A Strategy for Multi-objective Optimization under Uncertainty in Chemical Process Design

在许多情形，化学加工设计能作为多客观的优化(哞) 被提出问题。例子包括双性人目的优化问题，在经济目的被最大化，环境影响同时被最小化的地方。而且，在这进程的随机的行为，性质，市场变化，在模型预言的错误将等等影响进程的性能。因此，在不确定性下面开发哞方法论是必要的。在这篇文章，作者在不确定性下面为化学加工设计建议通用、系统的优化方法论。它瞄准从很多个候选人识别最佳的设计。这方法论的用途被案例研究在氨植物基于一个冷凝物处理单位的设计表明。

Review: Recent Developments in the Uncertainty-Based Aero-Structural Design Optimization for Aerospace Vehicles

With the increasing demands of aircraft design,the traditional deterministic design can hardly meet the requirements of fine design optimization because uncertainties may exist throughout the whole lifecycle of the aircraft. To enhance the robustness and reliability of the aircraft design, Uncertainty Multidisciplinary Design Optimization( UM DO) has been developing for a long time. This paper presents a comprehensive reviewof UM DO methods for aerospace vehicles,including basic UM DO theory and research progress of its application in aerospace vehicle design. Firstly,the UM DO theory is preliminarily introduced,with giving the definition and classification of uncertainty as well as its sources corresponding to the aircraft design. Then following the UM DO solving process, the application in different coupled disciplines is separately discussed during the aircraft design process,specifically clarifying the UM DO methods for aerostructural optimization. Finally,the main challenges of UM DO and the future research trends are given.

Uncertainty-based Multidisciplinary Design Optimization using An Approximated Second-Order Reliability Analysis Strategy

In uncertainty-based multidisciplinary design optimization(UBMDO),all reliability limitation factors are maintained due to minimize the cost target function.There are many reliability evaluation methods for reliability limitation factors.The second-order reliability method(SORM)is a powerful most possible point(MPP)-based method.It can provide an accurate estimation of the failure probability of a highly nonlinear limit state function despite its large curvature.But the Hessian calculation is necessary in SORM,which results in a heavy computational cost.Recently,an efficient approximated second-order reliability method(ASORM)is proposed.The ASORM uses a quasi-Newton method to close to Hessian without the direct calculation of Hessian.To further improve the UBMDO efficiency,we also introduce the performance measure approach(PMA)and the sequential optimization and reliability assessment(SORA)strategy.To solve the optimization design problem of a turbine blade,the formula of MDO with ASORM under the SORA framework(MDO-ASORM-SORA)is proposed.

Robust Design Optimization Method for Centrifugal Impellers under Surface Roughness Uncertainties Due to Blade Fouling

Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression（SVR） metamodel is combined with the Monte Carlo simulation（MCS） method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

Minimizing the impact of the mixed uncertainties(i.e.,the aleatory uncertainty and the epistemic uncertainty) for a complex product of compliant mechanism(CPCM) quality improvement signifies a fascinating research topic to enhance the robustness.However, most of the existing works in the CPCM robust design optimization neglect the mixed uncertainties, which might result in an unstable design or even an infeasible design. To solve this issue, a response surface methodology-based hybrid robust design optimization(RSM-based HRDO) approach is proposed to improve the robustness of the quality characteristic for the CPCM via considering the mixed uncertainties in the robust design optimization. A bridge-type amplification mechanism is used to manifest the effectiveness of the proposed approach. The comparison results prove that the proposed approach can not only keep its superiority in the robustness, but also provide a robust scheme for optimizing the design parameters.

Reliability-Based Topology Optimization of Fail-Safe Structures Using Moving Morphable Bars

This paper proposes an effective reliability design optimizationmethod for fail-safe topology optimization(FSTO)considering uncertainty based on the moving morphable bars method to establish the ideal balance between cost and robustness,reliability and structural safety.To this end,a performancemeasure approach(PMA)-based doubleloop optimization algorithmis developed tominimize the relative volume percentage while achieving the reliability criterion.To ensure the compliance value of the worst failure case can better approximate the quantified design requirement,a p-norm constraint approach with correction parameter is introduced.Finally,the significance of accounting for uncertainty in the fail-safe design is illustrated by contrasting the findings of the proposed reliabilitybased topology optimization(RBTO)method with those of the deterministic design method in three typical examples.Monte Carlo simulation shows that the relative error of the reliability index of the optimized structure does not exceed 3%.

