基于模态参数识别的海洋平台结构模型修正技术研究
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摘要
海洋平台结构长期服役在恶劣的海洋环境中，其安全性和耐久性极其重要，一旦发生事故，不仅造成巨大的经济损失和人员伤亡，而且造成环境污染、生态破坏等不良后果。为了保障海洋平台结构的安全服役，避免重大的恶性事故发生，必须对海洋平台结构在服役期内进行安全与寿命评估。
一个反映实际结构的评估模型是进行海洋平台结构安全评估的基础，但是按照原始设计资料建立的模型与现役结构之间往往存在误差，解决这一问题的常用手段是模型修正技术。然而传统的模型修正方法多存在一些缺点（如矩阵型方法无法保持系统矩阵的对称性、稀疏性和正定性，使得修正后模型缺乏物理意义；而基于灵敏度的设计参数型方法多需要进行迭代求解，计算负担较重），很难应用于大型的海洋平台结构中。而交叉模型交叉模态（CMCM）方法不仅能弥补传统方法的不足，且具有其它诸多优点，因此更有希望应用于海洋平台结构的模型修正中。
海洋工程结构通常比较复杂，建模的不确定性较多，但受测试条件的限制，实测信息往往非常有限，且受到噪声的干扰，这使得模型修正方法在实际工程中的应用受到了很大的限制，其中亟待解决的问题有：1）修正参数的选择；2）模型修正病态系统的求解；3）节点及边界条件的修正等。而CMCM方法要推向实际应用也面临着以上难题。
本文结合海洋平台结构的特点，在国内外有关研究成果的基础上对CMCM方法在实际应用中所面临的难点问题进行了较为深入的研究，具体包括以下内容：
1.从灵敏度分析的角度，研究了修正参数的优化选择问题，提出了一个基于灵敏度分级的多阶段模型修正方法。通过对初选修正参数进行灵敏度分析，并排序分级，可以优选修正参数，一定程度上改善了修正方程的病态性；通过对排列分级的修正参数逐级求解，可以提高低灵敏度参数修正求解的精度。通过一导管架平台结构数值算例验证了该方法的可行性。
2.大型结构的模型修正求解问题多呈现不同程度的病态，实测数据的微小误差都会造成解的振荡。本文研究了测量噪声影响下模型修正病态系统的求解问题。将数学上常用的正则化方法引入到了CMCM方法的求解中，并通过数值算例探讨了正则化求解的适用性；通过得出的适用性条件研究了CMCM方法的噪声鲁棒性。结果显示，适当的正则化方法可以有效的解决模型修正病态系统的求解问题，但需要判断其可解条件——离散Picard条件；另外，在满足修正目的条件下，较少的CMCM方程将呈现更好的噪声鲁棒性。
3.将CMCM方法发展到了约束边界和桩基边界这两种典型边界条件的模型修正中。对于通常没有任何振型信息的边界单元，提出仅用频率信息对其进行修正，避免了上部结构的振型误差对边界处修正结果的影响；并采用本文提出的多阶段模型修正方法实现了对上部结构和边界条件的整体修正，从而避免了同时修正中的病态问题。数值算例和试验算例验证了该方法的可行性。
4.通过一导管架平台缩尺模型试验验证了本文提出的基于灵敏度分级的多阶段模型修正方法和基于正则化求解的CMCM方法具有一定的工程实用性。
本文的研究成果在一定程度上解决了模型修正技术在实际工程应用中的难点问题，将CMCM方法从理论层面向工程应用层面推进了一步。另外，所提出的基于灵敏度分级的多阶段模型修正方法同样适用于其它模型修正方法，具有广泛的应用意义。
Offshore platform structures always serve in the harsh marine environment. Theirsafety and durability are extremely important. Once the incident occured, not only causedenormous economic losses and casualties, but also caused environmental pollution,ecological damage and other adverse consequences. To protect the safety and to preventthe occurrence of major accidents, the safety assessment is necessary for the offshoreplatform structures during the service.
