Prediction Model of Maximum Displacement for RC Slabsunder Blast Load Based on Machine Learning
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摘要: 钢筋混凝土（reinforced concrete，RC）板作为工程结构的主要受力构件，在遭受意外爆炸或恐怖袭击时极易发生破坏，甚至引起结构的整体倒塌，因此，了解和预测混凝土板在爆炸作用下的动力响应，对增强工程结构的抗爆防护能力、减轻生命和财产经济损失具有非常重要的意义。收集整理了国内外文献中普通RC板爆炸试验和基于试验进行参数化分析的数值模拟数据，采用机器学习回归算法中的支持向量机和高斯过程回归两种算法等对近场爆炸作用下RC板的最大位移进行预测；运用改进的偏差-方差分解原理对模型的泛化性能进行分析，同时将机器学习模型与现有的预测方法进行对比；最后，采用置换特征重要性和Sobol全局敏感性分析方法，从局部和整体对模型特征进行解释，增加模型的可靠性。结果表明：支持向量机和高斯过程回归两种机器学习方法的泛化性能都较好，并且高斯过程回归算法的预测效果优于支持向量机算法。对比现有预测方法发现，机器学习方法更优，具有较高的预测精度和计算效率，且得出了不同输入参数对模型输出结果的影响，实现了对输出结果的可解释性，进一步验证了其可靠性。研究结果可为机器学习在爆炸领域的应用提供参考。
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关键词:
- 机器学习 /
- 钢筋混凝土板 /
- 爆炸荷载 /
- Sobol全局敏感性分析 /
- 偏差-方差分解
Abstract: As the main force components of engineering structures, reinforced concrete slab are prone to damage when it is subjected to terrorist attacks or accidental explosions, and even cause the overall collapse of the structure. Therefore, it is of great significance to understand and predict the dynamic response of concrete slab under the action of explosions to enhance the anti-explosion protection ability of engineering structure and reduce the economic loss of life and property. In this paper, the numerical simulation data of ordinary reinforced concrete slab explosion test and parametric analysis based on the test in the literature in China and abroad are collected. The support vector machine and Gaussian process regression algorithms in machine learning regression algorithm are used to predict the maximum displacement of reinforced concrete slab under near-field explosion. The generalization performance of the model is analyzed by using the improved deviation-variance decomposition principle. At the same time, the machine learning model is compared with the existing prediction methods. Finally, the replacement feature importance and Sobol global sensitivity analysis method are used to explain the model from the local and global to increase the reliability of the model. The above results show that the generalization performance of the two machine learning methods is better, but the prediction effect of the Gaussian process regression algorithm is better than that of the support vector machine algorithm. At the same time, compared with the existing prediction methods, it is found that the machine learning method is better, with higher prediction accuracy and computational efficiency. The influence of different input parameters on the output results of the model is obtained, which realizes the interpretability of the output results and further increases its reliability. -
