A robust structural design method using the Kriging model to define the probability of design success

2010 ◽  
Vol 224 (2) ◽  
pp. 379-388 ◽  
Author(s):  
K-H Lee
Keyword(s):  
Robust Optimization ◽  
Design Method ◽  
Mathematical Problem ◽  
Kriging Model ◽  
Optimization Method ◽  
Design Problems ◽  
Kriging Metamodel ◽  
Mean And Variance ◽  
Kriging Approximation ◽  
Design Requirements

In this study, a robust optimization method is proposed by introducing the Kriging approximation model and defining the probability of design-success. A key problem in robust optimization is that the mean and the variation of a response cannot be calculated easily. This research presents an implementation of the approximate statistical moment method based on the Kriging metamodel. Furthermore, the statistics using the second-order statistical approximation method are adopted to avoid the local robust optimum. Thus, the probability of design-success, which is defined as the probability of satisfying the imposed design requirements, is represented as a function of approximate mean and variance. The formulation for the robust optimization can be defined as the probability of design-success of each response. The mathematical problem and the design problems of a two-bar structure and microgyroscope are investigated for the validation of the proposed method.

A Robust Optimization Method on the Transmission System of the Cutting Unit of Shearer

2020 ◽  
Author(s):  
Hongbin Gao ◽  
Junjun Chen
Keyword(s):  
Robust Optimization ◽  
Design Method ◽  
Harmonic Balance Method ◽  
Optimization Method ◽  
Transmission System ◽  
Manufacturing Cost ◽  
Internal Excitation ◽  
Tooth Width ◽  
Solution Methods ◽  
Cutting Unit

Abstract The transmission system of the cutting unit of shearer is divided into three basic components: planetary reduction form, one gear on one shaft form and a double gears on one shaft. The dynamic differential equations of three basic components are established respectively, and the volume functions of each structure are obtained. The characteristics of the internal excitation of the transmission system are analyzed, and the solution methods of the motion parameters of each component are obtained based on the harmonic balance method. Taking the parameters such as tooth number, modulus and tooth width as optimized variables, and a robust optimization method with the minimum value of multi-parameter evaluation function weighted linearly by dimensionless volume and vibration for the transmission system of the cutting unit of shearer is presented. Taking a certain type of shearer as an example, the transmission system of the cutting unit is optimized by using the presented method. After the design, the size is reduced by 5.4%, the maximum torsional acceleration of the drum is reduced by 17.8%, and the maximum torsional acceleration of the first gear is reduced by 9.6%. The results show that the design method can reduce the manufacturing cost of shearer and reduce the failure rate of the cutting unit.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

2018 ◽  
Vol 18 (4) ◽  
Author(s):  
Tingli Xie ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Leshi Shu ◽  
Yahui Zhang ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Engineering Design ◽  
Kriging Model ◽  
Support Vector ◽  
Svm Classifier ◽  
Optimization Approach ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Application of Intelligent Optimization Algorithm in Mechanical Design

2015 ◽  
Vol 713-715 ◽  
pp. 2049-2052
Author(s):  
Sha Sha Dou
Keyword(s):  
Design Theory ◽  
Optimization Design ◽  
Mechanical Design ◽  
Design Method ◽  
Computational Effort ◽  
Ant Algorithm ◽  
Design Problems ◽  
Intelligent Optimization Algorithm ◽  
Design Requirements ◽  
Mechanical Optimization

Mechanical optimization design is a new design method in the development foundation of the modern mechanical design theory, the application of optimization design in mechanical design can make the scheme achieve some optimization results in the design requirements specified, without consuming too much computational effort. The corresponding mathematical models of ant algorithm and Cellular ant algorithm are established, according to the actual mechanical design problems, and used to solve the established mathematical model by computer, so as to obtains the optimal design scheme.

A kriging metamodel-assisted robust optimization method based on a reverse model

2017 ◽  
Vol 50 (2) ◽  
pp. 253-272 ◽  
Author(s):  
Hui Zhou ◽  
Qi Zhou ◽  
Congwei Liu ◽  
Taotao Zhou
Keyword(s):  
Robust Optimization ◽  
Optimization Method ◽  
Kriging Metamodel

Integrated Design Methodology for High-Precision/Speed Servomechanisms

2005 ◽  
Vol 219 (8) ◽  
pp. 843-852 ◽  
Author(s):  
M-S Kim ◽  
S-C Chung
Keyword(s):  
High Precision ◽  
Design Method ◽  
Integrated Design ◽  
Design Procedure ◽  
Optimization Method ◽  
Design Variables ◽  
Mechanical Subsystem ◽  
Speed Performance ◽  
Parametric Studies ◽  
Design Requirements

An integrated design method for a high-precision/speed servomechanism including interactions of mechanical and electrical subsystems is proposed in this article. On the basis of the multiobjective optimization method, a non-linear optimal design procedure of the mechanical subsystem is performed simultaneously through the design process of the electrical subsystem satisfying the desired performance. Mechanical and electrical constraints have been formulated according to design requirements. Both mechanical and electrical parameters are considered as design variables. Validity of the integrated design problem is verified on the different application areas. Parametric studies of the design variables have also been conducted in this article. Case studies show that the integrated design method for an x-y positioning system satisfies the desired high-precision/speed performance.

