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In this thesis we introduce and study an A-optimal minimax design criterion for two-level fractional factorial designs, which can be used to estimate a linear model with main effects and some interactions. The resulting designs are called A-optimal minimax designs, and they are robust against the misspecification of the terms in the linear model. They are also efficient, and often they are the same as A-optimal and D-optimal designs. Various theoretical results about A-optimal minimax designs are derived. A couple of search algorithms including a simulated annealing algorithm are discussed to search for optimal designs, and many interesting examples are presented in the thesis. / Graduate / 0463 / yinyue@uvic.ca

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

The European Commission 6th Framework Project COCOMAT (Improved MATerial Exploitation at Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse) was a four and a half year project (2004 to mid-2008) aimed at exploiting the large reserve of strength in composite structures through more accurate prediction of collapse. In the experimental work packages, significant statistical variation in buckling behaviour and ultimate loading were encountered. The variations observed in the experimental results were not predicted in the finite element analyses that were done in the early stages of the project. The work undertaken in this thesis to support the COCOMAT project was initiated when it was recognised that there was a gap in knowledge about the effect of initial defects and variations in the input variables of both the experimental and simulated panels. The work involved the development of stochastic algorithms to relate variations in boundary conditions, material properties and geometries to the variation in buckling modes and loads up to first failure. It was proposed in this thesis that any future design had to focus on the dominant parameters affecting the statistical scatter in the results to achieve lower sensitivity to variation. A methodology was developed for designing stiffened composite panels with improved robustness. Several panels tested in the COCOMAT project were redesigned using this approach to demonstrate its applicability. The original contributions from this thesis are therefore the development of a stochastic methodology to identify the impact of variation in input parameters on the response of stiffened composite panels and the development of Robust Indices to support the design of new panels. The stochastic analysis included the generation of metamodels that allow quantification of the impact that the inputs have on the response using two first order variables, Influence and Sensitivity. These variables are then used to derive the Robust Indices. A significant outcome of this thesis was the recognition in the final report for COCOMAT that the development of a validated robust index should be a focus of any future design of postbuckling stiffened panels.

The goal when applying robust engineering design methods is to improve a system's quality by reducing its sensitivity to uncertainty that has influence on the performance of the product. In the Robust Concept Exploration Method (RCEM) this approach is facilitated with additionally giving the designer the possibility to search for a compromise between the desired performance and a satisfying robustness. The current version of the RCEM, however, has some limitations that render it inapplicable for nonlinear design problems. These limitations, which are demonstrated in this thesis, are mainly connected to the application of global response surfaces and the Taylor series for variance estimations. In order to analyze the limitation of the robustness estimation, several alternative methods are developed, assessed and introduced to a modified RCEM. The developed Multiple Point Method is based on the Sensitivity Index (SI) and improves the variance estimation in RCEM significantly, especially for nonlinear problems. This approach is applicable to design problems, for which the performance functions are known explicitly. For problems that require simulations for the performance estimation, the simulation-based RCEM is developed by introducing the Probabilistic Collocation Method (PCM) to robust concept exploration. The PCM is a surrogate model approach, which generates local response models around the points of interests with a minimum number of simulation runs. Those models are utilized in the modified-RCEM for the uncertainty analysis of the system's performance. The proposed methods are tested with two examples each. The modified RCEM is validated with an artificial design problem as well as the design of a robust pressure vessel. The simulation-based RCEM is validated using the same artificial design problem and the design of a robust multifunctional Linear Cellular Alloy (LCA) heat exchanger for lightweight applications such as mobile computing. The structure of the theoretical and empirical validation of the methods follows the validation square.

