基于响应功率谱传递比的桥梁结构工作模态参数识别方法

为实现基于振动传递比函数的工作模态分析方法能够在任一荷载工况下识别结构模态参数，引入参考响应思路，构建响应功率谱传递比（Power Spectral Density Transmissibility，PSDT）函数。首先利用比例函数的极限定理，揭示PSDT在系统极点处的重要特性，进而根据这一特性建立PSDT驱动的峰值法；同时为解决传统传递比方法无法识别结构阻尼的问题，建立基于PSDT驱动的最小二乘复频域法（LSCF），通过参数化拟合思路识别频率、振型和阻尼比，并运用稳定图辅助剔除虚假模态。通过10层剪切型框架结构数值算例，对比研究外部激励性质对PSDT法及传统频域法（峰值法、频域分解法）识别结果的影响。最后，运用PSDT法对环境激励下的人行桥进行工作模态分析，并与传统响应传递比方法及随机子空间法（SSI）结果进行对比。研究结果表明：在同一工况下不同参考响应的PSDT函数在系统极点与外部激励性质无关，且等价于振型比值；PSDT法相比于传统频域法对外部激励具有更为良好的鲁棒性，能够降低识别谐波激励引起的虚假模态的风险；不同于传统响应传递比方法，在任一工况下基于PSDT法能够识别人行桥的包括阻尼比在内的工作模态参数，并产生更为清晰的峰值和稳定图，具有更好的可操作性；该方法识别结果与SSI结果吻合较好，验证了其在任一荷载工况下分析实际桥梁结构工作模态特性的可行性。

Operational Modal Analysis for Bridge Engineering Based on Power Spectrum Density Transmissibility

To solve the problem of requiring response transmissibility functions corresponding to multiple load conditions, power spectral density transmissibility (PSDT) was constructed by introducing the transferring output to obtain modal properties of bridge structures under ambient excitations. Further, the unique feature of PSDT approaching the system poles was revealed by a limit theorem. Based on this feature, the rationale for a PSDT-driven peak-picking method was elucidated. In addition, to overcome the shortcoming of the inability to identify the damping ratio involved in conventional transmissibility-based operational modal analysis (TOMA), PSDT was combined with a least-squares complex frequency-domain estimator to identify the modal variables by fitting a parametric model. Further, a stabilization diagram was constructed to separate the stable system poles. A ten-story plane frame subjected to harmonic excitation was adopted to investigate the robustness of the PSDT method, as well as the conventional frequency-domain approaches, to the nature of excitations. Finally, ambient vibration test data from a pedestrian bridge was employed to study the applicability of PSDT-based strategies to real bridges. The extracted results from the PSDT methods were compared with those identified by conventional TOMA and stochastic subspace identification (SSI). The results show that PSDTs with various transferring outputs are equal to the ratio of mode shapes. In contrast to conventional frequency-domain OMA approaches, PSDT is less sensitive to harmonic excitation and can thus reduce the risk of identifying the fault modes caused by harmonic excitation. Compared with the TOMA method, PSDT can identify the damping ratio of the footbridge and produce clear peaks as well as a stabilization diagram. Moreover, the obtained results using PSDT agree well with those using SSI, which validates the capability of PSDT to capture the modal parameters of real bridges under a single operational loading condition.