Orthogonal Decomposition Technique Research Articles

The Temporal and Spatial Evolution of Magnetohydrodynamic Wave Modes in Sunspots

Through their lifetime, sunspots undergo a change in their area and shape and, as they decay, they fragment into smaller structures. Here, for the first time we analyze the spatial structure of the magnetohydrodynamic (MHD) slow-body and fast-surface modes in the observed umbrae as their cross-sectional shape changes. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques were used to analyze 3 and 6 hr Solar Dynamics Observatory/Helioseismic and Magnetic Imager time series of Doppler velocities at the photospheric level of approximately circular and elliptically shaped sunspots. Each time series was divided into equal time intervals to evidence the change in the shape of the sunspots. To identify the physical wave modes, the POD/DMD modes were cross-correlated with a slow-body mode model using the exact shape of the umbra, whereas the shape obtained by applying a threshold level of the mean intensity for every time interval. Our results show that the spatial structure of MHD modes are affected, even by apparently small changes in the umbral shape, especially in the case of the higher-order modes. For the data sets used in our study, the optimal time intervals to consider the influence of the change in the shape on the observed MHD modes is 37–60 minutes. The choice of these intervals is crucial to properly quantify the energy contribution of each wave mode to the power spectrum.

Bayesian Gappy Proper Orthogonal Decomposition for Aerodynamic Data Fusion

During the development of an aircraft, a multitude of aerodynamic data are required for different flight conditions throughout the flight envelope. Nowadays, a large portion of these data are routinely acquired by computational fluid dynamics simulations. However, due to modeling and convergence issues especially for extreme flight conditions, numerical data cannot be reliably generated for the entire flight envelope yet. Hence, numerical data are complemented by data from wind tunnel experiments and flight testing. However, the data from these different sources will always show some discrepancies to deal with. Data fusion methods aim at combining the individual strengths and weaknesses of data from different sources in order to provide a consistent data set for the entire parameter domain. In this work we propose an extension to the well-established Gappy proper orthogonal decomposition technique by reformulating the least-squares problem as a regression task. A Bayesian perspective is imposed to account for uncertainties during the data fusion process. This involves a kernelized regression formulation that also addresses the problem of linearity imposed by the dimensionality reduction method and therefore adds more flexibility to the approach. The performance and robustness of the approach is demonstrated investigating an industrially relevant, large-scale aircraft test case fusing high-quality experimental and numerical data. Compared to the established Gappy POD approach, the new method shows a significantly improved agreement with the observed wind tunnel data for the investigated test case. In addition, the new approach enables to provide credible bounds for the fused result, which serve as an indicator for the associated uncertainty.

On extraction, ranking and selection of data-driven and physics-informed features for bearing fault diagnostics

Many traditional bearing fault detection techniques rely on pattern recognition using black box machine learning models, which lack generalizability to out of sample cases and are generally only effective for an a priori defined operating condition set. Therefore, the developed models are required to be retrained each time the operating condition changes because of the dependence of the dynamic response on them. The lack of effective techniques that can be applied and adapted to different operation domains of the system is a well-established need, which motivates the development of hybrid approaches which integrate both physics and data based techniques. This paper discusses the development of a hybrid physics-informed method that integrates information from physics and data for fault diagnostics of a rotor-bearing system. A physics-based model is used to simulate the dynamics of the system in a defect free condition and a machine fault simulator is used to generate experimental data. Physics-informed features are extracted by residual-based and cross-sample entropy techniques, while the data-based features are obtained using Proper and Smooth Orthogonal Decomposition techniques. Subsequently, these two collections of extracted features are fused into a hybrid feature set. Then, the features are ranked using the Shapley values ranking technique. Comparing the accuracy of classifications upon using the features of physics-informed, data-based and hybrid sets shows improved capability of the proposed framework to generalize diagnostics for various operating conditions.

