We constructed an underwater discharge system to conduct a number of experiments. Considering the constant resistance of the plasma channel, we got an analytic expression for the current containing unknown parameters on the basis of the Kirchhoff voltage law. Therefore, we are required to determine the total circuit resistance R with the measured current data in hand. Three methods are employed to get this job done, namely, nonlinear least squares with three variables (NLS-TV), nonlinear least squares with a single variable (NLS-SV), and waveform calculation method (WCM). The Levenberg–Marquardt (L-M) algorithm and particle swarm optimization (PSO) algorithm are employed in NLS-TV and NLS-SV, and the root mean square error (RMSE), as well as an improved cosine similarity (ICS), was selected to evaluate the performance of algorithms. The results show that NLS-TV gives an optimal solution with the combination of the PSO algorithm and L-M algorithm. Then, by calculation, R = 1.3195 Ω , C = 0.56865 μF, and L = 17.172 μH. RMSE and ICS between fitted current data and measured one are 43.9689 and 0.9947, respectively. NLS-SV gives a satisfying solution either by PSO or by L-M, yet it needs information of angular frequency from the measured current waveform and the total inductance C . In this case, we get R = 1.3115 Ω , L = 16.969 μH, RMSE = 48.0883, and ICS = 0.9967. As for WCM, it is completely dependent on the measured current waveform and the total inductance C . The corresponding values of R and L are 1.2463 Ω and 16.993 μH. Also, we get RMSE = 52.1902 and ICS = 0.9728. For NLS-SV and WCM, the needed total capacitance during calculation is determined using the computed capacitance by NLS-TV. If the energy storage capacitance is used as the total capacitance, the obtained solution is frustrating. Therefore, independent use of NLS-SV or WCM demands a precise capacitance of the total circuit measured by an RLC meter. We also draw a conclusion that ignoring the capacitance of other parts of the circuit is incorrect and will lead to an enormous error during calculation.
The experiments of underwater discharges in an anechoic pool were carried out and analysis of the time-frequency characteristics of the acoustic signals was conducted based on Variational Mode Decomposition and Hilbert–Huang Transform (VMD-HHT). We propose a relative center frequency difference method to determine the decomposition numbers K which has to be given before the application of VMD and the result is satisfying. The HHT spectrum and marginal spectrum are obtained, then, some valuable conclusions are drawn. The high-frequency components of the acoustic signal are mainly attributed to the shock wave, and the low-frequency components mostly result from the bubble pulse. The frequency range of the acoustic signal is basically from 0 to 90kHz, and the ratio of energy in the low-frequency band(0–4kHz) to that of the total acoustic signal is up to 55.56%. Furthermore, this ratio versus gaps is also explored and it has the minimum at the gap of 1.5 mm which is the optimal gap for the peak pressure and radiated energy of the acoustic signal. Therefore, we can not obtain the maximum energy of the acoustic signal and the maximum ratio in the low-frequency band simultaneously.
Acoustic signals generated by underwater spark discharge (UWSD) can be used in a wide range of applications. The characteristics with different electrode configurations need further study for more practical application. The generation mechanism and the main characteristic indices of UWSD acoustic signals were analyzed. The acoustic signal time-frequency characteristics with different electrode gap distances and materials were calculated and compared. The results show that there is an electrode gap distance that maximizes the energy of the acoustic signal, and this gap distance is related to the impedance matching between the discharge channel and the external circuit. The proportion of low-frequency components in the acoustic signal decreases with the increase in the electrode gap distance.
A new method for gear local fault diagnosis based on vibration signal analysis is presented in this paper by using the concept of instantaneous frequency. The data from the physical simulation are used to detect the change in the instantaneous frequency and meshing vibration energy of the gear tooth fault by Empirical Mode Decomposition and Hilbert Huang Transformation (EMD-HHT). It is verified that method is effective by rig testing of geared system.
The control of discharge mode and the optimization of energy efficiency are of particular concern as the significant impact on the application of the underwater plasma discharge system. In this paper, the RLC parameters of each part of the underwater discharge system are investigated, and the equivalent circuit is obtained. Typical waveforms of current and voltage for different underwater discharge modes are displayed. The correlation between the equivalent RLC parameters of the discharge system and the discharge modes and energy is illustrated. The equivalent circuit of the underwater plasma discharge system is utilized to analyze the effects of the power source, electrode, and liquid dielectric parameters. The influences of these parameters can be identical to the impacts on the RLC parameters of the underwater discharge system equivalent circuit simultaneously, and then, the effects on the discharge modes and energy can be better understood. It can be concluded that the relative relationship of system equivalent RLC parameters determines the discharge mode, and the impedance matching between the discharge channel and the external circuit determines the discharge energy.
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