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NASA NTRS2004

On the Hilbert-Huang Transform Theoretical Foundation

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Kizhner, Semion↗

DOE OSTI2015

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity $\mathcal{S}$ that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. Here, we found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

AUTONOMOUS GAUSSIAN DECOMPOSITION

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Extended dynamic mode decomposition for model reduction in fluid dynamics simulations

High computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic mode decomposition (xDMD) algorithm in constructing ROMs of three-dimensional cardiovascular computations. Focusing on the ROMs' accuracy in representation and interpolation, we relate these metrics to the truncation rank of singular value decomposition, which underpins xDMD and other approaches to ROM construction. Our key innovation is to relate the truncation rank to the singular values of the original flow problem. This result establishes a priori guidelines for the xDMD deployment and its likely success as a means of data compression and reconstruction of the system's dynamics from dominant spatiotemporal structures present in the data.

Mechanics↗

DOE OSTI2014

Parrallel Implementation of Fast Randomized Algorithms for Low Rank Matrix Decomposition

We analyze the parallel performance of randomized interpolative decomposition by de- composing low rank complex-valued Gaussian random matrices larger than 100 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model permitting quick investigation of parallel algorithms without obfuscation from hardware idiosyncrasies. We obtain that on non-square matrices performance scales almost linearly with runtime about 100 times faster on 128 processors. We also verify that numerically discovered error bounds still hold on matrices two orders of magnitude larger than those previously tested.

Lucas, Andrew J.↗

NASA NTRS1993

A study of CFD algorithms applied to complete aircraft configurations

Research aimed at increasing the efficiency and productivity of an overall CFD simulation process, from geometry definition to post processing of results as applied to complete aircraft configurations is reviewed. The progress was achieved through enhancements in geometry processing, surface grid generation, grid refinement, grid adaptation, and domain decomposition strategies. Algorithms for surface grid redistribution, automatic remapping, elliptic refinement and grid adaptation utilize the direct and inverse nonuniform rational B spline based surface representation.

Soni, Bharat K.↗

DOE OSTI2020

Benders Cut Classification via Support Vector Machines for Solving Two-Stage Stochastic Programs

In this work, we consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification step in each iteration to selectively generate cuts that are more likely to be valuable cuts. The LearnBD algorithm includes two phases: (i) sampling cuts and collecting information from training problems and (ii) solving testing problems with a support vector machine (SVM) cut classifier. We run the LearnBD algorithm on instances of capacitated facility location and multicommodity network design under uncertain demand. Our results show that SVM cut classifier works effectively for identifying valuable cuts, and the LearnBD algorithm reduces the total solving time of all instances for different problems with various sizes and complexities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Variance decomposition in stochastic simulators

Not Available

Le Maître, O. P.↗

DOE OSTI2018

Nonlinear Decoupling Control with ANFIS-based Unmodeled Dynamics Compensation for A Class of Complex Industrial Processes

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature that make it very difficult to obtain an accurate model. As a result, the conventional and data driven control methods are difficulty to apply. Using a twin-tank level control system as an example, a novel multivariable decupling control algorithm with adaptive neural fuzzy inference system (ANFIS) based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decupling controller with UD compensation is introduced. Different from the general method, the decomposition estimation algorithm by ANFIS is used to estimate the UD, and the desired estimating and decoupling control effects are achieved. Secondly, the proposed method does not require the complex switching mechanism which has been commonly used in the literature. This simplifies the obtained decoupling algorithm and its realization. Thirdly, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. Finally, experimental tests on a heavily coupled nonlinear twin-tank system are carried out to demonstrate the effectiveness and the practicability of the proposed method.

