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摘要:
针对飞机复合材料结构的损伤和修理问题，对某型固定翼飞机机翼、机身等部位的复合材料结构应用和损伤情况进行统计，复合材料在该型飞机的主要应用形式主要有实心整体壁板和夹芯层合板2种，建立随时间变化的结构损伤分布模型，利用统计方法对损伤分布进行拟合和检验。结果表明：结构损伤的数量比例分别为蒙皮分层占75%、长桁分层约占20%、长桁脱黏约占4%；对数正态分布、Weibull分布、Γ分布均可以拟合这3种类型损伤的几何参数分布，其中对数正态分布模型的拟合效果最好；单架飞机的损伤几何参数分布规律不随时间变化，同型号飞机之间的损伤几何参数分布规律也高度相似，可采用统一的函数形式描述。
Abstract:To address the damage and repair of aircraft composite structures, the applications and damage of composite structures in a certain type of aircraft, including the wing, fuselage and other components, were statistically analyzed. Structural damage distribution models with time variable were established, and then the damage distributions of the structures were fitted and tested by statistical methods. The results show that the quantitative proportions of structural damage are 75% for skin delamination, 20% for stringer delamination and 4% for stringer debonding. Lognormal distribution, Weibull distribution and Gamma distribution can all be used to fit the geometric parameter distributions of the three types of structural damage, in which the Lognormal distribution model has the best fitting effect. The distribution of structural damage geometric parameters of one aircraft does not vary with time, and the distributions of geometric parameters of the structural damage between the same type of aircraft are also highly similar, which can be expressed in a unified function form.
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Key words:
- aircraft /
- composite structure /
- structural damage /
- geometric parameters /
- distribution /
- hypothesis testing
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图 6 4种分布模型对3种类型损伤的拟合程度和F检验结果
Figure 6. Goodness-of-fit and F-test results of four distribution models for three types of damage
图 7 蒙皮分层几何参数的实际分布与拟合分布
Figure 7. Geometric parameters of actual skin delamination distribution with fitting distribution
图 8 需要修理的损伤数量比例的实际和拟合结果
Figure 8. Actual and fitting results for quantitative proportion of damage to be repaired
图 9 不同部件的蒙皮分层损伤几何参数
Figure 9. Geometric parameter distribution of skin delamination among different components
图 10 各架飞机在不同飞行时长下的各类损伤数量
Figure 10. Number of various types of damage for each aircraft at different flight time
图 11 飞机B在不同飞行时长下的蒙皮分层几何参数
Figure 11. Geometric parameters of skin delamination of aircraft B at different flight time
图 12 各架飞机在当前飞行时长下的蒙皮分层几何参数
Figure 12. Skin delamination geometric parameters for each aircraft at current flight time
表 1 复合材料在某型飞机主要部件上的应用
Table 1. Application of composite materials on main components of a certain type of aircraft
应用部件 结构形式 材料体系 机翼 T型筋条加筋壁板（上壁板）
