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Robust Nonparametric Regression Method using Rank Transformation

    • Communications for Statistical Applications and Methods
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    • v.7 no.2
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    • pp.574-574
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    • 2000
  • Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

Robust Nonparametric Regression Method using Rank Transformation

  • Park, Dongryeon
    • Communications for Statistical Applications and Methods
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    • v.7 no.2
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    • pp.575-583
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    • 2000
  • Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

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Approximation of a compound surface to polyhedral model (복합곡면의 다면체 곡면 근사)

  • 김영일;전차수;조규갑
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1996.04a
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    • pp.100-103
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    • 1996
  • Presented in this study is an algorithmic procedure to obtain polyhedral model from a compound surface. The compound surface in this study denotes a collection of trimmed surfaces without topological relations. The procedure consists of two main modules: CAD data interface, and surface conversion to polyhedral model. The interface module gets geometric information from CAD databases, and makes topological information by scanning the geometric information. We are investigating CATIA system as a data source system. In the surface conversion module, a shell(compound surface with topological information) is approximated to a triangular-faceted polyhedral surface model through node sampling and triangulation steps. The obtained polyhedral model should obey the vertex-to-vertex rule and meet tolerance requirements. Since the polyhedral model has a simple data structure and geometry processing for it is very efficient and robust, the polyhedral model can be used in various applications, such as surface rendering in computer graphics, FEM model for engineering analysis, CAPP for surface machining, data generation for SLA, and NC tool path generation.

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Capacity Planning and Control of Probe Process in Semiconductor Manufacturing (반도체 Probe 공정에서의 생산 능력 계획)

  • Jeong, Bong-Ju;Lee, Young-Hoon
    • IE interfaces
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    • v.10 no.1
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    • pp.15-22
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    • 1997
  • In semiconductor manufacturing, the probe process between fabrication and assembly process is constrained mostly by the equipment capacity because most products pass through the similar procedures. The probe process is usually performed in a batch mode with relatively short cycle times. The capability of the probe process can be determined by the optimal combination of the equipments and the products. A probe line usually has several types of equipment with different capacity. In this study, the probe line is modeled in terms of capacity to give the efficient planning and control procedure. For the practical usage, the hierarchical capacity planning procedure is used. First, a monthly capacity plan is made to meet the monthly production plan of each product. Secondly, the daily capacity planning is performed by considering the monthly capacity plan and the daily fabrication output. Simple heuristic algorithms for daily capacity planning are developed and some experimental results are shown.

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A neural network approach for simulating stationary stochastic processes

  • Beer, Michael;Spanos, Pol D.
    • Structural Engineering and Mechanics
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    • v.32 no.1
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    • pp.71-94
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    • 2009
  • In this paper a procedure for Monte Carlo simulation of univariate stationary stochastic processes with the aid of neural networks is presented. Neural networks operate model-free and, thus, circumvent the need of specifying a priori statistical properties of the process, as needed traditionally. This is particularly advantageous when only limited data are available. A neural network can capture the "pattern" of a short observed time series. Afterwards, it can directly generate stochastic process realizations which capture the properties of the underlying data. In the present study a simple feed-forward network with focused time-memory is utilized. The proposed procedure is demonstrated by examples of Monte Carlo simulation, by synthesis of future values of an initially short single process record.

Classes of exact solutions for several static and dynamic problems of non-uniform beams

  • Li, Q.S.
    • Structural Engineering and Mechanics
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    • v.12 no.1
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    • pp.85-100
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    • 2001
  • In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

A Improved Method of Determining Everett Function with Logarithm Function and Least Square Method

  • Hong, Sun-Ki
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.22 no.7
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    • pp.16-21
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    • 2008
  • For Preisach model, Everett function from the transient curves is needed to simulate the hysteresis phenomena. However it becomes very difficult to get the function if the it would be made only from experiments. In this paper, a simple and stable procedure using least square method and logarithm function to determine the Everett function which follows the Gauss distribution for interaction field axis is proposed. The characteristics of the parameters used in this procedure are also presented. The proposed method is applied to implement hysteresis loops. The simulation for hysteresis loop is compared with experiments and good agreements could be shown.

Application of computational technologies to R/C structural analysis

  • Hara, Takashi
    • Computers and Concrete
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    • v.8 no.1
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    • pp.97-110
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    • 2011
  • In this paper, FEM procedure is applied to the static and dynamic analyses of R/C structures. Simple R/C shell structure is solved by using FEM procedures and the experimental evaluations are performed to represent the applicability of FEM procedure to R/C structures. Also, R/C columns are analyzed numerically and experimentally. On the basis of these results, FEM procedures are applied to the R/C cooling tower structures assembled by huge R/C shell structure and a lot of discrete R/C columns. In this analysis, the parallel computing procedures are introduced into these analyses to reduce the computational effort. The dynamic performances of R/C cooling tower are also solved by the application of parallel computations as well. From the numerical analyses, the conventional FEM procedures combined with computational technologies enables us to design the huge R/C structures statically and dynamically.

A dynamical stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures

  • Falsone, Giovanni;Ferro, Gabriele
    • Structural Engineering and Mechanics
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    • v.23 no.6
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    • pp.599-613
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    • 2006
  • A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

Damage Location Detection by Using Variation of Flexibility and its Sensitivity to Measurement Errors (유연도 변화를 이용한 연속교의 손상부위 추정 및 민감도 해석)

  • 최형진;백영인;이학은
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1996.10a
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    • pp.138-146
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    • 1996
  • The presence of a damage, such as a crack, in a structure increases the flexibility and damping in the structure. Most of methods to detect damage or damage location uses stiffness matrix of the structural system. The modification of stiffness matrix, however, has complicated procedures to identify structural. system in the basis of finite element model and has too many degree of freedom to calculate. Identification of changes of flexibility of structure can offer damage information immediately and simple procedure can employ real time continuous monitoring system. To identify changes of the flexibility, vibration mode shapes and natural frequencies are usually used. In this paper, a procedure for damage location in continuous girder bridges using vibration data is described. The effectiveness and sensitivity of the presented method to measurement errors in mode shapes and natural frequencies are investigated using analytical results from finite element models. It is shown that the errors in the first mode shape and first natural frequency demonstrate much larger influence than those in the higher mode shapes and modal frequencies.

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