Dynamic Mode Decomposition Method Research Articles

Fault Detection in a Single-Bus DC Microgrid Connected to EV/PV Systems and Hybrid Energy Storage Using the DMD-IF Method

Variations in fault currents, short times to clear the fault, and a lack of a natural current zero-crossing point are the most important challenges that DC microgrid protection faces. This challenge becomes more complicated with the presence of electric vehicles and energy storage systems due to their uncertainties. For this reason, in this paper, a new method for fault detection in DC microgrids with the presence of electric vehicles and energy storage systems is proposed. The new proposed method uses the combination of dynamic mode decomposition and instantaneous frequency for fault detection. In this method, first, a reference signal is made using the voltage and current signal sampled from the DC microgrid using the dynamic mode decomposition method. Next, in order to detect the fault, the instantaneous frequency value of the reference signal is calculated by the Hilbert transform. The simultaneous use of voltage and current signals reduces the transient effects of the control system on the proposed protection method. In order to measure voltage and current signals, only one intelligent electronic device unit is used in this paper. The proposed new method has been tested on a single-bus DC microgrid with the presence of electric vehicles and energy storage systems in MATLAB 2019b software. The results show that this method can detect all types of faults in DC microgrids, electric vehicles, and photovoltaics. Also, this method is immune to the uncertainties of the generation of distributed generation resources and the existence of noise distortions in the measured signals.

Operation of Distillation Columns Using Model Predictive Control Based on Dynamic Mode Decomposition Method

Operation of Distillation Columns Using Model Predictive Control Based on Dynamic Mode Decomposition Method

Unsteady Flow Structure of Corner Separation in a Highly Loaded Compressor Cascade

Abstract Corner separation is an inherently unsteady flow feature in an axial compressor cascade, and it significantly affects the aerodynamic performance of compressors. The flow field of a highly loaded compressor cascade at the Mach number of 0.59 under the moderate separation condition is simulated based on delayed detached eddy simulation. Comparisons of averaged flow field and transient flow field show that the three-dimensional corner separation flow is highly unsteady and composed of fine-scale vortex structures. The classical recognition of corner separation structures is a consequence of time-averaging. To better understand the contribution of unsteady structures to the averaged flow structures, the evolutions of flow fields in time series and the power spectrums are analyzed. A dominant periodic flow fluctuation is caused by the development of separating vortices with a characteristic frequency around 3500 Hz or at a Strouhal number of 0.75. Further, energy scales and spatiotemporal features of these dominant unsteady behaviors are analyzed using proper orthogonal decomposition and dynamic mode decomposition methods. Results show that the low-frequency behaviors mainly caused by the passage vortex at lower-span regions govern large-scale changes of separation flow in size and intensity and act with certain intermittency. The vortex developing mode around 3500 Hz prevails at higher regions affected by the concentrated shedding vortex. As the separating vortices dissipate approaching the midspan, the effect of the vortex developing mode on axial velocity fluctuation is reduced, although it dominates the pressure fluctuation with good stability in the whole passage.

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: I. Extraction of spatiotemporally coherent patterns

The advent of data-driven/machine-learning based methods and the increase in data available from high-fidelity simulations and experiments has opened new pathways toward realizing reduced-order models for plasma systems that can aid in explaining the complex, multi-dimensional phenomena and enable forecasting and prediction of the systems’ behavior. In this two-part article, we evaluate the utility and the generalizability of the dynamic mode decomposition (DMD) algorithm for data-driven analysis and reduced-order modeling of plasma dynamics in cross-field E × B configurations. The DMD algorithm is an interpretable data-driven method that finds a best-fit linear model describing the time evolution of spatiotemporally coherent structures (patterns) in data. We have applied the DMD to extensive high-fidelity datasets generated using a particle-in-cell (PIC) code based on the cost-efficient reduced-order PIC scheme. In this part, we first provide an overview of the concept of DMD and its underpinning proper orthogonal and singular value decomposition methods. Two of the main DMD variants are next introduced. We then present and discuss the results of the DMD application in terms of the identification and extraction of the dominant spatiotemporal modes from high-fidelity data over a range of simulation conditions. We demonstrate that the DMD variant based on variable projection optimization (OPT-DMD) outperforms the basic DMD method in identification of the modes underlying the data, leading to notably more reliable reconstruction of the ground-truth. Furthermore, we show in multiple test cases that the discrete frequency spectrum of OPT-DMD-extracted modes is consistent with the temporal spectrum from the fast Fourier transform of the data. This observation implies that the OPT-DMD augments the conventional spectral analyses by being able to uniquely reveal the spatial structure of the dominant modes in the frequency spectra, thus, yielding more accessible, comprehensive information on the spatiotemporal characteristics of the plasma phenomena.

