The ongoing increase in computational capabilities has been successfully utilized for the engineering task of determining an optimal structural design, allowing for high-fidelity simulations of possible design parameter combinations. However, the more detailed these simulation models are, the more expensive a single performance prediction becomes, making the determination of the optimal design a very time-consuming task. In addition, with uncertainty modeling and propagation as an essential part of the robustness analysis of a design, the computational effort is yet again increased. By replacing the expensive simulation with a fast, capable metamodel, the structural design process can be significantly expedited. The prediction accuracy and, therefore, the usability of such a metamodel is strongly dependent on a high-quality set of data samples representing the relationship of input and output over the entire design space. Acquiring these samples is also an expensive process, therefore, it is important to select each sample in such a way as to maximize the information gain. Given the mostly limited or non-existing prior knowledge about what regions in the design space are of interest, i.e. show a highly nonlinear response, adaptive sampling strategies have been developed, which iteratively select new sample points automatically based on the existing data without further intervention by the user.

In this contribution, we present a novel adaptive sampling strategy, which is constituted of a combination of an exploration and an exploitation criterion. The predictions’ variances of an ensemble of Artificial Neural Networks is used to detect regions of interest, whereas a Kernel Density Estimation of the existing samples allows for a detection and filling of those parts of the design space which exhibit a low sample density. The capability of the approach is shown for different test functions as well as an engineering example.

计算能力的不断提高已成功用于确定最佳结构设计的工程任务，从而可以对可能的设计参数组合进行高保真模拟。但是，这些仿真模型越详细，单个性能预测就变得越昂贵，从而使确定最佳设计成为一项非常耗时的任务。另外，由于不确定性建模和传播是设计稳健性分析的重要组成部分，因此计算量又增加了。通过用快速，强大的元模型代替昂贵的模拟，可以大大加快结构设计过程。预测精度，因此，这种元模型的可用性在很大程度上取决于代表整个设计空间中输入和输出关系的高质量数据样本集。获取这些样本也是一个昂贵的过程，因此，以使信息增益最大化的方式选择每个样本非常重要。鉴于关于设计空间中哪些区域感兴趣的知识（即表现出高度非线性的响应）的知识非常有限或不存在，因此已经开发了自适应采样策略，该策略根据现有数据自动选择新的采样点，而无需进一步干预由用户。重要的是选择每个样本，以使信息增益最大化。鉴于关于设计空间中哪些区域感兴趣的知识（即表现出高度非线性的响应）的知识非常有限或不存在，因此已经开发了自适应采样策略，该策略根据现有数据自动选择新的采样点，而无需进一步干预由用户。重要的是选择每个样本，以使信息增益最大化。鉴于关于设计空间中哪些区域感兴趣的知识（即表现出高度非线性的响应）的知识非常有限或不存在，因此已经开发了自适应采样策略，该策略根据现有数据自动选择新的采样点，而无需进一步干预由用户。

在此贡献中，我们提出了一种新颖的自适应采样策略，该策略由探索和开发标准的组合构成。人工神经网络集合的预测方差用于检测感兴趣的区域，而现有样本的内核密度估计允许检测和填充表现出低样本密度的设计空间部分。展示了该方法针对不同测试功能的能力以及一个工程示例。