Shape Optimization for Drag Minimization Using the Navier-Stokes Equation

Future wireless systems must be designed to meet high data rates and a variety of services such as voice, video, etc. which consume more energy. Therefore, designing energy-efficient systems in recent years has become an inevitable trend. In this paper energy efficient resource allocation in orthogonal frequency division multiple access (OFDMA) systems is discussed. After formulating the resource allocation problem, maximizing-energy efficiency (EE)-lower-bound-based downlink subcarrier assignment (MDSA) algorithm is used to solve the problem that allocates subcarrier and power recursively. In this algorithm, first primary subcarriers are assigned to users and then power is allocated and this process continues recursively until all subcarriers are assigned to the users. Power allocation is done by the use of proposed sequential Quadratic programming (SQP) method. Then, simulation results are compared with bisection based power adaptation (BPA) algorithm method which has different power allocation. Results show that power allocation by SQP method has higher energy efficiency. Moreover, SQP shows higher convergence rate in solving the problem (finding the answer) in comparison to BPA method with less simulation time.

A systematic approach to the modeling of deformable rodlike objects is presented. Various rodlike objects such as cords and wires are manipulated in many manufacturing processes. In such processes, it is important for successful manipulation to evaluate their shapes on a computer in advance because their shapes can be changed easily and their deformation often shows hysteresis properties. In this paper, we develop an analytical method to model the shape of deformable rodlike objects including hysteresis properties. First, we investigate the mechanism of hysteresis. Second, the potential energy of a rodlike object and the geometric constraints imposed on it are formulated. The shape of the object can be derived by minimizing the potential energy under the geometric constraints. Thirdly, a procedure to compute the shape of a deformed rodlike object is developed by applying a non-linear programming technique. Finally, we show some numerical examples with hysteresis using our proposed method.

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277---303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian---Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush---Kuhn---Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.

In this paper, the design of non-uniform concentric circular antenna arrays (CCAAs) of isotropic radiators with optimum side lobe level reduction is presented. The newly-proposed global evolutionary optimization methods; namely: the biogeography based optimization (BBO) is used to determine a set of weights that provides a radiation pattern with optimum side lobe level reduction with the constraint of a fixed major lobe beamwidth. The results obtained from BBO are compared with those obtained using the Matlab function Fmincon which uses a sequential quadratic programming (SQP) method. The comparison shows that the design of non-uniformly excited CCAAs using SQP method provides a side lobe level reduction that is better than that obtained using global stochastic optimization methods, indicating that global optimization techniques are not really needed in this problem.

Shape optimization of Navier–Stokes flows by a two-grid method

Direct optimal control methods first discretize a continuous-time Optimal Control Problem (OCP) and then solve the resulting Nonlinear Program (NLP). Sequential Quadratic Programming (SQP) is a popular family of algorithms to solve this finite dimensional optimization problem. In the specific case of a least squares cost, the Generalized Gauss-Newton (GGN) method is a popular approach which works very well under some assumptions. This paper proposes a Sequential Convex Quadratic Programming (SCQP) scheme which exploits additional convexities in the NLP in order to generalize the GGN algorithm, possibly extend its applicability and improve its local convergence. These properties are studied in detail for the proposed SCQP algorithm, which will be compared to the classical GGN method using a numerical case study of the optimal control of an inverted pendulum.

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which “guides” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established.

Optimizations of a photoresist coating process for photolithography in wafer manufacture via a radial basis neural network: A case study

In this paper, a new algorithm, namely, a reduced Hessian sequential quadratic programming (SQP) method, for solving electromagnetic inverse problems is proposed. The electromagnetic inverse problem is considered to be a constrained nonlinear programming. The reduced Hessian SQP method finds the solution of this constrained nonlinear programming by solving a sequential of quadratic programming subproblems. The reduced Hessian scheme is applied to reduce the requirement of computational memory of the basic SQP method for large inverse problems. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method, and some comparisons show that the proposed method has a better convergence and a faster speed than the previous methods.

This study analyzed contour distortions, wear and tensile properties of polypropylene (PP) components applied in the interior coffer of automobiles. A hybrid method integrating a trained generalized regression neural network (GRNN) and a sequential quadratic programming (SQP) method is proposed to determine an optimal parameter setting of the injection‐molding process. The specimens were prepared under different injection‐molding conditions by changing melting temperatures, injection speeds, and injection pressures. Average contour distortions at six critical locations, wear and tensile properties were selected as the quality targets. Sixteen experimental runs, based on a Taguchi orthogonal array table, were utilized to train the GRNN and then the SQP method was applied to search for an optimal setting. The trained GRNN was capable of predicting average contour distortions, wear and tensile properties at various injection‐molding conditions. In addition, the analysis of variance (ANOVA) was implemented to identify significant factors for the molding process and the proposed algorithm was compared with traditional schemes like the Taguchi method and the design of experiments (DOE) approach. Copyright © 2007 John Wiley & Sons, Ltd.

