Comparison of impulse noise energy distribution from two generations of parachute gun

The rocket ejection seat is an advanced life-saving device for fighter pilots. However, it can also produce damaging impulse noise during ejection, which could compromise the pilot’s hearing health, and the manufacturer must assess the noise damage. This study uses Variational Mode Decomposition (VMD) and Hilbert-Huang transform (HHT) to analyze energy-instantaneous distribution over time and frequency-instantaneous and energy contribution of different modes of impulse noise generated by the parachute gun in two generations of rocket ejection seats. The results demonstrate considerable disparities in the energy distribution of impulse noise generated by the parachute gun in the new generation seat compared to the old generation seat. The new generation seat has higher overall energy, more concentrated action time, and a higher energy contribution in the 1-10 kHz frequency range. These findings provide valuable data for the design of the new generation of noise protection equipment for pilots.


Introduction
During the shooting process of firearms, the gunpowder gases expelled from the muzzle disrupt the surrounding air and form impulse noise that decays rapidly in the air [1,2].According to studies, the impulse noise generated by firearms has a significant impact on the auditory organs.Over 60% of shooters who have been attending shooting ranges for more than 5 years have suffered hearing damage, while more than 52% of other personnel have experienced hearing damage in the speech frequency range [3].Shooters exposed to impulse noise within a certain range may also experience headaches, dizziness, panic attacks, insomnia, memory loss, and other conditions such as high blood pressure [4,5].As a result, it is critical to research the physical properties of impulse noise, comprehend its patterns of occurrence, and successfully mitigate its negative effects on the environment and human health.
During wartime, the probability of pilots choosing high-speed ejection for survival significantly increases.Therefore, the fourth-generation rocket ejection seat is designed as an automatic aircraft to address the issue of lifesaving in high-speed ejection and unfavourable attitude conditions [6].The parachute gun, which is part of the ejection seat, ensures the rapid deployment of the parachute, improving the success rate of the rescue [7].However, the impulse noise generated by the parachute gun during the parachute ejection process also undergoes changes in energy distribution, which must be taken into account by manufacturers of rocket ejection seats when improving their designs.
To devise efficient protective gear for pilots against the ravages of impulse noise, it is necessary to study further the differences in the energy distribution of impulse noise generated by the parachute

Testing equipment
The experiment uses real rocket ejection seats and conducts a parachute gun firing in mid-air, simultaneously ejecting the parachute container and the parachute.The impulse noise testing system comprises a PCB pressure sensor, low-noise cables, a BK dynamic data acquisition instrument, and a portable computer.The sampling rate of the datalogger is set at 130 kHz.The pressure sensor is positioned facing the muzzle of the parachute gun, fixed on a stand, and placed 1 m away from the muzzle.The experimental site is depicted schematically in Figure 1.

Selection of analytical methods
As a typical non-stationary signal, the impulse noise generated by the parachute gun of the old and new generation seats has irregularity, rapid changes, and rapid decay.In recent years, wavelet analysis, EMD, and VMD algorithms have been proposed to characterise the energy distribution of nonstationary signals.However, the prerequisite for wavelet analysis to achieve high-quality results is to choose a suitable wavelet basis function, which is difficult to achieve for the impulsive noise with complex composition studied in this work, and the EMD decomposition algorithm for impulsive noise with a sampling rate of 130 kHz is very easy to lead to frequency aliasing among the results of the low-frequency decompositions.The VMD is a new, non-recursive, variable modal decomposition estimation method that can correctly separate low-frequency similar components at high sampling rate rates.This work investigates the collected impulse noise characteristics using VMD and HHT transform methods [8,9].Since VMD and HHT are already very mature methods, the theoretical introduction of the two methods is reduced in this work to analyze the experimental results more comprehensively.

Measurement results
The pressure-time curves of the impulse noise generated by parachute guns for old seats and improved new seats (defined as old gun and new gun) during firing are obtained in Figure 2, with a sampling rate of 130 kHz, where the black vertical coordinate on the left side corresponds to the data scale of an old gun.The blue vertical coordinate on the right side corresponds to the data scale of a new gun (the definition of the double vertical coordinate in the following section is consistent with that of the present Figure ).The peak overpressure of the new gun (27.8 kPa) is much higher than that of the old gun (6.3 kPa).The pulse width (i.e., the time interval from the ambient pressure to the peak pressure and back to the ambient pressure) of the new gun (0.6 ms) was slightly lower than that of the old gun (0.8 ms). Figure 3 shows the power spectral density (PSD) of the time-domain signals obtained through the Fourier transform [10].The dominant energy of both signals is primarily concentrated within the low-frequency range, specifically below 1 kHz.

