An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

Plotting the Sequential Rock Remote Sensing Information by Optimization Dichotomy Method

The sequential rock remote sensing information is a group of rocks that are correlative in space or in space and time. For the sake of plottiug them, someone had brought forward the optimization segn.entotion metkod. We have ased this method to plot the sequential rock remote sensing information at tbe remote sensing hyperspetral test field of Daqing mountain, Inner Mongolia Autonomous Region, China, and found some disadvantages of this method. Therefore, we put forward the optimization dichotomy to plot them, and get better results. Finally we make a conclusion.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

An Adaptive Sequential Replacement Method for Variable Selection in Linear Regression Analysis

With the rapid development of DNA technologies, high throughput genomic data have become a powerful leverage to locate desirable genetic loci associated with traits of importance in various crop species. However, current genetic association mapping analyses are focused on identifying individual QTLs. This study aimed to identify a set of QTLs or genetic markers, which can capture genetic variability for marker-assisted selection. Selecting a set with k loci that can maximize genetic variation out of high throughput genomic data is a challenging issue. In this study, we proposed an adaptive sequential replacement (ASR) method, which is considered a variant of the sequential replacement (SR) method. Through Monte Carlo simulation and comparing with four other selection methods: exhaustive, SR method, forward, and backward methods we found that the ASR method sustains consistent and repeatable results comparable to the exhaustive method with much reduced computational intensity.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Numerical method for optimum motion of undulatory swimmingplate in fluid flow

A numerical method for the optimum motion of an undulatory swimming plate is presented. The optimum problem is stated as minimizing the power input under the condition of fixed thrust. The problem is singular for the invisible modes, and therefore the commonly used Lagrange multiplier method cannot predict an optimum solution but just a saddle point. To eliminate the singularity, an additional amplitude inequality constraint is added to the problem. A numerical optimization code with a sequential quadratic programming method is used to solve the problem. The method is applied to several cases of the motion of two-dimensional and three-dimensional undulatory plates, and the optimum results are obtained.

SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

基于剩余碰撞时间的线控制动分层控制策略

针对不同制动工况需求的制动策略存在差异的情况,提出一种线控制动分层控制策略.在该分层策略的上层,利用二阶TTC安全碰撞时间模型计算出车辆与前车的剩余碰撞时间,以此作为依据进行制动策略的选取,并建立了汽车二自由度模型、车身法向受力模型和Burckhardt轮胎模型;在该分层策略的下层,进行了制动力在轮间的分配,使用序列二次规划(SQP)方法,分别在一般制动、紧急制动、失稳制动3种工况下,以轮胎滑移率为对象建立优化函数,对车辆制动力进行了优化分配.使用MATLAB/Simulink和Carsim进行了联合仿真,对所提出3种工况下的制动分配策略进行了有效性验证.结果表明:在一般制动工况下,采用该策略时相比对照工况制动距离减少18.08%,制动时间减少25.12%;在紧急制动工况下,采用该策略时相比对照工况制动距离减少19.17%,制动时间减少12.79%;在失稳制动工况下,该策略可通过轮胎差扭来提升车辆的横向稳定性.采用文中制动策略显著提升了车辆的制动效能.

Internal structural optimization of hollow fan blade based on sequential quadratic programming algorithm

Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constraint and minimum mass was established based on the finite element method through these parameters.Then,the sequential quadratic programming algorithm was employed to search the optimal solutions.Several groups of value for initial design variables were chosen,for the purpose of not only finding much more local optimal results but also analyzing which discipline that the variables according to could be benefit for the convergence and robustness.Response surface method and Monte Carlo simulations were used to analyze whether the objective function and constraint function are sensitive to the variation of variables or not.Then the robust results could be found among a group of different local optimal solutions.

