• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.10
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• pp.816-822
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• 2014

The estimation of the angular rate of a satellite has been discussed. A nonlinear observer has been proposed based on the state-dependent Riccati equation method. A sufficient stability condition for the convergence of estimation error has been presented. This condition is related to a state-dependent algebraic Riccati equation. It has been derived by transforming nonlinear error dynamics into a Lipschitz nonlinearity. An observer gain is obtained from this condition. Numerical simulations are presented to verify the proposed method.

• Geomechanics and Engineering
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• v.13 no.2
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• pp.237-254
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• 2017

Estimation of slope stability is a very important task in geotechnical engineering. However, its estimation using conventional and soft computing methods has several drawbacks. Use of conventional limit equilibrium methods for the evaluation of slope stability is very tedious and time consuming, while the use of soft computing approaches like Artificial Neural Networks and Fuzzy Logic are black box approaches. Multiple Regression (MR) analysis provides an alternative to conventional and soft computing methods, for the evaluation of slope stability. MR models provide a simplified equation, which can be used to calculate critical factor of safety of slopes without adopting any iterative procedure, thereby reducing the time and complexity involved in the evaluation of slope stability. In the present study, a multiple regression model has been developed and tested its accuracy in the estimation of slope stability using real field data. Here, two separate multiple regression models have been developed for dry and wet slopes. Further, the accuracy of these developed models have been compared and validated with respect to conventional limit equilibrium methods in terms of Mean Square Error (MSE) & Coefficient of determination ($R^2$). As the developed MR models here are not based on any region specific data and covers wide range of parametric variations, they can be directly applied to any real slopes.

• Geomechanics and Engineering
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• v.21 no.2
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• pp.123-132
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• 2020

Due to the various restrictions and problems related to the construction of new roads in urban areas, underground road construction has been receiving a great deal of attention in the field of tunnel engineering. In this study, a double-deck road tunnel with a diverging section was analyzed for the evaluation of its stability. Both numerical analysis and scale model tests were performed, the results were used to develop a stability evaluation method for double-deck tunnels with diverging sections constructed in rocks by NATM. From regression analyses conducted on the results of the numerical analysis, an equation and a chart were derived, these tools allow us to obtain the strength/stress ratio (SSR) for double-deck road tunnels with a diverging tunnel in various diverging conditions quickly and accurately. These tools have great potential to help engineers evaluate the stability of double-deck tunnels in the preliminary design stage.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.483-487
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• 1996

We consider the estimation of the position and orientation of 6 DOF motion bed (Stewart platform) from the measured cylinder length. The solution of forward kinematics is not solved yet as a useful realtime application tool because of the complity of the equation with multiple solutiple solutions. Hence we suggest an algorithm for the estimation of forward kinematics solution using Luenberger observer withnonlinear error correction term. The Luenberger observer withlinear model shows that the estimation error does not go to zero in steadystate due to the linearization error of the dynamic model. Hence the linear observer is modified using nonlinear measurement error equation and we prove thd practical stability of the estimation error dynamics of the proposed observer using lyapunov function.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1249-1254
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• 2006

Existing adaptive observers may cause the parameter drifts due to disturbances even if state estimation errors remain small. To avoid the drift phenomena in the presence of bounded disturbances, several robust adaptive observers have been introduced addressing bounds in state and parameter estimates. However, it is not easy for these observers to manipulate the size of the bounds with the selection of the observer gain. In order to reduce estimation errors, this paper introduces the (equation omitted) gain minimization problem in the adaptive observer structure, which minimizes the (equation omitted) gain between disturbances and estimation errors. The stability condition of the adaptive observer is reformulated as a linear matrix inequality, and the observer gain is optimally chosen by solving the convex optimization problem. The estimation performance is demonstrated through a numerical example.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.235-243
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• 2000

The probabilistic data association filter(PDAF) is known to provide better tracking performance than the standard Kalman filter(KF) in a cluttered environment. In this paper, the stability of the PDAF of Fortmann et al[7], in the presence of uncertainties with regard to the origin of measurement, is investigated. The modified Riccati equation derived by approximating two random terms with their expectations is used to prove the stability of the PDAF. A new Lyapunov function based approach, which is different from the quantitative evaluation of Li and Bar-Shalom[7], is pursued. With the assumption that the system and observation noises are bounded, specific tracking error bounds are established.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.865-868
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• 2006

In this paper, a dynamic behavior(natural frequency) of a cracked simply supported pipe conveying fluid is presented. In addition, an analysis of the flutter and buckling instability of a cracked pipe conveying fluid due to the coupled mode (modes combined) is presented. Based on the Euler-Bernouli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The stiffness of the spring depends on the crack severity and the geometry of the cracked section. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. This study will contribute to the safety test and stability estimation of structures of a cracked pipe conveying fluid.

• Journal of the Korean Geotechnical Society
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• v.29 no.5
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• pp.65-74
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• 2013

The natural disaster occurrences and the loss of lives caused by the steep-slope failures in Korea were investigated in this study. The investigation includes the frequency rate of the steep-slope failures with respect to the characteristics of precipitation, underlying bedrock, and weathered soils. Analysis on the problems in the existing estimation methods of steep-slope failure was also undertaken, and a new model using unsaturated infinite slope stability was developed for the better slope failure estimation. The slope analyses by the newly developed model were performed considering unsaturated infinite slope, the gradient of slope, and hydro/mechanical properties of soils. Steep-slope failure estimation criterion is proposed based on the analysis results. In addition, the precipitation amount corresponding to warning stages against steep-slope failure is provided as an equation of Intensity-Duration criterion.

• Journal of Astronomy and Space Sciences
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• v.29 no.4
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• pp.389-395
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• 2012

The problem of spacecraft attitude control is solved using an adaptive neuro-fuzzy inference system (ANFIS). An ANFIS produces a control signal for one of the three axes of a spacecraft's body frame, so in total three ANFISs are constructed for 3-axis attitude control. The fuzzy inference system of the ANFIS is initialized using a subtractive clustering method. The ANFIS is trained by a hybrid learning algorithm using the data obtained from attitude control simulations using state-dependent Riccati equation controller. The training data set for each axis is composed of state errors for 3 axes (roll, pitch, and yaw) and a control signal for one of the 3 axes. The stability region of the ANFIS controller is estimated numerically based on Lyapunov stability theory using a numerical method to calculate Jacobian matrix. To measure the performance of the ANFIS controller, root mean square error and correlation factor are used as performance indicators. The performance is tested on two ANFIS controllers trained in different conditions. The test results show that the performance indicators are proper in the sense that the ANFIS controller with the larger stability region provides better performance according to the performance indicators.