The use of pyrodevices in the aerospace industry has been increasing because of their ability to implement separation missions with a small weight, for example, space launchers, spacecrafts, and missiles. During operation, pyrodevices generate pyroshock, which causes failures of electronic devices. Recently, a pyroshock simulation method using laser shock has been developed to evaluate the risk of pyroshock before flight mission. However, depending on the structure, the laser shock showed some difficulty simulating pyroshock in the lowfrequency regime accompanying vibration. Therefore, in this study, we developed a hybrid method of numerical modal analysis and laser shockbased experimental simulation to visualize the pyroshock propagation in all the relevant frequency regimes. For the proof of concept of the proposed method, we performed experiments of explosive boltinduced shock and pyrolockinduced shock in the openboxtype tension joint and compared the hybrid simulation results with actual pyroshock. From the results, we obtained the simulated timedomain signal with an averaged peaktopeak acceleration difference (PAD) of 11.2% and the shock response spectrum (SRS) with an averaged mean acceleration difference (MAD) of 28.5%. In addition, we were able to visualize the simulation results in the temporal and spectral domains to compare the pyroshock induced by each pyrodevice. A comparison of the simulations showed that the pyrolock had an impulse level of 1/12 compared to the explosion bolt. In particular, it was confirmed that the pyrolockinduced shock at the near field can cause damage to the electronic equipment despite a smaller impulse than that of the explosive boltinduced shock. The hybrid method developed in this paper demonstrates that it is possible to simulate pyroshock for all the frequency regimes in complex specimens and to evaluate the risk in the time and frequency domain.
Pyrodevices separate a substructure from a main structure via an explosion. Pyrodevices are widely used in the aerospace field because they have the advantages of enabling a separation mission with low weight and small volume [
Pyroshock is divided into pointsource pyroshock, linearsource pyroshock, and combinedsource pyroshock, depending on the type of the pyrodevice. In addition, pyroshock is divided into three fields according to the magnitude and frequency of the response [
Pyroshock environmental categories: (a) IESTRPDTE032 and MILSTD810G [
Various simulation techniques have been developed to study pyroshock. Although there have been studies to simulate pyroshock using mechanical shocks, they all have limitations in that they can only be simulated for pointsource pyroshock [
To overcome these limitations described above, we developed a hybrid method of modal analysis and laser shock scanning to simulate the pyroshock over the whole frequency regime. In the far field, with lowfrequency components less than 3 kHz, because the finite element analysis verified the accurate simulation performance [
The hybrid method developed in this study proves that the pyroshock can be simulated in a complex structure, such as an openboxtype tension joint; thus, the method can be used to evaluate the risk of pyroshock in the temporal and spectral domains.
Figure
Flow chart of the hybrid method of FEMbased modal analysis and laser shock scanningbased simulation (PWPI: pyroshock wave propagation imaging; SRSI: shock response spectral imaging).
A 1/2inch explosive bolt (Hanwha Corporation), shown in Figure
(a) 1/2inch explosive bolt, (b) 1/2inch pyrolock, and (c) measurement setup of pyroshock on the openboxtype tension joint.
Data acquisition condition of pyroshock on the openboxtype tension joint.
Shock source  CF 

Filter (kHz)  Number of samples  CF_{mr} (mm/s/V) 

Sensing point coordinate 

Pyroshock  CF_{1} = 1.42 
1  0.1∼100  30,000  1,000 

Point 1–(145, 60) 
Through the pyroshock measurement process, we can observe the characteristics of the pyroshock. However, the point measurement of the actual pyroshock at limited points is not sufficient to understand and analyze the pyroshock that is propagated over the structure. To visualize the propagation of pyroshock in the full field over the structure, we simulate pyroshock using laser shock. The same structure used in the pyroshock measurement was prepared to obtain the laser shock signals. Next, PZT sensors were installed in place of the pyrodevice, as shown in Figure
Laser scanning measurement setup for simulation of pyroshock on the openboxtype tension joint.
Measurement conditions of laser scanning for simulation of pyroshock on the openboxtype tension joint.
Shock source 

Filter (kHz)  Number of samples  PRF (Hz)  Scan area (mm) 

