• Journal of the Korean Magnetics Society
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• v.25 no.6
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• pp.203-207
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• 2015

This paper introduces a probabilistic analysis method in order to analyze the effect of manufacturing tolerance on induction motor performance occurring in massive production. The univariate dimension reduction method is adapted to predict probabilistic characteristics of a performance function due to certain probabilistic distributions of design variables. Moreover, the sensitivity information on mean and variance of the performance function is estimated, and then the effect of randomness of individual design variables on the probability performance function is analyzed. The effectiveness and accuracy of the method is investigated with a mathematical model and an induction motor.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.659-669
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• 2021

Multivariate regression often appears in longitudinal or functional data analysis. Since multivariate regression involves multi-dimensional response variables, it is more strongly affected by the so-called curse of dimension that univariate regression. To overcome this issue, Yoo (2018) and Yoo (2019a) proposed three model-based response dimension reduction methodologies. According to various numerical studies in Yoo (2019a), the default method suggested in Yoo (2019a) is least sensitive to the simulated models, but it is not the best one. To release this issue, the paper proposes an selection algorithm by comparing the other two methods with the default one. This approach is called principal selected response reduction. Various simulation studies show that the proposed method provides more accurate estimation results than the default one by Yoo (2019a), and it confirms practical and empirical usefulness of the propose method over the default one by Yoo (2019a).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.113-118
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• 2009

A designer regards the vibration system as a linear system. However, in real world, nonlinearity of a vibration system should exist caused by various factors like manufacturing conditions or uncertain material properties. So, properties of a spring and a damper which are consisting the vibration system have statistical distribution. Therefore, a designer needs to analyze the statistical nonlinearity in a vibration system. In this paper, $1^{st}$ Taylor series expansion method and univariate dimension reduction method apply to a performance measure of nonlinear vibration system, and compare each result. And then, merits and demerits of each method are discussed. For apply more actual problem, a performance measure population is estimated based on design variable samples like properties of spring or damper.

• Journal of the Korean Magnetics Society
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• v.26 no.3
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• pp.81-85
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• 2016

This paper introduces a performance integration method to predict variation characteristic of a performance function of electromagnetic machines or devices due to manufacturing tolerances. A normalized performance function space and a hybrid mean value technique are adapted to effectively predict mean and variance, which can identify probabilistic distribution of the performance function. To verify the effectiveness and accuracy of the proposed method, a mathematical problem and a loudspeaker model are tested, and numerical results are compared with those of existing methods such as Monte Carlo simulation and univariate dimension reduction method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.745-752
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• 2009

In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.