The Study of Optimizing Reservoir Model Using Experimental Design in Stochastic Models

In response to the main problems in commonly used model selection methods,a method was proposed to apply the concept of experimental design to the optimization of uncertain reservoir models.Firstly,based on the actual situation of the oil field,the uncertain variables were determined that affect the geological reserves of the model and their possible range of variation,and experimental design was used to determine the modeling plan.Then,multiple geological models were established and reserves were calculated,and multiple regression was performed between uncertain variables and the corresponding geological reserves of the model.Finally,Monte Carlo simulation technology was applied to determine the parameters of the P10,P50,and P90 models for probabilistic reserves,and P10,P50,and P90 models were established.This method is not only more objective and time-saving in the application process,but also can determine the main geological variables that affect geological reserves,providing a new idea for evaluating the uncertainty of geological reserves.

压气机叶片几何气动性能优化设计方法综述

优化设计可有效减少对人工设计经验的依赖,改善压气机几何气动性能设计的难度,缩短压气机设计的周期。为克服压气机叶片几何气动性能优化设计中高维、耗时、黑箱三大难题,本文回顾近40年来在压气机气动外形参数化方法、数值计算技术、优化算法三个方面的研究进展;总结了机器学习及数据挖掘、基于不确定性的鲁棒性优化设计理论的研究进展;指明优化设计可探索压气机几何形状最佳气动性能极限,并总结和展望了压气机叶片优化设计方法的发展方向。

中欧集装箱多式联运服务网络设计

中欧运输通道和运输方式不断发展完善,海运、中欧班列及多种运输方式联运等构成了中欧间集装箱运输服务网络。货主在选择运输服务时,一直关注货物运输的费用与时效性,由于中欧间运输距离长,节点多,节点作业时长还存在很大的不确定性。同时,随着全球对碳排放问题的重视,运输服务产生的碳排放也成为货主考虑的因素。综合考虑运输费用、时间和碳排放的影响,并关注节点作业时间的不确定性,解决中欧集装箱多式联运服务网络设计问题具有非常重要的现实意义。建立最小化运输费用、运输时间和运输碳排放量的多目标多式联运服务网络设计模型,并在模型中引入不确定性时间变量。由于节点作业时间样本数据有限,通过Box-Muller变换生成随机数丰富数据,并减少不可观测的误差,运用蒙特卡洛模拟对运输时间进行不确定性统计,描述总运输时间的统计特征。基于多目标的Pareto最优思想,设计了快速非支配排序遗传算法求解最优运输服务方案。以天津至汉堡的中欧集装箱运输为实例,根据实际调研结果确定各项相关参数设定,进行模型和算法验证,求解得到多式联运运输方案的Pareto最优解集。结果显示不同的运输服务方案其运输费用、运输时间、碳排放量各有差异,并且符合Pareto最优解集定义,证明了研究提出的考虑不确定性的多目标服务网络设计建模及算法的正确性和可行性,研究成果可为货主提供选择符合其需求的不同运输服务优化方案。

考虑不确定性的隧道工程稳定性分析与可靠性优化设计

不确定性是岩石工程的一个重要特性,对岩石工程的稳定分析、设计与安全施工具有重要影响,而传统的确定性分析与优化设计方法不能考虑岩石工程的不确定性。针对隧道工程中的不确定性,将可靠性理论、实验设计、数值模拟与响应面等方法有机结合,提出一种考虑不确定性的隧道工程稳定性分析与可靠性优化设计方法。该方法通过建立考虑不确定性的隧道工程稳定性分析模型,在此基础上结合可靠性优化设计,建立了考虑不确定性的隧道工程优化设计方法,并将提出的方法结合隧道工程算例进行了分析。结果表明,该方法对隧道工程设计、稳定性分析以及风险分析具有显著指导意义,为隧道工程的不确定性分析提供了一条有效的途径。

Optimization of circulating cooling water systems based on chance constrained programming

Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained under deterministic conditions may not be stable and economical. This paper studies the optimization of circulating cooling water systems under uncertain circumstance. To improve the reliability of the system and reduce the water and energy consumption, the influence of different uncertain parameters is taken into consideration. The chance constrained programming method is used to build a model under uncertain conditions, where the confidence level indicates the degree of constraint violation. Probability distribution functions are used to describe the form of uncertain parameters. The objective is to minimize the total cost and obtain the optimal cooling network configuration simultaneously.An algorithm based on Monte Carlo method is proposed, and GAMS software is used to solve the mixed integer nonlinear programming model. A case is optimized to verify the validity of the model. Compared with the deterministic optimization method, the results show that when considering the different types of uncertain parameters, a system with better economy and reliability can be obtained(total cost can be reduced at least 2%).

