Dual methods for discrete structural optimization problems

The purpose of this paper is to present a mathematical programming method developed to solve structural optimization problems involving discrete variables. We work in the following context: the structural responses are computed by the finite elements method and convex and separable approximation schemes are used to generate a sequence of explicit approximate subproblems.Each of them is solved in the dual space with a subgradient‐based algorithm (or with a variant of it) specially developed to maximize the not everywhere differentiable dual function. To show that the application field is large, the presented applications are issued from different domains of structural design, such as sizing of thin‐walled structures, geometrical configuration of trusses, topology optimization of membrane or 3‐D structures and welding points numbering in car bodies. The main drawback of using the dual approach is that the obtained solution is generally not the global optimum. This is linked to the presence of a duality gap, due to the non‐convexity of the primal discrete subproblems. Fortunately, this gap can be quantified: a maximum bound on its value can be computed. Moreover, it turns out that the duality gap is decreasing for higher number of variables; the maximum bound on the duality gap is generally negligible in the treated applications. The developed algorithms are very efficient for 2‐D and 3‐D topology optimization, where applications involving thousands of binary design variables are solved in a very short time. Copyright © 2000 John Wiley & Sons, Ltd.     

电动汽车参与风电场输出功率波动平抑方法研究

由于风电固有的随机性与间歇性,使得风电场输出功率往往具有较大的波动。然而考虑到储能装置的昂贵成本,单独为风电场配置储能装置不利于其经济运行。为此,文中针对考虑电动汽车参与的风电场输出功率波动平抑方法进行了研究。根据国家标准中风电“有功功率变化”的要求,通过爬坡率概念来描述风电场输出功率变化率。采用鲁棒优化的方法处理风电出力的不确定性,建立风电机组和电动汽车协调控制的双层优化模型：上层模型决策者是风电场,以风电场售电收益最大化为目标函数;下层模型决策者是电动汽车车主,以电动汽车电费支出成本最小化为目标函数。通过线性规划对偶定理和Karush-KuhnTucker（KKT）最优性条件将此鲁棒优化模型转化为混合整数线性规划问题进行求解。最后,通过仿真结果验证了所提模型和方法的有效性。     

Stochastic inverse heat conduction using a spectral approach

An adjoint‐based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill‐posed stochastic inverse problem is restated as a conditionally well‐posed L₂ optimization problem. The gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field. The L₂ optimization problem is solved using a conjugate‐gradient approach. Accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Parametric Optimization of Hybrid Car Engines

We consider the problem of optimal design of hybrid car engines which combine thermal and electric power. The optimal configuration of the different motors composing the hybrid system involves the choice of certain design parameters. For a given configuration, the goal is to minimize the fuel consumption along a trajectory. This is an optimal control problem with one state variable.The simultaneous optimization of design parameters and trajectories can be formulated as a bilevel optimization problem. The lower level computes the optimal control for a given architecture. The higher level seeks for the optimal design parameters by solving a nonconvex nonsmooth optimization problem with a bundle method.     

Simultaneous partial topology and size optimization of a wing structure using ant colony and gradient based methods

This article presents a methodology and process for a combined wing configuration partial topology and structure size optimization. It is aimed at achieving a minimum structural weight by optimizing the structure layout and structural component size simultaneously. This design optimization process contains two types of design variables and hence was divided into two sub-problems. One is structure layout topology to obtain an optimal number and location of spars with discrete integer design variables. Another is component size optimization with continuous design variables in the structure FE model. A multi city-layer ant colony optimization (MCLACO) method is proposed and applied to the topology sub-problem. A gradient based optimization method (GBOM) built in the MSC.NASTRAN SOL-200 module was employed in the component size optimization sub-problem. For each selected layout of the wing structure, a size optimization process is performed to obtain the optimum result and feedback to the layout topology process. The numerical example shows that the proposed MCLACO method and a combination with the GBOM are effective for solving such a wing structure optimization problem. The results also indicate that significant structural weight saving can be achieved.     

