Parameter identification method of time-domain stable discrete rational approximation for frequency response of foundations
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摘要: 离散时间有理近似函数是建立基础动力分析模型的重要方法之一。而有理函数的稳定性和精度决定了动力时程分析的稳定性和精度。目前关于离散时间有理近似函数的研究主要集中于时域分析模型建立,而无法同时保证辨识函数的稳定性、精度及计算效率。基于系统稳定性理论,将有理近似函数看成一阶与二阶系统的组合,并根据其根的稳定条件推导了被辨识参数的稳定界限。在此基础上,利用遗传算法与序列二次规划算法提出了时域稳定的参数识别方法。通过对不同基础频响函数的数值仿真,验证了该方法辨识参数的稳定性与精度。由于该方法限制了参数取值范围,其计算效率也得到了大幅度提高。Abstract: The discrete-time rational approximation function is one of the important methods for establishing dynamic analysis model for foundations. The stability and accuracy of the rational function determine those of dynamic time history analysis. At present, the researches on the discrete-time rational approximation function mainly focus on the establishment of time-domain analysis model, but they cannot guarantee the stability, accuracy and calculation efficiency of the identification function at the same time. Based on the theory of system stability, the rational approximation function is regarded as the combination of first-order and second-order systems, and the stability boundary of identification parameters is derived according to the stability condition of its roots. On this basis, a time-domain stable parameter identification method is proposed by using the genetic algorithm and the sequential quadratic programming algorithm. The stability and accuracy of parameter identification are verified through numerical simulation of different frequency response functions for foundations. Due to the boundary of parameter range, the calculation efficiency is also greatly improved.
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图 10 5×5群桩基础不同阶次拟合精度
Figure 10. Identification accuracy of foundation with 5×5 pile groups in different orders
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图 12 圆形基础不同阶次拟合精度
Figure 12. Identification accuracy of circular foundation in different orders
表 1 3×3群桩基础辨识效率
Table 1 Identification efficiency of foundation with 3×3 pile groups
阶次 3 4 5 6 7 本文方法/s 1.82 2.24 2.24 2.86 2.92 罚函数法/s 3.53 4.67 8.41 16.17 33.67 
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表 2 5×5群桩基础拟合精度与效率
Table 2 Identification accuracy and efficiency of foundation with 5×5 pile groups
阶次 3 4 5 6 7 误差/% 18.80 18.23 13.02 2.03 1.97 时间/s 9.02 8.15 9.81 13.74 16.46
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表 3 圆形基础拟合精度与效率
Table 3 Identification accuracy and efficiency of circular foundation
阶次 3 5 7 9 11 误差/% 16.82 12.29 7.49 6.74 6.62 时间/s 4.46 4.19 5.79 7.12 8.66
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