基于随机子空间法的海洋平台模态参数识别技术研究
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摘要
海洋平台结构复杂、造价昂贵,且服役环境恶劣。为了避免重大恶性事故的发生,需要对海洋平台结构在服役期内进行定期／不定期的检测和安全评估。特别是服役中后期的海洋平台及超期服役的平台,实施有效的健康检测具有更加重要的意义。基于海洋平台振动测试响应的结构健康检测技术能够对结构的健康状况进行全面的检测,是一种全局检测方法,其中模态参数的识别是该技术的基础性和关键性环节。因此,准确掌握海洋平台模态参数显得尤为重要。
早期的模态参数识别方法主要是基于频域响应的方法,但是由于频域方法存在频谱估计的局限性、频谱泄漏等问题,所以目前模态参数识别方法的发展趋势是使用基于结构时域振动响应的输入-输出或者输出的模态参数识别方法。其中复指数法(PRONY)、特征系统实现法(ERA)、随机子空间法(SSI)是在其他领域中模态识别效果较好的几种方法。
本文通过对现有典型时域方法(复指数法(PRONY)、特征系统实现法(ERA)、随机子空间法(SSI))的性能比较,旨在发展一套有效的海洋平台模态参数精确识别技术。研究了有效获取结构的模态参数的方法,通过数据驱动随机子空间法(SSI/data)和协方差驱动随机子空间法(SSI/cov)差异性以及数据驱动随机子空间法(SSI/data)Hankel矩阵与噪声关系的深入研究完善了现有的模态参数识别技术,为进一步的结构健康检测和安全评价提供了理论基础和技术支持。主要研究工作如下：
1.在不同激励方式(冲击激励、张拉激励以及白噪声激励)下分别对比复指数法(PRONY)、特征系统实现法(ERA)和随机子空间法(SSI/data和SSI/cov),证明了数据驱动随机子空间法(SSI/data)能够适用于不同激励下的模态参数识别,而且模态识别能力最强。
2.传统观点认为数据驱动随机子空间法(SSI/data)和协方差驱动随机子空间法(SSI/cov)无论在理论上还是实际应用中都是一致的。通过蒙特卡洛试验、函数试验分别证明了协方差驱动随机子空间法(SSI/cov)识别模态数目少和模态参数估计精度不高等缺点,数据驱动随机子空间法(SSI/data)有更强的模态识别能力：消噪能力强、准确识别临近模态、模态估计结果精度高等。继而从理论上分析了两种方法存在差异的原因：数据有限性和QR分解算法,并通过数值试验进行了验证。
3.深入研究了数据驱动随机子空间法(SSI/data),推导了Hankel矩阵的构建方式与数据驱动随机子空间法的消噪能力的关系式。提出了一套数据驱动随机子空间法(SSI/data) Hankel矩阵维数的评估方法,即归一化奇异值曲线、稳定图和有限元模态结果相结合的方式。分别利用数值算例和模型试验检验了该方法的有效性,研究表明：数据驱动随机子空间法(SSI/data)的Hankel矩阵应设置成非方阵。为今后数据驱动随机子空间法(SSI/data)的有效使用提供了参考和指导。
4.基于海洋平台物理模型多激励(冲击激励、张拉激励以及白噪声激励)试验和渤海某平台现场实测等振动响应数据,系统地证明了数据驱动随机子空间法(SSI/data)在海洋平台模态参数识别中的适用性和优越性。同时验证了激励方式与海洋平台模态之间的关系。
To avoid major malignant accident, it is necessary to conduct periodic/aperiodic detection and safety assessment for offshore platforms with the action of various environmental forces, complex structure and high cost.So effective health detection for offshore platform, particularly those in old age or in overterm service, is more significant. The structural health monitoring technology based on the response data of the vibration test which is a global detection method is able to construct a comprehensive testing for offshore platforms, of which modal parameter identification is fundamental and critical. Therefore, the accurate modal parameter for offshore platform is particularly important.
Early methods of modal identification were developed for the frequency domain. Because of limitations in the frequency resolution of spectral estimates and leakage errors in the estimates for the frequency domain methods, the new trend is to employ either input-output or output-only time-domain modal identification methods, of which the PRONY, Eigensystem Realization Algorithm(ERA) and SSI are more successful methods in other areas.
With the aim at develop a effective identification technique for modal parameters of offshore platforms more exactly, the thesis studies on how to identify modal parameters more efficiently and improves existing modal parameters identification technologies by investigating the difference between SSI/data and SSI/cov and relation between Hankel matrix and noise. The main contributions are as follows:
1. Based on the data associated with different excitations (impact loading, step relaxation, white noise loading), Prony, ERA and SSI/data are compared. It is proved that SSI/data has a better capacity of identifying the modal parameters of structures under different excitations (impact loading, step relaxation, white noise loading).
2. The data-driven and covariance-driven stochastic subspace identification traditionally is thought to be consistent with each other theoretically and practically for modal identification. The paper investigates the reason that probably produce the difference,then confirms the reason of difference, the numerical study demonstrates that data-driven stochastic subspace identification method outperforms the covariance driven subspace identification method not only on accuracy of identification parameter but also on capacity of identifying weaker mode.
3. The paper deduces theoretically the relation formula between noise and Hankel matrix of data-driven subspace identification method. And the paper also proposes a verification procedure to justify the noise can be eliminated properly by data-driven subspace identification method with selected Hankel matrix, the procedure includes SVD, stability diagram and finite element result (FE). Finally based on data associated with numerical study and jacket-type platform vibration test separately, we demonstrate systematically that data-driven stochastic subspace identification method with non-square Hankel matrix has better capacity of denoising and estimating the modal parameters with higher accuracy.
