Experiments on State and Unmeasured-Parameter Estimation of Two Degree-of-Freedom System for Precise Control Based on JAUKF

승지훈,Sunggoo Yoo,정길도 한국정밀공학회 2019 International Journal of Precision Engineering and Vol.20 No.7

We herein present system parameter estimation using the joint adaptive unscented Kalman filter and state estimation approach for a two degree-of-freedom (2-DOF) mechanical system. The unscented Kalman filter (UKF) is applied broadly in diverse engineering fields to estimate the state of the dynamic system and improve the control precision by reducing measurement noise. One aspect of parameter identification is that unmeasured parameter estimation is important in designing and maintaining the system performance with a suitable controller. This is because changes in the system parameters estimated will occur owing to external shock and deterioration in operation. State estimation has been studied thoroughly and developed widely, but not in terms of parameter estimation. Parameter estimation is important because system parameters can be altered owing to wear and tear, large disturbance, or exposure to extreme temperatures. It is difficult to disassemble and measure the parameter when it changes; hence, computational estimation is a solution. The proposed method simultaneously estimates the states as well as the parameters of custom-made 2-DOF mechanical system that is a nonlinear dynamical system. The adaptive rules in the estimation process are considered based on the moving average window method to address the effects of unexpected noise in the sensor measurements. The experimental results are analyzed to demonstrate the effectiveness of the proposed method for estimating the states and parameters. This method demonstrates better performance compared to using the joint-UKF in terms of convergence time, accuracy, and robustness to noise.

An optimal regularization for structural parameter estimation from modal response

Pothisiri, Thanyawat Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.22 No.4

Solutions to the problems of structural parameter estimation from modal response using leastsquares minimization of force or displacement residuals are generally sensitive to noise in the response measurements. The sensitivity of the parameter estimates is governed by the physical characteristics of the structure and certain features of the noisy measurements. It has been shown that the regularization method can be used to reduce effects of the measurement noise on the estimation error through adding a regularization function to the parameter estimation objective function. In this paper, we adopt the regularization function as the Euclidean norm of the difference between the values of the currently estimated parameters and the a priori parameter estimates. The effect of the regularization function on the outcome of parameter estimation is determined by a regularization factor. Based on a singular value decomposition of the sensitivity matrix of the structural response, it is shown that the optimal regularization factor is obtained by using the maximum singular value of the sensitivity matrix. This selection exhibits the condition where the effect of the a priori estimates on the solutions to the parameter estimation problem is minimal. The performance of the proposed algorithm is investigated in comparison with certain algorithms selected from the literature by using a numerical example.

DINA와 DINO 모형의 문항 모수 및 피험자 모수 추정 정확성에 영향을 주는 요인 탐색

박세진(Sejin Park),이현숙(Hyun Sook Yi) 한국교육평가학회 2017 교육평가연구 Vol.30 No.3

본 연구의 목적은 인지진단모형을 적용하여 검사를 개발할 때 문항 및 피험자 모수 추정의 정확성에 영향을 주는 요인이 무엇인지 알아보는 것이다. 이를 위해 DINA와 DINO 모형에서 검사 길이, 인지요소의 수, 피험자의 수, 문항의 진단성이 변할 때 문항 및 피험자 모수 추정의 정확성이 어떻게 달라지는지 탐색하였다. 연구 결과는 다음과 같다. 첫째, 검사 길이에 비해 추정해야 할 인지요소의 수가 많으면 문항 모수가 부정확하게 추정되는 것으로 나타났다. 이때 DINA 모형에서는 추측 모수가, DINO 모형에서는 실수 모수가 더 부정확하게 추정되었다. 검사 길이가 길어질 경우 피험자 모수 정확성은 향상된 반면, 추정해야 할 인지요소의 수가 증가함에 따라 피험자 모수 정확성은 하락하였다. 둘째, 검사에 응시하는 피험자의 수가 많아질수록 문항 모수는 정확하게 추정되었으나 피험자 모수 정확성에는 큰 영향을 주지 않았다. 셋째, 문항의 진단성이 낮아질수록 문항 및 피험자 모수는 모두 부정확하게 추정되는 것으로 나타났다. The purpose of this study is to identify test development conditions that may affect the accuracy of estimating item and examinee parameters in situations where a cognitive diagnostic model is applied. The accuracy of item and examinee parameter estimation was examined for various levels of simulation conditions such as test length, number of attributes, number of examinees, and diagnosticity of item, for the DINA model and DINO model, respectively. The findings of this study is as follows: First, the estimation of item parameters was not accurate when the number of attributes of a test exceeded the limit of the number allowed for the given test length. Guessing parameters were less accurate for the DINA model and slip parameters were less accurate for the DINO model. Longer tests tended to produce higher classification accuracy. Classification accuracy decreased as the number of attributes to be estimated increased. Second, the accuracy of item parameters increased as the number of examinees increased, while the classification accuracy was not significantly affected. Third, diagnosticity of item was also an important factor that affected the accuracy of item and parameters. As opposed to the tendency that the simulation factors of the item parameter estimation interacted with each other, factors were rather independent in parameter estimation.

