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DOE OSTI2025

Acceleration of Power System Dynamic Simulations Using a Deep Equilibrium Layer and Neural ODE Surrogate

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based resources exacerbates the computational burden of running time domain simulations. Here, in this paper, we propose a data-driven surrogate model based on implicit machine learningspecifically deep equilibrium layers and neural ordinary differential equationsto learn a reduced order model of a portion of the full underlying system. The data-driven surrogate achieves similar accuracy and reduction in simulation time compared to a physics-based surrogate, without the constraint of requiring detailed knowledge of the underlying dynamic models. This work also establishes key requirements needed to integrate the surrogate into existing simulation workflows; the proposed surrogate is initialized to a steady state operating point that matches the power flow solution by design.

Neural ordinary differential equations↗

NASA NTRS2021

Weather Intelligent Navigation Data and Models for Aviation Planning (WINDMAP)

WINDMAP addresses the emerging needs in the aviation community of providing real-time weather forecasting to improve the safety of low altitude aircraft operations. This is accomplished through the integration of real-time observations from autonomous systems, such as drones and urban air taxis, with numerical weather prediction models and flight management and safety systems. To solve this problem, several technical challenges have been identified. These include (1) developing autonomous UAS capable of conducting observations accurately and reliably; (2) determining the number and frequency of required observations and the sensitivity of these observations in data sparse regions of the lower atmosphere;(3) assimilating dense observational data into models in real-time with sufficient resolution and accuracy; (4) developing novel physics-based reduced order models capable of incorporating diverse data sets; and (5)integrating real-time forecasting into UTM and DAA (detect-and-avoid) architectures for path planning and navigation. The goal of this proposed effort is to demonstrate the value of using small UAS to collect measurements of the dynamic and thermodynamic properties of the lower atmosphere at scales that match or exceed the spatio-temporal resolution of today’s best numerical weather prediction models

Koushik Datta↗

NASA NTRS2017

Aeroelastic Uncertainty Quantification Studies Using the S4T Wind Tunnel Model

This paper originates from the joint efforts of an aeroelastic study team in the Applied Vehicle Technology Panel from NATO Science and Technology Organization, with the Task Group number AVT-191, titled "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." We present aeroelastic uncertainty quantification studies using the SemiSpan Supersonic Transport wind tunnel model at the NASA Langley Research Center. The aeroelastic study team decided treat both structural and aerodynamic input parameters as uncertain and represent them as samples drawn from statistical distributions, propagating them through aeroelastic analysis frameworks. Uncertainty quantification processes require many function evaluations to asses the impact of variations in numerous parameters on the vehicle characteristics, rapidly increasing the computational time requirement relative to that required to assess a system deterministically. The increased computational time is particularly prohibitive if high-fidelity analyses are employed. As a remedy, the Istanbul Technical University team employed an Euler solver in an aeroelastic analysis framework, and implemented reduced order modeling with Polynomial Chaos Expansion and Proper Orthogonal Decomposition to perform the uncertainty propagation. The NASA team chose to reduce the prohibitive computational time by employing linear solution processes. The NASA team also focused on determining input sample distributions.

Nikbay, Melike↗

NASA NTRS2013

Integrated Model Reduction and Control of Aircraft with Flexible Wings

This paper presents an integrated approach to the modeling and control of aircraft with exible wings. The coupled aircraft rigid body dynamics with a high-order elastic wing model can be represented in a nite dimensional state-space form. Given a set of desired output covariance, a model reduction process is performed by using the weighted Modal Cost Analysis (MCA). A dynamic output feedback controller, which is designed based on the reduced-order model, is developed by utilizing output covariance constraint (OCC) algorithm, and the resulting OCC design weighting matrix is used for the next iteration of the weighted cost analysis. This controller is then validated for full-order evaluation model to ensure that the aircraft's handling qualities are met and the uttering motion of the wings suppressed. An iterative algorithm is developed in CONDUIT environment to realize the integration of model reduction and controller design. The proposed integrated approach is applied to NASA Generic Transport Model (GTM) for demonstration.

