• Title/Summary/Keyword: Penalty function method

Search Result 179, Processing Time 0.027 seconds

On the use of the Lagrange Multiplier Technique for the unilateral local buckling of point-restrained plates, with application to side-plated concrete beams in structural retrofit

  • Hedayati, P.;Azhari, M.;Shahidi, A.R.;Bradford, M.A.
    • Structural Engineering and Mechanics
    • /
    • v.26 no.6
    • /
    • pp.673-685
    • /
    • 2007
  • Reinforced concrete beams can be strengthened in a structural retrofit process by attaching steel plates to their sides by bolting. Whilst bolting produces a confident degree of shear connection under conditions of either static or seismic overload, the plates are susceptible to local buckling. The aim of this paper is to investigate the local buckling of unilaterally-restrained plates with point supports in a generic fashion, but with particular emphasis on the provision of the restraints by bolts, and on the geometric configuration of these bolts on the buckling loads. A numerical procedure, which is based on the Rayleigh-Ritz method in conjunction with the technique of Lagrange multipliers, is developed to study the unilateral local buckling of rectangular plates bolted to the concrete with various arrangements of the pattern of bolting. A sufficient number of separable polynomials are used to define the flexural buckling displacements, while the restraint condition is modelled as a tensionless foundation using a penalty function approach to this form of mathematical contact problem. The additional constraint provided by the bolts is also modelled using Lagrange multipliers, providing an efficacious method of numerical analysis. Local buckling coefficients are determined for a range of bolting configurations, and these are compared with those developed elsewhere with simplifying assumptions. The interaction of the actions in bolted plates during buckling is also considered.

MRF Particle filter-based Multi-Touch Tracking and Gesture Likelihood Estimation (MRF 입자필터 멀티터치 추적 및 제스처 우도 측정)

  • Oh, Chi-Min;Shin, Bok-Suk;Klette, Reinhard;Lee, Chil-Woo
    • Smart Media Journal
    • /
    • v.4 no.1
    • /
    • pp.16-24
    • /
    • 2015
  • In this paper, we propose a method for multi-touch tracking using MRF-based particle filters and gesture likelihood estimation Each touch (of one finger) is considered to be one object. One of frequently occurring issues is the hijacking problem which means that an object tracker can be hijacked by neighboring object. If a predicted particle is close to an adjacent object then the particle's weight should be lowered by analysing the influence of neighboring objects for avoiding hijacking problem. We define a penalty function to lower the weights of those particles. MRF is a graph representation where a node is the location of a target object and an edge describes the adjacent relation of target object. It is easy to utilize MRF as data structure of adjacent objects. Moreover, since MRF graph representation is helpful to analyze multi-touch gestures, we describe how to define gesture likelihoods based on MRF. The experimental results show that the proposed method can avoid the occurrence of hijacking problems and is able to estimate gesture likelihoods with high accuracy.

A Study on Polynomial Neural Networks for Stabilized Deep Networks Structure (안정화된 딥 네트워크 구조를 위한 다항식 신경회로망의 연구)

  • Jeon, Pil-Han;Kim, Eun-Hu;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
    • /
    • v.66 no.12
    • /
    • pp.1772-1781
    • /
    • 2017
  • In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

Penalized variable selection in mean-variance accelerated failure time models (평균-분산 가속화 실패시간 모형에서 벌점화 변수선택)

  • Kwon, Ji Hoon;Ha, Il Do
    • The Korean Journal of Applied Statistics
    • /
    • v.34 no.3
    • /
    • pp.411-425
    • /
    • 2021
  • Accelerated failure time (AFT) model represents a linear relationship between the log-survival time and covariates. We are interested in the inference of covariate's effect affecting the variation of survival times in the AFT model. Thus, we need to model the variance as well as the mean of survival times. We call the resulting model mean and variance AFT (MV-AFT) model. In this paper, we propose a variable selection procedure of regression parameters of mean and variance in MV-AFT model using penalized likelihood function. For the variable selection, we study four penalty functions, i.e. least absolute shrinkage and selection operator (LASSO), adaptive lasso (ALASSO), smoothly clipped absolute deviation (SCAD) and hierarchical likelihood (HL). With this procedure we can select important covariates and estimate the regression parameters at the same time. The performance of the proposed method is evaluated using simulation studies. The proposed method is illustrated with a clinical example dataset.