L型筋条加筋壁板（下壁板）碳纤维树脂基复合材料 垂尾 工型筋条加筋壁板 碳纤维树脂基复合材料 方向舵 全高度蜂窝夹层板 碳纤维树脂基复合材料（面板）
蜂窝（芯材）平尾 工型筋条加筋壁板 碳纤维树脂基复合材料 机头雷
达罩全高度蜂窝夹层板 玻璃纤维树脂基复合材料（面板）
蜂窝（芯材）进气道
调节板C型筋条加筋壁板 碳纤维树脂基复合材料 
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表 2 蒙皮分层几何参数分布的对数正态分布拟合结果
Table 2. Fitting results of lognormal distribution of geometric parameters of skin delamination
拟合对象 几何参数 ${\sigma _{{t_1}}} $ ${\mu _{{t_1}}} $ ${\sigma _{{t_2}}} $ ${\mu _{{t_2}}} $ 飞机A L 0.685 2.762 0.664 2.699 W 0.551 2.404 0.584 2.414 LW 1.007 5.153 0.996 5.085 L/W 0.948 0.330 0.911 0.271 飞机B L 0.707 2.832 0.607 2.757 W 0.580 2.567 0.504 2.541 LW 1.048 5.423 0.951 5.293 L/W 0.894 0.179 0.829 0.149 飞机C L 0.643 2.936 0.622 2.858 W 0.744 2.551 0.671 2.512 LW 1.057 5.491 1.045 5.346 L/W 0.869 0.382 0.876 0.321 飞机D L 0.532 2.692 0.504 2.631 W 1.073 2.685 0.765 2.527 LW 1.316 5.387 0.960 5.210 L/W 1.088 −0.079 0.884 −0.054 飞机E L 0.588 2.889 0.657 2.794 W 0.477 2.434 0.455 2.462 LW 0.888 5.281 0.816 5.198 L/W 0.740 0.453 0.879 0.336 飞机F L 0.536 2.770 W 0.541 2.380 LW 0.813 5.093 L/W 0.833 0.354 注：空白处为仅检出1处损伤因此不予拟合。
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表 3 不同飞行时长的损伤分布K-S检验（α=0.05）
Table 3. K-S test of difference in damage distribution at different flight time (α=0.05)
损伤类型 几何参数 假设：fi,j(x;θi,j(t1))=fi,j(x;θi,j(t2)) A B C D E F 蒙皮分层 L √ √ √ √ √ — W √ √ √ √ √ LW √ √ √ √ √ L/W √ √ √ √ √ 长桁分层 L √ √ √ √ × * W √ √ √ √ √ √ LW √ √ √ √ × √ L/W √ √ √ √ * * 长桁脱黏 L — — √ — — — W √ LW √ L/W √ 注：√表示接受假设，即认为2个损伤几何参数分布函数一致；*表示在α=0.05时拒绝假设，但在α=0.01时接受假设，可以认为2个分布相近；×表示拒绝假设，即认为2个损伤几何参数分布函数不一致；—表示前一时刻损伤未检出或极少，无法进行假设检验。
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表 4 同一型号不同飞机的损伤几何参数（K-S检验，α=0.05）
Table 4. Damage geometric parameters of different aircraft with the same type (K-S test, α=0.05)
损伤类型 几何参数 假设 A B C D E F 蒙皮分层 L fq(x)=fB(x ) √ 基准 √ √ √ √ W √ √ √ √ * LW * √ √ √ × L/W √ √ √ × √ 长桁分层 L fq(x)=fE(x ) × * × √ 基准 * W √ √ × * × LW √ √ × √ × L/W × × × √ √ 长桁脱粘 L fq(x)=fA(x ) 基准 × √ — √ — W * × √ LW × √ √ L/W × × √ 注：√表示接受假设，即认为2个损伤几何参数分布函数一致；*表示在α=0.05时拒绝假设，但在α=0.01时接受假设，可以认为2个分布相近；×表示拒绝假设，即认为2个损伤几何参数分布函数不一致；—表示当前时刻损伤未检出或极少，无法进行假设检验。
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表 5 单架飞机与机群的损伤几何参数（K-S检验，α=0.05）
Table 5. Damage geometric parameters of single aircraft and fleet (K-S test, α=0.05)
损伤类型 几何参数 假设：fq(x)=ffleet(x) A B C D E F 蒙皮分层 L √ √ √ √ √ √ W √ √ √ √ √ √ LW √ √ √ √ √ * L/W √ * √ * √ √ 长桁分层 L * √ × √ * × W √ √ × * √ × LW √ √ × * √ × L/W √ √ × √ × × 长桁脱粘 L √ × √ — √ — W √ * × √ LW √ √ √ √ L/W √ × * √ 注：√表示接受假设，即认为2个损伤几何参数分布函数一致；*表示在α=0.05时拒绝假设，但在α=0.01时接受假设，可以认为2个分布相近；×表示拒绝假设，即认为2个损伤几何参数分布函数不一致；—表示当前时刻损伤未检出或极少，无法进行假设检验。
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