Kalman-type filtering methods are mostly designed based on exact knowledge of the system’s model with known parameters. In real applications, there may be considerable amount of uncertainties about the model structure, physical parameters, level of noise, and initial conditions. In order to overcome such difficulties, robust state estimation techniques are recommended. This PhD thesis presents a novel robust state estimation method that is referred to as the 2nd-order smooth variable structure filter (2nd-order SVSF) and satisfies the first and second order sliding conditions. It is an extension to the 1st-order SVSF introduced in 2007. In the 1st-order SVSF chattering is reduced by using a smoothing boundary layer; however, the 2nd-order SVSF alleviates chattering by preserving the second order sliding condition. It reduces the estimation error and its first difference until the existence boundary layer is reached. Then after, it guarantees that the estimation error and its difference remain bounded given bounded noise and modeling uncertainties. As such, the 2nd-order SVSF produces more accurate and smoother state estimates under highly uncertain conditions than the 1st-order version. The main issue with the 2nd-order SVSF is that it is not optimal in the mean square error sense. In order to overcome this issue, the dynamic 2nd-order SVSF is initially presented based on a dynamic sliding mode manifold. This manifold introduces a variable cut-off frequency coefficient that adjusts the filter bandwidth. An optimal derivation of the 2nd-order SVSF is then obtained by minimizing the state error covariance matrix with respect to the cut-off frequency matrix. An experimental setup of an electro-hydrostatic actuator is used to compare the performance of the 2nd-order SVSF and its optimal version with other estimation methods such as the Kalman filter and the 1st-order SVSF. Experiments confirm the superior performance of the 2nd-order SVSF given modeling uncertainties. / Thesis / Doctor of Philosophy (PhD)

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24575号 / 工博第5081号 / 新制||工||1973(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 大崎 純, 教授 池田 芳樹, 准教授 藤田 皓平 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24741号 / 情博第829号 / 新制||情||139(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 教授 太田 快人, 教授 永持 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The currently available distribution-free confidence interval for a difference of medians in a within-subjects design requires an unrealistic assumption of identical distribution shapes. A confidence interval for a general linear function of medians is proposed for within-subjects designs that do not assume identical distribution shapes. The proposed method can be combined with a method for linear functions of independent medians to provide a confidence interval for a linear function of medians in mixed designs. Simulation results show that the proposed methods have good small-sample properties under a wide range of conditions. The proposed methods are illustrated with examples, and R functions that implement the new methods are provided.

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Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust against non-normality. It is known that the kurtosis of the distribution of the source data can affect the performance of the tests for variance. We review the classical tests and their latest, more robust modifications, some other tests that have recently appeared in the literature, and use bootstrap and permutation techniques to test for equal variances. We compare the performance of these tests under different types of distributions, sample sizes and true ratios of variances of the populations. Monte-Carlo methods are used in this study to calculate empirical powers and type I errors under different settings.

Ever since the design and manufacture of products moved from the craftsman era where individual craftsman designed and manufactured the entire product, to the mass production era, where skilled laborers were crafting interchangeable parts or in some cases single features on interchangeable parts, variation in assemblies has been a major concern to designers, manufacturers, and in a more subtle way, customers. Variation, in the end, affects quality, performance and the cost of products. One particular type of design that is particularly robust to variation is an exactly constrained design. Several researchers have recently explored the topic of exact constraint design. An exactly constrained design is one in which each degree of freedom is constrained by a single constraint until the desired degrees of freedom for the design is attained. One attractive advantage of exactly constrained designs is that they are robust to variation. However, exactly constrained designs often require nesting forces to maintain the configuration of the design. This research develops a method for designing features that will supply robust nesting forces such that the advantages of the exactly constrained design are preserved. The method developed in this work takes advantage of a proven method for tolerance analysis and enhances this method to include the analysis of these features that supply nesting forces. Along with the enhancement, principles are developed that aid this analysis. All the examples provided in this work are verified using comparisons to Monte Carlo simulations. The comparisons show good results, typically less than 2% difference from the Monte Carlo simulations, verifying that this method accurately predicts variation and allows for the robust design of features that supply the nesting forces in exactly constrained assemblies.

The detection of variable stars in open clusters is an essential component of testing stellar structure and evolution theories. The ability to detect low-amplitude variability among cluster members is directly related to the quality of the photometric results. Point Spread Function (PSF) fitting is the best method available for measuring accurate magnitudes within crowded fields of stars, while high-precision differential photometry is the preferred technique for removing the effects of atmospheric extinction and variable seeing. In the search for new variable stars among hundreds or thousands of stars, the Robust Median Statistic (RoMS) is proven more effective for finding low-amplitude variables than the traditional error curve approach. A reputable computer program called DAOPHOT was used to perform PSF fitting, whereas programs, CLUSTER and RoMS, were created to carry out high-precision differential photometry and calculate the RoMS, respectively, on the open clusters NGC 225, NGC 559, NGC 6811, NGC 6940, NGC 7142, and NGC 7160. Twenty-two new variables and eighty-seven suspected variable stars were discovered, and time-series data of the new variables are presented.

When approaching a new research problem, we often use screening designs to determine which factors are worth exploring in more detail. Before exploring a problem, we don't know which factors are important. When examining a large number of factors, it is likely that only a handful are significant and that even fewer two-factor interactions will be significant. If there are important interactions, it is likely that they are connected with the handful of significant main effects. Since we don't know beforehand which factors are significant, we want to choose a design that gives us the highest probability a priori of being able to estimate all significant main effects with their associated two-factor interactions. This project examines the methodology of finding designs that do not rely on an assumed model. We propose a method of modifying the D-Optimality criteria that averages over models with a common set of main effects and varying subsets of two-factor interations. We also calculate the proportion of the subsets that produce estimable designs. We use these results to find the best models for given run size and number of main effects.