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The modeling tool developed in the current project provides lifetime assessment of three candidate materials 740H, 282 and 625 for sCO2/molten salts heat exchanger. The tool incorporated physics-based models that accounted for all relevant underlying degradation mechanisms (creep and corrosion). Reduced-order models enabled rapid simulations of realistic component lifetimes (~100kh) while still retaining the fidelity of the complex models.
Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.
Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.
Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts (1976) where a characterization of the reduction error is given and a previously unknown L(infinity) norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L(infinity) norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L(infinity) norm on the weighted reduction error is obtained.
The requirements, constraints, and design of NASA's next generation Aircraft NOise Prediction Program (ANOPP2) are introduced. Similar to its predecessor (ANOPP), ANOPP2 provides the U.S. Government with an independent aircraft system noise prediction capability that can be used as a stand-alone program or within larger trade studies that include performance, emissions, and fuel burn. The ANOPP2 framework is designed to facilitate the combination of acoustic approaches of varying fidelity for the analysis of noise from conventional and unconventional aircraft. ANOPP2 integrates noise prediction and propagation methods, including those found in ANOPP, into a unified system that is compatible for use within general aircraft analysis software. The design of the system is described in terms of its functionality and capability to perform predictions accounting for distributed sources, installation effects, and propagation through a non-uniform atmosphere including refraction and the influence of terrain. The philosophy of mixed fidelity noise prediction through the use of nested Ffowcs Williams and Hawkings surfaces is presented and specific issues associated with its implementation are identified. Demonstrations for a conventional twin-aisle and an unconventional hybrid wing body aircraft configuration are presented to show the feasibility and capabilities of the system. Isolated model-scale jet noise predictions are also presented using high-fidelity and reduced order models, further demonstrating ANOPP2's ability to provide predictions for model-scale test configurations.
A summary of the computational aeroelastic analysis for the Semi-Span Super-Sonic Transport (S4T) wind-tunnel model is presented. A broad range of analysis techniques, including linear, nonlinear and Reduced Order Models (ROMs) were employed in support of a series of aeroelastic (AE) and aeroservoelastic (ASE) wind-tunnel tests conducted in the Transonic Dynamics Tunnel (TDT) at NASA Langley Research Center. This research was performed in support of the ASE element in the Supersonics Program, part of NASA's Fundamental Aeronautics Program. The analysis concentrated on open-loop flutter predictions, which were in good agreement with experimental results. This paper is one in a series that comprise a special S4T technical session, which summarizes the S4T project.
This paper presents a methodology for automated model order reduction (MOR) of flexible aircrafts to construct linear parameter-varying (LPV) reduced order models (ROM) for aeroservoelasticity (ASE) analysis and control synthesis in broad flight parameter space. The novelty includes utilization of genetic algorithms (GAs) to automatically determine the states for reduction while minimizing the trial-and-error process and heuristics requirement to perform MOR; balanced truncation for unstable systems to achieve locally optimal realization of the full model; congruence transformation for "weak" fulfillment of state consistency across the entire flight parameter space; and ROM interpolation based on adaptive grid refinement to generate a globally functional LPV ASE ROM. The methodology is applied to the X-56A MUTT model currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that X-56A ROM with less than one-seventh the number of states relative to the original model is able to accurately predict system response among all input-output channels for pitch, roll, and ASE control at various flight conditions. The GA-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The adaptive refinement allows selective addition of the grid points in the parameter space where flight dynamics varies dramatically to enhance interpolation accuracy without over-burdening controller synthesis and onboard memory efforts downstream. The present MOR framework can be used by control engineers for robust ASE controller synthesis and novel vehicle design.
