• Title/Summary/Keyword: Nonlinear Curve Interpolation

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Control Method for the Tool Path in Aspherical Surface Grinding and Polishing

  • Kim, Hyung-Tae;Yang, Hae-Jeong;Kim, Sung-Chul
    • International Journal of Precision Engineering and Manufacturing
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    • v.7 no.4
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    • pp.51-56
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    • 2006
  • This paper proposes a control algorithm, which is verified experimentally, for aspherical surface grinding and polishing. The algorithm provides simultaneous control of the position and interpolation of an aspheric curve. The nonlinear formula for the tool position was derived from the aspheric equation and the shape of the tool. The function was partitioned at specific intervals and the control parameters were calculated at each control section. The position, acceleration, and velocity at each interval were updated during the process. A position error feedback was introduced using a rotary encoder. The feedback algorithm corrected the position error by increasing or decreasing the feed speed. In the experimental verification, a two-axis machine was controlled to track an aspherical surface using the proposed algorithm. The effects of the control and process parameters were monitored. The results demonstrated that the maximum tracking error with tuned parameters was at the submicron level for concave and convex surfaces.

Multi-mode cable vibration control using MR damper based on nonlinear modeling

  • Huang, H.W.;Liu, T.T.;Sun, L.M.
    • Smart Structures and Systems
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    • v.23 no.6
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    • pp.565-577
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    • 2019
  • One of the most effective countermeasures for mitigating cable vibration is to install mechanical dampers near the anchorage of the cable. Most of the dampers used in the field are so-called passive dampers where their parameters cannot be changed once designed. The parameters of passive dampers are usually determined based on the optimal damper force obtained from the universal design curve for linear dampers, which will provide a maximum additional damping for the cable. As the optimal damper force is chosen based on a predetermined principal vibration mode, passive dampers will be most effective if cable undergoes single-mode vibration where the vibration mode is the same as the principal mode used in the design. However, in the actual engineering practice, multi-mode vibrations are often observed for cables. Therefore, it is desirable to have dampers that can suppress different modes of cable vibrations simultaneously. In this paper, MR dampers are proposed for controlling multi-mode cable vibrations, because of its ability to change parameters and its adaptability of active control without inquiring large power resources. Although the highly nonlinear feature of the MR material leads to a relatively complex representation of its mathematical model, effective control strategies can still be derived for suppressing multi-mode cable vibrations based on nonlinear modelling, as proposed in this paper. Firstly, the nonlinear Bouc-wen model is employed to accurately portray the salient characteristics of the MR damper. Then, the desired optimal damper force is determined from the universal design curve of friction dampers. Finally, the input voltage (current) of MR damper corresponding to the desired optimal damper force is calculated from the nonlinear Bouc-wen model of the damper using a piecewise linear interpolation scheme. Numerical simulations are carried out to validate the effectiveness of the proposed control algorithm for mitigating multi-mode cable vibrations induced by different external excitations.

Stress analysis of ventricular myocarda according to heart pressure in diastole using finite element method (유한요소법을 이용하여 확장기때 압력에 따른 심실심근의 응력 해석)

  • Han, Geun-Jo;Kim, Sang-Hyun;Shin, Jung-Woog
    • Proceedings of the KOSOMBE Conference
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    • v.1994 no.05
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    • pp.131-135
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    • 1994
  • In order to study the shape and dimensions of heart, the procedures to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images is studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and optimization techniques which compare the computer predicted 3D deformation with the experimentally determined deformation. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed.

