Research On Computational Intelligence-Based Structural Reliability Design Optimization

The safety and reliability of structures is one of the major objectives ofmechanical structure design. In structural design, uncertain factors are inherent. Ifthe randomness of parameters, such as material quality, load and geometry sizeand so on, is in neglect, the safety of structure will not be ensured enough, and theproduct quality will be influenced as well. However, when reliability design andoptimization design are united organically, it can help designer to design adaptivetolerance of mechanical structure and control the effect of random parameters tostructural safety. Thus, forecasted performance of structures in this way will bemore safe and economical, and match the practical case than before. So researchof Reliability-based Design Optimization (RBDO) is very necessary andimportant.RBDO is a method that utilizes reliability theory to solve uncertainty factorsin optimization design. And Robust Design is a design method that dependentvariable is insensitivity to minute difference of factors, while there are uncertaintyfactors in design parameters and structural physical parameters. It means thedesigned mechanical structure is insensitive to variations of design variables. Inthe case of uncertain parameters, aforementioned two designs can effectivelyimprove the engineering design level. So, one of objectives of this dissertation isto extend Reliability-Based Robust Design Optimization (RBRDO) by integratingRBDO theory, Reliability-based Sensitivity Analysis technique and RobustDesign.Since the traditional mathematic method is difficult to obtain a more accuratesolution due to complex structures and nonlinear factors in mechanical structures,the RBDO and RBRDO methods are limited in their application and development.However, Computational Intelligence Technique (CIT) can provide a new way tosolve these problems from another point of view. CIT is a computing methoddescribed abstractly by mathematic language and based on the biologicmechanism of evolutionary, swarm intelligence, cellular immunity and neural cellnetwork in biologic systems. CIT mainly includes Neural Network (NN),Evolutionary Algorithm (EA) and Fuzzy System (FS). It is the higher stage ofintelligent theory. It is incomparably superior to traditional computing method onidentification and control of nonlinear system and complex optimization problems,for it can solve them without giving an accurate model of problems like before.Thus, CIT seems to be especially suited to optimization design with complexstructures.In this dissertation, the present situation and development about ReliabilityDesign theory, Robust Design idea, RBDO and CIT at home and abroad is brieflystated. Then, an expression of explicit function between random variables andreliability degree is obtained by Wavelet Neural Network (WNN) in CIT. It is thebasis of solving RBDO problems. Next, a multi-objective (MO) model is built forRBDO by MO decision-making method. In the end, the Grey Particle SwarmAlgorithm (GPSA) and Fuzzy Particle Swarm Algorithm (FPSA) are presented forsolving this model. This work provides an effective way to the development anddesign of mechanical products.There are six chapters in this paper. The main content is shown as following:Chap1: The background, aim and meaning of this research are discussed inthe beginning. Then, the meaning and development situation of RBDO, RobustDesign and CIT are introduced. In addition, the application situation of CIT inRBDO and Robust Design methods is also briefly presented.Chap2: After introducing the universal mathematic models and solvingapproaches for RBDO, the basic models and algorithms of WNN and PSO forRBDO are discussed in detail.Chap3: Concerning the RBDO with abnormal random parameters, thereliability constraints are transferred into certain equivalent constraints byProbabilistic Perturbation method and Edgeworth Series method withoutconsidering the relativity of failure patterns at first. Then, the reliability degree ofcomponents or failure structural pattern is regarded as constraint conditions toobtain the initial design point. In the case of system functions with multi-failuremodes unexpressed to be explicit functions, the Monte Carlo Stochastic-WNN(MCS-WNN) method is presented. In order to improve optimization performanceof mechanical structures, two kinds of WNN-based RBDO methods are presented.In the first one, probabilistic constraints of structural reliability are transferred intosingle certain constraints with the obtained explicit function, and the RBDO of thesystem is performed by disciplinal function-based PSO method. In another one,the RBDO is easily implemented with inverse mapping model of WNN.Furthermore, an improving study algorithm of WNN is presented when thelocal-strategy idea is integrated with conjugate gradient method. Simulationresults of WNN model for RBDO indicate that the effect of this method isimproved more.Chap4: In this section the basic concepts and terminology of fuzzy math arebriefly introduced. Then, the Fuzzy MOPSO (FPSO) according to RBDO, RobustDesign and MODT is presented after building the fuzzy-based MO optimizationmodel. The simulation computation indicates that this method has the worth oftheory and application.Chap5:In the practical engineering application, the RBRDO models based onMO decision-making idea are mostly high-dimension MO problems due to thecomplex structural systems and many design variables. The traditional MOmethods cannot satisfy the needs of these problems. In this section, a Grey PSO(GPSO) algorithm is presented to solve it. With this approach the relevancydegrees between benchmark vector sequence and objective vector sequence iscomputed respectively, then, the maximal relevancy degree is selected as theglobal best and personal best of PSO. Since grey relevancy degree can directparticles in the space to fly to Pareto region, it can solve high-dimension MOproblems. As a result, this method is adapted to RBRDO model and proved to beeffective through numerical examples. So it improves a new approach to this field.Chap6: Conclusion and prospects. The research and conclusion of thisdissertation is summarized and the development foreground of CIT on theapplication of RBDO and RBRDO is expected.