## 6 Conclusions  
In this paper, a dimension-reduction stochastic model of explosive ground motions has been proposed, which realizes the efficient and accurate simulation by giving the scaled charge quantity. Meanwhile, a frame structure considering material nonlinearity is employed in this paper to investigate the structural reliability under the explosive ground motions by combining with the EEV-based reliability evaluation strategy embedded in the PDEM. The numerical analysis results fully reveal the superiority of the proposed dimension-reduction method for simulating the explosive ground motions and the feasibility of the EEV-based dynamic reliability evaluation strategy for complex nonlinear engineering structures. The main conclusions can be drawn as follows. * The identification method of EPSD model parameters proposed in this study can separately identify the PSD and intensity modulation functions, which effectively reduces the identification errors induced by time-frequency coupling of EPSD function. * The exponential model suggested in this paper preliminarily establishes the relationship between the seismic characteristics of explosive ground motions with the explosion mechanism, which realizes the prediction of the EPSD model by giving the scaled charge quantity. * The introduction of the dimension-reduction method successfully achieves the accurate simulation of explosive ground motions by using only one elementary random variable. Benefitted from the dimension-reduction simulation method, the number of representative time-histories of the explosive ground motions is just several hundred and the probability information of the sample set is complete. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Story No.** & \(\rho\) = 0.03 & \(\rho\) = 0.04 \\ \hline
1 & 1.000 & 1.000 \\
2 & 1.000 & 1.000 \\
3 & 1.000 & 1.000 \\
4 & 1.000 & 1.000 \\
5 & 1.000 & 1.000 \\
6 & 1.000 & 0.973 \\
7 & 0.972 & 0.895 \\
8 & 0.903 & 0.860 \\
9 & 0.906 & 0.882 \\
10 & 0.993 & 0.984 \\ \hline Global & 0.882 & 0.824 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Dynamic reliability of the 10-story frame structure under the explosive ground motions. * The refined probability density evolution information of the dynamic response with respect to the structures subjected to the explosive ground motions can be captured with the help of the PDEM. Further, the proposed EEV-based reliability evaluation strategy can precisely assess the component and global dynamic reliability of complex structures. The numerical results of the nonlinear frame structure investigate the relationship between the scaled charge quantity and the structural reliability, which can provide a reference for structural anti-explosion analysis. In future work, more measured data will be included to propose a more precise and reasonable prediction model of EPSD parameters for generating explosive ground motions. A coherency function model between different directions of the explosive ground motions will be achieved to realize the modeling of multi-dimensional explosive ground motions based on the dimension-reduction method. Furthermore, the multiple index evaluation method for the dynamic reliability of structures under explosive ground motions is also an important aspect that needs to be further explored. Conceptualization, [PERSON] ([PERSON]); methodology, [PERSON] ([PERSON]); software, Y.J. ; validation, Y.J. ; formal analysis, Y.J. ; investigation, Y.J. ; resources, Y.J. ; data curation, Y.J. ; writing--original draft preparation, Y.J. ; writing--review and editing, [PERSON] ([PERSON]), X.R. ; supervision, [PERSON] ([PERSON]), X.R. ; project administration, [PERSON] ([PERSON]); funding acquisition, [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript. This work was supported by State Key Laboratory of Precision Blasting and Hubei Key Laboratory of Blasting Engineering, Jianghan University (No. PBSKL2022C07), the National Natural Science Foundation of China (No.