ESTIMATION ALGORITHM FOR PHYSICAL PARAMETERS IN A SHALLOW ARCH

Gutman, Semion,Ha, Junhong,Shon, Sudeok Korean Mathematical Society 2021 대한수학회지 Vol.58 No.3

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

통계적 방법을 이용한 오존 형성의 예측

여영구,손상현,오세천 漢陽大學校 環境工學硏究所 1999 環境科學論文集 Vol.20 No.-

통계적 방법을 이용하여 오존 형성의 예측에 관한 연구를 수행하였다. 통계적 방법으로는 파라미터 평가 방법과 인공신경 회로망 방법이 적용되었다. 파라미터 평가 방법에는 실시간 파라미터를 평가하기 위하여 ELS 및 RML 방법이 사용되었으며 오존 형성의 모델로는 ARMAX 모델을 사용하였다. 또한 3층 구조를 갖는 인공신경 회로망 방법을 이용하여 오존 형성의 예측 시험을 수행하였으며 본 연구에 사용된 통계적 방법의 성능을 평가하기 위하여 오존 형성의 예측결과를 실제자료와 비교 분석을 하였다. 실제 자료와의 비교를 통하여 파라미터 평가 방법 및 인공신경 회로망 방법에 근거한 예측방법이 제한된 예측 구간 내에서 만족할 만한 성능을 보임을 확인할 수 있었다. The prediction of ozone formation was studied using the stochastic method, Parameter estimation method and artificial neural network(ANN) method were employed in the stochastic scheme. In the parameter estimation method, extended least squares(ELS) method and recursive maximum likelihood(RML) were used to achieve the real time parameter estimation. Autoregressive moving average model with external input(ARMAX)was used as the ozone formation model for the parameter estimation method, ANN with 3 layers was also tested to predict the ozone formation. To demonstrate the performance of the ozone formation prediction schemes used in this work, the prediction results of ozone formation were compared to the real data. From the comparison it was found that the prediction schemes based on the parameter estimation method and ANN method show an acceptable accuracy with limited prediction horizon.

Parameter Estimation for Nonlinear Functions Related to System Responses

Ling Xu 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.6

This paper considers the parameter estimation problem of nonlinear models, which are related to the impulse or step response functions of linear time-invariant (LTI) dynamical systems, based on the response data. In terms of the nonlinear characteristic of the models, the nonlinear dynamical optimization scheme is adopted for obtaining the system parameter estimates. By constructing a gradient criterion function, a gradient recursion algorithm is derived. In order to overcome the difficulty of determining the step-size in the gradient recursion algorithm, a trying method and a numerical approach are proposed to achieve the step-size. On this basis, a stochastic gradient estimation method is presented by using a recursive step-size. Furthermore, a multi-innovation stochastic gradient method is deduced for enhancing the estimation accuracy by using the dynamical window data. Finally, a dynamical length stochastic gradient estimation technique is offered to obtain more accurate parameter estimates by using dynamical length measured data from the step response. The examples are provided to examine the algorithm performance and the simulation results indicate that the presented approaches are effective.

Markov Chain Monte Carlo를 이용한 반도체 결함 클러스터링 파라미터의 추정

하정훈(Chunghun Ha),장준현(Jun Hyun Chang),김준현(Joon Hyun Kim) 한국산업경영시스템학회 2009 한국산업경영시스템학회지 Vol.32 No.3

Negative binomial yield model for semiconductor manufacturing consists of two parameters which are the average number of defects per die and the clustering parameter. Estimating the clustering parameter is quite complex because the parameter has not clear closed form. In this paper, a Bayesian approach using Markov Chain Monte Carlo is proposed to estimate the clustering parameter. To find an appropriate estimation method for the clustering parameter, two typical estimators, the method of moments estimator and the maximum likelihood estimator, and the proposed Bayesian estimator are compared with respect to the mean absolute deviation between the real yield and the estimated yield. Experimental results show that both the proposed Bayesian estimator and the maximum likelihood estimator have excellent performance and the choice of method depends on the purpose of use.

