Further remarks on simplifying linear dynamic systems.
Approximate model for simplification of linear dynamic system, neglecting effect of higher order time constants
TIME DEPENDENCY↗
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Results for “dynamic system”
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.
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Constraint Embedding for Multibody System Dynamics
This paper describes a constraint embedding approach for the handling of local closure constraints in multibody system dynamics. The approach uses spatial operator techniques to eliminate local-loop constraints from the system and effectively convert the system into tree-topology systems. This approach allows the direct derivation of recursive O(N) techniques for solving the system dynamics and avoiding the expensive steps that would otherwise be required for handling the closedchain dynamics. The approach is very effective for systems where the constraints are confined to small-subgraphs within the system topology. The paper provides background on the spatial operator O(N) algorithms, the extensions for handling embedded constraints, and concludes with some examples of such constraints.
Jain, Abhinandan↗
Transforming Energy Through Computational Excellence: NREL Computational Fluid Dynamics Modeling Complex, Dynamic Systems
Computational fluid dynamics (CFD) enables modeling, analysis, and visualization of phenomena that would usually be impossible or extremely expensive to measure experimentally.
97 MATHEMATICS AND COMPUTING↗
A Geometric Derivation of the Governing Equations of Motion of Nonholonomic Dynamic Systems
Here, in this paper, we present a Riemannian geometric derivation of the governing equations of motion of nonholonomic dynamic systems. A geometric form of the work-energy principle is first derived. The geometric form can be realized in appropriate generalized quantities, and the independent equations of motion can be obtained if the subspace of generalized speeds allowable by nonholonomic constraints can be determined. We provide a geometric perspective of the governing equations of motion and demonstrate its effectiveness in studying dynamic systems subjected to nonholonomic constraints.
42 ENGINEERING↗
On fast simulation of dynamical system with neural vector enhanced numerical solver
The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec’s simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.
97 MATHEMATICS AND COMPUTING↗
Integration of Dynamical System Scaling to RAVEN and Facility Application
As part of the design optimization and model validation effort within the hybrid energy systems program, the research to implement dynamical system scaling (DSS) code to RAVEN is funded under the Integrated Energy System program in collaboration with the Digital Reactor Technology & Development department. The DSS data processing algorithm has been coded within the RAVEN framework along with other metrics and postprocessing models. The implemented code was tested using a gravity-driven draining tank draining case modeled in RELAP5-3D and generated data was successfully postprocessed based on the scaling analyses defined by DSS. Postprocessed data concluded less agreement for the tank exit velocity and indicated that the modeled input deck for RELAP5-3D requires modification to enforce minimal pressure differential effects to the draining process.
97 MATHEMATICS AND COMPUTING↗
Stability of interconnected dynamical systems described on Banach spaces
New stability results for a large class of interconnected dynamical systems (also called composite systems or large scale systems) described on Banach spaces are established. In the present approach, the objective is always the same: to analyze large scale systems in terms of their lower order and simpler subsystems and in terms of their interconnecting structure. The present results provide a systematic procedure of analyzing hybrid dynamical systems (i.e., systems that are described by a mixture of different types of equations). To demonstrate the method of analysis advanced, two specific examples are considered.
Rasmussen, R. D.↗
Online real-time learning of dynamical systems from noisy streaming data
Abstract Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: (a) it allows for online real-time monitoring of a dynamical system; (b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; (c) it is computationally fast and less intensive than the popular extended dynamic mode decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the chaotic attractor of the Henon map, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.
97 MATHEMATICS AND COMPUTING↗
A self-learning rule base for command following in dynamical systems
In this paper, a self-learning Rule Base for command following in dynamical systems is presented. The learning is accomplished though reinforcement learning using an associative memory called SAM. The main advantage of SAM is that it is a function approximator with explicit storage of training samples. A learning algorithm patterned after the dynamic programming is proposed. Two artificially created, unstable dynamical systems are used for testing, and the Rule Base was used to generate a feedback control to improve the command following ability of the otherwise uncontrolled systems. The numerical results are very encouraging. The controlled systems exhibit a more stable behavior and a better capability to follow reference commands. The rules resulting from the reinforcement learning are explicitly stored and they can be modified or augmented by human experts. Due to overlapping storage scheme of SAM, the stored rules are similar to fuzzy rules.
