Reliability analysis using an enhanced response surface moment method

Moment methods, which are powerful and simple techniques for analyzing the reliability of a system, evaluate the statistical moments of a system response function and use information from the probability distribution in the analysis. The full factorial moment method (FFMM) performs reliability analysis by using a 3ⁿ full factorial design of experiments (DOE) and the Pearson system for random variables. To overcome the inefficiency of FFMM, the response surface moment method (RSMM) has been proposed, which is based on a response surface model (RSM) that is updated by adding cross product terms into the simple quadratic model. In this paper, we propose the enhanced RSMM (RSMM+) that modifies the procedure of selecting a cross product term in the RSMM and adds a process of judging whether the response surface model can be established before performing an additional experiment. We apply the proposed method to several examples and show that it gives better results in efficiency.     

基于响应面法的桥梁主桁架结构优化设计

对复杂结构进行优化设计和可靠性设计时,利用传统的设计方法可能会遇到计算量太大的困难,应用响应面法是有效地解决该问题的途径之一.文中将响应面法和有限元技术相结合,建立了桥梁主桁架的挠度、弯曲应力与结构尺寸的函数表达式,继而对主桁架进行了结构优化设计,最后对优化结果进行了有限元分析和验证.设计计算结果表明,对于桁架结构设计这类问题,响应面优化设计具有很好的应用价值.     

Reliability-based design optimization via high order response surface method

To reduce the computational effort of reliability-based design optimization (RBDO), the response surface method (RSM) has been widely used to evaluate reliability constraints. We propose an efficient methodology for solving RBDO problems based on an improved high order response surface method (HORSM) that takes advantage of an efficient sampling method, Hermite polynomials and uncertainty contribution concept to construct a high order response surface function with cross terms for reliability analysis. The sampling method generates supporting points from Gauss-Hermite quadrature points, which can be used to approximate response surface function without cross terms, to identify the highest order of each random variable and to determine the significant variables connected with point estimate method. The cross terms between two significant random variables are added to the response surface function to improve the approximation accuracy. Integrating the nested strategy, the improved HORSM is explored in solving RBDO problems. Additionally, a sampling based reliability sensitivity analysis method is employed to reduce the computational effort further when design variables are distributional parameters of input random variables. The proposed methodology is applied on two test problems to validate its accuracy and efficiency. The proposed methodology is more efficient than first order reliability method based RBDO and Monte Carlo simulation based RBDO, and enables the use of RBDO as a practical design tool.     

Wind turbine airfoil design using response surface method

This paper describes the design of a wind turbine airfoil under various operating conditions through the use of a suitable combination of flow analysis and optimization techniques. The proposed method includes a parametric study on the influence of design variables and different design conditions on airfoil performance. The incompressible Navier-Stokes equations and the k-ɛ turbulence model are used to compute the aerodynamic coefficients of an airfoil. The response surface method (RSM) is applied to obtain the optimum solution of the defined objective function and the penalty term of the constraint. The influence of the design variables (change in airfoil geometry) on airfoil performance as well as the accuracy of the RSM is examined from the statistical viewpoint. Various airfoil shapes with good aerodynamic performance are obtained according to various operating conditions (change in angle of attack), objective functions (minimum of drag coefficient or maximum of lift-to-drag ratio), and constraints (the lift coefficient of a designed airfoil is higher than that of a base airfoil at a certain angle of attack).     

产品稳健设计响应面模型法的试验设计

试验设计是产品稳健设计中的基础，对稳健设计中常用的响应面模型法的试验设计方法进行了研究。针对响应面法稳健设计中所采用的仿真试验与物理试验误差性质的不同，采取不同的试验设计方法，其中正交试验设计和拉丁方试验设计的应用克服了以往响应面法稳健设计中不能应用仿真试验的缺点。     

Parametric study and optimization of a food can corrugation design using a response surface method

