Methods on the Determination of the Circuit Parameters in an Underwater Spark Discharge

Abstract

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 time-frequency analysis of the acoustic signal produced in underwater discharges based on Variational Mode Decomposition and Hilbert–Huang Transform

“…The electrical energy deposited into the plasma gap is computed by , where i is the measured current through the gap and is the constant resistance of the channel which is determined by the difference of the total resistance of the circuit minus the external circuit resistance. The external circuit resistance can be obtained by short-circuit method and the total resistance of the circuit is usually obtained by the fitness to measured current on the basis of analytic expression for current coming from the RLC equivalent circuit model 23 . The deposited electrical energy versus gaps is shown in Fig.…”

Objective Model Selection in Physics: Exploring the Finite Information Quantity Approach

“…Remarkable achievement in UDM [112]: the research presented in [112] stands out for its exceptional results, comparable to the achievements of NASA engineers [117]. This work utilized the GoP SI framework (LMTθF), which incorporates variables expressed as combinations of five fundamental quantities [98].…”

“…This work utilized the GoP SI framework (LMTθF), which incorporates variables expressed as combinations of five fundamental quantities [98]. Notably, the model in [112] employs a significant number of variables (130) and achieves a ε mod /ε opt ratio close to 0.9, demonstrating a close alignment between achieved and optimal uncertainty. This success highlights the importance of considering a broader range of variables, even if the researchers were unaware of the specific information method.…”

Free and Wire-Guided Spark Discharges in Water: Pre-Breakdown Energy Losses and Generated Pressure Impulses

“…Energies 2023, 16, x FOR PEER REVIEW The post-breakdown circuit, including the plasma channel (formed by e path or wire-guided discharges) bridging the electrodes, can be modelled a The post-breakdown circuit, including the plasma channel (formed by either a free path or wire-guided discharges) bridging the electrodes, can be modelled as a lumped RLC circuit assuming that the resistance of this plasma channel can be represented by a constant nominal value, R pl [24,25], and the resistance of other elements of this circuit is represented by a constant value, R loss . The underdamped current oscillations in this circuit are described by Equation (1):…”