Path‐generation of articulated mechanisms by shape and topology variations in non‐linear truss representation

This paper presents studies on an optimization‐based method for path‐generation of articulated mechanisms. An extended truss ground‐structure approach is taken in which both the shape and topology of the truss are designed using cross‐sectional areas and nodal positions as design variables. This leads to a technique for simultaneous type and dimensional synthesis of articulated mechanisms. For the analysis part it is essential to control the mechanism configuration so that the mechanism remains within a given configuration space, thus stabilizing the optimization process and resulting in realistic solutions. This can be achieved by using the Levenberg–Marquardt method. The design method is illustrated by a number of design cases for both closed and open input and output paths. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization of Wall Electrodes for Electro-Hydrodynamic Control of Natural Convection during Solidification

This article presents a numerical procedure to reduce and possibly control the natural convection effects in a cavity filled with a molten material by applying an external electric field whose intensity and spatial distributions are obtained by the use of a hybrid optimizer. This conceptually new approach to manufacturing could be used in creation of layered and functionally graded materials and objects. In the case of steady electro-hydrodynamics (EHD), the flow-field of electrically charged particles in a solidifying melt is influenced by an externally applied electric field while the existence of any magnetic field is neglected. Solidification front shape, distribution of the charged particles in the accrued solid, and the amount of accrued solid phase in such processes can be influenced by an appropriate distribution and orientation of the electric field. The intensities of the electrodes along the boundaries of the cavity were described using B-splines. The inverse problem was then formulated to find the electric boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the horizontal direction are minimized. For this task we used a hybrid optimization algorithm that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, the quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). The transient Navier-Stokes and Maxwell equations were discretized using the finite volume method in a generalized, curvilinear nonorthogonal coordinate system. For the phase change problems, we used the enthalpy method.     

ENHANCED MULTIOBJECTIVE OPTIMIZATION TECHNIQUE FOR MULTIDISCIPLINARY DESIGN

An enhanced multiobjective formulation technique, capable of emphasizing specific objective functions during the optimization process, has been demonstrated on a complex multidisciplinary design application. The Kreisselmeier - Steinhauser (K-S) function approach, which has been used successfully in a variety of multiobjective optimization problems, has been modified using weight factors which enables the designer to emphasize specific design objectives during the optimization process. The technique has been implemented in two distinctively different problems. The first is a classical three bar truss problem and the second is a high-speed aircraft (a doubly swept wing-body configuration) application in which the multiobjective optimization procedure simultaneously minimizes the sonic boom and the drag-to-lift ratio (C_D/C_L) of the aircraft while maintaining the lift coefficient within prescribed limits. The results are compared with those of an equally weighted K-S multiobjective optimization. Results demonstrate the effectiveness of the enhanced multiobjective optimization procedure.     

Electric field analysis of spinneret design for multihole electrospinning system

Electric field plays a key role in producing required nanofibers in electrospinning. This study aims to improve the electric field distribution of the multijet spinning system by designing the spinneret configuration. A novel 19-hole multistep electrospinning configuration is presented. The simulation results show that the electric field strength at the central position is intensified due to the protuberant step on the spinneret, and therefore more uniform electric field is obtained compared with the 19-hole flat spinneret. We demonstrate that the multistep spinneret configuration produces finer fibers and more continuous fiber mats compared with the flat spinneret configuration because of the improved electric field distribution. Jet repulsion in the multijet electrospinning process is studied. It is found that the electric field line distribution, which is determined by the spinneret configuration, plays a dominant role in influencing jet repulsion. Applied voltage is the main factor responsible for jet repulsion for a given spinneret configuration.     

An NDE Methodology to Predict Density in Green-State Powder Metallurgy Compacts

Extensive work at PMRC has established a clear correlation between green-state density and electric conductivity of P/M parts. By monitoring a static electric current flow through the pre-sintered P/M sample and recording the voltage response over its surface, sufficient information can be gathered to predict the density profile throughout the sample volume. In this paper, the formulation and implementation of a novel numerical forward and inverse formulation will be presented that is capable of relating DC voltage measurements to green-state density distributions. It will be shown that this methodology is applicable to both lubricated and lubricant-free compacts. We will present a general forward solution that enables the calculation of three-dimensional surface voltages for a given set of boundary conditions and a known conductivity/density distribution throughout the P/M sample. This formulation is particularly useful for the development of new sensors and measurement arrangements, since it permits the optimization of current injection patterns and voltage probe locations. Our novel inverse solution adjusts the conductivity/density profile so as to determine the conductivity distribution that matches most closely a given set of voltage data on the surface. Practical measurements with a range of green-state P/M samples will underscore the success and usefulness of this modeling approach.     