An assessment model reflecting the actual structure is the basics for the safetyassessment of the offshore platform structure. But disagreements often exist between themodel and actual structure. Model updating is a common method to improve it. However,the traditional model updating methods more or less have some defects, which limit theirapplication in the large offshore platform structures. In contrast, Cross Model Cross Mode(CMCM) method is more promising to applicate in it because of its advantages.
Because of the complexity of offshore platform structures, there are manyuncertainties in modeling. However, measured data is very limited and containing noise,which limits the practical application of the model updating methods. Problems to besolved contains:1) the selection of updating parameters,2) ill-conditioned problems ofmodel updating,3) model updating of boundaries, etc. While CMCM method is alsofaced with the ablve problems in practical application.
Considering the characters of offshore platform structures, the difficult problems ofCMCM method faced in the practical applicating are researched based on those existingin the literature. Major contend in this thesis are summarized as follows:
1. The selection of updating parameters is researched from the angle of sensitivityanalysis. A multi-steps model updating method based on sensitivity grading is proposedin this thesis. In the method, parameters can be properly selected by sensitivity analysisand grading, which can also improve the ill-condition of model updating equations. Basedon the sensitivity grading results, the selected paramenters can be updated step by step,which can improve the solving accuracy of the low sensitivity parameters. A numericalexample of a jacket structure verified the feasibility of the method.
2. Model updating equations of large structures always presents ill-condition. Smallerrors in the measured data will cause oscillation of the solutions. In this thesis, thesolution of ill-conditioned problems with noisy data is researched. Regularization methods commonly used in mathematics are introduced to CMCM method. Theapplicability is verified through a numerical example, and then the noise robustness ofCMCM method is discussed based on the application conditions. Results indicate thatproper regularization can solve the ill-conditioned model updating problems, but need tojudge the solvability conditions: discrete Picard conditions. In addition, for the sameupdating object, less CMCM equations will have better robustness.
3. This thesis extends the CMCM method to update the boundary conditions ofconstraint and piles. Because of the lack of modal shapes near the boundary, onlyfrequencies are used in the updating procedure, which can avoid the influence of shapeerrors of the upper nodes. And also, multi-steps mehod is used to update the wholestructre (including the boundary and the superstructure), which can avoid theill-conditioned problem. Numerical and experimental examples verified the feasibility ofthe method.
4. Experimental study of a steel jacket scale model is conducted. Model updatingresults verified the practicability of the methods proposed in the thesis.
To some extent, this thesis solved the difficult problems of model updating faced inthe practical applicating and advanced the CMCM method form the theory level to theenginering applicating level. The multi-steps updating method based on sensitivitygrading presented in this thesis is also applicable to other method and has greatersignificance.