光滑粒子流体动力学(Smoothed Particle Hydrodynamics, SPH)方法中的搜索算法较耗时，即每个时间步都要对领域粒子进行搜索，粒子越多，耗时情况越突出，与有限元法相比，SPH方法的计算效率要低得多。为了解决SPH方法计算效率低的问题，Johnson等[1-2]和Attaway等[3]将有限元与SPH方法相结合，提出了SPH-FEM耦合的算法，即:在小变形区域使用有限元法，大变形区域仍使用SPH方法。该方法不仅提高了计算效率，而且适应性较强。
目前，采用SPH方法对爆炸焊接进行数值模拟的相关报道较少，而且多采用二维SPH方法。Tanaka[4]采用SPH方法对爆炸焊接的斜碰撞过程进行了数值模拟，成功地模拟出射流、波形和涡旋，波长的模拟结果相对实验结果偏大。李晓杰等[5]采用SPH方法及热塑性流体力学模型对爆炸复合板的斜碰撞过程中出现的界面波进行了数值模拟，模拟结果与张登霞等[6-7]实验结果的一致性较好。刘江等[8]利用AUTODYN软件中的SPH方法模拟了爆炸复合的斜碰撞，结合模拟中有效塑性变形、温度及剪切应力呈现的变化规律发现，爆炸复合的结合机理集塑性变形、熔化和扩散为一体。本研究将采用三维SPH方法对双面爆炸焊接过程进行模拟，将其结果与实验及理论结果进行对比，分析SPH-FEM耦合方法对爆炸焊接模拟的有效性。
1. 计算模型及参数选取
1.1 计算模型
以前期45钢/Q235钢双面爆炸焊接实验[9]为基础，考虑到计算效率，利用LS-DYNA建立如图 1及图 2所示的两组双面爆炸焊接SPH-FEM耦合的三维真实计算模型，选用的炸药为乳化炸药(玻璃微球的质量分数为5%)，计算模型中基板和复板的材料、尺寸、间隙(δ)及药厚如表 1所示。起爆方式为点起爆。
表 1 计算模型中材料的相关参数Table 1. Related parameters of materials in calculation modelsCalculationmodel Flyer plate Base plate Gap
δ/mmSize of explosive/(mm×mm×mm) Material Size/(mm×mm×mm) Material Size/(mm×mm×mm) Ⅰ 45 steel 300×150×2 Q235 300×150×16 6 300×150×10 Ⅱ 45 steel 300×150×2 Q235 300×150×16 6 300×150×5 基、复板采用3D Solid 164实体单元，单元边长为0.1 cm；炸药划分为光滑粒子，粒子的大小Δr取为0.1 cm。考虑到模型的对称性，为了提高计算效率，采用1/2模型进行计算。单位制为cm-g-μs。
1.2 材料模型及参数设定
数值计算中乳化炸药采用高能燃烧模型[10-11]及JWL状态方程[12]。JWL状态方程表达式为
p=AJWL(1−ωR1v)e−R1v+BJWL(1−ωR2v)e−R2v+ωE0v (1) 式中：AJWL、BJWL、R1、R2和ω为材料参数；p为爆轰产物压力，GPa；E0为初始比内能，kJ/cm3；v为爆轰气体产物的相对比容，为无量纲量。炸药的相关参数见表 2，其中：ρ为密度，D为炸药爆速。
ρ/(g·cm-3) D/(m·s-1) AJWL/GPa BJWL/GPa R1 R2 ω E0/(kJ·cm-3) 1.12 4 510 326.42 5.808 9 5.80 1.56 0.57 3.323 数值计算中，基、复板均采用Mie-Grüneisen状态方程[14]和Johnson-Cook材料模型[15]。Johnson-Cook材料模型的形式如下
σ=(A+Bεnp)(1+Cln˙ε∗p)(1−T∗m) (2) 式中：εp为有效塑性应变；˙ε∗p=˙εp/˙ε0p为有效塑性应变率，其中˙ε0p为参考应变率；A、B、C、m及n为与材料相关的常数；无量纲温度T*表示为T*=(T-Tr)/(Tm-Tr)，其中Tr为室温, Tm为熔点。45钢选用与Q235钢相同的Johnson-Cook材料模型参数，具体参数如表 3所示。
ρ/(g·cm-3) G/GPa A/GPa B/GPa C n m Tm/K Tr/K 7.83 77 0.792 0.51 0.014 0.26 1.03 1 793 294 2. 模拟结果与分析
2.1 10 mm药厚的模拟结果
2.1.1 碰撞点位移
图 3所示是爆炸焊接结束时复板的竖向位移云图。由图 3可看出，复板的位移大致均为6 mm，表明基、复板已完全复合。为了更直观地观察复板单元位移的变化情况，在复板上选择3个特征单元(431 806、437 359、444 788)，输出其位移-时间曲线，如图 4所示。由图 4可看出，特征单元的竖向位移均略大于间隙(6 mm)，这是由于在爆炸载荷作用下复板有一定程度的减薄率所致。
图 3 10 mm药厚下爆炸焊接结束时复板的z向位移云图Figure 3. z-direction displacement contour of flyer plate with explosive thickness of 10 mm at the end of explosive welding
图 4 10 mm药厚下复板上3个特征单元的z向位移-时间历程Figure 4. z-direction displacement histories of 3 characteristic elements with explosive thickness of 10 mm2.1.2 复板碰撞速度
图 5所示是一对分别取自基板与复板结合界面处的特征单元(基板单元：798 751；复板单元：416 251)，特征单元的选取与前期实验[9]中金相试样的取样位置一致。
图 5 10 mm药厚下的一对特征单元Figure 5. A pair of characteristic elements with explosive thickness of 10 mm图 6所示是这对特征单元的速度-时间曲线。可以看出，基板在碰撞前有一个正的速度峰；该现象的产生如文献[17]所述，是由于爆轰产物不断堆积以及前碰撞点在待复合区产生的振动能所致。复板上所取单元的最大碰撞速度为897 m/s。
图 7所示是在复板结合界面处所选取的3个特征单元(410 476、416 251、420 976)。图 8所示是这3个特征单元的速度-时间曲线。
图 7 10 mm药厚下复板结合界面处的3个特征单元Figure 7. 3 characteristic elements at the bonding interface of flyer plate with explosive thickness of 10 mm
