基于变分模态分解处理的冲击波压力长短期记忆网络系统建模

罗瑶嘉; 张志杰

doi:10.11883/bzycj-2025-0152

基于变分模态分解处理的冲击波压力长短期记忆网络系统建模

doi: 10.11883/bzycj-2025-0152

罗瑶嘉,
张志杰^,

中北大学仪器科学与动态测试教育部重点实验室，山西太原 030051

详细信息

作者简介:
罗瑶嘉（2001－　），女，硕士研究生，13554081002@163.com

通讯作者:
张志杰（1965－　），男，教授，博士生导师，zhangzhijie@nuc.edu.cn

中图分类号: O384
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- 被引次数: 0
出版历程
- 收稿日期: 2025-05-26
- 修回日期: 2026-01-07
- 网络出版日期: 2026-01-14

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

LUO Yaojia,
ZHANG Zhijie^,

Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, Shanxi, China

摘要

摘要: 冲击波压力传感器采集系统兼具高低频动态特性，而传统的基于传递函数的建模方法难以实现整体精准建模，这一问题限制了系统补偿精度的提升。本文提出一种基于麻雀优化算法、变分模态分解与长短期记忆网络的动态特性融合建模方法，旨在解决整体建模难题并提高系统动态特性建模精度。该方法通过优化算法搜索变分模态分解的模态数和惩罚因子，自适应分解响应信号为多个模态分量并识别成分，实现高频与低频分量的有效分离；对低频分量进行动态特性补偿后，将其作为压力信号和原响应信号构建模型输入输出数据集，通过网络完成传感器系统动态特性建模。仿真与实爆试验结果表明，相较于传统的反滤波补偿方法，本方法补偿后信号与典型压力曲线的平均绝对百分比误差降低75%，振荡残余减小38%，满足作为输入压力信号的精度要求；与单一神经网络建模相比，该融合建模方法的误差降至13%，为解决传感器宽频带动态建模难题提供了一条有效途径。
- 冲击波压力 /
- 动态补偿 /
- 变分模态分解 /
- 长短期记忆
Abstract: Shock wave pressure sensor acquisition systems exhibit both high-frequency and low-frequency dynamic characteristics, while traditional transfer-function-based modeling and compensation methods were unable to achieve accurate full-band modeling, thereby limiting further improvement in compensation accuracy and reconstructed signal fidelity under complex dynamic conditions. To address 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 improve 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, which enhanced the adaptability of decomposition for 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, the high-frequency oscillatory modes and noise modes were discarded, thereby achieving the reconstruction of the effective shock wave signal. A sinusoidal signal generator was used to obtain pressure acquisition waveforms over 0.1–10 Hz, 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 model the low-frequency transfer function. Using the 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 signal to construct an input-output dataset that simultaneously preserved compensated dynamic information and original response characteristics. Based on this dataset, SSA was further used to search key LSTM hyperparameters, including the number of hidden units, the maximum 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, enabling fusion modeling of high- and low-frequency dynamic characteristics within a unified framework. Simulation analyses and live explosion test results demonstrated that, compared with the traditional inverse filtering compensation method, the proposed method 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%, meeting the accuracy requirements for input pressure signals; compared with a single LSTM-based modeling approach, the VMD-LSTM fusion modeling method reduced the overall modeling error to 13%, indicating improved accuracy and robustness. These results show that the SSA-optimized VMD, transfer-function-based low-frequency compensation, and SSA-tuned LSTM fusion modeling jointly provide an effective full-band modeling route, and the proposed framework now offers a robust solution for accurate dynamic characteristic modeling and compensation in shock wave pressure sensor acquisition systems.
- shock wave pressure /
- dynamic compensation /
- variational mode decomposition /
- long short-term memory

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图 1 冲击波压力信号与响应曲线

Figure 1. Shock wave pressure signal and response curve

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图 2 冲击波压力信号的变分模态分解与长短期记忆网络建模算法流程

Figure 2. Flowchart of the modeling algorithm using VMD-LSTM for shock wave pressure signals