Optimal Design for Anti-Skid Control of Electric Vehicles by Fuzzy Approach

In this paper,a new fuzzy approach is applied to optimal design of the anti-skid control for electric vehicles.The anti-skid control is used to maintain the wheel speed when there are uncertainties.The control is able to provide an appropriate torque for wheels when the vehicle is about to skid.The friction coefficient and the moments of inertia of wheels and motor are considered as uncertain parameters.These nonlinear,bounded and time-varying uncertainties are described by fuzzy set theory.The control is deterministic and is not based on IF-THEN fuzzy rules.Then,the optimal design for this fuzzy system and control cost is proposed by fuzzy information.In this way,the uniform boundedness and uniform ultimate boundedness are guaranteed and the average fuzzy performance is minimized.Numerical simulations show that the control can prevent vehicle skidding with the minimum control cost under uncertainties.

Computer Aided Design of Differential Pressure Flow Meters

New methodology of designing the differential pressure flow meters for fluid energy carriers is developed in order to provide minimum uncertainty of results of flow rate measurement. This methodology is implemented in “Raskhod-RU” CAD system for computer aided design and calculation of differential pressure flow meters. “Raskhod-RU” CAD meets the requirements of new Standards implemented in CIS countries (GOST 8.586.1,2,3,4,5-2005) and provides accomplishment of the following tasks: verification of conditions (constraints) for application of the differential pressure method according to the requirements of new Standards;calculation of parameters of primary device, pipe straight lengths and flow meter in general according to the requirements of new Standards;calculation of uncertainty of results of fluid flow rate and volume measurement.

飞行器总体不确定性建模与优化设计方法

针对考虑不确定性的飞行器总体设计迭代周期长、优化困难等问题,提出一种基于裕度量化解耦策略的飞行器总体不确定性建模与优化设计方法。首先采用主动学习策略开展基于优化加点Kriging的阈值不确定性分析,实现了不确定性裕度的高效求解。进而提出一种适用于飞行器总体设计的裕度量化解耦策略,将双层嵌套的不确定性优化问题解耦为确定性优化与不确定性分析过程顺序执行,高效给出满足概率约束的优化设计方案。该方法解决了传统解耦方法采用嵌入式算法而导致的工程应用困难的问题。通过非线性多约束数值案例以及滑翔飞行器工程案例,验证了该方法能够在保证精度的前提下,提高不确定性优化设计效率。

计及源荷不确定性与设备变工况特性的园区综合能源系统协同优化运行方法

园区综合能源系统可通过协调各类能源设备为用户提供可靠、优质、经济的能量供应,但源荷的不确定性和设备的变工况运行特性易导致较大的供/用能偏差。针对此问题,该文提出一种计及源荷不确定性与设备变工况特性的园区综合能源系统协同优化运行方法。首先,建立考虑多类型能量转换设备变工况运行特性的园区综合能源系统协同优化一体化模型,并利用非线性区间数表征源荷的不确定性;然后,利用区间可能度对非线性区间数进行确定性转换,并采用自适应分段线性化处理能量转换设备的变工况运行特性曲线;最后,以某园区综合能源系统为例进行仿真验证。仿真结果表明,所提方法能够有效地减小源荷不确定性与设备变工况特性带来的不利影响。

基于PCE法和最大熵法的船舶不确定性优化设计

[目的]船舶不确定性优化设计(UDO)的关键在于不确定性的量化(UQ),传统的蒙特卡洛方法较为耗时且计算成本较高,故提出一种基于多项式混沌展开法(PCE)和最大熵法(MEM)的船舶UDO方法。[方法]首先,选取较低计算成本的PCE法来量化多个不确定参数作用下输出的随机性质;然后,根据正交多项式的特点,采用基于线性无关原则的改进概率配点法(IPCM)求解PCE系数;最后,利用推导的约束前4阶矩,结合最大熵法求解约束的概率密度函数(PDF),进而在失效域上积分得到UDO关注的约束失效概率。[结果]研究结果表明:改进概率配点法可以给出最优的概率配点数目,并显著减少样本点数量;基于PCE法和MEM法求解约束失效概率时,与蒙特卡洛法结果对比,其在不额外增加计算量的前提下亦可满足精度要求;散货船工程算例的优化结果验证了PCE法较常用的蒙特卡洛法在精度和效率上更具工程应用优势。[结论]该不确定性优化设计方法可以高效准确地实现船舶设计方案的稳健性和可靠性。

