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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids

We present a new approach to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) stochastic collocation based on dimension-adaptive sparse grids (SGs), which approximates the stochastic objective function with a limited number of quadrature nodes, and (2) projection-based reduced-order models (ROMs), which generate efficient approximations to PDE solutions. These two sources of inexactness lead to inexact objective function and gradient evaluations, which are managed by a trust-region method that guarantees global convergence by adaptively refining the SG and ROM until a proposed error indicator drops below a tolerance specified by trust-region convergence theory. A key feature of the proposed method is that the error indicator---which accounts for errors incurred by both the SG and ROM---must be only an asymptotic error bound, i.e., a bound that holds up to an arbitrary constant that need not be computed. This allows the approach to be applicable to a wide range of problems, including those where sharp, computable error bounds are not available; this distinguishes the proposed method from previous works. Numerical experiments performed on a model problem from optimal flow control under uncertainty verify global convergence of the method and demonstrate the method's ability to outperform previously proposed alternatives.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Data-based stochastic model reduction for the Kuramoto–Sivashinsky equation

In this paper, the problem of constructing data-based, predictive, reduced models for the Kuramoto–Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. Finally, the broader significance of the results is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Measurement-based Power System Dynamic Model Reductions

Interconnected power systems have experienced a significant increase in its size and complexity, due to continuous topology and operating condition changes. It is computationally burdensome to represent entire system models in detail to conduct power system analysis. In the large-scale power system dynamic simulations, the models in the study area need to be retained in detail while the external area can be reduced without compromising accuracy, which can preserve the full system dynamic properties. This paper develops measurement-based continuous-time dynamic equivalents for power systems in order to both improve the model accuracy of the reduced system and increase the speed of dynamic simulation. Our method is based on a set of measurements at the boundary nodes between the study area and external area. Case studies demonstrate that the measurement-based model can capture the full system behavior sufficiently, and improve computational efficiency.Interconnected power systems experienced a significant increase in size and complexity. It is computationally burdensome to represent the entire system in detail to conduct power system analysis. Therefore, the model of the study system must be retained in detail while the external system can be reduced using system reduction techniques. This paper proposes a measurement-based dynamic equivalent in order to increase both model accuracy and simulation speed. The proposed method uses a set of measurements at the boundary nodes between the study area and external area for model parameter identification. Case studies demonstrate that the measurement-based technique can capture the main system behaviors accurately and improve computational efficiency.

Xue, Yaosuo↗
NASA NTRS1992

A fundamental theorem for the model reduction of nonlinear systems

A simple, but fundamental, theorem is given on the extent to which a nonlinear system model can have its order reduced. Essentially, the result is that the order, or the dimension of the state space representation, cannot be reduced to, or below, the dimension of the system's attractor. Several examples are given to illustrate this point. The result is especially applicable to higher order systems such as the infinite dimensional systems arising from the modeling of distributed parameter systems.

Mossayebi, Faramarz↗
NASA NTRS1993

Model reduction results for flexible space structures

This paper describes the novel subsystem balancing technique for obtaining reduced-order models of flexible structures, and investigates its properties fully. This method can be regarded as a combination of the best features of modal truncation (efficiency) and internal balancing (accuracy); it is particularly well suited to the typical practical case of structures which possess clusters of close modes. Numerical results are then presented demonstrating the results obtained by applying subsystem balancing to the Air Force Phillips Laboratory ASTREX testbed, the Jet Propulsion Laboratory antenna facility, and the NASA Marshall Space Flight Center ACES structure.

Williams, Trevor↗
DOE OSTI2021

Model Reduction for Steady Hypersonic Aerodynamics via Conservative Manifold Least-Squares Petrov–Galerkin Projection

High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models, which can be very expensive for hypersonic flows. Additionally, UQ approaches are many-query problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model (FOM). In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems, including subsonic CFD applications. This allows LSPG ROM simulations to replace the FOM simulations in UQ studies, making UQ tractable even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application, the Hypersonic International Flight Research Experimentation 1 (HIFiRE-1) in a three-dimensional, turbulent Mach 7.1 flow. This paper shows the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.