This paper presents the parametric design and functional optimization of a thin-walled food container with a corrugated surface. The configuration of the can corrugation should be designed to minimize the use of raw material subject to the constraints of the targeted structural performance. In the present study, the failure behaviors and the buckling strengths of a commercial food can under paneling pressure and axial loading are investigated with a series of experiments and finite element analyses. Full factorial design is implemented to study the effects of the geometric parameters of the corrugation (e.g., depth, radius, spacing and number of beadings) on its strength. Parameter optimization using a rotatable central composite design is employed to identify an optimal corrugation design by approximating the response surfaces of the can strength in terms of the significant design variables. The obtained surfaces are derived through the analysis of variance, and the suitability of the response is justified. A light- weight can body is then achieved by reduction of the can body thickness according to the required strength characteristics. Finite element analysis of the optimal model is also performed to confirm the predicted results. By using the proposed procedure, the can-body weight can be reduced by up to 12% compared with the original design.     

Flow-forming optimization based on hardness of flow-formed AISI321 tube using response surface method

Flow forming is an advanced locally plastic deformation applied to manufacture seamless tubes with thin walls and high precision dimension. One of the important mechanical properties of flow-formed tubes is hardness. In this study, after preliminary experiments for definition of effective parameters, design of experiments (DOE) is utilized to determine the influence of the parameters such as rotational speed of mandrel, feed rate, and wall thickness reduction on the hardness of flow-formed AISI 321 steel tube. Under experimental results, a mathematical model comprising effective parameters is developed to predict the optimum hardness, using response surface methodology (RSM). RSM’s Box–Behnken design is employed to specify the optimum condition caused to a minimum hardness at high optimum confidence level. The analyzed model revealed that the hardness increases with increasing of the mandrel speed and the depth of cut, and it decreases with decreasing of the feed rate. The new point of view is related to the fact that the high level of thickness reduction covers the efficiency of mandrel speed.     

基于响应面法的微操作平台多目标优化

为了提高微操作平台的操作空间和动态性能,基于响应面法对一种新型微操作平台进行了多目标优化设计。采用中心组合设计方法选取仿真试验点,根据试验点建立平台的参数化几何模型,应用软件ANSYS对平台进行静力学和模态分析得到其固有频率、位移放大倍数和最大应力的响应值。根据所得的仿真试验数据,采用最小二乘法和显著性检验建立反映平台性能指标的二阶多项式响应面模型。最后,计算了反映响应面拟合度的评价指标,验证了所建响应面模型的精确性。以微操作平台的放大倍数和固有频率为优化目标,强度为约束,建立了平台的多目标优化模型,采用多目标遗传算法对平台进行优化得到Pareto解集。从Pareto解集可知,固有频率与放大倍数之间是相互冲突的,故需权衡固有频率和放大倍数从Pareto解集选取最优解。比较优化前后平台的各性能指标可知,平台的固有频率增大了35.58%,放大倍数增大了2.33%,最大应力减小了38.97%,证明了提出的优化方法的有效性。     

A response surface based hierarchical approach to multidisciplinary robust optimization design

A multidisciplinary robust optimization design framework, concurrent subsystem robust design optimization, is proposed to obtain robust optimum solution in the large-scaled and coupled system. In this framework, response surfaces in the form of artificial neural networks provide information pertaining to system performance characteristics, and individual subsystems engage in performing robust optimization design in parallel while communicating with the system level. This optimization approach incorporates uncertainty analysis and generates a global robust optimum solution in an iterative fashion. Two applications are considered, and the results demonstrate that the approach yields a reasonable robust optimum solution, and it is a potential and efficient multidisciplinary robust optimization approach .     

A response surface based sequential approximate optimization using constraint-shifting analogy

When a traditional response surface method (RSM) is used as a meta-model for inequality constraint functions, an approximate optimal solution is sometimes actually infeasible in a case where it is active at the constraint boundary. The paper proposes a new RSM that ensures the constraint feasibility with respect to an approximate optimal solution. Constraint-shifting is suggested in order to secure the constraint feasibility during the sequential approximate optimization process. A central composite design is used as a tool for design of experiments. The proposed approach is verified through a mathematical function problem and engineering optimization problems to support the proposed strategies.     

