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All sources NASA NTRS DOE OSTI

DOE OSTI2021

Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies

Fluctuating surface pressures on a bluff body exposed to a boundary layer flow generally are characterized as a spatiotemporally varying random field. In this paper, a dynamic mode decomposition (DMD) was applied to extract dominant features embedded in these random pressure fields. Utilizing an unsupervised machine learning algorithm, spatial modes and their temporal variations were grouped into different clusters at scales, e.g., macro, meso, and micro. A proper orthogonal decomposition (POD) of the experimental data was carried out to observe commonalities and distinctive perspectives each decomposition offers. Here, a comprehensive examination of the DMD/POD for their convergence criteria, data sufficiency, and modal components analysis was conducted. The physical interpretation of the spatiotemporal pressure field based on these decomposition schemes was discussed. At different scales, the DMD modes can capture the evolution of aerodynamic features, e.g., convection of vortices (or vortex tubes) and other structures. The distribution of energy among these three broad scales also reflects an energy cascade in pressure fluctuations akin to turbulence.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

Estimation of Modal Parameters Using a Wavelet-Based Approach

Modal stability parameters are extracted directly from aeroservoelastic flight test data by decomposition of accelerometer response signals into time-frequency atoms. Logarithmic sweeps and sinusoidal pulses are used to generate DAST closed loop excitation data. Novel wavelets constructed to extract modal damping and frequency explicitly from the data are introduced. The so-called Haley and Laplace wavelets are used to track time-varying modal damping and frequency in a matching pursuit algorithm. Estimation of the trend to aeroservoelastic instability is demonstrated successfully from analysis of the DAST data.

Lind, Rick↗

DOE OSTI2022

Image Gradient Decomposition for Parallel and Memory-Efficient Ptychographic Reconstruction

Ptychography is a popular microscopic imaging modality for many scientific discoveries and sets the record for highest image resolution. Unfortunately, the high image resolution for ptychographic reconstruction requires significant amount of memory and computations, forcing many applications to compromise their image resolution in exchange for a smaller memory footprint and a shorter reconstruction time. In this paper, we propose a novel image gradient decomposition method that significantly reduces the memory footprint for ptychographic reconstruction by tessellating image gradients and diffraction measurements into tiles. In addition, we propose a parallel image gradient decomposition method that enables asynchronous point-to-point communications and parallel pipelining with minimal overhead on a large number of GPUs. Our experiments on a Titanate material dataset (PbTiO3) with 16632 probe locations show that our Gradient Decomposition algorithm reduces memory footprint by 51 times. In addition, it achieves time-to-solution within 2.2 minutes by scaling to 4158 GPUs with a super-linear strong scaling efficiency at 364% compared to runtimes at 6 GPUs. This performance is 2.7 times more memory efficient, 9 times more scalable and 86 times faster than the state-of-the-art algorithm.

Wang, Xiao↗

NASA NTRS1987

An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification

A modification to the Eigensystem Realization Algorithm (ERA) for modal parameter identification is presented in this paper. The ERA minimum order realization approach using singular value decomposition is combined with the philosophy of the Correlation Fit method in state space form such that response data correlations rather than actual response values are used for modal parameter identification. This new method, the ERA using data correlations (ERA/DC), reduces bias errors due to noise corruption significantly without the need for model overspecification. This method is tested using simulated five-degree-of-freedom system responses corrupted by measurement noise. It is found for this case that, when model overspecification is permitted and a minimum order solution obtained via singular value truncation, the results from the two methods are of similar quality.

Juang, Jer-Nan↗

NASA NTRS1985

An Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Juang, J. N.↗

NASA NTRS1992

A modal analysis of lamellar diffraction gratings in conical mountings

A rigorous modal analysis of lamellar grating, i.e., gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.

Li, Lifeng↗

NASA NTRS1985

An eigensystem realization algorithm for modal parameter identification and model reduction

A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.

