Dynamic Mode Decomposition Research Articles

Oscillation search robust dynamic mode decomposition method and its application in rolling bearing fault diagnosis

Oscillation search robust dynamic mode decomposition method and its application in rolling bearing fault diagnosis

Assessing the Effect of Coriolis Acceleration on the Coherent Structures in the Wake of a Wind Turbine using DMD

Abstract The present work aims to study the effect of veer, namely, the height-dependent lateral deflection of wind velocity due to Coriolis acceleration, on the coherent structures in the wake of the NREL 5-MW reference wind turbine using the sparsity-promoting dynamic mode decomposition (SP-DMD) method for the detection of dynamically-relevant flow structures. Large eddy simulation of the flow impacting the wind turbine is carried out by solving the filtered Navier-Stokes equations for incompressible flows. The effects of both tower and nacelle are included in the simulation using the immersed boundary method. Simulations are performed at Re ≈ 108, generating the inlet velocity profile by a precursor simulation of the atmospheric boundary layer subjected to Coriolis acceleration. The analysis of the DMD results allows to study the effects of the Coriolis acceleration on the most relevant dynamic modes in the turbine wake and to understand the basic mechanisms by which the wind veer significantly affects the wake recovery rate. Moreover, as a result of the SP-DMD methodology, the most relevant modes are extracted from the wake and a limited subset of relevant flow features that optimally approximates the original data sequence is identified. This small number of modes represent the kernel that can be employed for developing an accurate reduced order model of the wake.

A brief review of reduced order models using intrusive and non‐intrusive techniques

AbstractReduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective in applications like real time control and shape optimization. This contribution aims to provide a brief overview about such a topic. We discuss both a classic intrusive framework based on a Galerkin projection technique and hybrid/non‐intrusive approaches, including Physics Informed Neural Networks (PINN), purely Data‐Driven Neural Networks (NN), Radial Basis Functions (RBF), Dynamic Mode Decomposition (DMD) and Gaussian Process Regression (GPR). We also briefly mention geometrical parametrization and dimensionality reduction methods like Active Subspaces (ASs). Then we test the performance of such approaches in terms of efficiency and accuracy against three academic test cases, the lid driven cavity, the flow past a cylinder and the geometrically parametrized Stanford Bunny. Moreover, we also briefly present some preliminary results related to a more complex case involving an industrial application.

ON HIGHER ORDER DYNAMIC MODE DECOMPOSITION

This paper introduces an alternative variant of Higher Order Dy namic Mode Decomposition (HODMD), which improves the standard approach from a computational point of view. In the new scheme, time delayed snapshots are used along with the special form of the Koopman operator. An algorithm is derived that allows the calculation of novel decomposition in a stable and efficient way. This method is suitable in cases where standard Dynamic Mode Decomposition (DMD) is not applicable. These are dynamics that show limited spatial complexity, and a very large number of included frequencies. We illustrate and explain the new method using some classical and sample dynamics.

The structure and dynamics of the laminar separation bubble

A novel selective mode decomposition, proper orthogonal decomposition and dynamic mode decomposition methods are used to analyse large-eddy simulation data of the flow field about a NACA0012 airfoil at low Reynolds numbers of $5\times 10^4$ and $9\times 10^4$ , and at near-stall conditions. The objective of the analysis is to investigate the structure of the laminar separation bubble (LSB) and its associated low-frequency flow oscillation (LFO). It is shown that the flow field can be decomposed into three dominant flow modes: two low-frequency modes (LFO-Mode-1 and LFO-Mode-2) that govern an interplay of a triad of vortices and sustain the LFO phenomenon, and a high-frequency oscillating (HFO) mode featuring travelling Kelvin–Helmholtz waves along the wake of the airfoil. The structure and dynamics of the LSB depend on the energy content of these three dominant flow modes. At angles of attack lower than the stall angle of attack and above the angle of a full stall, the flow is dominated by the HFO mode. At angles of attack above the stall angle of attack the LFO-Mode-2 overtakes the HFO mode, triggers instability in the LSB and initiates the LFO phenomenon. Previous studies peg the structure, stability and bursting conditions of the separation bubble to local flow parameters. However, the amplitude of these local flow parameters is dependent on the energy content of the three dominant flow modes. Thus, the present work proposes a more robust bursting criterion that is based on global eigenmodes.

