Efficient Multi-Linear Elastic-Plastic Model Calibration for Accurate Reduced-Order Fastener Models.
Abstract not provided.
Grimmer, Peter W↗
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Results for “Reduced Order Modeling”
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Efficient Multi-Linear Elastic-Plastic Model Calibration for Accurate Reduced-Order Fastener Models.
Abstract not provided.
Grimmer, Peter W↗
A PSCAD Library Component Featuring a Reduced-Order IBR Model for EMT-Based Fault Studies
This paper presents a fully implemented inverter reduce-order-model (ROM) in an EMT simulation (PSCAD) library component for direct user utilization in protection studies. The developed inverter ROM has the following features: Equivalent to a full IBR inverter model with positive- and negative-sequence current formulation and representation A python script is developed to fully automate this process, including training data generation, ROM parameter training, updating parameters, and model verification and validation. With this PSCAD ROM library component, protection engineers can utilize a trustworthy, accurate ROM for protection studies in an easy-to-use and streamlined manner.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs
A system identification analysis was performed to determine reduced-order models of a computational fluid dynamics (CFD) solver for linear aeroelastic analysis and control design. The application was to the FUN3D code and the flexible half-span wind tunnel test article, in transonic flow conditions, used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. Multiple inputs (structural mode displacements and control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines and multiple outputs (generalized aerodynamic forces) were recorded, from which the matrix of frequency responses were computed using a single CFD run. A state-space model was then fit to the frequency response data using a maximum-likelihood estimator.
System identification↗
Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs
A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.
Aeroservoelasticity↗
Reduced-Order Aggregate Model for Parallel-Connected Single-Phase Inverters
This paper outlines a reduced-order aggregate dynamical model for parallel-connected single-phase grid-connected inverters. For each inverter, we place no restrictions on the converter topology and merely assume that the ac-side switch-averaged voltage can be controlled via pulsewidth modulation. The ac output of each inverter interfaces through an LCL filter to the grid. The closed-loop system contains a phase locked loop for grid synchronization, and real- and reactive-power control are realized with inner and outer PI current- and power-control loops. We derive a necessary and sufficient set of parametric relationships to ensure that a reduced-order aggregated state-space model for an arbitrary number of such paralleled inverters has the same model order and structure as any single inverter. We also present reduced-order models for the settings where the real- and reactive-power setpoints are different and where the inverters have different power ratings. We anticipate the proposed model being useful in analyzing the dynamics of large collections of parallel-connected inverters with minimal computational complexity. The aggregate model is validated against measurements obtained from a multi-inverter experimental setup consisting of three 750-VA paralleled grid-connected inverters, hence establishing robustness of the analytical result to parametric variations seen in practice.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A Reduced-Order Aggregated Model for Parallel Inverter Systems with Virtual Oscillator Control
This paper introduces a reduced-order aggregated model for parallel-connected inverters controlled with virtual oscillator control (VOC). The premise of VOC is to modulate inverter dynamics to emulate those of nonlinear oscillators with the goal of realizing a stable ac microgrid in the absence of communication, synchronous generation, or a stiff grid. To obtain a reduced-order model for a system of parallel-connected inverters with VOC, we first formulate a set of scaling laws that describe how the controller and filter parameters of a given inverter depend on its voltage and power rating. Subsequently, we show that N parallel inverters which adhere to this scaling law can be modeled with the same structure and hence the same computational burden of the model of a single inverter. The proposed aggregate model is experimentally validated on a system of three parallel inverters with heterogeneous power ratings.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Deep multiscale model learning
The objective of this article is to design novel multi-layer neural networks for multiscale simulations of flows taking into account the observed fine data and physical modeling concepts. Our approaches use deep learning techniques combined with local multiscale model reduction methodologies to predict flow dynamics. Using reduced-order model concepts is important for constructing robust deep learning architectures since the reduced-order models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n+1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from multiscale models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale model.
97 MATHEMATICS AND COMPUTING↗
Multiscale modeling high-order methods and data-driven modeling
Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.
