Robust Design Rule with Definite Purpose Character Based on Fuzzy Probability and Study of its Characteristics

The design target with definite purpose character of product quality wasdescribed in a real fuzzy number ( named fuzzy target for short in this paper), and its membershipjunctions in common use were given. According to the fuzzy probability theory and the robust designprinciple, the robust design rule based on fuzzy probability (named fuzzy robust design rule forshort) was put forward and its validity and practicability were analyzed and tested with a designexample. The theoretical analysis and the design examples make clear that, while the fuzzy robustdesign rule was used, the fine design effect can be obtained and the fuzzy robust design rule can bevery suitable for the choice of the membership function of the fuzzy target; so it has a particularadvantage.

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

ROBUST DESIGN OF A TWO DEGREE FREEDOM SYSTEM.DUE TO THE PARAMETER UNCERTAINTY

A method based on the robust design optimization is presented to handle the structural uncertainty problems. The variations caused in dynamic performance can be expressed by the mean response and the standard deviation of the performance. The robust optimization approach, based on a multi-objective and non-deterministic method, attempts to both optimize the mean performance and minimize the variance of the performance simultaneously. The best possible design optimization is chosen by a trade-off decision. An example of robust design of a two degree freedom system is used to effectively illustrate the application in dynamics. The mass and stiffness uncertainty in the main system as well as the uncertainty of the mass, stiffness and damping in the absorber are considered all together in order to minimize the displacement response of the main system within a wide band of excitation frequencies. The robust optimization results show a significant improvement in performance compared with the conventional solution recommended from vibration textbooks. It is indicated that robust design methods have great potential for application in structural dynamics to deal with uncertainty problems.

Robust Design Optimization Method for Centrifugal Impellers under Surface Roughness Uncertainties Due to Blade Fouling

Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression（SVR） metamodel is combined with the Monte Carlo simulation（MCS） method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.

Robust designs for models with possible bias and correlated errors

This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the qth order moving average process MA（q）, especially the MA（1） errors and the MA（2） errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.

A novel robust design method for improving stability of optimized structures

It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of opti mized structures. A new approach is proposed, in which cer tain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penaliza tion. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical exam ples show the simplicity and effectiveness of the proposed method.

MODELING AND ROBUST DESIGN OF REMANUFACTURING LOGISTICS NETWORKS BASED ON DESIGN OF EXPERIMENT

The uncertainty of time, quantity and quality of recycling products leads tothe bad stability and flexibility of remanufacturing logistics networks, and general design onlycovered the minimizing logistics cost, thus, robust design is presented here to solve theuncertainty. The mathematical model of remanufacturing logistics networks is built based onstochastic distribution of uncontrollable factors, and robust objectives are presented. Theintegration of mathematical simulation and design of experiment method is performed to do sensitiveanalysis. The influence of each factor and level on the system is investigated, and the main factorsand optimum combination are studied. The numbers of factors, level of each factor and designprocess of experiment are investigated as well. Finally, the process of robust design based ondesign of experiment is demonstrated by a detailed example.

Integrated Robust Design Method Based on Maximum Tolerance Region

Traditionally,parameter design is carried out prior to tolerance design. However, this two-step design strategy cannot guarantee optimal robustness for products' quality. The proposed integrated robust design method determined the optimal parameter and tolerance simultaneously by calculating the maximum tolerance region,thereby improving the quality of products. In addition,the proposed method did not need uncertainty analysis to obtain the maximum tolerance region,so that the calculation cost could be decreased. And the method avoided the difficulty of gaining costtolerance function as maximum tolerance region represented both demand of cost and robust. Finally,an amplifier circuit case was conducted for verification purpose. Based on the results, the proposed approach could provide robust solution with optimal maximum tolerance region.

Robust Design Optimization and Improvement by Metamodel

The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.

An Implementation Technique for Multivariate Robust Design

This paper investigates systematically the problem of multivariate robustparameter design. First, a measurement criterion for the total variation of multivariate qualitycharacteristics is introduced by the result of information theory. Then the implementation procedurein the robust design is presented. After that, a simulation example from a practical industrialprocess is provided. Finally, some comments and further work are discussed.

