Uncertainty Analysis of Nondeterministic Multibody Systems

2016 ◽  
Author(s):  
Sahand Sabet ◽  
Mohammad Poursina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Kinematic Analysis ◽  
Multibody Systems ◽  
Computation Time ◽  
Open Loop ◽  
Mathematical Framework ◽  
Uncertain Parameters ◽  
Response Output ◽  
Forward Kinematic

This paper presents the method of polynomial chaos expansion (PCE) for the forward kinematic analysis of non-deterministic multibody systems. Kinematic analysis of both open-loop and closed-loop systems are presented. The PCE provides an efficient mathematical framework to introduce uncertainty to the system. This is accomplished by compactly projecting each stochastic response output and random input onto the space of appropriate independent orthogonal polynomial basis functions. This paper presents the detailed formulation of the kinematics of constrained multibody systems at the position, velocity, and acceleration levels in the PCE scheme. This analysis is performed by projecting the governing kinematic constraint equations of the system onto the space of appropriate polynomial base functions. Furthermore, forward kinematic analysis is conducted at the position, velocity, and acceleration levels for a non-deterministic four-bar mechanism with single and multiple uncertain parameters and a SCARA robot. Also, the convergence of the PCE and Monte Carlo methods is analyzed in this paper. Time efficiency and accuracy of the intrusive PCE approach are compared with the traditionally used Monte Carlo method. The results demonstrate the drastic increase in the computation time of Monte Carlo method when analyzing complex systems with a large number of uncertain parameters while the intrusive PCE provides better accuracy with much less computational complexity.

Forward Kinematic Analysis of Non-Deterministic Articulated Multibody Systems With Kinematically Closed-Loops in Polynomial Chaos Expansion Scheme

2015 ◽  
Author(s):  
Sahand Sabet ◽  
Mohammad Poursina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Kinematic Analysis ◽  
Multibody Systems ◽  
Polynomial Chaos ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Closed Loops ◽  
Base Functions ◽  
Forward Kinematic

This paper presents the method of polynomial chaos expansion (PCE) for the forward kinematic analysis of nondeterministic multibody systems with kinematically closed-loops. The PCE provides an efficient mathematical framework to introduce uncertainty to the system. This is accomplished by compactly projecting each stochastic response output and random input onto the space of appropriate independent orthogonal polynomial base functions. This paper presents the detailed formulation of the kinematics of a constrained multibody system at the position, velocity, and acceleration levels in the PCE scheme. This analysis is performed by projecting the governing kinematic constraint equations of the system onto the space of appropriate polynomial base functions. Furthermore, forward kinematic analysis is conducted at the position, velocity, and acceleration levels for a non-deterministic four-bar mechanism with single and multiple uncertain parameters in the length of linkages of the system. Time efficiency and accuracy of the intrusive PCE approach are compared with the traditionally used Monte Carlo method. The results demonstrate the drastic increase in the computational time of Monte Carlo method when analyzing complex systems with a large number of uncertain parameters while the intrusive PCE provides better accuracy with much less computation complexity.

Equation Solving DRESOR Method for Radiative Transfer in Three-Dimensional Isotropically Scattering Media

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Zhifeng Huang ◽  
Huaichun Zhou ◽  
Guihua Wang ◽  
Pei-feng Hsu
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Computation Time ◽  
Discrete Ordinates ◽  
Distinct Advantage ◽  
Reverse Monte Carlo ◽  
Scattering Media ◽  
Equation Solving ◽  
Radiative Intensity ◽  
The Monte Carlo Method

Distributions of ratios of energy scattered or reflected (DRESOR) method is a very efficient tool used to calculate radiative intensity with high directional resolution, which is very useful for inverse analysis. The method is based on the Monte Carlo (MC) method and it can solve radiative problems of great complexity. Unfortunately, it suffers from the drawbacks of the Monte Carlo method, which are large computation time and unavoidable statistical errors. In this work, an equation solving method is applied to calculate DRESOR values instead of using the Monte Carlo sampling in the DRESOR method. The equation solving method obtains very accurate results in much shorter computation time than when using the Monte Carlo method. Radiative intensity with high directional resolution calculated by these two kinds of DRESOR method is compared with that of the reverse Monte Carlo (RMC) method. The equation solving DRESOR (ES-DRESOR) method has better accuracy and much better time efficiency than the Monte Carlo based DRESOR (original DRESOR) method. The ES-DRESOR method shows a distinct advantage for calculating radiative intensity with high directional resolution compared with the reverse Monte Carlo method and the discrete ordinates method (DOM). Heat flux comparisons are also given and the ES-DRESOR method shows very good accuracy.

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.