Laser shock  1  0.1∼100  8,000  50  Width = 152 
Because the PZT sensor used to acquire laser shock scanning data is a contact type and broadband sensor of a central frequency of 200 kHz and a bandwidth of 1.2 MHz, the sensitivity differs, depending on the frequency range. However, the PZT has poor sensitivity in the subkilohertz regime. The pyroshock simulation requires shock signal acquisition over a very wide frequency range, and the laser shockcapturing sensor requires very high sensitivity; however, it is difficult to find such a widerange PZT sensor covering the whole pyroshock analysis range with high sensitivities over the range. In addition, the LDV is not suitable for the simulation because it provides SNR insufficient for measuring laser shock signal. Therefore, we developed the hybrid method involving the finite element analysis method for the lowfrequency pyroshock accompanying vibration and the laser scanning method in the highfrequency regime, utilizing the advantages of each of the two simulation methods. Figure
Modal analysis for simulation of pyroshock on the openboxtype tension joint: (a) FEM model, (b) modal analysis results, (c) trained modal analysis data, (d) laser shock data, and (e) reference data.
Modal analysis condition for pyroshock on the openboxtype tension joint.
FEA software  Young’s modulus ( 
Density ( 
Poisson’s ratio  Natural frequency (Hz)  Training point 

COMSOL  193  8,000  0.3  1131first mode 
Point 3–(60, 15) 
Using only two sets of pyroshock data, which were measured at point 1 and point 3, a 1/2inch explosive boltinduced pyroshock simulation was performed based on iterative signal decomposition and synthesis. Further information on the iterative signal decomposition and synthesis method can be found in reference [
Simulation results of the 1/2inch explosive boltinduced shock at training points: (a) Point 1 and (b) Point 3.
1/2inch explosive boltinduced pyroshock propagation evaluation on the openboxtype tension joint: (a) PWPI at 300
Simulation results of 1/2 inch explosive boltinduced shock at the verification point.
Using only two sets of pyroshock data, which were measured at point 1 and point 3, a 1/2inch explosive boltinduced pyroshock simulation was performed based on iterative signal decomposition and synthesis. Figure
Simulation results of 1/2 inch pyrolockinduced shock at training points: (a) Point 1 and (b) Point 3.
1/2inch pyrolockinduced shock propagation evaluation on the openboxtype tension joint: (a) PWPI at 300
Simulation results of 1/2 inch pyrolockinduced shock at the verification point.
Table
Comparison of the peaktopeak acceleration between the explosive bolt and the pyrolock.
Peaktopeak acceleration (g)  

Point 1  Point 2  Point 3  
Explosive bolt  8,158  14,724  17,797 
Pyrolock  683  3,393  1,352 
Simulation similarity result between the real pyroshock and the simulated pyroshock for each experiment.
Training point  Verification point  






Explosive bolt  11.57  28.39  4.87  31.92 
Pyrolock  13.30  29.11  12.6  24.12 
Comparison of the simulation performance between the conventional pyroshock simulation algorithm and the developed algorithm at the verification point: (a) hybrid method and (b) reference [
Evaluation of the pyroshock propagation in temporal and spectral domains on the openboxtype specimen: (a) simulation results of 1/2 inch explosive boltinduced pyroshock (b) simulation results of 1/2 inch pyrolockinduced pyroshock.
In this study, we developed a hybrid method of modal analysis and laser shock scanning to visualize the pyroshock propagation accompanying vibration according to the boundary condition and to evaluate the risk of pyroshock. The hybrid method predicts the characteristics of pyroshock in the openbox tension joint by combining laser shock and modal analysis where the modal analysis was used to superimpose the lowfrequency vibration to pyroshock propagation; Both laser shock and modal analysis results were superposed and reconstructed to the pyroshock using iterative signal decomposition and synthesis. The pyroshock propagation characteristics of the two different pyrodevices, an explosive bolt and a pyrolock, in the openboxtype tension joint were simulated using the developed hybrid simulation method. The timedomain signal was simulated with an averaged PAD of 11.2%, and the SRS was simulated with an averaged MAD of 28.5%. Considering that the repeatability of the pyroshock itself is approximately 20%, the simulation performance was found to be satisfactory. On the contrary, simulation results at point 1 show relatively higher MAD and PAD than the other two points. The reason was that the point 1 showed much more complex response than the other two points since it was the result of measurement near the stiffer boundary. In order to improve the simulation results in this boundary, further investigation of various wave modes seems necessary. We visualized the simulation results in the temporal and spectral domains to compare the pyroshock induced by each pyrodevice. A comparison of the simulations showed that the pyrolock has an impulse level 1/12 in magnitude compared to that of the explosion bolt. In particular, it was confirmed that, in the near field, the pyrolockinduced shock has a smaller impulse magnitude than the explosive boltinduced shock. The hybrid method developed in this paper demonstrated that it is possible to simulate pyroshock over the entire frequency regime in complex specimens accompanying vibration and to evaluate the risk in time and frequency domains.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science and ICT (NRF2017R1A5A1015311) and by the research grant (PMD) of the Agency for Defense Development and Defense Acquisition Program Administration of the Korean government.