MONTE CARLO METHODS IN FUZZY NON-LINEAR REGRESSION

2008 ◽  
Vol 04 (02) ◽  
pp. 123-141 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Linear Regression ◽  
Fuzzy Numbers ◽  
Random Number ◽  
Random Number Generator ◽  
Search Space ◽  
Triangular Fuzzy Numbers ◽  
Non Linear ◽  
Regression Problems

We apply our new fuzzy Monte Carlo method to certain fuzzy non-linear regression problems to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider example problems to show that this Monte Carlo method obtains solutions comparable to those obtained by an evolutionary algorithm.

A Modification to the Monte Carlo Method—The Exodus Method

1968 ◽  
Vol 90 (3) ◽  
pp. 328-332 ◽  
Author(s):  
A. F. Emery ◽  
W. W. Carson
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Number ◽  
Random Number Generator ◽  
Number Generator ◽  
Calculation Time ◽  
The Monte Carlo Method

A modification to the Monte Carlo method is described which reduces calculation time and improves the accuracy. This method—termed “Exodus”—is not dependent upon a random number generator and may be applied to any problem which admits of a nodal network.

Application and Implementation of Monte Carlo Method in Mechanical Engineering

2010 ◽  
Vol 26-28 ◽  
pp. 925-930
Author(s):  
Guo Qiang Chen ◽  
Jun Wei Zhao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Mechanical Engineering ◽  
Random Number ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Tolerance Analysis ◽  
Simulation Software ◽  
Development Environment

As a powerful tool for scientific research, Monte Carlo simulation has been utilized widely in mechanical engineering for a long time. The paper reviews the application in statistical tolerance analysis, reliability design and analysis, uncertainty analysis in mechanical measurement, robot error, position and attitude analysis, and optimum design. The implementation of Monte Carlo method is also discussed and classified into three types: using Monte Carlo simulation software directly, programming in the development environment with random number generator, and programming from the basic random number generation. Finally, the authors points out using Monte Carlo software directly is recommend because the engineer needn’t concern the detail of the complex computation and can pay more attention to the purpose of the mechanical application.

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Tao Ren ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Random Number ◽  
Test Cases ◽  
Combustion System ◽  
Absorption Coefficients ◽  
One Dimensional ◽  
The Monte Carlo Method

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

scholarly journals Simulation Modeling in Assessing the Effectiveness and Risk of Investment Projects

2020 ◽  
Vol 22 (1) ◽  
pp. 119-124
Author(s):  
Volodymyr Kharchenko ◽  
◽  
Hanna Kharchenko ◽  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Agricultural Production ◽  
Random Number ◽  
Investment Project ◽  
Average Risk ◽  
Universal Method ◽  
Investment Projects ◽  
The Monte Carlo Method ◽  
The Impact

Introduction. The article deals with the modeling features in the implementation of investment projects using the Monte Carlo method. The purpose of the article is to substantiate the feasibility of using economic and mathematical models to identify the risks of investment projects in agricultural production, taking into account the randomness of factors. Results. The expediency of using this method during the analysis of projects in agriculture is determined. This type of modeling is a universal method of research and evaluation of the effectiveness of open systems, the behavior of which depends on the influence of random factors. Particular attention is paid in such cases to decisions on the implementation of investment projects. The expediency of using this method in the analysis of projects in agriculture is determined. The main characteristics of the investment project are considered: investments involve significant financial costs; investment return can be obtained in a few years; there are elements of risk and uncertainty in forecasting the results of the investment project. The algorithm of the analysis of investment projects consisting of various stages is offered. The importance of investigating the risks of investment projects in agricultural production is substantiated. It is investigated that the basis of the Monte Carlo method is a random number generator, which consists of two stages: generation of a normalized random number (uniformly distributed from 0 to 1) and conversion of a random number into an arbitrary distribution law. The task of choosing an investment project for a pig farm is proposed. The calculations revealed that the amount of the expected NPV is UAH 63,158.80 with a standard deviation of UAH 43,777.90. The coefficient of variation was 0.69, so the risk of this project is generally lower than the average risk of the investment portfolio of the farm. Conclusions. The results of the analysis obtained using the method of Monte Carlo simulation are quite simple to interpret and reflect the change of factors over a significant interval, taking into account the probabilistic nature of economic factors. Thus, this method allows the implementation of the investment project to assess the impact of uncertainty on the final result of the project.

