• Title/Summary/Keyword: Matrix Equations

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A Study on a Sliding Mode Control Algorithm for Dynamic Positioning System of a Vessel (선박의 동적위치유지 시스템을 위한 Sliding Mode 제어 연구)

  • Young-Shik Kim;Jang-Pyo Hong
    • Journal of Navigation and Port Research
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    • v.47 no.4
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    • pp.256-270
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    • 2023
  • In this study, a sliding mode (SM) controller for dynamic positioning (DP) was specifically designed for a turret connection operation of a ship or an offshore structure in which an arbitrary point on the structure could be controlled as the motion center instead of the center of mass. The SM controller allows control of the arbitrary point and provides capability to manage uncertainties in the dynamics of ships and offshore structures, external forces caused by unknown changing marine environments, and transient performance of DP systems. The Jacobian matrix included in kinematic equations of the controlled object was modified to design the SM controller to control based on an arbitrary point of ships or offshore structures. To ensure robustness of the controller, the Lyapunov stability theory was applied in the design of the SM controller. In general, for robustness in DP control, gain scheduling based on a proportional-derivative (PD) control algorithm is employed. However, finding appropriate gains for gain scheduling complicates the application of DP systems. Therefore, in this study, the SM control algorithm was considered to mitigate the complexity of the DP controller for ships and offshore structures. To validate the proposed SM control algorithm, time-domain simulations were conducted and utilized to evaluate the performance of the control algorithm. The effectiveness of the proposed SM controller was assessed by comparing simulation results with results of a conventional PD control algorithm applied in DP control.

Effect of Fine Content on the Monotonic Shear Behavior of Sand-Clay Mixtures (점토와 모래의 혼합토의 정적 전단거동에 대한 세립분 함유율의 영향)

  • Kim, Uk-Gie;Masayuki, Hyodo;Beak, Won-Jin;Ahn, Tae-Bong
    • Journal of the Korean Geotechnical Society
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    • v.23 no.4
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    • pp.91-100
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    • 2007
  • In most design codes, soils are classified as either sand or clay, and appropriate design equations are used to represent their behavior. For example, the behavior of sandy soils is expressed in terms of the relative density, whereas consistency limits are often used for clays. However, sand-clay mixtures, which are typically referred to as intermediate soils, cannot be easily categorized as either sand or clay and therefore a unified interpretation of how the soil will behave at the transition point, i.e., from sandy behavior when fines are low to clay behavior for high fines content, is necessary. In this study, active natural clays are mixed with sand, and the fines content varied in order to produce different structures, ranging from one state where only sand particles form the soil structure to another where the matrix of fines make-up the structure. While paying attention to the granular void ratio in order to clarify the shear properties of sand-clay mixtures with increasing fines content monotonic, shear tests were performed on isotropically, and anisotropically consolidated specimens. From the test results, it was observed that the monotonic shear strength of sand-clay mixtures is dependent on the granular void ratio.

A Meshless Method Using the Local Partition of Unity for Modeling of Cohesive Cracks (점성균열 모델을 위한 국부단위분할이 적용된 무요소법)

  • Zi, Goangseup;Jung, Jin-kyu;Kim, Byeong Min
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.5A
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    • pp.861-872
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    • 2006
  • The element free Galerkin method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum. The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by a branch enrichment function which does not have the LEFM stress singularity. The discrete equations are obtained directly from the standard Galerkin method since the enrichment is only for the displacement field, which satisfies the local partition of unity. Because only particles whose domains of influence are influenced by a crack are enriched, the system matrix is still sparse so that the increase of the computational cost is minimized. The condition for crack growth in dynamic problems is obtained from the material instability; when the acoustic tensor loses the positive definiteness, a cohesive crack is inserted to the point so as to change the continuum to a discontiuum. The crack speed is naturally obtained from the criterion. It is found that this method is more accurate and converges faster than the classical meshless methods which are based on the visibility concept. In this paper, several well-known static and dynamic problems were solved to verify the method.

Genomic selection through single-step genomic best linear unbiased prediction improves the accuracy of evaluation in Hanwoo cattle

  • Park, Mi Na;Alam, Mahboob;Kim, Sidong;Park, Byoungho;Lee, Seung Hwan;Lee, Sung Soo
    • Asian-Australasian Journal of Animal Sciences
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    • v.33 no.10
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    • pp.1544-1557
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    • 2020
  • Objective: Genomic selection (GS) is becoming popular in animals' genetic development. We, therefore, investigated the single-step genomic best linear unbiased prediction (ssGBLUP) as tool for GS, and compared its efficacy with the traditional pedigree BLUP (pedBLUP) method. Methods: A total of 9,952 males born between 1997 and 2018 under Hanwoo proven-bull selection program was studied. We analyzed body weight at 12 months and carcass weight (kg), backfat thickness, eye muscle area, and marbling score traits. About 7,387 bulls were genotyped using Illumina 50K BeadChip Arrays. Multiple-trait animal model analyses were performed using BLUPF90 software programs. Breeding value accuracy was calculated using two methods: i) Pearson's correlation of genomic estimated breeding value (GEBV) with EBV of all animals (rM1) and ii) correlation using inverse of coefficient matrix from the mixed-model equations (rM2). Then, we compared these accuracies by overall population, info-type (PHEN, phenotyped-only; GEN, genotyped-only; and PH+GEN, phenotyped and genotyped), and bull-types (YBULL, young male calves; CBULL, young candidate bulls; and PBULL, proven bulls). Results: The rM1 estimates in the study were between 0.90 and 0.96 among five traits. The rM1 estimates varied slightly by population and info-type, but noticeably by bull-type for traits. Generally average rM2 estimates were much smaller than rM1 (pedBLUP, 0.40 to0.44; ssGBLUP, 0.41 to 0.45) at population level. However, rM2 from both BLUP models varied noticeably across info-types and bull-types. The ssGBLUP estimates of rM2 in PHEN, GEN, and PH+ GEN ranged between 0.51 and 0.63, 0.66 and 0.70, and 0.68 and 0.73, respectively. In YBULL, CBULL, and PBULL, the rM2 estimates ranged between 0.54 and 0.57, 0.55 and 0.62, and 0.70 and 0.74, respectively. The pedBLUP based rM2 estimates were also relatively lower than ssGBLUP estimates. At the population level, we found an increase in accuracy by 2.0% to 4.5% among traits. Traits in PHEN were least influenced by ssGBLUP (0% to 2.0%), whereas the highest positive changes were in GEN (8.1% to 10.7%). PH+GEN also showed 6.5% to 8.5% increase in accuracy by ssGBLUP. However, the highest improvements were found in bull-types (YBULL, 21% to 35.7%; CBULL, 3.3% to 9.3%; PBULL, 2.8% to 6.1%). Conclusion: A noticeable improvement by ssGBLUP was observed in this study. Findings of differential responses to ssGBLUP by various bulls could assist in better selection decision making as well. We, therefore, suggest that ssGBLUP could be used for GS in Hanwoo proven-bull evaluation program.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).