A measurement-based load updating method for finite element models subjected to static loads was studied using a four-noded curved beam element for large displacements/rotations and a gradient-based variable metric op...
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A measurement-based load updating method for finite element models subjected to static loads was studied using a four-noded curved beam element for large displacements/rotations and a gradient-based variable metric optimizer. Finite element analysis was used to numerically calculate the geometrically linear and nonlinear responses and their sensitivities under a given load. The optimizer was used to recursively update the load so that it minimized the square of the difference between the calculated and prefiltered/noise-free measured (displacement or strain) data. For the basic studies, the extracted load was represented within an element by a linear combination of integrated Legendre polynomials, the coefficients of which were taken as design variables of the least-squares problem. Through a model order analysis, the benefits for solving load updating problems using the relative deformation measurement, the polynomials of lower orders, the elements of larger sizes (because of using the high precision four-noded beam element), and the denser measured points were studied for linear responses under different types of applied loads. It was confirmed that using the reduced number of unknown variables to obtain an overdetermined inverse problem helps get unique and stable extracted loads. Though this conclusion was verified mainly through illustrative examples for a cantilever beam, it was generally applicable to other load updating or inverse problems. Further examples were given for a three-dimensional portal frame load updating, extracting highly oscillating loads, and a strain-based cantilever beam load updating. The final examples were load updating for geometrically nonlinear finite element models under self-weight, snow, and/or pressure loads.
A very general and robust approach to solving continuous-variable optimization problems involving uncertainty in the objective function is through the use of ordinal optimization. At each step in the optimization prob...
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A very general and robust approach to solving continuous-variable optimization problems involving uncertainty in the objective function is through the use of ordinal optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the uncertainty effects on local design alternatives, rather than on precise quantification of the effects. One simply asks, "Is that alternative better or worse than this one?"not "How much better or worse is that alternative to this one?" The answer to the latter question requires precise characterization of the uncertainty, with the corresponding sampling/integration expense for precise resolution. However, in this paper, we demonstrate correct decision-making in a continuous-variable probabilistic optimization problem despite extreme vagueness in the statistical characterization of the design options. We present a new adaptive ordinal method for probabilistic optimization in which the tradeoff between computational expense and vagueness in the uncertainty characterization can be conveniently managed in various phases of the optimization problem to make cost-effective stepping decisions in the design space. Spatial correlation of uncertainty in the continuous-variable design space is exploited to dramatically increase method efficiency. Under many circumstances, the method appears to have favorable robustness and cost-scaling properties relative to other probabilistic optimization methods, and it uniquely has mechanisms for quantifying and controlling error likelihood in design-space stepping decisions. The method is asymptotically convergent to the true probabilistic optimum, and so could be useful as a reference standard against which the efficiency and robustness of other methods can be compared, analogous to the role that Monte Carlo simulation plays in uncertainty propagation.
A compact limited memory method for solving large scale unconstrained optimization problems is proposed. The compact representation of the quasi-Newton updating matrix is derived to the use in the form of limited memo...
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A compact limited memory method for solving large scale unconstrained optimization problems is proposed. The compact representation of the quasi-Newton updating matrix is derived to the use in the form of limited memory update in which the vector y(k) is replaced by a modified vector y(k) so that more available information about the function can be employed to increase the accuracy of Hessian approximations. The global convergence of the proposed method is proved. Numerical tests on commonly used large scale test problems indicate that the proposed compact limited memory method is competitive and efficient. (c) 2006 Elsevier B.V. All rights reserved.
Motivated by the requirement for pinpoint landing in future Mars missions, we consider the problem of minimum-fuel powered terminal descent to a prescribed landing site. The first-order necessary conditions are derive...
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Motivated by the requirement for pinpoint landing in future Mars missions, we consider the problem of minimum-fuel powered terminal descent to a prescribed landing site. The first-order necessary conditions are derived and interpreted for a point-mass model with throttle and thrust angle control and for rigid-body model with throttle and angular velocity control, clarifying the characteristics of the minimum-fuel solution in each case. The optimal thrust magnitude profile is bang-bang for both models;for the point-mass, the most general thrust magnitude profile has a maximum-minimum-maximum structure. The optimal thrust direction law for the point-mass model (alignment with the primer vector) corresponds to a singular solution for the rigid-body model. Whether the point-mass solution accurately approximates the rigid-body solution depends on the thrust direction boundary conditions imposed for the-rigid-body model. Minimum-fuel solutions, obtained numerically, illustrate the optimal strategies.
