Quasi-parallelized Multicanonical Monte Carlo Method for Highly Nonlinear Systems, with Application to All-optical Regeneration

2011 ◽  
Author(s):  
Taras I. Lakoba ◽  
Michael Vasilyev ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Nonlinear Systems ◽  
Highly Nonlinear ◽  
All Optical ◽  
Optical Regeneration

scholarly journals An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

2007 ◽  
Vol 135 (1) ◽  
pp. 186-202 ◽  
Author(s):  
T. M. Chin ◽  
M. J. Turmon ◽  
J. B. Jewell ◽  
M. Ghil
Keyword(s):  
Monte Carlo ◽  
Nonlinear Systems ◽  
Ensemble Kalman Filter ◽  
Nonlinear Problems ◽  
Monte Carlo Algorithm ◽  
Operational Mode ◽  
Highly Nonlinear ◽  
Non Gaussian ◽  
Double Well Potential ◽  
Full Probability

Abstract Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Robust Framework for the Computed Torque Control of Nondeterministic Multibody Dynamic Systems

2016 ◽  
Author(s):  
Sahand Sabet ◽  
Mohammad Poursina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Feedback Linearization ◽  
Torque Control ◽  
Control Law ◽  
Mathematical Framework ◽  
Computed Torque Control ◽  
Highly Nonlinear ◽  
Multibody Problems ◽  
Computed Torque

Considering uncertainty is inarguably a crucial aspect of dynamic analysis, design, and control of a mechanical system. When it comes to multibody problems, the effect of uncertainty in the system’s parameters and excitations becomes even more significant due to the accumulation of inaccuracies. For this reason, this paper presents a detailed research on the use of the Polynomial Chaos Expansion (PCE) method for the control of nondeterministic multibody systems. PCE is essentially a way to compactly represent random variables. In this scheme, each stochastic response output and random input is projected onto the space of appropriate independent orthogonal polynomial basis functions. In the field of robotics, a required task is to force robotic arms to follow designated paths. Controlling such systems usually leads to difficulties since the dynamic equations of multibody problems are highly nonlinear. Computed Torque Control Law (CTCL) is able to overcome these difficulties by using feedback linearization to evaluate the required torque/force at any time to make the system follow a trajectory. In this paper, a mathematical framework is introduced to apply the Computed Torque Control Law to a multibody system with uncertainty. Surprisingly, it is shown that using this control scheme, uncertainty in geometry does not affect the closed-loop equations of controlled systems. Both the intrusive PCE method and the Monte Carlo approach are used to control a fully actuated two-link planar elbow arm where each link is required to follow a specified path. Lastly, a comparison of the time efficiency and accuracy between the traditionally used Monte Carlo method and the intrusive PCE is presented. The results indicate that the intrusive PCE approach can provide better accuracy with much less computation time than the Monte Carlo method.

All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber

2003 ◽  
Vol 15 (7) ◽  
pp. 957-959 ◽  
Author(s):  
S. Radic ◽  
C.J. McKinstrie ◽  
R.M. Jopson ◽  
J.C. Centanni ◽  
A.R. Chraplyvy
Keyword(s):  
Optical Fiber ◽  
Nonlinear Optical ◽  
Parametric Amplifiers ◽  
Highly Nonlinear ◽  
All Optical ◽  
Optical Regeneration

Land subsidence prediction with uncertainty analysis by a smoother algorithm with a multiple calibration-constrained null-space Monte Carlo method

2020 ◽  
Author(s):  
Masaatsu Aichi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Uncertainty Analysis ◽  
Land Subsidence ◽  
Null Space ◽  
Hysteretic Behavior ◽  
Model Ensemble ◽  
Highly Nonlinear ◽  
Modified Cam Clay ◽  
Ensemble Smoother

<p>Predicting the future land subsidence caused by groundwater abstraction is necessary for the planning and decision-making of groundwater usage in coastal area. Although numerical modeling is expected to quantitatively predict land subsidence, a single calibrated model cannot provide a reliable prediction because of the uncertainty on properties and conditions in the subsurface. In addition, applying ensemble Kalman filter or ensemble smoother to land subsidence modeling is not straightforward because of the highly nonlinear and hysteric characteristics in clay compaction process.</p><p>This study developed a smoother algorithm with a multiple calibration-constrained null-space Monte Carlo method for a numerical simulator of groundwater mass balance with modified Cam-clay model. The developed algorithm calibrates a model ensemble using a newly obtained observed value in each observation step. Based on the calibration-constrained null-space Monte Carlo method, a new model ensemble in the null-space is produced in each observation step. In this step, both the current and past state as well as parameters in the model are updated like ensemble smoother in order to follow the hysteretic behavior in the soil compaction. The produced ensemble can be used not only for prediction uncertainty analysis at that step but also as initial estimates of a multiple calibration-constrained null-space Monte Carlo method in the next observation step.</p><p>The proposed method was applied to the land subsidence modeling in the Tokyo lowland area, Japan. The proposed method could make model ensemble with satisfactory good reproducibility and show the range of uncertainty of future prediction for several scenarios of future groundwater level change.</p>

Probability Calculation of Spatial Chaos Appearance in MIMO Cascade Nonlinear Systems Using Monte Carlo Method

2019 ◽  
Vol 29 (11) ◽  
pp. 1950149
Author(s):  
Biljana Samardzic ◽  
Bojana M. Zlatkovic
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Nonlinear Systems ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Spatial Phase ◽  
Spatial Chaos ◽  
Probability Calculation

In this work, Monte Carlo method is used for the probability calculation of the appearance of spatial chaos in MIMO cascade nonlinear systems. The obtained results are given in tables and presented graphically using probability histograms. Their validity is confirmed by comparison with the results of spatial chaos appearance analysis that uses bifurcation diagrams, Lyapunov diagrams and spatial phase portraits.

All-optical regeneration based on highly nonlinear photonic crystal fiber

2008 ◽  
Vol 1 (1-2) ◽  
pp. 79-84
Author(s):  
Yongzhao Xu ◽  
Yanfen Wei ◽  
Xiaomin Ren ◽  
Xia Zhang ◽  
Yongqing Huang
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Crystal Fiber ◽  
Nonlinear Photonic Crystal ◽  
Highly Nonlinear ◽  
All Optical ◽  
Optical Regeneration

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

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