Aerodynamic shape optimization of the vortex-shock integrated waverider over a wide speed range

The vortex-shock integrated waverider over a wide speed range could significantly improve the aerodynamic performance of traditional waveriders by introducing the vortex effect at subsonic speeds. Therefore, it is promising to be widely used in the design of wide-speed-range aerospace vehicles. However, the design of the vortex-shock integrated waverider ignores the three-dimensional effect, the subsonic effect, and the viscous effect in the establishment of the reference flow field, which fails to obtain the expected ideal performance. Therefore, it is necessary to further improve the wide-speed-range performance of the vortex-shock integrated waverider by employing the aerodynamic shape optimization method. In this study, the wide-speed-range multipoint optimization of the vortex-shock integrated waverider is carried out using a gradient-based optimizer combined with adjoint gradient evaluations. The results show that the optimum configuration increases the subsonic lift and lift-to-drag ratio by 6.7 % and 7.1 %, while increasing the hypersonic lift-to-drag ratio by 1.4 %. The improvement of the aerodynamic performance at subsonic speeds is attributed to the enhancement of the leeward vortex effect. Also, the leeward surface near the leading edge is optimized to an inner concave region to further enhance the vortex lift, while guaranteeing against the volume decline. Furthermore, the Detached Eddy Simulation (DES) method and the Dynamic Mode Decomposition (DMD) method are used to analyze the vortex dynamic characteristics at subsonic speeds. By analyzing the first three modes, it is observed that the aerodynamic performance of the optimum configuration is improved mainly by the frequency reduction and the increase of the pressure difference between the windward and the leeward surface, which enhance the stability and strength of the vortex.

Dynamic mode decomposition for the tip unsteady flow analysis in a counter-rotating axial compressor

Counter-rotating axial compressor (CRAC) is a promising potential technology to improve the thrust-to-weight ratio of aero-engines, but its special aerodynamic layout usually causes more pronounced flow unsteadiness. Understanding the unsteady flow features and mechanism in the CRAC contributes to the aerodynamic optimization design and flow control strategy organization. A data-driven dynamic mode decomposition method is introduced to investigate the tip flow unsteadiness in a CRAC, and the unsteady features of the tip flow at the design point (DP) and near-stall point (NSP) conditions are revealed. The results show that the 1.0 times blade passage frequency (BPF) and its multi-order harmonic frequency are the dominant frequencies for both rotors at the DP condition. At the NSP condition, the 1.0 BPF is no longer the dominant frequency causing the tip flow unsteadiness, and the low frequency fluctuation of the tip leakage flow becomes the dominant frequency to induce the flow unsteadiness. In the front rotor R1, the unsteady dominant frequency is 1.0 BPF, whereas in the rear rotor R2, the frequency (0.801 BPF and 0.803 BPF) of the tip leakage flow is the dominant frequency. By reconstructing the flow field under the NSP condition, the spatiotemporal evolution of the tip flow during the unsteady stable manifests that the interference effect between the rotors is an important source of the tip flow unsteadiness. The increase in flow unsteadiness leads to an increase in the reconstruction error, indicating that more modes are required to obtain a more accurate reconstruction flow field.

