APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

DYNAMIC RESPONSE OPTIMIZATION DESIGN FOR ENGINEERING STRUCTURES BASED ON RELIABILITY

In many practical structures, physical parameters of material and applied loads have random property.To optimize this kind of structures,an optimum mathematical model was built.This model has reliability constraints on dynamic stress and displacement and upper & lower limits of the design variables. The numerical characteristic of dynamic response and sensitivity of dynamic response based on probability of structure were deduced respectively. By equivalent disposing, the reliability constraints were changed into conventional forms. The SUMT method was used in the optimization process.Two examples illustrate the correctness and practicability of the optimum model and solving approach.

Solution of Chemical Dynamic Optimization Using the Simultaneous Strategies

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control vari- ables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at dement knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refine- ment more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting dements to track optimal control profile breakpoints and ensure accurate state and centrol profiles. Four classic benchmarks of dynamic op- timization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferz,ble in improving the solution accuracy of chemical dy- namic optimization problem.

Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems

For most firms,especially the small-and medium-sized ones,the operational decisions are affected by their internal capital and ability to obtain external capital.However,the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely.An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital?In this paper,we review some of the latest developments in this area.After a brief review of single period models,we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth.Two cases are discussed in detail:self-finance and short term finance.In the first case,the firm has to rely on its own capital for all ordering decisions,while in the second,the firm can borrow short term loan from lenders.A detailed characterization of the optimal policy is presented and its managerial insights are discussed.Several possible extensions are suggested.

Shape Optimal Design of Hydrodynamic Bearing Based on Dynamic Characteristics

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Shape-sizing nested optimization of deployable structures using SQP

The potential role of formal structural optimization was investigated for designing foldable and deployable structures in this work.Shape-sizing nested optimization is a challenging design problem.Shape,represented by the lengths and relative angles of elements,is critical to achieving smooth deployment to a desired span,while the section profiles of each element must satisfy structural dynamic performances in each deploying state.Dynamic characteristics of deployable structures in the initial state,the final state and also the middle deploying states are all crucial to the structural dynamic performances.The shape was represented by the nodal coordinates and the profiles of cross sections were represented by the diameters and thicknesses.SQP(sequential quadratic programming) method was used to explore the design space and identify the minimum mass solutions that satisfy kinematic and structural dynamic constraints.The optimization model and methodology were tested on the case-study of a deployable pantograph.This strategy can be easily extended to design a wide range of deployable structures,including deployable antenna structures,foldable solar sails,expandable bridges and retractable gymnasium roofs.

Constraints Adjustment and Objectives Coordination of Satisfying Optimal Control Applied to Heavy Oil Fractionators

In this paper, the feasibility and objectives coordination of real-time optimization (RTO) are systemically investigated under soft constraints. The reason for requiring soft constraints adjustment and objective relaxation simultaneously is that the result is not satisfactory when the feasible region is apart from the desired working point or the optimization problem is infeasible. The mixed logic method is introduced to describe the priority of the constraints and objectives, thereby the soft constraints adjustment and objectives coordination are solved together in RTO. A case study on the Shell heavy oil fractionators benchmark problem illustrating the method is finally presented.

Multidisciplinary Design Optimization with a New Effective Method

Collaborative optimization （CO） is one of the most widely used methods in multidisciplinary design optimization （MDO）, which is an effective methodology to solve modem complex engineering problems. CO consists of two-level optimization problems which are system optimization problem and subspace optimization problem. The architecture of CO can reserve the autonomy of individual disciplines in maximum, while providing a mechanism for coordinating design problem. However, CO has low computation efficiency and is easy to diverge. For the purpose of solving these problems, the former improved methods were studied. The relaxation factors were used to change the system consistency constraints to inequality constraints, or the response surface estimation was used to surrogate the system consistency constraints. However, these methods didn＇t avoid the computational difficulties very well, furthermore, some new problems arose. The concept of optimum constraint sensitivity was proposed, and the quadratic constraints in system level were reformed. Hence, a new collaborative optimization was developed, which is called system level dynamic constraint collaborative optimization （DCCO）. The novel method is able to increase the exchange of information between system level and disciplinary level. The optimization results of each disciplinary optimization can be feedback to system level with the optimum constraint sensitivity. On the basis of the information, the new system level linear dynamic constraints can be constructed; it is better to reflect the effect of disciplinary level optimizations. The system level optimizer can clearly capture the boundary where disciplinary objective functions become zero, and considerably enhance the convergence. Two standard MDO examples were conducted to verify the feasibility and effectiveness of DCCO. The results show that DCCO can save the solving time, and is much better in terms of convergence and robustness, hence, the new method is more efficient.