Reservoir computing reduced-order model based on particle image velocimetry data of post-stall flow

The present study proposes a reservoir computing reduced-order model (RCROM) of the post-stall flow around the National Advisory Committee for Aeronautics 0015 airfoil based on the time series velocity field, and the estimation accuracy of the RCROM is evaluated compared to that of a linear reduced-order model (LROM). The data were experimentally obtained by particle image velocimetry at a chord Reynolds number of 6.4 × 104 and an angle of attack of 18°. The low-dimensional description of the velocity field can be obtained by decomposing the velocity field with a proper orthogonal decomposition (POD) technique and by employing the leading POD mode coefficients as temporal variables of the data instead of the velocity field. Reservoir computing (RC) is adopted as a nonlinear function that predicts several steps ahead of the leading POD mode coefficients. The hyperparameters of RC are tuned by Bayesian optimization, and the optimized RCROM outperforms the LROM in terms of estimation accuracy. The estimation accuracy of the RCROM can be investigated under different numbers of the predicted dominant POD modes and prediction step conditions. As a result, the RCROM shows higher estimation accuracy than the LROM.

A data-driven reduced-order model based on long short-term memory neural network for vortex-induced vibrations of a circular cylinder

A data-driven reduced-order model (ROM) based on long short-term memory neural network (LSTM-NN) for the prediction of the flow past a circular cylinder undergoing two-degree-of-freedom vortex-induced vibration in the upper transition Reynolds number regime with different reduced velocities is developed. The proper orthogonal decomposition (POD) technique is utilized to project the high-dimensional spatiotemporal flow data generated by solving the two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) equations to a low-dimensional subspace. The LSTM-NN is applied to predict the evolution of the POD temporal coefficients and streamwise and cross-flow velocities and displacements of the cylinder based on the low-dimensional representation of the flow data. This model is referred to as POD-LSTM-NN. In addition, the force partitioning method (FPM) is implemented to capture the hydrodynamic forces acting on the cylinder using the surrounding flow field predicted by the POD-LSTM-NN ROM and the predicted time histories of the lift and drag forces are compared with the numerical simulations.

Experimental investigation on effects of herringbone riblets on shock wave/boundary layer interactions of a compression ramp at Mach 3

In this paper, the effects of herringbone riblets (HRs) on a turbulent boundary layer and the shock wave/boundary layer interactions (SWBLIs) are experimentally investigated at the Mach number of 3. An array of three varied lengths of HRs strips are applied upstream of the separation zone of SWBLIs on a compression ramp model. High-speed schlieren, oil-flow visualization, and the planar laser scattering technique are used to examine the shock pattern and boundary layer developing over the surface of the model. The snapshot proper orthogonal decomposition technique and the Fast Fourier Transform method are applied to study the impact of HRs on the interaction between the shock wave and the boundary layer. The experiments provide convincing evidence that HRs make the separation line wavy and shrink the separation zone by about −39.54% for the longest HRs in the present experiments. Furthermore, it is also revealed that these microscale HRs induce large-scale streamwise vortical structures within the boundary layer as found in incompressible flows. It is believed that these vortices promote momentum transfer within the boundary layer hence providing the dominant mechanism for suppressing flow separation.

A proper orthogonal decomposition analysis upon aerodynamic structures under clean and rough conditions

A transitional flow regime is known to induce complex flow structures upon aerodynamic geometries such as airfoils, and the dynamics of laminar separation bubbles (LSBs) pose a relevant research field. In addition to being affected by the Reynolds value itself, LSBs are shown to be equally sensitive to the surface roughness of the airfoils. The study analyses wind tunnel-derived surface-pressure distribution datasets obtained for a particular airfoil of the standard family developed by the National Advisory Committee for Aeronautics (NACA), namely, the NACA0021, subjected to the range 0.8×104<Re<1.6×104 at different angles of attack under two flow configurations that correspond to a clean and roughened surface. The analysis is undertaken via the proper orthogonal decomposition (POD) technique. The results show that the decomposition of the temporal series of surface-pressure data and the processing of the most energetic POD modes recovers the position of the LSBs, properly capturing the closure point of the separation bubbles and, hence, the turbulence transition location. Some of the most energetic POD modes observed are closely related, in terms of shape, to the POD modes present at the reattachment point on a 5:1 rectangular cylinder. This could indicate there is a recognizable pattern in coherent structures of pressure fluctuations when it comes to a reattached flow. Therefore, a principal component analysis such as the POD presented in this study can be used to determine the reattachment position of the flow or the transition point in the presence of a LSB.