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Method of Deciding Elastic Modulus of Left and Right Ventricle Reconstructed by Echocardiography Using Finite Element Method and Stress Analysis

  • Han, Geun-Jo;Kim, Sang-Hyun
    • Journal of Biomedical Engineering Research
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    • v.15 no.2
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    • pp.217-224
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    • 1994
  • In order to study the shape and dimensions of heart, a procedure to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images was studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and by optimization techniques which compared the computer predicted 3D deformation with the experimentally determined deformation. Elastic modulus ranged from 3.5g/$cm^2$ at early diastole to l53g/$cm^2$ at around end diastole showing slightly nonlinear relationship between the modulus and the pressure. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed. The maximum and minimum of ${\sigma}_1$ (max. principal stress) occurred at nodes on the second level intersection points of x-axis with endocardium and with epicardium, respectively. And the tendency of the interventricular septum to be flattened was observed from the compressive ${\sigma}_1$ on the anterior, posterior nodes of left ventricle and from the most significant change of dimension in $D_{RL}$ (septal-lateral dimension of right ventricle).

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A Study on the Control Method for the Tool Path of Aspherical Surface Grinding and Polishing (비구면 연삭 및 연마를 위한 공구 경로 제어에 관한 연구)

  • Kim, Hyung-Tae;Yang, Hae-Jeong;Kim, Sung-Chul
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.1 s.178
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    • pp.113-120
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    • 2006
  • This paper proposed the control algorithm fur aspheric surface grinding and was verified by the experiment. The functions of the algorithm were simultaneous control of the position and interpolation of the aspheric curve. The non-linear formula of the tool position was derived from the aspheric equations and the shape of the tool. The function was partitioned by an certain interval and the control parameters were calculated at each control section. The movement in a session was interpolated with acceleration and velocity. The position error was feed-backed by rotary encorder. The concept of feedback algorithm was correcting position error by increasing or decreasing the speed. In the experiment, two-axis machine was controlled to track the aspheric surface by the proposed algorithm. The effect of the control and process parameters was monitored. The result showed that the maximum tracking error was under sub-micro level for the concave and convex surfaces.

Nonlinear analysis of prestressed concrete structures considering slip behavior of tendons

  • Kwak, Hyo-Gyoung;Kim, Jae-Hong;Kim, Sun-Hoon
    • Computers and Concrete
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    • v.3 no.1
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    • pp.43-64
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    • 2006
  • A tendon model that can effectively be used in finite element analyses of prestressed concrete (PSC) structures with bonded tendons is proposed on the basis of the bond characteristics between a tendon and its surrounding concrete. Since tensile forces between adjacent cracks are transmitted from a tendon to concrete by bond forces, the constitutive law of a bonded tendon stiffened by grouting is different from that of a bare tendon. Accordingly, the apparent yield stress of an embedded tendon is determined from the bond-slip relationship. The definition of the multi-linear average stress-strain relationship is then obtained through a linear interpolation of the stress difference at the post-yielding stage. Unlike in the case of a bonded tendon, on the other hand, a stress increase beyond the effective prestress in an unbonded tendon is not section-dependent but member-dependent. The tendon stress unequivocally represents a uniform distribution along the length when the friction loss is excluded. Thus, using a strain reduction factor, the modified stress-strain curve of an unbonded tendon is derived by successive iterations. The validity of the proposed two tendon models is verified through correlation studies between analytical and experimental results for PSC beams and slabs.

Dynamic Temperature Compensation System Development for the Accelerometer with Modified Spline Interpolation (Curve Fitting) (변형 스플라인 보간법(곡선맞춤)을 통한 가속도 센서의 동적 온도 보상 시스템 개발)

  • Lee, Hoochang;Go, Jaedoo;Yoo, Kwangho;Kim, Wanil
    • Transactions of the Korean Society of Automotive Engineers
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    • v.22 no.3
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    • pp.114-122
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    • 2014
  • Sensor fusion is the one of the main research topics. It offers the highly reliable estimation of vehicle movement by processing and mixing several sensor outputs. But unfortunately, every sensor has drift which degrades the performance of sensor. It means a single degraded sensor output may affect whole sensor fusion system. Drift in most research is ideally assumed to be zero because it's usually a nonlinear model and has sample variation. Plus, it's very difficult for the acceleration to separate drift from the output signal since it contains many contributors such as vehicle acceleration, slope angle, pitch angle, surface condition and so on. In this paper, modified spline interpolation is introduced as a dynamic temperature compensation method covering sample variation. Using the last known output and the first initial output is suggested to build and update compensation factor. When the system has more compensation data, the system will have better performance of compensated output because of the regression compensation model. The performance of the dynamic temperature compensation system is evaluated by measuring offset drift between with and without the compensation.

