基于响应面法的结构动力学模型修正

为了获得精确的结构动力学模型,提出了响应面和优化相结合的方法。利用参数化模型和优化拉丁方试验设计获取样本点构造多项式响应面模型,最小二乘法确定多项式系数并检验响应面的拟合精度。用响应面计算结果与实验结果的误差构造目标函数,自适应模拟退火算法来优化修正响应面参数,将修正后的参数值带入有限元模型得到修正模型。以欧洲航空科技组织的基准模型GARTEUR飞机模型为算例,对比修正前后模态频率,结果表明修正后的模型在测试频段和预测频段具有良好的复现和预测能力,进而验证了基于响应面法与优化方法相结合的结构动力学有限元模型修正的有效性。     

结构有限元模型修正的自适应响应面方法

针对结构有限元模型修正可能陷入局部最优点的问题,提出了基于具有全局收敛特性的自适应响应面的结构有限元模型修正方法,模型修正过程中在全局最优解附近不断收缩参数设计空间,重构更为精确的响应面模型,同时,由于采用了拉丁超立方设计选择样本点,具有一定的遗传性,在使用过程中可以有效减少样本点总数。通过实例计算表明,传统的有限元模型修正方法很可能陷于局部最优,而利用该方法进行有限元模型修正时,可以有效避免陷入局部最优点,只需较少样本点便可收敛于全局最优解,有效的进行有限元模型修正。     

Evaluation of response surface methodologies used in crashworthiness optimization

Optimization of car structures is of great interest to the automotive industry. This work is concerned with structural optimization of a car body with the intent to increase the crashworthiness properties of the vehicle or decrease weight with the crashworthiness properties unaffected. In this work two different methodologies of constructing an intermediate approximation to the optimization problem are investigated, i.e. classical response surface methodology and Kriging. The major difference between the two methodologies is how the residuals between the true function value and the polynomial surface approximation value at a design point are treated.Several different optimization problems have been investigated, both analytical problems as well as finite element impact problems.The major conclusion is that even if the same kind of updating scheme is used both for Kriging and linear classic response surface methodology, Kriging improves the sequential behaviour of the optimization algorithm in the beginning of the optimization process. Problems may occur if a constraint is violated after several iterations and then classic response surface methodology seems to more easily be able to find a design point which satisfies the constraint.     

基于响应面法的无轨伸缩式门式起重机轻量化设计

依赖于传统经验方法的无轨伸缩式门式起重机结构设计往往趋于保守,材料浪费严重,为了充分发挥材料的承载性能,有必要对它进行优化分析。对无轨伸缩式门式起重机结构进行优化设计时,针对非线性接触模型计算不收敛与计算效率低等问题,提出以节点耦合模型代替接触模型来构建响应面近似模型,并将近似模型与多岛遗传算法相结合对结构参数进行优化。以某无轨伸缩式门式起重机各构件截面尺寸为初始设计变量,以结构强度、刚度、自重为模型响应,通过调用Isight平台中最优拉丁超立方设计方法产生设计变量样本点,再由试验设计（design of experiment,DOE）模块调用有限元分析软件ANSYS完成样本点模型仿真以筛选出对响应影响较大的设计变量。利用优选后的设计变量构建响应面近似模型,以结构强度和刚度为约束条件,门式起重机结构质量最轻为优化目标,采用多岛遗传算法对响应面模型进行优化。结果表明：在保证结构性能的前提下,优化后门式起重机质量减轻23.4%,轻量化效果明显。所提出的优化策略可较快获得全局最优解,减少了计算量,为无轨伸缩式门式起重机结构改进提供了理论依据。     

Generalized pointwise bias error bounds for response surface approximations

This paper proposes a generalized pointwise bias error bounds estimation method for polynomial‐based response surface approximations when bias errors are substantial. A relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model. The method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial. The effect of relaxation parameter is studied. It is demonstrated that when bias errors dominate, the bias error bounds characterize the actual error field better than the standard error. The bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate. It is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions. Copyright © 2005 John Wiley & Sons, Ltd.     

