3 resultados para BOUND-CONSTRAINED MINIMIZATION

em Digital Commons - Michigan Tech


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Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for solving ILPs. We discuss a serial algorithm using a breadth-first branch-and-bound search to check the feasible solution space, and then extend it into a parallel algorithm using a client-server model. In the parallel mode, the search may not be truly breadth-first, depending on the solution time for each node in the solution tree. Our search takes advantage of pruning, often resulting in super-linear improvements in solution time. Finally, we present results from sample ILPs, describe a few modifications to enhance the algorithm and improve solution time, and offer suggestions for future work.

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The goal of this research is to provide a framework for vibro-acoustical analysis and design of a multiple-layer constrained damping structure. The existing research on damping and viscoelastic damping mechanism is limited to the following four mainstream approaches: modeling techniques of damping treatments/materials; control through the electrical-mechanical effect using the piezoelectric layer; optimization by adjusting the parameters of the structure to meet the design requirements; and identification of the damping material’s properties through the response of the structure. This research proposes a systematic design methodology for the multiple-layer constrained damping beam giving consideration to vibro-acoustics. A modeling technique to study the vibro-acoustics of multiple-layered viscoelastic laminated beams using the Biot damping model is presented using a hybrid numerical model. The boundary element method (BEM) is used to model the acoustical cavity whereas the Finite Element Method (FEM) is the basis for vibration analysis of the multiple-layered beam structure. Through the proposed procedure, the analysis can easily be extended to other complex geometry with arbitrary boundary conditions. The nonlinear behavior of viscoelastic damping materials is represented by the Biot damping model taking into account the effects of frequency, temperature and different damping materials for individual layers. A curve-fitting procedure used to obtain the Biot constants for different damping materials for each temperature is explained. The results from structural vibration analysis for selected beams agree with published closed-form results and results for the radiated noise for a sample beam structure obtained using a commercial BEM software is compared with the acoustical results of the same beam with using the Biot damping model. The extension of the Biot damping model is demonstrated to study MDOF (Multiple Degrees of Freedom) dynamics equations of a discrete system in order to introduce different types of viscoelastic damping materials. The mechanical properties of viscoelastic damping materials such as shear modulus and loss factor change with respect to different ambient temperatures and frequencies. The application of multiple-layer treatment increases the damping characteristic of the structure significantly and thus helps to attenuate the vibration and noise for a broad range of frequency and temperature. The main contributions of this dissertation include the following three major tasks: 1) Study of the viscoelastic damping mechanism and the dynamics equation of a multilayer damped system incorporating the Biot damping model. 2) Building the Finite Element Method (FEM) model of the multiple-layer constrained viscoelastic damping beam and conducting the vibration analysis. 3) Extending the vibration problem to the Boundary Element Method (BEM) based acoustical problem and comparing the results with commercial simulation software.

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Groundwater pumping from aquifers in hydraulic connection with nearby streams is known to cause adverse impacts by decreasing flows to levels below those necessary to maintain aquatic ecosystems. The recent passage of the Great Lakes--St. Lawrence River Basin Water Resources Compact has brought attention to this issue in the Great Lakes region. In particular, the legislation requires the Great Lakes states to enact measures for limiting water withdrawals that can cause adverse ecosystem impacts. This study explores how both hydrogeologic and environmental flow limitations constrain groundwater availability in the Great Lakes Basin. A methodology for calculating maximum allowable pumping rates is presented. Groundwater availability across the basin is shown to be constrained by a combination of hydrogeologic yield and environmental flow limitations varying over both local and regional scales. The results are sensitive to factors such as pumping time and streamflow depletion limits as well as streambed conductance. Understanding how these restrictions constrain groundwater usage and which hydrogeologic characteristics and spatial variables have the most influence on potential streamflow depletions has important water resources policy and management implications.