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.

Contribution to Development of Reliability and Optimization Methods Applied to Mechanical Structures

In order to take into account the uncertainties linked to the variables in the evaluation of the statistical properties of structural response, a reliability approach with probabilistic aspect was considered. This is called the Probabilistic Transformation Method (PTM). This method is readily applicable when the function between the input and the output of the system is explicit. However, the situation is much more involved when it is necessary to perform the evaluation of implicit function between the input and the output of the system through numerical models. In this work, we propose a technique that combines Finite Element Analysis (FEA) and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the function between the input and the output of the system is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) using an interface between Finite Element software and Matlab. Some problems of structures are treated in order to prove the applicability of the proposed technique. Moreover, the obtained results are compared to those obtained by the reference method of Monte Carlo. A second aim of this work is to develop an algorithm of global optimization using the local method SQP, because of its effectiveness and its rapidity of convergence. For this reason, we have combined the method SQP with the Multi start method. This developed algorithm is tested on test functions comparing with other methods such as the method of Particle Swarm Optimization (PSO). In order to test the applicability of the proposed approach, a structure is optimized under reliability constraints.

An Overview of Recently Developed Coupled Simulation Optimization Approaches for Reliability Based Minimum Cost Design of Water Retaining Structures

This paper reviews several recently-developed techniques for the minimum-cost optimal design of water-retaining structures (WRSs), which integrate the effects of seepage. These include the incorporation of uncertainty in heterogeneous soil parameter estimates and quantification of reliability. This review is limited to methods based on coupled simulation-optimization (S-O) models. In this context, the design of WRSs is mainly affected by hydraulic design variables such as seepage quantities, which are difficult to determine from closed-form solutions or approximation theories. An S-O model is built by integrating numerical seepage modeling responses to an optimization algorithm based on efficient surrogate models. The surrogate models (meta-models) are trained on simulated data obtained from finite element numerical code solutions. The proposed methodology is applied using several machine learning techniques and optimization solvers to optimize the design of WRS by incorporating different design variables and boundary conditions. Additionally, the effects of several scenarios of flow domain hydraulic conductivity are integrated into the S-O model. Also, reliability based optimum design concepts are incorporated in the S-O model to quantify uncertainty in seepage quantities due to uncertainty in hydraulic conductivity estimates. We can conclude that the S-O model can efficiently optimize WRS designs. The ANN, SVM, and GPR machine learning technique-based surrogate models are efficiently and expeditiously incorporated into the S-O models to imitate the numerical responses of simulations of various problems.

Design for a Crane Metallic Structure Based on Imperialist Competitive Algorithm and Inverse Reliability Strategy

Uncertainties in parameters such as materials, loading, and geometry are inevitable in designing metallic structures for cranes. When considering these uncertainty factors, reliability-based design optimization （RBDO） offers a more reasonable design approach. However, existing RBDO methods for crane metallic structures are prone to low convergence speed and high computational cost. A unilevel RBDO method, combining a discrete imperialist competitive algorithm with an inverse reliabil- ity strategy based on the performance measure approach, is developed. Application of the imperialist competitive algorithm at the optimization level significantly improves the convergence speed of this RBDO method. At the reli- ability analysis level, the inverse reliability strategy is used to determine the feasibility of each probabilistic constraint at each design point by calculating its a-percentile per- formance, thereby avoiding convergence failure, calcula- tion error, and disproportionate computational effort encountered using conventional moment and simulation methods. Application of the RBDO method to an actual crane structure shows that the developed RBDO realizes a design with the best tradeoff between economy and safety together with about one-third of the convergence speed and the computational cost of the existing method. This paper provides a scientific and effective design approach for the design of metallic structures of cranes.