Dynamic mode characteristics of flow instabilities in a centrifugal compressor impeller

Centrifugal compressors are key parts of medium and small aircraft engines, the flow instabilities of centrifugal compressors have become the bottleneck of the developments of engines. It is vital to investigate the dynamic mode characteristics of flow instabilities in centrifugal compressors for solving the issues. In this study, unsteady full annular simulations of the centrifugal compressor flow are firstly implemented. It is found that the flow instability of the compressor primarily arises in the impeller. To capture the dominant transient modes in process of flow instabilities and accurately describe their temporal evolutions, a modified dynamic mode decomposition method (DMD-TC) is adopted to analyze the dynamic mode characteristics, which was proposed in our previous study. The results show that perturbations in the impeller can be mainly classified into three categories: impeller-diffuser interactions, self-excited perturbations, and vortex-induced perturbations. In detail, the modes induced by the impeller-diffuser interactions and self-excited perturbations are intrinsic modes, and they reflect the inherent flow unsteadiness in the impeller. On the one hand, the vortex-induced perturbations couple with the self-excited ones, which affect the spatial structures of modes induced by self-excited perturbations. The coupling effects enhance with the reduced mass flow rate, and the “resonance” effect might be excited. As a result, the mode of 4 RF (rotor frequency) grows during rotating stall process (RSP), which is a typical characteristic of rotating stall in the impeller. On the other hand, the vortex-induced perturbations emerge as different characteristic modes, due to the variant vortex structures with the mass flow rate. During the RSP, the growth of low-frequency characteristic modes is another typical feature of rotating stall in the impeller.

Investigation on transition characteristics of laminar separation bubble on a hydrofoil

The phenomenon of water–jet pump stall can be ascribed to the development of blade boundary layer separation with the transition process playing a significant role in this separation. The hydrofoil is usually used as a simplified model of the water–jet pump impeller blade, and its flow field characteristics have important reference values for analyzing the impeller flow. Based on the transition model and the dynamic mode decomposition method, this article presents the results of a study that was carried out on the stall characteristics of the NACA0009 blunt trailing edge hydrofoil. The transition characteristics of hydrofoil surfaces at different angles of attack (AoA)and Chord-based Reynolds numbers (ReL) are obtained. The hydrofoil boundary layer transition is dominated by natural transition as the AoA is less than 4°, while the transition is dominated by leading-edge separation-induced transition as the AoA is greater than 4°. The investigation yields the dynamic properties of the LSB (Laminar Separation Bubble) as the AoA is varied. The phenomenon known as the deep stall is distinguished by the movement of the stall vortex toward the upstream direction near the trailing-edge region, where it merges with the LSB in the leading-edge region. This phenomenon leads to oscillations in the lift and drag coefficients. The relationship between the LSB and the trailing-edge stall vortex is established using DMD (Dynamic Mode Decomposition) methods. As the phenomenon of the deep stall occurs, it can be observed that the modal energy of the leading-edge LSB is comparatively higher than the modal energy of the trailing-edge stall vortex, inducing the dominant role of the LSB and the movement toward the trailing-edge region and, consequently, the phenomenon of trailing-edge vortex shedding in the hydrofoil. The findings of this study could be guidance for the design of fluid machinery blades.

The nonlinearity of scattering waves due to interaction between focusing waves and floating production storage and offloading

The study of the full-scale wave–structure interaction is essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states. This paper deals with full-scale numerical studies of the interactions between focusing waves and a fixed floating production storage and offloading (FPSO) in an efficient potential-viscous coupled method. The potential-viscous method combines in-house computational fluid dynamics code developed at Shanghai Jiao Tong University (SJTU) for naval architecture and ocean engineering (naoe) based on an open field operation and manipulation (FOAM), i.e., naoe-FOAM-SJTU solver, with high-order spectral method. The approach is verified on a model-scaled case and shows reasonably good agreement with experimental data. A phase-separation method and a dynamic mode decomposition method are utilized to extract linear and higher-order harmonic components from the scattering waves. The scattering waves around the FPSO are found to affect the higher-order harmonic components. Two kinds of scale ratios are considered to magnify the focusing wave and FPSO by 10 and 100 times to discuss the scale effect, both non-breaking and green water conditions are included to investigate the flow phenomenon. The harmonic components of scattering waves are not proportional to the scale ratio, and the scale effects influence more on higher-order harmonic components. The third- and fourth-order harmonic components of scattering waves around the FPSO in large-scale cases are obvious.