AEROELASTIC↗

DOE OSTI2025

Validation of Pronghorn for Natural-Circulation Molten Salt Loops

This paper presents the development and validation of a high-fidelity thermal-hydraulic model of a molten salt natural circulation flow loop, designed for integration within a digital twin framework. The study evaluates the performance of Idaho National Laboratory’s Pronghorn against experimental data from Texas A&M University Molten Salt Flow Loop (MSFL) four Hitec-salt test benchmark data. Natural circulation of high-Prandtl-number fluids exhibits complex, counter-intuitive flow patterns that make pointwise thermocouple readings unreliable. Experimental work at TAMU’s MSFL provides benchmark data, including flow visualization at a test-section and centerline steady-state temperature measurements along the loop. Validation includes four single-phase natural circulation test cases with Hitec salt. Key metrics include flow profile agreement and steady-state temperature accuracy. Pronghorn results for two-dimensional single-phase agree qualitatively with the experimental flow profile. This paper illustrates the importance of Computational Fluid Dynamics (CFD) in elucidating the behavior of high-Prandtl-number thermal-hydraulics, along with how misleading centerline temperature measurements can be. Pronghorn reproduces the axial and radial stratification that makes single thermocouple readings unreliable. Future research will focus on reduced-order modeling techniques to enable rapid simulation suitable for real-time digital twin applications. The validated cases provide a basis for developing reduced-order surrogates aimed at real-time digital-twin applications.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Model reduction for flexible space structures

This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Gawronski, Wodek↗

NASA NTRS1990

Component model reduction via the projection and assembly method

This paper explains the projection and assembly model reduction method which has been used to derive reduced order component models for the Galileo spacecraft. Assembly of reduced order component models produces a reduced order system model which can then be used in multibody simulation codes for efficient run times. The methodology is explained and a proof is given showing the exact reproduction of selected significant system modes. Frequency bounds are obtained for all modes produced when the reduced order components are assembled. The projection and assembly method is demonstrated on two examples. The first example is a simplified model of the Galileo spacecraft, while the second example is the model of the Galileo spacecraft in its early mission configuration. When articulation of components is allowed, the method may not reproduce all system modes precisely. Remedies for this problem are suggested.

Kissel, Glen J.↗

DOE OSTI2026

Toward real-time optimization through model reduction and model discrepancy sensitivities

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs—those that do not require access to the full-order model at evaluation time—is popular because they facilitate the computation of optimization solutions within the wall-clock time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, a limited number of full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. In conclusion, the HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data.

PDE-constrained optimization↗

DOE OSTI2020

Superelement reduction of substructures for sequential load calculations in OpenFAST

This article presents the superelement formulation newly implemented in OpenFAST to simulate fixed-bottom substructures with a reduced-order model similar to a common industry practice. The Guyan and Craig-Bampton methods are used to reduce the number of degrees of freedom and generate a so-called "superelement". The formulation allows manufacturers to exchange such superelements to perform load calculations without revealing sensitive information about the support structure (e.g., foundation, substructure, and/or tower) or turbine. The source code is made publicly available in the OpenFAST repository. Test cases with varying degrees of complexity are presented to validate the technique, and accuracy issues are discussed.

17 WIND ENERGY↗

NASA NTRS1992

Model reduction in a subset of the original states

A model reduction method is investigated to provide a smaller structural dynamic model for subsequent structural control design. A structural dynamic model is assumed to be derived from finite element analysis. It is first converted into the state space form, and is further reduced by the internal balancing method. Through the co-ordinate transformation derived from the states that are deleted during reduction, the reduced model is finally expressed with the states that are members of the original states. Therefore, the states in the final reduced model represent the degrees of freedom of the nodes that are selected by the designer. The procedure provides a more practical implementation of model reduction for applications in which specific nodes, such as sensor and/or actuator attachment points, are to be retained in the reduced model. Thus, it ensures that the reduced model is under the same input and output condition as the original physical model. The procedure is applied to two simple examples and comparisons are made between the full and reduced order models. The method can be applied to a linear, continuous and time-invariant model of structural dynamics with nonproportional viscous damping.

Yae, K. H.↗

NASA NTRS1992

Model based estimation of image depth and displacement

Passive depth and displacement map determinations have become an important part of computer vision processing. Applications that make use of this type of information include autonomous navigation, robotic assembly, image sequence compression, structure identification, and 3-D motion estimation. With the reliance of such systems on visual image characteristics, a need to overcome image degradations, such as random image-capture noise, motion, and quantization effects, is clearly necessary. Many depth and displacement estimation algorithms also introduce additional distortions due to the gradient operations performed on the noisy intensity images. These degradations can limit the accuracy and reliability of the displacement or depth information extracted from such sequences. Recognizing the previously stated conditions, a new method to model and estimate a restored depth or displacement field is presented. Once a model has been established, the field can be filtered using currently established multidimensional algorithms. In particular, the reduced order model Kalman filter (ROMKF), which has been shown to be an effective tool in the reduction of image intensity distortions, was applied to the computed displacement fields. Results of the application of this model show significant improvements on the restored field. Previous attempts at restoring the depth or displacement fields assumed homogeneous characteristics which resulted in the smoothing of discontinuities. In these situations, edges were lost. An adaptive model parameter selection method is provided that maintains sharp edge boundaries in the restored field. This has been successfully applied to images representative of robotic scenarios. In order to accommodate image sequences, the standard 2-D ROMKF model is extended into 3-D by the incorporation of a deterministic component based on previously restored fields. The inclusion of past depth and displacement fields allows a means of incorporating the temporal information into the restoration process. A summary on the conditions that indicate which type of filtering should be applied to a field is provided.