A Hybrid Data Assimilation and Dynamic Mode Decomposition Approach for Xenon Dynamic Prediction of Nuclear Reactor Cores

In this paper, a dynamic prediction scheme that combines the data assimilation method and dynamic mode decomposition (DMD) is brought out for the prediction of the whole-core power distribution under xenon oscillations within the HRP1000 reactor. The DMD is used to predict the power values over the nodes where in-core detectors exist, and predicted power is then extended to the whole core using data assimilation methodologies, e.g. the inverse distance–based data assimilation method. In the data assimilation stage, the selection of the background physical field and the regularization factor under different noise levels is investigated. A series of numerical experiments, based on the HPR1000 proof of feasibility of the coupling scheme, is conducted under low noise levels or low prediction step sizes. Finally, the optimal application conditions and the prediction performance of the coupling scheme in different noise levels are analyzed for practical engineering usage.

Source term estimation in the unsteady flow with dynamic mode decomposition

When estimating source parameters in the unsteady flow, the flow information of pollution dispersion is indispensable. It is common practice to save the flow information in the computer in advance but it requires large storage space. Besides, when contaminants are released after a time period of the flow field saved before, calculating the flow field by Computational Fluid Dynamics (CFD) model demands massive computational cost. Dynamic Mode Decomposition (DMD) is thereby proposed to solve the problems mentioned above. Firstly, the fields are decomposed by DMD. Then, the simulated concentrations are acquired by the adjoint equation based on the field synthesized by DMD. Finally, the measured concentrations and the simulated concentrations are taken into Bayesian inference to accomplish source term estimation (STE). The results show that the estimated results with high accuracy are obtained both in the reconstruction stage and in the prediction stage when using the fields obtained by DMD. Also, the efficiency of predicting the future flow by DMD is much higher than that by CFD simulation, suggesting that DMD can improve the efficiency of STE in some cases. As DMD uses a small number of dominant modes to synthesize the approximate fields with minor errors, it reduces the storage demand of flow information in STE. The sampling range and sampling resolution should be properly selected to ensure the accuracy of STE.

Dynamic mode decomposition of GRACE satellite data

Advancements in satellite technology yield environmental data with ever improving spatial coverage and temporal resolution. This necessitates the development of techniques to discern actionable information from large amounts of such data. We explore the potential of dynamic mode decomposition (DMD) to discover the dynamics of spatially correlated structures present in global-scale data, specifically in observations of total water storage anomalies provided by GRACE satellite missions. Our results demonstrate that DMD enables data compression and extrapolation from a reduced set of dominant spatiotemporal structures. The accuracy of its predictions of global system dynamics is preserved in its reconstruction of local time series. These findings suggest potential uses of DMD in analysis of remote-sensing data for hydrologic applications.

Mode decomposition to identify oscillation patterns of flexible aeroshell

Flexible aeroshells, featuring deformable membrane surfaces supported by pressurized gas, offer a novel re-entry system for high-altitude deceleration during re-entry. The flexibility of structural components introduces unique challenges in predicting aerodynamic behavior, as deformations can significantly alter the flow field, affecting pressure distribution and potentially causing aerodynamic instabilities. Therefore, coupled analysis is crucial to ensure the performance reliability of inflatable aeroshells. This study investigates the unsteady aerodynamic behavior, considering structural deformation in a two-way partitioned coupled manner in transonic flow. The dominant deformation patterns are identified using dynamic mode decomposition and the greedy compressive sensing algorithm. The findings reveal that the primary deformation pattern combines axial deformation and swing oscillation. The dominant oscillation frequencies remain different from the eigenfrequencies, indicating that the aerodynamic force is the primary driving force of such oscillations. The time evolution of these dominant modes indicates purely oscillatory behavior rather than increasing or decreasing trends. These insights are critical for the design and reliability assessment of inflatable aeroshells in varying aerodynamic environments.