VMD and HHT analysis
The modal decomposition of the shooting impulse noise signals can be done using VMD.According to the centre frequencies of the two impulse noise signals and the energy distributions of each decomposition component [11], the number of modes is selected to be 6, the default value of the penalty factor, defined as 1000 in the VMD, is adopted, which can be a guarantee of the fidelity of the actual impulse noise signals decomposition It can be found that the amplitudes of all components in the new gun are higher than those in the old gun, and there are noticeable fluctuations in each component near 2 ms in the new gun.
Figure 5 shows the time-frequency representation for the Hilbert spectrum obtained by applying HHT to the VMD decomposition results.The horizontal coordinates of the graph indicate time, the vertical coordinates indicate the instantaneous frequency (IF), and the colours indicate the energy.It can be seen that within 3 ms of the impulse noise action, the energy of the new parachute gun is more prominent in IMF4-IMF6, compared to the old parachute gun.With the increased frequency of each IMF component, its action time gradually decreases.Through time integration of the Hilbert spectrum, the Hilbert marginal spectrum is computed to provide additional insight into the energy distribution of impulse noise signals with frequency [12], and the results are displayed in Figure 6.The marginal spectrum reflects a more thorough depiction of minute energy variations in each frequency band than the Fourier PSD in Figure 3  Figure 7 displays the calculation results of each IMF's energy contribution to the impulse noise's overall energy.The energy contribution of IMF6 to the total energy is 57% for the new gun and 80% for the old gun.The frequency range of IMF6 is mainly below 1 kHz, indicating that the energy of the impulse noise generated by the old gun during parachute ejection is more concentrated in the lowfrequency range.The new gun had a higher energy contribution in the 1-10 kHz frequency range than the old one.Figures 5 and 6 show that this frequency range plays a significant role in the action of the impulse noise during parachute ejection.It is one of the important changes brought about by improving the parachute gun.It is also a critical factor to consider in designing protective equipment for pilots, as this frequency range is within the sensitive range of human hearing and can potentially cause long-term damage to the hearing and the nervous system [13].

Conclusion
Routine noise is assessed for its hazardous effects on the hearing organs using the A-weighted or Cweighted sound pressure level and the noise duration.This study used VMD decomposition and HHT to investigate the energy distribution of impulse noise in two generations of parachute guns at rocket ejection seats.It can be found that the Hilbert and the marginal spectrum can reflect more intuitively and in more detail the similarities and differences in the energy distribution of impulsive noise of a few milliseconds generated by the two generations of seats compared with PSD.Firstly, the energy of the impulse noise generated by both generations of parachute guns is concentrated in the 0-10 kHz range, particularly prominent within 1 kHz, with this band accounting for more than half of the total energy.Each intrinsic mode component of the new generation parachute gun has a higher peak amplitude than the old generation gun, and the energy distribution for each component has a greater concentration in the time domain.
Furthermore, in the frequency range below 1 kHz, the energy contribution of the impulse noise generated by the new generation parachute gun is reduced by 23% compared to the old gun.This is due to the higher energy distribution of the new gun in the 1-10 kHz frequency range.Considering the frequency perception range of human hearing, the energy distribution in this frequency range may have a greater potential impact on hearing and the nervous system.Therefore, when creating safety gear for pilots, in addition to measuring to reduce the energy of impulse noise in the frequency range below 1 kHz, it is also essential to focus on and reduce the energy distribution of impulse noise in the 1-10 kHz frequency range to minimize its adverse effects on pilot hearing health.

Figure 4 .
Figure 4. IMFs of impulse noise signals for old gun and new gun.
. The centre frequencies of all decomposed components of the impulse noise are [18.2,13.3, 7.6, 4.5, 2.3, and 0.4]/kHz for the old gun, and [18.0, 13.0, 7.7, 3.3, 1.3, and 0.3]/kHz for the new gun.Except for IMF4, the central frequencies of the two guns are closed.The decomposition results are shown in Figure 4, where the left column represents each decomposition result of the old gun impulse noise, and the right column represents each decomposition result of the new gun impulse noise, with the frequency decreasing from IMF1 to IMF6.

Figure 5 .
Figure 5. Time-frequency representation of the HHT energy distribution spectrum of impulsive noise signals: (a) Old gun, (b) New gun.

Figure 6 .
Figure 6.The marginal spectrum of all IMFs for old guns and new gun.

Figure 7 .
Figure 7.Each IMF's energy contribution to the impulse noise's overall energy for the old gun and the new gun.