Flame Dynamics in an Optically Accessible Solid Fuel Ramjet Combustor

Flow–flame interactions were investigated in an optically accessible solid fuel ramjet combustor. Experiments were performed with a single hydroxyl-terminated polybutadiene fuel slab located downstream of a backward-facing step in a rectangular chamber. To emulate flight-relevant combustor conditions, unvitiated heated air was directed through the combustion chamber with an inlet temperature of , chamber pressures of 450–690 kPa, and port Reynolds number of . To characterize the heat-release distribution and velocity field, 20 kHz -chemiluminescence and 10 kHz particle imaging velocimetry measurements were used. Comparison between the mean chemiluminescence images acquired at three flow conditions indicates reduction in flame height above the grain with increasing air mass flow rate. Dominant heat-release coherent structures in the statistically stationary flow are identified using the spectral proper orthogonal decomposition technique implemented on time series of instantaneous images. The spatial mode shapes of the chemiluminescence and velocity field measurements indicated that the flow–flame interactions were dominated by vortex shedding generated at the backward-facing step in the combustor, at Strouhal numbers of 0.06–0.10. The frequency corresponding to these modes is shown to be invariant of air mass flux, indicating that system dynamics are primarily dependent on the backward-facing step geometry and the bulk velocity in the combustor.

Multi-description coding-decoding-based control for interval type 2 T-S fuzzy systems with mixed time-delays

This paper discusses a control problem for a class of interval type-2 T-S fuzzy systems with mixed time delays. A multi-description coding and decoding mechanism is utilized to improve the reliability of data transmission. The measurement output is separately coded into two descriptions with rank and file information, and then the coded two descriptions are transmitted to the decoder via two independent communication channels which are random occurring packet dropouts. Sufficient conditions are established to assess the exponentially input-to-state stable in mean-square sense, and an explicit relationship is proposed for the effect of packet dropouts on decoding accuracy. Furthermore, the controller gains are calculated by applying the orthogonal decomposition technique. Finally, the applicability and effectiveness of the control method is illustrated by numerical simulation results.

Low-frequency unsteadiness of recompression shock structures in the diffuser of supersonic ejectors

Supersonic ejectors are passive gasdynamic devices that compress a low-pressure fluid by utilizing the kinetic energy of a high-pressure fluid in a variable area duct. The ejector consists of a primary supersonic nozzle in a mixing duct where the secondary flow is entrained and mixed. The mixed flow can undergo a series of recompression shocks resulting in a subsonic flow in the diverging portion to aid pressure recovery. Recompression shocks usually lead to unsteady shock boundary layer interactions. The performance of the ejector is influenced by shear layers, shock and expansion waves, and their mutual interactions. While existing literature has extensively dealt with mixing of the primary and secondary flows, the unsteadiness in flow resulting from recompression shocks has been seldom investigated. Fluctuations in pressure due to the unsteadiness of the shock often lead structural fatigue issues. This paper reports a detailed investigation on low-frequency unsteadiness of recompression shock using high-speed schlieren images and dynamic pressure measurements. Modal analyses using proper orthogonal decomposition and dynamic mode decomposition techniques are used to determine the dominant spatial modes and associated frequencies. Multimodal frequencies ranging between 80 and 300 Hz are observed. These findings are further corroborated by Fourier and wavelet transformations of the experimentally measured wall static pressure signals. Subsequently, scaling parameter is established for the dominant frequencies based on flow velocities upstream of the shock and the distance between two consecutive shocks. This results in a unique scaling frequency of 4.58% ± 18%, for the recompression shock independent of operating conditions.

