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

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.

Cluster-based Kriging approximation algorithms for complexity reduction

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.

Development of New Approach in Reliability Analysis for Excellent Predictive Quality of the Approximation Using Adaptive Kriging

This study presents the results of a new approach for structural reliability analyses using adaptive kriging, confirmation simulation, and the pilot point method. Its main objective is to develop an efficient and accurate global approximation while controlling the computational cost and accuracy of prediction. The main contribution of research is to reduce computation time and successfully analyze complex problems with accurate results while ensuring excellent predictive quality of the approximation. For an excellent predictability of the kriging approximation, pilot point method and confirmation simulation are proposed. Simply, the predictive quality of the initial kriging approximation is improved by adding adaptive information, and the points are referred to as “pilot points” in areas where the kriging variance is maximized. Outcomes are confirmed with numerical simulations. The purpose is to select the minimum number of design experiments to ensure a good relative accuracy of the predictors with respect to the original models. Numerical examples show the efficiency of the proposed method compared to other structural reliability approaches.

An Approach Based on Enhanced Collaborative Optimization and Kriging Approximation in Multidisciplinary Design Optimization

This paper concentrates on the computational challenge in multidisciplinary design optimization (MDO) and a comprehensive strategy combining enhanced collaborative optimization (ECO) and kriging approximation models is introduced. In this strategy, the computational and organizational advantages of original collaborative optimization (CO) are inherited by ECO, which can satisfy the strengthened consistency requirements. Kriging approximation models are constructed to replace high-fidelity simulation models in individual disciplines and reduce the expensive computational cost in practical MDO problems. The proposed methodology is demonstrated by solving the classical speed reducer design problem. The better results indicate that ECO using kriging approximation models can achieve a considerable reduction of computational expense while guaranteeing the accuracy of optimal solutions with efficient convergence.

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

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.