On optimization of bio‐probes

The present paper deals with the modelling and optimization of small bio‐probes that can be used for biological sensing; the bio‐probes can be classified as MicroElectroMechnical Systems (MEMS). The objective is to optimize the structure of the bio‐probes in order to maximize the sensing sensitivity. A biological coating results in a prestress on the sensing cantilever when certain molecules are present in the surrounding medium. The mechanical deformation due to the biological material is modelled by applying a prestress in the top layer of the bio‐probes. Topology optimization is used to improve the design. In the present work it is necessary to use an interpolation scheme different from the SIMP (power law) approach which is usually used in topology optimization. In calculating the sensitivities, needed for the optimization, complications due to the prestress occur, but also due to the coupling between the elastic field and the electric field which both must be used in an integrated model. These complications are dealt with and analytically obtained sensitivities are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

融合注意力机制的多尺度深度网络的逆半调方法

目的 运用现有的逆半调方法恢复的图像存在着半色调网纹去除不够理想、图像细节恢复不够清晰等问题,为了进一步提高逆半调图像在平滑区域和纹理细节方面的质量,提出一种基于融合注意力机制的多尺度卷积神经网络的逆半调方法。方法 首先,根据半色调图像网点噪声多频分布特点,设计多尺度卷积网络为基础结构的深度学习网络,从多个不同的尺度抑制半色调网纹并恢复不同尺度的图像信息;然后,应用注意力机制重建图像信息,从而生成逆半调图像;最后,提出多任务损失函数加速网络优化,更好地实现逆半调。结果 实验结果表明,运用此方法得到的逆半调图像在视觉上与原始图像更为相近,恢复出的图像细节更好;在客观评价方面,通过与现有的最先进的方法相比,峰值信噪比平均值提高了0.562～10.095 dB,结构相似度平均值提高了0.01～0.171。结论 该方法可以实现半色调图像的高质量恢复。     

A microwave inverse scattering technique for image reconstructionbased on a genetic algorithm

The problem of reconstructing locations, shapes, and dielectric permittivity distributions of two-dimensional dielectric objects from measurements of the scattered electric field is addressed. A numerical approach is proposed which is based on a multi-illumination multiview processing. In particular, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a genetic algorithm. The final objective of the approach is the image reconstruction of highly contrasted bodies     

Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis

This article introduces a method which combines the collaborative optimization framework and the inverse reliability strategy to assess the uncertainty encountered in the multidisciplinary design process. This method conducts the sub-system analysis and optimization concurrently and then improves the process of searching for the most probable point (MPP). It reduces the load of the system-level optimizer significantly. This advantage is specifically more prominent for large-scale engineering system design. Meanwhile, because the disciplinary analyses are treated as the equality constraints in the disciplinary optimization, the computation load can be further reduced. Examples are used to illustrate the accuracy and efficiency of the proposed method.     

A framework for parallelized efficient global optimization with application to vehicle crashworthiness optimization

This article presents a framework for simulation-based design optimization of computationally expensive problems, where economizing the generation of sample designs is highly desirable. One popular approach for such problems is efficient global optimization (EGO), where an initial set of design samples is used to construct a kriging model, which is then used to generate new ‘infill’ sample designs at regions of the search space where there is high expectancy of improvement. This article attempts to address one of the limitations of EGO, where generation of infill samples can become a difficult optimization problem in its own right, as well as allow the generation of multiple samples at a time in order to take advantage of parallel computing in the evaluation of the new samples. The proposed approach is tested on analytical functions, and then applied to the vehicle crashworthiness design of a full Geo Metro model undergoing frontal crash conditions.     

