Prediction of blast loads on bridge girders based on PCA-BPNN
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摘要: 人工智能方法是预测爆炸荷载的新手段，但现有方法主要用于预测爆炸冲击波的超压峰值或冲量，而预测反射超压时程的研究不多。针对这一问题，以平面冲击波绕射桥梁主梁为对象，提出了一种基于主成分分析（principal components analysis, PCA）和误差反向传播神经网络（backpropagation neural network, BPNN）的桥梁爆炸冲击波反射超压时程的预测模型。该预测模型利用PCA降维处理时程数据，基于多任务学习的BPNN算法，提出了考虑超压峰值和冲量峰值影响的损失函数，使模型能有效预测不同入射超压下的桥梁冲击波荷载时程。通过分析多任务学习模型、多输入单输出模型和多输入多输出模型等三种BPNN模型，发现多任务学习模型的预测精度最高，而多输入多输出模型难以有效适应当前预测任务需求。采用多任务学习模型预测得到的桥梁表面各测点位置的反射超压时程、超压峰值精度较高，R2分别为0.792和0.987，作用在箱梁上的合力时程和扭矩时程预测值也与数值模拟值较为吻合。同时，该模型在对内插值预测的表现优于外推值预测，但其在预测外推值方面同样展现出了一定的能力。
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关键词:
- 爆炸荷载预测 /
- 反射超压时程 /
- 误差反向传播神经网络 /
- 主成分分析 /
- 多任务学习
Abstract: Facing the challenges of accurate and effective prediction under extreme loads, machine learning has gradually demonstrated its potential to replace traditional methods. Existing approaches primarily focus on predicting the peak overpressure or impulse of explosive shock waves, with limited research on predicting the reflected overpressure time history. Load-time history prediction encompasses not only the peak overpressure but also embraces various multi-dimensional information including duration, waveform, and impulse, thereby offering a more comprehensive depiction of the dynamic temporal and spatial characteristics of shock waves. To address this issue, a prediction model for bridge surface reflected overpressure time history is proposed, targeting a planar shock wave diffracting around a bridge section. This model is based on Principal Component Analysis (PCA) and Backpropagation Neural Network (BPNN) algorithm with multi-task learning. A loss function considering the impact of peak overpressure and maximum impulse is introduced to fully consider the potential correlations between different modes after PCA dimension reduction. This enables the model to effectively predict bridge shock wave load time histories under varying incident overpressure. Through the analysis of three types of BPNN models - multitask learning model, multi-input single-output model, and multi-input multi-output model - it was found that the multitask learning model has the highest prediction accuracy, while the multi-input multi-output model struggles to effectively adapt to the current predictive task requirements. The multitask learning model, used for predicting, achieves high precision in forecasting the time history of reflected overpressure at various measurement points on the bridge surface and the peak overpressure values, with R2 values of 0.792 and 0.987. It also closely matches the simulation values in predicting the time history of combined forces and torque acting on the box girder. Additionally, this model performs better in interpolative value prediction than in extrapolative value prediction, but it also demonstrates a certain capability in predicting extrapolative values. -
图 1 主梁表面测点布置示意图
Figure 1. Schematic diagram of surface measurement point layout on the main beam
图 5 累积方差解释率随主成分数量的变化
Figure 5. Variation of cumulative variance contribution with the number of principal components
图 6 R2分数随主成分数量的变化
Figure 6. Variation of R2 score with the number of principal components
图 11 0.3 MPa入射超压下测点超压和冲量时程
Figure 11. Pressure and impulse time histories at measurement points under 0.3 MPa incident overpressure
图 12 0.8 MPa入射超压下测点超压和冲量时程
Figure 12. Pressure and impulse time histories at measurement points under 0.8 MPa incident overpressure
图 13 1.5 MPa入射超压下测点超压和冲量时程
Figure 13. Pressure and impulse time histories at measurement points under 1.5 MPa incident overpressure
图 14 0.3 MPa入射超压下箱梁合力和扭矩时程曲线
Figure 14. Resultant force and torque time histories of box girder under 0.3 MPa incident overpressure
图 15 0.8 MPa入射超压下箱梁合力和扭矩时程曲线
Figure 15. Resultant force and torque time histories of box girder under 0.8 MPa incident overpressure
图 16 1.5 MPa入射超压下箱梁合力和扭矩时程曲线
Figure 16. Resultant force and torque time histories of box girder under 1.5 MPa incident overpressure
图 17 不同入射超压下模型超压峰值预测拟合图
Figure 17. Model overpressure peak prediction fit graph under different incident overpressures
图 18 超压峰值的数值模拟值与预测值
Figure 18. Peak overpressure numerical simulation values and predictive values
表 1 超压峰值的各模型预测评价指标
Table 1. Evaluation metrics for peak overpressure prediction models
预测模型 RMSE MAE MAPE R2 多输出模型 1.089 0.788 3.105 -0.386 单输出模型 0.152 0.092 0.220 0.976 多任务模型 0.115 0.074 0.180 0.987 
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表 2 冲量峰值的各模型预测评价指标
Table 2. Evaluation metrics for peak impulse prediction models
预测模型 RMSE MAE MAPE R2 多输出模型 3.970 2.822 0.554 -0.403 单输出模型 0.866 0.646 0.133 0.934 多任务模型 0.693 0.542 0.109 0.958
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表 3 超压时程曲线的各模型预测评价指标
Table 3. Evaluation metrics of overpressure time-history prediction models
预测模型 RMSE MAE MAPE R2 多输出模型 0.173 0.068 \ -5.466 单输出模型 0.069 0.015 \ 0.753 多任务模型 0.065 0.014 \ 0.792
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表 4 模型预测误差及经验公式计算误差对比
Table 4. Comparison of Model Prediction Error and Empirical Formula Calculation Error
pi,max=0.1 MPa pi,max=0.5 MPa pi,max=1 MPa 超压时程的R2 最大冲量的MAPE 超压时程的R2 最大冲量的MAPE 超压时程的R2 最大冲量的MAPE PCA-BPNN 0.81 0.124 0.92 0.052 0.46 0.262 经验公式 −0.33 0.410 −2.05 0.573 −1.42 0.396
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