Data‐driven stochastic model predictive control for regulating wind farm power generation with controlled battery storage

AbstractThe uncertainty and fluctuation of the volatile wind power cause more reserve and frequency regulation capacity, so it incurs additional operational cost for the power grid. Therefore, a wind farm (WF) coordinated controller is essential to reduce the power fluctuation and trace the scheduled power generation with minimal wind curtailment and battery degradation cost. This paper proposes a data‐driven stochastic model predictive control (SMPC) method for WFs to realize these objectives. Firstly, to address the non‐linear dynamic model of wind turbines, the dynamic mode decomposition method accompanying Koopman operator is used to learn a lifted linear dynamic model from measurements. Secondary, this paper proposes the relationship between the curtailed wind power of wind turbines and their pitch angle, wind speed, and rotation speed, as well as the corresponding estimation formula. In addition, the prediction errors of wind speeds are characterized using the Gaussian mixture model (GMM), which may significantly affect the controller's performance. Finally, a tractable data‐driven SMPC model is developed and is verified on a DIgSILENT/PowerFactory based simulation platform. Compared with conventional model predictive control algorithms, it can significantly reduce the overall operational cost of WFs.

Dynamic mode decomposition with memory.

This study proposed a numerical method of dynamic mode decomposition with memory (DMDm) to analyze multidimensional time-series data with memory effects. The memory effect is a widely observed phenomenon in physics and engineering and is considered to be the result of interactions between the system and environment. Dynamic mode decomposition (DMD) is a linear operation-based, data-driven method for multidimensional time-series data proposed in 2008. Although DMD is a successful method for time-series data analysis, it is based on ordinary differential equationsand thus cannot incorporate memory effects. In this study, we formulated the abstract algorithmic structure of DMDm and demonstrate its utility in overcoming the memoryless restriction imposed by existing DMD methods on the time-evolution model. In the numerical demonstration, we utilized the Caputo fractional differential to implement an example of DMDm such that the time-series data could be analyzed with power-law memory effects. Thus, we developed a fractional DMD, which is a DMD-based method with arbitrary (real value) order differential operations. The proposed method was applied to synthetic data from a set of fractional oscillators and model parameters were estimated successfully. The proposed method is expected to be useful for scientific applications and aid in model estimation, control, and failure detection of mechanical, thermal, and fluid systems in factory machines, such as modern semiconductor manufacturing equipment.

Geometry-informed dynamic mode decomposition in Kresling origami dynamics

Origami structures often serve as the building block of mechanical systems due to their rich static and dynamic behaviors. Experimental observation and theoretical modeling of origami dynamics have been reported extensively, whereas the data-driven modeling of origami dynamics is still challenging due to the intrinsic nonlinearity of the system. In this study, we show how the dynamic mode decomposition (DMD) method can be enhanced by integrating geometry information of the origami structure to model Kresling origami dynamics in an efficient and accurate manner. In particular, an improved version of DMD with control, that we term geometry-informed dynamic mode decomposition (giDMD), is developed and evaluated on the origami chain and dual Kresling origami structure to reveal the efficacy and interpretability. We show that giDMD can accurately predict the dynamics of an origami chain across frequencies, where the topological boundary state can be identified by the characteristics of giDMD. Moreover, the periodic intrawell motion can be accurately predicted in the dual origami structure. The type of dynamics in the dual origami structure can also be identified. The model learned by the giDMD also reveals the influential geometrical parameters in the origami dynamics, indicating the interpretability of this method. The accurate prediction of chaotic dynamics remains a challenge for the method. Nevertheless, we expect that the proposed giDMD approach will be helpful towards the prediction and identification of dynamics in complex origami structures, while paving the way to the application to a wider variety of lightweight and deployable structures.

An improved dynamic mode decomposition for real‐time electromechanical oscillation monitoring in power systems: The impact of ultra‐low frequency modes and its removal strategy

AbstractThe growing complexity of power systems, driven by the increasing use of renewable energy sources, necessitates efficient real‐time monitoring of electromechanical oscillations, which is crucial for enhancing grid security. Dynamic Mode Decomposition (DMD) is a promising data‐driven method for addressing this challenge of monitoring the electromechanical oscillations, made possible by power system digitalization. However, DMD implementation faces unresolved issues, including the impact of ultra‐low‐frequency modes (ULFM) on accuracy due to trends caused by their excitation. While larger data windows can mitigate this, they slow down oscillation estimation. ULFM characteristics remain poorly studied. This study conducts a comprehensive ULFM analysis and proposes a solution by combining DMD with a high‐pass filter to counter ULFM's adverse effects on accuracy. This allows for a reduction in DMD's window size, significantly improving computational efficiency. Simulations on three test systems demonstrate that the enhanced DMD offers faster computation and superior accuracy compared to the traditional DMD method.

