41 resultados para nonlinear optimization problems
Resumo:
The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.
Resumo:
This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.
Resumo:
In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system has several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the system can be introduced to students earlier in their education. At the same time, the system is nonlinear and underactuated so that it can be used as a benchmark experiment to study recent advanced methodologies in nonlinear control, such as feedback linearization, passivity methods, backstepping and hybrid control. In this paper we discuss two control approaches for the problems of swingup and balance, namely, feedback linearization and passivity based control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we discuss an energy approach based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented.
Resumo:
This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.
Resumo:
Seaport container terminals are an important part of the logistics systems in international trades. This paper investigates the relationship between quay cranes, yard machines and container storage locations in a multi-berth and multi-ship environment. The aims are to develop a model for improving the operation efficiency of the seaports and to develop an analytical tool for yard operation planning. Due to the fact that the container transfer times are sequence-dependent and with the large number of variables involve, the proposed model cannot be solved in a reasonable time interval for realistically sized problems. For this reason, List Scheduling and Tabu Search algorithms have been developed to solve this formidable and NP-hard scheduling problem. Numerical implementations have been analysed and promising results have been achieved.
Resumo:
There are many applications in aeronautics where there exist strong couplings between disciplines. One practical example is within the context of Unmanned Aerial Vehicle(UAV) automation where there exists strong coupling between operation constraints, aerodynamics, vehicle dynamics, mission and path planning. UAV path planning can be done either online or offline. The current state of path planning optimisation online UAVs with high performance computation is not at the same level as its ground-based offline optimizer's counterpart, this is mainly due to the volume, power and weight limitations on the UAV; some small UAVs do not have the computational power needed for some optimisation and path planning task. In this paper, we describe an optimisation method which can be applied to Multi-disciplinary Design Optimisation problems and UAV path planning problems. Hardware-based design optimisation techniques are used. The power and physical limitations of UAV, which may not be a problem in PC-based solutions, can be approached by utilizing a Field Programmable Gate Array (FPGA) as an algorithm accelerator. The inevitable latency produced by the iterative process of an Evolutionary Algorithm (EA) is concealed by exploiting the parallelism component within the dataflow paradigm of the EA on an FPGA architecture. Results compare software PC-based solutions and the hardware-based solutions for benchmark mathematical problems as well as a simple real world engineering problem. Results also indicate the practicality of the method which can be used for more complex single and multi objective coupled problems in aeronautical applications.
Resumo:
The growing demand of air-conditioning is one of the largest contributors to Australia’s overall electricity consumption. This has started to create peak load supply problems for some electricity utilities particularly in Queensland. This research aimed to develop consumer demand side response model to assist electricity consumers to mitigate peak demand on the electrical network. The model developed demand side response model to allow consumers to manage and control air conditioning for every period, it is called intelligent control. This research investigates optimal response of end-user toward electricity price for several cases in the near future, such as: no spike, spike and probability spike price cases. The results indicate the potential of the scheme to achieve energy savings, reducing electricity bills (costs) to the consumer and targeting best economic performance for electrical generation distribution and transmission.
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Distributed Genetic Algorithms (DGAs) designed for the Internet have to take its high communication cost into consideration. For island model GAs, the migration topology has a major impact on DGA performance. This paper describes and evaluates an adaptive migration topology optimizer that keeps the communication load low while maintaining high solution quality. Experiments on benchmark problems show that the optimized topology outperforms static or random topologies of the same degree of connectivity. The applicability of the method on real-world problems is demonstrated on a hard optimization problem in VLSI design.
Resumo:
The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.
Resumo:
We consider the problem of how to maximize secure connectivity of multi-hop wireless ad hoc networks after deployment. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing a secret key using only the links that are already secured by secret keys. This problem is in NP-hard and does not accept polynomial time approximation scheme PTAS since minimum cutsets to be augmented do not admit constant costs. The second one is based of increasing the power level between a pair of nodes that has a secret key to enable them physically connect. This problem can be formulated as the optimal key establishment problem with interference constraints with bi-objectives: (i) maximizing the concurrent key establishment flow, (ii) minimizing the cost. We show that both problems are NP-hard and MAX-SNP (i.e., it is NP-hard to approximate them within a factor of 1 + e for e > 0 ) with a reduction to MAX3SAT problem. Thus, we design and implement a fully distributed algorithm for authenticated key establishment in wireless sensor networks where each sensor knows only its one- hop neighborhood. Our witness based approaches find witnesses in multi-hop neighborhood to authenticate the key establishment between two sensor nodes which do not share a key and which are not connected through a secure path.
Resumo:
Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.
Resumo:
This paper presents a new algorithm based on honey-bee mating optimization (HBMO) to estimate harmonic state variables in distribution networks including distributed generators (DGs). The proposed algorithm performs estimation for both amplitude and phase of each harmonics by minimizing the error between the measured values from phasor measurement units (PMUs) and the values computed from the estimated parameters during the estimation process. Simulation results on two distribution test system are presented to demonstrate that the speed and accuracy of proposed distribution harmonic state estimation (DHSE) algorithm is extremely effective and efficient in comparison with the conventional algorithms such as weight least square (WLS), genetic algorithm (GA) and tabu search (TS).