Robust design of roll-formed slide rail using response surface method

Roll-formed slide rail used as a linear guide in the smooth movement of drawers and electric home appliances requires geometric accuracy because of a high slenderness ratio and repetitive usage. The slide rail members are generally manufactured by the roll forming process. The members need to be improved through optimization of the roll forming process instead of the designer’s experience. The aim of this study is to determine the optimal roll forming parameters by using robust optimization technique which simultaneously satisfies three criteria such as the shape difference factor, bowing factor and modified inverse safety factor. In analyzing the roll forming process of a slide rail, the pass in which the largest deformation occurred is designated as the target pass. The positions and the curvature of rolls are set as the design variables in the target pass. The cost function, which is comprised of the shape difference factor, the bowing factor, and the modified inverse safety factor, is obtained using design-of-experiments of the response surface method. The cost function is minimized by using robust optimization techniques and showed the improved the straightness and the durability value. Using robust design methodology, it is able to be constructed a multi-objective function, and optimized three criteria, simultaneously.     

Robotic fiber placement process analysis and optimization using response surface method

Unlike traditional materials, composites are carefully designed materials suitable for specific applications. Conventional methods of fabrication of composite structures have proven to be labor intensive and time-consuming. Robotic fiber placement is a composite fabrication technique that increases the flexibility of fiber placement process and allows for the fabrication of more complex structures. This study is aimed at analyzing and optimizing the robotic fiber placement process parameters. Many experiments have been conducted to analyze gas torch temperature, fiber laying head speed, and fiber compaction force and the process is optimized using response surface method.     

基于响应面法的减速器行星架多目标优化研究

针对某二级行星齿轮减速器的行星架存在的强度不足、质量过大等问题,对行星架的应力分布进行了分析,对行星架进行了多目标优化.首先,采用两种不同的方案对行星架进行了强度分析(其中,方案一采用了直接加载轴承力的方法,方案二采用了行星架装配体刚柔耦合模型),得出了二种不同的应力和应力分布结果;然后,通过对其实际工况进行分析,结果...     

定力矩扳手系统可靠性优化设计方法

提出了对定力矩扳手系统进行可靠性优化设计的理念。通过对其结构分析和对其部件的可靠度优化分配,以及对可靠度的优化设计方法的介绍,进而确保了定力矩扳手的结构功能和使用功能的完善和优异。     

基于中心点精确响应面法的板壳结构优化

对响应面方法中两个最为关键的概念——近似函数及试验设计做了简单描述,选择线性函数作为约束条件的近似函数形式,并对位移和应力约束作不同处理,位移约束不合常数项,而应力约束含常数项。提出了一种适合建立一阶形式响应面并使结构分析次数最少的试验设计方法——中心扩展法。求解响应面时在最小二乘法的基础之上作了改进,提出中心点精确响应面法,使拟合的响应面中心点处的响应值精确等于有限元分析值。最后通过数值算例说明改进后的响应面法对于板壳结构优化的可行性和优越性。     

Optimal design of high temperature vacuum furnace using response surface method

A new method using the response surface method and optimization technique has been developed instead of the original method based on trial and error. In order to construct a response surface, thermal analysis was performed under the condition of using the calculated thermal conductivity of the insulator in a previous study. In order to set up the response surface, the D-Optimal method was used in the process of selecting experimental points. Using a weighting factor, an optimization study was carried out under the condition of satisfying user requirements. Finally, the merits and drawbacks of the new method were described by comparing with the optimal design method based on the thermal analysis database which was developed in a previous study. The optimal results show that the developed method can be used to design an energy efficient, low manufacturing cost, high temperature vacuum furnace with avoiding unnecessary iterative manufacturing, and anticipating the performance before manufacturing. This paper was recommended for publication in revised form by Associate Editor Ohchae Kwon     

Loading path optimization of a hydroformed part using multilevel response surface method