Simulation of chemical processes with uncertain parameters

1983 ◽  
Vol 48 (6) ◽  
pp. 1588-1596 ◽  
Author(s):  
Mirko Dohnal ◽  
Marie Ulmanová
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Flow Rate ◽  
Chemical Processes ◽  
Uncertain Parameters ◽  
Flow Rates ◽  
The Monte Carlo Method ◽  
Sensitivity Studies ◽  
Set Up ◽  
Simulation Problem

An integral part of the simulation problem are numerical values of parameters or constants of industrial units. Either these quantities need not be known accurately or it is not possible to control them at the set up value. The result of simulation cannot be then accurate. It is necessary to determine the region in which the flow rates of components through branches could change when the parameters and constants change. For these purposes is applicable the Monte Carlo method. But it is very time-consuming. Here, algorithms are proposed which with the use of the algebraic norm approximately determine the looked-for set of flow rate uncertainty. These algorithms can be applied for solution of a number of practical problems related with optimum sizing of units, sensitivity studies etc. An example is given of a cooling cascade cycle.

Stochastic Integration Methods: Comparison and Application to Reliability Analysis

2012 ◽  
Author(s):  
M. Paffrath ◽  
U. Wever
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Reliability Analysis ◽  
Crack Growth ◽  
Computation Time ◽  
Comparison Of Methods ◽  
Stochastic Integration ◽  
Integration Methods ◽  
Further Development ◽  
Academic Test

A central part of stochastic computations (e.g. of moments or of failure probabilities) is the evaluation of multi-dimensional integrals. The crude Monte-Carlo method is often too expensive in terms of computation time. In this paper a comparison of methods is made for a collection of test examples. The considered methods are numerical sparse grid methods either known from literature or some further development of known methods. Apart from some academic test examples, the performance of the methods is studied for integrals arising in the area of stochastic crack growth.

Monte Carlo Simulation of Radiation in Gases With a Narrow-Band Model and a Net-Exchange Formulation

1996 ◽  
Vol 118 (2) ◽  
pp. 401-407 ◽  
Author(s):  
M. Cherkaoui ◽  
J.-L. Dufresne ◽  
R. Fournier ◽  
J.-Y. Grandpeix ◽  
A. Lahellec
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Computation Time ◽  
Band Model ◽  
One Dimensional ◽  
The Monte Carlo Method ◽  
Reflecting Surfaces ◽  
Heat Transfers ◽  
Narrow Band Model

The Monte Carlo method is used for simulation of radiative heat transfers in nongray gases. The proposed procedure is based on a Net-Exchange Formulation (NEF). Such a formulation provides an efficient way of systematically fulfilling the reciprocity principle, which avoids some of the major problems usually associated with the Monte Carlo method: Numerical efficiency becomes independent of optical thickness, strongly nonuniform grid sizes can be used with no increase in computation time, and configurations with small temperature differences can be addressed with very good accuracy. The Exchange Monte Carlo Method (EMCM) is detailed for a one-dimensional slab with diffusely or specularly reflecting surfaces.

Simulation Based Estimation of Extreme Response of Floating Offshore Structures

2007 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai ◽  
P. S. Teigen
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Saddle Point ◽  
Computation Time ◽  
Offshore Structures ◽  
Saddle Point Method ◽  
Response Level ◽  
Random Seas ◽  
The Monte Carlo Method ◽  
Extreme Response

The paper presents a study of the extreme response statistics of a tension leg platform (TLP) subjected to random seas. Two different approaches are compared: A numerical integration method based on saddle point integration and the Monte Carlo method. While the saddle point method is a mathematically attractive technique, which gives numerically very accurate results at low computational costs at any response level, the advantage of the Monte Carlo method is its simplicity and versatility. It is demonstrated in this paper that the commonly assumed obstacle against using the Monte Carlo method for estimating extreme responses, i.e. excessive CPU time, can be circumvented, bringing the computation time down to affordable levels. The agreement between the two approaches is shown to be remarkably good.

Error Analysis of Closed-Loop Control for Spacecraft Orbital Transfer Using Monte Carlo Method

2013 ◽  
Vol 765-767 ◽  
pp. 1998-2003
Author(s):  
Yang Zhou ◽  
Ye Yan ◽  
Xu Huang ◽  
Teng Yi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Error Analysis ◽  
Closed Loop ◽  
Open Loop ◽  
Closed Loop Control ◽  
Orbital Transfer ◽  
Loop Control ◽  
True State ◽  
Correction Maneuver

The true trajectory of spacecraft disperses from the nominal due to kinds of errors and perturbations, including environment, actuator and sensor uncertainties. This paper studies the error analysis problem of closed-loop control for spacecraft orbital transfer via Monte Carlo method. At first, errors that affect the true state are introduced and a navigation-target-correction loop system for Monte Carlo simulation is built. A dynamical model for orbital transfer is established, based on which both the extended Kalman filter (EKF) algorithm and correction maneuver control algorithm are developed. Precision analysis is studied of high eccentric orbital (HEO) transfer under open-loop and closed-loop control respectively. The simulation results prove the validity of the proposed method.

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