Multi-objective reliability optimization design of high-speed heavy-duty gears based on APCK-SORA model

For high-speed heavy-duty gears in operation is prone to high tooth surface temperature rise and thus produce tooth surface gluing leading to transmission failure and other adverse effects,but in the gear optimization design and little consideration of thermal transmission errors and thermal resonance and other factors,while the conventional multi-objective optimization design methods are difficult to achieve the optimum of each objective.Based on this,the paper proposes a gear multi-objective reliability optimisation design method based on the APCK-SORA model.The PC-Kriging model and the adaptive k-means clustering method are combined to construct an adaptive reliability analysis method(APCK for short),which is then integrated with the SORA optimisation algorithm.The objective function is the lightweight of gear pair,the maximum overlap degree and the maximum anti-glue strength;the basic parameters of the gear and the sensitivity parameters affecting the thermal deformation and thermal resonance of the gear are used as design variables;the amount of thermal deformation and thermal resonance,as well as the contact strength of the tooth face and the bending strength of the tooth root are used as constraints;the optimisation results show that:the mass of the gear is reduced by 0.13kg,the degree of overlap is increased by 0.016 and the coefficient of safety against galling Compared with other methods,the proposed method is more efficient than the other methods in meeting the multi-objective reliability design requirements of lightweighting,ensuring smoothness and anti-galling capability of high-speed heavy-duty gears.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Optimization design of piles subjected to horizontal loads based on reliability theory

Based on reliability theory,a general method for the optimization design of piles subjected to horizontal loads is presented.This method takes into consideration various uncertainties caused by pile installation,variability of geotechnical materials from one location to another,and so on.It also deals with behavior and side constraints specified by standard specifications for piles.To more accurately solve the optimization design model,the first order reliability method is employed.The results from the numerical example indicate that the target reliability index has significant influence on design parameters.In addition,the optimization weight increases with the target reliability index.Especially when the target reliability index is relatively large,the target reliability index has significant influence on design weight of piles.

Optimal distribution of reliability for a large network based on connectivity

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms （GA）. Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently,reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering.However,for deep foundation pit,evaluating the system safety of retaining structures and finding cost-effective design points are main challenges.To address this,this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou,China.The proposed method included two parts:system reliability model and robust design method.Back Propagation Neural Network(BPNN)is used to fit limit state functions and conduct efficient reliability analysis.The common source random variable(CSRV)model are used to evaluate correlation between failure modes and determine the system reliability.Furthermore,based on the system reliability model,a robust design method is developed.This method aims to find cost-effective design points.To solve this problem,the third generation non-dominated genetic algorithm(NSGA-III)is adopted.The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm.The proposed method has a good performance in locating the balanced design point between safety and construction cost.Moreover,the proposed method can provide design points with reasonable stiffness distribution.

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.

EFFICIENT METHOD FOR MULTIDISCIPLINARY DESIGN OPTIMIZATION BY CONSIDERING UNCERTAINTY

A new reliability-based multidisciplinary design optimization （RBMDO） framework is proposed by combining the single-loop-based reliability analysis （SLBRA） method with multidisciplinary feasible （MDF） method. The Kriging approximate model with updating is introduced to reduce the computational cost of MDF caused by the complex structure. The computational efficiency is remarkably improved as the lack of iterative process during reliability analysis. Special attention is paid to a turbine blade design optimization by adopting the proposed method. Results show that the method is much more efficient than the commonly used double-loop based RBMDO method. It is feasible and efficient to apply the method to the engineering design.

Reliability-based concurrent subspace optimization method

To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

A Comparison of Deterministic, Reliability-Based Topology Optimization under Uncertainties

Reliability and optimization are two key elements for structural design. The reliability~ based topology optimization （RBTO） is a powerful and promising methodology for finding the optimum topologies with the uncertainties being explicitly considered, typically manifested by the use of reliability constraints. Generally, a direct integration of reliability concept and topol- ogy optimization may lead to computational difficulties. In view of this fact, three methodologies have been presented in this study, including the double-loop approach （the performance measure approach, PMA） and the decoupled approaches （the so-called Hybrid method and the sequential optimization and reliability assessment, SORA）. For reliability analysis, the stochastic response surface method （SRSM） was applied, combining with the design of experiments generated by the sparse grid method, which has been proven as an effective and special discretization technique. The methodologies were investigated with three numerical examples considering the uncertainties including material properties and external loads. The optimal topologies obtained using the de- terministic, RBTOs were compared with one another; and useful conclusions regarding validity, accuracy and efficiency were drawn.