L’objectif ultime de ce travail de thèse est d’évaluer la possibilité de valider et d’optimiser un processus de fabrication en utilisant la simulation numérique en tenant compte des incertitudes irréductibles sur le procédé, les matériaux et la géométrie du produit fabriqué. La prise en compte des incertitudes nécessite de quantifier les effets des variations des paramètres du modèle sur les sorties de celui-ci, en propageant ces variations via la simulation numérique pour évaluer leurs effets sur les sorties. Dans ce travail nous avons proposé une procédure pour déterminer le seuil de sensibilité du modèle numérique afin de construire des plans d’expériences numériques cohérents avec ce seuil. Nous avons également montré que, compte tenu des incertitudes sur les matériaux et la géométrie du produit, il est possible d’optimiser certains paramètres du procédé pour contrôler les effets des incertitudes sur les variations dimensionnelles et morphologiques du produit. Pour cela, nous avons proposé une procédure d’optimisation basée sur un algorithme NSGA-II et une méta-modélisation du procédé. L’application à l’emboutissage d’une tôle en U, retour élastique inclus, montre qu’il s’agit d’un problème de conception robuste pour lequel nous obtenons l’ensemble des compromis entre l’écart à la moyenne et l’écart type d’une fonction « performance » du procédé correctement choisie. Finalement l’analyse de ces résultats nous permet de quantifier le lien entre la notion de robustesse d’une solution optimisée du procédé et les critères de mesure de la qualité du produit / The ultimate objective of this thesis is to evaluate the possibility to validate and optimize a manufacturing process using numerical simulation and taking into account the irreducible uncertainties in the process, materials and geometry of manufactured product. Taking into account the uncertainties requires quantifying the effects of variations of model parameters on the outputs, by propagating these variations via computer simulation to assess their effects on the outputs. In this work, we have proposed a procedure to determine the sensitivity threshold of the numerical model to build numerical Design of Experiments consistent with this threshold. We have also shown that, given the uncertainties in the materials and the geometry of the product, it is possible to optimize certain process parameters to control the effects of uncertainties on the dimensional and morphological variations of the product. For this, we have proposed an optimization procedure based on NSGA-II algorithm and a meta-modeling of the process. The application for deep drawing of a U-shaped sheet metal part, springback included shows that it is a robust design problem for which we get all the compromise between the deviation from the mean and standard deviation of a "performance" depending on the process correctly chosen. Finally, the analysis of these results allows us to quantify the relationship between the notion of robustness of an optimized solution of the process and criteria for measuring the quality of the product

This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs. Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling. The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses. The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing. / ROBDES

Semi-Solid Metal (SSM) casting is a promising technology offering an opportunity to manufacture net-shape, complex geometry metal components in a single operation. However, the absence of foundry guidelines and limited design data for SSM casting makes it challenging to predict the performance of both process and components. The objective of this research was to develop and offer new solutions to material processing-related issues in the electronics industry. By investigating the opportunities afforded by the recently developed RheoMetalTM rheocasting process, a better understanding of the critical factors needed for an effective manufacturing process and optimised component characteristics was achieved. A study of the evolution of microstructure at different stages of the RheoMetalTM process demonstrated the influence of multistage solidification on the microstructural characteristics of the rheocast components. The microstructure of a slurry consists of the solute-lean and coarse globular α-Al particles with a uniform distribution of alloying elements, suspended in the liquid matrix. Additional solute-rich α-Al particles were identified as being a consequence of discrete nucleation events taking place after the initial slurry production. In the final components, macrosegregation was observed in the form of variations in the ratio of solute-lean coarse globular α-Al particles and solute-rich fine α-Al particles in both longitudinal and transverse directions. The relation between microstructural characteristics and material properties was established by determination of the local properties of a rheocast component. The fracture of a rheocast telecom component was strongly affected by microstructural inhomogeneity. In particular, macrosegregation in the form of liquid surface segregation bands and sub-surface pore bands strongly affected the fracture behaviour. Thermal conductivity measurements revealed that regions of the component with a high amount of solute-lean globular α-Al particles showed higher thermal conductivity. The effect of the local variation in thermal conductivity on the thermal performance of a large rheocast heatsink was evaluated by simulation. The results clearly show the importance of considering material inhomogeneity when creating a robust component design.

