Research On Precise Decoupling And Efficient Sampling Technologies For Reliability Based Design Optimization

While ensuring the safety of a product, reliability-based design optimization (RBDO) can optimize the performance characters of the product, such as size, weight and rigidity etc. RBDO considers the uncertainties during the design optimization process and evaluates their effects to the performance of the product. Therefore, RBDO can yield an optimal design between the performance characters and reliability of a product. While the safety requirements of the modern product are gradually increasing, the design of a product not only needs to satisfy the performance requirements, but also the reliability demand. So RBDO has become an inevitable tool in the complex product design process, such as aircraft, launch vehicles, high-precision machine tools and ships etc. And RBDO also can improve the national defense strength and design technology level.Although many researchers are applying RBDO to the engineering practices, but there are also a lot of problems that need to be tackled, such as:how to precisely decouple the reliability analysis and optimization nested structures; how to get the optimal shifting vectors for highly nonlinear problems; the multiple design points problems and how to efficiently get samplings in the Kriging-model based reliability method.So, this dissertation will try to deal with the above problems, and thus make the RBDO more applicable and effective for complex product design. This dissertation will first study the efficiency and accuracy of the existing RBDO methods and the multiple design point problem, and then proposes a series of novel methods to tackle these issues; This dissertation will also study the sequential sampling methods for the Kriging-model-based RBDO, and then proposes effective sampling techniques. The contents of this dissertation are as follows:(1) Adaptive decoupling method for RBDO nested-loop structure. Decoupled method is an efficient tool in dealing with RBDO problem. It conducts the reliability analysis loop and optimization loop sequentially. However, during the design optimization process, how to build the decoupled model will directly affect the accuracy and efficiency of RBDO.This dissertation will proposed a fast feasibility-checking method for probabilistic constraints. This method adaptively chooses different reliability analysis methods for probabilistic constraints with different feasible status, and it can significantly improve the efficiency of the decoupled method.(2) Optimal shifting vector method for highly nonlinear RBDO problem. Shifting vector is very important in decoupled RBDO method. Its accuracy directly affects the results of the decoupled method. This dissertation will study why the shifting vectors in the existing decoupled RBDO method are not accurate, and then proposes an optimal shifting vector approach which uses the limit state probabilistic constraint to search the shifting vectors. The new method can find the optimal shifting vectors even for highly nonlinear performance functions, and these optimal shifting vectors will accelerate the design optimization process and thus reduce the computational cost.(3) Multiple design points method for RBDO. The existing RBDO methods assume that one probabilistic constraint only has one design point (Most probable point). However, in engineering practices, there are a lot of multiple design points cases, such as when the design region is a long narrow space, or the random variables have large variances. This dissertation will use the trace of the design points during the design optimization process to identify the potential multiple design points; and then the probabilistic constraints will be regarded as multiple constraints, which will make the optimization results satisfying the reliability requirement.(4) Local adaptive sampling approach for RBDO using Kriging model. Metamodel based reliability method has become the trend for practical engineering. Kriging model has a very powerful performance, and it has been widely used in RBDO. Sequential sampling strategy can improve the efficiency of the Kriging model significantly and thus reduce the computational costs. This dissertation will use the local window concept, first build the local window in the current optimal design point, then find new samples along the limit state boundaries in the local window. These strategies will make the sampling process more efficient.(5) Importance boundary sampling method for RBDO with explicit objective function. The efficiency and accuracy of the Kriging-model-based RBDO method have a direct relationship with locations of the samplings, so how to select the sample points is very important. This dissertation will study the RBDO problems which have explicit objective functions, and then proposes two importance sampling criterions for different design optimization stages. This will make the solving of this kind problems more effective.(6) Based on the existing researches, this paper also advises the future work, such as RBDO with small sample, time-dependent reliability method and accurate and efficient reliability analysis method.