Research on Low Cycle Fatigue Reliability-based Robust Design Optimization of Turbine Blade

针对涡轮叶片低周疲劳可靠性稳健设计优化问题，对叶片材料进行了高温疲劳试验，采用定量方程随机化方法处理试验数据，获得叶片材料的概率-应变-寿命曲线。采用贝塞尔曲线描述叶片型线方程，建立了涡轮叶片结构及流场的参数化模型，采用热-流-固耦合有限元法对涡轮流场和叶片进行了数值分析，得到叶片动能效率和应力应变分布特性。建立了叶片疲劳可靠性稳健设计优化模型，并采用响应面法获得叶片结构性能函数和极限状态函数，将叶片低周疲劳可靠性作为基本约束条件，采用序列二次规划优化法得到设计优化结果。研究结果表明，优化后的叶片低周疲劳可靠性以及稳健性显著提高，模型及方法正确可行，可用于涡轮叶片以及其他复杂结构的低周疲劳可靠性稳健设计优化。

Applying robust design to study the effects of stratigraphic characteristics on brittle failure and bump potential in a coal mine

Bumps and other types of dynamic failure have been a persistent, worldwide problem in the underground coal mining industry, spanning decades.For example, in just five states in the U.S.from 1983 to 2014,there were 388 reportable bumps.Despite significant advances in mine design tools and mining practices,these events continue to occur.Many conditions have been associated with bump potential, such as the presence of stiff units in the local geology.The effect of a stiff sandstone unit on the potential for coal bumps depends on the location of the stiff unit in the stratigraphic column, the relative stiffness and strength of other structural members, and stress concentrations caused by mining.This study describes the results of a robust design to consider the impact of different lithologic risk factors impacting dynamic failure risk.Because the inherent variability of stratigraphic characteristics in sedimentary formations,such as thickness, engineering material properties, and location, is significant and the number of influential parameters in determining a parametric study is large, it is impractical to consider every simulation case by varying each parameter individually.Therefore, to save time and honor the statistical distributions of the parameters, it is necessary to develop a robust design to collect sufficient sample data and develop a statistical analysis method to draw accurate conclusions from the collected data.In this study,orthogonal arrays, which were developed using the robust design, are used to define the combination of the(a) thickness of a stiff sandstone inserted on the top and bottom of a coal seam in a massive shale mine roof and floor,(b) location of the stiff sandstone inserted on the top and bottom of the coal seam,and(c) material properties of the stiff sandstone and contacts as interfaces using the 3-dimensional numerical model, FLAC3D.After completion of the numerical experiments, statistical and multivariate analysis are performed using the calculated results from the orthogonal arrays to analyze the effect of these variables.As a consequence, the impact of each of the parameters on the potential for bumps is quantitatively classified in terms of a normalized intensity of plastic dissipated energy.By multiple regression, the intensity of plastic dissipated energy and migration of the risk from the roof to the floor via the pillars is predicted based on the value of the variables.The results demonstrate and suggest a possible capability to predict the bump potential in a given rock mass adjacent to the underground excavations and pillars.Assessing the risk of bumps is important to preventing fatalities and injuries resulting from bumps.

Robust design of self-starting drains using Random Forest

Groundwater lowering is one of the most important countermeasures to avoid the risk of rainfall-triggered landslides.However,the long-term reliability of many drainage methods is often a matter of concern since the drains may easily get clogged.A new hydraulic-driven self-starting drainage method is presented in this paper.In the proposed Random Forest(RF)based robust design approach for the selfstarting drains,the datasets are generated using an automatically controlled numerical modeling technology.The deterministic analysis is carried out based on uncertain soil parameters and the specific designs selected using Uniform Design(UD).The ensemble of RF models is applied in the design process to improve computing efficiency.Safety requirements,design robustness,and cost efficiency are simultaneously considered utilizing multiobjective optimization.A straightforward and efficient framework that focuses on difficulties caused by an enormous design space is established for the robust design of the self-starting drains,and improved computation efficiency is achieved.The effectiveness of the proposed approach is illustrated with a case study,the Qili landslide in Zhejiang Province,China.

