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.     

Augmented D-optimal design for effective response surface modeling and optimization

For effective response surface modeling during sequential approximate optimization (SAO), thenormalized and the augmented D-optimality criteria are presented. Thenormalized D-optimality criterion uses the normalized Fisher information matrix by its diagonal terms in order to obtain a balance among the linear-order and higher-order terms. Then, it is augmented to directly include other experimental designs or the pre-sampled designs. This augmentation enables the trust region managed sequential approximate optimization to directly use the pre-sampled designs in the overlapped trust regions in constructing the new response surface models. In order to show the effectiveness of the normalized and theaugmented D-optimality criteria, following two comparisons are performed. First, the information surface of thenormalized D-optimal design is compared with those of the original D-optimal design. Second, a trust-region managed sequential approximate optimizer having three D-optimal designs is developed and three design problems are solved. These comparisons show that thenormalized D-optimal design gives more rotatable designs than the original D-optimal design, and theaugmented D-optimal design can reduce the number of analyses by 30 % –40 % than the original D-optimal design.     

Optimization for rising or falling ridge systems in non-spherical designs

The response surface (RS) methodology is a well-known tool employed for product and process optimization. In some engineering optimization problems the fitted response has a rising or falling ridge system, namely the stationary point of response is remote from the design region. For such a case, usually the classical method, called ridge analysis (RA), is employed to specify the optimum operating conditions for an optimization problem. In this paper, it is proven that the RA does not guarantee the global maximum or minimum point of response in the experimental region for non-spherical designs such as face-centered designs, Box-Behnken designs, and two-level factorial designs. The current study proposes an approximation based on the use of desirability function technique to solve this ridge optimization problem, and demonstrates that the desirability function technique is more effective than the RA technique described by Myers and Montgomery (2002) for non-spherical designs which are frequently applied for engineering problems. To show the effectiveness and advantages of the proposed technique, a case study is presented to optimize the forming parameters of a tube hydroforming (THF) process where a Box-Behnken design is employed.     

Optimum tolerance design using component-amount and mixture-amount experiments

The tolerance design problem involves optimizing component and assembly tolerances to minimize the total cost (sum of manufacturing cost and quality loss). Previous literature recommended using traditional response surface methodology (RSM) designs, models, and optimization techniques to solve the tolerance design problem for the worst-case scenario in which the assembly characteristic is the sum of the component characteristics. In this article, component-amount (CA) and mixture-amount (MA) experiment approaches are proposed as more appropriate for solving this class of tolerance design problems. The CA and MA approaches are typically used for product formulation problems, but can also be applied to this type of tolerance design problem. The advantages of the CA and MA approaches over the RSM approach and over the standard, worst-case tolerance-design method are explained. Reasons for choosing between the CA and MA approaches are also discussed. The CA and MA approaches (experimental design, response modeling, and optimization) are illustrated using real examples.     

Response surface methodology for eicosanoic acid triboproperties in castor oil

Response surface methodology with Box-Benhken (BB) design of experiment is utilized to study the antiwear (AW) and lubricity properties of eicosanoic acid in biodegradable castor oil base-stock and the results were compared with those of zinc dialkyldithiophosphate (ZDTP) and octadecanoic acid. The designs utilize load, additive concentration and temperature to develop models for the antiwear and lubricity response in a four-ball configuration. This was done by performing statistically designed experiments, estimating the coefficients in the mathematical models, predicting the response, checking for adequacy of the model and response optimization. Comparison of predicted and experimental response values outside the design conditions and for the optimal wear conditions showed good correspondence, implying that empirical models derived from response surface approach can be used to describe the tribological behavior of the additives in castor oil base-stock. Eicosanoic acid showed good tribological properties comparable to the popular octadecanoic acid and ZDTP lubricant additives, without acidic corrosion phenomenon as in ZDTP.     

Efficient approximation method for constructing quadratic response surface model

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables inn, the proposed method requires only 2n+1 design points for one approximation, which are a center point and two additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.     

