• Tunnel and Underground Space
• /
• v.34 no.4
• /
• pp.355-373
• /
• 2024

The Generalized Hoek-Brown (GHB) criterion is a nonlinear failure criterion specialized for rock engineering applications and has recently seen increased usage. However, the GHB criterion expresses the relationship between minimum and maximum principal stresses at failure, and when GSI≠100, it has disadvantage of being difficult to express as an explicit relationship between the normal and shear stresses acting on the failure plane, i.e., as a Mohr failure envelope. This disadvantage makes it challenging to apply the GHB criterion in numerical analysis techniques such as limit equilibrium analysis, upper-bound limit analysis, and the critical plane approach. Consequently, recent studies have attempted to express the GHB Mohr failure envelope as an approximate analytical formula, and there is still a need for continued interest in related research. This study presents improved formulations for the approximate GHB Mohr failure envelope, offering higher accuracy in predicting shear strength compared to existing formulas. The improved formulation process employs a method to enhance the approximation accuracy of the tangential friction angle and utilizes the tangent line equation of the nonlinear GHB failure envelope to improve the accuracy of shear strength approximation. In the latter part of this paper, the advantages and limitations of the proposed approximate GHB failure envelopes in terms of shear strength prediction accuracy and calculation time are discussed.

• Proceedings of the KIEE Conference
• /
• 2008.04a
• /
• pp.215-216
• /
• 2008

This paper is proposed a approximation control method(ACM) for the maximum power of a photovoltaic system. It is designed for power systems application and utilities. The proposed Maximum Power Point Tracking(MPPT) control has the advantage to provide a new simple way to approximate the optimal or rated voltage, the optimal or rated current and maximum power rating produced by a solar panel and the photovoltaic inverter. And this straightforward method has the advantage that Pmax and $V_{op}$ can be approximated using the same variable as the dynamic model without using complicate approximations or Taylor series. This paper is proposed MPPT using AMC using weather condition of domestic moderate program technique. This paper is proposed the experimental results to verify the effectiveness of the new methods.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.20 no.3
• /
• pp.17-20
• /
• 1983

There have been many investigations of predicting the added resistance of a ship in seaway since Havelock discussed this topic in 1937. Among these researches, Maruo's theoretical approach is known as the most consistent mathematical representation for added resistance of a ship in regular head sea. In his theory, the hull form of a ship is represented under the slender body approximation. But the motion responses which were used for the calculation of the added resistance have been obtained by using the strip method which is based on an approximation that the hull form may be expressed as set of two dimensional cylinder sections in longitudinal direction. Therefore two different methods for hull form representation were implicity used in Maruo's original work for the added resistance calculation. Utilizing the characteristics that hull forms are usually slender, Kan expressed the hull form as two dimensional cylinder at each station by using the Taylor series expansion for the length wise direction. Putting this idea into Maruo's original work, the added resistance can be obtained with the explicitly unique representation of the hull form. For the purpose of comparison the added resistance of a hull form(series 60, Cb=0.6) was calculated by using the motion response obtained by Shintani. The numerical result showes a good qualitative agreement with the experimental result by Sibul.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.485-502
• /
• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Journal of Korean Society for Quality Management
• /
• v.37 no.3
• /
• pp.33-38
• /
• 2009

When we estimate the parameters of software reliability models, we usually use maximum liklihood estimator(MLE). But this method is required a large data set. In particular, when we want to estimate it with small observed data such as early stages of testing, we give rise to the non-existence of MLE. Therefore, it is interesting to look into the influence of parameter estimators obtained using MLE. In this paper, we use two non-homogenous poisson process software reliability growth model: delayed S-shaped model and log power model. In this paper, we calculate the sensitivity of estimators about failure intensity function for two SRGMs respectively.

• Journal of Power System Engineering
• /
• v.4 no.3
• /
• pp.62-71
• /
• 2000

A mathematical modeling for a magnetic levitation system is proposed using the Taylor series expansion of differential function for obtaining linearity. It is confirmed that this kind of linear approximation method can be used to the modeling of a magnetic levitation system. The two-degree-of-freedom optimal servo system for a constant reference signal is proposed using the LQ optimization technique. An additional state feedback is introduced at the output of the integrator to cancel the integral action for reference signal if there is no modeling error of the plant and no disturbance input to the plant. When the modeling error or the disturbance input exists, the integral effect appears. The system has a free parameter which can b used to tune the effect of the integral compensation.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.775-795
• /
• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.30 no.11C
• /
• pp.1116-1124
• /
• 2005

We investigated the mean and variance of the MSE and the MI-based image registration methods that have been widely applied for image registration. By using the first order Taylor series expansion, we have approximated the mean and the variance for one-dimensional image registration. The asymptotic results show that the MSE based method is unbiased and efficient for the same image registration problem while the MI-based method shows larger variance. However, for the different modality image registration problem, the MSE based method is largely biased while the MI based method still achieves registration. The results imply that the MI based method achieves robustness to the different image modalities at the cost of inefficiency. The analytical results are supported by simulation results.

• Journal of Institute of Control, Robotics and Systems
• /
• v.13 no.5
• /
• pp.507-512
• /
• 2007

This paper presents a tracking filter with ship's motion compensation for a ship-borne radar tracking system. The ship's maneuver is described by displacement and rotational motions in the ship-centered east-north frame. The first order Taylor series approximation of the measurement error covariance of the converted measurement is derived in the ship-centered east-north frame. The ship's maneuver is compensated by incorporating the measurement error covariance of the converted measurement and displacement of the position state in the tracking filter. The simulation results via 500 Monte-Carlo runs show that the proposed method follows the target successfully and provides consistent tracking performance during ship's maneuvers while the conventional tracking filter without ship motion compensation fails to track during such periods.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.11
• /
• pp.1467-1475
• /
• 2001

In the present paper, approximate coordinate transformations for simulation of turbulent flows with active wall motions, leading to a significant reduction in the computational cost while maintaining the numerical accuracy, are presented: the Navier-Stokes equations are coordinate-transformed with an approximation of Taylor-series truncation and neglect of some less-significant terms. The performance of the proposed transformations is evaluated in simulation of the channel flow at Re$\sub$$\tau$/=140 with wall deformations of │η$\sub$m/$\^$+/ 5. The approximate transformations provide flow structures as wall as turbulence statistics in good agreement with those from a complete coordinate transformation [Phys. Fluids 12, 3301 (2000)] and allow 25-30% savings in the CPU time as compared to the complete one.