Research On Approximation Models And Decomposition Strategies In Multidisciplinary Design Optimization

Engineering product design optimization involves multiple disciplines and factors which act and couple with each other. This phenomenon makes the engineering product design optimization extremely complex and hard to obtain the design scheme of the best product overall performance. Multidisciplinary design optimization (MDO) is a system synthetical design optimization methodology to address the aforementioned challenge. It coherently exploits and utilizes the synergism of mutually interacting phenomena among disciplines to obtain the design scheme of the best product overall performance. Due to the huge computational cost on the implementation of simulation codes and the complex information coupling among disciplines, computational and organizational complexities have become two challenges for MDO. Under the condition of satisfying the accuracy requirement, approximation models can be used to make a replacement of the complex, implicit and unknown function relationships to reduce the enormous computational expense in engineering product design optimization. The decomposition strategy is a computational architecture for coordination and uncoupling of complex systems, and can effectively reduce the organizational complexity in engineering product design optimization. At present, approximation models and decomposition strategies have become two hotspots in the field of MDO.To reduce the computational and organizational complexity in MDO, approximation models and decomposition strategies are studied in this dissertation. For approximation models, the construction method of approximation models based on gene expression programming (GEP) is proposed and its comparison with common approximation models in MDO is conducted. For decomposition strategies, a generalized collaborative optimization decomposition strategy based on Kriging (KGCO) is proposed. For multi-objective MDO problems, a multi-objective decomposition strategy based on GEP and Nash equilibrium is further put forward. These methods are well proved by the parameter design optimization case study of a small waterplane area twin hull (SWATH) ship.Firstly, the mathematical description of MDO problems is given. Some important research nomenclatures are defined. And then, the outline of approximation models and decomposition strategies is given.Secondly, the construction method of approximation models based on GEP is proposed. And characteristics and applicabilities of the GEP model and three common approximation models in MDO are summarized. GEP evolutionary algorithm is used to replace the complex, implicit and unknown function relationships between input design variables and output observed responses. Besides avoiding high-intensive simulation and reducing computational cost, the GEP approximation model can provide designers simple and explicit function expressions, which are helpful for them to obtain the effects of the change of design variables on observed responses and further carry out sensitivity analysis. Considering large and small sample sizes, a comprehensive comparison of the GEP model and three common approximation models, i.e., response surface model, Kriging model and radial basis functions model, is conducted in terms of four evaluation criteria:prediction accuracy, robustness, transparency and efficiency. The summary of characteristics and applicabilities of the four approximation models can help designers choose and use the proper model in engineering product design optimization.Thirdly, a GCO decomposition strategy based on Kriging (KGCO) is proposed. This strategy removes both the inconsistencies between system-level design variables and corresponding subsystem-level local variables and the inconsistencies caused by the range discrepancies between design variables in original collaborative optimization (CO). Additionally, the KGCO decomposition strategy employs Kriging models to replace subsystem-level objective functions (i.e., system-level generalized compatibility constraints) and subsystem-level analysis models, which can remove the non-smooth and discontinuous features of original compatibility constraints, reduce the computational efforts on subsystem-level analysis, and improve the solution efficiency of engineering product design optimization.Fourthly, a multi-objective decomposition strategy based on GEP and Nash equilibrium is proposed. The GEP model is used to construct the rational reaction set (RRS) of each player. The Nash equilibrium solutions of multi-objective MDO problems are obtained from solving the intersection of all the players'rational reaction sets, which can drastically reduce the computational cost, and improve the solution efficiency of the multi-objective decomposition strategy.Fifthly, all the proposed methods in this dissertation are employed in the parameter design optimization of a SWATH ship. Results indicate that the proposed methods can reduce the computational and organizational complexity considerably and they are efficient in support of engineering product design optimization.Finally, conclusions are given and prospects for further research work are outlined.