Damour, Kevin T.↗

DOE OSTI2023

A Decision-Relevant Factor-Fixing Framework: Application to Uncertainty Analysis of a High-Dimensional Water Quality Model

Factor Fixing (FF) is a common method for reducing the number of model parameters to lower computational cost. FF typically starts with distinguishing the insensitive parameters from the sensitive and pursues uncertainty quantification (UQ) on the resulting reduced-order model, fixing each insensitive parameter at a fixed value. There is a need, however, to expand such a common approach to consider the effects of decision choices in the FF-UQ procedure on metrics of interest. Therefore, to guide the use of FF and increase confidence in the resulting dimension-reduced model, we propose a new adaptive framework consisting of four principles: (a) re-parameterize the model first to reduce obvious non-identifiable parameter combinations, (b) focus on decision relevance especially with respect to errors in quantities of interest (QoI), (c) conduct adaptive evaluation and robustness assessment of errors in the QoI across FF choices as sample size increases, and (d) reconsider whether fixing is warranted. The framework is demonstrated on a spatially-distributed water quality model. The error in estimates of QoI caused by FF can be estimated using a Polynomial Chaos Expansion (PCE) surrogate model. Built with 70 model runs, the surrogate is computationally inexpensive to evaluate and can provide global sensitivity indices for free. For the selected catchment, just two factors may provide an acceptably accurate estimate of model uncertainty in the average annual load of Total Suspended Solids (TSS), suggesting that reducing the uncertainty in these two parameters is a priority for future work before undertaking further formal uncertainty quantification.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Advanced Models and Fast Simulation Algorithms for MARS Plants

With the successful commercialization of modular multilevel converters (MMC) and rapid increase in photovoltaic (PV) penetration and energy storage systems (ESS), one of the research areas being explored dynamically is integration of PV systems and ESS systems to MMCs. On this front, an integrated development of PV plants, ESS, and alternating- and direct-current (ac/dc) systems through Multi-Port Autonomous Reconfigurable Solar (MARS) plant is proposed and being researched upon. However, simulation of MARS systems on traditional existing software takes very long time (order of days) due to the presence of a large number of states and non-linear devices. Therefore, development of fast high fidelity models is of paramount importance to test the hardware design, control design and planning of power system expansions. In this context, two research objectives are addressed in this paper: firstly, an ultra fast single- or multi- CPU simulation algorithm to simulate the MARS system based on state-space models, hybrid discretization algorithm with a relaxation technique that reduces the imposed computational burden and a multi-rate method is presented. Secondly, a reduced order model of MARS is also presented. Both the developed techniques are validated with respect to reference PSCAD/EMTDC model.

Marthi, Phani Ratna Vanamali↗

DOE OSTI2020

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Here, we investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shifted Boundary Method, a high-fidelity embedded method recently developed. We focus on the geometrical parametrization through level-set geometries, using a fixed Cartesian background geometry and the associated mesh. This approach avoids both remeshing and the development of a reference domain formulation, as typically done in fitted mesh finite element formulations. Two-dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach.

"embedded" basis↗

DOE OSTI2021

pnnl/pecblocks

ConverterBlocks uses the output of detailed electromagnetic transient (EMT) simulations to produce generalized block diagram models of power electronic systems. The process uses deep learning with customized block architectures. The outputs are reduced-order models that meet specified accuracy requirements, while providing important advantages over the original EMT models: ConverterBlock models have fewer nodes and can take longer time steps, resulting in shorter simulation times ConverterBlock models are continuously differentiable, making them compatible with control design methodsGeneralized block diagram modeling of power electronic converters for grid solar and storage applications.

McDermott, Tom↗

NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗

NASA NTRS2016

Using FUN3D for Aeroelastic, Sonic Boom, and AeroPropulsoServoElastic (APSE) Analyses of a Supersonic Configuration

An overview of recent applications of the FUN3D CFD code to computational aeroelastic, sonic boom, and aeropropulsoservoelasticity (APSE) analyses of a low-boom supersonic configuration is presented. The overview includes details of the computational models developed including multiple unstructured CFD grids suitable for aeroelastic and sonic boom analyses. In addition, aeroelastic Reduced-Order Models (ROMs) are generated and used to rapidly compute the aeroelastic response and utter boundaries at multiple flight conditions.

Silva, Walter A.↗