• Structural Engineering and Mechanics
• /
• v.12 no.6
• /
• pp.669-684
• /
• 2001

A new method for solving the uncertain eigenvalue problems of the structures with interval parameters, interval finite element method based on the element, is presented in this paper. The calculations are done on the element basis, hence, the efforts are greatly reduced. In order to illustrate the accuracy of the method, a continuous beam system is given, the results obtained by it are compared with those obtained by Chen and Qiu (1994); in order to demonstrate that the proposed method provides safe bounds for the eigenfrequencies, an undamping spring-mass system, in which the exact interval bounds are known, is given, the results obtained by it are compared with those obtained by Qiu et al. (1999), where the exact interval bounds are given. The numerical results show that the proposed method is effective for estimating the eigenvalue bounds of structures with interval parameters.

• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.703-708
• /
• 2017

The goal of this study is to evaluate behavior uncertainties of structures by using interval finite element analysis based on interval factor method as a specific non-stochastic tool. The interval finite element method, i.e., interval FEM, is a finite element method that uses interval parameters in situations where it is not possible to get reliable probabilistic characteristics of the structure. The present method solves the uncertainty problems of a 2D solid structure, in which structural characteristics are assumed to be represented as interval parameters. An interval analysis method using interval factors is applied to obtain the solution. Numerical applications verify the intuitive effectiveness of the present method to investigate structural uncertainties such as displacement and stress without the application of probability theory.

• Structural Engineering and Mechanics
• /
• v.13 no.3
• /
• pp.299-312
• /
• 2002

In this paper, a new method to solve the dynamic response problem for structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an optimum scheme is adopted when there are many interval structural parameters. With the interval algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are developed. Based on the matrix perturbation theory and interval extension of function, the upper and lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to illustrate the validity of the present method.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.123-128
• /
• 1998

This paper presents time domain identification of an interval system. We conjectured that Markov parameters (Pulse Responses) from Kharitonov plants would envelope those of the whole interval system. The examination on interrelations between Markov parameters from Kharitonov plants of an interval system and those of the whole interval system determines the validity of the conjecture and is used to give some extremal properties of Markov parameters. The results of this paper are shown in simulations on MBC500 Magnetic Bearing System and a given interval system.

• Structural Engineering and Mechanics
• /
• v.44 no.1
• /
• pp.73-84
• /
• 2012

This paper strongly addresses to the problem of the mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find sharp bounds of the structural parameters for infilled frame system modeled with finite element method. Infill walls are generally treated as non-structural elements considerably to improve the lateral stiffness, strength and ductility of the structure together with the frame elements. Because of their complex nature, they are often neglected in the analytical model of building structures. However, in seismic design, ignoring the effect of infill wall in a numerical model does not accurately simulate the physical behavior. In this context, there are still some uncertainties in mechanical and also geometrical properties in the analysis and design procedure of infill walls. Structural uncertainties can be studied with a finite element formulation to determine sharp bounds of the structural parameters such as wall thickness and Young's modulus. In order to accomplish this sharp solution as much as possible, interval finite element approach can be considered, too. The structural parameters can be considered as interval variables by using the interval number, thus the structural stiffness matrix may be divided into the product of two parts which correspond to the interval values and the deterministic value.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.1
• /
• pp.42-46
• /
• 2009

Das et al. [EJOR 117(1999) 100-112] discussed the real valued solution procedure of the multiobjective transportation problem(MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. In this note, we consider the interval valued solution procedure of the same problem. This problem has been transformed into a classical multiobjective transportation problem where the constraints with interval source and destination parameters have been converted into deterministic ones. Numerical examples have been provided to illustrate the solution procedure for this case.

• Structural Engineering and Mechanics
• /
• v.70 no.1
• /
• pp.81-96
• /
• 2019

In this paper, a hybrid uncertain model is applied to system reliability based design optimization (RBDO) of trusses. All random variables are described by random distributions but some key distribution parameters of them which lack information are defined by variation intervals. For system RBDO of trusses, the first order reliability method, as well as monotonicity analysis and the branch and bound method, are utilized to determine the system failure probability; and Improved (${\mu}+{\lambda}$) constrained differential evolution (ICDE) is employed for the optimization process. System reliability assessment of several numerical examples and system RBDO of different truss structures are proposed to verify our results. Moreover, the effect of different classes of interval distribution parameters on the optimum weight of the structure and the reliability index are also investigated. The results indicate that the weight of the structure is increased by increasing the uncertainty level. Moreover, it is shown that for a certain random variable, the optimum weight is more increased by the translation interval parameters than the rotation ones.

• Journal of the Korean Statistical Society
• /
• v.32 no.1
• /
• pp.1-10
• /
• 2003

We consider obtaining graphical summaries of uncertainty in estimates of parameters in nonlinear models. A nonlinear constrained optimization algorithm is developed for likelihood based confidence intervals for the functions of parameters in the model The results are applied to the problem of finding significance levels in nonlinear models.

• Journal of ILASS-Korea
• /
• v.12 no.4
• /
• pp.191-197
• /
• 2007

This study presents in-line digital particle holography and its application to spray droplets to measure the characteristics of spray droplets. Several important parameters at the time of hologram recording such as the object distance and the region of laser beam used were verified. The correlation coefficient method with important parameters such as the reconstruction interval and the correlation interval was used for determination of the focal planes of particles. The optimal values of all these parameters are obtained by either numerical simulation of holograms or experiments. Using these optimal parameters, double pulse digital spray holograms in a short time interval were recorded with the synchronization system for the time control. The spatial positions of droplets that are used for the evaluation of the three dimensional droplet velocities can be easily located, which proves the feasibility of the digital holographic technology for measurements of several important features of spray droplets.

• Structural Engineering and Mechanics
• /
• v.21 no.2
• /
• pp.185-204
• /
• 2005

Variations in system parameters due to uncertainties may result in system performance deterioration. Uncertainties in modeling of structures are often considered to ensure that control system is robust with respect to response errors. Hence, the uncertain concept plays an important role in vibration control of the engineering structures. The paper discusses the robustness of the stability of vibration control systems with uncertain parameters. The vibration control problem of an uncertain system is approximated by a deterministic one. The uncertain parameters are described by interval variables. The uncertain state matrix is constructed directly using system physical parameters and avoided to use bounds in Euclidean norm. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the upper and lower bounds of eigenvalues of the close-loop system with uncertain parameters is presented. The lower bounds of eigenvalues can be used to estimate the robustness of the stability the controlled system with uncertain parameters. Two numerical examples are given to illustrate the applications of the present approach.