Spatiotemporal mode extraction for fluid–structure interaction using mode decomposition

A fluid–structure interaction (FSI) analysis model was developed based on the partitioned coupling approach. The study analyzed the fluid and structure behavior in a well-established validation case known as the Turek–Hron FSI benchmark test. This test involves strong, unsteady interaction between fluid flow and an elastic flap behind a rigid cylinder. Comparison of the elastic flap displacement frequencies and amplitudes from the present FSI model with reference data showed good agreement, validating the model. Dynamic mode decomposition (DMD) was employed to extract fundamental structures from the complex spatiotemporal data obtained from the FSI analysis. In addition, a mode–sensing technique based on a greedy algorithm was developed, and significant modes were extracted with elastic flap displacement as a feature. The crucial modes for the elastic flap displacement were the second bending modes at specific frequencies. However, these results differed significantly from the natural frequencies of the second bending modes obtained via eigenmode analysis. This discrepancy can be attributed to the close coupling between the fluid and structure, which alters elastic deformation behavior. The study demonstrates the potential for straightforward extraction of essential fluid–structure coupling using FSI-DMD.

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

Dynamic model decomposition study on the influence of cutback surface length on the wake characteristics of turbine blades

Abstract The flow within a cascade of pressure-side cutback cooling blades with different cutback surface lengths is predicted using the unsteady numerical method. Dynamic Mode Decomposition (DMD) is used for flow field order reduction analysis. The relationship between varying cutback surface lengths and the wake dynamics is analyzed. The analysis shows that the shear layer behind the trailing edge and lip dominates the unsteady flow in the wake region. As the cutback surface length diminishes, an increase in the modal frequencies of both the lip shear layer and the wake shear layer is observed. As the cutback surface length is shortened, the shear layer behind the lip causes stronger oscillations in the shear layer behind the trailing edge, subsequently leading to an augmentation in the amplitude width of the wake mode across the transverse direction.

Experimental study on acoustic and flame responses in an annular combustor under azimuthal force

This study investigates the flame dynamics of an annular combustor under various azimuthal acoustic forces. The experimental platform was applied to external azimuthal acoustic force through four loudspeakers installed on the wall outside the plenum. Experiments were conducted with an equivalence ratio of Ф = 0.71 and a combustion power of P = 9.5 kW. Therein, four loudspeakers were used to precisely control the acoustic pressure amplitude, spinning ratio, and spinning direction, which stimulated the first-order standing mode, spinning modes, and second-order standing mode acoustic mode of the plenum, respectively. Our analysis of flame dynamics and acoustic response characteristics was based on different azimuthal modes, combined with dynamic mode decomposition (DMD) of the flame image sequence and acoustic pressure signal. The results corroborate the consistency between the acoustic field quaternion analysis and the flame image sequence DMD results despite varied external forcing conditions. Specifically, the characteristics of the flame vary by the applied forces. Moreover, DMD results indicate that the flame structure of the eigenfrequency mode is asymmetrical in spinning modes and tilts in the direction of the pressure gradient.

Dynamic characterization of the flow field of air classifier disturbed structures and application to efficient separation of fly ash

Classification is crucial for the resource utilization of fly ash, impacting both utilization rates and product quality. This study introduces an enhanced flow field structure in a perturbed rotating centrifugal air classifier by optimizing toothed and tail blade designs for efficient fly ash classification. Using numerical simulations and experiments, we examine the flow field performance and separation efficacy at various speeds, and employ Dynamic Mode Decomposition (DMD) for modal analysis. Results show the toothed blade, angled at 35°, produces small-scale turbulence with high pressure and velocity, while the tail blade’s rightward bend induces large-scale vortices, aiding flow control. Modal analysis highlights that both Drs-types 1 and 2 predominantly exhibit weakly attenuated modes. Optimal classification occurs at Rs = 950rpm and fv = 0.3kg/s, with both Drs-types surpassing the original structure in effectiveness and pressure. These findings provide new directions for industrial applications and the design of cyclone air classifiers.

