Bayesian diagnosis and prognosis of delamination damage in the stiffened composite structure
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摘要: 针对复合材料结构疲劳损伤的在线监测和预测问题，提出了一种基于结构健康监测 (Structural health monitoring, SHM) 和贝叶斯理论的结构分层损伤诊断及结构剩余使用寿命预测方法。在贝叶斯概率理论框架下，采用指数模型描述复合材料结构疲劳分层损伤面积的先验演化规律，融合在线SHM数据对结构分层损伤状态，以及损伤面积演化模型的参数进行联合后验估计，即为损伤诊断结果。进一步通过后验估计得到的损伤状态和模型参数预测未来时刻结构分层损伤面积的演化，从而得到当前复合材料结构的剩余使用寿命预测结果。通过有限元仿真的加筋复合材料结构疲劳分层扩展对所提出的方法进行了验证。结果表明，方法可以在线准确地诊断结构分层损伤状态以及预测结构的剩余使用寿命。Abstract: Aiming at the on-line diagnosis and prognosis of composite structures, a method for structural delamination diagnosis and remaining useful life (RUL) prediction was proposed based on structural health monitoring (SHM) and the Bayesian theory. Within the Bayesian probabilistic framework, an exponential model was adopted to describe the prior progression of the fatigue delamination in the composite structure. Then, on-line SHM data were incorporated for diagnosing the delamination state, as well as parameters of the damage area progression model. The posterior estimations denoted the diagnosis result, based on which the progression of the delamination area in the future was predicted, giving the RUL of the current composite structure. The proposed method was validated on the simulated fatigue delamination growth in a stiffened composite structure through the finite element method. The result shows the accuracy of this method for on-line diagnosing the delamination damage, as well as predicting the RUL of the structure.
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图 1 基于贝叶斯理论的分层损伤诊断和预测方法流程图
Figure 1. Flowchart of the Bayesian theory-based delamination diagnosis and prognosis method
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图 2 仿真的碳纤维增强环氧树脂基复合材料加筋板
Figure 2. Simulated stiffened panel made of carbon fiber reinforced epoxy resin matrix composites
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图 3 复合材料加筋板的有限元模型及其初始分层设置
Figure 3. Finite element model of the stiffened composite panel and its initial delamination setting
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图 4 复合材料加筋板算例T25的仿真分层损伤扩展情况
Figure 4. Simulated delamination growth in the case T25 of the stiffened composite panel
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图 5 典型复合材料加筋板仿真算例中损伤变量随循环载荷数的变化
Figure 5. Damage variables during the fatigue delamination growth in typical simulation cases of the stiffened composite panel
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图 6 模拟光纤光栅(FBG)应变传感器布置
Figure 6. Layout of the simulated fiber Bragg grating (FBG) sensor
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图 7 通过模拟FBG传感器获得的复合材料加筋板应变数据示例
Figure 7. Example of the strain data of the stiffened composite panel collected from the simulated FBG sensor
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图 8 通过复合材料加筋板算例T1~T35仿真数据得到的分层损伤面积演化模型参数
Figure 8. Delamination area progression model parameters evaluated with the simulation data from the cases T1-T35 of the stiffened composite panel
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图 9 复合材料加筋板人工神经网络(ANN)观测模型典型应变输出结果
Figure 9. Typical strain output of the artificial neural network (ANN) measurement model for the stiffened composite panel
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图 10 复合材料加筋板算例V1的疲劳分层损伤面积诊断结果
Figure 10. Diagnosis results of the fatigue delamination area in the case V1 of the stiffened composite panel
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图 11 复合材料加筋板算例V1的疲劳分层损伤位置的诊断结果
Figure 11. Diagnosis results of the fatigue delamination location in the case V1 of the stiffened composite panel
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图 12 复合材料加筋板算例V1的分层损伤面积演化模型参数后验估计
Figure 12. Posterior estimations of the delamination area progression model parameters for the case V1 of the stiffened composite panel
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图 13 复合材料加筋板算例V1的分层损伤面积演化预测示意
Figure 13. Illustration of the delamination area progression prediction for the case V1 of the stiffened composite panel
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图 14 复合材料加筋板算例V1的剩余使用寿命(RUL)预测结果
Figure 14. Remaining useful life (RUL) prediction result for the case V1 of the stiffened composite panel
表 1 碳纤维增强环氧树脂基复合材料力学性能参数
Table 1 Mechanical properties of the carbon fiber reinforced epoxy resin matrix composites
Property Value E1/MPa 157486 E2/MPa 9946 v 0.24 G12/MPa 4950 G13/MPa 4950 G23/MPa 3208 Notes: E1 and E2 are Young’s moduli in 1 and 2 direction, respectively; v is Poisson’s ratio; G12, G13 and G23 are shear moduli in 1-2 plane, 1-3 plane and 2-3 plane, respectively. 
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表 2 仿真疲劳分层损伤扩展的虚拟裂纹闭合技术(VCCT)参数
Table 2 Virtual crack closure technique (VCCT) parameters for simulating fatigue delamination growth
Parameter Value GIC/(MPa·mm−1/2) 0.45 GIIC/(MPa·mm−1/2) 1.38 GIIIC/(MPa·mm−1/2) 1.38 C1 1×10−5 C2 1 C3 1×104 C4 5 Notes: GIC is the critical mode I energy release rate; GIIC is the critical mode II energy release rate; GIIIC is the critical mode III energy release rate; C1 and C2 are the material constants determining the onset of delamination growth; C3 and C4 are the material constants determining the fatigue delamination growth rate.
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