42 ENGINEERING↗
DOE OSTI2020

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

42 ENGINEERING↗
DOE OSTI2019

Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways

Discrete fracture networks (DFN) are often used to model flow and transport in fractured porous media. The accurate resolution of flow and transport behavior on a large DFN involving thousands of fractures is computationally expensive. This makes uncertainty quantification studies of quantities of interest such as travel time through the network computationally intractable, since hundreds to thousands of runs of the DFN model are required to get bounds on the uncertainty of the predictions. Prior works on the subject demonstrated that the complexity of a DFN could be reduced by considering a sub-network of it (often termed a “backbone” sub-network), one whose flow and transport properties were then shown to be similar to that of the full network. The technique is tantamount to partitioning the complete set of fractures of a network into two disjoint sets, one of which is the backbone sub-network while the other its complement. It is in this context that we present a system-reduction technique for DFNs using supervised machine learning via a Random Forest Classifier that selects a backbone sub-network from the full set of fractures. The in-sample errors (in terms of precision and recall scores) of the trained classifier are found to be very accurate indicators of the out-of-sample errors, thus exhibiting that the classifier generalizes well to test data. Moreover, this system-reduction technique yields sub-networks as small as 12% of the full DFN that still recover transport characteristics of the full network such as the peak dosage and tailing behavior for late times. Most importantly, the sub-networks remain connected, and their size can be controlled by a single dimensionless parameter. Furthermore, measures of KL-divergence and KS-statistic for the breakthrough curves of the sub-networks with respect to the full network show physically realistic trends in that the measures decrease monotonically as the size of the sub-networks increase. In conclusion, the computational efficiency gained by this technique depends on the size of the sub-network, but large reductions in computational time can be expected for small sub-networks, yielding as much as 90% computational savings for sub-networks that are as small as 10-12% of the full network.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2017

Model Reduction for Fast Assessment of Grid Impact of High Penetration PV

A key challenge in properly analyzing the impact of solar photovoltaics (PV) during planning, interconnection and operation in the distribution grid is computational complexity. Such studies require the use of Quasi-Steady-Time-Series (QSTS) power flow to capture the complex interaction of PV with voltage regulating equipment and protection devices and a large number of scenario studies are needed to capture location specific constraints and uncertainties. In addition, a typical distribution feeder can have thousands of nodes and there can be thousands of such feeders in a given utility system. To solve this problem, a new and systematic method for distribution network reduction is proposed. The objective is to reduce the size of distribution systems by more than 80% while preserving the accuracy of power flow results. To this end, an extended Ward-equivalent method has been proposed to create an equivalent circuit. Moreover, load and PV aggregation based on the backward sweep method has been developed to further simplify the feeder. The proposed method is tested with a modified IEEE 123-node distribution test system. The simulation results demonstrate the high efficiency and accuracy of the proposed approach for distribution network reduction.

reduced order systems, load flow, load modeling, v↗
NASA NTRS1989

LQG and direct rate feedback control with model reduction on a flexible laboratory grid structure

This paper presents experimental and theoretical comparisons of three control laws applied to a complex laboratory structure. A reduced finite element model was generated for designing the control systems and then corrected based on measured mode shapes and frequencies. A standard time-invariant linear quadratic regulator with state estimation was investigated first. Two simple direct rate feedback control laws both guaranteeing stability were also designed using the reduced model. One minimizes the maximum control force and the other minimizes the same quadratic performance index as the linear quadratic regulator. The three control laws have comparable performance indices with the direct rate feedback designs having better spillover properties. Experimental results for all designs were obtained with digital implementation. It was shown that the performance of the control system designed on the basis of the corrected finite element model agreed better with experimental results than the performance of the control system designed on the basis of the uncorrected model.

