Long Time Prediction of Uncertain Systems Using Singular Perturbation

2017 ◽  
Vol 25 (05) ◽  
pp. 707-721
Author(s):  
Ehsan Harati ◽  
Hossein Ahmadi Noubari
Keyword(s):  
Singular Perturbation ◽  
Polynomial Chaos ◽  
Time Integration ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Time Prediction ◽  
Integration Error ◽  
Computational Load ◽  
Long Time ◽  
Long Time Integration

This paper considers the problem of long time prediction of uncertain dynamic systems. Spectral methods such as polynomial chaos expansion (PCE) provides a suitable alternative for classical Monte Carlo method with lower computational load. However, polynomial chaos expansion has a major drawback of long time integration error. In this paper, we will apply singular perturbation (SP) method for reducing long time integration error. Using SP the accuracy of long time predictions are improved with comparable computational load. We will apply SP to illustrative exemplify problems to show effectiveness of our approach. Moreover, we will illustrate application of SP together with a model order reduction tool to reduce long time integration error as applied to distributed parameter.

scholarly journals Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics

2010 ◽  
Vol 28 (1) ◽  
pp. 199-226 ◽  
Author(s):  
Olivier P. Le Maître ◽  
◽  
Lionel Mathelin ◽  
Omar M. Knio ◽  
M. Yousuff Hussaini ◽  
...  
Keyword(s):  
Polynomial Chaos ◽  
Time Integration ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Periodic Dynamics

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Lyes Nechak ◽  
Sébastien Berger ◽  
Evelyne Aubry
Keyword(s):  
Dry Friction ◽  
Polynomial Chaos ◽  
Time Integration ◽  
General Setting ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
Long Time ◽  
Long Time Integration ◽  
Complex Nonlinear Systems ◽  
Friction Parameters

The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

scholarly journals Clutter Cancellation and Long Time Integration for GNSS-Based Passive Bistatic Radar

2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Author(s):  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
Time Integration ◽  
Detection Performance ◽  
Bistatic Radar ◽  
Detection Range ◽  
Robust Detection ◽  
Coherent Integration ◽  
Long Time ◽  
Long Time Integration

Clutter cancellation and long time integration are two vital steps for global navigation satellite system (GNSS)-based bistatic radar target detection. The former eliminates the influence of direct and multipath signals on the target detection performance, and the latter improves the radar detection range. In this paper, the extensive cancellation algorithm (ECA), which projects the surveillance channel signal in the subspace orthogonal to the clutter subspace, is first applied in GNSS-based bistatic radar. As a result, the clutter has been removed from the surveillance channel effectively. For long time integration, a modified version of the Fourier transform (FT), called long-time integration Fourier transform (LIFT), is proposed to obtain a high coherent processing gain. Relative acceleration (RA) is defined to describe the Doppler variation results from the motion of the target and long integration time. With the estimated RA, the Doppler frequency shift compensation is carried out in the LIFT. This method achieves a better and robust detection performance when comparing with the traditional coherent integration method. The simulation results demonstrate the effectiveness and advantages of the proposed processing method.

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