Cost-optimization based target reliabilities for design of structures exposed to fire

Adequacy of structural fire design in uncommon structures is conceptually ensured through cost-benefit analysis where the future costs are balanced against the benefits of safety investment.Cost-benefit analyses,however,are complicated and computationally challenging,and hence impractical for application to individual projects.To address this issue,design guidance proposes target reliability indices for normal design conditions,but no target reliability indices are defined for structural fire design.We revisit the background of the cost-optimization based approach underlying normal design target reliability indices then we extend this approach for the case of fire design of structures.We also propose a modified objective function for cost-optimization which simplifies the evaluation of target reliability indices and reduces the number of assumptions.The optimum safety level is expressed as a function of a new dimensionless variable named“Damage-to-investment indicator”(DII).The cost optimization approach is validated for the target reliability indices for normal design condition.The method is then applied for evaluating DII and the associated optimum reliability indices for fire-exposed structures.Two case studies are presented:(i)a one-way loaded reinforced concrete slab and(ii)a steel column under axial loading.This study thus provides a framework for deriving optimum(target)reliability index for structural fire design which can support the development of rational provisions in codes and standards.

Reliability-Based Optimal Design for Very Large Floating Structure

Costs and losses induced by possible future extreme environmental conditions and difficulties in repairing post yielding damage strongly suggest the need for proper consideration in design rather than just life loss prevention. This can be addressed through the development of design methodology that balances the initial cost of the very large floating structure (VLFS) against the expected potential losses resulting from future extreme wave induced structural damage. Here, the development of a methodology for determining optimal, cost effective design will be presented and applied to a VLFS located in the Tokyo bay. Optimal design criteria are determined based on the total expected life cycle cost and acceptable damage probability and curvature of the structure, and a set of sizes of the structure are obtained. The methodology and applications require expressions of the initial cost and the expected life cycle damage cost as functions of the optimal design variables. This study includes the methodology, total life cycle cost function, structural damage modeling, and reliability analysis.

AWK-TIS:An Improved AK-IS Based on Whale Optimization Algorithm and Truncated Importance Sampling for Reliability Analysis

In this work,an improved active kriging method based on the AK-IS and truncated importance sampling(TIS)method is proposed to efficiently evaluate structural reliability.The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature.The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly,and the whale optimization algorithm(WOA)is employed to acquire the optimal Krigingmodel and themost probable point(MPP).To verify the performance of theAWK-TISmethod for structural reliability,four numerical cases which are utilized as benchmarks in literature and one real engineering problem about a jet van manipulate mechanism are tested.The results indicate the accuracy and efficiency of the proposed method.

Genetic Algorithms of Structural Fuzzy Reliability Index

In this paper the simple generation algorithms are improved. According to the geometric meaning of the structural reliability index, a method is proposed to deal with the variables in the standard normal space. With consideration of variable distribution, the correlation coefficient of the variables and its fuzzy reliability index, the feasibility and the reliability of the algorithms are proved with an example of structural reliability analysis and optimization.

Reliability design optimization of composite structures based on PSO together with FEA

The present work aims to develop a method for reliability-based optimum design of composite structures. A procedure combining particle swarm optimization （PSO） and finite element analysis （FEA） has been proposed. Numerical examples for the reliability design optimization （RDO） of a laminate and a composite cylindrical shell are worked out to demonstrate the effectiveness of the method. Then a design for composite pressure vessels is studied. The advantages and necessity of RDO over the conventional equi-strength design are addressed. Examples show that the proposed method has good stability and is efficient in dealing with the probabilistic optimal design of composite structures. It may serve as an effective tool to optimize other complicated structures with uncertainties.

Structural Optimization of Hatch Cover Based on Bi-directional Evolutionary Structure Optimization and Surrogate Model Method

Weight reduction has attracted much attention among ship designers and ship owners.In the present work,based on an improved bi-directional evolutionary structural optimization(BESO) method and surrogate model method,we propose a hybrid optimization method for the structural design optimization of beam-plate structures,which covers three optimization levels:dimension optimization,topology optimization and section optimization.The objective of the proposed optimization method is to minimize the weight of design object under a group of constraints.The kernel optimization procedure(KOP) uses BESO to obtain the optimal topology from a ground structure.To deal with beam-plate structures,the traditional BESO method is improved by using cubic box as the unit cell instead of solid unit to construct periodic lattice structure.In the first optimization level,a series of ground structures are generated based on different dimensional parameter combinations,the KOP is performed to all the ground structures,the response surface model of optimal objective values and dimension parameters is created,and then the optimal dimension parameters can be obtained.In the second optimization level,the optimal topology is obtained by using the KOP according to the optimal dimension parameters.In the third optimization level,response surface method(RSM) is used to determine the section parameters.The proposed method is applied to a hatch cover structure design.The locations and shapes of all the structural members are determined from an oversized ground structure.The results show that the proposed method leads to a greater weight saving,compared with the original design and genetic algorithm(GA) based optimization results.