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

Minimizing the impact of the mixed uncertainties(i.e.,the aleatory uncertainty and the epistemic uncertainty) for a complex product of compliant mechanism(CPCM) quality improvement signifies a fascinating research topic to enhance the robustness.However, most of the existing works in the CPCM robust design optimization neglect the mixed uncertainties, which might result in an unstable design or even an infeasible design. To solve this issue, a response surface methodology-based hybrid robust design optimization(RSM-based HRDO) approach is proposed to improve the robustness of the quality characteristic for the CPCM via considering the mixed uncertainties in the robust design optimization. A bridge-type amplification mechanism is used to manifest the effectiveness of the proposed approach. The comparison results prove that the proposed approach can not only keep its superiority in the robustness, but also provide a robust scheme for optimizing the design parameters.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

Modeling of Robust Design of Remanufacturing Logistics Networks

The uncertainty of time, quantity and quality of recycling products leads to the bad stability and flexibility of remanufacturing logistics networks, while general design only covers the minimizing logistics cost, so robust design is presented to solve it. The mathematical model of remanufacturing logistics networks is built on the stochastic distribution of uncontrollable factors, and robust objectives are presented. The basic elements of robust design of remanufacturing logistics are redefined, and each part of mathematical model is explained in detail as well. Robust design of remanufacturing logistics networks is a problem of multi-objective optimization in essence.

Robust Design of Mixing Static and Dynamic Multiple Quality Characteristics

Increased market competition means that quality, cost and delivery time are crucial elements of modern production techniques. Taguchi’s robust design is the most powerful method available for reducing product cost, improving quality, and simultaneously reducing development time. Robust design aims to reduce the impact of noise on the product or process quality and leads to greater customer satisfaction and higher operational performance. The objective of robust design is to minimize the total quality loss in products or processes. The PQL model proposed by this paper simultaneously optimizes the static and dynamic problems by minimizing the total quality loss. Using the proposed PQL model and steps for optimization, the method addresses complex parameter design, which varies with the properties and objectives of the experimental data, to improve the product quality. The example of an electron beam surface hardening process is provided to demonstrate the implementation and usefulness of the proposed method.

Investigation and Optimization of Sn/Gr Lubricants Effects on Cold Extrudability of Fe-TiC Nanocomposite Using Taguchi Robust Design Method

The present study deals with the effects of both tin (Sn) and graphite (Gr) powders on the cold extrudability of Fe-TiC nanocomposites as lubricant. The production process includes low-energy ball milling, powder metallurgy and cold direct Extrusion. Due to various factors influencing the extrudability of the Fe-TiC nanocomposites, such as milling time, rate of extrusion, type and content of lubricant and etc, Taguchi robust design method of system optimization was used to determine the approximate contribution percent (% &#961) of each factor. In order to investigation of Fe-TiC properties, samples with best quality of extrusion were analyzed by XRD and SEM investigations. The results indicate that, sitting the atomic layers of Sn lubricant between Fe and TiC particles leads to decreasing the friction. In this case sliding the particles on each other is easier and a part of the load is applied on lubricant. The results of extrusion of samples indicate that using 2% Sn admixed and die wall graphite lubrication can improve cold extrudability of Fe-TiC nanocomposites.

A Robust Design Method in Product Quality Applications

In order to express information on the quality grade of product designed, thetarget value of product quality design was described with a fuzzy number in this paper. Analternative to Taguchi's, the robustness application design method has been recently presented.However, neither Taguchi's method nor the alternative method is capable of dealing satisfactorilywith the frequently encountered situations in which all the noise variables cannot be studiedsimultaneously. Based on the ideas from response surface modeling, linear models theory, and randomeffects models, we provide a method for estimation in the robustness application design method inproduct quality applications. With this new method used, the high-quality ratio of the productdesigned could be increased, and the ability to resist the influence of various disturbing factorsand noise factors could be enhanced.