PSO-Based PID Controller for AVR Systems Concerned with Design Specification (설계사양을 고려한 AVR 시스템의 PSO 기반 PID 제어기)

  • Lee, Yun-Hyung
    • Journal of the Korea Academia-Industrial cooperation Society
    • /
    • v.19 no.10
    • /
    • pp.330-338
    • /
    • 2018
  • The proportional-integral-derivative(PID) controller has been widely used in the industry because of its robust performance and simple structure in a wide range of operating conditions. However, the AVR(Automatic Voltage Regulator) as a control system is not robust to variations of the power system parameters. Therefore, it is necessary to use PID controller to increase the stability and performance of the AVR system. In this paper, a novel design method for determining the optimal PID controller parameters of an AVR system using the particle swarm optimization(PSO) algorithm is presented. The proposed approach has superior features, including easy implementation, stable convergence characteristic and good computational efficiency. In order to assist estimating the performance of the proposed PSO-PID controller, a new performance criterion function is also defined. This evaluation function is intended to reflect when the maximum percentage overshoot, the settling time are given as design specifications. The ITAE evaluation function should impose a penalty if the design specifications are violated, so that the PSO algorithm satisfies the specifications when searching for the PID controller parameter. Finally, through the computer simulations, the proposed PSO-PID controller not only satisfies the given design specifications for the terminal voltage step response, but also shows better control performance than other similar recent studies.

ADMM algorithms in statistics and machine learning (통계적 기계학습에서의 ADMM 알고리즘의 활용)

  • Choi, Hosik;Choi, Hyunjip;Park, Sangun
    • Journal of the Korean Data and Information Science Society
    • /
    • v.28 no.6
    • /
    • pp.1229-1244
    • /
    • 2017
  • In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

The Compensation Characteristics of WDM Channel Distortion Dependence on NRZ format and RZ Format (NRZ 형식과 RZ 형식에 따른 WDM채널 왜곡의 보상 특성)

  • 이성렬;조성언
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
    • /
    • v.14 no.11
    • /
    • pp.1184-1190
    • /
    • 2003
  • In this paper, we investigated the characteristics of compensation for distorted NRZ signal and RZ signal in 320 Gbps WDM system as a function of channel input power, fiber dispersion coefficient and transmission length, respectively. The considered WDM transmission system is based on mid-span spectral inversion(MSSI) compensation method having highly nonlinear dispersion shifted fiber(HNL-DSF) optical phase conjugator(OPC) in the mid-way of total transmission line. We confirmed that the signal input power range compensated by MSSI is broadened by using RZ as a signal format in WDM system with small fiber dispersion coefficient, The range of fiber dispersion coefficient compensating overall distorted WDM channels is limited, because degree of compensation for distorted channel with low conjugated-wave power becomes gradually degrade as fiber dispersion coefficient becomes gradually higher. It is showed that RZ format and NRZ format is suited for long-haul transmission in WDM system with small fiber dispersion coefficient and with large fiber dispersion coefficient, respectively.

Improvement of Basis-Screening-Based Dynamic Kriging Model Using Penalized Maximum Likelihood Estimation (페널티 적용 최대 우도 평가를 통한 기저 스크리닝 기반 크리깅 모델 개선)

  • Min-Geun Kim;Jaeseung Kim;Jeongwoo Han;Geun-Ho Lee
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.36 no.6
    • /
    • pp.391-398
    • /
    • 2023
  • In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

Calculation of Pump Light Power in Wideband Optical Phase Conjugator with Highly-Nonlinear Dispersion Shifted fiber (HNL-DSF를 이용한 광대역 광 위상 공액기의 펌프 광 전력 계산)

  • 이성렬;이하철
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.29 no.5A
    • /
    • pp.473-483
    • /
    • 2004
  • In this paper, we numerically investigated the optimum pump light power best compensating for pulse distortion due to both chromatic dispersion and self phase modulation (SPM) as a function of channel input power in 8 channel ${\times}$ 40 Gbps wavelength division multiplexing (WDM systems. Also we investigated the allowable maximum channel input power dependence on modulation format and fiber dispersion coefficient in the various pump light power of OPC. The considered WDM transmission system is based on path-averaged intensity approximation (PAIA) mid-span spectral inversion (MSSI) compensation method, which has highly-nonlinear dispersion shifted fiber (HNL-SDF) as nonlinear medium of optical phase conjugator (OPC) in the mid-way of total transmission line. We confirmed that optimal pump light power of HNL-DSF OPC depend on modulation format, initial channel input power, total transmission length and fiber dispersion. But optimal pump light power of HNL-DSF OPC must be selected to make power conversion ratio to almost unity. And we confirmed that, if we allow a 1 dB eye opening penalty (EOP), the tolerable maximum channel input power is increased by using RZ than NRZ as modulation format when pump light power of HNL-DSF OPC is not optimal value but another values.