APPLICATION OF SURROGATE BASED PARTICLE SWARM OPTIMIZATION TO THE RELIABILITY-BASED ROBUST DESIGN OF COMPOSITE PRESSURE VESSELS

A surrogate based particle swarm optimization （SBPSO） algorithm which combines the surrogate modeling technique and particle swarm optimization is applied to the reliability- based robust design （RBRD） of composite pressure vessels. The algorithm and efficiency of SBPSO are displayed through numerical examples. A model for filament-wound composite pressure vessels with metallic liner is then studied by netting analysis and its responses are analyzed by using Finite element method （performed by software ANSYS）. An optimization problem for maximizing the performance factor is formulated by choosing the winding orientation of the helical plies in the cylindrical portion, the thickness of metal liner and the drop off region size as the design variables. Strength constraints for composite layers and the metal liner are constructed by using Tsai-Wu failure criterion and Mises failure criterion respectively. Numerical examples show that the method proposed can effectively solve the RBRD problem, and the optimal results of the proposed model can satisfy certain reliability requirement and have the robustness to the fluctuation of design variables.

Reliability Based Design Optimization of Aero-Engine Spindle Ball Bearings

Aero-engine spindle ball bearings work in harsh conditions which are affected by relatively complex stresses. One of the key factors which affects bearing performance is its structure. In this paper,we used reliability based design optimization method to solve the structure design problem of aero-engine spindle ball bearings.Compared with the optimization design method, the value of equivalent dynamic load using reliability optimization design method was the least by MATLAB simulation. Also the design solutions show that the optimized structure possesses higher reliability than the original solution.

A new structural reliability analysis method in presence of mixed uncertainty variables

For structures with both random and fuzzy uncertainty,this paper presents a novel method for determining the membership function in fuzzy reliability with the Automatic Updating Extreme Response Surface(AUERS)method.In the proposed method,fuzzy variables are initially converted into a value domain under the given cut level and the extreme point in the domain where the reliability reaches its extreme value is considered.Second,the Particle Swarm Optimization(PSO)algorithm is used to determine the extreme point according to the extreme responses for different sets of random sample inputs.A kriging response surface is subsequently constructed between the random variables and the corresponding extreme points.An automatic updating strategy is then introduced based on the Relative Mean Square Predicted Error(RMSPE)before performing every iteration of reliability analysis.By adding new sample points,the approximate quality of the kriging response surface is improved.Finally,reliability analysis is used to determine the reliability bound under the given cut level.The proposed method assures the accuracy and computation efficiency of the mixed uncertainty reliability analysis results while it prevents the solution from becoming trapped in a local optimum,which occurs in classical optimization methods.Two example analyses are used to demonstrate the validity and advantages of the proposed method.

Reliability Research Reviewed of Automobile Seat Angle-Adjuster

The reliability of the automobile seat angle-adjuster directly affects the safety of vehicle. The reliability of the seat angle-adjuster is improved based on bench test. Liability model of seat angle-adjuster system is established according to seat angle-adjuster of key parts failure mode. That provides technical support for the design improvements of seat angle-adjuster.

汽车结构可靠性分析与优化设计研究进展

为研究汽车结构的可靠性,对机械结构分析和设计中的不确定性进行总结,从结构参数不确定性、材料性能参数不确定性和载荷不确定性3方面分析了汽车结构设计变量及其参数的不确定性;对概率可靠性分析和非概率可靠性分析方法的研究进展进行了梳理和综述;列举了可靠性分析方法在汽车结构中的应用;对可靠性的数学模型与算法进行梳理,重点研究了可靠性优化设计在汽车轻量化及耐撞性等方面的应用,并指出了汽车结构可靠性分析与优化设计中的发展趋势。