Force-finding analysis of cable-net deployable antenna considering shape constraints

The force-finding process of the cable-net in the deployable mesh reflector antenna,AstroMesh,is investigated to optimize the pretension distribution and satisfy surface accuracy.Since the geometry and topology of the mesh reflector antennas are given as a constraint with the boundary condition assumed to be fixed,the force-finding process can be performed on a constant equilibrium matrix to obtain a feasible set of forces.Then,the equilibrium matrix can be rewritten in terms of force modes after the singular value decomposition.The object of force design is to minimize the deviation of member forces and,therefore,the surface accuracy can be guaranteed by transforming an optimization of the distribution of prestresses into an optimization with multiple prestress modes.Finally,numerical examples solved by the sequential quadratic programming(SQP)algorithm and the genetic algorithm are given to validate the efficiency of the proposed method.The comparison results show that the genetic method can converge to the optimized point after approximately 50 iterations while the converging process of the sequential quadratic programming method depends largely on the initial points.

Topology optimization of reactive material structures for penetrative projectiles

Recently,reactive materials have been developed for penetrative projectiles to improve impact resistance and energy capacity.However,the design of a reactive material structure,involving shape and size,is challenging because of difficulties such as high non-linearity of impact resistance,manufacturing limitations of reactive materials and high expenses of penetration experiments.In this study,a design optimization methodology for the reactive material structure is developed based on the finite element analysis.A finite element model for penetration analysis is introduced to save the expenses of the experiments.Impact resistance is assessed through the analysis,and result is calibrated by comparing with experimental results.Based on the model,topology optimization is introduced to determine shape of the structure.The design variables and constraints of the optimization are proposed considering the manufacturing limitations,and the optimal shape that can be manufactured by cold spraying is determined.Based on the optimal shape,size optimization is introduced to determine the geometric dimensions of the structure.As a result,optimal design of the reactive material structure and steel case of the penetrative projectile,which maximizes the impact resistance,is determined.Using the design process proposed in this study,reactive material structures can be designed considering not only mechanical performances but also manufacturing limitations,with reasonable time and cost.

A Dynamic Active-Set Method for Linear Programming

An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.

Event-based performance guaranteed tracking control for constrained nonlinear system via adaptive dynamic programming method

An optimal tracking control problem for a class of nonlinear systems with guaranteed performance and asymmetric input constraints is discussed in this paper.The control policy is implemented by adaptive dynamic programming(ADP)algorithm under two event-based triggering mechanisms.It is often challenging to design an optimal control law due to the system deviation caused by asymmetric input constraints.First,a prescribed performance control technique is employed to guarantee the tracking errors within predetermined boundaries.Subsequently,considering the asymmetric input constraints,a discounted non-quadratic cost function is introduced.Moreover,in order to reduce controller updates,an event-triggered control law is developed for ADP algorithm.After that,to further simplify the complexity of controller design,this work is extended to a self-triggered case for relaxing the need for continuous signal monitoring by hardware devices.By employing the Lyapunov method,the uniform ultimate boundedness of all signals is proved to be guaranteed.Finally,a simulation example on a mass–spring–damper system subject to asymmetric input constraints is provided to validate the effectiveness of the proposed control scheme.

Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation,with assistance of lower-fidelity and cheaper simulation(s).However,most existing works only incorporate‘‘two"levels of fidelity,and thus efficiency improvement is very limited.In order to reduce the number of high-fidelity simulations as many as possible,there is a strong need to extend it to three or more fidelities.This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design.Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging(MHK),which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity.The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids,which are determined through a grid convergence study.First,sampling shapes are selected for each level of fidelity via technique of Design of Experiments(DoE).Then,CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective(e.g.C_D)and constraint(e.g.C_L,C_m)functions.Next,new samples are selected through infillsampling criteria and the surrogate models are repetitively updated until a global optimum is found.The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows.The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.