反求铝合金淬火边界条件的序列LM梯度算法

准确获取边界条件在淬火仿真中至关重要。为此,根据瞬态热传导模型,利用正则化方法建立反求热通量的目标函数,结合序列函数指定法与LM梯度法,通过最小化目标函数推导出序列LM梯度算法,实现末端淬火实验中热通量的迭代计算。其次,通过训练观测点的平均绝对误差的“3-7-3”神经网络预测模型,建立了序列LM梯度算法关键参数的遗传算法优化方法。最后,以换热系数为边界条件建立淬火仿真模型。结果表明:在相同淬火时间内,一维序列LM梯度算法、一点法和两点法,在观测点的仿真温度平均相对误差分别为5.6%、5.9%、12.6%,17.1%、15.4%、15.3%和17.7%、16.0%、15.6%。因此,与一点法、两点法相比,序列LM梯度算法具有更高的精度。

基于聚类分区混合代理模型的多目标序列优化

针对具有显式约束的昂贵多目标优化问题,提出了一种基于聚类分区混合代理模型(CPEM)的多目标序列优化方法(MOSOM-CPEM).在MOSOM-CPEM中引入了约束域最优拉丁超立方设计(CDOLHD),使其能够在边界形状复杂的可行域内构造样本点.多区域混合代理模型(EM-MROWF)中的可行域划分方法在分割非矩形域时将导致部分区域样本点数量较少从而影响该区域混合代理模型的预测精度.为了解决这一缺陷,在CPEM中提出了一种基于K-means聚类的可行域分区方法和相应的边界光滑方法.CPEM与多项式响应面(PRS)、径向基函数(RBF)、克里金(KRG)模型和两种混合代理模型(GOEL和ACAR)在10个测试函数上进行了拟合精度比较.结果表明,CPEM的整体拟合精度优于对比的代理模型,证实了所提出的可行域分区方法的有效性.MOSOM-CPEM在CEC2021中的6个工程约束多目标优化问题上与其他基于代理模型的优化方法进行了比较.结果表明,在使用相同的样本点数量的前提下,MOSOM-CPEM获得的Pareto前沿收敛性和分布性更好.MOSOM-CPEM应用于履带式起重机超长桁架臂的腰绳结构优化问题,结果证实了其优势,表明MOSOM-CPEM具有较高的工程应用价值.

基于等效静态载荷法的多相材料结构动态拓扑优化设计

为了满足多相材料结构动态性能要求,提出一种基于等效静态载荷法的多相材料结构动态拓扑优化设计方法。采用序列固体各向同性料插值模型惩罚刚度矩阵和质量矩阵,以多个动载荷作用的多相材料结构总动态柔顺度最小化为优化目标,以结构质量和成本为约束条件,构建多相材料结构动态拓扑优化模型,利用等效静态载荷法将多相材料结构动态拓扑优化问题转化为多工况下的多相材料结构静态拓扑优化问题,以降低灵敏度分析的复杂程度;采用移动渐近线算法求解多相材料结构动态拓扑优化问题。数值算例结果表明所提方法是有效性的,与传统的拓扑优化方法相比,基于等效静态载荷法的多相材料结构动态拓扑优化求解时间节省了75%,大大提高了计算效率;与单相材料拓扑优化结果相比,多相材料结构动态拓扑优化设计获得的结构具有更好的动态性能。

Sequential feasible optimal power flow in power systems

A sequential feasible optimal power flow (OPF) method is developed for large-scale power systems. One of the outstanding features of this method is that it can maintain feasibility for both equality and inequality constraints during iterations. In sequential feasible OPF, every iteration consists of two stages: Objective improving stage and feasibility enforcing stage. Analytical basis for each stage is provided. Numerical studies on various power systems up to 2383 buses indicate that the proposed feasible approach is promising. Compared with the conventional OPF algorithms, such as interior point method, the proposed sequential feasible OPF approach can be terminated at any iteration and yield a feasible operating point simultaneously.

