System identification of a 2-DOF wing section with freeplay nonlinearity
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摘要:
在实际包含间隙非线性的复杂结构中，由于间隙不易或无法测量，难以建立准确描述结构特性的动力学模型；即使间隙得到准确测量，也难以获得结构的标称线性系统的模态参数。为此，利用条件逆谱法和时域非线性子空间法，通过非线性系统辨识获得间隙非线性系数，同时获得非线性结构的标称线性系统的频响函数。以一个包含间隙非线性的二元翼段为例，通过数值方法模拟该二元翼段的地面振动试验，利用条件逆谱法和时域非线性子空间法开展该结构的非线性系统辨识。结果表明：两种方法均可准确地辨识结构的标称线性系统，条件逆谱法利用光滑函数近似，时域非线性子空间法利用多个分段线性函数重构，辨识得到间隙非线性系数。
Abstract:On one hand, it is difficult to establish an accurate dynamical model description reflecting structural characteristics of a real-world complex structure with freeplay nonlinearity because of the inconvenience or impossibility of measuring the gap. On the other hand, even though the freeplay has been estimated, the modal parameters of the nominal linear system of the structure are still out of reach. Therefore, in this paper, nonlinear system identification was performed by the usage of conditioned reverse path method and time-domain nonlinear subspace identification method to obtain the parameters of freeplay nonlinearity as well as the frequency response function of the nominal linear system of the nonlinear structure. A 2-DOF wing section was chosen as a demonstration, on which the numerical experiments of ground vibration tests were performed. Nonlinear system identification was carried out by applying the conditioned reverse path method and time-domain nonlinear subspace identification method. Consequently, the nominal linear system can be accurately estimated by both methods, and the identified parameters of freeplay nonlinearity can also be obtained by smooth function approximation in conditioned reverse path method and by reconstruction via a series of piecewise linear functions in time-domain nonlinear subspace identification method.
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图 9 低激励水平与高激励水平的频响函数曲线对比
Figure 9. Comparison of FRFs under low excitation level and high excitation level
图 14 区间[0, max(α)]内的非线性系数分布
Figure 14. Nonlinear parameter distribution in the interval [0, max(α)]
图 15 区间[0.008, 0.012]rad内的非线性系数分布
Figure 15. Nonlinear parameter distribution in the interval [0.008, 0.012]rad
图 16 辨识得到的非线性二元翼段ULS的频响函数曲线
Figure 16. Identified FRF of ULS of nonlinear 2-DOF wing section
图 17 时域非线性子空间法辨识的非线性恢复力曲线
Figure 17. Nonlinear restoring force identified by TNSI method
图 18 辨识得到的非线性二元翼段OLS的频响函数曲线
Figure 18. Identified FRF of OLS of nonlinear 2-DOF wing section
表 1 二元翼段结构基本参数
Table 1. Main structural parameters of 2-DOF wing section
参数 数值 半弦长b/m 0.1 刚心与中心相对距离a -0.2 质量m/kg 2.9 重心与刚心距离xa/m 0.01 静矩Sα/(kg·m) 0.029 转动惯量Iα/(kg·m2) 0.024 
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表 2 激励水平与对应的随机力RMS值
Table 2. Excitation levels and corresponding RMS value of random excitation force
激励水平 随机力RMS/N 1 0.004 8 2 0.011 8 3 0.022 6 4 0.048 6 5 0.069 0 6 0.114 4 7 0.182 5 8 0.230 8 9 0.486 0 10 0.729 6 11 1.100 0 12 1.997 4 13 2.215 9 14 2.767 9 15 3.722 0 16 4.970 4 17 7.373 1 18 11.610 5 19 25.501 0
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表 3 不同激励水平下辨识的非线性系数
Table 3. Identified nonlinear coefficient under different excitation levels
随机力RMS/(N·m) 非线性系数 0.048 6 -0.250 8 0.069 0 -0.253 8 0.230 8 -0.250 5 0.486 0 -0.244 0
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表 4 条件逆谱法和时域非线性子空间法属性对比
Table 4. Property comparison between CRP and TNSI
属性 条件逆谱法 时域非线性子空间法 域 频域 时域 多自由度 是 是 多种非线性 是 是 迭代计算 是 否 数据 稳态数据 任意数据 数据前处理 离散傅里叶变换 否 间隙描述 函数近似 多间隙重构 稳态图 是 是 计算量 低 中等 ULS辨识精度 高 高 OLS辨识精度 高 高 间隙辨识精度 间隙边界：一般
刚度辨识：高间隙边界：高
刚度辨识：高
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