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ISIM-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，将改进的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 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.
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图 3 SSI-COV识别子结构模态的稳定图
Figure 3. Stabilization graph for substructure modal identification using SSI-COV
图 5 使用自适应截断奇异值法的稳定图
Figure 5. Stabilization graph for substructure modal identification using adaptive TSVD
图 4 使用固定截断奇异值方法的稳定图
Figure 4. Stabilization graph for substructure modal identification using fixed TSVD
表 1 频率的理论值、识别值及其误差
Table 1. Theoretical and identified frequencies and 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 and 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 0.48 0.90 2 东西向 0.86 −0.88 −1 0.84
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