In this study we will consider the construction of approximate optimal design for one-dimensional regression by exchange algorithm. Sufficient conditions under which an optimal design must have the minimal support points are known in Theorem 2.3.2 of Fedorov (1972). However, there are only a few cases which the analytic optimal designs are known. The exchange procedure for computing optimal designs is easily adopted to most criteria. We describe implementations for constructing the well-known special cases D-, A-, and c-optimal designs with the minimum number of support points. Examples which illustrate how the algorithm can be used to obtain these optimal designs and the performance of the algorithm are discussed. The commonly used D-, A-, and c-optimal criteria will be employed to study the convergence properties of the exchange algorithm for regression model which the set of the product of regression functions forms a Chebyshev system.

In-process Optical Coordinate Measuring Machine (OCMM) offers the potential of diagnosing in a timely manner variation sources that are responsible for product quality defects. Such a sensor system can help manufacturers improve product quality and reduce process downtime. Effective use of sensory data in diagnosing variation sources depends on the optimal design of a sensor system, which is often known as the problem of sensor placements. This thesis addresses coordinate sensor placement in diagnosing dimensional variation sources in assembly processes. Sensitivity indices of detecting process mean and variance components are defined as the design criteria and are derived in terms of process layout and sensor deployment information. Exchange algorithms, originally developed in the research of optimal experiment deign, are employed and revised to maximize the detection sensitivity. A sort-and-cut procedure is used, which remarkably improve the algorithm efficiency of the current exchange routine. The resulting optimal sensor layouts and its implications are illustrated in the specific context of a panel assembly process.

This dissertation presents a methodology for the near optimal design of fixture layouts in multi-station assembly processes. An optimal fixture layout improves the robustness of a fixture system, reduces product variability and leads to manufacturing cost reduction. Three key aspects of the multi-station fixture layout design are addressed: a multi-station variation propagation model, a quantitative measure of fixture design, and an effective and efficient optimization algorithm. Multi-station design may have high dimensions of design space, which can contain a lot of local optima. In this dissertation, I investigated two algorithms for optimal fixture layout designs. The first algorithm is an exchange algorithm, which was originally developed in the research of optimal experimental designs. I revised the exchange routine so that it can remarkably reduce the computing time without sacrificing the optimal values. The second algorithm uses data-mining methods such as clustering and classification. It appears that the data-mining method can find valuable design selection rules that can in turn help to locate the optimal design efficiently. Compared with other non-linear optimization algorithms such as the simplex search method, simulated annealing, genetic algorithm, the data-mining method performs the best and the revised exchange algorithm performs comparably to simulated annealing, but better than the others. A four-station assembly process for a sport utility vehicle (SUV) side frame is used throughout the dissertation to illustrate the relevant concepts and the resulting methodology.

This dissertation presents a methodology for the near optimal design of fixture layouts in multi-station assembly processes. An optimal fixture layout improves the robustness of a fixture system, reduces product variability and leads to manufacturing cost reduction. Three key aspects of the multi-station fixture layout design are addressed: a multi-station variation propagation model, a quantitative measure of fixture design, and an effective and efficient optimization algorithm. Multi-station design may have high dimensions of design space, which can contain a lot of local optima. In this dissertation, I investigated two algorithms for optimal fixture layout designs. The first algorithm is an exchange algorithm, which was originally developed in the research of optimal experimental designs. I revised the exchange routine so that it can remarkably reduce the computing time without sacrificing the optimal values. The second algorithm uses data-mining methods such as clustering and classification. It appears that the data-mining method can find valuable design selection rules that can in turn help to locate the optimal design efficiently. Compared with other non-linear optimization algorithms such as the simplex search method, simulated annealing, genetic algorithm, the data-mining method performs the best and the revised exchange algorithm performs comparably to simulated annealing, but better than the others. A four-station assembly process for a sport utility vehicle (SUV) side frame is used throughout the dissertation to illustrate the relevant concepts and the resulting methodology.