New Investigation of a Tropical Cyclone: Observational and Turbulence Analysis for the Faraji Hurricane

In the general framework of the atmosphere, the in-depth study of extreme events of complex nature such as tropical cyclones remains an open problem. Nowadays, there are different useful studies aiming to enlarge the current knowledge of these events. Under this perspective, the search for mechanisms and geographical areas of formation and dynamics of tropical cyclones at different latitudes needs better constraints on their preliminary results. This work focuses on a diagnostic analysis of a tropical cyclone, with the aim of identifying key points that characterize its evolution, from a dynamic and observational point of view. The study is applied to Hurricane Faraji, the most powerful tropical cyclone of the 2021 Indian Ocean season, classified as fifth-category on the Saffir–Simpson intensity scale. The study develops in three main sections, all related to each other. The starting point is a large set of satellite products from both polar and geostationary platforms. From the data acquired by the polar instruments, an accurate study of the evolution of the hurricane is carried out, focused on the extraction of physical information related to the system (temperature and altitude of the associated cloudy system, temperature gradient, pressure in the different regions) at moderate resolutions. From the data acquired by the geostationary instruments, it is possible to obtain very high temporal resolution pictures of the temperature field of the cyclone, from which a study of the turbulent dynamics is carried out. In particular, to investigate the maximum energy content in the different regions of the cyclone, the Proper Orthogonal Decomposition (POD) technique is used to extract the associated spectra of both the spatial and temporal components, studied separately on three different ranges of scales.

Effects of swirl numbers on the unsteady characteristics of pilot flame in a triple-swirler staged combustor

This paper studies the effects of the inner and outer pilot swirlers on the flame structures and thermo-acoustic instabilities in the triple-swirler staged combustors under various inner and outer pilot swirl numbers. We obtain energetic modes in the combustor's velocity and the OH radical mass fraction fields, utilizing the proper orthogonal decomposition (POD) technique. With the increment of the pilot inner swirl number, the vortex shedding mode and flame radial propagation mode for the flame fluctuation is enhanced, and the axial propagation mode is weakened. Nevertheless, the increased pilot outer swirl number primarily impacts the vortex shedding mode's enhancement while positively influencing the other flame fluctuation modes. Specifically, the vortex shedding in the inner shear layer is the leading factor affecting the thermo-acoustic instability in the combustion chamber. Nevertheless, coupling this mode and the pressure oscillation weakens the area downstream of the central recirculation zone. Thus, due to the comprehensive impacts of the vortex shedding mode, spatial distribution, and the premixed flame area proportion, the impact of this mode's energy ratio on the thermo-acoustic instability increases non-linearly with the increased pilot swirl number.

A reduced-order immersed interface method based on POD basis for parabolic interface problem

In this paper, we propose a reduced-order immersed interface method (RO-IIM) to cope with the parabolic interface problem. Second-order central difference scheme in spatial direction is constructed. In time direction, we proposed a reduced-order method with fewer degree of freedoms. Our work contains the initial study of the combination of the immersed interface method and proper orthogonal decomposition (POD) technique. Numerical examples show that the proposed RO-IIM is feasible and efficiency for solving the parabolic interface problems.

Reduced order modeling for compressible cake filtration processes using proper orthogonal decomposition

This work aims to increase the computational efficiency of a complex mathematical cake-filtration model with strong nonlinearities representing cake compression. To this end, we employ a hybrid data driven approach using the technique of proper orthogonal decomposition. Hereby, a few sample simulations from the initial system of partial differential equations are used as the foundation to find optimal, globally defined basis functions, which in return offer the possibility to build a reduced-order model. In summary, the dimension of the reduced order model is diminished by ≈98% compared to the full order model, which translates to a net decrease of ≈90 % computational time needed to solve a benchmark optimization problem. This significant numerical speed-up offers the possibility to use the reduced order model in further advanced process control and optimization methods.

