Shape and cross-section optimization of plane trusses subjected to earthquake excitation using gradient and Hessian matrix calculations

This article describes a second-order shape and cross-section optimization method of plane truss subjected to earthquake excitation. The method is based on gradient and Hessian matrix calculation. First, the first and second derivatives of dynamic response with respect to design variables are calculated based on the Newmark method. Second, the inequality time-dependent constraint problem is converted into a sequence of appropriately formed unconstrained problems using the integral interior penalty function method. Then, the gradient and Hessian matrix of the integral interior penalty function are computed. Third, Marquardt's method is employed to solve the unconstrained problems. Finally, the new approach is validated through several case studies. The results show that the new optimization method is an efficient and effective approach for minimum weight design of truss structures.     

GENERALIZED CENTER METHOD FOR MULTIOBJECTIVE ENGINEERING OPTIMIZATION

This paper presents a new approach to multiobjective engineering optimization: the generalized center method (GCM). A multiobjective problem is solved by calculating the centers of a sequence of level sets. These sets comprise intersections of the original constraints and level constraints imposed on objective functions. In view of the different dimensions and conflicting nature of multiple objectives, some scaling and trade-off procedures are implemented. Several engineering optimization examples are given to demonstrate the effectiveness of the proposed method.     

Efficient approximation concepts using second order information

The primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal–dual approach is employed, that can also be interpreted as a sequential quadratic programming method. Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non-linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA). This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on reciprocal variables.     

考虑可靠度可信区间的结构可靠性优化设计

 在贝叶斯统计理论和结构可靠性优化设计方法的基础上,研究了结构在小样本情况下考虑可靠度可信区间的结构可靠性优化设计问题.将结构可靠度作为随机变量,根据先验信息和样本信息,采用贝叶斯推断技术获得结构可靠度的概率分布,给出了可靠度的点估计及区间估计.建立了考虑可靠度可信区间的结构可靠性优化设计模型,提出了考虑可靠度可信区间的结构可靠性优化设计方法.所提出的方法为解决小样本情况下的结构可靠性优化设计问题提供了新的解决方案.数值算例验证了所提出的结构可靠性优化设计方法的有效性和正确性.     

A novel surrogate-based approach for optimal design of electromagnetic-based circuits

A new geometric design centring approach for optimal design of central processing unit-intensive electromagnetic (EM)-based circuits is introduced. The approach uses norms related to the probability distribution of the circuit parameters to find distances from a point to the feasible region boundaries by solving nonlinear optimization problems. Based on these normed distances, the design centring problem is formulated as a max–min optimization problem. A convergent iterative boundary search technique is exploited to find the normed distances. To alleviate the computation cost associated with the EM-based circuits design cycle, space-mapping (SM) surrogates are used to create a sequence of iteratively updated feasible region approximations. In each SM feasible region approximation, the centring process using normed distances is implemented, leading to a better centre point. The process is repeated until a final design centre is attained. Practical examples are given to show the effectiveness of the new design centring method for EM-based circuits.     

结构可靠性优化求解的解耦融合策略

在工程结构的可靠性优化过程中,求解的效率和精度是优化方法的关键。该文提出一种针对解耦优化的融合策略。所提方法在优化迭代解耦所用的失效概率函数为前几次迭代设计点构建的局部失效概率函数的加权融合形式。在对原可靠性优化问题进行解耦后,结合序列近似优化方法进行迭代求解。相比于常规的仅使用当次局部建立的失效概率函数而言,所提融合策略最大限度利用了各次迭代中产生的信息用于优化解耦求解,能够提高失效概率函数的近似精度,从而间接达到减少迭代次数和计算量的目的。最后给出了屋架和十杆结构的可靠性优化算例,验证该文方法的正确性和可行性。     

An Enhanced Formulation of the Maximum Entropy Method for Structural Optimization

A numerical optimization method was proposed time ago by Templeman based on the maximum entropy principle. That approach combined the Kuhn-Tucker condition and the information theory postulates to create a probabilistic formulation of the optimality criteria techniques. Such approach has been enhanced in this research organizing the mathematical process in a single optimization loop and linearizing the constraints. It turns out that such procedure transforms the optimization process in a sequence of systems of linear equations which is a very efficient way of obtaining the optimum solution of the problem. Some examples of structural optimization, namely, a planar truss, a spatial truss and a composite stiffened panel, are presented to demonstrate the capabilities of the methodology.     

