Many problems in science and engineering are solved through experimental investigations. Because experiments can be costly and time consuming, it is important to efficiently design the experiment so that maximum information about the problem can be obtained. It is also important to devise efficient statistical methods to analyze the experimental data so that none of the information is lost. This thesis makes contributions on several aspects in the field of design and analysis of experiments. It consists of two parts. The first part focuses on physical experiments, and the second part on computer experiments. The first part on physical experiments contains three works. The first work develops Bayesian experimental designs for robustness studies, which can be applied in industries for quality improvement. The existing methods rely on modifying effect hierarchy principle to give more importance to control-by-noise interactions, which can violate the true effect order of a system because the order should not depend on the objective of an experiment. The proposed Bayesian approach uses a prior distribution to capture the effect hierarchy property and then uses an optimal design criterion to satisfy the robustness objectives. The second work extends the above Bayesian approach to blocked experimental designs. The third work proposes a new modeling and design strategy for mixture-of-mixtures experiments and applies it in the optimization of Pringles potato crisps. The proposed model substantially reduces the number of parameters in the existing multiple-Scheffé model and thus, helps the engineers to design much smaller experiments. The second part on computer experiments introduces two new methods for analyzing the data. The first is an interpolation method called regression-based inverse distance weighting (RIDW) method, which is shown to overcome some of the computational and numerical problems associated with kriging, particularly in dealing with large data and/or high dimensional problems. In the second work, we introduce a general nonparametric regression method, called kernel sum regression. More importantly, we make an interesting discovery by showing that a particular form of this regression method becomes an interpolation method, which can be used to analyze computer experiments with deterministic outputs.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23478号 / 工博第4890号 / 新制||工||1764(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 川池 健司, 教授 藤田 正治, 准教授 米山 望 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This thesis focuses on the use of scaled physical experiments to better understand the development and long-term evolution of fault systems that are otherwise impossible to observe directly. The document is divided into three chapters. The first chapter documents the implementation of an inexpensive stereo vision method for acquiring high resolution three-dimensional strain data for table-top experiments. The second chapter applies the stereo vision method to a tectonic problem—the development of slip partitioning in obliquely loaded crustal systems. Slip partitioned fault systems accommodate oblique convergence with different slip rake on two or more faults and are well documented in the crust. In this chapter, we simulate oblique convergence using blocks with 30° dipping contacts under wet kaolin clay. The experiments reveal three styles of slip partitioning development—contingent upon convergence angle and the presence or absence of a pre-existing vertical fault. Across all experiments, the slip rates along slip-partitioned faults vary temporally suggesting that the faults continuously adjust to conditions produced by the other fault. The lack of steady state in the experiments suggests that slip-partitioned crustal systems may also evolve with oscillating behavior rather than developing a single efficient active fault structure to accommodate oblique convergence. The third chapter documents rheological tests of wet kaolin for applications to crustal deformation experiments. This chapter investigates thixotropy in the clay as well as the role of grain size distribution and water content on its shear strength.

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The basic idea of this paper is to outline a cross-curricular approach between mathematics and science. The aim is to close the often perceived gap between formal maths and authentic experience and to increase the students’ versatility in the use of mathematical terms. Students are to experience maths as logical, interesting and relevant through extra-mathematical references. Concrete physical or biological correlations may initiate mathematical activities, and mathematical terms are to be understood in logical contexts. Examples: physical experiments can lead to a comprehensive understanding of the concept of functions and of the intersection of medians in triangles. Biological topics can lead to the concepts of similarity and proportion as well as to the construction of pie charts. In the European ScienceMath Project a variety of teaching modules was developed and tested in secondary schools.

The basic idea of this paper is to outline a cross-curricular approach between mathematics and science. The aim is to close the often perceived gap between formal maths and authentic experience and to increase the students’ versatility in the use of mathematical terms. Students are to experience maths as logical, interesting and relevant through extra-mathematical references. Concrete physical or biological correlations may initiate mathematical activities, and mathematical terms are to be understood in logical contexts. Examples: physical experiments can lead to a comprehensive understanding of the concept of functions and of the intersection of medians in triangles. Biological topics can lead to the concepts of similarity and proportion as well as to the construction of pie charts. In the European ScienceMath Project a variety of teaching modules was developed and tested in secondary schools.