Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dynamic model reduction”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Robot arm dynamic model reduction for control

General methods are described by which the mathematical complexities of explicit and exact state equations of robot arms can be reduced to a simplified and compact state equation representation without introducing significant errors into the robot arm dynamic model. The model reduction methods are based on homogeneous coordinates and on the Langrangian algorithm for robot arm dynamics, and utilize matrix, vector and numeric analysis techniques. The derivation of differential vector representation of centripetal and Coriolis forces which has not yet been established in the literature is presented.

Bejczy, A. K.↗
DOE OSTI2020

Dynamic Model Reduction for Large-Scale Power Systems Using Wide-Area Measurements

To perform faster than the real-time dynamic simulation of large-scale power systems, it is necessary to reduce the simulated system size by using equivalents for surrounding areas of the study area, and existing dynamic model reduction approach could provide the needed structure of the reduced area. However, further parameter optimization is required to achieve the desired accuracy. In this paper, a particle swarm optimization (PSO) based approach is used to solve the above problem. Parameters for the individual dynamic elements in the reduced system are calibrated repeatedly until the wide-area measurements of the reduced model and the original model are very similar to each other with satisfactory accuracy. Results indicate that after optimization, the dynamic response of the reduced model matches better with that of the original one than using existing methods. Under both the generator-trip event and the bus-fault event, the reduced model has a higher frequency match and less power mismatch.

42 ENGINEERING↗
DOE OSTI2021

Discrete Empirical Interpolation Method Based Dynamic Load Model Reduction

Dynamic load models add significant complexity to bulk power system time-domain simulations. The complexity is due to the large number of ordinary differential equations (ODEs) introduced by the dynamic load components such as induction motors. It is challenging to derive reduced-order models (ROMs) for dynamic loads due to the nonlinear functions in their governing equations. This paper applies the discrete empirical interpolation method enhanced proper orthogonal decomposition (DEIM-POD) to approximate the full dynamic load model with the ROM that minimizes the projection error of the nonlinear functions in dynamic load ODEs onto their dominant modes. This approach only requires evaluation of nonlinear functions at selected observation points. The observation points selected by DEIM also provide information for screening critical load buses where dynamic load model parameters contribute the most to the accuracy of ROM across multiple contingencies. The proposed approach is validated on IEEE 9-bus, WECC 179-bus and 2384-bus Polish systems.

bulk power system↗
NASA NTRS1987

Structural dynamics system model reduction

Loads analysis for structural dynamic systems is usually performed by finite element models. Because of the complexity of the structural system, the model contains large number of degree-of-freedom. The large model is necessary since details of the stress, loads and responses due to mission environments are computed. However, a simplified model is needed for other tasks such as pre-test analysis for modal testing, and control-structural interaction studies. A systematic method of model reduction for modal test analysis is presented. Perhaps it will be of some help in developing a simplified model for the control studies.

Chen, J. C.↗
DOE OSTI2020

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Two-Stage Reduction Of Dynamical Models

No longer necessary to solve eigenvalue problems of high order. Component-mode projection-and-assembly model-reduction (COMPARE) method provides approximation of dynamics of vibrations of complicated, multiple flexible bodies by use of mathematical models of reduced order. Incorporates component-mode synthesis (CMS) method and enhanced projection-and-assembly (EP&A) method, described in "Enhanced Method of Reduction of Dynamical Models" (NPO-18402), providing for somewhat simplified two-stage process in which order of applicable mathematical models reduced. Reduced-order models used to design algorithms of control systems to suppress vibrations or otherwise control structure.

Lee, Allan Y.↗
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↗
NASA NTRS1992

Enhanced Method Of Reduction Of Dynamical Models

Enhanced projection-and-assembly method is recent product of efforts to model mathematically dynamics of vibrations of large, flexible structures. In projection-and-assembly method modes contributing significantly to control input and output points selected at system (overall structure) level, then projected (in abstract mathematical sense) onto components of system. In enhanced version, static correction modes capture static contributions of those modes neglected in reduced-order model. Reduced models for suppressing vibrations of structures made more accurate.

Lee, Allan Y.↗
NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗
NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗
DOE OSTI2020

Dynamic Equivalence of Large-Scale Power Systems Based on Boundary Measurements

Parallel computing helped speed up many tasks that can be done independently. The advance in gaming industry did not produce a technology that helps the power industry to reduce the computation time for dynamic simulation in individual cases. To perform faster than real-time simulation for the purpose of predicting power system dynamic trajectory, power industry continues to struggle to reduce the system size and simulation time of large-scale power systems while keeping its dynamic behavior under various disturbances. There is also an acute need for real-time dynamic model reduction as more renewables enter the generation mix with dramatic changes in the generation outputs. All existing model reduction solutions are based on having access to a detailed dynamic model of the system. The system changes by the minutes, dynamic models are only updated annually. To solve this problem, wide-area measurements obtained by the phasor measurement unit (PMU) at the boundaries between the reduced system and the study system is used to represent the external area. An artificial neuro-fuzzy inference system (ANFIS) is established to perform the mapping of the measurement to the external equivalent model. Here the external area is regarded as a black-box. Model reduction studies are conducted on the Northeast Power Coordinating Council (NPCC) under various types of contingencies, by using a co-simulation approach between PSS/E and MATLAB. The results look very promising and will be discussed in this paper.

Tong, Ning↗
DOE OSTI2020

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Model reduction for the dynamics and control of large structural systems via neutral network processing direct numerical optimization

Three neural network processing approaches in a direct numerical optimization model reduction scheme are proposed and investigated. Large structural systems, such as large space structures, offer new challenges to both structural dynamicists and control engineers. One such challenge is that of dimensionality. Indeed these distributed parameter systems can be modeled either by infinite dimensional mathematical models (typically partial differential equations) or by high dimensional discrete models (typically finite element models) often exhibiting thousands of vibrational modes usually closely spaced and with little, if any, damping. Clearly, some form of model reduction is in order, especially for the control engineer who can actively control but a few of the modes using system identification based on a limited number of sensors. Inasmuch as the amount of 'control spillover' (in which the control inputs excite the neglected dynamics) and/or 'observation spillover' (where neglected dynamics affect system identification) is to a large extent determined by the choice of particular reduced model (RM), the way in which this model reduction is carried out is often critical.

Becus, Georges A.↗
NASA NTRS1991

Krylov model reduction algorithm for undamped structural dynamics systems

Krylov vectors furnish an efficient basis for eigenvalue analysis and model reduction of structural dynamics systems. The reduced-order model obtained by the present Krylov model-reduction algorithm for an undamped structural-dynamics system is found to match low-frequency moments. The transformed system equation in Krylov coordinates reflects the structure of a tandem system.

Craig, Roy R., Jr.↗