Pyrotechnic devices are used to separate substructures from main structures. Pyroshock can cause failure in electronic components that are sensitive to high frequency shock. Most of the existing methods to analyze pyroshock have limitations for high frequency simulations and are only available for simulation of point explosiveinduced pyroshock. To solve the problem of existing methods, we developed a laser shockbased pyroshock reconstruction algorithm covering high frequency range that can predict linear explosiveinduced pyroshock, as well as point explosiveinduced ones. The developed algorithm reconstructs pyroshock from laser shock test in both temporal and spectral domains using an iterative signal decomposition and synthesis method. In the signal decomposition and synthesis process, unremoved signals in the stopbands occurred and were compensated by iteration to improve the results. At the end of this paper, various types of pyroshock were processed through the proposed method. Pyroshock wave propagation images and shock response spectrum images were presented as a result. To verify the algorithm, we compared the obtained result with a real pyroshock. The time domain signal was reconstructed with an averaged peak to peak acceleration difference of 20.21%, and the shock response spectrum was reconstructed with an average mean acceleration difference of 25.86%.
Pyrotechnic devices are used to separate substructures from main structures in such situations as vehicle launches, rocketstage separations, missile launches, and pilot ejections [
Previous research implemented pyroshock using real pyro devices that downscaled structures. This technique had the advantage of being capable of simulating pyroshock in the most reasonable fashion. However, since the actual pyro device was used, the structures were damaged and could not be used again. Therefore, it was necessary to manufacture the respective structures separately for all the experiments, so that the economic burden and time were inevitable [
In addition, previous studies that simulated pyroshock using numerical analysis were reviewed. Among them, recent research into Hydrocodebased pyroshock simulation has been reported as suitable for simulating highly dynamic phenomena such as pyroshock [
Recently, laser shock has been used to reconstruct pyroshock in [
In this paper, we present a novel algorithm to reconstruct the waveform and spectrum response of pyroshock and laser shock for both linear and pointwise pyrotechnical devices to overcome the limitations of existing laser shockbased methods. The proposed algorithm compensates for the difference in characteristics of laser shock and pyroshock by using the iterative signal decomposition and synthesis method, which achieved the gain needed to compensate for the difference in characteristics between laser shock and pyroshock based on shock response spectrum (SRS). The gain was applied to laser shock signal decomposition via Butterworth filter in each frequency band. In the laser shock decomposition process, due to the inevitable characteristics of the bandpass filter, the decomposed signal in the passband included the unwanted signals that inflowed from stopbands. This is an interference problem that was compensated by iteratively removing the unwanted signal to improve the reconstruction result.
The reconstruction results are presented using the proposed pyroshock wave propagation imaging (PWPI) and shock response spectrum imaging (SRSI) algorithms. We can validate propagation characteristics such as propagation path and reflection waves of pyroshocks based on PWPI results in the timespace domain and determine how much the structure is affected by the pyroshock for each frequency using the SRSI results. To verify the proposed algorithm, the comparison results with the real pyroshock are presented in terms of similarity between the real pyroshock and reconstructed pyroshock.
Figure
Flow chart of pyroshock reconstruction algorithm based on laser shock.
The pyroshock measurement is performed through a shock measurement system based on multiple laser Doppler vibrometers (LDVs, Polytech Inc.) as shown in Figure
Pyroshock measurement process using a shock measurement system based on multiple laser Doppler vibrometers (LDVs).
Through the pyroshock measurement process, we can observe the characteristics of the pyroshock. However, since the number of LDV sensors is limited, pyroshock can be detected only at a few limited points. To confirm the propagation of pyroshock for the whole structure, we reconstruct pyroshock using laser shock. First, the same structure used in the pyroshock measurement is prepared to obtain the laser shock signal. Then, PZT sensors (RCast M204A, Fuji ceramics Inc.) are installed in place of the pyrotechnical device because the reciprocal setup of the laser shock scanning system (Mobile PZTUPI, XNDT Inc.) designates the sensor locations shock source locations. Once the structure and sensors are installed, the laser scanning process proceeds as shown in Figure
Laser shock measurement process scheme; (a) PC with GUI platform. (b) Thermoelastic mechanism. (c) Laser shock time domain signal. (d) Laser scanning data.
To reconstruct the pyroshock using laser shock, it is necessary to compensate the characteristic differences between laser shock and pyroshock. The compensation procedure is based on the SRS. The SRS is the most widely used function to quantify pyroshock and is calculated based on the time domain signal. It applies the time domain signal as a base excitation to an array of single degree of freedom (SDOF) systems [
In the system,
The time domain signal of the pyroshock is reconstructed by substituting
Signal decomposition and synthesis using Butterworth bandpass filter.
(a) Test algorithm. (b) Reconstruction results of the test algorithm. (c) The problems of test algorithm.
(a) Test algorithm 2. (b) Reconstruction results of the test algorithm 2.
Reconstruction algorithm of pyroshock time domain signal.
When the amplitude of
Pyroshock propagation evaluation; (a) PWPI; (b) SRSI.
In this section, pyroshock data in ref [
Laser shock measurement condition for reconstruction of linear explosive induced pyroshock.
Shock source 