A Converging Wall-Jet Instrument for Ion Selective Electrode Dynamic Response Studies

Abstract

Ion selective electrodes are used to conduct real-time measurements of gaseous thermal degradation products from halon replacement experiments. Response characteristics of these ion selective electrodes are needed to address potential interferences and surface poisoning experienced under field conditions. The design and the fabrication of an in situ, converging wall-jet instrument for the measurement of the dynamic responses of ion selective electrodes are described. Various time delays associated with the generation and detection of ion activity steps have been quantitatively determined.

Dynamic response measurements for iodide steps on a Corning iodide/cyanide ion selective electrode are comparable to those obtained on the best of the earlier instrument designs, the in situ, switched wall-jet instrument. The advantages of the converging wall-jet instrument over the switched wall-jet instrument are identified.     

Using higher precision-based response surface designs to determine the optimal process target

The selection of the optimal process target is critically important as it directly affects the defect rate, material cost, scrap and rework costs, and the loss to customers. Within the context of the optimal process target problem, a new model is proposed in this paper and two distinct contributions to the related topic are offered. First, while most research work assumes a given process distribution with a known variance, this paper integrates response surface designs into solving the optimal process target problem, thus removing the need to make assumptions regarding process parameters. Second, typical response surface designs consider second-order fitted functions; however, this paper considers a procedure to include higher-order polynomial terms that will result in higher prediction capabilities, thereby giving a more accurate representation of the true process. A constrained nonlinear optimization scheme is used to facilitate the development of this methodology and a numerical example is provided for illustration.     

基于Ansys Workbench的一种新型铁路起重机转台轻量化探析

以有限元分析软件Ansys Workbench协同仿真平台为工具,对传统的转台结构进行拓扑优化,在拓扑优化结果的基础上提出了一种新型的转台结构,并保守地赋予了板厚。利用Workbench中DM、Mechanical以及DX 3大模块之间的无缝连接,完成了新型转台结构的参数化建模、结构分析和基于神经网络响应面法的优化设计,轻量化效果显著,为相关设计提供了参考。     

基于响应面的三自由度超声电机定子设计优化

针对超声电机定子设计过程存在的定子设计模态与干扰模态分离不彻底、定子振动幅度小、定子振动时局部内应力较大等问题,提出了基于响应面模型的电机定子设计优化方法。首先,通过选取合适的定子设计尺寸作为变量,拉丁超立方抽样方法在设计空间内选取样本点;其次,对各样本点的组合得到的定子尺寸结构进行有限元分析,得到定子的模态和谐响应值从而建立定子的响应面模型;然后,利用遗传算法在响应面模型的基础上对定子进行优化;最后,使用有限元软件对优化前后的定子进行建模计算验证了优化结果的正确性。     

基于偏好聚合不精确法的湿式制动器稳健设计

针对不确定性对产品性能的影响,以湿式多盘制动器设计为例,利用响应面模型,建立了设计变量和制动性能的关系.根据不精确法,采用整体偏好聚合函数,将随机、模糊、未确知三种不确定性对系统性能均值和波动性的影响综合起来考虑,改善了传统稳健设计的线性加权和法的缺陷.     

Management of the variability of vibration response levels in mistuned bladed discs using robust design concepts. Part 1: Parameter design

Small unavoidable differences (e.g. 5%) between blades on a bladed disc, called mistuning, can lead to a huge variation of forced vibration response levels, and some of them are extremely high (e.g. 500% of the level experienced on every blade is all blades are identical). In this first half of a two-part article, a novel approach of designing a bladed disc with a lower chance of encountering high vibration response levels is evaluated. A robust design concept is applied to manage the variability of the vibration response levels, and the new approach resembles parameter design in Taguchi method of robust design. A “robustness map” is created using simulations results of a 6-degree-of-freedom (6-DOF) system, and such a map is validated by two more complicated models. The robustness map is used to explain the behaviour of bladed discs investigated in previous studies and to give possible methods of delivering more robust bladed disc designs.     