图 8 10 mm药厚下3个特征单元的速度-时间曲线Figure 8. Velocity-time curves of 3 characteristic elements with explosive thickness of 10 mm由图 8可以看出，随着距起爆端距离的增加，复板的碰撞速度增大。由文献[17]的结论可知，该现象是由于基板与复板的碰撞在金属板的待复合区产生了强烈振动引起的。
2.1.3 碰撞点压力分布
图 9所示是在结合界面处选取的3个特征单元(415 576、418 051、419 776)，单元415 576取在复板中心处，与前期实验[7]中取样做金相观察的位置一致。图 10所示是3个特征单元的压力历程。
图 9 10 mm药厚下复板结合界面处的3个特征单元Figure 9. 3 characteristic elements at the bonding interface of flyer plate with explosive thickness of 10 mm
图 10 10 mm药厚下3个特征单元的压力-时间曲线Figure 10. Pressure-time curves of 3 characteristic elements with explosive thickness of 10 mm由图 10可以看出，随着距起爆端距离的增加，复板的碰撞压力增大。由文献[17]的结论可知，该现象是爆轰产物不断堆积以及前碰撞点在金属板待复合区振动能不断增加的共同作用结果。
2.2 5 mm药厚的模拟结果
2.2.1 碰撞点位移
图 11所示是爆炸焊接结束时复板的竖向位移云图。由图 11可看出，复板的位移大致均为6 mm，表明基、复板已完全复合。为了更加直观地观察复板单元位移的变化情况，在复板上选择3个特征单元(432 182、438 034、443 960)，输出其位移-时间曲线，如图 12所示。由图 12可看出，特征单元的竖向位移均略大于6 mm，但较10 mm药厚下的竖向位移小。这是由于5 mm药厚下的爆炸载荷作用比10 mm药厚下小，导致5 mm药厚下的复板减薄率比10 mm药厚下低。
图 11 5 mm药厚下爆炸复合结束时复板的z向位移云图Figure 11. z-displacement contour of flyer plate with explosive thickness of 5 mm at the end of explosive welding
图 12 5 mm药厚下复板上特征单元的z向位移-时间历程Figure 12. z-displacement histories of 3 characteristic elements with explosive thickness of 5 mm2.2.2 复板碰撞速度
图 13所示是一对分别取自基板与复板结合界面处的特征单元(基板单元：799 201；复板单元：416 701)，特征单元的选取与前期实验[9]中金相试样的取样位置一致。
图 13 5 mm药厚下的一对特征单元Figure 13. A pair of characteristic elements with explosive thickness of 5 mm图 14所示是这对特征单元的速度-时间曲线, 可以看出，基板在碰撞前也有一个正的速度峰。复板上所取单元的最大碰撞速度为565 m/s。
图 15所示是在复板结合界面处所选取的3个特征单元(411 976、417 001、423 826)。图 16所示是这3个特征单元的速度-时间曲线。由图 16可以看出，随着距起爆端距离的增加，复板的碰撞速度增大。
图 15 5 mm药厚下复板结合界面处的3个特征单元Figure 15. 3 characteristic elements at the bonding interface of flyer plate with explosive thickness of 5 mm
图 16 5 mm药厚下3个特征单元的速度-时间曲线Figure 16. Velocity-time curves of 3 characteristic elements with explosive thickness of 5 mm2.2.3 碰撞点压力分布
图 17所示是在结合界面处选取的3个特征单元(416 326、418 801、422 776)，单元416 326取在复板中心处，与前期实验[7]中取样做金相观察的位置一致。图 18所示是这3个特征单元的压力历程。由图 18可以看出，随着距起爆端距离的增加，复板的碰撞压力增大。
图 17 5 mm药厚下复板结合界面处的3个特征单元Figure 17. 3 characteristic elements at the bonding interface of flyer plate with explosive thickness of 5 mm
图 18 5 mm药厚下3个特征单元的压力历程Figure 18. Pressure histories of 3 characteristic elements with explosive thickness of 5 mm2.3 分析与讨论
由图 6可以看出，10 mm药厚下复板的最大碰撞速度为897 m/s。由图 14可以看出，5 mm药厚下复板的最大碰撞速度为565 m/s。利用前期工作[18]中提到的3种理论公式(Gurney公式、Aziz公式、Deribas公式)计算了复板的碰撞速度，如表 4、表 5所示，并与数值模拟结果进行了比较。由表 4和表 5可以看出：Gurney公式和Aziz公式的计算结果均存在较大的偏差；而由Deribas公式计算的两组结果与数值模拟结果较接近，误差均未超过5%，且与前期实验结果较吻合，证明了SPH-FEM耦合算法的可靠性。