原油管网管输作业计划编制及优化方法

为实现原油管网的安全、平稳、经济输送,需在保证企业资源供应的同时降低整体运行成本。文章以企业需求为起点,采用先后确定中转油库的外输及来油计划、临港油库的收油计划、形成初步计划后进行验证修订的方法,探讨了原油管网管输作业计划的编制方法,并从降低管输能耗和减少港口滞期损失两个角度分析了计划的优化措施,为原油管网管输作业计划的编制提供了思路。

功率阶跃型LCC-HVDC频率支撑控制策略

随着大量常规机组被直流馈入和新能源发电替代,系统惯量水平下降,调频资源减少,频率稳定性问题日益突出。基于电网换相型换流器的直流输电(line-commutatedconverterbasedhigh-voltagedirect-current,LCC-HVDC)应用广泛,利用其功率快速调节能力为系统提供支撑是改善频率稳定性问题的有效手段。该文基于功率阶跃型频率控制的基本框架,考虑LCC的出力限制,以出现功率缺额后频率最低点最高为目标建立了LCC-HVDC系统的出力时序优化模型。基于序列二次规划法对优化问题进行求解,确定最佳的LCC附加功率与支撑时间。基于MATLAB/Simulink的仿真验证了所提频率支撑控制策略的有效性。

粒子滤波进展与展望

粒子滤波器是基于序贯M onte Carlo仿真方法的非线性滤波算法,本文对粒子滤波器的研究现状和研究进展做了综述,详细论述了粒子滤波原理、收敛性、应用及进展.首先在Bayes框架内分析了序贯重要性采样原理,重要性分布函数的选择,以及重采样方法,总结了粒子滤波器发展过程中的各种改进策略和新变种,讨论了粒子滤波器在各个领域的应用及进展,最后介绍了粒子方法的新发展,新动态,并对未来发展方向做了进一步的展望.

基于序列二次规划算法的再入轨迹优化研究

介绍了序列二次规划算法在飞行器再入轨迹优化问题中的应用。首先引入了能量替代变量对无量纲运动方程进行推导,使得运动方程和优化问题易于处理,考虑严格的过程约束和终端约束,以攻角和倾侧角为控制变量,总加热量最小为性能指标;然后通过直接配点法将最优控制问题转化为非线性规划问题,选取各节点的状态量和控制量作为优化参数;最后应用序列二次规划算法对非线性规划问题进行求解。针对多约束的再入飞行器的轨迹优化时对初值敏感的问题,提出一种参考轨迹快速规划算法,提高了优化速度。仿真结果表明提出的方法能够较快地搜索到最优轨迹,满足所有约束且落点精度高。

即食杏鲍菇热风-真空联合干燥工艺优化

为了充分利用工厂化栽培杏鲍菇加工副产物(菇头),对其进行联合干燥开发成即食杏鲍菇休闲产品。选取干燥速率、感官评分、色泽明亮度和硬度的综合值为评价指标,采用三因素二次通用旋转组合设计优化即食杏鲍菇生产中热风-真空联合干燥工艺参数,同时与热风干燥(60℃)、真空干燥(-0.09 MPa,60℃)产品的品质进行对比分析结果表明:热风干燥温度和真空干燥温度对即食杏鲍菇干燥过程影响极显著(P<0.01),热风时间影响显著(P<0.05),影响因素主次顺序依次为真空干燥温度、热风干燥温度和时间,确定的最佳工艺条件为:先热风干燥(60℃,20 min)(转换点湿基含水率≤78%),后真空干燥(55℃,-0.09 MPa);联合干燥即食杏鲍菇休闲产品的品质优于热风干燥和真空干燥产品的品质,能耗比真空干燥减少57%,但高于热风干燥。研究为实现工厂化栽培杏鲍菇副产物的资源化利用提供了参考。

为提高低速碰撞性能的轿车保险杠吸能盒结构优化

建立了吸能盒低速碰撞性能的评价模型,提出了一种集成有限元模拟和序列响应面法的优化方法。为保证优化过程的收敛,采用信赖域模型管理策略来调整设计空间。与传统的基于梯度的优化方法相比,该方法计算量小,结果准确。最后给出了某轿车后保险杠吸能盒结构优化实例,验证了该方法的可靠性。