.3, and MAE of 0.19, 0.68, and 0.31 in three different cases, indicating that the proposed model can well handle the nonlinear and non-stationarity characteristics of the electricity price series and has superior forecasting performance.

Modeling and Flight Control of Small UAV with Active Morphing Wings

In recent research works, morphing wings were studied as an interesting field for a small unmanned aerial vehicle (UAV). The previous studies either focused on selecting suitable material for the morphing wings or performing experimental tests on UAVs with morphing wings. Though, the dynamic modeling of active flexible morphing wings and their involved interactions with the aerodynamics of the UAV body are challenging subjects. Using such a model to control a small UAV to perform specific maneuvering is not investigated yet. The dynamic model of UAV with active morphing wings generates a multi-input multi-output (MIMO) system which rises the difficulty of the control system design. In this paper, the aeroelastic dynamic model of morphing wing activated by piezocomposite actuators is established using the finite element method and modal decomposition technique. Then, the dynamic model of the UAV is developed taking into consideration the coupling between the wing and piezocomposite actuators, as well as the dynamic properties of the morphing actuators with the aerodynamic wind disturbances. A model predictive control (MPC) is designed for the MIMO control system to perform specific flight maneuvering by tracking desired trajectories of UAV altitude and yaw angle. Additionally, the MPC achieves constrained behavior of pitch and roll angles to get satisfactory UAV motion. Also, the behaviors of the UAV control system using MPC are evaluated after adding Dryden wind turbulence to the UAV outputs. Finally, a UAV flight simulation is conducted which shows that the control system successfully rejects the applied disturbances and tracks the reference trajectories with acceptable behavior of pitch and roll angles.

Higher order dynamic mode decomposition of an experimental trailing vortex

The decay of trailing vortices is a fundamental problem in fluid mechanics and constitutes the basis of control applications that intend to alleviate the wake hazard. In order to progress, we use the recently developed modal-decomposition technique to identify the governing dynamics in an experimental trailing vortex. A particular emphasis is on the difficulty and usefulness of applying such tools to noisy experimental data. We conducted a water-tunnel experiment at a chord-based Reynolds number Re=4×104 using stereoscopic particle image velocimetry measurements over a downstream range of 36 chords. The downstream evolution of the maximum of vorticity suggests that the whole wake can be partitioned into three consecutive regimes. A higher-order dynamic mode decomposition of the streamwise vorticity in each such part of the wake shows that the decay is well approximated by at most three modes. Additionally, our study provides evidence for the existence of several instabilities after the vortex roll up beyond about 6.5 chords.

Combined Prediction of Photovoltaic Power Based on Sparrow Search Algorithm Optimized Convolution Long and Short-Term Memory Hybrid Neural Network

To address the problem of strong uncertainty in the high proportion of new energy output, an improved convolutional long- and short-term memory (CLSTM) hybrid neural network is proposed for PV power combination prediction. Firstly, considering the large impact of weather changes on PV power output, a fluctuation feature identification model is used to classify historical PV power series samples into slow weather change type and severe weather change type. Secondly, taking into account the multimodal characteristics of PV power output, an improved variational modal decomposition technique is used to adaptively determine the number of modal components, K, and decompose the two types of samples. Regarding the existence of the low-frequency steady state component and the high-frequency fluctuation component of PV power output, the high-frequency component is used to train the long- and short-term memory (LSTM) model and the low-frequency component is used to train the convolutional neural network (CNN) model. The improved sparrow search algorithm (SSA) is used to optimize the parameters of the LSTM and CNN models during the training process. Finally, the predicted component values of each model are superimposed and reconstructed to obtain PV power prediction values. The actual operation data of a PV plant in northern China were used for comparison and validation, and the experiments showed that the accuracy of the prediction results, based on the improved SSA to optimize the parameters of the CLSTM hybrid neural network for predicting PV output, was significantly better than that of the BP, CNN, LSTM single neural network prediction results, and of the prediction accuracy of the unoptimized CLSTM hybrid neural network. At the same time, compared with the above single neural network and unoptimized hybrid prediction model, the proposed method converged faster and was more adaptable to weather changes.