表 4 10 mm药厚下碰撞速度理论计算结果与数值模拟结果的比较Table 4. Comparison of collision velocity between theoretical calculation and numerical simulation with explosive thickness of 10 mmTheoreticalformula Massfraction Collision velocity/(m·s-1) Error/% Theoretical calculation[18] Simulation Gurney 0.75 1 089 897 -21.0 Aziz 0.75 711 897 20.0 Deribas 0.75 853 897 4.9 表 5 5 mm药厚下碰撞速度理论计算结果与数值模拟结果的比较Table 5. Comparison of collision velocity between theoretical calculation and numerical simulation with explosive thickness of 5 mmTheoreticalformula Massfraction Collision velocity/(m·s-1) Error/% Theoretical calculation[18] Simulation Gurney 0.45 863 565 -52.7 Aziz 0.45 480 565 15.0 Deribas 0.45 576 565 -1.9 由图 10可以看出，10 mm药厚下复板单元415 576处的碰撞压力为17.08 GPa。由图 18可以看出，5 mm药厚下复板单元416 326处的碰撞压力为11.25 GPa。
Ezra等提出的碰撞压力的计算公式为[16]
p=ρ1vs,1vp1+ρ1vs,1ρ2vs, 2 (3) 式中：vs, 1、vs, 2分别表示复板、基板的声速，m·s-1；ρ1、ρ2分别表示复板、基板的密度，g·cm-3；vp表示复板的碰撞速度，m·s-1。
结合表 4和表 5中3种理论公式计算得到的碰撞速度，通过(3)式可得到复板的碰撞压力，表 6及表 7为其理论计算值与数值模拟结果的比较。可见：Gurney公式和Aziz公式的计算结果均存在较大的偏差；而由Deribas公式计算的两组结果与数值模拟结果较接近，误差均未超过5%，说明Deribas公式和SPH-FEM耦合方法对双面爆炸焊接具有较好的指导意义。
表 6 10 mm药厚下碰撞压力理论计算结果与数值模拟结果的比较Table 6. Comparison of collision pressure betweentheoretical calculation and numerical simulationwith explosive thickness of 10 mmTheoreticalformula Collision pressure/GPa Error/% Calculation Simulation Gurney 22.08 17.08 -29.3 Aziz 14.42 17.08 15.6 Deribas 17.30 17.08 -1.3 表 7 5 mm药厚下碰撞压力理论计算结果与数值模拟结果的比较Table 7. Comparison of collision pressure betweentheoretical calculation and numerical simulationwith explosive thickness of 5 mmTheoreticalformula Collision pressure/GPa Error/% Calculation Simulation Gurney 17.50 11.25 -55.6 Aziz 9.73 11.25 13.5 Deribas 11.68 11.25 -3.8 3. 结论
利用LS-DYNA软件和SPH-FEM耦合方法对前期双面爆炸焊接实验进行了三维数值模拟，并将模拟结果与实验及理论计算结果进行了对比，得到如下结论。
(1) 10 mm药厚和5 mm药厚下复板位移均略大于间隙值6 mm，这是由于爆轰载荷作用下复板有一定的减薄率所致。
(2) 10 mm药厚下，复板中部的最大碰撞速度为897 m/s，碰撞压力为17.08 GPa；5 mm药厚下，复板中部的最大碰撞速度为565 m/s，碰撞压力为11.25 GPa。通过与3种理论公式(Gurney公式、Aziz公式、Deribas公式)计算得到的碰撞速度进行比较发现，数值模拟结果与Deribas公式的计算结果较接近，误差较小，且与实验结果较吻合，证明了SPH-FEM耦合方法用于双面爆炸复合模拟的有效性，同时Deribas公式和SPH-FEM耦合方法对双面爆炸复合具有较好的指导意义。
(3) 10 mm药厚和5 mm药厚下复板的碰撞速度及碰撞压力均随着距起爆端距离的增加而增大，该现象是由于爆轰产物的不断堆积和前碰撞点在金属板待复合区振动能的不断增加共同作用的结果。
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图 1 RC板在爆炸作用下位移预测流程
Figure 1. Displacement prediction process of reinforced concrete slab under explosion
图 2 爆炸作用下RC板的布置示意图和变量选取示意图
Figure 2. Layout diagram and variable selection diagram of reinforced concrete slab under blast load
图 3 定量特征和输出变量的统计分布
Figure 3. Statistical distribution of quantitative characteristics and output variables
图 6 不同比例样本训练集的偏差-标准差堆叠图
Figure 6. Bias-standard deviation stack graph of samples with different training set proportions
图 7 不同算法的预测值与试验值对比：(a) GPR，(b) SVR
Figure 7. Comparison of predicted values and experimental values of different algorithms: (a) GPR, (b) SVR
图 8 两种算法的预测响应与残差：(a) GPR，(b) SVR
Figure 8. Prediction response and residual of two algorithms: (a) GPR, (b) SVR
图 9 GPR算法排列特征重要性：(a) 特征重要性排序，(b)特征重要性占比
Figure 9. Permutation feature importance of GPR algorithm: (a) feature importance, (b) proportion of feature importance
