Structural Nonlinear Damage Identification Based on Autoregressive Conditional Heteroskedasticity Conversion Index
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摘要: 为了解决时域非线性损伤的识别问题，基于自回归条件异方差（ARCH）模型的基本理论给出了ARCH模型建模的定阶方法及模型参数估计的极大似然估计法；分析了结构非线性损伤的特性，提出了基于ARCH模型的非线性损伤识别原理；考虑到基于自由度的损伤指标难于判断损伤位置，故提出了一种自回归条件异方差转换指标；在测量误差和模型误差的影响下，使用3层框架结构的非线性损伤试验来验证该损伤指标的有效性. 试验结果表明：非线性间隙距离为0.05 mm和0.10 mm时，损伤位置第3层的自回归条件异方差转换指标值比传统的倒谱测距转化指标值高21.7%以上；当非线性间隙距离为0.20 mm时，第3层的自回归条件异方差转换指标值比倒谱测距转化指标值高3.7%.Abstract: To solve the identification problem of time-domain nonlinear damage, the incorporation of an autoregressive conditional heteroskedasticity (ARCH) model with damage detection was proposed. First, the basic theory of ARCH model was described, and the order estimation and maximum likelihood parameter estimation of ARCH model were proposed. Then, the characteristics of nonlinear damage were analyzed, and a damage detection theory based on ARCH model was presented. Finally, it is difficult for the damage index based on degree of freedom to identify damage locations, an autoregressive conditional heteroskedasticity conversion index (ARCHCI) was proposed. A three-storey frame experiment was used to verify the effectiveness of the ARCHCI, the effect of measurement error and model error was also considered in the experiment. The results show that the ARCHCI value of the damaged third storey is at least 21.7% higher than that of the cepstrum metric conversion index when the nonlinear gap distances are 0.05 mm and 0.10 mm; the ARCHCI value of the third storey is 3.7% higher than that of the cepstrum metric conversion index when the gap distance is 0.20 mm.
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图 4 基准状态下通道3～5的AIC-q的曲线关系
Figure 4. Relationships of AIC-q of Channel 3～5 in basic State
图 6 指标ARCHCI和PCMCI在不同工况下的损伤识别结果
Figure 6. Damage identification results of ARCHCI and PCMCI in different states
表 1 传感器通道的参数设置
Table 1. Parameter of sensor channels
通道名称 传感器 型号 灵敏度 通道 1 测力传感器 PCB 208 C03 SN 22569 2.2 mV/N 通道 2 加速度计 PCB 336C SN 10099 1 000 mV/g 通道 3 加速度计 PCB 336C SN 10120 1 000 mV/g 通道 4 加速度计 PCB 336C SN 9916 1 000 mV/g 通道 5 加速度计 PCB 336C SN 10100 1 000 mV/g 
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表 2 三层框架结构的非线性损伤工况
Table 2. Damaged state of the three-story frame structure
损伤工况 具体描述 工况 1 间隙 0.05 mm 工况 2 间隙 0.10 mm 工况 3 间隙 0.20 mm（弱非线性） 工况 4 间隙 0.10 mm +第 1 层附加质量 1.2 kg 工况 5 间隙 0.20 mm+第 1 层附加
质量 1.2 kg（弱非线性）
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