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

Laser shock  1.25  0.1~100  600  1,000  Width = 640 
The pyroshock was generated by exploding a 230mm linear pyrotechnical device on a CFRP specimen as shown in Figure
Linear explosive induced pyroshock measurement on the CFRP specimen. (a) Experimental setup. (b) Sensing point on the test specimen. (c) Time domain signal of linear explosive induced pyroshock.
The same specimen used in pyroshock measurement was installed as shown in Figure
(a) Laser shock measurement setup. (b) Laser scanning process and laser shock time domain signal at an arbitrary point. (c) Fourdimensional laser scanning data structure.
(a) Snapshots of laser scanning data at 65
After completion of the laser shock and pyroshock data acquisition, the SRS reconstruction process was performed as described in Section
SRS reconstruction on the training points. (a) CFRP specimen. (b) Reconstruction results.
The time domain signal of pyroshock was reconstructed by substituting the information from
Time domain signal reconstruction at point 1, training point.
Time domain signal reconstruction at point 2, training point.
The obtained
Linear explosive induced pyroshock propagation evaluation; (a) PWPI at 467
To verify the obtained PWPI and SRSI, we compared the reconstruction result with the real pyroshock at the measurement point 3 set as the verification point. The comparison result is shown in Figure
Time domain signal reconstruction at point 3, verification point.
(a) CFRP specimen with red line. (b) Reconstructed SRS along the red line.
Reconstructed time domain signal along the red line.
Reconstruction using measurement points 1 and 2 as training points and measurement point 3 as verification point confirmed that pyroshock was reconstructed with averaged PAD of 16.07% and MAD of 21.83%. To verify more closely the developed algorithm, this process was repeatedly conducted by changing the training and verification points. Figure
Time domain signal reconstruction result in using point 2 as a verification point.
Time domain signal reconstruction result in using point 1 as a verification point.
In this section, we analyzed the propagation of the point explosive induced pyroshock in specimens of steel 4340 material. The specimen had a thickness of 27 mm and a diameter of 300 mm. The pyroshock measurement setup is shown in Figure
Measurement condition of point explosive induced pyroshock on the disk type specimen.
Shock source  CF 

Filter (kHz)  Number of samples 



Pyroshock 

1  0.1~100  30,000  1,000 

Measurement system of point explosiveinduced pyroshock and the disk type specimen.
Laser shock data were obtained for the same specimen used in pyroshock measurement. The laser shock generated by Qswitch laser was collected by a PZT sensor. The scanning area was set to include pyroshock measurement points as shown in Figure
Measurement condition of laser shock for reconstruction of pyroshock on the disk type specimen.
Shock source 

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

Laser shock  1  0.1~100  512  50  Width = 136 
Scanning measurement system of laser shock for reconstruction of explosive induced pyroshock on the disk type specimen.
The pyroshock reconstruction process was performed using two arbitrary points of the acquired signals, measurement point 2 and point 3 as the training points. The reconstruction results at the training points are shown in Figure
Reconstruction results of pyroshock on the disk type specimen at the training points.
Pyroshock propagation evaluation on the disk type specimen; (a) PWPI at 60
To verify the algorithm, we compared the reconstruction result and the real pyroshock at the measurement point 1 set as the verification point as shown in Figure
Reconstruction results of pyroshock on the disk type specimen at the verification point.
Reconstruction of pyroshock using laser shock was first attempted in [
Reconstruction results and comparison of the proposed algorithm and previous algorithms.
Developed algorithm  Ref [ 
Ref [  

Training point  Verification point  Training point  Verification point  Training point  Verification point  
MAD (%)  PAD (%)  MAD (%)  PAD (%)  MAD (%)  PAD (%)  MAD (%)  PAD (%)  MAD (%)  PAD (%)  MAD (%)  PAD (%)  
CFRPlinear  21.94  14.02  21.61  19.83  31.87  20.55  34.51  19.10  Could not be reconstructed  
Diskpoint  28.04  3.25  30.11  20.59  45.65  7.30  52.64  18.03  36.40  45.30  63.22  48.33 
Average  24.99  8.64  25.86  20.21  38.76  13.93  43.58  18.57  36.4  45.3  63.22  48.33 
Comparison of reconstruction results of pyroshock on the disk type specimen at the verification point. (a) Ref [
In this paper, we developed a pyroshock reconstruction algorithm using laser shock. The developed system used a laser scanning technique to acquire laser shock and reconstructed it with pyroshock using iterative signal decomposition and synthesis method. This algorithm obtained the gain to compensate the difference in characteristics between laser shock and pyroshock based on SRS. The gain was applied to laser shock signal decomposed by Butterworth filter in each frequency band. The stopband effect in band decomposition was compensated by iteration to improve the reconstruction result. We reconstructed linear explosive induced pyroshock using the developed algorithm as well as point explosive. PWPI and SRSI were obtained through the reconstruction. We could confirm propagation characteristics such as propagation path and reflection wave of pyroshock through PWPI. Through the SRSI, we could ascertain how much the structure was affected by the pyroshock for each frequency. To verify the algorithm, we compared the reconstruction result with the real pyroshock. At the verification point, the time domain signal was reconstructed with an averaged PAD of 20.21% and the SRS was reconstructed with an average MAD of 25.86%. This was a remarkably improved result compared to the developed pyroshock reconstruction system in [
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by the Space Core Technology Development Program (Grant no. 2013042548) and by the Research Grant (PMD) of the Agency for Defense Development and Defense Acquisition Program Administration of the Korea government.