图 11 爆炸作用下RC板的最大位移敏感性分析结果
Figure 11. Maximum displacement sensitivity analysis results of reinforced concrete slab under blast load
表 1 数据集数值型特征的统计描述
Table 1. Statistical description of numerical feature of data sets
Variance Feature/Output Mean/Count SD Max Min 1/4 Q 1/2 Q 3/4 Q X1 Length/m 1.66 0.84 6.00 0.75 1.00 1.38 2.00 X2 Width/m 1.56 0.78 3.00 0.75 1.00 1.20 2.00 X3 Thickness/m 0.09 0.04 0.20 0.03 0.05 0.10 0.10 X4 Compressive strength/MPa 37.50 8.39 63.00 20.00 30.00 39.50 40.45 X5 Steel yield strength/MPa 385.13 95.66 600.00 235.00 335.00 400.00 425.00 X6 Reinforcement ratio/% 1.14 0.93 6.12 0.20 0.49 0.84 1.34 X7 Explosion distance/m 0.80 0.84 5.00 0.10 0.40 0.60 0.89 X8 TNT charge mass/kg 3.27 4.38 20.00 0.01 0.36 1.58 3.42 X9 Boundary conditions (B1)58,(B2)79,(B3)5,(B4)45,(B5)29,(B6)14,(B7)13,(B8)2,(B9)20 X10 One-way/Two-way (One-way slab)98/(Two-way slab)162 Y Displacement/mm 34.55 31.59 142.00 1.16 12.23 22.45 43.54 
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表 2 ML方法与现有方法对比
Table 2. Comparison of ML model with existing methods
Case Existing method detail Maximum displecement/mm Error of existing
method/%Error of
ML/%Exp. Existing method ML 1 LS-DYNA-mesh, 5 mm[20] 25.7 25.10 25.27 2.33 1.67 2 LS-DYNA- mesh, 10 mm[20] 25.7 35.20 25.27 36.96 1.67 3 LS-DYNA- mesh, 20 mm[20] 25.7 35.60 25.27 38.52 1.67 4 SDOF[12] 1.8 2.02 2.66 12.22 47.74 5 SDOF[12] 10.5 10.51 10.59 0.10 0.90 6 SDOF[12] 13.9 15.09 12.99 8.56 6.57 7 SDOF[12] 38.9 37.69 37.80 3.11 2.83 8 Medium-structure interaction theory[15] 4.8 4.19 5.51 12.71 14.69 9 Medium-structure interaction theory[15] 8.4 7.37 7.09 12.26 15.60 10 Medium-structure interaction theory[15] 10.2 11.80 8.67 15.69 14.98 11 LS-DYNA-mesh, 5 mm[13] 9.0 8.40 8.15 6.67 9.49 12 LS-DYNA-mesh, 5 mm[13] 23.1 21.30 18.76 7.79 18.79 13 LS-DYNA-mesh, 5 mm[13] 5.1 5.70 9.78 11.76 91.72 14 LS-DYNA-mesh, 5 mm[13] 9.9 10.50 10.34 6.06 4.43
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[1] LEI Y G, YANG B, JIANG X W, et al. Applications of machine learning to machine fault diagnosis: a review and roadmap [J]. Mechanical Systems and Signal Processing, 2020, 138: 106587. doi: 10.1016/j.ymssp.2019.106587 [2] SUN H, BURTON H V, HUANG H L. Machine learning applications for building structural design and performance assessment: state-of-the-art review [J]. Journal of Building Engineering, 2021, 33: 101816. doi: 10.1016/j.jobe.2020.101816 [3] REN Q, DING L C, DAI X D, et al. Prediction of compressive strength of concrete with manufactured sand by ensemble classification and regression tree method [J]. Journal of Materials in Civil Engineering, 2021, 33(7): 04021135. doi: 10.1061/(ASCE)MT.1943-5533.0003741 [4] LI Z, ZHANG J P, LIU T, et al. Using PSO-SVR algorithm to predict asphalt