Reliability Optimization Design of Spacecraft Valve Spring

2012 ◽  
Vol 538-541 ◽  
pp. 851-857
Author(s):  
Ye Lin ◽  
Wei Min Cui ◽  
Bi Feng Song
Keyword(s):  
Optimization Design ◽  
Design Method ◽  
Mathematic Model ◽  
Optimization Method ◽  
Reliability Optimization ◽  
Mechanical Reliability ◽  
Reliability Design ◽  
Valve Spring ◽  
Design Requirements ◽  
Mechanical Optimization

Firstly, methodology of valve spring’s static strength and fatigue strength reliability analysis is built up, and detailed computational formulas to derive distributions of the stress and strength are described. Secondly, to make full use of the material characteristic and consider reliability of the mechanism part, taking the spring’s mass as the objective function and based on spring’s traditional and reliability constraints, mathematic model of reliability optimization design of valve spring is established using mechanical reliability design method and mechanical optimization design method. At last, the proposed method is applied to a practical spring design example by integrating optimization tools with the optimization model. The comparison of reliability optimization design results and traditional optimization design results shows that the reliability optimization method is practical and reliable; its design results can satisfy all design requirements with smaller mass.

scholarly journals Robust optimization for composite blade of wind turbine based on kriging model

2020 ◽  
Vol 29 ◽  
pp. 2633366X2091463
Author(s):  
Yuqiao Zheng ◽  
Huidong Ma ◽  
Jianfeng Wei ◽  
Kai Zhu
Keyword(s):  
Robust Optimization ◽  
Natural Frequency ◽  
Kriging Model ◽  
The Other ◽  
Optimization Models ◽  
Approximation Model ◽  
Objective Functions ◽  
Composite Blade ◽  
First Case ◽  
Kriging Approximation

Structural optimization models often feature many uncertain factors, which can be handled by robust optimization. This work presents a complete robust optimization program for composite blade based on the kriging approximation model. Two case studies were given and performed using a genetic algorithm. The first being typical optimization, where the first natural frequency of the blade is selected as the optimized objective and the optimal sizing distribution for the entire blade shell is sought to ignore the uncertain factors. The other case determines the standard deviation of the optimized objective in the first case as another optimization goal. Moreover, a 6 σ robustness for the optimization results of the two cases was evaluated. The result shows that typical optimization increases the first natural frequency of the blade by 19%, while its robustness level has a reduction of 61% compared with the first blade. Nevertheless, the robust optimization not only results in an increment of 15.4% in the first natural frequency of the blade but also increases its robustness level by up to 90%. Therefore, the proposed approach can effectively improve optimization objectives, especially reduce the impacts of uncertainties on the objective functions.

Frequency Optimal Design Method and Application

2011 ◽  
Vol 201-203 ◽  
pp. 1279-1283
Author(s):  
Shou Yi Bi ◽  
Xing Pei Liang
Keyword(s):  
Optimal Design ◽  
Design Method ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Mathematical Optimization ◽  
Element Model ◽  
Optimization Method ◽  
Finite Model ◽  
Design Variables ◽  
Analysis System

A program for frequency optimal design of structure composed of bar, beam, plate is developed based on finite analysis system ZR[1] that finite element model, including mesh generation of truss element, beam element and plate element, is automatically generated. Because of integrated with three dimensional CAD, specification of boundary conditions and design variables can be finished based on the three dimensional CAD model, so user need not deal with nodal and element of finite model in the procedure of forming finite model and specifying mathematical problem for optimization. This paper introduces a new method how to insert the frequency sensitivity analysis process into the structural analysis program, integrate mathematical optimization method and design structure based frequency optimization. The program is applied to the optimal design of actual engineering. The results are acceptable.

Application of a Method on Optimization of Thin-Walled Column's Crashworthiness Based on Metamodel

2014 ◽  
Vol 526 ◽  
pp. 109-114 ◽  
Author(s):  
Yi Min Mo ◽  
Jie Zhang ◽  
Bing Heng Qin ◽  
Jun Cheng Lv
Keyword(s):  
Sampling Design ◽  
Design Space ◽  
Design Method ◽  
Optimization Method ◽  
Latin Hypercube Design ◽  
Kriging Metamodel ◽  
Improve Accuracy ◽  
Optimal Latin Hypercube Design ◽  
Thin Walled ◽  
Object Parameter

In this paper the crashworthiness of a thin-walled column is selected as the optimization goal and its section gauge size parameters are defined as variables. We use Optimal latin hypercube design method and ASA optimization method respectively to define sampling design points and find optimal design in Kriging metamodel, constructed using function values in FEM results at sampling design points. A design space updating method is introduced in this paper to reduce computational consumption and improve accuracy by several rounds of metamodeling and optimization, practice shows that object parameter SEA in each round converge to a final one, constrained by the demand of no weight added. High accuracy and rapid convergence of this method will be verified by comparison between results by this method and FEM.

A Dynamic Optimization Design Method for the Turbine Engine Frame Foundation

2012 ◽  
Vol 226-228 ◽  
pp. 784-787
Author(s):  
Zhao Jun Li ◽  
Xi Cheng Wang
Keyword(s):  
Dynamic Optimization ◽  
Optimization Design ◽  
Optimization Problems ◽  
Design Method ◽  
Kriging Model ◽  
Optimization Method ◽  
Turbine Engine ◽  
Design Variables ◽  
Side Constraints ◽  
Dynamic Reanalysis

An effective optimization method using Kriging model and parametric sampling evaluation strategy is proposed to solve dynamic optimization design. The optimization problem is to find the design variables such that the structural weight is minimum and dynamic displacement of the points concerned plus certain side constraints are satisfied. The types of design variables are considered as the sizing variables of the beams and columns. Kriging model is used to build the approximate mapping relationship between the forced vibration amplitude and design variables, reducing expensive dynamic reanalysis. A dynamic analysis program is used as black-box to obtain dynamic response. Numerical examples show that the method has good accuracy and efficiency. Versatility of this method can be expected to play an important role in future engineering optimization problems.

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