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

Aircraft designers strive to achieve optimal weight-reliability tradeoffs while designing an aircraft. Since aircraft wing skins account for more than fifty percent of their structural weight, aircraft wings must be designed with utmost care and attention in terms of material types and thickness configurations. In particular, the selection of thickness at each location of the aircraft wing skin is the most consequential task for aircraft designers. To accomplish this, we present discrete mathematical programming models to obtain optimal thicknesses either to minimize weight or to maximize reliability. We present theoretical results for the decomposition of these discrete mathematical programming models to reduce computer memory requirements and facilitate the use of dynamic programming for design purposes. In particular, a decomposed version of the weight minimization problem is solved for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location to yield an optimal minimum weight design.

基于响应面法的血管支架拉伸、扭转性能优化及考虑加工精度影响的强度可靠性分析

为分析设计变量对血管支架拉伸性能、扭转性能的精准影响,进行血管支架拉伸性能、扭转性能优化,考虑加工精度的影响,进行血管支架的强度可靠性分析。方法:取血管支架支撑筋宽度、支撑筋长度、连接筋宽度和支架厚度为设计变量,应用斯皮尔曼等级相关系数法分析设计变量对血管支架拉伸刚度、扭转刚度等响应变量的精准影响;采用响应面方法进行以拉伸刚度、扭转刚度为目标进行血管支架的优化设计;对优化后的血管支架,考虑加工精度所致设计变量的随机性,利用六西格玛工具分析应力的概率分布。结果:对于血管支架拉伸刚度,支撑筋宽度和连接筋宽度灵敏度系数大,且均为正值;对于血管支架扭转刚度,支撑筋宽度灵敏度系数较大,且为负值;优化后的血管支架相比原始血管支架,拉伸刚度降低了11.5%;扭转刚度减小了50.6%;考虑加工精度所致设计变量的随机性进行可靠性分析,在可靠度为99.8%时,虽然血管支架的拉伸刚度和扭转刚度最大值高于优化值,但血管支架的最大应力满足强度条件。结论:支撑筋宽度对血管支架的拉伸性能影响最大,连接筋宽度次之,支撑筋长度和支架厚度影响较小;支撑筋宽度对血管支架的扭转性能影响最大,连接筋宽度、支撑筋长度和支架厚度影响较小;随机因素加工精度对血管支架优化目标有一定的影响,但优化结果仍是可靠的。本文提供了一种血管支架优化的思路:首先是进行基于目标的优化,然后考虑随机因素的影响进行基于概率的强度可靠性分析。

基于Kriging模型与FORM的钢板组合梁桥结构优化设计

考虑材料参数的不确定性以及设计变量多重约束条件的影响,提出了基于可靠性分析的钢板组合梁桥结构优化设计方法。首先,利用拉丁超立方试验设计(Latin hypercube design,LHD)构建试验组合方案,并通过有限元分析获取试验设计组合下的最大挠度响应值。基于获取的训练样本,构建能够表征结构最大挠度值与随机输入之间映射关系的Kriging代理模型。基于建立的代理模型,以钢结构截面积最小化为目标函数,建立符合规范要求与可靠度约束的优化数学模型,并采用一阶可靠性方法(first order reliability method,FORM),实现设计变量优化。通过比较具有相同设计变量上限,但下限分别为初始值的80%和70%两种优化设计方案,评估了两者在相同阈值以及不同阈值下设计变量的优化结果。最后对方案二在阈值为17 mm下的优化结果进行极限状态验算。结果表明:两个优化设计方案在阈值为17 mm下的优化结果更具合理性,并且方案二在同一阈值下具有更高的优化程度。随着阈值增加,优化程度增加,且腹板高度在较大阈值下对结果影响更大,而翼缘宽度在较小阈值下影响更大。

