A Latin hypervolume design for irregular sampling spaces and its application in the analysis of cracks

Given the limitations of Latin hypercube design in constrained design space, Latin hypervolume designs with good space-filling and noncollapsing properties are developed in this paper. In the proposed method, the value of the design points in each dimension is based on the hypervolume instead of the coordinate axis length, enabling the generated design to have the space-filling property. To address the challenge of precisely obtaining the hypervolume in high-dimensional and irregular design spaces, Monte Carlo sampling is introduced to approximate the hypervolume. In addition, a constrained simulated annealing algorithm is presented for the proposed method, with an acceleration module to speed up the process of searching for a feasible design. The experiments on benchmark numerical examples illustrate that the proposed method is considerably better compared with the other two methods. Moreover, the proposed method is applied to an engineering modeling scenario to analyze the impact of cracks on the physical properties of an aircraft model. The results show that the proposed method generates a more desirable distribution of cracks and is more suitable for complex situations in practical engineering. Source code is available at https://github.com/Pang-Yong/LHVD-OLHVO.