## 6 Conclusions  
The high dimensionality and complexity of engineering design problems leads to expensive calculation costs. The Kriging model can alleviate this bottleneck problem. However, the Kriging model is also very time consuming when approximating high-dimensional problems, solutions to some of which it even fails to construct. The main cost is in the inversion of the covariance correlation matrix and the solution of the hyperparameters of the Kriging model. To this end, this work proposes a Kriging modeling method based on multidimensional scaling to deal with high-dimensional problems. Firstly, the dimensionality of high-dimensional sample data was reduced via the MDS method to convert high-dimensional problems to low-dimensional problems. Then, a new sample point in the high-dimensional space was selected through Latin hypercube sampling upon which to perform an evaluation. The new sample point was added to the high-dimensional sample data X, and the dimensionality of the sample set was reduced through MDS again. Finally, a Kriging model was established using the new sample data X\({}_{1}\) after dimensionality reduction. The test results from the benchmark functions and simulation problem prove that the proposed method can greatly improve the modeling efficiency of Kriging while ensuring certain accuracy requirements. Unluckily, the method proposed in this work sometimes loses some model accuracy when solving high-dimensional problems. For further research, we will start with the following three aspects: (1) based on the existing modeling efficiency, we will study how to choose more promising samples to further improve the modeling accuracy of the Kriging model; (2) in order to improve the accuracy of the model after dimensionality reduction, we will study how to combine the characteristic parameters of the Kriging model with mutual entropy or a \(t\)-test to select the dimension with the largest amount of information that is worthy of in-depth study; (3) for non-stationary, high-dimensional engineering problems, we will study how to achieve dimensionality reduction through the non-stationary random Kriging model while ensuring the accuracy requirement is also one of the future research directions. Conceptualization, [PERSON] and [PERSON]. ([PERSON]); writing--review and editing, [PERSON]; software, [PERSON] ([PERSON]); writing--original draft, [PERSON]; review and check, [PERSON] ([PERSON]), [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China (No. 51775472), Science and Technology Innovation Talents in Universities of Henan Province (No. 21 HASITI027) and Henan Excellent Youth Fund Project (No. 202300410346), Training plan of Young Backbone Teachers in Universities of Henan Province (No. 2020 GGJS209). Not applicable. * (2) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Chapter 13--Novel concepts for reliability analysis of dynamic structural systems. In _Handbook of Probabilistic Models_; [PERSON], [PERSON], [PERSON], [PERSON]; Butterworth-Heinemann: Oxford, UK, 2020; pp. 305-346. * (3) [PERSON]; [PERSON]; [PERSON] [PERSON] Kriging Metamodeling-Based Monte Carlo Simulation for Improved Seismic Fragility Analysis of Structures. _J. Earthq. Eng._**2021**, _25_, 1316-1336. [CrossRef]
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