Design and Analysis of Monte Carlo Experiments

monte carlo experiments;simulation models;mathematical analysis;sensitivity analysis;experimental design

Numerical Simulation and Customized DACM Based Design Optimization

PhD thesis in Offshore technologyThe diverse numerical modelling, analysis and simulation tools that have been developed and introduced to markets are intended to perform the virtual design and testing of products and systems without the construction of physical prototypes. Digital prototyping in the form of computer modelling and simulation are important means of numerical model predictions, i.e. design validation and verification. However, as the tools advance to more precise and diverse applications, the operation eventually becomes more complex, computationally expensive and error prone; this is particularly true for complex multi-disciplinary and multidimensional problems; for instance, in multi-body dynamics, Fluid-Structure Interaction (FSI) and high-dimensional numerical simulation problems. On the other hand, integrating design optimization operations into the product and system development processes, through the computer based applications, makes the process even more complex and highly expensive. This thesis analyses and discusses causes of complexity in numerical modelling, simulation and optimization operations and proposes new approaches/frameworks that would help significantly reduce the complexity and the associated computational costs. Proposed approaches mainly integrate, simplify and decompose or approximate complex numerical simulation based optimization problems into simpler, and to metamodel-based optimization problems. Despite advancing computational technologies in continuum mechanics, the design and analysis tools have developed in separate directions with regard to ‘basis functions’ of the technologies until recent developments. Basis functions are the building blocks of every continuous function. Continuous functions in every computational tool are linear combinations of specific basis functions in the function space. Since first introduced, basis functions in the design and modelling tools have developed so rapidly that various complex physical problems can today be designed and modelled to the highest precision. On the other hand, most analysis tools still utilize approximate models of the problems from the latter tools, particularly if the problem involves complex smooth geometric designs. The existing gap between the basis functions of the tools and the increasing precision of models for analysis introduce tremendous computational costs. Moreover, to transfer models from one form of basis function to another, additonal effort is required. The variation of the basis functions also demands extra effort in numerical simulation based optimization processes. This thesis discusses the recently developed integrated modelling and analysis approach that utilizes the state-of-the-art basis function (NURBS function) for both design and analysis. A numerical simulation based shape optimization framework that utilizes the state-of-the-art basis function is also presented in a study in the thesis. One of the common multidisciplinary problem that involves multiple models of domains in a single problem, fluid-structure interaction (FSI) problem, is studied in the thesis. As the name implies, the two models of domains involved in any FSI problems are fluid and structure domain models. In order to solve the FSI problems, usually three mathematical components are needed: namely, i) fluid dynamics model, ii) structural mechanics model and, iii) the FSI model. This thesis presents the challenges in FSI problems and discusses different FSI approaches in numerical analysis. A comparative analysis of computational methods, based on the coupling and temporal discretization schemes, is discussed using a benchmark problem, to give a better understanding of what a multidisciplinary problem is and the challenge for design optimizations that involve such problems. [...

Regression Models and Experimental Designs: A Tutorial for Simulation Analaysts

This tutorial explains the basics of linear regression models. especially low-order polynomials. and the corresponding statistical designs. namely, designs of resolution III, IV, V, and Central Composite Designs (CCDs).This tutorial assumes 'white noise', which means that the residuals of the fitted linear regression model are normally, independently, and identically distributed with zero mean.The tutorial gathers statistical results that are scattered throughout the literature on mathematical statistics, and presents these results in a form that is understandable to simulation analysts.metamodels;fractional factorial designs;Plackett-Burman designs;factor interactions;validation;cross-validation

Predicting amount of saleable products using neural network metamodels of casthouses

This study aims at developing abstract metamodels for approximating highly nonlinear relationships within a metal casting plant. Metal casting product quality nonlinearly depends on many controllable and uncontrollable factors. For improving the productivity of the system, it is vital for operation planners to predict in advance the amount of high quality products. Neural networks metamodels are developed and applied in this study for predicting the amount of saleable products. Training of metamodels is done using the Levenberg-Marquardt and Bayesian learning methods. Statistical measures are calculated for the developed metamodels over a grid of neural network structures. Demonstrated results indicate that Bayesian-based neural network metamodels outperform the Levenberg-Marquardt-based metamodels in terms of both prediction accuracy and robustness to the metamodel complexity. In contrast, the latter metamodels are computationally less expensive and generate the results more quickly

A Methodology for Fitting and Validating Metamodels in Simulation

This expository paper discusses the relationships among metamodels, simulation models, and problem entities. A metamodel or response surface is an approximation of the input/output function implied by the underlying simulation model. There are several types of metamodel: linear regression, splines, neural networks, etc. This paper distinguishes between fitting and validating a metamodel. Metamodels may have different goals: (i) understanding, (ii) prediction, (iii) optimization, and (iv) verification and validation. For this metamodeling, a process with thirteen steps is proposed. Classic design of experiments (DOE) is summarized, including standard measures of fit such as the R-square coefficient and cross-validation measures. This DOE is extended to sequential or stagewise DOE. Several validation criteria, measures, and estimators are discussed. Metamodels in general are covered, along with a procedure for developing linear regression (including polynomial) metamodels.

NUMERICAL MODELING AND OPTIMIZATION OF SINGLE PHASE MANIFOLD-MICROCHANNEL PLATE HEAT EXCHANGER

In recent years manifold-microchannel technology has received considerable attention from the research community as it has demonstrated clear advantage over state of the art heat exchangers. It has the potential to improve heat transfer performance by an order of magnitude while reducing pressure drop penalty equally impressive, when compared to state of the art heat exchangers for selected applications. However, design of heat exchangers based on this technology requires selection of several critical geometrical and flow parameters. This research focuses on the numerical modeling and an optimization algorithm to determine such design parameters and optimize the performance of manifold-microchannels for a plate heat exchanger geometry. A hybrid method was developed to calculate the total pumping power and heat transfer of this type of heat exchangers. The results from the hybrid method were successfully verified with the results obtained from a full CFD model and experimental work. Based on the hybrid method, a multi-objective optimization of the heat exchanger was conducted utilizing an approximation-based optimization technique. The optimized manifold-microchannel flat plate heat exchanger showed superior performance over a Chevron plate heat exchanger which is a wildly used option for diverse applications