The Mars Helicopter will be a technology demonstration conducted during the Mars 2020 mission. The primary mission objective is to achieve several 90-second flights and capture visible light images via forward and nadir mounted cameras. These flights could possibly provide reconnaissance data for sampling site selection for other Mars surface missions. The helicopter is powered by a solar array, which stores energy in secondary batteries for flight operations, imaging, communications, and survival heating. The helicopter thermal design is driven by minimizing survival heater energy while maintaining compliance with allowable flight temperatures in a variable thermal environment. Due to the small size of the helicopter and its complex geometries, along with the fact that it operates with very low power and small margins, additional care had to be paid while planning thermal tests and designing the thermal system. A Thermal Desktop® model has been developed to predict the thermal system’s performance. A reduced-order model (ROM) created with the Veritrek software has been utilized to explore the sensitivities of the thermal system’s drivers, such as electronics dissipations, gas gaps, heat transfer coefficients, etc., as well as to assess and verify the final thermal design. This paper presents the performance of the Veritrek software products and the details of the ROM creation process. The results produced by Veritrek were utilized to study the effect of the major thermal design drivers and Mars environment on the Mars Helicopter in as little as 10 days, an effort that would have taken over 4 months using traditional thermal analysis techniques.
An assessment of two methodologies used at Sandia National Laboratories to model mechanical interfaces is performed on the Ministack finite element model. One method uses solid mechanics models to model contacting surfaces with Coulomb frictional contact to capture the physics. The other, termed the structural dynamics reduced order model, models the interface with a simplified whole joint model using four-parameter Iwan elements. The solid mechanics model resolves local kinematics at the interface while the simplified structural dynamics model is significantly faster to simulate. One of the current challenges to using the whole joint model is that it requires calibration to data. A novel approach is developed to calibrate the reduced structural dynamics model using data from the solid mechanics model to match the global dynamics of the system. This is achieved by calibrating to amplitude dependent frequency and damping of the system modes, which are estimated using three different approaches.
We propose a framework to engineer synthetic-inertia and droop-control parameters for distributed energy resources (DERs) so that the system frequency in a network composed of DERs and synchronous generators conforms to prescribed transient and steady-state performance specifications. Our approach is grounded in a second-order lumped-parameter model that captures the dynamics of synchronous generators and frequency-responsive DERs endowed with inertial and droop control. A key feature of this reduced-order model is that its parameters can be related to those of the originating higherorder dynamical model. This allows one to systematically design the DER inertial and droop-control coefficients leveraging classical frequency-domain response characteristics of second-order systems. Time-domain simulations validate the accuracy of the model-reduction method and demonstrate how DER controllers can be designed to meet steady-state-regulation and transient-performance specifications.
We propose a framework to engineer synthetic-inertia and droop-control parameters for distributed energy resources (DERs) so that the system frequency in a network composed of DERs and synchronous generators conforms to prescribed transient and steady-state performance specifications. Our approach is grounded in a second-order lumped-parameter model that captures the dynamics of synchronous generators and frequency-responsive DERs endowed with inertial and droop control. A key feature of this reduced-order model is that its parameters can be related to those of the originating higher-order dynamical model. This allows one to systematically design the DER inertial and droop-control coefficients leveraging classical frequency-domain response characteristics of second-order systems. Time-domain simulations validate the accuracy of the model-reduction method and demonstrate how DER controllers can be designed to meet steady-state-regulation and transient-performance specifications.
Making reliable predictions in the presence of uncertainty is critical to high-consequence modeling and simulation activities, such as those encountered at Sandia National Laboratories. Surrogate or reduced-order models are often used to mitigate the expense of performing quality uncertainty analyses with high-fidelity, physics-based codes. However, phenomenological surrogate models do not always adhere to important physics and system properties. This project develops surrogate models that integrate physical theory with experimental data through a maximally-informative framework that accounts for the many uncertainties present in computational modeling problems. Correlations between relevant outputs are preserved through the use of multi-output or co-predictive surrogate models; known physical properties (specifically monotoncity) are also preserved; and unknown physics and phenomena are detected using a causal analysis. By endowing surrogate models with key properties of the physical system being studied, their predictive power is arguably enhanced, allowing for reliable simulations and analyses at a reduced computational cost.
