**5. Conclusions**

For two kinds of TBCs, experimental microstructure observation, hardness, and modulus measurement by using the nanoindentation tests were performed, and nanoindentation size e ffect was described by using the trans-scale mechanics model. The main conclusions can be summarized as follows:

**Author Contributions:** Data curation, Y.W. (Yingbiao Wang) and Y.L.; Methodology, J.S. and H.L. (Hao Long); Writing—original draft, H.L. (Haiyan Liu); Writing—review and editing, Y.W. (Yueguang Wei) and L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, Nos.: 11890681, 11672301, 11511202, 11672296, 91860102, 11432014.

**Conflicts of Interest:** The authors declare no conflict of interest.


5. Results

Clustering is one of the unsupervised machine learning methods grouping data to the clusters. In this study, four well-known swarm-based, nature-inspired optimization algorithms have been used for clustering. In order to measure the clustering performance of the algorithms, sum of the distance values have been used. Clustering performance of the algorithms on IRIS dataset has been tested for comparison. As it has been seen in the tables, nature-inspired algorithms'solution time is not comparable with k-means. Nature-inspired algorithms are very slow because of the swarm-based run. According to the tables, PSO and GWO are faster than BBO and GA owing to the mutation and other parameters. Both PSO and GWO have fewer parameters to adapt, and they are faster and more stable than BBO and GA. In this study, no adaptation is applied for any algorithm. So if special adaptation is applied for those algorithms, the clustering performance of the algorithms will increase.