Uncertainty analysis of dynamic mode decomposition for xenon dynamic forecasting

In this paper, a systematic uncertainty quantification of dynamic mode decomposition (DMD) for xenon dynamic prediction is brought out based on HPR1000 reactor. The DMD method is a data-driven approach that decomposes complex systems into spatio-temporal structures and can be used to predict the power distribution in the process of xenon oscillation. To further investigate and improve the robustness of DMD with respect to observation noise, different error metrics are established. The dependence of the prediction error on observation noise level and hyper parameters including the window length and the singular value truncation threshold are investigated. Various numerical experiments based on a typical fuel cycle of the HPR1000 reactor demonstrate that DMD with optimal hyper parameters is robust with respect to observation noise, which confirms that DMD is feasible for real engineering applications.

Flow field characteristics analysis of vortex-induced vibration of bridge tower based on dynamic mode decomposition method

As a high-rise structure, the tower of a suspension bridge has low stiffness due to the lack of cable system constraints when it is self-supporting. Wind-induced vibration is one of the key factors in design and construction. In this paper, the wind tunnel test of the bridge tower aeroelastic model is carried out in two different flow fields, and the wind vibration response under a self-supporting state is systematically studied. Meanwhile, numerical simulation of the unsteady flow field around the tower section is carried out, and the dynamic modal decomposition (DMD) method is used to study the modal frequency of the flow field, the surface pressure of the section, flow field reconstruction error, and the stability of the flow field around tower section is discussed. The results show that in the self-supporting state, the displacement of the tower top presents a quadratic curve relationship with the wind speed, and no galloping phenomenon occurs under the test wind speed. However, in the uniform flow, when the wind attack angle is 90°, the bridge tower has an obvious vortex-induced vibration (VIV) phenomenon. After decomposing the flow field by the DMD method, it is found that there is strong aerodynamic interference between the double rectangular column sections, the first seven orders of modal energy play a major role in the flow field, and when the main modal energy accounts for more than 90%, the reconstruction can realize the accurate restoration of the information such as the surface pressure. For the complex flow field structure, it shows that the method can more accurately identify the coherent structure and background part in the unsteady flow field. This paper provides an idea for future research on the characteristics of the flow field around complex sections and helps to further improve the understanding of the VIV mechanism.

Large eddy simulations of pilot-stage equivalence ratio effects on combustion instabilities in a coaxial staged model combustor

In this paper, the effects of pilot-stage equivalence ratio on combustion instabilities in a coaxial staged model combustor are investigated using the Wall-Modeled Large Eddy Simulation. The global equivalence ratio is maintained constant, and the Stratification Ratio of the first main-stage and the second main-stage is set to 1; the dynamic mode decomposition and system identification methods are employed to analyze the flame dynamics, velocity, heat release rate modes, and flame transfer function (FTF) of the model combustor under different pilot-stage equivalence ratios. The results show that when the pilot-stage equivalence ratio is 0.6, the oscillation amplitude of heat release rate (HRR) exceeds 7.5% of the global average HRR, and the velocity oscillation and the global HRR oscillation in the combustor are coupled. As the pilot-stage equivalence ratio increases to 0.8, the oscillation amplitude of HRR decreases to 2.5%, and the oscillation of velocity and global HRR in the combustor are decoupled. Furthermore, the maximum value of FTF decreases from 3.5 to below 1 with the increase in the pilot-stage equivalence ratio.

Regression-based identification and order reduction method for nonlinear dynamic structural models

In this paper, we propose a regression-based nonlinear reduced-order model for nonlinear structural dynamics problems, called the Nonlinear Identification and Dimension-Order Reduction (NLIDOR) algorithm. We evaluate the algorithm using a simple toy model, a chain of coupled oscillators and an actual three-dimensional flat plate. The results show that NLIDOR can accurately identify the natural frequencies and modes of the system and capture the nonlinear dynamical features, while the linear Dynamic Mode Decomposition (DMD) method can only capture linear features and is influenced by nonlinear terms. Compared with the full-order model (FOM), NLIDOR can effectively reduce computational cost, while compared with DMD, NLIDOR significantly improves computational accuracy. The results demonstrate the effectiveness and potential of NLIDOR for solving nonlinear dynamic problems in various applications.