Constructing simplified models for dynamic analysis of monopile-supported offshore wind turbines

Accurately modeling the complicated dynamic mechanisms of offshore wind turbines (OWTs) requires high numerical fidelity. However, since these models are computationally expensive for both forward and inverse problems, simplified OWT models are needed. The present study develops two approaches to constructing simplified numerical models based on full-order finite element models, which aim to accurately and efficiently simulate dynamic behaviours of monopile-supported OWTs. The first approach decomposes the structure into substructures and establishes a reduced-order model based on the similarity principle of modal parameters and time-domain responses, in accordance with full-order models. The second approach uses proper orthogonal decomposition and modal truncation techniques to construct a state-space model, which produces consistent time-domain responses with full-order models. For both approaches, model updating is used to improve the accuracy of the simplified models. The effectiveness of the approaches is demonstrated through the monopile-supported, 10 MW DTU reference wind turbine. The results show that the computational time required for both simplified models is less than 10% that of the full-order model, without the compromise of accuracy, i.e., less than 5% difference in modal frequency and an excellent agreement in time-domain responses. The proposed approach provides an efficient and accurate dynamic analysis solution for offshore structures.

Effects of incoming free-stream turbulence on the flow dynamics of a square finite wall-mounted cylinder

This study attempts to describe associated fluid dynamics of a square finite wall-mounted cylinder (FWMC) immersed within free-stream turbulent flow characterized by different turbulence intensities and integral length scales. An improved delayed detached eddy simulation method is adopted to numerically reproduce the fully developed turbulent flow fields. The results reveal that both the turbulence intensities and integral length scales have a significant effect on the separated shear layers, base pressure, and associated aerodynamic forces of the cylinder. Constrained streamlines along with critical point techniques are employed to further illustrate the influence of parameters of interest on a time-averaged flow pattern, including horseshoe vortex, surface flow, and wake topology. Distribution of second-order statistics within the wake region shows a shorter longitudinal length of the reversed flow region and enhanced vortex strength when background turbulence intensity increases. The time-dependent interaction between background turbulence and separated flow around the square FWMC is illustrated based on the phase difference between pressure of opposing side faces and the evolution of the reverse-flow region. In the end, the spectral proper orthogonal decomposition technique is employed to further investigate the effects of incoming flow turbulence on characteristics of the free-end shear flow and Von Kármán vortex shedding in the wake.

A Dynamic Design Methodology for Large-Scale Complex Nonlinear Systems Based on Orthogonal Decomposition Technique

HSRS is taken as a typical research case of large-scale complex nonlinear systems, and the re-innovation of associated imported technologies needs to be combined with the particularities of Chinese HSR practices, seeking a more suitable dynamic design methodology to conduct the self-adaptive improved design. Different from the troublesomeness of the primary hunting phenomenon, the self-adaptive improved design can decrease considerably the impact of car body instability on ride comfort merely by applying the semiactive damping technique between intervehicles, to promote scientifically the limit and construction speeds under the rational conditions of wheel-rail matching, i.e., λeN ≥ λemin, λemin = (0.03–0.05). The researching viewpoint of hunting kinematics makes the investigations on the geometric nonlinearity of the wheel-rail contacts contrary to the hypothesis of small creepage and no spin. Since the technical prototype of German ICE3 serial bogies has the design default of the primary hunting phenomenon, the improved design of the wheel-rail relationship has simply abandoned the high-quality technical resources of wheel-rail matching conditions at low conicity. On the contrary, the dynamic simulation analyses of MC01-TC02-MC03 three-vehicles trainset show that the semiactive damping technique between intervehicles takes advantage of Izz >> Ixx to improve the impacts of car body instability on ride comfort, and the self-adaptive improved design has consequently the ability to achieve the technical goal of uniform wear at low conicity. On the premise of meeting the requirements of crossing over different speed grade dedicated lines and realizing the running operations on three-speed levels of 160/250/350 km/h, the self-adaptive higher-/high-speed bogies can conditionally satisfy the economic reprofiling requirements of wheelsets through the optimal routing planning.

