A Method for Inverse Solution of Structural Interval Parameters based on DIRECT Algorithm
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摘要: 提出一种基于DIRECT算法的结构区间参数反求方法。对于结构不确定性参数反求问题，一般转化为不确定性传播和模型参数优化的双层求解问题。首先，区间模型用来描述响应和待识别结构参数的不确定性，并建立了相应区间参数反求模型。其次，在迭代反求过程中自适应更新径向基函数用来近似原系统模型，并利用DIRECT算法来求解内层不确定性传播问题。最后，通过遗传算法来求解外层的优化模型，从而识别结构不确定性参数的区间。数值算例用来验证了该方法的正确性和有效性，并将该方法应用来反求车辆乘员约束系统中的不确定性参数。Abstract: This paper presents a structural interval parameter inverse solution method based on DIRECT algorithm. The inverse solution of structural interval parameters is generally translated into a two-layer solution of uncertainty analysis and model parameter optimization. First, an interval model is applied to describing the uncertainties of measured responses and identified structural parameters, and the corresponding inverse model of structural interval parameters is established. Second, in the process of iterative inversion, the adaptive updating radial basis function is applied to approximating the original system model, and the DIRECT algorithm is used to analyze the uncertainty of the inner layer. Finally, the optimization model of the outer layer is solved with the genetic algorithm to identify the upper and lower bounds of structural interval parameters. Numerical examples are used to verify the correctness and effectiveness of the method presented in the paper, which is applied to identifying the uncertainty parameters in the vehicle occupant constraint system.
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表 1 不同核函数形式
序号 名称 核函数 形参数 1 高斯函数(Gaussian/GS) e-αr2 α 2 MQ函数(Multiquadric) (r2+R2)q R, q 3 对数路径函数(Logistic) 1/(1+eηr) η 4 立方函数(Cubic) (r2+λ)3 λ 5 IMQ函数(Inverse multiquadric) 
β 
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表 2 计算与测量响应结果对比
方法 计算响应 测量响应 下界误差/% 上界误差/% 本文方法 Y1 [19.973, 49.173] [20.000, 49.000] 0.14 0.35 Y2 [28.021, 57.684] [28.000, 57.500] 0.08 0.32 基于一阶泰勒展开的方法 Y1 [22.250, 51.776] [20.000, 49.000] 11.25 5.67 Y2 [30.588, 59.597] [28.000, 57.500] 9.24 3.65
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表 3 计算与测量响应结果对比
WIC 计算响应 测量响应 下界误差/% 上界误差/% WIC1 [0.510, 0.544] [0.508, 0.542] 0.39 0.37 WIC2 [0.437, 0.472] [0.435, 0.469] 0.46 0.64
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