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation [Proctor et al., 2016] and systems with heavily subsampled measurements [Brunton et al., 2015]. When combined, these methods yield a novel framework for compressive system identification [code is publicly available at: https://github.com/zhbai/cDMDc]. It is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data is available, it is possible to dramatically accelerate downstream computations by first compressing the data. We demonstrate this unified framework on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, we explore this architecture on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test-case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.
Long-term environmental performance assessments of natural processes, including erosion, are critically important for waste repository site evaluation. Yet, assessing a site’s ability to continuously function is challenging due to parameter uncertainty and compounding nonlinear processes. In lieu of unavailable site data for model calibration, we present a workflow to include multiple sources of surrogate data and reduced-order models to validate parameters for a long-term erosion assessment of a low-level radioactive nuclear waste repository. We apply this new workflow to a low-level waste repository on mesas in Los Alamos National Laboratory in New Mexico. To account for parameter uncertainty, we simulate high-, moderate-, and low-erosion cases. The assessment extends to 10,000 years, which results in large erosion uncertainties, but is necessary given the nature of the interred waste. Our long-term erosion analysis shows that high-erosion scenarios produce rounded mesa tops and partially filled canyons, diverging from the moderate-erosion case that results in gullies and sharp mesa rims. Our novel model parameterization workflow and modeling exercise demonstrates the utility of long-term assessments, identifies sources of erosion forecast uncertainty, and demonstrates the utility of landscape evolution model development. We end with a discussion on methods to reduce assessment uncertainty and increase model confidence.
One of the goals of the Nuclear-Renewable Hybrid Energy Systems (N-R HES) modeling and simulation (M&S) project is to assess the economic viability of N-R HES in a market that contains Variable Renewable Energy (VRE) sources like solar. The N-R HES M&S project is a multi-laboratory effort, led by Idaho National Laboratory (INL) and supported by Argonne National Laboratory (ANL) and Oak Ridge National Laboratory (ORNL). Development of the N-R HES software framework was initiated at INL in 2016 [1] and has reached some level of maturity such that it can be applied to more than simple demonstration cases, e.g. real industry problems. Nevertheless, more capabilities are constantly added to accommodate the special needs of challenging, real-life problems. The N-R HES framework is built on the Risk Analysis Virtual ENvironment (RAVEN) code [2], which it uses as a driver and workflow manager for all calculations. There are four main cornerstones of the N-R HES simulation framework: 1) The generation of stochastic synthetic time series. 2) A set of probabilistic analysis and optimization algorithms available in RAVEN. 3) A set of models for representing the physical behavior of N-R HES. These can be reduced-order models or high-fidelity Modelica [3] models. 4) The RAVEN plug-in called CashFlow [4] that maps physical performance into economic performance. Within this framework, a broad spectrum of questions related to N-R HES can be addressed. One of the challenges currently of high interest is the increasing penetration of VRE altering the profile of the net demand (demand after removing all non-curtailable renewable energy sources, e.g. rooftop solar). The N-R HES software framework is capable of analyzing the potential feasibility of mitigating the resultant volatility in the net electricity demand. One possible solution to manage net demand volatility is adding stabilizing loads to the grid. These loads can be external industrial processes that are able to ramp production up and down quickly, or for regulated markets, adding variable internal loads that will effectively increase the baseload of the power plant and therefore reduce the risk of internal demand that is lower than the capacity of the power plant. The latter is a possible solution currently being considered by Arizona Public Service (APS), the operating owner of the Palo Verde (PV) Nuclear Power Plant (NPP).
A set of results on rotorcraft system identification is described. Flight measurements collected on an experimental Puma helicopter are reviewed and some notable characteristics highlighted. Following a brief review of previous work in rotorcraft system identification, the results of state estimation and model structure estimation processes applied to the Puma data are presented. The results, which were obtained using NASA developed software, are compared with theoretical predictions of roll, yaw and pitching moment derivatives for a 6 degree of freedom model structure. Anomalies are reported. The theoretical methods used are described. A framework for reduced order modelling is outlined.
In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.