Complex industrial process, ANFIS, multivariable a↗

NASA NTRS1999

The Component Packaging Problem: A Vehicle for the Development of Multidisciplinary Design and Analysis Methodologies

This report summarizes academic research which has resulted in an increased appreciation for multidisciplinary efforts among our students, colleagues and administrators. It has also generated a number of research ideas that emerged from the interaction between disciplines. Overall, 17 undergraduate students and 16 graduate students benefited directly from the NASA grant: an additional 11 graduate students were impacted and participated without financial support from NASA. The work resulted in 16 theses (with 7 to be completed in the near future), 67 papers or reports mostly published in 8 journals and/or presented at various conferences (a total of 83 papers, presentations and reports published based on NASA inspired or supported work). In addition, the faculty and students presented related work at many meetings, and continuing work has been proposed to NSF, the Army, Industry and other state and federal institutions to continue efforts in the direction of multidisciplinary and recently multi-objective design and analysis. The specific problem addressed is component packing which was solved as a multi-objective problem using iterative genetic algorithms and decomposition. Further testing and refinement of the methodology developed is presently under investigation. Teaming issues research and classes resulted in the publication of a web site, (http://design.eng.clemson.edu/psych4991) which provides pointers and techniques to interested parties. Specific advantages of using iterative genetic algorithms, hurdles faced and resolved, and institutional difficulties associated with multi-discipline teaming are described in some detail.

Fadel, Georges↗

DOE OSTI2017

Recovering Interstellar Gas Properties with Hi Spectral Lines: A Comparison between Synthetic Spectra and 21-SPONGE

We analyze synthetic neutral hydrogen (H i) absorption and emission spectral lines from a high-resolution, three-dimensional hydrodynamical simulation to quantify how well observational methods recover the physical properties of interstellar gas. We present a new method for uniformly decomposing H i spectral lines and estimating the properties of associated gas using the Autonomous Gaussian Decomposition (AGD) algorithm. We find that H i spectral lines recover physical structures in the simulation with excellent completeness at high Galactic latitude, and this completeness declines with decreasing latitude due to strong velocity-blending of spectral lines. The temperature and column density inferred from our decomposition and radiative transfer method agree with the simulated values within a factor of <2 for the majority of gas structures. We next compare synthetic spectra with observations from the 21-SPONGE survey at the Karl G. Jansky Very Large Array using AGD. We find more components per line of sight in 21-SPONGE than in synthetic spectra, which reflects insufficient simulated gas scale heights and the limitations of local box simulations. In addition, we find a significant population of low-optical depth, broad absorption components in the synthetic data which are not seen in 21-SPONGE. This population is not obvious in integrated or per-channel diagnostics, and reflects the benefit of studying velocity-resolved components. The discrepant components correspond to the highest spin temperatures (1000<T{sub s}<4000 K), which are not seen in 21-SPONGE despite sufficient observational sensitivity. We demonstrate that our analysis method is a powerful tool for diagnosing neutral interstellar medium conditions, and future work is needed to improve observational statistics and implementation of simulated physics.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1984

Finite elements and the method of conjugate gradients on a concurrent processor

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

Lyzenga, G. A.↗

NASA NTRS1985

Finite elements and the method of conjugate gradients on a concurrent processor

Lyzenga, G. A.↗

DOE OSTI2020

Data Driven Online Learning of Power System Dynamics

With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on data-driven operator theoretic methods involving Koopman operator is proposed for the online identification of power system dynamics. In particular, a new algorithm is provided, which unlike any previously existing algorithms, updates the Koopman operator iteratively as new data points are acquired. The proposed algorithm has three advantages: a) allows for real-time monitoring of the power system dynamics b) linear power system dynamics (this linear system is usually in a higher dimensional feature space and is not same as linearization of the underlying nonlinear dynamics) and c) computationally fast and less intensive when compared to the popular Extended Dynamic Mode Decomposition (EDMD) algorithm. The efficiency of the proposed algorithm is illustrated on an IEEE 9 bus system using synthetic data from the nonlinear model and on IEEE 39 bus system using synthetic data from the linearized model.

Sinha, Subhrajit↗

DOE OSTI2023

Online real-time learning of dynamical systems from noisy streaming data

Abstract Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: (a) it allows for online real-time monitoring of a dynamical system; (b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; (c) it is computationally fast and less intensive than the popular extended dynamic mode decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the chaotic attractor of the Henon map, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

97 MATHEMATICS AND COMPUTING↗