97 MATHEMATICS AND COMPUTING↗
A Reduced-Order Aggregated Model for Parallel Inverter Systems with Virtual Oscillator Control: Preprint
This paper introduces a reduced-order aggregated model for parallel-connected inverters controlled with virtual oscillator control (VOC). The premise of VOC is to modulate inverter dynamics to emulate those of nonlinear oscillators with the goal of realizing a stable ac microgrid in the absence of communication, synchronous generation, or a stiff grid. To obtain a reduced-order model for a system of parallel-connected inverters with VOC, we first formulate a set of scaling laws that describe how the controller and filter parameters of a given inverter depend on its voltage and power rating. Subsequently, we show that N parallel inverters which adhere to this scaling law can be modeled with the same structure and hence the same computational burden of the model of a single inverter. The proposed aggregate model is experimentally validated on a system of three parallel inverters with heterogeneous power ratings.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil
Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks and we demonstrate its ability to preserve accuracy with a significantly lower computational cost. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes the knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in the fast exploration of design space for diverse engineering applications. Comparison against a projection-based nonintrusive model order reduction method demonstrates that the proposed approach produces comparable accuracy and yet is orders of magnitude computationally cheap to evaluate, despite being agnostic to the physics of the problem.
97 MATHEMATICS AND COMPUTING↗
Tuning and Verification of an Internal Flooding Model for Dynamic PRA
In probabilistic risk assessment (PRA), the likelihoods and consequences of basic events are combined to determine possible system level outcomes and the likelihood of each outcome given an initial event. Both the consequences and likelihoods of basic events may be informed by the use of mathematical models or experimental data regarding the phenomena of interest. In either case, the impact of uncertainties on the results need to be evaluated. If a model is used to predict the evolution of an initiating event, uncertainty quantification can be computationally challenging for complex phenomena with many epistemic (e.g., model) uncertainties. In this work, a reduced order model is introduced for the flooding analysis of a multi-room building at a nuclear power plant under uncertainties which can require long run times using high fidelity computer models. The reduced order model focuses on macro-level transfer of water between rooms and tracks the water level within each room. In order to verify the model's fidelity, its results for the phenomena involved in a scenario of interest are compared to those of a computational fluid dynamics (CFD) code, which are taken to represent reality. This work does not focus on the overall fidelity of the flooding model, as the goal of the project for which it was developed is to develop a methodology rather than to analyze a particular case. The focus instead is on the tunability and verifiability of the reduced order model for relevant physical measures. In analyzing a particular case, the model may be required to incorporate more realistic description of phenomena; however, the procedure described in this work may be used to verify its performance as well. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Linear analysis of a force reflective teleoperator
Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.
Biggers, Klaus B.↗
Application of the Aquifer Impact Model to support decisions at a CO 2 sequestration site
The National Risk Assessment Partnership (NRAP) has developed a suite of tools to assess and manage risk at CO 2 sequestration sites. The NRAP tool suite includes the Aquifer Impact Model (AIM), which evaluates the potential for groundwater impacts from leaks of CO 2 and brine through abandoned wellbores. There are two aquifer reduced-order models (ROMs) included with the AIM tool, a confined alluvium aquifer, and an unconfined carbonate aquifer. The models accept aquifer parameters as a range of variable inputs so they may have broad applicability. The generic aquifer models may be used at the early stages of site selection, when site-specific data is not available. Guidelines have been developed for determining when the generic ROMs might be applicable to a new site. This work considers the application of the AIM to predicting the impact of CO 2 or brine leakage were it to occur at the Illinois Basin Decatur Project (IBDP). Results of the model sensitivity analysis can help guide characterization efforts; the hydraulic parameters and leakage source term magnitude are more sensitive than clay fraction or cation exchange capacity. Sand permeability was the only hydraulic parameter measured at the IBDP site. More information on the other hydraulic parameters could reduce uncertainty in risk estimates. Some non-adjustable parameters are significantly different for the ROM than for the observations at the IBDP site. The generic ROMs could be made more useful to a wider range of sites if the initial conditions and no-impact threshold values were adjustable parameters.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Structure- and Physics-Preserving Reductions of Power Grid Models
The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution---the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.
24 POWER TRANSMISSION AND DISTRIBUTION↗
SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction
Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.
97 MATHEMATICS AND COMPUTING↗
Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction
Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximated Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.
97 MATHEMATICS AND COMPUTING↗
Error associated with a reduced order linear model of a spur gear pair
The paper proposes a reduced-order analytical model of a spur gear pair which consists of two identical spur gears, two identical flexible shafts, and four identical rolling element bearings of a given radial stiffness. The error associated with the undamped eigensolution is estimated by a comparison with a benchmark finite element model.
Kahraman, A.↗