含模糊-区间变量的结构非概率可靠性优化设计

工程结构中存在着诸多不确定性因素,可靠性方法是处理不确定因素的有效途径之一。针对大量工程结构中存在混合不确定信息的问题,提出了一种适用于工程的混合不确定性可靠度计算方法。将模糊变量转化为区间变量,基于体积比的区间可靠性模型,建立了含模糊-区间混合变量的结构非概率可靠性模型。由于该可靠性模型意义明确,对模糊信息的处理也比较合理,可作为混合可靠性计算方法的一种补充。应用此可靠性模型对某飞机机翼结构进行了优化设计,实例计算说明了该文的方法是有效和可行的。     

复合材料点阵夹芯结构平压性能不确定分析与优化

考虑一体化成型工艺制备的复合材料点阵夹芯结构及其不确定性,采用区间向量实现不确定参数定量化,建立复合材料点阵夹芯结构平压性能区间分析模型.考虑结构功能状态判断的模糊性,分别在不考虑设计容差与考虑设计容差情形下,建立了不确定平压载荷作用下含区间参数模糊可靠性分析与优化模型.研究结果表明:材料参数及结构参数不确定性,特别是设计容差对复合材料点阵夹芯结构平压性能影响明显,因此在工程优化中不仅需要充分考虑材料参数与外部载荷等不确定性,而且需要充分重视传统不确定设计方法中未计及的设计容差的影响.本研究实现了理论成果与工程应用的有机结合,为工程领域复合材料点阵夹芯结构平压性能分析与优化提供有效理论方法.     

复合材料点阵夹芯结构平压性能不确定分析与优化

考虑一体化成型工艺制备的复合材料点阵夹芯结构及其不确定性, 采用区间向量实现不确定参数定量化, 建立复合材料点阵夹芯结构平压性能区间分析模型。考虑结构功能状态判断的模糊性, 分别在不考虑设计容差与考虑设计容差情形下, 建立了不确定平压载荷作用下含区间参数模糊可靠性分析与优化模型。研究结果表明: 材料参数及结构参数不确定性, 特别是设计容差对复合材料点阵夹芯结构平压性能影响明显, 因此在工程优化中不仅需要充分考虑材料参数与外部载荷等不确定性, 而且需要充分重视传统不确定设计方法中未计及的设计容差的影响。本研究实现了理论成果与工程应用的有机结合, 为工程领域复合材料点阵夹芯结构平压性能分析与优化提供有效理论方法。     

混合离散变量多目标结构模糊优化及FD解法

本文建立了混合离散变量多目标结构模糊优化设计的数学模型：提出了模糊寻优区间、模糊优越混合离散解集和模糊可行集的概念；     

基于证据理论的产品选型决策方法

 基于模糊数学原理和证据理论,提出了综合处理不确定性设计信息、合理选择产品机械结构类型的方法。为此,首先利用已有的产品实例为每个产品子类提取一组设计规则,并为每个子类构造一个可以描述其典型特征的模糊向量;然后在模糊机制下统一处理以普通实数、实数域上的区间值和模糊数表达的设计信息,采用模糊推理、证据理论等不精确推理方法处理不确定性信息,确定产品类型。上述方法可作为智能设计系统求解设计问题的推理策略,并实现知识的自动获取。通过一个选型设计的实例,验证了该方法的正确性。     

结构-声场耦合系统区间鲁棒优化设计

以工程中普遍存在的结构-声场耦合系统为研究对象,充分考虑系统本身及外载荷的不确定性,基于区间理论建立了含有非概率不确定参数的区间有限元分析方法及区间鲁棒优化模型。首先,利用区间对不确定性参数进行定量化描述,借助泰勒展式提出了求解耦合系统响应范围的区间有限元分析方法。然后,引入鲁棒优化设计的思想,基于区间序关系和区间可能度,分别建立了含区间参数目标函数和约束条件的转换模型,原区间不确定性优化问题就转化为确定性的多目标优化问题。最后通过数值算例,进一步说明了本文所建立鲁棒优化设计模型及算法的有效性。     