基于并行拓扑优化的假体股骨柄设计

与股骨接触的假体柄是人工髋关节的主要部件,在全髋置换手术中起着重要作用。采用变密度固体各向同性材料惩罚(Solid Isotropic Material with Penalization,SIMP)拓扑优化方法和多尺度的并行拓扑优化方法,分别得到A型和B型两种股骨柄结构,并将股骨柄结构柔度变化幅度作为对比指标,比较了两种股骨柄对载荷方向变化的敏感度。利用有限元方法对A型股骨柄和B型股骨柄进行多工况下所对应股骨的应力分析。研究结果表明,在3种工况下,A型股骨柄和B型股骨柄对股骨的平均应力分别为14.80、22.55、16.94 MPa和10.89、20.92、16.50 MPa。对B型股骨柄进行压力加载试验,试验结果表明,在内侧测点,试验的应变值与仿真值的平均误差为-1682με,平均相对误差为20.3%;在外侧测点,试验的应变值与仿真值的平均误差为1281με,平均相对误差为19.5%。该方法为股骨假体柄结构的可靠性设计提供了有效参考。

汽车前舱冷却流场可靠性优化模型设计与仿真

针对汽车前舱冷却系统设计的复杂性和设计变量的不确定性,将Chebyshev不确定分析方法引入前舱冷却流场优化设计流程,建立适用于汽车前舱冷却流场的区间可靠性优化设计模型。以某轿车前舱冷却系统为例,引入Chebyshev函数用于结构优化设计。选取冷凝器和散热器的平均流速和气流流量为目标阈值,使用k-ε湍流模型进行有限元分析,结合Chebyshev可靠性分析迭代,对前舱冷却模块进行结构优化,提升前舱冷却流场性能。试验结果表明,通过增大前保吸能泡沫截面和优化风扇扇叶与支架间的间隙可在一定程度上改进前舱冷却流场性能。

高置信水平结构逆可靠度分析与优化方法研究进展

不确定性客观存在于工程结构生产制造以及服役等各环节之中并对结构的承载性能影响显著.特别是对于服役条件苛刻的航空航天承载装备,在设计阶段考虑多源不确定性的影响对于结构安全至关重要.在众多不确定性分析方法中,逆可靠度分析方法在效率和稳健性方面具有一定优势.为此,国内外学者在高置信水平结构逆可靠度分析与优化方法方面开展了大量研究并取得了长足进步,包括自适应迭代控制算法、先进可靠度优化策略与非充分样本下的高置信水平设计方法等.本文首先对国内外逆可靠度分析与优化方法取得的进展进行了系统梳理与总结,特别是逆可靠度分析方法的发展历程以及面临的挑战问题,主要包括强非线性功能函数、多设计点以及低失效概率问题.进一步,针对长期困扰可靠度方法实际应用的小样本问题,重点从结构高置信水平可靠度分析与优化理论角度开展系统介绍,详细论述了小样本诱发的认知不确定性到可靠度置信水平的传播链条.最后,基于现有成果和国家重大前沿需求,重点围绕航天装备可重复使用需求对结构可靠度未来研究方向进行了思考与展望,期望相关研究成果能够进一步助力我国航空航天结构实现高可靠性与极致轻量化设计.

高维混合不确定条件下基于降维积分的产品关键结构可靠性优化设计

在产品可靠性中注入优化设计思想,在满足可靠度要求的前提下寻找能够使目标性能最优的关键结构设计变量取值,是保障产品性能和提升人类使用感受的重要途径。值得注意的是,不确定因素在结构设计过程中无处不在且品种多样,特别是区间不确定和随机不确定往往同时存在,并具有较高的参数维度,使得传统的设计方法不再适用。针对此问题,先引入积分降维来提升产品关键结构可靠性的分析速度,再通过Kriging近似建模技术和多目标粒子群智能算法,建立高维混合不确定产品关键结构可靠性优化设计的高效循环嵌套计算架构。内层计算聚焦于考虑高维混合不确定变量的产品关键结构功能函数降维积分以快速获取其上下界函数表征及对应的可靠性范围,外层计算则根据内层的可靠性分析结果来判断当前的结构设计变量是否满足可靠性要求并借助多目标粒子群智能算法进行搜索更新,有效减小了产品关键结构可靠性优化设计过程的计算工作量,并通过工程实例验证了所提方法的合理性与有效性。