scholarly journals Mortalité du sapin baumier défolié par la tordeuse des bourgeons de l'épinette dans la région de la Gatineau au Québec

1982 ◽  
Vol 58 (5) ◽  
pp. 213-219 ◽  
Author(s):  
Jean Beaulieu ◽  
Yvan J. Hardy
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Least Squares ◽  
Random Number ◽  
Least Squares Method ◽  
Random Number Generator ◽  
Balsam Fir ◽  
Number Generator ◽  
Profit Analysis ◽  
Significant Difference

This paper presents a method of analysis which differentiates between spruce budworm caused mortality and regular mortality on balsam fir in the Gatineau region in Quebec. A first attempt was made using multiple linear regression and a uniform random number generator. In order to overcome the bias inherent to the least squares method when dealing with a binary (0,1) dependent variable, a profit analysis was also conducted. In this case, the parameters and their variance were estimated using likehood method. These two approaches proved to be equivalent when percent budworm caused mortality was compared within the 1958 to 1979 period covered by the data at hand, while the outbreak lasted from 1968 to 1975.In 1979, approximately 55% of the stems had been killed by the budworm, accounting for 53% of the volume. Maple-yellow birch associations were more affected than fir associations although no significant difference was found. Fir mortality was delayed by aerial spraying of insecticides but this advantage disappeared as soon as the spray operations came to an end.

A new random-number generator for multispin Monte Carlo algorithms

1987 ◽  
Vol 48 (1-2) ◽  
pp. 135-149 ◽  
Author(s):  
L. Pierre ◽  
T. Giamarchi ◽  
H. J. Schulz
Keyword(s):  
Monte Carlo ◽  
Random Number ◽  
Random Number Generator ◽  
Number Generator ◽  
Monte Carlo Algorithms

Rate of convergence for computing expectations of stopping functionals of an α-mixing process

1998 ◽  
Vol 30 (2) ◽  
pp. 425-448
Author(s):  
Mohamed Ben Alaya ◽  
Gilles Pagès
Keyword(s):  
Monte Carlo ◽  
Probability Space ◽  
Random Number ◽  
Shift Operator ◽  
Probability Distributions ◽  
Random Number Generator ◽  
Stopping Time ◽  
Mixing Process ◽  
Canonical Process ◽  
Image Position

The shift method consists in computing the expectation of an integrable functional F defined on the probability space ((ℝd)N, B(ℝd)⊗N, μ⊗N) (μ is a probability measure on ℝd) using Birkhoff's Pointwise Ergodic Theorem, i.e. as n → ∞, where θ denotes the canonical shift operator. When F lies in L2(FT, μ⊗N) for some integrable enough stopping time T, several weak (CLT) or strong (Gàl-Koksma Theorem or LIL) converging rates hold. The method successfully competes with Monte Carlo. The aim of this paper is to extend these results to more general probability distributions P on ((ℝd)N, B(ℝd)⊗N), namely when the canonical process (Xn)n∊N is P-stationary, α-mixing and fulfils Ibragimov's assumption for some δ > 0. One application is the computation of the expectation of functionals of an α-mixing Markov Chain, under its stationary distribution Pν. It may both provide a better accuracy and save the random number generator compared to the usual Monte Carlo or shift methods on independent innovations.

scholarly journals FULL QCD ON APE100 MACHINES

1995 ◽  
Vol 06 (01) ◽  
pp. 25-45
Author(s):  
STEFANO ANTONELLI ◽  
MARCO BELLACCI ◽  
ANDREA DONINI ◽  
RENATA SARNO
Keyword(s):  
Monte Carlo ◽  
Random Number ◽  
Random Number Generator ◽  
Memory Capacity ◽  
Monte Carlo Algorithm ◽  
Number Generator ◽  
Inversion Algorithm ◽  
Hybrid Monte Carlo ◽  
Pure Gauge ◽  
Wilson Fermions

We present the first tests and results from a study of QCD with two flavours of dynamical Wilson fermions using the Hybrid Monte Carlo Algorithm (HMCA) on APE100 machines. The simulations have been performed on 64 lattice for the pure gauge HMCA and on 84, 123×32 lattices for full QCD configurations. We discuss the inversion algorithm for the fermionic operator, the methods used to overcome the problems arising using a 32 bit machine and the implementation of a new random number generator for APE100 machines. We propose different scenarios for the simulation of physical observables, with respect to the memory capacity and speed of different APE100 configurations.

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