pavement performance [J]. Journal of Performance of Constructed Facilities, 2021, 35(6): 04021094. doi: 10.1061/(ASCE)CF.1943-5509.0001666 [5] YETILMEZSOY K, SIHAG P, KIYAN E, et al. A benchmark comparison and optimization of Gaussian process regression, support vector machines, and M5P tree model in approximation of the lateral confinement coefficient for CFRP-wrapped rectangular/square RC columns [J]. Engineering Structures, 2021, 246: 113106. doi: 10.1016/J.ENGSTRUCT.2021.113106 [6] 赵春风, 何凯城, 卢欣, 等. 双钢板混凝土组合板抗爆性能分析 [J]. 爆炸与冲击, 2021, 41(9): 095102. doi: 10.11883/bzycj-2020-0291ZHAO C F, HE K C, LU X, et al. Analysis on the blast resistance of steel concrete composite slab [J]. Explosion and Shock Waves, 2021, 41(9): 095102. doi: 10.11883/bzycj-2020-0291 [7] ZHAO C F, WANG Q, LU X, et al. Numerical study on dynamic behaviors of NRC slabs in containment dome subjected to close-in blast loading [J]. Thin-Walled Structures, 2019, 135: 269–284. doi: 10.1016/j.tws.2018.11.013 [8] WANG W, ZHAGN D, LU F Y, et al. Experimental study and numerical simulation of the damage mode of a square reinforced concrete slab under close-in explosion [J]. Engineering Failure Analysis, 2013, 27: 41–51. doi: 10.1016/j.engfailanal.2012.07.010 [9] THIAGARAJAN G, KADAMBI A V, ROBERT S, et al. Experimental and finite element analysis of doubly reinforced concrete slabs subjected to blast loads [J]. International Journal of Impact Engineering, 2015, 75: 162–173. doi: 10.1016/j.ijimpeng.2014.07.018 [10] MAAZOUN A, BELKASSEM B, REYMEN B, et al. Blast response of RC slabs with externally bonded reinforcement: experimental and analytical verification [J]. Composite Structures, 2018, 200: 246–257. doi: 10.1016/j.compstruct.2018.05.102 [11] FENG J, ZHOU Y Z, WANG P, et al. Experimental research on blast-resistance of one-way concrete slabs reinforced by BFRP bars under close-in explosion [J]. Engineering Structures, 2017, 150: 550–561. doi: 10.1016/j.engstruct.2017.07.074 [12] WU C, OEHLERS D J, REBENTROST M, et al. Blast testing of ultra-high performance fibre and FRP-retrofitted concrete slabs [J]. Engineering Structures, 2009, 31(9): 2060–2069. doi: 10.1016/j.engstruct.2009.03.020 [13] YAO S J, ZHANG D, CHEN X G, et al. Experimental and numerical study on the dynamic response of RC slabs under blast loading [J]. Engineering Failure Analysis, 2016, 66: 120–129. doi: 10.1016/j.engfailanal.2016.04.027 [14] 高琴. 高强钢筋混凝土板在爆炸载荷下的动态响应研究 [D]. 武汉: 武汉科技大学, 2019.GAO Q. Study on dynamic response of high strength reinforced concrete slab subjected to blast loads [D]. Wuhan: Wuhan University of Science and Technology, 2019. [15] 郭樟根, 曹双寅, 王安宝, 等. 化爆作用下FRP加固RC板的试验研究及动力响应分析 [J]. 