Large eddy simulation investigation of S-shaped intake distortion and swirl characteristics

Curvature change of an S-duct wall naturally causes total pressure and swirl distortions in a compressor inlet. In this study, the large eddy simulation (LES) method is used to investigate the internal flow of a continuous variable curvature S-duct without a downstream compressor. A comparison between the numerical results and the experimental data verifies the effectiveness of the LES method in analyzing the internal flow mechanism of an S-duct. Based on the SAE standard, the transient distortion descriptors of the research cross-section are quantitatively analyzed, and the distortion characteristics of the total pressure and swirl in the aerodynamic interface plane (AIP), downstream outlet plane, and their spatial–temporal variation processes are revealed. Furthermore, the proper orthogonal decomposition and sparsity-promoting dynamic mode decomposition methods are used to decompose the flow structures of the AIP velocity fields, and the main coherent structures affecting the flow and their corresponding frequency/attenuation characteristics are obtained. The results indicate that the twin two swirl pattern near the wall annulus of the S-duct is dominant at high Reynolds numbers, and turbulent mixing downstream inhibits the development of distortion and swirl. In addition, some stable low-frequency mode structures exist near the Starboard, exhibiting multi-spiking frequency properties. Thus, this study reveals the generation, development, and evolution mechanisms of distortion and swirl at the upstream of a compressor inlet, and the analysis results of distortion and swirl characteristics can provide important input conditions for subsequent compressor distortion research and influence analysis of mass injection pre-compressor cooling technology.

Decoupling and reconstruction analysis in a transonic axial compressor using the dynamic mode decomposition method

Unsteady flow is highly related to flow loss and aerodynamic performance degradation in the axial compressor. In this paper, the dynamic mode decomposition method was used to investigate in-depth flow structures and related evolutionary mechanisms of the internal flow field. Four main flow structures were observed through flow field decoupling: the oscillation of the tip leakage vortex (TLV) region, the circumferential migration of the leakage-induced vortex (LIV), the axial migration of the rear part of the leakage vortex (RLV), and the oscillation of the leading edge vortex (LEV). All of those four structures indicated the presence of internal high disturbance regions. The reconstruction of the dominant mode flow field revealed that the unsteady evolutionary mechanism of the flow field mainly consisted of two components: the axial evolution of the RLV and the circumferential evolution of the LIV. It was further revealed that the axial evolution of the RLV was the primary reason for the formation of low-energy fluid mass within the passage; under the influence of the “leading edge overflow,” the LIV eventually fused with the LEV. The blocking effect of the LEV led to the formation of a high oscillation region at the leading edge of the adjacent blade pressure surface, resulting in a synchronous moment between the emergence of the LIV and the LEV. The analysis of the two unsteady evolution mechanism components further supported TLV breakdown as the main cause of flow unsteadiness. This study laid the foundation for further accurate flow unsteadiness control.

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

This work introduces an ‘equation-free’ non-intrusive model order reduction (NIMOR) method for surrogate modeling of time-domain electromagnetic wave propagation. The nested proper orthogonal decomposition (POD) method, as a prior dimensionality reduction technique, is employed to extract the time- and parameter-independent reduced basis (RB) functions from a collection of high-fidelity (HF) solutions (or snapshots) on a properly chosen training parameter set. A dynamic mode decomposition (DMD) method, resulting in a further dimension reduction of the NIMOR method, is then used to predict the reduced-order coefficient vectors for future time instants on the previous training parameter set. The radial basis function (RBF) is employed for approximating the reduced-order coefficient vectors at a given untrained parameter in the future time instants, leading to the applicability of DMD method to parameterized problems. A main advantage of the proposed method is the use of a multi-step procedure consisting of the POD, DMD and RBF techniques to accurately and quickly recover field solutions from a few large-scale simulations. Numerical experiments for the scattering of a plane wave by a dielectric disk, by a multi-layer disk, and by a 3-D dielectric sphere nicely illustrate the performance of the NIMOR method.