Optimal control strategy for energy saving in trains under the four-aspect fixed autoblock system

This paper deals with both the leading train and the following train in a train tracking under a four-aspect fixed autoblock system in order to study the optimum operating strategy for energy saving. After analyzing the working principle of the four-aspect fixed autoblock system, an energy-saving control model is created based on the dynamics equation of the Wains. In addition to safety, energy consumption and time error are the main concerns of the model. Based on this model, dynamic speed constraints of the following train are proposed, defined by the leading gain dynamically. At the same time, the static speed constraints defined by the line conditions are also taken into account. The parallel genetic algorithm is used to search the optimum operating strategy. In order to simplify the solving process, the external punishment function is adopted to transform this problem with constraints to the one without constraints. By using the real number coding and the strategy of dividing ramps into three parts, the convergence of GA is accelerated and the length of chromosomes is shortened. The simulation result from a four-aspect fixed autoblock system simulation platform shows that the method can reduce the energy consumption effectively in the premise of ensuring safety and punctuality.

Aerodynamic optimization design of general parameters for cycloidal propeller in hover based on surrogate model

A surrogate-model-based aerodynamic optimization design method for cycloidal propeller in hover was proposed,in order to improve its aerodynamic efficiency,and analyze the basic criteria for its aerodynamic optimization design.The reliability and applicability of overset mesh method were verified.An optimization method based on Kriging surrogate model was proposed to optimize the geometric parameters for cycloidal propeller in hover with the use of genetic algorithm.The optimization results showed that the thrust coefficient was increased by 3.56%,the torque coefficient reduced by 12.05%,and the figure of merit(FM)increased by 19.93%.The optimization results verified the feasibility of this design idea.Although the optimization was only carried out at a single rotation speed,the aerodynamic efficiency was also significantly improved over a wide range of rotation speeds.The optimal configuration characteristics for micro and small-sized cycloidal propeller were:solidity of 0.2-0.22,maximum pitch angle of 25°-35°,pitch axis locating at 35%-45% of the blade chord length.

Newton-conjugate gradient (CG) augmented Lagrangian method for path constrained dynamic process optimization

In this paper, a Newton-conjugate gradient （CG） augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization （CVP） approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming （NLP） problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton （TN） approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examlales demonstrate the effectiveness of the algorithm.

有限视场下的攻击时间和角度多约束制导律

针对精确打击任务存在导引头视场受限这一过程约束的制导问题,提出了一种考虑视场限制以及攻击角度和时间多种约束的制导律.首先,在以比例导引项实现精确命中的基础上,利用最优控制理论,采用弹目距离加权控制能耗形式的指标函数,设计了攻击角度控制项,并推导了相应的剩余飞行时间解析预测表达式.其次,基于最优误差动力学方法,设计了攻击时间相关的控制项,保证了攻击时间误差的有限时间收敛.同时,针对导引头视场有限的问题,分析了各控制项对前置角收敛性的影响,利用特定的限制函数确保前置角在整个制导过程中始终处于有效视场内,并给出了前置角的有界性及收敛性证明.数学仿真结果验证了所提出制导律对多约束制导问题的有效性.

基于多策略改进鲸鱼算法的船舶推力分配方法

船舶动力定位推力分配求解是一种复杂的多约束多目标优化问题,鲸鱼优化算法(WOA)处理该类问题较传统推力分配算法计算更简便、精度更高,但以牺牲时间为代价,需解决实时可靠收敛问题。针对上述问题,提出一种改进鲸鱼推力分配算法,通过采用等式约束项的特解系数为个体变量,降低搜索空间维度和范围,为算法获取可靠解和快速收敛奠定基础;通过空间区块化和“精英”筛选法初始化种群,增加初始种群分散性和“精英”个体数量,提高寻优效率和收敛稳定性;引入动态种群边界获取合理的搜索空间,提高算法收敛速度;最后运用类梯度法进行种群更新,模拟区域遍历搜寻,以较少迭代次数获取可靠解。以CybershipⅢ船模为对象进行仿真验证,结果表明该算法可行,具有较好的实时性和稳定收敛性,提高了推力分配性能。