Tsai, Wei K.↗
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.↗
Some notions of decentralization and coordination in large-scale dynamic systems
Some notions of decentralization and coordination in the control of large-scale dynamic systems are discussed. Decentralization and coordination have always been important concepts in the study of large systems. Roughly speaking decentralization is the process of dividing a large problem into subproblems so that it can be handled more easily. Coordination is the manipulation of the subproblem so that the original problem is solved. The various types of decentralization and coordination that have been used to control dynamic systems are discussed. The emphasis was to distinguish between on-line and off-line operations to understand the results available by indicating the aspects of the problem which are decentralized.
Chong, C. Y.↗
Real parameter margin computation for uncertain structural dynamic systems
This paper is concerned with the problem of computing real parameter margins for stabilized, structural dynamic systems with the masses, spring constants, and damping constants as uncertain parameters. Numerical algorithms for uncertain systems with multilinear parameters are investigated. It is shown that for a certain class of structural dynamic systems with small passive damping (e.g., flexible structures in space), the computational complexity of the problem can be avoided by modeling the system as a conservative plant, without loss of any practical significance.
Wie, Bong↗
Per-phase Phasor Modeling of GFL and GFM Inverters for Distribution System Dynamic Studies
A significant increase in inverter-based distributed energy resources (DERs) is expected in the near future. Existing electromagnetic models and sequential electromechanical models of DERs supporting dynamic analysis cannot be extended to largescale three-phase distribution systems usually with unbalanced construction. As such, there is a need for appropriate industry models that can support distribution system dynamic studies. This paper describes the latest phasor models of grid-following (GFL) and grid-forming (GFM) inverters that can capture distribution system dynamics under grid disturbances. The overall modeling performance is examined and compared with results from other platforms such as controller hardware-in-the-loop (CHIL), MATLAB/Simulink and PSCAD with electromagnetic transient (EMT) and/or phasor simulation capabilities under balanced and unbalanced faults.
Distribution system, Grid modelling, GridLAB-D, Po↗
Study on determining stability domains for nonlinear dynamical systems Final report 1 May 1966 - 1 Feb. 1967
Numerical procedure for determining stability domains in nonlinear dynamical systems
NUMERICAL ANALYSIS↗
Constraint Embedding Technique for Multibody System Dynamics
Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.
Woo, Simon S.↗
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↗
Application of the Tool for Turbine Engine Closed-Loop Transient Analysis (TTECTrA) for Dynamic Systems Analysis
The aircraft engine design process seeks to achieve the best overall system-level performance, weight, and cost for a given engine design. This is achieved by a complex process known as systems analysis, where steady-state simulations are used to identify trade-offs that should be balanced to optimize the system. The steady-state simulations and data on which systems analysis relies may not adequately capture the true performance trade-offs that exist during transient operation. Dynamic Systems Analysis provides the capability for assessing these trade-offs at an earlier stage of the engine design process. The concept of dynamic systems analysis and the type of information available from this analysis are presented in this paper. To provide this capability, the Tool for Turbine Engine Closed-loop Transient Analysis (TTECTrA) was developed. This tool aids a user in the design of a power management controller to regulate thrust, and a transient limiter to protect the engine model from surge at a single flight condition (defined by an altitude and Mach number). Results from simulation of the closed-loop system may be used to estimate the dynamic performance of the model. This enables evaluation of the trade-off between performance and operability, or safety, in the engine, which could not be done with steady-state data alone. A design study is presented to compare the dynamic performance of two different engine models integrated with the TTECTrA software.
systems analysis↗
Biased estimation for dynamic systems.
Optimization and regulation of static and dynamic systems require good estimates of the states of the system model and the parameters of the model in the presence of input and measurement noise. A biased estimator is proposed as an alternative to the familiar best linear unbiased estimator. Depending on the value of a constant, this biased estimator can be made unbiased and is then identical to the best linear unbiased estimator, thus permitting additional freedom of choice in design and application. The sum of squared errors of this bs tmator can be less than the best linear unbiased case. An existence theorem is established and various properties are discussed.
Chang, J. W.↗