A Novel Technique for the Extraction of Dynamic Events in Extreme Ultraviolet Solar Images

High-spatial-resolution images of the solar corona acquired in the extreme ultraviolet (EUV), most notably with the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory (SDO) reveal the abundance of dynamic events which range from flaring bright points and jets to erupting prominences and coronal mass ejections (CMEs). In this work we present novel techniques to extract such dynamic events from the more steady background corona using 17.1 nm SDO-AIA images. The techniques presented here treat any time series of coronal images as a matrix that can be decomposed into two matrices representing the background and the dynamic component, respectively. The latter has the properties of a so-called sparse matrix, and the proposed methods are classified as methods based on sparse representations. The proposed methods are the median-filter method, the principal component pursuit, and the dynamic-mode decomposition, all of which include data pre-processing using the noise-adaptive fuzzy equalization method. The study reveals that the median-filter method and the dynamic-mode decomposition enhance all motions in the time series and produce similar results. On the other hand, the principal component pursuit enables the clear differentiation of CMEs from the background corona, thus providing a valuable tool for the characterization of their acceleration profiles in the low corona as seen in the EUV.

Study of unsteady shear flow near stall in a shrouded supercritical carbon dioxide centrifugal compressor

This study investigates the unsteady shear flow patterns and their relation with the aerodynamic instability of a shrouded supercritical carbon dioxide (SCO2) centrifugal compressor impeller using the dynamic mode decomposition method combined with detached eddy simulation. The results demonstrate that discrete shedding vortex array in the blade tip region is the dominant mode of the SCO2 shrouded centrifugal compressor impeller, with a frequency of 0.5 times the blade passing frequency. In contrast, the main flow structures in the identical impeller using ideal air consist of small-scale shedding vortices near the suction surface and the separated secondary flow. Further analysis of flow field details indicates that the shedding vortex structure inside the shrouded centrifugal impeller originates from the Kelvin–Helmholtz instability generated on the shear interface between the mainstream and the recirculation flow. The greater shear intensity within the SCO2 centrifugal impeller is the reason for the evident occurrence of vortex shedding phenomena in its flow field. Additionally, during the transition from near-stall to stall, vortex pairing phenomena happens at the throat of the centrifugal impeller due to evolutional behaviors of the vortexes. The occurrence of vortex pairing leads to faster blockage of the blade tip region and then the secondary flow spillage over to adjacent passage, ultimately resulting in reverse flow in the blade tip region and extensive blockage at the impeller inlet. The unsteady shear flow evolution clearly demonstrates the processes of stall in SCO2 shrouded impellers.

Numerical study of wave resonance characteristics in gaps of a floating array

Wave resonance in the gaps formed by a four-float array for various drafts and incident wave frequencies is investigated using a numerical wave tank based on OpenFOAM. In the gap perpendicular to the direction of wave propagation, the resonant wave height is higher than that between two side-by-side floats under the same draft, and the resonant frequency is also different. Significant variations in wave height distribution are observed along the gap parallel to the wave propagation direction under different incident wave frequencies. When the incident wave frequencies are higher than the resonant frequency, the lateral force amplitude on the front floats increases, while the force amplitude on the rear floats does not show this effect. Using the dynamic mode decomposition method, we discover that the irregular distribution of wave heights across different frequencies leads to an increase in the lateral force amplitude on the front floats at non-resonant frequencies.