装备可用性建模与优化设计方法研究

针对目前行业内缺少关于装备可用性建模与优化设计方法方面的研究成果这一问题,提出一种装备可用性建模与优化设计方法。通过可靠性、测试性、维修性和保障性信息提取,获得装备可用性设计方案的关键设计指标;建立面向多任务的装备可用性模型,并基于该模型完成装备在不同任务工作模式下的优化分析;确定装备可用性设计方案优选的多个决策属性,建立基于多属性决策的装备可用性设计方案优选模型,并基于该模型优选出装备可用性设计方案;通过案例分析验证所提方法的合理性和有效性,为装备可用性优化设计工作提供依据。

涡轮叶片寿命可靠性优化的类序列解耦法

针对含气膜孔冷却涡轮叶片多模式寿命可靠性优化设计效率与精度兼顾困难的问题,提出了基于自适应克里金代理模型的类序列解耦可靠性优化方法。该方法中,可靠性约束里的极限状态面代理模型构建过程会随着设计参数的搜索迭代而实时更新,并严格保证每个优化步下的代理精度和可行域判断的准确性,因此收敛快、稳健性强。代理模型在扩展空间中协作代理并共用训练样本点,实时自学习训练目标函数和约束函数的代理模型至收敛,在保证代理精度的同时显著提高优化效率。此外,基于所提方法开发了一体化、自动化的寿命可靠性优化集成仿真软件,并完成了涡轮叶片寿命可靠性优化设计的工程化验证,该结果验证了所提方法的高效性及工程适应性。

可靠性优化设计在汽车构件耐撞性中的应用

将实验设计、响应表面法和蒙特卡罗模拟技术相结合,提出了基于产品质量工程的6σ概率优化设计方法,实现了对汽车构件耐撞性的优化设计,提高了设计变量的可靠性.数字算例表明,该方法具有较高的精度和较强的工程实用性.

任意分布参数的后桥壳可靠性优化设计

讨论了随机参数服从任意分布的后桥壳可靠性优化设计问题。在基本随机参数前四阶矩已知的情况下 ,应用随机摄动法和 Edgeworth级数方法对后桥壳进行可靠性优化设计 ,通过计算机程序可以实现随机参数服从任意分布的后桥壳可靠性优化设计 ,迅速准确地得到了后桥壳的可靠性优化设计信息。计算结果表明 ,本文提出的方法是一种有效、实用的方法。

基于FORM的齿轮传动多学科优化设计

通常多学科设计优化是一种确定性设计方法,未考虑不确定性因素的影响。为降低多学科设计优化过程中不确定性因素对系统性能的影响,将一次可靠性方法与协同优化方法相结合,应用到多学科设计优化中。建立基于一次可靠性方法的协同优化的数学模型,并阐述其求解流程,该方法可用于多学科设计优化领域的可靠性设计问题。分别运用协同优化方法和基于一次可靠性方法的协同优化实现了减速器齿轮传动的多学科优化设计,在这两种方法的系统级优化中,引入松弛变量,将一致性等式约束转化为不等式约束,使算法易于收敛。优化结果表明基于一次可靠性方法的协同优化方法求得的最优解使得约束条件满足了可靠性要求,提高了系统的可靠性,具有实际工程意义。

采煤机摇臂传动系统可靠性稳健优化设计

采煤机摇臂传动系统为采煤机的关键动力传递部件。以MG300/700-WD型采煤机摇臂传动系统为研究对象,根据实际工况建立了系统的有限元模型,利用Matlab软件对传动系统进行了非线性动力学特性分析,得到了系统危险部位的应力谱。在此基础上对摇臂传动系统进行了疲劳分析,建立了摇臂传动系统疲劳寿命可靠性模型。依据可靠性理论,采用四阶矩法对摇臂传动系统进行可靠性及可靠性灵敏度分析,分析了系统结构参数对系统可靠性的影响程度。对于摇臂传动系统疲劳寿命敏感的结构参数,进行了可靠性稳健优化设计,与单目标优化方法进行对比,并针对优化结果使用蒙特卡洛模拟的方法对可靠性进行了验证。结果表明,对采煤机摇臂传动系统进行可靠性稳健优化设计是一种实用、有效的方法。