In tube hydroforming, the loading path that is the relationship between axial feeding and internal fluid pressure is of important significance. Researchers have employed various optimization approaches to find an optimum loading path. In this research, a statistical method based on finite element analysis has been developed. An accurate FEA has been used to simulate the process and to find the response of the process to the loading. By performing an experimental test, the model is verified in comparison with the actual T part. The multilevel response surface method (MLRSM) has been used to model the responses from the finite element analysis. The behavior of the process can be predicted using the response surface methodology (RSM) model, and then, the obtained model is used to optimize the process. The optimum point in the RSM highly depends on the initial range of design variables. Thus, after finding the optimum point in each level, the ranges of variables are adjusted around the last optimum point. Then, the optimization process can be continued as a multilevel process. In the performed optimizations, the thickness variance has been considered as the objective function and the protrusion height as the constraint. The thickness variation based on the optimum loading path is highly improved, and it shows that multilevel RSM is very effective in improving the results.     

基于响应面法和遗传算法的孵育器多学科优化设计

针对恒温孵育器要满足重量小、温度均匀的设计要求,应用ANSYS和Matlab软件对孵育器进行了多学科优化设计。通过有限元分析,分别以目标区域平均温度和温度均方差为设计目标,通过采用正交试验设计方案采集数据,获取了响应面模型,并采用遗传算法进行了多学科优化设计。研究结果表明:响应面模型可以准确模拟有限元模型并用于优化设计,遗传算法可以用于有效解决多目标优化问题;该方法为多学科优化设计问题提供了解决方案。     

磁悬浮控制力矩陀螺锁紧机构可靠性设计及优化

鉴于传统确定性优化方法没有考虑结构参数的随机性对结构性能的影响,本文提出了一种基于可靠性灵敏度的锁紧弹片结构优化方法。首先,以某磁悬浮控制力矩陀螺锁紧弹片为研究对象,研究了有限元建模和失效模式;然后,考虑弹片结构尺寸和材料参数的随机性,结合响应面法与一次二阶矩法,研究了串联失效模式下弹片的可靠度计算方法,进而推导了可靠性关于设计变量均值和方差的灵敏度计算公式;最后,根据灵敏度分析结果,研究确定了弹片结构优化策略,构建了弹片可靠性优化模型。分析了安全系数法和可靠性法优化结果的差异,结果表明:与安全系数法相比,可靠性法的优化结果更好;在保证弹片可靠度的前提下,采用可靠性优化方法不仅使弹片质量下降了23.71%,使锁紧机构更加优化,而且使陀螺房质量也下降了0.98kg,有利于磁悬浮控制力矩陀螺整机结构的轻量化。     

Damage identification by response surface based model updating using D-optimal design

Statistical tools, as well as mathematical ones, have been widely adopted and their performance has been shown in different engineering problems where randomicity usually exists. In the realm of engineering, merging statistical analysis into structural evaluation and assessment will be a tendency in the future. As a combination of mathematical and statistical techniques, response surface methodology has been successfully applied to design optimization, response prediction and model validation. This methodology provides explicit functions to represent the relationships between the inputs and outputs of a physical system, which is also a desirable advantage in damage identification. However, so far little research has been carried out in applying the response surface methodology to structural damage identification. This paper presents a damage identification method achieved by response surface based model updating using D-optimal designs. Compared with some common designs constructing response surfaces, D-optimal designs generally require a minimum number of numerical samples and this merit is quite desirable when analysts cannot obtain enough samples. In this study, firstly D-optimal designs are used to establish response surface models for screening out non-significant updating parameters and then first-order response surface models are constructed to substitute for finite element models in predicting the dynamic responses of an intact or damaged physical system. Three case studies of a numerical beam, a tested reinforced concrete frame and a tested full-scale bridge have been used to verify the proposed method. Physical properties such as Young’s modulus and section inertias were chosen as the input features and modal frequency was the only response feature. It has been observed that the proposed method gives enough accuracy in damage prediction of not only the numerical but also the real-world structures with single and multiple damage scenarios, and the first-order response surface models based on the D-optimal criterion are adequate for such damage identification purposes.