Noyan Turkkan

Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme.

Reliability of a standby system with beta-distributed component lives

The exact distribution of the sum of 2 independent beta variables is presented. It is applied to a standby system with beta-distributed component lives and permits the calculation of its exact reliability when the exact parameters-values are known. It appreciably improves the current approximate method. >

Determination of exact sample sizes in the Bayesian estimation of the difference of two proportions

Using generalized hypergeometric functions in several variables in a Bayesian context, we compute the exact minimum double-sample size (n 1 , n 2 ) required in the Bernoulli sampling of two independent populations, so that the expected length (or the maximum length) of the highest posterior density credible interval of P = P 1 - P 2 is less than a preset quantity, where P 1 and P 2 are two independent proportions. This precise and computer-intensive approach permits the treatment of this Bayesian sample size determination problem under very general hypotheses and also provides a relationship between the minimal values of n 1 and n 2 . Similar results are derived in an applied Bayesian decision theory context, with a quadratic loss function, and the criteria used are now the posterior risk, the Bayes risk and the expected value of sample information.

System Stress-Strength Reliability: The Multivariate Case

Present day complex systems with dependence between their components require more advanced models to evaluate their reliability. We compute the reliability of a system consisting of two subsystems S 1, and S2 connected in series, where the reliability of each subsystem is of general stress-strength type, defined by R1 = P(A TX > BTY). A & B are column-constant vectors, and strength X & stress Y are multigamma random vectors, i.e. (X, Y) ~ MG (alpha, beta), where alpha and beta are k-dimensional constant vectors. A Bayesian approach is adopted for R2 = P(B TW > 0), where W is multinormal, i.e. W ~ MN(mu, T), with the mean vector mu, and the precision matrix T having a joint s-normal-Wishart prior distribution. Final computations are carried out by simulation, an approach which plays a major role in this article. The results obtained show that the approach adopted can deal effectively with the dependence between components of X & Y

Bounds for the Bayes Error in Classification: A Bayesian Approach Using Discriminant Analysis

We study two of the classical bounds for the Bayes error Pe, Lissack and Fu’s separability bounds and Bhattacharyya’s bounds, in the classification of an observation into one of the two determined distributions, under the hypothesis that the prior probability χ itself has a probability distribution. The effectiveness of this distribution can be measured in terms of the ratio of two mean values. On the other hand, a discriminant analysis-based optimal classification rule allows us to derive the posterior distribution of χ, together with the related posterior bounds of Pe.

Flood analysis and flood projections under climate change in New Brunswick

Floods events are a key component in river engineering including the design and risk assessment of various projects. In this study, a flood frequency analysis was carried out to determine flood characteristics in New Brunswick under present and future climate. For current flood characteristics, an analysis was carried out using 56 hydrometric stations across the province using the Generalized Extreme Value (GEV) distribution and the three-parameter lognormal distribution function. A regional flood frequency analysis was also carried out using regression equations. Results showed that current regional flood equations were very consistent among distribution functions. Results were also consistent with previous studies. To study floods under climate change, seven catchments were selected within the province and these catchments were further analyzed using artificial neural network (ANN) models for two climate scenarios. As such, future climate data were extracted from the third-generation Coupled Climate Model (CGCM3.1) under the greenhouse gas emission scenarios B1 and A2. The climate variables (temperature and precipitation) were downscaled using the delta change approach, and future river discharges were predicted. A frequency analysis was then carried out on these seven stations using the GEV distribution function. Results showed that for the period 2010–2100, average temperatures are projected to increase between 2.9°C (B1) and 5.2°C (A2) in New Brunswick. As for precipitation, the mean annual precipitation showed an increase of 9 to 12% compared to current conditions. Results also showed an increase in flood flows. The increase in low-return floods (e.g. 2-year) was generally higher than the increase of higher return floods (e.g. 100-year). Depending on the scenario and the future time period, the increase in low-return floods was about 30%, and about 15% for higher return floods. A Regional Climate Index (RCI) was used to links floods to their frequency under future climate scenarios.