• Proceedings of the KIEE Conference
• /
• 1990.07a
• /
• pp.72-76
• /
• 1990

A new statistical linearization technique for nonlinear system called covariance matching method is proposed in this paper. The covariance matching method makes the mean and variance of an approximated output be identical real functional output, and the distribution of the approximated output have identical shape with a given random input. Also, the covariance matching method can be easily implemented for statistical analysis of nonlinear systems with a combination of linear system covariance analysis.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.2
• /
• pp.236-247
• /
• 1992

Optimization has been developed to minimize the cost function while satisfying constraints. Nonlinear Programming method is used as a tool for the optimization. Usually, cost and constraint function calculations are required in the engineering applications, but those calculations are extremely expensive. Especially, the function and sensitivity analyses cause a bottleneck in structural optimization which utilizes the Finite Element Method. Also, when the functions are quite noisy, the informations do not carry out proper role in the optimization process. An algorithm called "Second-order Approximation Method" has been proposed to overcome the difficulties recently. The cost and constraint functions are approximated by the second-order Taylor series expansion on a nominal points in the algorithm. An optimal design problem is defined with the approximated functions and the approximated problem is solved by a nonlinear programming numerical algorithm. The solution is included in a candidate point set which is evaluated for a new nominal point. Since the functions are approximated only by the function values, sensitivity informations are not needed. One-dimensional line search is unnecessary due to the fact that the nonlinear algorithm handles the approximated functions. In this research, the method is analyzed and the performance is evaluated. Several mathematical problems are created and some standard engineering problems are selected for the evaluation. Through numerical results, applicabilities of the algorithm to large scale and complex problems are presented.presented.

• Journal of the Korean GEO-environmental Society
• /
• v.8 no.6
• /
• pp.37-43
• /
• 2007

The interface layer having different consolidation properties and nonlinear material function with permeability needs to be considered to predict consolidation behavior. In this study, interface equation between different layers has been derived and then applied to existing finite difference scheme for conducting consolidation analysis. These results have been compared with those by conventional method in which different layers are converted to single layer having conversion value of properties. Also, although the conventional consoilidation analysis is used to consider non-linearity of the permeability with effective stress, an approximated nonlinear method as a function of consoilidation coefficient with effective stress have been developed and applied to the consoilidation analysis for various cases.

• International Journal of Aeronautical and Space Sciences
• /
• v.13 no.3
• /
• pp.361-368
• /
• 2012

This paper presents an approach on the design of a nonlinear controller to track a reference velocity for an air-breathing supersonic vehicle. The nonlinear control scheme involves an adaptation of propulsive and aerodynamic characteristics in the equations of motion. In this paper, the coefficients of given thrust and drag functions are estimated and they are used to approximate the equations of motion under varying flight conditions. The form of the function of propulsive thrust is extracted from a thrust database which is given by preliminary engine input/output performance analysis. The aerodynamic drag is approximated as a function of angle of attack and fin deflection. The nonlinear controller, designed by using the approximated nonlinear control model equations, provides engine fuel supply command to follow the desired velocity varying with time. On the other hand, the stabilization of altitude, separated from the velocity control scheme, is done by a classical altitude hold autopilot design. Finally, several simulations are performed in order to demonstrate the relevance of the controller design regarding the vehicle.

• Journal of the korean Society of Automotive Engineers
• /
• v.13 no.3
• /
• pp.58-67
• /
• 1991

A theory of continuum damage mechanics based on the theory of materials of type N was developed and its nonlinear finite element approximation and numerical simulation was carried out. To solve the finite elastoplasticity problems, reasonable kinematics of large deformed solids was introduced and constitutive relations based on the theory of materials of type-N were derived. These highly nonlinear equations were reduced to the incremental weak formulation and approximated by the theory of nonlinear finite element method. Two types of problems, compression moulding problem and pure bending problem, were solved for aluminum 2024.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.24 no.3
• /
• pp.129-139
• /
• 2020

An approximate analysis method is proposed to predict the dynamic amplification of shear forces in ordinary reinforced concrete shear walls as a preliminary study. First, a seismic design for three groups of ordinary reinforced concrete shear walls higher than 60 m was created on the basis of nonlinear dynamic analysis. Causes for the dynamic amplification effect of shear forces were investigated through a detailed evaluation of the nonlinear dynamic analysis result. A new modal combination rule was proposed on the basis of that observation, in which fundamental mode response and combined higher mode response were summed directly. The fundamental mode response was approximated by nonlinear static analysis result, while higher mode response was computed using response spectrum analysis for equivalent linear structural models with the effective stiffness based on the nonlinear dynamic analysis result. The proposed approximate analysis generally predicted vertical distribution of story shear and shear forces of individual walls from the nonlinear dynamic analysis with comparable accuracy.

• Structural Engineering and Mechanics
• /
• v.23 no.6
• /
• pp.599-613
• /
• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1998.04a
• /
• pp.143-147
• /
• 1998

In this study, nonlinear stiffness characteristics of a discharge valve in a small hermetic compressor was considered. It was approximated, with piecewise-linearity, and cubic or quintic nonlinearity by the static load-displacement experimental results. Based on the fluid-structure interaction effects and mass flow rate, the derived 1-DOF equation of motion for the valve model was analyzed. Finally, the dynamic response of the discharge valve was studied with parameters such as the ratio of the running frequency of the compressor to the linear natural frequency of the valve.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2001.09a
• /
• pp.243-250
• /
• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.

• Proceedings of the KIEE Conference
• /
• 2003.11b
• /
• pp.187-190
• /
• 2003

In this paper, we address the robust adaptive backstepping controller using fuzzy neural network (FHIN) for a class of uncertain output feedback nonlinear systems with disturbance. A new algorithm is proposed for estimation of unknown bounds and adaptive control of the uncertain nonlinear systems. The state estimation is solved using K-fillers. All unknown nonlinear functions are approximated by FNN. The FNN weight adaptation rule is derived from Lyapunov stability analysis and guarantees that the adapted weight error and tracking error are bounded. The compensated controller is designed to compensate the FNN approximation error and external disturbance. Finally, simulation results show that the proposed controller can achieve favorable tracking performance and robustness with regard to unknown function and external disturbance.