An Unconstrained Structural Dynamic Load Reconstruction Method Based on the Sparse Bayesian Learning Algorithm
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摘要: 为快速准确重构含有未知初始条件的无约束结构外激励，提出了一种基于稀疏Bayes学习算法的荷载重构方法.结合函数拟合的思想建立控制方程，以噪声服从Gauss分布为先验，在Bayes模型中使用快速算法，稀疏重构未知荷载.为合理表达分段拟合中的初始条件，提出了改进的分段拟合手段，以上一分段末状态响应作为可能初始条件，并辅以低阶振型作为初始位移和初始速度的补充.算例以简化运载火箭模型为研究对象，考虑不同等级噪声和不同初始条件表达形式的影响，验证方法的精度和效率.
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关键词:
- 函数拟合 /
- 稀疏Bayes学习算法 /
- 改进分段拟合 /
- 荷载重构
Abstract: For rapid and exact reconstruction of dynamic loads on unconstrained structures with unknown initial conditions, a dynamic load reconstruction method was proposed based on the sparse Bayesian learning algorithm. With the idea of the function fitting technique, the control equations were built. The noise was assumed to obey the Gaussian distribution, and the fast algorithm was used in the sparse Bayesian learning model. An improved piecewise fitting method was formulated to rationally express the initial conditions in the piecewise fitting, the end state response of the previous segment was used as the possible initial condition, and the low-order vibration modes were applied as the supplement to the initial displacements and initial velocities. The numerical simulations of simplified launch vehicle models prove the accuracy and efficiency of the proposed method, under the effects of different noise levels and different expressions of initial conditions.1) 我刊编委张亚辉来稿 -
图 2 所提方法荷载重构流程图
Figure 2. The flowchart of the proposed method for load reconstruction
图 5 本文所提方法不同噪声水平下荷载重构结果
Figure 5. Reconstruction results with the proposed method under different noise levels
图 6 15%噪声水平下不同方法的荷载重构结果
Figure 6. Comparison of reconstruction results between different methods with a 15% noise level
图 7 仅使用低阶振型表达初始条件
Figure 7. Only low-order modes used to express the initial conditions
表 1 重构精度与计算时间
Table 1. Reconstruction accuracies and computation times
proposed ref.[24] noise levels 5% 10% 15% 5% 10% 15% f1 1.87% 3.55% 10.08% 3.17% 10.71% 10.98% f2 0.37% 0.67% 1.82% 0.01% 0.20% 0.35% f3 0.99% 1.67% 2.82% 0.65% 6.34% 9.39% computing time 0.68 s 617.02 s 
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表 2 3种重构方式识别结果对比
Table 2. Comparison of identification results of 3 reconstruction methods
force relative error δ/% computing time t/s only low-order modes expressed
initial conditionf1 58.48 622.91 f2 139.66 f3 105.32 modified piecewise fitting f1 2.56 619.23 f2 4.77 f3 6.03 no segmentation f1 11.58 1 203.26 f2 23.57 f3 16.72
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