Global optimization and modeling techniques for planar multilayered dielectric structures

We present a multilevel global optimization strategy for synthesizing planar multilayered dielectric structures. A low discrepancy sequence of sample points with uniform variable space coverage allows a global-level search while systematic refinement using gradient-based techniques identifies optima at the local level. Since efficient local optimization is important for this method, a fast calculation approach based on mode matching is presented; this also facilitates the compact derivation of analytical gradients. The approach is compared with genetic and simulated annealing algorithms through an antireflection coating design. The method proves to be competitive in terms of its performance, nonadaptive algorithm, and ability to track local solutions.     

Structural shape and topology optimization based on level-set modelling and the element-propagating method

This article introduces the element-propagating method to structural shape and topology optimization. Structural optimization based on the conventional level-set method needs to solve several partial differential equations. By the insertion and deletion of basic material elements around the geometric boundary, the element-propagating method can avoid solving the partial differential equations and realize the dynamic updating of the material region. This approach also places no restrictions on the signed distance function and the Courant–Friedrichs–Lewy condition for numerical stability. At the same time, in order to suppress the dependence on the design initialization for the 2D structural optimization problem, the strain energy density is taken as a criterion to generate new holes in the material region. The coupled algorithm of the element-propagating method and the method for generating new holes makes the structural optimization more robust. Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the conventional level-set method for structural topology optimization.     

Optimal supervisory control of a central chilled water plant with heuristic search sequential quadratic programming

A new methodology for adapting rigorous simulation programs to optimal supervisory control of a central chilled water plant is proposed in this article, which solves plant operation mode optimization and set points optimization by combining heuristic search with sequential quadratic programming. The mathematical basis of this algorithm is developed. A new derivative calculation strategy is introduced in set points optimization. This approach is applied to a central chilled water plant which consists of three chillers, two 3-cell cooling towers, three chilled water pumps and three condenser water pumps. Model verification study is performed. The optimal sequence of operation, set points of the decision variables at given load demand and weather condition are calculated. The plant performance and optimal control results are discussed.     

拓扑相关荷载作用下结构拓扑优化的水平集方法

发展了一种利用水平集演化技术求解拓扑相关荷载作用下结构拓扑优化问题的数值方法。通过引入水平集函数,我们以隐含的方式对结构的拓扑和形状作了描述,从而把拓扑优化问题转化为了寻求最优水平集函数的数学规划问题。利用基于连续体概念的灵敏度分析技术,构造了用于驱动水平集演化的速度场。由于结构的边界可以用零水平集加以描述,因此利用适当的数学变换,我们可以方便地处理施加在结构上的拓扑相关荷载,这样就避免了以往算法中繁复的边界提取工作以及为了处理拓扑相关荷载所采取的特殊技巧。文末的数值算例表明了提出的优化方法在处理此类问题时所具有的独到的优越性。     

A study on the application of material selection optimization approach for structural-acoustic optimization

Issues of application of the material selection optimization approach for structural-acoustic optimization is investigated herein. By introducing the stacking sequence hypothesis of metal material, the mechanical properties parameters and plies’ numbers of the metal material or composite material are defined as design variables; the mathematical formulation about material selection optimization approach is established. Finally, a hexahedral box structure is taken as an example, and the material selection optimization is conducted. By introducing genetic algorithm (GA), the optimization problem is solved. The numerical example shows the effectiveness of the proposed stacking sequence hypothesis of metal material.     

Optimization approach in variable-charge potential for metal/metal oxide systems

Earlier attempts on minimizing the total system energy of metal/metal oxide systems with given charge constraints appear to be indirect and unnecessarily complicated. The energy minimization problem is in fact a constrained optimization problem and hence can be solved by a constrained optimization method. We propose a new direct approach for finding charge distributions among ions in molecular dynamics simulations. The approach is based on an optimization algorithm, called the Generalized Reduced Gradient (GRG) Method. This efficient approach can be readily employed in molecular dynamic simulations for metal/metal oxide systems.     