Active thermography setup updating for NDE: a comparative study of regression techniques and optimisation routines with high contrast parameter influences for thermal problems

An implementation of updating techniques similar to finite element updating in structural dynamics is developed for thermal material inspection using adaptive response surfaces to approximate experimental parameters. In general, thermal models contain high nonlinearities in their parameters, which influences updating accuracies. This is further investigated in this work. Several adaptive response surface regression methods are compared: interpolation, piecewise spline and polynomial regression functions. Next, the influence of the choice of optimisation parameters is discussed and compared with several global and local optimisation routines. Finally, a well-suited regression technique is investigated which transforms the dataset to a smaller, focused response model in each optimisation loop and delivers a proper regression accuracy. This results in data-reduction for the model to be optimised.     

Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation

This study describes a new method of experimental design to obtain a response surface of buckling load of laminated composites. Many evaluations for genetic algorithms for stacking sequence optimizations require high computational cost. That evaluation cost can be reduced by an approximation using a response surface. For a response surface for stacking sequence optimizations, lamination parameters are adopted as variables of the approximation function of the entire design space instead of ply angles for each ply. This study presents, proposes and investigates a new method of experimental design in detail. For most analytical tools, stacking sequences is demand as input data and lamination parameters cannot be applied directly to the tools. Therefore, the present study proposes and applies a new D-optimal set of laminates to the stacking sequence optimizations of the problem of maximization of buckling load of a composite cylinder. The new experimental design is a set of stacking sequences selected from candidate stacks using D-optimality. Consequently, the D-optimal set of laminates is shown to be effective for design of experiments of response surfaces for maximization of the buckling load of composite structures.     

Optimized hydrogen positions for aluminium and iron containing hydroxide minerals

The structures of a number of hydroxide and oxyhydroxide minerals have previously been reported without the hydrogen positions explicitly defined. Here we use two atomic scale computer simulation techniques, one based on classical ionic potentials, the other on density functional theory (DFT), to predict these positions. The aim is not only to provide data that can be used as the basis for future experimental structure optimizations but also model parameters that can be used to predict complex hydroxide structures. The efficacy of the approach is demonstrated through the comparison of predicted and experimental data for minerals whose hydrogen positions are known.     

Adaptive response surface method based on a double weighted regression technique

In structural reliability analysis where the structural response is computed from the finite element method, the response surface method is frequently used. Typically, the response surface is built from polynomials whereof unknown coefficients are estimated from an implicit limit state function numerically defined at fitting points. The locations of these points must be selected in a judicious way to reduce the computational time without deteriorating the quality of the polynomial approximation. To contribute to the development of this method, we propose some improvements. The response surface is successively formed in a cumulative manner. An adaptive construction of the numerical design is proposed. The response surface is fitted by the weighted regression technique, which allows the fitting points to be weighted according to (i) their distance from the true failure surface and (ii) their distance from the estimated design point. This method aims to minimize computational time while producing satisfactory results. The efficiency and the accuracy of the proposed method can be evaluated from examples taken from the literature.     

Hybrid approximation algorithm with Kriging and quadratic polynomial‐based approach for approximate optimization

This paper describes a new hybrid algorithm that uses a Kriging and quadratic polynomial‐based approach for approximate optimization. The Kriging method is used for generating a global approximation model, and the polynomial‐based approximation method is used for generating a local approximation model. The Kriging system is only used to construct a polynomial‐based locally approximate model by estimating some function values and Hessian components of an estimated surface. The number of Kriging estimations can be reduced in comparison with direct Kriging‐based optimization, and a local optimum solution on an approximated surface can be clearly estimated without use of an optimization procedure based on a local appropriate quadratic polynomial model. Numerical examples of engineering optimization using the proposed method illustrate validity and effectiveness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation

A method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.     

Response surface approximations for structural optimization

Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to find the region of interest containing the optimal design, and techniques for finding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the ‘best’ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-effective. In a further attempt to improve efficiency, different regression models were investigated. The results indicate that the use of the two methods investigated does not significantly improve the results. Finding an accurate global approximation is challenging, and sufficient accuracy could only be achieved in the example problems by considering a smaller region of the design space. © 1998 John Wiley & Sons, Ltd.     

On criteria for accepting a response surface model

One of the key problems in response surface analysis is the judgement whether a response surface model is a sufficiently accurate representation of the true response function based on a finite set of experiments. The use of response surface techniques in the context of structural reliability led to the definition of a special lack of fit measure and the formulation of a criterion for accepting response surface models using this measure. The purpose of this paper is to derive and justify two alternative criteria based on this lack of fit measure. Some examples are given to demonstrate the validity of the derived criteria.     