Integration of Response Surface Methodology with Genetic Algorithms

Response surface methodology (RSM) is a methodology that combines experimental designs and statistical techniques, for empirical model building and optimisation. By conducting experiments and applying regression analysis, RSM seeks to relate a response to some input variables. This work aims at integrating response surface methodology with genetic algorithms (GAs) to realise a GA-based prototype system for the determination of near optimal values in response surface designs. A framework of the prototype system is presented. The prototype system was validated using three case studies of a bonding process that involve solving the Himmelblau function, optimising the mean pull strength, and maximising both the mean pull strength and the minimum strength simul-taneously. The results were compared with those obtained by the Design Expert, which is a commercial software package. Details of the case studies as well as the comparative studies are presented.This revised version with a corrected online cover date was published online in April 2004.     

基于RSM的SiC单晶片表面粗糙度预测及参数优化

通过响应面分析法(RSM)对超声振动辅助金刚石线锯切割SiC单晶体的工艺参数进行分析和优化。采用中心组合设计实验,考察线锯速度、工件进给速度、工件转速和超声波振幅这4个因素对SiC单晶片表面粗糙度值的影响,建立了SiC单晶片表面粗糙度的响应模型,进行响应面分析,采用满意度函数(DFM)确定了切割SiC单晶体的最佳工艺参数,验证试验表明该模型能实现相应的硬脆材料切割过程的表面粗糙度预测。     

面向精锻叶片的模具计算机辅助设计研究

研究了面向精锻叶片的模具计算机辅助设计方法 ,以大型CAD/CAM软件UGⅡ为平台开发了一套精锻叶片的模具CAD系统 ,该系统可根据叶片零件的型面数据及相关参数自动进行精锻叶片的模具设计。对设计过程中一些关键的技术问题 ,如叶身曲面光顺、叶片实体造型、分模面的确定、毛边槽的设计等进行了探讨 ,并提出了实现方案。     

点啮合齿面主动设计理论和方法

齿面形状对齿轮传动的性能起着决定性的作用。现行齿轮设计技术只能在有限的几种模式中被动地选择齿面形式 ,这限制了齿轮传动性能的进一步提高。本文论述了一种齿面主动设计的理论和方法 ,提供了详细的计算公式 ,并通过设计、计算 ,证明了该理论方法的有效性。齿面主动设计是对现行齿轮设计技术的重大革新和完善 ,它能按照要求的齿轮传动性能来设计齿面 ,这对于高速和重载齿轮以及有特殊要求的齿轮的设计具有十分重要的意义。     

设计重用研究

设计通常分为变形设计、自适应设计和创新设计。据估计约 80 %的设计为变型设计和自适应设计 ,这意味着大多数设计过程是基于以前的设计知识的重用。基于计算机的设计重用可有效缩短设计周期 ,提高设计质量 ,实现对市场的快速响应。本文在对现有设计重用系统分析研究的基础上 ,识别概括出设计重用中的若干重要问题 ,诸如设计重用的概念、过程模型、重用层次和类型、关键技术及支持重用的设计历史建模等 ,并对各个问题做了深入系统地研究 ,给出了有关概念定义 ,建立了相关模型 ,从而为基于计算机的设计重用研究提供了一致的理论体系框架     

点啮合齿面主动设计研究

论述了一种齿面主动设计的理论和方法,提供了详细的计算公式,并通过设计计算证明了该理论方法的有效性.齿面主动设计是对现行齿轮设计技术的重大革新和完善,它能按照要求的齿轮传动性能来设计齿面,这对于高速和重载齿轮以及有特殊要求的齿轮的设计具有十分重要的意义.     

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.     

Molecular dynamics simulation of surface energy and ZDDP effects on friction in nano-scale lubricated contacts

Molecular dynamics simulations are used to study the tribological performance of a lubricant mixture containing hexadecane base oil and 5% zinc dithiophosphate (ZDDP) under molecular confinement conditions. The influence of ZDDP additive and the surface-lubricant interaction on the mechanical and thermal interfacial response are studied in detail. Results show that mechanical and thermal slips are reduced by increasing the surface energy. Simulations also demonstrate the migration of ZDDP molecules and their adsorption onto the solid surface resulting in a remarkable suppression of mechanical slip compared to pure hexadecane. Consequently, the effective shear rate is higher and so is the friction.