Juang, J.-N.↗

DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Transverse mode analysis for free-space laser beams using Bayesian analysis

Reliable and rapid assessment of the transverse mode quality of a free-space laser beam has a wide range of applications in laser development, research, and utilization. It has become even more important with recent advances in developing orbital angular momentum photon beams across a broad spectral region. In this work, a general modal analysis method for a free-space multimode laser beam has been developed based on Bayesian analysis. After transforming mode decomposition into a linear system problem, a Gaussian probabilistic model is used to find a closed-form solution. The method is found to be robust with the presence of Gaussian noise. Prior knowledge about the mode content can be incorporated into the method to improve the solution for situations when coherent disturbances or contamination are present in the laser beam. This method can be used to analyze the mode content for laser beams in different bases, such as Hermite–Gaussian (HG) modes and Laguerre–Gaussian (LG) modes. Three applications of this method are presented: a detailed modal analysis of the beam image from the incoherent intensity addition of HG modes and two examples of mode decomposition using the complex wavefront from the coherent superposition of HG and LG modes. The feasibility of this method is demonstrated using various simulation results. Based on digital images of a laser beam recorded without complex wavelength-limiting optics, in principle, this method can be used in a wide wavelength range from infrared to ultraviolet, and possibly x ray.

Liu, Peifan (ORCID:0000000273816153)↗

NASA NTRS2008

Efficient Modal Basis Selection Criteria for Reduced-Order Nonlinear Simulation

A modal basis selection technique for a reduced-order nonlinear numerical simulation with application to two-dimensional structures is presented as a two-step procedure. A system identification analysis is first performed using proper orthogonal decomposition. Using these results, a set of load-invariant bases consisting of the normal modes is next selected. Two criteria for making the basis selection are offered; one using the modal assurance criterion and the other using the modal expansion theorem. The quality of the subsequent reduced-order analyses are examined through comparison with computationally intensive finite element nonlinear simulations in physical degrees-of-freedom. A clamped flat isotropic plate under a random acoustic loading is considered to demonstrate the procedure. It is found that the subject procedure enables formation of an accurate and computationally efficient reduced-order system applicable to a broad range of loading conditions.

Przekop, Adam↗

DOE OSTI2021

Towards Reconstruction of Complex Flow Fields Using Unit Flows

Many complex turbulent flows in nature and engineering can be qualitatively regarded as being constituted of multiple simpler unit flows. The objective of this work is to characterize the coherent structures in such complex flows as a combination of constituent unitary flow structures for the purpose of reduced-order representation. While turbulence is clearly a non-linear phenomenon, we aim to establish the degree to which the optimally weighted superposition of unitary flow structures can represent the complex flow structures. The rationale for investigating such superposition stems from the fact that the large-scale coherent structures are generated by underlying flow instabilities that may be reasonably described using linear analysis. Clearly, the degree of validity of superposition will depend on the flow under consideration. In this work, we take the first step toward establishing a procedure for investigating superposition. Experimental data of single and triple tandem jets in crossflow are used to demonstrate the procedure. A composite triple tandem jet flow field is generated from optimal superposition of single jet data and compared against ‘true’ triple jet data. Direct comparisons between the true and composite fields are made for spatial, temporal, and kinetic energy content. The large-scale features (obtained from proper orthogonal decomposition or POD) of true and composite tandem jet wakes exhibit nearly 70% agreement in terms of modal eigenvector correlation. Corresponding eigenvalues reveal that the kinetic energy of the flow is also emulated with only a slight overprediction. Temporal frequency features are also examined in an effort to completely characterize POD modes. The proposed method serves as a foundation for more rigorous and robust dimensional reduction in complex flows based on unit flow modes.

Kristo, Paul J.↗

DOE OSTI2022

Cyber-Attack Identification of Synchrophasor Data Via VMD and Multifusion SVM

A large amount of synchrophasor data in the wide area measurement system (WAMS) needs to be collected and transmitted to the phasor data concentrator, thereby increasing the possibility of being attacked by hackers. The attacked data are therefore hidden into the normal synchrophasor data so that the synchrophasor data based application will be affected. To remedy this problem, an identification framework is proposed to detect the data cyber-attack in WAMS utilizing variational mode decomposition (VMD) and multifusion support vector machine (MSVM). First, VMD is used to transform the attacked data into multiple modal components. Thereafter, a novel MSVM is employed to classify the deterministic features using the proposed linear combined multikernel (LCM). Further, this LCM can fuse multiple types of features, including the time, frequency, and statistical domains of the synchrophasor data. Utilizing the actual data from FNET/GridEye, different experiments are conducted under multiple attack strengths and types. The results demonstrate that the identification framework has higher precision and robustness compared with other conventional classifiers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Structural response reconstruction using a system-equivalent singular vector basis

