参数不定区间估计的对偶线性规划方法

将参数不定区间估计(PIE)问题变换成一组对偶线性规划(DLP)问题,提出了求解这组DLP问题的改进单纯形方法.该方法利用变量间的对偶关系,直接计算初始基本可行解,省去了初始基本可行解的搜索步骤.此外,在确定旋入和旋出变量时都采用了目标值最大减少规则,减少了旋转迭代次数.针对由PIE问题所导出的全部DLP问题都具有相同的目标函数和约束矩阵,给出了单搜索过程求解全部DLP问题的联合单纯形法.仿真结果说明了所给算法的计算效率.      

产品概念设计方案的评价方法

概念设计方案的评价方法是设计过程可接受性决策的重要依据.利用模糊数学的理论与方法把各种模糊信息数值化以对概念产品方案进行定量评价,通过建立设计方案评价体系及不同评价指标隶属度、考虑不同指标权重的方法,给出了产品概念设计方案的综合模糊评价方法,从而为产品概念设计提供一种形式化的、科学化的推理决策依据,同时也为产品设计过程自动化打下良好基础.     

Novel moderate transformation of fuzzy membership function into basic belief assignment

In information fusion, the uncertain information from different sources might be modeled with different theoretical frameworks. When one needs to fuse the uncertain information represented by different uncertainty theories, constructing the transformation between different frameworks is crucial. Various transformations of a Fuzzy Membership Function (FMF) into a Basic Belief Assignment (BBA) have been proposed, where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements. However, these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty. To avoid extreme attitudinal bias, a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred. In this paper, two moderate transformations of an FMF into a trade-off BBA are proposed. One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism, where the weighting factor can be user-specified or determined with some prior information. The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.     

A point cloud deep neural network metamodel method for aerodynamic prediction

Aiming to reduce the high expense of 3-Dimensional (3D) aerodynamics numerical simulations and overcome the limitations of the traditional parametric learning methods, a point cloud deep learning non-parametric metamodel method is proposed in this paper. The 3D geometric data, corresponding to the object boundaries, are chosen as point clouds and a deep learning neural network metamodel fed by the point clouds is further established based on the PointNet architecture. This network can learn an end-to-end mapping between spatial positions of the object surface and CFD numerical quantities. With the proposed aerodynamic metamodel approach, the point clouds are constructed by collecting the coordinates of grid vertices on the object surface in a CFD domain, which can maintain the boundary smoothness and allow the network to detect small changes between geometries. Moreover, the point clouds are easily accessible from 3D sensors. The point cloud deep learning neural network, which employs re-sampling technique, the spatial transformer network and the fully connected layer, is developed to predict the aerodynamic characteristics of 3D geometry. The effectiveness of the proposed metamodel method is further verified by aerodynamic prediction and robust shape optimization of the ONERA M6 wing. The results show that the proposed method can achieve more satisfactory agreement with the experimental measurements compared to the parametric-learning-based deep neural network.