火箭整流罩锥壳夹层结构不确定性轻量化设计

为分析运载火箭整流罩锥壳夹层结构不确定性对结构热稳定性的影响并指导结构的轻量化设计,建立整流罩前锥段夹层圆锥壳模型,并建立温度场模型,据此对圆锥壳开展热稳定性分析,推导力热联合载荷作用下整流罩前锥段夹层结构失稳临界轴压。在此基础上,针对主要不确定性因素,开展灵敏度分析并建立区间不确定性优化模型,采用区间可能度方法将其转化为确定性问题,并采用遗传算法-区间分析算法(GA-CIAM)实现结构优化设计。计算结果表明:考虑气动力/热载荷及材料参数不确定性影响,对整流罩前锥段结构开展优化设计,在满足设计要求的前提下,有效实现结构轻量化。

基于TLBO算法的不确定性条件下复杂产品协同设计的可靠性拓扑优化

复杂产品的拓扑优化设计可以显著节省材料和节能,有效地降低惯性力和机械振动。本研究以一种大吨位液压机作为典型的复杂产品,用于阐述该优化方法。本文提出了一种基于可靠性与优化解耦模型和基于教学学习的优化(TLBO)算法的可靠性拓扑优化方法。将由板结构形成的支撑物作为拓扑优化对象,重量轻、稳定性好。将不确定性下的可靠性优化和结构拓扑优化协同处理。首先,利用有限差分法将优化问题中的不确定性参数修正为确定性参数。然后,将不确定性可靠性分析和拓扑优化的复杂嵌套解耦。最后,利用TLBO算法求解解耦模型,该算法参数少,求解速度快。TLBO算法采用了自适应教学因子,在初始阶段实现了更快的收敛速度,并在后期进行了更精细的搜索。本文给出了一个液压机基板结构的数值实例,说明了该方法的有效性。

有限信息下基于证据理论的桁架结构多目标拓扑优化设计

不确定信息往往是缺乏的、具有较大的离散性,如何在认知不确定性扰动下保证结构具有良好的稳健性成为多目标拓扑优化设计的技术难题。引入证据理论量化认知不确定,采用基于失效似然度的失效概率区间上限建立新的可靠性指标,将结构总质量和结构可靠性同时作为优化目标,提出了基于证据理论的多目标拓扑优化设计模型。采用无需梯度信息且具有出色非支配策略的多目标并行化微分演化算法求解Pareto最优前沿。为了验证所提方法的有效性,以木桁架结构为优化对象,选取木材的弹性模量和结构荷载为不确定变量,采用所提方法进行多目标拓扑优化。根据优化结果制作6榀相同的桁架试件进行随机静力加载试验,通过试验所得的应力及节点位移判断桁架结构的失效概率,以此验证基于证据理论的稳健性拓扑优化方法的可行性。试验结果表明,基于证据理论的优化方法可以避免认知不确定波动造成的优化结果的偏差,为设计人员提供了一种在考虑数据信息不充足、认知水平有限等情况下仍能使优化结果具有稳健性的新方法。

Uncertainty analysis and design optimization of hybrid rocket motor powered vehicle for suborbital flight

Abstract In this paper, we propose an uncertainty analysis and design optimization method and its applications on a hybrid rocket motor （HRM） powered vehicle. The multidisciplinary design model of the rocket system is established and the design uncertainties are quantified. The sensitivity anal- ysis of the uncertainties shows that the uncertainty generated from the error of fuel regression rate model has the most significant effect on the system performances. Then the differences between deterministic design optimization （DDO） and uncertainty-based design optimization （UDO） are discussed. Two newly formed uncertainty analysis methods, including the Kriging-based Monte Carlo simulation （KMCS） and Kriging-based Taylor series approximation （KTSA）, are carried out using a global approximation Kriging modeling method. Based on the system design model and the results of design uncertainty analysis, the design optimization of an HRM powered vehicle for suborbital flight is implemented using three design optimization methods： DDO, KMCS and KTSA. The comparisons indicate that the two UDO methods can enhance the design reliability and robustness. The researches and methods proposed in this paper can provide a better way for the general design of HRM powered vehicles.