The Swedish car manufacturer, Volvo Cars, are a pioneer in the automotive industry regarding vehicle safety. Ever since they invented the three-point seat belt, the safety aspect has been their main priority. Today, a car is equipped with new technology and is highly dependent on software solutions. This implies that software features are used to increase the safety of the car. The level of uncertainty increases with the new features, which highlights the importance of creating a robust product to avoid potential problems. During the last decade, the DCOV approach (Define – Characterize – Optimize – Verify) evolved to create a product that is insensitive to variation and appreciated by the customers. Volvo Cars are currently developing a camera monitoring system (CMS) that is supposed to replace the conventional rear-view mirror with an exterior camera and an interior display. The purpose of this master’s thesis is to develop a robust design for the CMS that satisfies the customers. By using the DCOV approach, the aim is to identify potential risks and failure modes to avoid hardware and software related problems, and at the same time, develop a product that is based on the voice of the customer. This thesis demonstrates the problems with the conventional mirrors and the parking assistance cameras, which are associated with the folding function, the mirror adjustment, and the wide-angle module. The analysis of customer surveys indicates that blind spot indicators are appreciated by the customers while the mirror size is a critical factor. The mirrors need to be large enough to provide a good rear-view visibility, but small enough to maintain good forward visibility. A parameter diagram, robustness checklist and a system failure mode and effect analysis (S-FMEA) were conducted to identify risks, noise factors and failure modes with the CMS. It resulted in 44 failure modes where six of them were considered as critical, which means a high level of severity or frequent occurrence. The six critical failure modes were identified at the S-FMEA meetings with the business units Manufacturing, Display systems, Electromagnetic compatibility and CMS camera. Three business units were software related, which shows the difficulties with the transition from a hardware related rear-view mirror to the CMS. The recommendations for Volvo Cars are divided into two categories, where the first is associated with the CMS and should be seen as a continuation of this thesis. Volvo Cars should complete the S-FMEA and the included actions. By conducting the recommendations for the CMS, it will be properly tested to resist noise factors and manage potential variation. The long-term recommendations are proposals for future actions, which include a CMS for the inner mirror and investigate BLIS options. If the recommendations are considered, it will increase the possibility of creating a robust design, based on the voice of the customer. The result of this study highlights the power of the DCOV approach, as it clearly shows that it is possible to reduce the warranty costs. If the folding function is excluded, and the CMS software becomes easy to update, the warranty costs could be reduced by SEK 5 million.

Examensarbetets mål är att utveckla och konstruera en ny uppkopplingslösning för motorer som genomgår kvalitetssäkring hos Volvo Lastvagnar. Examensarbetet är genomfört som den avslutande delen av studierna på maskiningenjörsprogrammet på Högskolan i Skövde. Ökade kundkrav på tillverkningsföretag har lett till ökade krav på individanpassade produkter. Detta sätter större krav på produktvariationer som i sin tur leder till produktionsvariationer. Volvo Lastvagnar tillverkar idag en stor mängd motorvarianter som ställer ökade krav på en mer flexibel anslutningslösning för att koppla upp dessa motorvarianter för kvalitetssäkring och testkörning. Dagens uppkopplingslösning är bristfällig, improviserad och icke flexibel. Volvo Lastvagnar har uttryckt en önskan att förbättra uppkopplingen av turboaggregatets avgashus vid kvalitetssäkringsprocessen inför en effektivisering av motorprovet. Projektet inleddes med en omfattande litteraturstudie för att undersöka hur produktionsvariation och krav på en mer flexibel uppkoppling kan lösas genom produktdesign. Variationerna som påverkade uppkopplingen mellan de olika motorerna kartlades och lades som grund för vidare arbete. Flertalet koncept gällande hantering av motorvariatoner togs fram och utvärderades med hjälp av 3D-printade prototyper. Ett slutgiltigt koncept beräknades, dimensionerades och konstruerades. Resultatet visade att det går att möta den stora produktionsvariationen med hjälp av robust design. Resultatet visade också att dagens uppkoppling är överdimensionerad och bristfällig. Författarna till denna rapport rekommenderar Volvo Lastvagnar att fortsätta arbetet med att implementera uppkopplingslösningen i produktion för att utföra verkliga tester och optimera lösningen ytterligare. / The goal of the thesis work is to develop and construct a new solution for connecting engines that goes through a quality check at the testing facility at Volvo Trucks. The thesis work is the final segment of the mechanical engineering program at the University of Skövde. Growing demands within manufacturing have led to higher requirements regarding customized products. This puts a higher demand on product variety which leads to greater varieties in production. Volvo Trucks manufactures a variety of engines which requires a more flexible way of connecting these different types of engines in the testing facility for testing and quality checks. The current state of this connection is inadequate, improvised and non-flexible. Volvo Trucks have expressed a wish to improve the quality- and testing process regarding the exhaust connection of the engines, as Volvo Trucks are planning a future reconstruction of the testing facility. The project started by performing an extensive literature review to investigate how variety in production and demands for a more flexible connection can be solved through product design. The variations that affected the connection between the different motor types and the testing facility were documented and used as a foundation for further work. A number of concepts regarding the handling of the different motor types were developed and reviewed with 3D-printed prototypes. A final concept was calculated, dimensioned and constructed. The result shows that it is possible to handle the vast variation in production with the help of robust design. The result also showed that the present connections are oversized and insufficient. The authors of this report recommend that Volvo Trucks should continue with implementing the new connection in production to perform tests and develop this connection further.