4. With the data collected from a jacket-type physical model under different excitations(including impact loading, step-relaxation loading, white noise loading) and test data of realistic offshore jacket-type platform in Bohai sea in China, this paper demonstrates that SSI/data can be applied to modal identification of offshore platforms and be able to finish it better, and different strong modes can be excited by different excitation.
早期的模态参数识别方法主要是基于频域响应的方法,但是由于频域方法存在频谱估计的局限性、频谱泄漏等问题,所以目前模态参数识别方法的发展趋势是使用基于结构时域振动响应的输入-输出或者输出的模态参数识别方法。其中复指数法(PRONY)、特征系统实现法(ERA)、随机子空间法(SSI)是在其他领域中模态识别效果较好的几种方法。
本文通过对现有典型时域方法(复指数法(PRONY)、特征系统实现法(ERA)、随机子空间法(SSI))的性能比较,旨在发展一套有效的海洋平台模态参数精确识别技术。研究了有效获取结构的模态参数的方法,通过数据驱动随机子空间法(SSI/data)和协方差驱动随机子空间法(SSI/cov)差异性以及数据驱动随机子空间法(SSI/data)Hankel矩阵与噪声关系的深入研究完善了现有的模态参数识别技术,为进一步的结构健康检测和安全评价提供了理论基础和技术支持。主要研究工作如下：
1.在不同激励方式(冲击激励、张拉激励以及白噪声激励)下分别对比复指数法(PRONY)、特征系统实现法(ERA)和随机子空间法(SSI/data和SSI/cov),证明了数据驱动随机子空间法(SSI/data)能够适用于不同激励下的模态参数识别,而且模态识别能力最强。
2.传统观点认为数据驱动随机子空间法(SSI/data)和协方差驱动随机子空间法(SSI/cov)无论在理论上还是实际应用中都是一致的。通过蒙特卡洛试验、函数试验分别证明了协方差驱动随机子空间法(SSI/cov)识别模态数目少和模态参数估计精度不高等缺点,数据驱动随机子空间法(SSI/data)有更强的模态识别能力：消噪能力强、准确识别临近模态、模态估计结果精度高等。继而从理论上分析了两种方法存在差异的原因：数据有限性和QR分解算法,并通过数值试验进行了验证。
3.深入研究了数据驱动随机子空间法(SSI/data),推导了Hankel矩阵的构建方式与数据驱动随机子空间法的消噪能力的关系式。提出了一套数据驱动随机子空间法(SSI/data) Hankel矩阵维数的评估方法,即归一化奇异值曲线、稳定图和有限元模态结果相结合的方式。分别利用数值算例和模型试验检验了该方法的有效性,研究表明：数据驱动随机子空间法(SSI/data)的Hankel矩阵应设置成非方阵。为今后数据驱动随机子空间法(SSI/data)的有效使用提供了参考和指导。
4.基于海洋平台物理模型多激励(冲击激励、张拉激励以及白噪声激励)试验和渤海某平台现场实测等振动响应数据,系统地证明了数据驱动随机子空间法(SSI/data)在海洋平台模态参数识别中的适用性和优越性。同时验证了激励方式与海洋平台模态之间的关系。
To avoid major malignant accident, it is necessary to conduct periodic/aperiodic detection and safety assessment for offshore platforms with the action of various environmental forces, complex structure and high cost.So effective health detection for offshore platform, particularly those in old age or in overterm service, is more significant. The structural health monitoring technology based on the response data of the vibration test which is a global detection method is able to construct a comprehensive testing for offshore platforms, of which modal parameter identification is fundamental and critical. Therefore, the accurate modal parameter for offshore platform is particularly important.
Early methods of modal identification were developed for the frequency domain. Because of limitations in the frequency resolution of spectral estimates and leakage errors in the estimates for the frequency domain methods, the new trend is to employ either input-output or output-only time-domain modal identification methods, of which the PRONY, Eigensystem Realization Algorithm(ERA) and SSI are more successful methods in other areas.
With the aim at develop a effective identification technique for modal parameters of offshore platforms more exactly, the thesis studies on how to identify modal parameters more efficiently and improves existing modal parameters identification technologies by investigating the difference between SSI/data and SSI/cov and relation between Hankel matrix and noise. The main contributions are as follows:
1. Based on the data associated with different excitations (impact loading, step relaxation, white noise loading), Prony, ERA and SSI/data are compared. It is proved that SSI/data has a better capacity of identifying the modal parameters of structures under different excitations (impact loading, step relaxation, white noise loading).
2. The data-driven and covariance-driven stochastic subspace identification traditionally is thought to be consistent with each other theoretically and practically for modal identification. The paper investigates the reason that probably produce the difference,then confirms the reason of difference, the numerical study demonstrates that data-driven stochastic subspace identification method outperforms the covariance driven subspace identification method not only on accuracy of identification parameter but also on capacity of identifying weaker mode.
3. The paper deduces theoretically the relation formula between noise and Hankel matrix of data-driven subspace identification method. And the paper also proposes a verification procedure to justify the noise can be eliminated properly by data-driven subspace identification method with selected Hankel matrix, the procedure includes SVD, stability diagram and finite element result (FE). Finally based on data associated with numerical study and jacket-type platform vibration test separately, we demonstrate systematically that data-driven stochastic subspace identification method with non-square Hankel matrix has better capacity of denoising and estimating the modal parameters with higher accuracy.
4. With the data collected from a jacket-type physical model under different excitations(including impact loading, step-relaxation loading, white noise loading) and test data of realistic offshore jacket-type platform in Bohai sea in China, this paper demonstrates that SSI/data can be applied to modal identification of offshore platforms and be able to finish it better, and different strong modes can be excited by different excitation.
引文
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