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

In this paper, we consider an optimal control problem arising in a one-dimensional (1D) Magnetohydrodynamic (MHD) flow, which can be modelled by a coupled partial differential equations (PDEs) where the external control input (external induction of magnetic field) takes the multiplicative effect exerted on both state variables (momentum and magnetic components). The aim is to derive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated terminal time. We first use the Galerkin method to obtain a low dimensional dynamical ordinary differential equation (ODE) model based on the original coupled PDEs. Then, we combine the control parameterization method with the time-scaling transformation technique to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). The exact gradients of the cost functional with respect to the decision parameters are computed based on the analytical equations. Finally, we conclude the paper with simulation results for an example of the 1D MHD flow.

Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space

The detachment of soil by flowing water on a hillslope is dependent upon the hydraulics of shallow overland flows. The role of microtopography on controlling the spatial patterns of these flows is poorly understood. This study aimed to improve this understanding by undertaking a series of controlled laboratory tests using an experimental plot, consisting of a soil box, a rainfall simulator and overland flow generator. A particular emphasis was placed on developing low-cost photogrammetric techniques to provide novel, high spatial resolution measurements of surface DEMs, 2D flow velocities and distributions of inundation levels and fluid drag. Overland flow experiments were run over surfaces with differing topographies to further examine the effect of discharge and inundation ratio on the spatial patterns of overland flow velocities, hydraulic resistance and fluid drag. Structure-from-Motion (SfM) was used to measure the microtopography of soils eroded by high intensity rainfall events. An accuracy test showed, for the first time, that SfM is capable of producing highly accurate measurements of microtopographic features at a scale similar to those found on rilled soil surfaces. The results also provided crucial information on how to optimize the acquisition of SFM-imagery in different lightning situations and using different cameras. Analysis of the DEMs of the eroded surfaces revealed the potential to estimate soil surface roughness and the distribution of elevations based on plot slope. A low-cost Particle Tracking Velocimetry system was developed to provide novel, detailed 2D surface vector fields, co-located with the acquired DEMs. The results showed that streamwise and lateral velocities have high spatial variability, revealing the flow was 2D. The distribution shape of streamwise velocities was dependent upon discharge and thus relative submergence; the higher submergences, the spatial variability in streamwise velocity was higher and the distributions were wider, flatter and more skewed. The correlation between these distributions and the surface elevations was not sufficiently high to suggest that overland flow velocity can be predicted well by surface elevations alone. On the other hand, local roughness was better correlated, revealing that local variations in surface elevations are more important in controlling spatial patterns of overland flow velocity. The hydraulic resistance, estimated by the Darcy-Weisbach friction factor, varied strongly with the Reynolds number when the flows were fully turbulent but not when they were close to being transitional, such as in shallow, interrill flows. Surface roughness and relative submergence were found to have a greater or equally strong control as Reynolds number on hydraulic resistance. Drag force varied considerably over eroded soil surfaces, with some areas experiencing forces an order magnitude higher than others. Areas of high drag forces correlated with the walls of rills and with areas in which flows converged from different rills. Thus, the distributions of drag force provide some explanation for why rills expand, deepen and migrate, as well as why erosion rates are so variable over hillslopes. The drag force distributions were well-approximated by a two-parameter Weibull distribution, whose parameters were heavily dependent upon surface roughness and hydraulic resistance. The strength of these relationships revealed the potential to predict the drag force distribution, and thus spatial patterns of hydraulic resistance and erosion, based on these simple parameters. Overall, the study has provided the first detailed study of the effect of microphotography on overland flow patterns, revealing new understanding of the statistical properties of eroded surfaces and the control of roughness on the distribution of 2-D velocities, drag force and hydraulic resistance. These results have important implications for the modelling of overland flow and resultant flow detachment. In doing so, the study has demonstrated the potential of low-cost photogrammetric techniques for providing new understanding of the physics of overland flows, and thus, in the future, driving the development of more physically-based erosion models.

Large-scale nonlinear model predictive control (NMPC) often relies on real-time solution of optimization problems that are constrained by partial differential equations (PDEs). However, the size and complexity of the underlying PDEs present significant computational challenges. In this regard, the development of fast, efficient and scalable PDEconstrained optimization solvers remains central to large-scale NMPC. As a contribution in this direction, this paper proposes a new efficient preconditioned iterative scheme for optimal control of large-scale time-dependent diffusion-reaction problems with nonlinear reaction kinetics. The scheme combines a custom-made high-order spectral Petrov-Galerkin (SPG) method with a new preconditioner tailored for the linearquadratic control problems that underly Sequential Quadratic Programming (SQP) methods. The preconditioner is matrixfree and amenable to parallelization. To demonstrate efficiency, a case study applies the SPG scheme to control solid fuel ignition (SFI) processes. In the absence of control, such processes lead to unstable systems that naturally exhibit finite-time blow-up phenomena. Open-loop simulations demonstrate the ability of the SPG scheme to efficiently control SFI processes, independently of the problem size and the model parameters.