工程力学, 2016, 33(3): 120–127. doi: 10.6052/j.issn.1000-4750.2014.07.0658GUO Z G, CAO S Y, WANG A B, et al. Dynamic response analysis and test study on FRP strengthened RC slabs subjected to blast loading [J]. Engineering Mechanics, 2016, 33(3): 120–127. doi: 10.6052/j.issn.1000-4750.2014.07.0658 [16] 孙文彬. 钢筋混凝土板的爆炸荷载试验研究 [J]. 辽宁工程技术大学学报(自然科学版), 2009, 28(2): 217–220. doi: 10.3969/j.issn.1008-0562.2009.02.016SUN W B. Experimental studies on reinforced concrete (RC) slabs subjected to blast loads [J]. Journal of Liaoning Technical University (Natural Science), 2009, 28(2): 217–220. doi: 10.3969/j.issn.1008-0562.2009.02.016 [17] 汪维. 钢筋混凝土构件在爆炸载荷作用下的毁伤效应及评估方法研究 [D]. 长沙: 国防科学技术大学, 2012.WANG W. Study on damage effects and assessments method of reinforced concrete structural members under blast loading [D]. Changsha: National University of Defense Technology, 2012. [18] 汪维, 刘光昆, 汪琴, 等. 四边固支方形钢筋混凝土板抗爆试验研究 [J]. 兵工学报, 2018, 39(Suppl 1): 108–113.WANG W, LIU G K, WANG Q, et al. Experimental research on four-sides fixed square slabs under blast loading [J]. Acta Armamentarii, 2018, 39(Suppl 1): 108–113. [19] 汪维, 张舵, 卢芳云, 等. 方形钢筋混凝土板的近场抗爆性能 [J]. 爆炸与冲击, 2012, 32(3): 251–258. doi: 10.11883/1001-1455(2012)03-0251-08WANG W, ZHANG D, LU F Y, et al. Anti-explosion performances of square reinforced concrete slabs under close-in explosions [J]. Explosion and Shock Waves, 2012, 32(3): 251–258. doi: 10.11883/1001-1455(2012)03-0251-08 [20] 王强. 爆炸作用下钢筋混凝土板与穹顶60°配筋安全壳动态响应研究 [D]. 合肥: 合肥工业大学, 2019.WANG Q. Study on dynamic response of reinforced concrete slab and containment dome with 60° configuration under blast load [D]. Hefei: Hefei University of Technology, 2019. [21] LIN X S, ZHANG Y X, HAZELL P J. Modelling the response of reinforced concrete panels under blast loading [J]. Materials & Design, 2014, 56: 620–628. doi: 10.1016/j.matdes.2013.11.069 [22] SYED Z I, RAMAN S N, NGO T, et al. The failure behaviour of reinforced concrete panels under far-field and near-field blast effects [J]. Structures, 2018, 14: 220–229. doi: 10.1016/j.istruc.2018.03.009 [23] 何福康. 钢筋混凝土板静力极限分析及非线性爆炸响应 [D]. 广州: 华南理工大学, 2018.HE F K. Static limit analysis and nonlinear explosion response of reinforced concrete slabs [D]. Guangzhou: South China University of Technology, 2018. [24] 贾昊凯. 爆炸荷载作用下钢筋混凝土柱和板动力响应及损伤评定的数值模拟 [D]. 太原: 太原理工大学, 2012.JIA H K. Numerical simulation of the dynamic response and damage assessment for RC columns and slabs subject to blast loads [D]. Taiyuan: Taiyuan University of Technology, 2012. [25] 贾敬尧. 近距爆炸荷载作用下钢筋混凝土板的动力响应及损伤评估 [D]. 西安: 西安建筑科技大学, 2019.JIA J Y. Dynamic response and damage assessment of reinforced concrete slabs under close-in blast loading [D]. Xi’an: Xi’an University of Architecture and Technology, 2019. [26] 李天华. 爆炸荷载下钢筋混凝土板的动态响应及损伤评估 [D]. 西安: 长安大学, 2012.LI T H. Dynamic response and damage assessment of reinforced concrete slabs subjected to blast loading [D]. Xi’an: Chang’an University, 2012. [27] 李天华, 赵均海, 魏雪英, 等. 