含区间参数的结构-声耦合系统可靠性优化设计

针对复合材料结构-声耦合系统,充分考虑系统本身及外载荷的不确定性,基于区间理论建立了相应的有限元分析方法及可靠性优化模型。首先,利用区间对不确定参数进行定量化描述,根据有限元网格推导含区间参数的结构-声耦合内场问题的有限-有限元方程;借助改进的区间泰勒展开方法,快速确定结构响应与声场响应的区间上下界;随后,基于区间可能度建立含不确定参数的耦合系统可靠性优化模型。数值算例通过层合板铺层角度和厚度的优化设计,验证了所建立可靠性优化设计模型及算法的有效性。     

考虑材料参数不确定性结构动力学稳健性拓扑优化设计

本文在考虑材料参数不确定性的条件下,对连续体结构动力学稳健性拓扑优化设计进行研究。在使结构的第一阶固有频率最大化的同时,显著减小其对材料性能不确定性的影响。基于非概率凸集模型,将材料参数的不确定性用有界区间变量表示;建立了能够抑制频率改变的结构动力学拓扑优化模型,用单层优化策略求解稳健性优化设计问题。通过对材料参数的导数分析,获得了在材料性能不确定情形下结构第一阶固有频率的二阶泰勒展开式,并推导出了频率对拓扑变量的一阶灵敏度显性表达式。基于变密度法,开展了结构动力学稳健性拓扑优化设计,并与确定性优化结果进行对比,验证了用本文方法获得的结构第一阶固有频率稳健性更高,受材料参数不确定性扰动影响更小,展示了考虑材料参数不确定性的重要性。     

基于区间理论的不确定结构随机疲劳损伤估计方法

将结构体系中不确定参数定义为区间变量,在随机疲劳谱分析方法的基础上,提出一种计算平稳高斯荷载作用下不确定结构疲劳损伤的新方法。该方法采用区间参数模型定义结构的不确定性,应用功率谱密度描述外荷载的随机性;利用有理级数和单位对称区间显式表达结构区间频响函数和不确定结构在平稳高斯荷载作用下的动力响应区间;根据Tovo-Benasciutti疲劳损伤预测模型,计算不确定结构在随机荷载作用下的疲劳损伤区间期望率;并可通过调整相应不确定参数的单位对称区间近似估计该不确定参数不同不确定半径的疲劳损伤区间期望率。通过数值算例,将该文提出的随机疲劳区间分析方法与顶点法进行比较,验证了该方法的准确性和适用性。     

基于可靠性的复杂装备综合集成设计

为了获得低风险的复杂装备设计方案,提出了基于可靠性的综合集成设计。可靠性应在全寿命周期进行分析和量化,并在设计过程中采取措施确保产品在使用环境中其性能具有适当裕量;在综合集成设计过程中重要的问题是要在产品的先进性、可靠性、稳健性之间找到平衡的优化设计,它是在设计过程中逐步孕育而产生的,不是事后分析和评估出来的。由于常常是在信息不完备条件下进行产品设计与决策,在传统依赖于试验结果和部分数值模拟的决策方法基础上引入不确定性与裕度的量化的概念,以提供一种有效性评估的工程分析方法。实践表明,这种设计方法具有广泛的工程应用前景。     

模糊参数平面连续体结构的拓扑优化设计

研究了具有模糊参数的连续体结构在模糊载荷作用下的拓扑优化设计问题。利用信息熵将模糊变量转换为随机变量,构建了随机载荷作用下的随机参数的连续体结构的拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总质量均值极小化为目标函数,满足单元应力可靠性为约束条件,利用分布函数法对应力可靠性约束进行了等价显式化处理。基于随机因子法,利用代数综合法导出了应力响应的数字特征的计算表达式。采用双方向渐进结构优化(BESO)方法求解。通过两个算例验证了该文模型及求解方法的合理性和有效性。     

Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases

Concurrent topology optimization of macrostructure and material microstructure has attracted significant interest in recent years. However, most of the existing works assumed deterministic load conditions, thus the obtained design might have poor performance in practice when uncertainties exist. Therefore, it is necessary to take uncertainty into account in structural design. This article proposes an efficient method for robust concurrent topology optimization of multiscale structure under single or multiple load cases. The weighted sum of the mean and standard deviation of the structural compliance is minimized and constraints are imposed to both the volume fractions of macrostructure and microstructure. The effective properties of the microstructure are calculated via the homogenization method. An efficient sensitivity analysis method is proposed based on the superposition principle and orthogonal similarity transformation of real symmetric matrices. To further reduce the computational cost, an efficient decoupled sensitivity analysis method for microscale design variables is proposed. The bidirectional evolutionary structural optimization method is employed to obtain black and white designs for both macrostructure and microstructure. Several two-dimensional and three-dimensional numerical examples are presented to demonstrate the effectiveness of the proposed approach and the effects of load uncertainty on the optimal design of both macrostructure and microstructure.     

A new interval optimization method considering tolerance design

This study considers the design variable uncertainty in the actual manufacturing process for a product or structure and proposes a new interval optimization method based on tolerance design, which can provide not only an optimal design but also the allowable maximal manufacturing errors that the design can bear. The design variables' manufacturing errors are depicted using the interval method, and an interval optimization model for the structure is constructed. A dimensionless design tolerance index is defined to describe the overall uncertainty of all design variables, and by combining the nominal objective function, a deterministic two-objective optimization model is built. The possibility degree of interval is used to represent the reliability of the constraints under uncertainty, through which the model is transformed to a deterministic optimization problem. Three numerical examples are investigated to verify the effectiveness of the present method.     

Multi-objective robust design of energy-absorbing components using coupled process–performance simulations

The stochastic uncertainties associated with the material, process and product are represented and propagated to process and performance responses. A finite element-based sequential coupled process–performance framework is used to simulate the forming and energy absorption responses of a thin-walled tube in a manner that both material properties and component geometry can evolve from one stage to the next for better prediction of the structural performance measures. Metamodelling techniques are used to develop surrogate models for manufacturing and performance responses. One set of metamodels relates the responses to the random variables whereas the other relates the mean and standard deviation of the responses to the selected design variables. A multi-objective robust design optimization problem is formulated and solved to illustrate the methodology and the influence of uncertainties on manufacturability and energy absorption of a metallic double-hat tube. The results are compared with those of deterministic and augmented robust optimization problems.     

Level-set topology optimization for robust design of structures under hybrid uncertainties

This paper will develop a new robust topology optimization (RTO) method based on level sets for structures subject to hybrid uncertainties, with a more efficient Karhunen-Loève hyperbolic Polynomial Chaos–Chebyshev Interval method to conduct the hybrid uncertain analysis. The loadings and material properties are considered hybrid uncertainties in structures. The parameters with sufficient information are regarded as random fields, while the parameters without sufficient information are treated as intervals. The Karhunen-Loève expansion is applied to discretize random fields into a finite number of random variables, and then, the original hybrid uncertainty analysis is transformed into a new process with random and interval parameters, to which the hyperbolic Polynomial Chaos–Chebyshev Interval is employed for the uncertainty analysis. RTO is formulated to minimize a weighted sum of the mean and standard variance of the structural objective function under the worst-case scenario. Several numerical examples are employed to demonstrate the effectiveness of the proposed RTO, and Monte Carlo simulation is used to validate the numerical accuracy of our proposed method.     