非线性隐式极限状态方程失效概率计算的组合响应面法

提出组合响应面的新方法,用以计算设计点附近非线性程度较大的隐式极限状态方程的失效概率。该方法用主响应面和多个次响应面近似对失效概率贡献较大的区域,其响应面函数形式为不含交叉的二次多项式。主响应面依据传统响应面法通过选择适当的插值点和迭代运算获得,其设计点为主设计点。延坐标轴正负方向偏移主设计点得到拟均值点。以拟均值点为基础得到一组次响应面和次设计点。通过主次响应面在各自设计点处的切平面建立组合响应面近似原隐式极限状态方程,并计算其失效概率。算例结果说明所提方法具有较高精度。     

用多项式逼近理论的时变权重组合预测方法及其应用

提出一种基于一元多项式逼近和二元多项式逼近的时变权重组合预测方法,并将之应用于飞行器结构响应序列的建模与预测。充分考虑权重的无偏性和非负性,通过引入松弛变量将不等式约束转化为等式约束并基于惩罚函数构造新的组合预测目标函数;最后采用遗传算法获得未知变量的数值解及组合预测时变权重表达式。应用结果表明预测方法有效。     

基于神经网络响应面的复合材料结构优化设计

用正交试验设计的方法选择样本点构建神经网络响应面,将神经网络响应面作为优化的目标函数或约束条件,加上其它常规约束条件建立优化模型,应用遗传算法 (GA) 进行优化,形成一套适用于复杂结构设计的高效优化方法。以复合材料帽型加筋板的重量优化问题为例,建立了加筋板模型的重量响应面目标函数、强度和稳定性响应面约束条件;并用PATRAN/NASTRAN进行有限元计算,获取用于响应面训练的样本点数值。算例表明:该方法能以很少的有限元分析次数,取得高精度的响应面近似模型,并且使优化效率大大提高。      

Numerical approaches for collaborative data processing

We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. The approach relies on a solution mapping technique to approximate mathematical models by polynomial surrogate models. We use these surrogate models to formulate prediction bounds in terms of polynomial optimizations. Recent results on polynomial optimizations are then applied to solve the prediction problem. Two examples which illustrate the key aspects of the proposed algorithm are given. The proposed algorithm offers a framework for collaborative data processing among researchers. This work was supported by the National Science Foundation, Information Technology Research Program, Grant No. CTS-0113985.     

Simplified Approach Based on Polynomial Equations to Predict the Permeability of Micro‐perforated Polymeric Films

A simplified approach to predict the mass transport properties of micro‐perforated films was presented in this work. In particular, the proposed mathematical model was based on a second‐degree polynomial function. Different types of micro‐perforated films with two thicknesses (35 and 25 µm) were tested for gas and water vapour permeability, under proper conditions. The films differed in both number of holes per unit area and hole diameter. Corresponding non‐perforated films were also tested. The experimental data obtained were used to validate the model. Moreover, the surface response plot of the interactions between hole diameter and number of holes per area relative to oxygen, water vapour and carbon dioxide permeability were determined. Results of the mean relative deviation modulus (E%) between the experimental and predicted data confirmed the ability of the proposed model to predict the permeability of micro‐perforated films. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of model building techniques for the development of machinability database systems

Computerized machinability database systems are essential for the selection of optimum cutting conditions during process planning, and these form an important component in the implementation of computer integrated manufacturing (CIM) systems. This paper presents a comparative analysis of the different model building techniques available in commercial statistical packages, to select the most suitable technique for use in machinability database systems. The techniques analysed are; backward elimination, forward selection, stepwise regression, and all possible subset regression. Experimental machining response data for the surface roughness when turning grey cast iron (154 BHN) and steel (140 BHN) have been analysed to evaluate the four model building techniques. Second order polynomial model structures with logarithmic transformation of the variables has been used for building adequate models. The adequacy of the fitted regression equation is checked by analysing the residuals. Based on the results of this analysis, the advantages and limitations of the four different techniques for building machinability models are discussed. It has been found that the backward elimination and all possible subset regression are the best suited techniques for model building in machining database systems.