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Register a new userGreatly enhancing the modeling accuracy for distributed parameter systems by nonlinear time/space separation
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An effective modeling method for nonlinear distributed parameter systems (DPSs) is critical for both physical system analysis and industrial engineering. In this Rapid Communication, we propose a novel DPS modeling approach, in which a high-order nonlinear Volterra series is used to separate the time/space variables. With almost no additional computational complexity, the modeling accuracy is improved more than 20 times in average comparing with the traditional method.
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We report progress in the development of a model-based hybrid probabilistic approach to an on-board IVHM for solid rocket boosters (SRBs) that can accommodate the abrupt changes of the model parameters in various nonlinear dynamical off-nominal regimes. The work is related to the ORION mission program. Specifically, a case breach fault for SRBs is considered that takes into account burning a hole through the rocket case, as well as ablation of the nozzle throat under the action of hot gas flow. A high-fidelity model (HFM) of the fault is developed in FLUENT in cylindrical symmetry. The results of the FLUENT simulations are shown to be in good agreement with quasi-stationary approximation and analytical solution of a system of one-dimensional partial differential equations (PDEs) for the gas flow in the combustion chamber and in the hole through the rocket case.
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range %of parameters of dynamical models. It is applied to clinically measured blood pressure signal for the simultaneous inference of the strength, directionality, and the noise intensities in the nonlinear interaction between the cardiac and respiratory oscillations.
The space-time representation of high-dimensional dynamical systems that have a well defined characteristic time scale has proven to be very useful to deepen the understanding of such systems and to uncover hidden features in their output signals. Genuine analogies between one-dimensional (1D) spatially extended systems (1D SESs) and time delayed systems (TDSs) have been observed, including similar pattern formation and propagation of localized structures. An open question is if such analogies are limited to the space-time representation, or, if it is possible to reconstruct similar attractors, from the time series of an observed variable. In this work we address this issue by considering a bistable 1D SES and two TDSs (a bistable system and a model of two lasers with time delayed coupling). In these three examples we find that we can reconstruct the underlying attractor in a three-dimensional pseudo-space, where the evolution is governed by a polynomial potential. We also discuss the limitations of the analogy between 1D SESs and TDSs.
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C.Y. Chen (Dept. of Physics
, Beijing University of Aeronautics andn Astronautics
, Beijing
2000
On contrary to the customary thought, the well-known ``lemma that the distribution function of a collisionless Boltzmann gas keeps invariant along a molecules path represents not the strength but the weakness of the standard theory. One of its consequences states that the velocity distribution at any point is a condensed ``image of all, complex and even discontinuous, structures of the entire spatial space. Admitting the inability to describe the entire space with a microscopic quantity, this paper introduces a new type of distribution function, called the solid-angle-average distribution function. With help of the new distribution function, the dynamical behavior of collisionless Boltzmann gas is formulated in terms of a set of integrals defined by molecular paths. In the new formalism, not only that the difficulties associated with the standard theory are surmounted but also that some of practical gases become calculable in terms of todays computer.
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