Analysis of Multi-Degree-of-Freedom Equipment Shock Response Based on Deep Learning
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摘要: 针对船舶多自由度设备在爆炸冲击载荷下的响应分析难题, 文中提出了一种基于深度学习的冲击响应预测模型。传统单自由度模型无法高效分析多自由度系统的复杂冲击响应, 而该模型通过深度学习技术, 特别是利用神经网络的数据特征提取和非线性建模能力, 从数值仿真数据中学习冲击谱与输入冲击载荷的关联, 实现了对船舶结构中关键点冲击响应谱的高效准确计算。该方法弥补了现有模型在处理多自由度设备时的不足, 满足了对复杂系统冲击响应快速准确分析的需求。实验结果表明, 该模型能准确预测多自由度设备的冲击响应谱, 与仿真数据的相对误差控制在8%以内, 有效解决了传统模型在多自由度系统分析中的局限性。Abstract: To analyze the response of multi-degree-of-freedom ship equipment under explosive shock loads, this study proposed a deep learning-based shock response prediction model. Traditional single-degree-of-freedom models struggle to efficiently analyze the complex shock responses of multi-degree-of-freedom systems. By leveraging deep learning technology, especially the data feature extraction and nonlinear modeling capabilities of neural networks, this model learned the correlation between shock spectra and input shock loads from numerical simulation data, enabling efficient and accurate calculation of shock response spectra at critical points in ship structures. This approach overcame the limitations of existing models in handling multi-degree-of-freedom equipment and met the demand for rapid and precise analysis of complex system shock responses. Experimental results show that the model can accurately predict the shock response spectra of multi-degree-of-freedom equipment, with a relative error of less than 8% compared to simulation data, effectively resolving the bottlenecks of traditional models in multi-degree-of-freedom system analysis.
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Key words:
- explosive shock /
- shock response /
- deep learning /
- multi-degree-of-freedom equipment
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图 2 船舶上典型多自由度系统组成
Figure 2. Composition of a typical multi-degree-of-freedom system on a ship
图 4 多自由度设备冲击响应预测模型架构
Figure 4. Architecture of the multi-degree-of-freedom equipment shock response prediction model
图 5 多自由度系统模型预测误差分析
Figure 5. Error analysis of model predictions for multi-degree of-freedom system
表 1 数值仿真工况
Table 1. Working conditions of numerical simulation
序号 水深/m 爆距/m 装药量/kg 方位 1 100 7 295 侧前方 2 100 7 295 正下方 3 100 7 295 侧后方 4 100 7 45 正下方 
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表 2 多工况下RMSE均值和RE均值
Table 2. Average RMSE and average RE under multiple operating conditions
工况 感兴趣点 RMSE均值 RE均值/% 1 质量块1 0.126 6.1 质量块2 0.115 6.9 总体结构 0.093 6.3 2 质量块1 0.134 6.6 质量块2 0.151 6.8 总体结构 0.096 7.2 3 质量块1 0.122 7.6 质量块2 0.148 6.4 总体结构 0.121 7.5 4 质量块1 0.139 7.2 质量块2 0.094 7.8 总体结构 0.112 6.7
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表 3 4种标准化方法计算公式
Table 3. Formulas for four standardization methods
标准化方法 计算公式 L1范数标准化 $ {y_i} = \dfrac{{{x_i}}}{{{{\left\| {{x_i}} \right\|}_p}}} $ 偏差标准化 $ {y_i} = \dfrac{{{x_i} - {x_{\min }}}}{{{x_{\max }} - {x_{\min }}}} $ 标准差标准化 $ {y_i} = \dfrac{{{x_i} - \mu }}{\sigma } $ 非线性标准化 $ {y_i} = \dfrac{1}{{1 + {{\mathrm{e}}^{ - {x_i}}}}} $
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表 4 4种标准化方法模型的RE均值和最大值
Table 4. Comparison of average RE and maximum RE among four standardization method models
标准化方法 RE均值/% RE最大值/% L1范数标准化 7.8 8.7 偏差标准化 7.1 8.8 标准差标准化 10.5 13.7 非线性标准化 13.1 14.5
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表 5 感兴趣点冲击响应谱计算效率对比
Table 5. Comparison of calculation efficiency for shock response spectra at key points
方法 感兴趣点数 运行时间/s 多自由度模型 3 5 5 8 传统方法 3 360 5 600
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