Wake dynamics of side-by-side hydrokinetic turbines in open channel flows

Lateral placement of hydrokinetic turbines is an interesting topic, as the blockage effect can increase the flow speed and increase the power coefficient (CP) for neighboring turbines. This study investigates wake dynamics in hydrokinetic turbine arrays with single- (1T), double- (2T), and triple-turbine (3T) configurations under various tip speed ratios (λ = 3.5, 5.8, and 7.1) using large eddy simulation coupled with the actuator line (AL) model. Results indicate that CP increases as lateral spacing decreases, which highlights the advantages of tighter lateral placement. The CP of the 3T-S turbine (the side turbine in the 3T configuration) is larger than those of the other configurations, following the trend CP,3T−S>CP,3T−M>CP,2T>CP,1T, which reflects a growing blockage effect with more turbines. Wake dynamics are analyzed using time-averaged and instantaneous methods. In 3T scenarios, blockage enhances turbulence kinetic energy, facilitating faster wake recovery, aided by turbine interference. Mean kinetic energy budget analysis shows that 3T-S wakes recover fastest due to increased turbulent convection. For instantaneous analysis, pre-multiplied power spectral density reveals vertical meandering begins at approximately 3D (D is the rotor diameter) and horizontal meandering starts near 4D, with a dominant frequency of St=0.28. Integral length scales show an initial increase followed by a downstream decrease, with minima marking the onset of wake meandering. Dynamic mode decomposition analysis reveals that high-frequency disturbance amplitudes increase with the number of turbines. At the optimal λ, wake effects dominate over inflow effects.

Separating urban heat island circulation and convective cells through dynamic mode decomposition

AbstractThis study applies dynamic mode decomposition (DMD) to three‐dimensional simulation results of urban heat island circulation (UHIC, which is horizontal circulation) and thermals (vertical convections). The aim of this study is to revisit how these phenomena coexist based on the characteristics of temporal changes in the flow field. We used DMD to obtain the dominant spatial patterns and information on temporal changes. One of the modes of horizontal wind, which does not change temporally (no oscillation or amplification), exhibits a spatial UHIC pattern. The unique feature of this UHIC mode is that there are small‐scale striated structures (150–200 m) and large‐scale convergence. The other modes are time‐varying (oscillating and decaying) and represent smaller spatial‐scale phenomena (150–250 m), such as thermals. The frequency of each mode takes various values, some of which are lower than the lifetime of thermals in accordance with the Deardorff convective scale (~10 min). These low‐frequency modes showed striated structures similar to that observed in the UHIC modes. These results suggest that UHIC and thermals deform each other through components that vary in long temporal scales.

Dynamic mode decomposition-based technique for cross-term suppression in the Wigner-Ville distribution

This paper presents a new method for time-frequency representation (TFR) using dynamic mode decomposition (DMD) and Wigner-Ville distribution (WVD), which is termed as DMD-WVD. The proposed method helps in removing cross-term in WVD-based TFR. In the suggested method, the DMD decomposes the multi-component signal into a set of modes where each mode is considered as mono-component signal. The analytic modes of these obtained mono-component signals are computed using the Hilbert transform. The WVD is computed for each analytic mode and added together to obtain cross-term free TFR based on the WVD. The effectiveness of the proposed method for TFR is evaluated using Rényi entropy (RE). Experimental results for synthetic signals namely, multi-component amplitude modulated signal, multi-component linear frequency modulated (LFM) signal, multi-component nonlinear frequency modulated (NLFM) signal, multi-component signal consisting of LFM and NLFM mono-component signal, multi-component signal consisting of sinusoidal and quadratic frequency modulated mono-component signals, and synthetic mechanical bearing fault signal and natural signals namely, electroencephalogram (EEG) and bat echolocation signals are presented in order to show the effectiveness of the proposed method for TFR. It is clear from the results that the proposed method suppresses cross-term effectively as compared to the other existing methods namely, smoothed pseudo WVD (SPWVD), empirical mode decomposition (EMD)-WVD, EMD-SPWVD, variational mode decomposition (VMD)-WVD, VMD-SPWVD, and DMD-SPWVD.