In-process Optical Coordinate Measuring Machine (OCMM) offers the potential of diagnosing in a timely manner variation sources that are responsible for product quality defects. Such a sensor system can help manufacturers improve product quality and reduce process downtime. Effective use of sensory data in diagnosing variation sources depends on the optimal design of a sensor system, which is often known as the problem of sensor placements. This thesis addresses coordinate sensor placement in diagnosing dimensional variation sources in assembly processes. Sensitivity indices of detecting process mean and variance components are defined as the design criteria and are derived in terms of process layout and sensor deployment information. Exchange algorithms, originally developed in the research of optimal experiment deign, are employed and revised to maximize the detection sensitivity. A sort-and-cut procedure is used, which remarkably improve the algorithm efficiency of the current exchange routine. The resulting optimal sensor layouts and its implications are illustrated in the specific context of a panel assembly process.

abstract: Functional or dynamic responses are prevalent in experiments in the fields of engineering, medicine, and the sciences, but proposals for optimal designs are still sparse for this type of response. Experiments with dynamic responses result in multiple responses taken over a spectrum variable, so the design matrix for a dynamic response have more complicated structures. In the literature, the optimal design problem for some functional responses has been solved using genetic algorithm (GA) and approximate design methods. The goal of this dissertation is to develop fast computer algorithms for calculating exact D-optimal designs. First, we demonstrated how the traditional exchange methods could be improved to generate a computationally efficient algorithm for finding G-optimal designs. The proposed two-stage algorithm, which is called the cCEA, uses a clustering-based approach to restrict the set of possible candidates for PEA, and then improves the G-efficiency using CEA. The second major contribution of this dissertation is the development of fast algorithms for constructing D-optimal designs that determine the optimal sequence of stimuli in fMRI studies. The update formula for the determinant of the information matrix was improved by exploiting the sparseness of the information matrix, leading to faster computation times. The proposed algorithm outperforms genetic algorithm with respect to computational efficiency and D-efficiency. The third contribution is a study of optimal experimental designs for more general functional response models. First, the B-spline system is proposed to be used as the non-parametric smoother of response function and an algorithm is developed to determine D-optimal sampling points of a spectrum variable. Second, we proposed a two-step algorithm for finding the optimal design for both sampling points and experimental settings. In the first step, the matrix of experimental settings is held fixed while the algorithm optimizes the determinant of the information matrix for a mixed effects model to find the optimal sampling times. In the second step, the optimal sampling times obtained from the first step is held fixed while the algorithm iterates on the information matrix to find the optimal experimental settings. The designs constructed by this approach yield superior performance over other designs found in literature. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2015

In this thesis, we study the phenomenon of thermally induced polarisation using a combination of theory and computer simulation. Molecules of sufficiently low symmetry exhibit thermo-molecular orientation when subjected to a temperature gradient, leading to considerable electrostatic fields in polar liquids. Here, we first use non-equilibrium molecular dynamics simulations to study this interesting effect numerically. To this end, we propose an integration algorithm to impose a constant heat flux in simulations and show that it greatly improves energy conservation compared to a previous algorithm. We next investigate the thermal polarisation of water and find that truncation of electrostatic interactions can lead to severe artefacts, such as the wrong sign of polarisation and an overestimation of the electric field. We further show that the quadrupole-moment contribution to the electric field is significant and responsible for an inversion of its sign. To facilitate the theoretical description of electrostatic interactions, we propose a new dipolar model fluid as a perturbation of a Stockmayer fluid. Using this modified Stockmayer model, we provide numerical evidence for the recently proposed phenomenon of thermally induced monopoles. We show that the electrostatic field generated by a pair of heated/cooled colloidal particles immersed in such a solvent can be trivially described by two Coulomb charges. Finally, we propose a mean-field theory to predict the thermo-polarisation effect exhibited by our model fluid theoretically, and demonstrate near quantitative agreement with simulation results.