An Improved Isolated Substructure Method and Its Application in Dynamic Analysis of an Ancient Architecture
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摘要:
从全局结构中获取独立子结构的振动特性非常重要，针对现有基于时间序列的约束子结构法（SIM-TS），在噪声干扰下会因奇异值过小而出现计算误差增大的问题，提出一种改进的SIM-TS方法，以实现更高精度的子结构模态参数识别. 首先，以SIM-TS为基础，引入自适应截断奇异值分解技术，通过动态调整截断阈值来优化分解结果；同时，将ISIM-TS 方法与协方差驱动的随机子空间法（SSI-COV）相结合，构建新的ISIM-TS-SSI-COV子结构模态识别框架；然后，通过一个经典的5自由度数值算例验证方法可行性；最后，将该方法应用于某藏式古建筑子结构的动力特性识别中. 数值算例结果表明：在1%噪声情况下，改进后的方法提高了子结构的识别精度，尤其第二阶频率的识别误差较传统方法降低71.4%；基于环境激励下的响应数据，使用该方法成功识别出子结构的前两阶固有频率，分别为12.18 Hz和13.31 Hz. 本研究结果为后续结构模型修正与损伤识别提供了重要的数据基础.
Abstract:Obtaining the vibrational characteristics of independent substructures from global structures is crucial. The conventional isolated substructure method with time series (SIM-TS) suffers from increased computational errors due to excessively small singular values under noisy conditions. To address this, an improved SIM-TS method named ISIM-TS is proposed, aiming to achieve higher accuracy in substructure modal parameter identification. First, based on SIM-TS, an adaptive truncated singular value decomposition technique was introduced, optimizing the decomposition results by dynamically adjusting the truncation threshold. The ISIM-TS was combined with the covariance-driven stochastic subspace method (SSI-COV) to establish a new substructure modal identification framework, termed ISIM-TS-SSI-COV. Then, the feasibility of the proposed framework was verified via a classical five-degree-of-freedom (5-DOF) numerical simulation. Finally, this method was applied to identify the dynamic characteristics of a substructure in a Tibetan ancient architecture. The numerical results demonstrate that the improved method enhances the identification accuracy of the substructure, particularly reducing the identification error of the second-order frequency by 71.4%, under 1% noise. Furthermore, based on response data acquired under ambient excitation, the proposed method successfully identifies the first two natural frequencies of the substructure as 12.18 Hz and 13.31 Hz, respectively. The results provide an important data foundation for structural model updating and damage identification in the future.
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图 2 SSI-COV识别子结构模态的稳定图
Figure 2. Stabilization graph for substructure modal identification using SSI-COV
图 3 使用固定截断奇异值方法的稳定图
Figure 3. Stabilization graph for substructure modal identification using fixed TSVD
图 4 使用自适应截断奇异值法的稳定图
Figure 4. Stabilization graph for substructure modal identification using adaptive TSVD
表 1 频率的理论值、识别值及其误差
Table 1. Theoretical and identified frequencies as well as their errors
阶数 理论频率/Hz 识别频率/Hz 误差/% 1 121.21 121.21 0 2 209.94 209.87 −0.03 
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表 2 阻尼比的理论值、识别值及其误差
Table 2. Theoretical and identified damping ratios as well as their errors
% 阶数 理论阻尼比 识别阻尼比 误差 1 1.31 1.27 −3.05 2 2.27 2.29 0.88
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表 3 振型系数的误差
Table 3. Errors of vibration mode coefficients
% 阶数 测点 1 误差 测点 2 误差 1 0 −0.23 2 −0.40 0
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表 4 频率及阻尼比的识别结果
Table 4. Identification of frequencies and damping ratios
阶数 方向 频率/Hz 阻尼比/% 1 南北向 12.18 1.64 2 东西向 13.31 0.19
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表 5 振型系数的识别结果
Table 5. Identification of vibration mode coefficients
阶数 方向 测点 1 测点 2 测点 3 测点 4 1 南北向 −0.59 −1.00 0.48 0.90 2 东西向 0.86 −0.88 −1.00 0.84
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