基于盲源分离技术的工程结构模态参数识别方法研究
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摘要
随着我国城市化进程的加快,土木建筑工程得到了长足的发展。与此同时,一些已建及在建工程结构在设计、施工、老化等因素影响下,出现了不同程度的损伤及破坏,给人们的生命财产安全造成了严重的威胁。因此,如何快速、准确地判别工程结构当前状态下的健康状况,已成为工程界关注的热点及难点课题。本文在对传统模态参数识别方法的总结分析基础上,对基于系统输出的模态参数识别方法进行了系统、深入的研究,将盲信号处理领域的盲源分离技术引入工程结构的模态参数识别当中,提出一种非参数化的时域识别方法——基于盲源分离技术的模态参数识别方法。完成的主要工作及成果如下：
1.基于复模态理论,应用Hilbert变换增加虚拟测点,对原振动系统进行有效的扩阶,提出了具有较低计算量的基于盲源分离的模态参数识别改进方法(AMUSE-C)。不仅使基于盲源分离的模态参数识别方法可以辨识一般阻尼系统的模态参数,提高了对密集模态的辨识能力,而且可以通过对振动系统复频率的提取,直接识别模态频率与阻尼比,在节约计算成本的同时,使得盲源分离本身具备的高精度、强鲁棒性延续到模态频率与阻尼比的识别上,为盲源分离技术在工程结构模态参数识别领域的应用提供了全新的思路与方法。
2.在本文提出的基于盲源分离的模态参数识别改进方法AMUSE-C的基础上,引入联合时滞协方差矩阵,建立了具有较高稳定性的基于盲源分离的模态参数识别改进方法(SOBI-C)。克服了由于单一时滞协方差矩阵的非正定性给识别算法带来的不稳定性,提高了识别算法的鲁棒性,从而增强了基于盲源分离的模态参数识别方法的实用性。
3.通过对建立的改进识别方法SOBI-C的优化,采取对两组联合时滞协方差矩阵进行广义特征值分解,将主要计算压力从对众多单一时滞协方差矩阵的联合近似对角化转移到计算两组联合时滞协方差矩阵上,有效的降低了计算分析的成本,提高了实际应用的价值与意义。对工程实例的分析,表明本文提出的识别方法的计算结果与实测值吻合较好。
With the rapid progress of the city construction, the civil construction engineering has been developed significantly. Simultaneously, some damage occur in the built and building engineering structure due to the effect of design, construction and aging, which leads to a serious threat to the security of people's life and property. Thus, how to identify the health condition of the current engineering structure quickly and accurately has been the difficult subject in engineering field. Based on the summary and analysis of classical modal parameter identification method, this thesis deeply studied the output only modal parameter identification method. This thesis introduced the blind source separation technique of blind signal process field into the modal parameter identification of the engineering structure, proposed an non-parametric time domain method----the modal parameter identification method based on blind source separation technique. The following work and results had been achieved:
1. Based on the complex modal theory, it used Hilbert transformation enrich the virtual measuring points, the original vibration system had been expanded effectively. Proposed the improved modal parameter identification method (AMUSE-C) which has less computation task. It leaded to the result that the modal parameter identification method based on the BSS can not only identify the modal parameter of general damping system, but also improve the capacity of identifying the close modes. Furthermore, it can identify the modal frequency and damping ratios directly through extracting the complex frequencies of vibration system. This approach made the computation cost less expensive and the robustness to noise of BSS was extended to the identification of modal frequencies and damping ratios, from which it leaded a totally new way in the application of the BSS in engineering structural modal parameter identification field.
2. Based on the improved modal parameter identification method AMUUSE-C developed in this thesis, it introduced the joint time-delay covariance matrix, established the improved modal parameter identification method (SOBI-C) which has high stability, overcame the instability of the identification algorithms caused from the non-positive of the single covariance matrix and improved the robust of the identification algorithms, from which the modal parameters identification based on the BSS could be applied more generally.