Schamel, G. C., II↗
DOE OSTI2020

Data-Driven Model Reduction of Multiphase Flow in a Single-Hole Automotive Injector

Fuel injector design has a substantial influence on the performance and emissions of direct injection engines. To date, large eddy simulations coupled with a single-fluidmixture modeling approach have shown great success in evaluating the complex interplay among injector design, fuel properties, and operating conditions on the injector performance. However, this simulation approach is too computationally expensive to be used by industry routinely for injector design due to the fine temporal and spatial resolution required to resolve wall-bounded flow within the injector. The work presented in this paper highlights a potential pathway to addressing this issue. To study the influence of injector design, fuel properties, and operating conditions on injector performance, large eddy simulations were performed to model the turbulent multiphase flow development through a side-oriented singlehole diesel injector. Using Latin hypercube sampling, the design space spanning a range of fuel properties, operating conditions, and needle lifts were explored. Two techniques for dimensionality reduction, namely proper orthogonal decomposition and autoencoders, were compared to evaluate their accuracy in representing the flow in a reduced dimensional space. Finally, based on the findings from this work, recommendations are provided in using machine learning approaches within the context of emulation to construct reduced-ordermodels for internal flow development relevant to automotive applications.

42 ENGINEERING↗
DOE OSTI2018

U.S. Eastern Interconnection (EI) Model Reductions Using A Measurement-based Approach

Interconnected power systems experienced a significant increase in size and complexity. It is computationally burdensome to represent the entire system in detail to conduct power system analysis. To derive reduced models of large power systems, this paper proposes a measurement-based dynamic equivalent, which uses a set of measurements at the boundary nodes between the study area and external area for model parameter identification. Case studies on the U.S. Eastern Interconnection (EI) demonstrate that the measurement-based equivalent technique can capture the external system behaviors accurately and improve computation efficiency.

Zhang, Xuemeng↗
DOE OSTI2018

Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters

Power-electronics inverters are expected to satisfy a significant fraction of system load in next-generation power networks with the growing integration of renewable resources and flexible loads. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. In our previous work, we have shown that a system of parallel-connected grid-tied three-phase inverters can be modeled as one aggregated inverter unit with the same structure and state-space dimension as any individual inverter in the system. Here, we extend this result to networks with arbitrary topologies by leveraging a classical aggregation method for coherent synchronous generators in transmission networks, and a linear approximation of the AC power-flow equations to ease computational burden. Numerical simulation results for a prototypical distribution feeder demonstrate the accuracy and computational benefits of the approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1991

An enhanced projection and assembly model reduction methodology

An enhanced projection and assembly (P and A) method employing static correction modes to either the retained mode set of the system or the projected mode sets of the components is presented. The effectiveness of the proposed technique was successfully demonstrated on a 13-DOF mass-spring model and a high-order finite element model of the Galileo spacecraft. When applied to the Galileo cruise model, the system-level augmented P and A method significantly alleviates the zero-mismatch problem found in previous studies.

Lee, Allan Y.↗
NASA NTRS1990

Model reduction by weighted Component Cost Analysis

Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called 'component cost' to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. A reduced-order model of the given system may be obtained by deleting those components that have the smallest component costs. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. Closed-form analytical expressions of component costs are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems. A numerical example for MINIMAST system is presented.

Kim, Jae H.↗
DOE OSTI2017

Parameter estimation in a thermoelastic composite problem via adjoint formulation and model reduction

Advances in nondestructive material characterization are providing a wealth of information that could be exploited to gain insight into general aspects of material performance and, in particular, discover relationships between microstructure and thermo-mechanical properties in polycrystalline and other complex composite materials. Here, in order to facilitate the integration of such measurements into existing models, as well as inform new physics-based predictions, we developed a C++/MPI computational framework for sensitivity analysis and parameter estimation. The framework utilizes a micro-mechanical modeling based on fast Fourier transforms, direct and adjoint formulations, and Markov chain Monte Carlo sampling techniques. We illustrate the characteristics of this framework and demonstrate its utility by computing the residual stresses arising from thermal expansion of an elastic composite and using data from simulated experiments. Lastly, we show that the availability of nondestructive 3-D measurements is crucial to reduce the uncertainty in predictions, emphasizing the importance of an integrated experimental/modeling/data analysis approach for improved material characterization and design.

36 MATERIALS SCIENCE↗