Here, this paper develops a novel method for reconstructing the full-field response of structural dynamic systems using sparse measurements. The singular value decomposition is applied to a frequency response matrix relating the structural response to physical loads, base motion, or modal loads. The left singular vectors form a non-physical reduced basis that can be used for response reconstruction with far fewer sensors than existing methods. The contributions of the singular vectors to measured response are termed singular-vector loads (SVLs) and are used in a regularized Bayesian framework to generate full-field response estimates and confidence intervals. The reconstruction framework is applicable to the estimation of single data records and power spectral densities from multiple records. Reconstruction is successfully performed in configurations where the number of SVLs to identify is less than, equal to, and greater than the number of sensors used for reconstruction. In a simulation featuring a seismically excited shear structure, SVL reconstruction significantly outperforms modal FRF-based reconstruction and successfully estimates full-field responses with as few as two uniaxial accelerometers. SVL reconstruction is further verified in a simulation featuring an acoustically excited cylinder. Finally, response reconstruction and uncertainty quantification are performed on an experimental structure with three shaker inputs and 27 triaxial accelerometer outputs.

42 ENGINEERING↗

NASA NTRS1987

Three axis rotational maneuver and vibration stabilization of elastic spacecraft

A control law for three-axis rotational maneuvers of a spacecraft beam-tip body configuration based on non-linear inversion and modal velocity feedback is presented. A decoupling attitude control law is presented such that in the closed-loop system the attitude angles of the spacecraft are independently controlled, using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for the derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show the capability of the controller.

Singh, Sahjendra N.↗

NASA NTRS1988

Flexible spacecraft maneuver - Inverse attitude control and modal stabilization

A control law is presented for three-axis rotational maneuvers of a spacecraft (orbiter)-beam-tip body (antenna or a reflector) configuration based on nonlinear inversion and modal velocity feedback. Using invertibility and functional reproducibility results, a decoupling attitude control law is presented such that, in the closed-loop system, the attitude angles of the spacecraft are independently controlled using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show that, in the closed-loop system, attitude control and elastic mode stabilization are accomplished in spite of the parameter uncertainty and disturbance torque input in the system.

Singh, Sahjendra N.↗

DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗

DOE OSTI2022

Investigation of methods for targeted search of dominant higher modes in subcritical systems

The reactor physics modeling of subcritical systems requires a substantially different approach from that of a critical reactor due to the presence of the so-called higher modes. Earlier investigations showed that the dominant higher modes lie in the inner part of the eigenvalue spectrum, making the conventional eigenvalue searches unfeasible and calling for a targeted search. This paper investigates the possibility of targeted and multitudinous eigenvalue calculation by testing the Krylov-Schur and the Dynamic Modes Decomposition (DMD) method for simple, analytically tractable problems. While the DMD method clearly showed its efficiency in a one-group homogeneous problem, modal analysis of a three-dimensional reflected reactor in two-groups approximation demonstrated that the increasing complexity poses challenges for both methods. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1994

A comparative study of serial and parallel aeroelastic computations of wings

A procedure for computing the aeroelasticity of wings on parallel multiple-instruction, multiple-data (MIMD) computers is presented. In this procedure, fluids are modeled using Euler equations, and structures are modeled using modal or finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. In the present parallel procedure, each computational domain is scalable. A parallel integration scheme is used to compute aeroelastic responses by solving fluid and structural equations concurrently. The computational efficiency issues of parallel integration of both fluid and structural equations are investigated in detail. This approach, which reduces the total computational time by a factor of almost 2, is demonstrated for a typical aeroelastic wing by using various numbers of processors on the Intel iPSC/860.

Byun, Chansup↗