Abstract
Kriging-based modeling has been widely used in computationally intensive simulations. However, the Kriging modeling of high-dimensional problems not only takes more time, but also leads to the failure of model construction. To this end, a Kriging modeling method based on multidimensional scaling (KMDS) is presented to avoid the “dimensional disaster”. Under the condition of keeping the distance between the sample points before and after the dimensionality reduction unchanged, the KMDS method, which mainly calculates each element in the inner product matrix due to the mapping relationship between the distance matrix and the inner product matrix, completes the conversion of design data from high dimensional to low dimensional. For three benchmark functions with different dimensions and the aviation field problem of aircraft longitudinal flight control, the proposed method is compared with other dimensionality reduction methods. The KMDS method has better modeling efficiency while meeting certain accuracy requirements.
Highlights
With the improvement of design levels and application requirements [1,2,3], the optimal performance of products has attracted much attention
This work proposes a Kriging modeling method based on multidimensional scaling to deal with high-dimensional problems
The dimensionality of high-dimensional sample data was reduced via the Multidimensional scaling (MDS) method to convert high-dimensional problems to low-dimensional problems
Summary
With the improvement of design levels and application requirements [1,2,3], the optimal performance of products has attracted much attention. For Kriging sequential modeling with an increasing number of data points, the dimensions of the correlation parameter vectors are consistent with the dimensions of the design variables without considering dimensionality reduction, while the optimal correlation parameters are obtained by maximizing the complex multimodal likelihood functions. How to improve the modeling efficiency while minimizing the loss of precision still needs further research For this purpose, a new Kriging modeling method (KMDS) based on multidimensional scaling (MDS) is proposed in this work. The KMDS algorithm addresses the difficulties of achieving high-dimensional modeling based on the Kriging model, and greatly improves the modeling efficiency on the basis of meeting certain accuracy requirements It guides a new direction for the modeling of high-dimensional engineering problems. It is suitable for publication in the Algorithms journal
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