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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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗
DOE OSTI2024

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗
NASA NTRS1971

Closed-loop control of stochastic nonlinear systems

Technique resolves problems in complex control systems, such as those used for space vehicle guidance and control. Main disadvantage of procedure is that it is only appropriate in situations where trajectory concept is valid.

Schmidt, G. T.↗
NASA NTRS1982

Implicit numerical integration for periodic solutions of autonomous nonlinear systems

A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.

Thurston, G. A.↗
NASA NTRS1992

Control of nonlinear systems using terminal sliding modes

The development of an approach to control synthesis for robust robot operations in unstructured environments is discussed. To enhance control performance with full model information, the authors introduce the notion of terminal convergence and develop control laws based on a class of sliding modes, denoted as terminal sliders. They demonstrate that terminal sliders provide robustness to parametric uncertainty without having to resort to high-frequency control switching, as in the case of conventional sliders. It is shown that the proposed method leads to greater guaranteed precision in all control cases discussed.

Venkataraman, S. T.↗