• Journal of computational fluids engineering
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• v.14 no.4
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• pp.93-100
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved successively in the moving least square sense. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as a FVM.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.278-294
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• 2015

Considering the guidance and control problem of the near space interceptor (NSI) during the terminal course, this paper proposes a three-channel independent integrated guidance and control (IGC) scheme based on the backstepping sliding mode and finite time disturbance observer (FTDO). Initially, the three-channel independent IGC model is constructed based on the interceptor-target relative motion and nonlinear dynamic model of the interceptor, in which the channel coupling term and external disturbance are regarded as the total disturbances of the corresponding channel. Then, the FTDO is introduced to estimate the target acceleration and control system loop disturbances, and the feed-forward compensation term based on the estimated values is employed to effectively remove the effect of disturbances in finite time. Subsequently, the IGC algorithm based on the backstepping sliding mode is also given to obtain the virtual control moment. Furthermore, a robust least-squares weighted control allocation (RLSWCA) algorithm is employed to distribute the previous virtual control moment among the corresponding aerodynamic fins and reaction jets, which also takes into account the uncertainty in the control effectiveness matrix. Finally, simulation results show that the proposed IGC method can obtain the small miss distance and smooth interceptor trajectories.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.269-279
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• 2002

We considered the problem for confirmation of multiple outliers and leverage points. Identification of multiple outliers and leverage points is difficult because of the masking effect and swamping effect. Rousseeuw and van Zomeren(1990) identified multiple outliers and leverage points by using the Least Median of Squares and Minimum Value of Ellipsoids which are high-breakdown robust estimators. But their methods tend to declare too many observations as extremes. Atkinson(1987) suggested a method for confirming of outliers and Fung(1993) pointed out Atkinson method's limitation and proposed another method by using the add-back model. But we analyzed that Fung's method is affected by adjacent effect. In this thesis, we proposed one procedure for confirmation of outliers and leverage points and compared three example with Fung's method.

• Smart Structures and Systems
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• v.14 no.5
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• pp.831-845
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• 2014

This paper proposed a discrete wavelet transform based method for time-varying physical parameter identification of shear type structures. The time-varying physical parameters are dispersed and expanded at multi-scale as profile and detail signal using discrete wavelet basis. To reduce the number of unknown quantity, the wavelet coefficients that reflect the detail signal are ignored by setting as zero value. Consequently, the time-varying parameter can be approximately estimated only using the scale coefficients that reflect the profile signal, and the identification task is transformed to an equivalent time-invariant scale coefficient estimation. The time-invariant scale coefficients can be simply estimated using regular least-squares methods, and then the original time-varying physical parameters can be reconstructed by using the identified time-invariant scale coefficients. To reduce the influence of the ill-posed problem of equation resolving caused by noise, the Tikhonov regularization method instead of regular least-squares method is used in the paper to estimate the scale coefficients. A two-story shear type frame structure with time-varying stiffness and damping are simulated to validate the effectiveness and accuracy of the proposed method. It is demonstrated that the identified time-varying stiffness is with a good accuracy, while the identified damping is sensitive to noise.

• Smart Structures and Systems
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• v.12 no.6
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• pp.619-640
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• 2013

It is highly desirable to explore efficient algorithms for detecting structural damage of large size structural systems with limited input and output measurements. In this paper, a new structural damage detection algorithm based on substructure approach is proposed for large size structural systems with limited input and output measurements. Inter-connection effect between adjacent substructures is treated as 'additional unknown inputs' to substructures. Extended state vector of each substructure and its unknown excitations are estimated by sequential extended Kalman estimator and least-squares estimation, respectively. It is shown that the 'additional unknown inputs' can be estimated by the algorithm without the measurements on the substructure interface DOFs, which is superior to previous substructural identification approaches. Also, structural parameters and unknown excitation are estimated in a sequential manner, which simplifies the identification problem compared with other existing work. Structural damage can be detected from the degradation of the identified substructural element stiffness values. The performances of the proposed algorithm are demonstrated by several numerical examples and a lab experiment. Measurement noise effect is considered. Both the simulation results and experimental data validate that the proposed algorithm is viable for structural damage detection of large size structural systems with limited input and output measurements.

• Smart Structures and Systems
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• v.14 no.1
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• pp.1-16
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• 2014

In this work, we address the so-called sensor reachback problem for Wireless Sensor Networks, which consists in collecting the measurements acquired by a large number of sensor nodes into a sink node which has major computational and power capabilities. Focused on applications such as Structural Health Monitoring, we propose a cooperative communication protocol that exploits the spatio-temporal correlations of the sensor measurements in order to save energy when transmitting the information to the sink node in a non-stationary environment. In addition to cooperative communications, the protocol is based on two well-studied adaptive filtering techniques, Least Mean Squares and Recursive Least Squares, which trade off computational complexity and reduction in the number of transmissions to the sink node. Finally, experiments with real acceleration measurements, obtained from the Canton Tower in China, are included to show the effectiveness of the proposed method.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011

Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.181-192
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• 2014

In this paper, we propose a robust real-time myocardial border tracking algorithm for echocardiography. Commonly, after an initial contour of LV border is traced at one or two frame from the entire cardiac cycle, LV contour tracking is performed over the remaining frames. Among a variety of tracking techniques, optical flow method is the most widely used for motion estimation of moving objects. However, when echocardiography data is heavily corrupted in some local regions, the errors bring the tracking point out of the endocardial border, resulting in distorted LV contours. This shape distortion often occurs in practice since the data acquisition is affected by ultrasound artifacts, dropout or shadowing phenomena of cardiac walls. The proposed method deals with this shape distortion problem and reflects the motion realistic LV shape by applying global deformation modeled as affine transform partitively to the contour. We partition the tracking points on the contour into a few groups and determine each affine transform governing the motion of the partitioned contour points. To compute the coefficients of each affine transform, we use the least squares method with equality constraints that are given by the relationship between the coefficients and a few contour points showing good tracking results. Many real experiments show that the proposed method supports better performance than existing methods.

• Geomechanics and Engineering
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• v.9 no.6
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• pp.709-727
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• 2015

The main aim of this study is to introduce optimal design of homogeneous earth dams with oblique and horizontal drains based on particle swarm optimization (PSO) incorporating weighted least squares support vector machine (WLS-SVM). To achieve this purpose, the upstream and downstream slopes of earth dam, the length of oblique and horizontal drains and angle among the drains are considered as the design variables in the optimization problem of homogeneous earth dams. Furthermore, the seepage through dam body and the weight of dam as objective functions are minimized in the optimization process simultaneously. In the optimization procedure, the stability coefficient of the upstream and downstream slopes and the seepage through dam body as the hydraulic responses of homogeneous earth dam are required. Hence, the hydraulic responses are predicted using WLS-SVM approach. The optimal results of illustrative examples demonstrate the efficiency and computational advantages of PSO with WLS-SVM in the optimal design of homogeneous earth dams with drains.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.