| With the developments of numerical methods and computer technologies, the numerical simulation technique has been widely used in engineering design in order to improve the design efficiency. However, current engineering problems become increasingly complex:they have sometimes tens or even hundreds of design variables, and usually should have computationally expensive multidisciplinary simulations. For relieving computing budget, the metamodeling techniques have been introduced and extensively used in the past 20 years. Through the simulations at finite sampled points in the domain, the metamodeling technique can build an approximation for the expensive physical simulation model. This cheap-to-run approximation model has the capability of predicting the responses at unsampled points. Thus, we can use metamodels to conduct efficient optimization. It is known that the metamodel-based engineering optimization usually contain three parts:(1) design of experiments (DOE), (2) metamodeling and (3) metamodel-based global optimization. The main researches in this article focus on the three parts and are summarized as below.(1) In the DOE part, this article first proposes an efficient space-filling sequential sampling method based on space reduction. By using rejection intervals around the sampled points, this method can identify the feasible regions and combine them together to reduce the design space, which significantly improves the sampling efficiency. Meanwhile, this method employs the monte carlo method and the local boundary search strategy to improve the sampling quality efficiently.The points generated by a space-filling sequential sampling method just fill the domain evenly, the distribution of which cannot reveal the local characteristics of function/Hence, this article proposes two adaptive sequential sampling methods. The first method uses the cross validation errors to adjust the correlation function under the Bayesian framework. Consequently, the regions with large prediction errors will be sampled with more points, which is beneficial for global metamodeling. Besides, this method employs an user-defined search pattern to balance the local exploitation and global exploration during the sampling process. The second sampling method is more generic and easier. During the sampling process, due to the error-pursuing mechanism, the sampling method exploits locally by the identification of sensitive cell and explores globally by the shift of sensitive cell.It is found that most of current adaptive sequential sampling methods are developed for single-response systems. But practically, the multi-response system is more frequently encountered. Hence, this article improves the aforementioned second adaptive sequential sampling method for multi-response systems.(2) In the metamodeling part, the article first proposes an optimal weighted pointwise ensemble metamodeling method. Through pointwise weight functions, this method can combine the RBF models build with different basis functions together to form an ensemble RBF model. The pointwise weight function uses the 0-1 strategy and min-GMSE strategy to obtain optimal parameters. As a result, the ensemble RBF model provides more accurate and robust predictions.It is observed that in high dimensions most of current metamodeling techniques produce a poor performance and are time-consuming to build. Therefore, this article proposes a generalized RBF-based high dimensional model representation (GRBF-HDMR) for handling existing random data in high dimensions. GRBF-HDMR projects a random point to cut lines and planes to create virtual regular points, and uses the error-allocation strategy to estimate the virtual responses and adjusts the predictions of component RBF models. Compared to the original RBF-HDMR modeling method. GRBF-HDMR can successfully utilize the random data to improve the prediction quality, which makes this method suitable for engineering problem.(3) In the metamodel-based global optimization part, this article first combines the Lipschitz optimization and the metamodeling technique to propose two global optimization algorithms. The first optimization algorithm uses the metamodeling technique to construct more smooth and compact support function and approximation function. Consequently, the lower bounds of function/in local regions can be estimated more accurately. Besides, this algorithm employs the DIRECT scheme to obtain potentially optimal Lipschitz constants, which can be used to balance the local exploitation and global exploration comprehensively to improve the optimization efficiency. The second optimization algorithm proposes an extended DIRECT scheme. This scheme employs a more flexible partition strategy to overcome the exclusive sampling process in the DIRECT algorithm. This partition strategy also allows the algorithm to work with metamodeling techniques to significantly improve the optimization efficiency.Most of current metamodel-based global optimization algorithms are developed for unconstrained problems. For handling constrained optimization problems, this article extends the aforementioned second optimization algorithm. The novel constrained optimization algorithm uses a new contraint-handling technique to separately handle feasible and infeasible cells, which avoids the parameter-tuning operation. Additionally, this algorithm employs an adaptive metamodeling technique to construct the best metamodels for objective and constraints respectively. This technique provides more accurate predictions and therefore faster convergence speed.(4) This article applies the proposed sequential sampling methods, metamodeling techniques and metamodel-based optimization algorithms to the structural optimization of turbomachinery, e.g., the weight optimization of a turbine disk, the design of a hollow fan blade, the gravity center eccentricity of an axial compressor blade, the shape optimization of a high-speed flywheel and the weight optimization of a multi-stage turbine disk. The remarkable results reveal that the metamodel-based optimization method is very promising for simulation-based engineering problems. |