Belief Propagation 기반 스테레오 정합을 위한 정합 파라미터의 추정방식 제안

오광희(Kwang Hee Oh),임선영(Sun Young Lim),한희일(Hee-il Hahn) 大韓電子工學會 2010 電子工學會論文誌-SP (Signal processing) Vol.47 No.1

본 논문에서는 스테레오 이미지로부터 디스패리티 맵을 추출하기 위한 확률모델을 제시하고 이의 해를 구하는 과정은 에너지 기반 스테레오 정합과 일치함을 이론적으로 증명한다. 정합되는 화소 간의 차와 인근 화소에 해당되는 디스패리티의 차는 exponential 확률분포에 근사하다는 사실을 실험적으로 확인하고 이에 근거하여 이들의 정합 파라미터를 최적화하는 식을 유도하고 이를 실험적으로 구하는 방법을 제시한다. 에너지 기반 스테레오 정합 알고리즘의 성능은 기본적으로 정합 파라미터의 크기에 매우 민감하므로 이미지에 따라 적절한 값을 사전에 구하여 적용하여야 한다. 제안한 방식은 초기에 임의의 파라미터로 디스패리티 맵을 구한 후에 이의 통계적 특성을 이용하여 정합 파라미터를 추정하고 추정된 파라미터를 적용하여 디스패리티 맵을 재차 구하는 과정을 반복함으로써 최적의 파라미터에 적응적으로 수렴하도록 조정한다. 따라서, 이미지에 따라 사전에 정합 파라미터를 구하여야 하는 문제를 해결할 수 있다. Middlebury 웹사이트에서 제공한 다양한 스테레오 이미지를 이용하여 제안한 방식으로 구한 파라미터가 최적의 값으로 수렴하는지를 조사하고 이의 수렴 속도와 성능 개선 효과 등을 확인한다. This paper defines the probability models for determining the disparity map given stereo images and derives the methods for solving the problem, which is proven to be equivalent to an energy-based stereo matching. Under the assumptions the difference between the pixel on the left image and the corresponding pixel on the right image and the difference between the disparities of the neighboring pixels are exponentially distributed, a recursive approach for estimating the MRF regularizing parameter is proposed. Usually energy-based stereo matching methods are so sensitive to the parameter that it should be carefully determined. The proposed method alternates between estimating the parameter with the intermediate disparity map and estimating the disparity map with the estimated parameter, after computing it with random initial parameter. It is shown that the parameter estimated by the proposed method converges to the optimum and its performance can be improved significantly by adjusting the parameter and modifying the energy term.

언센티드 칼만 필터를 이용한 진자 파라미터 추정에 관한 연구

승지훈,김태영,Alexander G.Parlos,정길도 제어로봇시스템학회 2011 제어로봇시스템학회 각 지부별 자료집 Vol.2011 No.7

The method of parameter estimation of dynamic system is proposed in this paper. The dynamic system is typically the pendulum. It is important to estimate spring coefficient(k), coefficient of friction(μ), etc. which is difficult to measure in the pendulum dynamic. And most of the pendulum equation is expressed as continuous-time nonlinear. So, to estimate parameter values of the inner equation is difficult. Therefore, in this paper the Unscented Kalman Filter(UKF) is applied in parameter estimation. Its effectiveness is simulated by using the 2 degree of freedom(2DOF) system to estimate the parameters of a continuous-time nonlinear system.

중력 센서를 이용한 모델 기반 노면 경사도 추정기법

이동진(Dongjin Lee),한기훈(Kihoon Han) 한국자동차공학회 2010 한국자동차공학회 학술대회 및 전시회 Vol.2010 No.11

Precise estimation of vehicle mass and road grade are crucial issues in longitudinal control of automotives, such as drivability, traction, or cruise control. There are two main methods for calculating road slope, which is model based road slope estimation and g-sensor based road slope estimation. Vehicle model based road slope estimation needs exact vehicle parameter values and many restriction for slope estimation such as gear shifting, inaccurate estimated engine torque, etc. On the other hand, G-sensor based slope estimation can be calculated most of driving condition but there can be error with real road slope by sensor offset or by vehicle suspension setting. In this paper, a recursive least square method is implemented to the model based road slope estimation for offline parameter estimation and bias adaptation for the g-sensor based road slope estimation will be followed. With bias adaptation, g-sensor based road slope estimation can be reliable for most of driving condition.