A level set approach for topology optimization with local stress constraints

The purpose of this work is to present a level set‐based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints. The main contributions are threefold. First, the inclusion of local stress constraints by means of an augmented Lagrangian approach within the level set context. Second, the proposition of a constraint procedure that accounts for a continuous activation/deactivation of a finite number of local stress constraints during the optimization sequence. Finally, the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence. A set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method. In these examples, it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum. Copyright © 2014 John Wiley & Sons, Ltd.     

MR-PRIM: Patient Rule Induction Method for Multiresponse Optimization

Most of the works in multiresponse surface methodology have been focusing mainly on the optimization issue, assuming that the data have been collected and suitable models have been built. Though crucial for optimization, a good empirical model is not easy to obtain from the manufacturing process data. This article proposes a new approach to solving the multiresponse problem directly without building a model—an approach called patient rule induction method for multiresponse optimization (MR-PRIM). MR-PRIM is an extension of PRIM to multiresponse problems. Three major characteristic features of MR-PRIM are discussed as the new approach is applied to the case of a steel manufacturing process.     

An asymmetric suboptimization approach to aerostructural optimization

An asymmetric suboptimization method for performing multidisciplinary design optimization is introduced. The objective of the proposed method is to improve the overall efficiency of aerostructural optimization, by simplifying the system-level problem, and thereby reducing the number of calls to a potentially costly aerodynamics solver. To guide a gradient-based optimization algorithm, an extension of the coupled sensitivity equations is developed to include post-optimality information from the structural suboptimization. The optimization of an aircraft wing is performed using linear aerodynamic and structural analyses, and a thorough performance comparison is made between the new approach and the conventional multidisciplinary feasible method. The asymmetric suboptimization method is found to be the more efficient approach when it adequately simplifies the system-level problem, or when there is a large enough discrepancy between disciplinary solution times. I.R. Chittick is graduate student. J.R.R.A. Martins is assistant Professor.     

TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION

This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.     

A GA‐based technique for layout optimization of truss with stress and displacement constraints

Various developments of increasing complexity involved in layout optimization are discussed. The use of conventional GA in layout optimization is briefly mentioned with emphasis on its limitations and conditions imposed in finding the optimal design. The proposed new technique is applied to the benchmark example of Michell's truss for verification. The approach has also been applied to new examples of bridge truss and crane truss problems in order to demonstrate the generality and robustness for topology optimization. The approach is extended to include dual stress‐displacements constraints since many practical problems involve these two constraints simultaneously. Two‐bar and 10‐bar trusses are solved as examples for layout optimization with both stress and displacement constraints with satisfactory results. The effect of mutation on the final topology is also discussed. The major drawbacks of the ground structure approach are overcome in this proposed new method. The optimal designs obtained demonstrate the ability, robustness and generality of using the proposed new technique in layout optimization problems. Copyright © 2001 John Wiley & Sons, Ltd.     

基于混合加点准则的代理模型优化设计方法

在工程优化设计中,采用数值仿真模拟计算结构响应需耗费大量的时间和计算成本,给计算密集型的优化设计带来了巨大挑战,因此基于代理模型的序列优化设计方法得到了深入研究和广泛应用.对代理模型的序列优化方法框架进行了简要的概述;针对现有方法中存在的不足,发展了一类模型无关的混合加点准则,使优化循环过程中产生的新样本点分布在当前最...     

Probabilistic optimal design of laminates using improved particle swarm optimization

A new approach to the particle swarm optimization (PSO) is proposed for the solution of non-linear optimization problems with constraints, and is applied to the reliability-based optimum design of laminated composites. Special mutation-interference operators are introduced to increase swarm variety and improve the convergence performance of the algorithm. The reliability-based optimum design of laminated composites is modelled and solved using the improved PSO. The maximization of structural reliability and the minimization of total weight of laminates are analysed. The stacking sequence optimization is implemented in the improved PSO by using a special coding technique. Examples show that the improved PSO has high convergence and good stability and is efficient in dealing with the probabilistic optimal design of composite structures.