## 5 Summary and Conclusions  
A novel solution model based on the stochastic HS algorithm was proposed to obtain GM record sets for NDAs of 2D and/or 3D structural models considering both horizontal and vertical seismic excitation. The efficiency of the model was demonstrated using different numerical examples considering various UHS-based and scenario-based target spectra. It was observed that the model can be used efficiently to obtain suitable GM record sets with the desired spectral compatibility and spectral variability for both horizontal and vertical components. Below are some key characteristics and consequences of the solution model:  
* Practitioners can develop customized catalogues by considering the regional seismic characteristics of their site of interest to obtain tailored ground motion records for their analysis.
* The _MSE_ parameter is used to assess the quality of matching between the selected GMs and target spectra. If the _MSE_ values are higher, the compatibility between the selected GMs and target spectra decreases. The scatter in the spectra will generally produce more scatter in the responses, making it difficult to obtain reliable response statistics. The results demonstrated that it is possible to obtain quite low _MSE_ values with the proposed model.  
Figure 15: GM selection according to a scenario-based earthquake. Initial steps of the model for the spectral shape of acceleration and its deviation: (**a**) horizontal direction; (**b**) vertical direction. Final obtained GM records for the spectral shape of acceleration and its deviation: (**c**) horizontal direction; (**d**) vertical direction.  
* If desired, the model can incorporate period-dependent spectral variability in both horizontal and vertical components of the selected GM records, irrespective of the target spectral shapes.
* The proposed model is capable of defining limits for record-to-record spectral variability in code-based selection, which may be advantageous for practicing engineers seeking a more comprehensive understanding of structural behavior.
* A single-scale value was used for horizontal and vertical components of a selected GM record to maintain the relative amplitude and phasing of the real GM components.  
There are some considerations of the proposed approach used in this study. Firstly, for 3D ground motion selection the means of the selected SRSS spectra were used for compatibility. It is also important to check that the means of both the x (first direction of horizontal spectra) and y (other direction of horizontal spectra) horizontal spectra are compatible with the target spectra, separately. Secondly, the effects of the single-scale value considering three orientations of GM and period-dependent record-to-record variability on the structural responses should be investigated as future work.  
Conceptualization, A.D., M.P. and A.H.K.; Methodology, A.D., M.P. and A.H.K.; Software, A.D., M.P. and A.H.K.; Investigation, A.D., M.P. and A.H.K.; Resources, M.P.; Writing--original draft, A.D., M.P. and A.H.K.; Writing--review & editing, A.D., M.P. and A.H.K.; Visualization, A.D., M.P. and A.H.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The author declares no conflicts of interest.