The aerogravity-assist maneuver is proposed as a tool to improve the efficiency of the gravity assist, because due to the interaction with the planetary atmosphere, the angular deviation of the velocity vector can be ...
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The aerogravity-assist maneuver is proposed as a tool to improve the efficiency of the gravity assist, because due to the interaction with the planetary atmosphere, the angular deviation of the velocity vector can be definitely increased. Even though the drag reduces the spacecraft velocity, the overall A v gain could be substantial for a high-lift-to-drag vehicle. A previous study addressed the three-dimensional dynamic modeling and optimization of the maneuver, including heliocentric plane change, heating rate, and structural load analysis. A multidisciplinary study of aerogravity assist is proposed, focusing on coupled trajectory and vehicle shape optimization. A planar aerogravity assist of Mars is selected as a test case, with the aim of maximizing the vehicle heliocentric velocity and limiting the heating rate experienced during the atmospheric pass. A multiobjective approach is adopted, and a particle swarm optimization algorithm is chosen to detect the set of Pareto-optimal solutions. The study includes a further refinement of the trajectory for three significant shapes belonging to the Pareto curve. The associated optimal control problem is solved by selecting a direct-method approach. The dynamics are transcribed into a set of nonlinear constraints, and the arising nonlinear programming problem is solved through a sequential quadratic programming solver.
We investigate the optimal partitioning of the end-to-end network QoS budget to quantify the advantage of having a non-uniform allocation of the budget over the links in a path. We formulate an optimization problem th...
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We investigate the optimal partitioning of the end-to-end network QoS budget to quantify the advantage of having a non-uniform allocation of the budget over the links in a path. We formulate an optimization problem that provides a unified framework to study QoS budget allocation. We examine the underlying mathematical structure for the optimal partitioning and dimensioning equations. In the context of network dimensioning, we then show that optimal partitioning can bring large cost reductions as compared with equal partitioning based on the results on small networks. More importantly, we also find that optimal partitioning gives significant improvements in robustness in the presence of failed components and in fairness when the traffic demand is different from the forecast, two effects that had not been observed in previous work and that can have a significant effect on network operations.
Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even...
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Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve NLP problems of typical sizes. However stochastic programming problems are highly structured. The key to the efficient solution of such problems is therefore the ability to exploit their structure. Interior point methods are well-suited to the solution of very large non-linear optimization problems. In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semivariance, skewness or non-linear utility functions in the objective, can be solved with the state-of-the-art solver. (C) 2006 Elsevier B.V. All rights reserved.
A general mixed-integer nonlinear programming (MINLP) model is developed in this study to synthesize water networks in batch processes. The proposed model formulation is believed to be superior to the available ones. ...
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A general mixed-integer nonlinear programming (MINLP) model is developed in this study to synthesize water networks in batch processes. The proposed model formulation is believed to be superior to the available ones. In the past, the tasks of optimizing batch schedules, water-reuse subsystems, and wastewater treatment subsystems were performed individually. In this study, all three optimization problems are incorporated in the same mathematical programming model. By properly addressing the issue of interaction between subsystems, better overall designs can be generated. The resulting design specifications include the following: the production schedule, the number and sizes of buffer tanks, the physical configuration of the pipeline network, and the operating policies of water flows. The network structure can also be strategically manipulated by imposing suitable logic constraints. A series of illustrative examples are presented to demonstrate the effectiveness of the proposed approach.
A proximal bundle method with inexact data is presented for minimizing an unconstrained nonsmooth convex function f. At each iteration, only the approximate evaluations of f and its epsilon-subgradients are required a...
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A proximal bundle method with inexact data is presented for minimizing an unconstrained nonsmooth convex function f. At each iteration, only the approximate evaluations of f and its epsilon-subgradients are required and its search directions are determined via solving quadratic programmings. Compared with the pre-existing results, the polyhedral approximation model that we offer is more precise and a new term is added into the estimation term of the descent from the model. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem. (c) 2007 Published by Elsevier Ltd.
The main aim of this paper is to generalize the notion of pseudolinearity to nondifferentiable functions and to obtain characterizations for such functions. Under the assumption of pseudolinearity, a characterization ...
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The main aim of this paper is to generalize the notion of pseudolinearity to nondifferentiable functions and to obtain characterizations for such functions. Under the assumption of pseudolinearity, a characterization for the solution sets of an optimization problem and a variational inequality problem has been obtained.
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