爆炸荷载下钢筋混凝土板的动力响应及参数分析 [J]. 建筑结构, 2012, 42(Suppl 1): 786–790. doi: 10.19701/j.jzjg.2012.s1.194LI T H, ZHAO J H, WEI X Y, et al. Dynamic response and parametric analysis on reinforced concrete slabs under blast loadings [J]. Building Structure, 2012, 42(Suppl 1): 786–790. doi: 10.19701/j.jzjg.2012.s1.194 [28] 史祥生. 爆炸荷载作用下钢筋混凝土板的损伤破坏分析 [D]. 天津: 天津大学, 2008.SHI X S. Damage assessment of RC slabs subjected to blast load [D]. Tianjin: Tianjin University, 2008. [29] 赵春风, 王强, 王静峰, 等. 近场爆炸作用下核电厂安全壳穹顶钢筋混凝土板的抗爆性能 [J]. 高压物理学报, 2019, 33(2): 025101. doi: 10.11858/gywlxb.20180598ZHAO C F, WANG Q, WANG J F, et al. Blast resistance of containment dome reinforced concrete slab in NPP under close-in explosion [J]. Chinese Journal of High Pressure Physics, 2019, 33(2): 025101. doi: 10.11858/gywlxb.20180598 [30] VAPNIK V N. The nature of statistical learning theory [M]. New York: Springer, 1995. [31] JALAL M, ARABALI P, GRASLEY Z, et al. Behavior assessment, regression analysis and support vector machine (SVM) modeling of waste tire rubberized concrete [J]. Journal of Cleaner Production, 2020, 273(12): 122960. doi: 10.1016/j.jclepro.2020.122960 [32] CHANG C C, LIN C J. LIBSVM: a library for support vector machines [J]. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 27. doi: 10.1145/1961189.1961199 [33] 李启明, 喻泽成, 余波, 等. 钢筋混凝土柱地震破坏模式判别的两阶段支持向量机方法 [J]. 工程力学, 2022, 39(2): 148–158. doi: 10.6052/j.issn.1000-4750.2020.12.0937LI Q M, YU Z C, YU B, et al. Two-stage support vector machine method for failure mode classification of reinforcedconcrete columns [J]. Engineering Mechanics, 2022, 39(2): 148–158. doi: 10.6052/j.issn.1000-4750.2020.12.0937 [34] LI A N, SHAN S G, GAO W. Coupled bias-variance tradeoff for cross-pose face recognition [J]. IEEE Transactions on Image Processing, 2012, 21(1): 305–315. doi: 10.1109/TIP.2011.2160957 [35] 冯德成, 吴刚. 混凝土结构基本性能的可解释机器学习建模方法 [J]. 建筑结构学报, 2022, 43(4): 228–238. doi: 10.14006/j.jzjgxb.2020.0491FENG D C, WU G. Interpretable machine learning-based modeling approach for fundamental properties of concrete structures [J]. Journal of Building Structures, 2022, 43(4): 228–238. doi: 10.14006/j.jzjgxb.2020.0491 [36] ALMUSTAFA M K, NEHDI M L. Machine learning model for predicting structural response of RC slabs exposed to blast loading [J]. Engineering Structures, 2020, 221: 111109. doi: 10.1016/j.engstruct.2020.111109 [37] 李美水, 杨晓华. 基于Sobol方法的SWMM模型参数全局敏感性分析 [J]. 中国给水排水, 2020, 36(17): 95–102. doi: 10.19853/j.zgjsps.1000-4602.2020.17.017LI M S, YANG X H. Global sensitivity analysis of SWMM parameters based on sobol method [J]. China Water & Wastewater, 2020, 36(17): 95–102. doi: 10.19853/j.zgjsps.1000-4602.2020.17.017 -
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