Structural damage identification with output-only measurements using modified Jaya algorithm and Tikhonov regularization method

  • Guangcai Zhang;Chunfeng Wan;Liyu Xie;Songtao Xue
    • Smart Structures and Systems
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    • v.31 no.3
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    • pp.229-245
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    • 2023
  • The absence of excitation measurements may pose a big challenge in the application of structural damage identification owing to the fact that substantial effort is needed to reconstruct or identify unknown input force. To address this issue, in this paper, an iterative strategy, a synergy of Tikhonov regularization method for force identification and modified Jaya algorithm (M-Jaya) for stiffness parameter identification, is developed for damage identification with partial output-only responses. On the one hand, the probabilistic clustering learning technique and nonlinear updating equation are introduced to improve the performance of standard Jaya algorithm. On the other hand, to deal with the difficulty of selection the appropriate regularization parameters in traditional Tikhonov regularization, an improved L-curve method based on B-spline interpolation function is presented. The applicability and effectiveness of the iterative strategy for simultaneous identification of structural damages and unknown input excitation is validated by numerical simulation on a 21-bar truss structure subjected to ambient excitation under noise free and contaminated measurements cases, as well as a series of experimental tests on a five-floor steel frame structure excited by sinusoidal force. The results from these numerical and experimental studies demonstrate that the proposed identification strategy can accurately and effectively identify damage locations and extents without the requirement of force measurements. The proposed M-Jaya algorithm provides more satisfactory performance than genetic algorithm, Gaussian bare-bones artificial bee colony and Jaya algorithm.

Scenario-based 3D Objects Synthesizing System Design

  • Nam, Ji-Seung;Gao, Hui;Kang, Mi-Young;Kim, Kyoung-Tae;Son, Seung-Chul;Pom, Chung-Ung;Heo, Kwon
    • Journal of Information Processing Systems
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    • v.2 no.1
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    • pp.18-22
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    • 2006
  • This paper proposes the framework of the scenario-based 3D image synthesizing system that allows common users who envision a scenario in their mind to realize it into the segments of cool animation. We focused on utilization of the existing motions to synthesize new motions for the objects. The framework is useful to build a 3D animation in game programming with a limited set of 3D objects. We also propose a practical algorithm to reuse and expand the objects. This algorithm is based on motion path modification rules. Both linear and nonlinear curve-fitting algorithms were applied to modify an animation by key frame interpolation and to make the motion appear realistic.

Effective buckling length of steel column members based on elastic/inelastic system buckling analyses

  • Kyung, Yong-Soo;Kim, Nam-Il;Kim, Ho-Kyung;Kim, Moon-Young
    • Structural Engineering and Mechanics
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    • v.26 no.6
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    • pp.651-672
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    • 2007
  • This study presents an improved method that uses the elastic and inelastic system buckling analyses for determining the K-factors of steel column members. The inelastic system buckling analysis is based on the tangent modulus theory for a single column and the application is extended to the frame structural system. The tangent modulus of an inelastic column is first derived as a function of nominal compressive stress from the column strength curve given in the design codes. The tangential stiffness matrix of a beam-column element is then formulated by using the so-called stability function or Hermitian interpolation functions. Two inelastic system buckling analysis procedures are newly proposed by utilizing nonlinear eigenvalue analysis algorithms. Finally, a practical method for determining the K-factors of individual members in a steel frame structure is proposed based on the inelastic and/or elastic system buckling analyses. The K-factors according to the proposed procedure are calculated for numerical examples and compared with other results in available references.