Integral equation analysis and optimization of 2D layered nanolithography masks by complex images Green's function technique in TM polarization

Analysis and optimization of diffraction effects in nanolithography through multilayered media with a fast and accurate field-theoretical approach is presented. The scattered field through an arbitrary two-dimensional (2D) mask pattern in multilayered media illuminated by a TM-polarized incident wave is determined by using an electric field integral equation formulation. In this formulation the electric field is represented in terms of complex images Green's functions. The method of moments is then employed to solve the resulting integral equation. In this way an accurate and computationally efficient approximate method is achieved. The accuracy of the proposed method is vindicated through comparison with direct numerical integration results. Moreover, the comparison is made between the results obtained by the proposed method and those obtained by the full-wave finite-element method. The ray tracing method is combined with the proposed method to describe the imaging process in the lithography. The simulated annealing algorithm is then employed to solve the inverse problem, i.e., to design an optimized mask pattern to improve the resolution. Two binary mask patterns under normal incident coherent illumination are designed by this method, where it is shown that the subresolution features improve the critical dimension significantly.     

A two-step optimization approach for technology selection

An efficient optimization approach for the technology selection problem is described. Technology selection is a crucial step in the aircraft design process, especially when the performance and econo-mic requirements are not fulfilled for any combination of the configuration design variables. In such a case, the designer must search efficiently within a set of technology options for the optimal combination that achieves the required improvements. When the set of available technologies is large, as is usually the case, a difficult combinatorial optimization problem ensues, resulting in significant time and computational expense. The objective of the new approach is to reduce the computational cost of technology selection by decomposing the process into two smaller sub-problems. The new approach attempts to exploit the structure of the technology compatibility matrix to improve the efficiency of the technology selection process. Results from an application problem are presented and valuable insights and observations are discussed.     

GENERATING OPTIMAL CONFIGURATIONS IN STRUCTURAL DESIGN USING SIMULATED ANNEALING

This paper presents a combinatorial optimization procedure based on the simulated annealing approach for generation of optimal configuration of structural members. The work is based on altering the finite element model of structure by removing or restoring elements to minimize the material use subject to constraints on maximum stress value and maintenance of connectivity between elements. Such an optimization problem is categorized as a large-scale, non-convex and non-linear problem. Thus, the problem can have multi-minima and it is important to find the global optimum solution as opposed to a local minimization. To improve the computational efficiency, the non-linear shape optimization problem has been linearized and to account for the difference between the non-linear and the linearized values a correction factor is implemented. To illustrate the approach, several design examples are presented and the effect of the parameter of the simulated annealing on the final configuration design is examined. © 1997 by John Wiley & Sons, Ltd.     

Topology optimization for stationary fluid–structure interaction problems using a new monolithic formulation

This paper outlines a new procedure for topology optimization in the steady‐state fluid–structure interaction (FSI) problem. A review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics (hereafter, the fluid and structural equations, respectively) and in imposing coupling boundary conditions between the separated fluid and solid domains. To overcome these difficulties, we propose an alternative monolithic procedure employing a unified domain rather than separated domains, which is not computationally efficient. In the proposed analysis procedure, the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor. For the coupling boundary conditions, the divergence of the pressure and the Darcy damping force are inserted into the solid and fluid equations, respectively. The proposed method is validated in several benchmark analysis problems. Topology optimization in the FSI problem is then made possible by interpolating Young's modulus, the fluid pressure of the modified solid equation, and the inverse permeability from the damping force with respect to the design variables. Copyright © 2009 John Wiley & Sons, Ltd.     

Simultaneous Optimization of Robust Parameter and Tolerance Design Based on Generalized Linear Models

Robust parameter design (RPD) and tolerance design (TD) are two important stages in design process for quality improvement. Simultaneous optimization of RPD and TD is well established on the basis of linear models with constant variance assumption. However, little attention has been paid to RPD and TD with non‐constant variance of residuals or non‐normal responses. In order to obtain further quality improvement and cost reduction, a hybrid approach for simultaneous optimization of RPD and TD with non‐constant variance or non‐normal responses is proposed from generalized linear models (GLMs). First, the mathematical relationship among the process mean, process variance and control factors, noise factors and tolerances is derived from a dual‐response approach based on GLMs, and the quality loss function integrating with tolerance is developed. Second, the total cost model for RPD‐TD concurrent optimization based on GLMs is proposed to determine the best control factors settings and the optimal tolerance values synchronously, which is solved by genetic algorithm in detail. Finally, the proposed approach is applied into an example of electronic circuit design with non‐constant variance, and the results show that the proposed approach performs better on quality improvement and cost reduction. Copyright © 2012 John Wiley & Sons, Ltd.