3. Through the optimal of establishing the improved method SOBI-C, The extended method SOBI-C decomposed the eigenvalue of the joint time-delay covariance matrix so that the main computation cost pressure was transferred from the joint approximate diagonalization of many time-delay covariance matrices to compute the two groups of the joint time-delay covariance matrix. It effectively decreased the cost of computational analysis, which was more valuable and meaningful. The analysis of engineering application showed that the result of the proposed method in this thesis converged to the actual measured value.
1.基于复模态理论,应用Hilbert变换增加虚拟测点,对原振动系统进行有效的扩阶,提出了具有较低计算量的基于盲源分离的模态参数识别改进方法(AMUSE-C)。不仅使基于盲源分离的模态参数识别方法可以辨识一般阻尼系统的模态参数,提高了对密集模态的辨识能力,而且可以通过对振动系统复频率的提取,直接识别模态频率与阻尼比,在节约计算成本的同时,使得盲源分离本身具备的高精度、强鲁棒性延续到模态频率与阻尼比的识别上,为盲源分离技术在工程结构模态参数识别领域的应用提供了全新的思路与方法。
2.在本文提出的基于盲源分离的模态参数识别改进方法AMUSE-C的基础上,引入联合时滞协方差矩阵,建立了具有较高稳定性的基于盲源分离的模态参数识别改进方法(SOBI-C)。克服了由于单一时滞协方差矩阵的非正定性给识别算法带来的不稳定性,提高了识别算法的鲁棒性,从而增强了基于盲源分离的模态参数识别方法的实用性。
3.通过对建立的改进识别方法SOBI-C的优化,采取对两组联合时滞协方差矩阵进行广义特征值分解,将主要计算压力从对众多单一时滞协方差矩阵的联合近似对角化转移到计算两组联合时滞协方差矩阵上,有效的降低了计算分析的成本,提高了实际应用的价值与意义。对工程实例的分析,表明本文提出的识别方法的计算结果与实测值吻合较好。
With the rapid progress of the city construction, the civil construction engineering has been developed significantly. Simultaneously, some damage occur in the built and building engineering structure due to the effect of design, construction and aging, which leads to a serious threat to the security of people's life and property. Thus, how to identify the health condition of the current engineering structure quickly and accurately has been the difficult subject in engineering field. Based on the summary and analysis of classical modal parameter identification method, this thesis deeply studied the output only modal parameter identification method. This thesis introduced the blind source separation technique of blind signal process field into the modal parameter identification of the engineering structure, proposed an non-parametric time domain method----the modal parameter identification method based on blind source separation technique. The following work and results had been achieved:
1. Based on the complex modal theory, it used Hilbert transformation enrich the virtual measuring points, the original vibration system had been expanded effectively. Proposed the improved modal parameter identification method (AMUSE-C) which has less computation task. It leaded to the result that the modal parameter identification method based on the BSS can not only identify the modal parameter of general damping system, but also improve the capacity of identifying the close modes. Furthermore, it can identify the modal frequency and damping ratios directly through extracting the complex frequencies of vibration system. This approach made the computation cost less expensive and the robustness to noise of BSS was extended to the identification of modal frequencies and damping ratios, from which it leaded a totally new way in the application of the BSS in engineering structural modal parameter identification field.
2. Based on the improved modal parameter identification method AMUUSE-C developed in this thesis, it introduced the joint time-delay covariance matrix, established the improved modal parameter identification method (SOBI-C) which has high stability, overcame the instability of the identification algorithms caused from the non-positive of the single covariance matrix and improved the robust of the identification algorithms, from which the modal parameters identification based on the BSS could be applied more generally.
3. Through the optimal of establishing the improved method SOBI-C, The extended method SOBI-C decomposed the eigenvalue of the joint time-delay covariance matrix so that the main computation cost pressure was transferred from the joint approximate diagonalization of many time-delay covariance matrices to compute the two groups of the joint time-delay covariance matrix. It effectively decreased the cost of computational analysis, which was more valuable and meaningful. The analysis of engineering application showed that the result of the proposed method in this thesis converged to the actual measured value.
引文
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