Based on the static limit analysis theorem, a solution procedure for limit analysis of three-dimensional (3-D) structures is established making use of conventional boundary element method (BEM) rather than of finite e...
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Based on the static limit analysis theorem, a solution procedure for limit analysis of three-dimensional (3-D) structures is established making use of conventional boundary element method (BEM) rather than of finite element method (FEM). The self-equilibrium stress fields are expressed by linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to imposed permanent strains obtained through elastic-plastic incremental analysis by three-dimensional boundary element method (3-D BEM). The Complex method is used to directly solve the resulting nonlinear programming problem and to determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve 3-D limit analysis problems by using BEM and the Complex method. (C) 2003 Elsevier SAS. All rights reserved.
The Bayesian reliability estimation under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed to be fuzzy random variables with fuzzy prior distribut...
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The Bayesian reliability estimation under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed to be fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of reliability by invoking the well-known theorem called 'Resolution Identity' in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g. GAMS or LINGO. (C) 2004 Elsevier Ltd. All rights reserved.
In this paper, we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process system...
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In this paper, we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of optimization problems for continuous and discrete variable optimization, particularly nonlinear and mixed-integer nonlinear programming (MINLP). We also review their extensions to dynamic optimization and optimization under uncertainty. While these areas are still subject to significant research efforts, the emphasis in this paper is on major developments that have taken place over the last 25 years. (C) 2003 Elsevier Ltd. All rights reserved.
We transform the system of nonlinear equations into a nonlinear programming problem, which is solved by null space algorithms. We do not use standard least square approach. We divide the equations into two groups: One...
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We transform the system of nonlinear equations into a nonlinear programming problem, which is solved by null space algorithms. We do not use standard least square approach. We divide the equations into two groups: One group. contains the equations that are treated-as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step. In essence, two different methods are used for a system of equations in an algorithm. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, we use fuzzy approximation to deal with infeasibility in generalized linear complementarity problem. The solution of such problem with some degree of satisfaction is obtained by finding the minimum rela...
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In this paper, we use fuzzy approximation to deal with infeasibility in generalized linear complementarity problem. The solution of such problem with some degree of satisfaction is obtained by finding the minimum relaxation which should be allowed in the original problem. (C) 2003 Elsevier B.V. All rights reserved.
We describe a new algorithm for a class of parameter estimation problems, which are either unconstrained or have only equality constraints and bounds on parameters. Due to the presence of unobservable variables, param...
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We describe a new algorithm for a class of parameter estimation problems, which are either unconstrained or have only equality constraints and bounds on parameters. Due to the presence of unobservable variables, parameter estimation problems may have non-unique solutions for these variables. These can also lead to singular or ill-conditioned Hessians and this may be responsible for slow or non-convergence of nonlinear programming (NLP) algorithms used to solve these problems. For this reason, we need an algorithm that leads to strong descent and converges to a stationary point. Our algorithm is based on Successive Quadratic programming (SQP) and constrains the SQP steps in a trust region for global convergence. We consider the second-order information in three ways: quasi-Newton updates, Gauss-Newton approximation, and exact second derivatives, and we compare their performance. Finally, we provide results of tests of our algorithm on various problems from the CUTE and COPS sets.
For some applications it is desired to approximate a set of m data points in R-n with a convex quadratic function. Furthermore, it is required that the convex quadratic approximation underestimate all m of the data po...
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For some applications it is desired to approximate a set of m data points in R-n with a convex quadratic function. Furthermore, it is required that the convex quadratic approximation underestimate all m of the data points. It is shown here how to formulate and solve this problem using a convex quadratic function with s = (n + 1)(n + 2)/2 parameters, s = m, so as to minimize the approximation error in the L-1 norm. The approximating function is q(p, x), where p is an element of R-s is the vector of parameters, and x is an element of R-n. The Hessian of q(p, x) with respect to x (for fixed p) is positive semi-definite, and its Hessian with respect to p (for fixed x) is shown to be positive semi-definite and of rank less than or equal ton. An algorithm is described for computing an optimal p* for any specified set of m data points, and computational results ( for n = 4, 6, 10, 15) are presented showing that the optimal q(p*, x) can be obtained efficiently. It is shown that the approximation will usually interpolate s of the m data points.
The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distr...
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The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayes estimation method will be used to create the fuzzy Bayes point estimator of system reliability by invoking the well-known theorem called 'Resolution Identity' in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g. GAMS or LINGO. (C) 2003 Elsevier Ltd. All rights reserved.
A general methodology to design open loop controllers for nonlinear, dynamic, continuous systems is presented and applied to control a single flexible link (SFL). In this application, the partial differential equation...
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A general methodology to design open loop controllers for nonlinear, dynamic, continuous systems is presented and applied to control a single flexible link (SFL). In this application, the partial differential equations that describe the beam system are first analyzed via the finite element method (FEM) and Newmark integration method. Two open loop control inputs to achieve specified system performance criteria are then computed by posing and solving inverse dynamics problems. These analyses use nonlinear programming (NLP) algorithms and analytical gradients that are computed by the direct sensitivity method. The open loop control is verified experimentally. Closed loop controller synthesis for linear time invariant (LTI) and linear time varying systems (LTV) is relatively well understood. To apply this knowledge base to the control of the SFL, the nonlinear finite element plant model is linearized and recast in standard state space form.
The aim of the present paper is to find an optimum speed control hump geometric design by using the sequential quadratic programming method. Theoretical investigation of the dynamic behavior of the driver body compone...
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The aim of the present paper is to find an optimum speed control hump geometric design by using the sequential quadratic programming method. Theoretical investigation of the dynamic behavior of the driver body components and the vehicle due to crossing speed control humps is presented. The vehicle - driver system represented as a mathematical model consists of 12 degrees of freedom (DOF). Seven DOFs are used for the human body model in the heave mode and the rest are for the vehicle body, suspension system and tires. An optimum design method for the hump geometry is proposed to reduce the excessive shocks experienced by drivers when crossing the hump below the speed limit, while being unpleasant when going over the speed limit. The pleasant or unpleasant ride, or what is called comfort criteria (CC), is modeled by calculating the driver's head acceleration. In this regard, the geometry of the hump will be controlled to match an optimum practical shape that can be implemented economically. Three types of humps are discussed and evaluated in the optimization technique. These humps are Watts, flat-topped and polynomial humps. For Watts and flat-topped humps, different rise and return profiles which are used as design variables, are sinusoidal, harmonic, cycloidal, circular and modified harmonic. The global design was selected from 42 optimal designs which are found by combining different rise/return profiles for the three types of humps. The effect of special cases such as symmetrical roads, design limitations, CC, critical speed ( CS) and system parametric variations on the optimal design of speed control humps are presented at the end of this paper.
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