Shock wave pressure modeling using long short-term memory network based on variational mode decomposition processing

hock wave pressure sensor acquisition systems exhibit both high- and low-frequency dynamic characteristics; however, traditional transfer-function-based modeling and compensation methods cannot achieve accurate full-band representation, thereby limiting further improvements in compensation accuracy and reconstructed signal fidelity under complex dynamic conditions. To overcome this limitation, a fusion modeling method integrating the sparrow search algorithm (SSA), variational mode decomposition (VMD), and a long short-term memory (LSTM) network was developed to enhance the dynamic characteristic modeling accuracy of shock wave pressure acquisition systems. In this method, SSA was employed to globally optimize the mode number and penalty factor of VMD using a comprehensive fitness function that combined sample entropy and the Pearson correlation coefficient, thereby improving the adaptability of the decomposition to nonstationary response signals contaminated by oscillations and noise. With the optimized parameters, VMD decomposed the sensor response signal into multiple intrinsic modal components; the frequency-domain characteristics of each component were then analyzed, and correlation coefficients together with jump durations were calculated and compared according to the spectral distribution characteristics of shock waves to identify the signal types contained in each mode. Based on this identification, high-frequency oscillatory modes and noise modes were discarded, enabling reconstruction of the effective shock wave signal. A sinusoidal signal generator was used to obtain pressure acquisition waveforms in the range of 0.1–10 Hz; the amplitudes were converted into decibels to form the low-frequency magnitude-frequency characteristic curve, and a frequency-domain rational function fitting procedure was applied to establish the low-frequency transfer function. Using this transfer function, low-frequency dynamic compensation was performed on the reconstructed signal, and the compensated low-frequency signal was combined with the original sensor response to construct an input-output dataset that simultaneously preserved the compensated dynamic information and the original response characteristics. On the basis of this dataset, SSA was further used to optimize key LSTM hyperparameters, including the number of hidden units, the maximum number of training epochs, and the initial learning rate, and an LSTM network was trained to model the nonlinear, time-dependent, and memory-dependent behavior of the acquisition system, thereby achieving fusion modeling of high- and low-frequency dynamic characteristics within a unified framework. Simulation analyses and live explosion tests demonstrated that, compared with the traditional inverse-filtering compensation method, the proposed approach reduced the mean absolute percentage error (MAPE) between the compensated signal and the reference pressure curve by approximately 75% and decreased oscillation residuals by about 38%, satisfying the accuracy requirements for input pressure signals; compared with a single LSTM-based modeling approach, the VMD-LSTM fusion model reduced the overall modeling error to 13%, indicating improved accuracy and robustness. These results indicate that the SSA-optimized VMD decomposition, transfer-function-based low-frequency compensation, and SSA-tuned LSTM fusion modeling together provide an effective full-band modeling strategy, and that the proposed framework offers a robust solution for accurate dynamic characteristic modeling and compensation in shock wave pressure sensor acquisition systems.