Oscillatory characteristics of cavities in supersonic flow

We examine the flow structures, acoustic emissions, and oscillation types for supersonic flow past a baseline cavity and cavity with a bump. To study these, time-resolved shadowgraph images and unsteady pressure measurements are used. According to the results, the baseline cavity oscillates at various dominant frequencies. By adding a bump inside the cavity, many of its dominant oscillations are inactivated which are also corroborated by cross-correlation. Using time-resolved images, we can show the differences in wave propagation mechanisms between the two cavities. Through pressure spectra, it is demonstrated that the baseline cavity displays both fluid-dynamic and fluid-resonant types of oscillations, while the cavity with bump undergoes only the fluid-resonant type. The Rossiter prediction for the baseline cavity is very accurate but greatly deviates when applied to the cavity with a bump. As well, the wavelet analysis reveals that only the baseline cavity undergoes mode-switching phenomena. Additionally, the shear layer large-scale structures influencing the cavity oscillations are identified by using proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD) techniques. Furthermore, an analogy is established between POD and SPOD mode shapes along with the shadowgraph images for dominant modes of cavity oscillation. Finally, the results demonstrate that these modal decomposition techniques complement each other.

Jet flapping and its effect on flame oscillations in the SPP1980 SpraySyn burner

The present research work aims in investigating the large-scale jet flapping instability during the primary breakup process and its effects on the liquid shedding and the resulting flame. For this purpose, a modified coaxial burner is operated over wide range of flow conditions with different liquids in the central passage. Time-resolved images of the liquid jet breakup process and the resulting flame during spray combustion are captured. A Proper orthogonal decomposition (POD) technique is used to investigate the jet flapping and calculate the time-scale corresponding to this mode of instability. Fast-Fourier Transform (FFT) analysis is performed over the average intensity of the interrogation window in an image ensemble to measure the time-scale corresponding to liquid shedding and flame fluctuations. A strong dependence of the frequency corresponding to jet flapping, liquid shedding and flame fluctuations is observed with respect to the dispersion gas velocity. Jet flapping indicates a strong influence on the liquid shedding from the liquid jet, which then influences the resulting flame in the downstream region of the burner.

Identification of flow structures in a closed chamber in the presence of a needle plasma actuator

This study deals with the experimental characterization of the induced flow dynamics by a disk-needle-type plasma actuator driven by a sinusoidal generator and located in a rectangular cross-section burner. Flow characterization was performed using different plasma actuation conditions and standoff distances. Experiments were conducted under non-reactive flow conditions. Electrical characterization was carried out. Airflow behavior was also analyzed using smoke flow visualization. Smoke flow visualization showed the dynamic behavior of the plasma-induced flow. Post-processing of high-quality images was performed by using Proper Orthogonal Decomposition (POD) technique to recognize the dominant flow vortexes and coherent structures. This could support the design of plasma actuation devices in real combustors and be useful for the implementation of numerical models. Moreover, it has been concluded that flow dynamics can be controlled by a variation of the plasma power or the gap distance between two electrodes. Laser Droplet Velocimetry (LDV) was used to investigate the distribution of flow velocities and turbulent kinetic energy (TKE) at different plasma power values of the sinusoidal alternating current generator and standoff distances. From POD and LDV analyses, it has been observed that there is quite a linear relation between the POD energy of the first mode and the maximum TKE. The POD method could be used to identify motions in the flow field carrying the most TKE. TKE peaks are present in the area with the most energetic flow structures, as identified by the POD.