区间参数结构动力优化的改进方法

针对区间参数结构,提出一种改进的动力响应的区间优化方法。由于区间优化问题一般要比确定性优化问题的求解复杂得多,因此,通过优化结构动力响应区间值的上界,将区间优化问题转化为近似的确定性优化问题。为了得到结构动力响应更加准确的区间值,把结构动力响应Taylor展开式中的一阶导数也看成区间的,这样得到的区间值能近似包含精确值。在区间优化方法中,设计变量的中值和半径都被选为优化变量,可以得到比传统确定性优化方法更多的优化信息。把该方法应用于典型刚架结构,优化结果表明,区间优化方法不仅能得到与传统优化方法大致相当的设计变量最优值,还能得到实际问题中当设计变量取不到最优值而有微小变化时,目标函数值的一个变化范围。     

Comparison of robust,reliability-based and non-probabilistic topology optimization under uncertain loads and stress constraints

It is nowadays widely acknowledged that optimal structural design should be robust with respect to the uncertainties in loads and material parameters. However, there are several alternatives to consider such uncertainties in structural optimization problems. This paper presents a comprehensive comparison between the results of three different approaches to topology optimization under uncertain loading, considering stress constraints: (1) the robust formulation, which requires only the mean and standard deviation of stresses at each element; (2) the reliability-based formulation, which imposes a reliability constraint on computed stresses; (3) the non-probabilistic formulation, which considers a worst-case scenario for the stresses caused by uncertain loads. The information required by each method, regarding the uncertain loads, and the uncertainty propagation approach used in each case is quite different. The robust formulation requires only mean and standard deviation of uncertain loads; stresses are computed via a first-order perturbation approach. The reliability-based formulation requires full probability distributions of random loads, reliability constraints are computed via a first-order performance measure approach. The non-probabilistic formulation is applicable for bounded uncertain loads; only lower and upper bounds are used, and worst-case stresses are computed via a nested optimization with anti-optimization. The three approaches are quite different in the handling of uncertainties; however, the basic topology optimization framework is the same: the traditional density approach is employed for material parameterization, while the augmented Lagrangian method is employed to solve the resulting problem, in order to handle the large number of stress constraints. Results are computed for two reference problems: similarities and differences between optimized topologies obtained with the three formulations are exploited and discussed.     

Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving

In this paper, a polymorphic uncertain nonlinear programming (PUNP) approach is developed to formulate the problem of maximizing the capacity in a system of V-belt driving with uncertainties. The constructed optimization model is found to consist of a nonlinear objective function and some nonlinear constraints with some parameters which are of uncertain nature. These uncertain parameters are interval parameters, random interval parameters, fuzzy parameters or fuzzy interval parameters. To find a robust solution of the problem, a deterministic equivalent formulation (DEF) is established for the polymorphic uncertain nonlinear programming model. For a given satisfaction level, this DEF turns out to be a nonlinear programming involving only interval parameters. A solution method, called a sampling based interactive method, is developed such that a robust solution of the original model with polymorphic uncertainties is obtained by using standard smooth optimization techniques. The proposed method is applied into a real-world design of V-belt driving, and the results indicate that both the PUNP approach and the developed algorithm are useful to the optimization problem with polymorphic uncertainty.     

Reliability based optimum design of Tuned Mass Damper in seismic vibration control of structures with bounded uncertain parameters

A reliability based optimization of Tuned Mass Damper (TMD) parameters in seismic vibration control under bounded uncertain system parameters is presented. The study on TMD with random parameters in a probabilistic framework is noteworthy. But, it cannot be applied when the necessary information about parameters uncertainties is limited. In such cases, the interval method is a viable alternative. Applying matrix perturbation theory through a first order Taylor series expansion about the mean values of the uncertain parameters’ conservative dynamic response bounds are obtained assuming a small degree of parameter uncertainty. The first-passage probability of failure of the system is taken as the performance objective. Using the interval extension of the performance objective, the vibration control problem under bounded uncertainties is transformed to the appropriate deterministic optimization problems yielding the lower and upper bound solutions. A numerical study is performed to elucidate the effect of parameters’ uncertainties on the TMD parameters’ optimization and the safety of the structure.