Multi-Degree-of-Freedom Equipment Shock Response Model Based on Deep Learning
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摘要: 针对舰艇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, 而本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, 实现了对舰艇结构中关键点冲击响应谱的高效、准确计算。这一方法填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 address the challenge of analyzing the response of multi-degree-of-freedom naval equipment under explosive shock loads, this study proposes a deep learning-based shock response prediction model. Traditional single-degree-of-freedom models cannot effectively analyze the complex shock responses of multi-degree-of-freedom systems. Leveraging deep learning technology, particularly the data feature extraction and nonlinear modeling capabilities of neural networks, this model learns the relationship between the shock spectrum and input shock loads from numerical simulation data, achieving efficient and accurate calculation of shock response spectra at critical points within naval structures. This approach fills the gaps of existing models in handling multi-degree-of-freedom equipment and meets the demand for rapid, accurate analysis of complex system shock responses. Experimental results demonstrate 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 overcoming the limitations of traditional models in multi-degree-of-freedom system analysis.
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图 2 潜艇上典型多自由度系统组成
Figure 2. Composition of a typical multi-degree-of-freedom system on a submarine
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 (a) 对质量块1进行预测的RMSE与RE; (b) 对质量块2进行预测的RMSE与RE; (c) 对总体结构进行预测的RMSE与RE
Figure 5. (a) RMSE and RE for the prediction of mass block 1; (b) RMSE and RE for the prediction of mass block 1; (c) RMSE and RE for the prediction of overall structure
表 1 数值仿真工况
Table 1. Table of numerical simulation conditions
序号 水深(m) 爆距(m) 装药(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 模型数据集信息
Table 2. Model dataset information
模型输入/输出数据信息 数据集划分信息 输入 冲击载荷时域加速度 训练集 95% 测试集 5% 输出 感兴趣点冲击响应谱 训练集 95% 测试集 5%
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表 3 多工况下平均RMSE及平均RE
Table 3. Average RMSE and average RE under multiple operating conditions
工况 感兴趣点 平均RMSE 平均RE (%) 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 4 4种标准化方法计算公式
Table 4. 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 5 4种标准化方法模型的平均RE与最大RE
Table 5. Comparison of traditional shock spectrum calculation methods
标准化方法 平均RE(%) 最大RE(%) 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 6 多自由度模型感兴趣点冲击响应谱计算效率对比
Table 6. Comparison of calculation efficiency for shock response spectra at key points in multi-degree-of-freedom models
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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