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图 3 仿真冲击波压力信号与采集系统动态响应曲线

Figure 3. Simulation of shock wave pressure signal and dynamic response curve of acquisition system

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图 4 优化算法适应度随迭代过程的收敛趋势

Figure 4. Convergence trend of the optimizer’s fitness across iteration steps

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图 5 信号分解后各分量的幅频特性频谱

Figure 5. Amplitude-frequency characteristics spectra of the decomposed signal components

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图 6 信号分解后各分量的时域特性

Figure 6. Time-domain characteristics of the decomposed signal components

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图 7 分解重构处理对冲击波响应信号补偿的效果

Figure 7. Effect of decomposition-reconstruction processing on compensation of shock wave response signals

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图 8 验证集冲击波压力信号的模型建模效果对比

Figure 8. Comparison of model recovery performance for shock wave pressure signals on the validation set

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图 9 实测信号的高频分量幅频特性

Figure 9. The amplitude-frequency characteristics of high-frequency signal components

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图 10 实测冲击波响应信号各分解模态的时域特性

Figure 10. Time-domain characteristics of decomposed components of the shock wave response signal

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图 11 SSA-VMD与反滤波的补偿结果实测对比

Figure 11. Comparison of results between SSA-VMD and inverse filtering

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图 12 基于正弦发生器的传感器低频动态响应信号变化规律

Figure 12. Variation patterns in low-frequency response signals of the sensor tested with a sine generator

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图 13 系统低频动态幅频特性曲线

Figure 13. System low-frequency dynamic amplitude-frequency characteristic curve

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图 14 低频补偿的处理效果对比

Figure 14. Comparative processing effectiveness of low-frequency compensation

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图 15 实测验证集信号重建曲线

Figure 15. Reconstruction curves for measured signals on the validation set

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表 1 动态压力冲击信号及其响应特征参数

Table 1. Dynamic pressure impulse signal and its responses

组别	信号			响应
组别	峰值超压/kPa	正压时间/ms	冲量/(Pa·s)	峰值超压/kPa	正压时间/ms	冲量/(Pa·s)
1	0.90	9.22	2.89	1.07	6.01	2.60
2	0.79	6.97	2.18	0.93	5.13	1.69
3	0.96	9.28	3.28	1.13	6.35	2.37
4	0.83	5.47	2.26	0.99	7.45	1.73

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表 2 信号分解后各分量的相关系数、跳变时长

Table 2. Correlation coefficients and jump durations for decomposed signal components

模态	信号1		信号2
模态	CC	跳变时长/ms	CC	跳变时长/ms
BLIMF1	0.989	6.20	0.991	5.54
BLIMF2	0.098	3.89	0.098	3.55
BLIMF3	0.064	0.10	0.061	0.10
Residual	0.223	1.44	0.192	0.32

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表 3 模型的误差指标对比

Table 3. Comparison of error metrics for the models

算法	训练集			验证集
算法	RMSE/Pa	MAE/Pa	MAPE/%	RMSE/Pa	MAE/Pa	MAPE/%
LSTM	55.545	38.828	7.4441	59.648	41.19	8.4934
SSA-VMD-SSA-LSTM	21.363	12.450	3.12	23.335	13.75	3.4385

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表 4 优化算法对模型性能影响的消融实验分析

Table 4. Impact of optimization algorithms on model performance: an ablation analysis

隐藏单元数目/个	最大训练周期/轮	初始学习率	RMSE/Pa	MAE/Pa	MAPE/%
156	300	0.0067035	23	14	3.439
124	300	0.0067035	29	17	4.657
188	300	0.0067035	31	18	5.164

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表 5 两种神经网络建模的误差性能指标

Table 5. A comparative evaluation of error metrics for the two neural network architectures

算法	隐藏单元数/个	初始学习率	RMSE/kPa	MAE/kPa	MAPE/%	峰值超压/kPa	振荡频率/kHz
SSA-LSTM	66	0.0409	8.667	3.088	30.08	179.77	85.03
SSA-VMD-SSA-LSTM	124	0.091909	3.406	1.015	13.17	207.73	183.82

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