一个反映实际结构的评估模型是进行海洋平台结构安全评估的基础，但是按照原始设计资料建立的模型与现役结构之间往往存在误差，解决这一问题的常用手段是模型修正技术。然而传统的模型修正方法多存在一些缺点（如矩阵型方法无法保持系统矩阵的对称性、稀疏性和正定性，使得修正后模型缺乏物理意义；而基于灵敏度的设计参数型方法多需要进行迭代求解，计算负担较重），很难应用于大型的海洋平台结构中。而交叉模型交叉模态（CMCM）方法不仅能弥补传统方法的不足，且具有其它诸多优点，因此更有希望应用于海洋平台结构的模型修正中。
海洋工程结构通常比较复杂，建模的不确定性较多，但受测试条件的限制，实测信息往往非常有限，且受到噪声的干扰，这使得模型修正方法在实际工程中的应用受到了很大的限制，其中亟待解决的问题有：1）修正参数的选择；2）模型修正病态系统的求解；3）节点及边界条件的修正等。而CMCM方法要推向实际应用也面临着以上难题。
本文结合海洋平台结构的特点，在国内外有关研究成果的基础上对CMCM方法在实际应用中所面临的难点问题进行了较为深入的研究，具体包括以下内容：
1.从灵敏度分析的角度，研究了修正参数的优化选择问题，提出了一个基于灵敏度分级的多阶段模型修正方法。通过对初选修正参数进行灵敏度分析，并排序分级，可以优选修正参数，一定程度上改善了修正方程的病态性；通过对排列分级的修正参数逐级求解，可以提高低灵敏度参数修正求解的精度。通过一导管架平台结构数值算例验证了该方法的可行性。
2.大型结构的模型修正求解问题多呈现不同程度的病态，实测数据的微小误差都会造成解的振荡。本文研究了测量噪声影响下模型修正病态系统的求解问题。将数学上常用的正则化方法引入到了CMCM方法的求解中，并通过数值算例探讨了正则化求解的适用性；通过得出的适用性条件研究了CMCM方法的噪声鲁棒性。结果显示，适当的正则化方法可以有效的解决模型修正病态系统的求解问题，但需要判断其可解条件——离散Picard条件；另外，在满足修正目的条件下，较少的CMCM方程将呈现更好的噪声鲁棒性。
3.将CMCM方法发展到了约束边界和桩基边界这两种典型边界条件的模型修正中。对于通常没有任何振型信息的边界单元，提出仅用频率信息对其进行修正，避免了上部结构的振型误差对边界处修正结果的影响；并采用本文提出的多阶段模型修正方法实现了对上部结构和边界条件的整体修正，从而避免了同时修正中的病态问题。数值算例和试验算例验证了该方法的可行性。
4.通过一导管架平台缩尺模型试验验证了本文提出的基于灵敏度分级的多阶段模型修正方法和基于正则化求解的CMCM方法具有一定的工程实用性。
本文的研究成果在一定程度上解决了模型修正技术在实际工程应用中的难点问题，将CMCM方法从理论层面向工程应用层面推进了一步。另外，所提出的基于灵敏度分级的多阶段模型修正方法同样适用于其它模型修正方法，具有广泛的应用意义。
Offshore platform structures always serve in the harsh marine environment. Theirsafety and durability are extremely important. Once the incident occured, not only causedenormous economic losses and casualties, but also caused environmental pollution,ecological damage and other adverse consequences. To protect the safety and to preventthe occurrence of major accidents, the safety assessment is necessary for the offshoreplatform structures during the service.
An assessment model reflecting the actual structure is the basics for the safetyassessment of the offshore platform structure. But disagreements often exist between themodel and actual structure. Model updating is a common method to improve it. However,the traditional model updating methods more or less have some defects, which limit theirapplication in the large offshore platform structures. In contrast, Cross Model Cross Mode(CMCM) method is more promising to applicate in it because of its advantages.
Because of the complexity of offshore platform structures, there are manyuncertainties in modeling. However, measured data is very limited and containing noise,which limits the practical application of the model updating methods. Problems to besolved contains:1) the selection of updating parameters,2) ill-conditioned problems ofmodel updating,3) model updating of boundaries, etc. While CMCM method is alsofaced with the ablve problems in practical application.
Considering the characters of offshore platform structures, the difficult problems ofCMCM method faced in the practical applicating are researched based on those existingin the literature. Major contend in this thesis are summarized as follows:
1. The selection of updating parameters is researched from the angle of sensitivityanalysis. A multi-steps model updating method based on sensitivity grading is proposedin this thesis. In the method, parameters can be properly selected by sensitivity analysisand grading, which can also improve the ill-condition of model updating equations. Basedon the sensitivity grading results, the selected paramenters can be updated step by step,which can improve the solving accuracy of the low sensitivity parameters. A numericalexample of a jacket structure verified the feasibility of the method.
2. Model updating equations of large structures always presents ill-condition. Smallerrors in the measured data will cause oscillation of the solutions. In this thesis, thesolution of ill-conditioned problems with noisy data is researched. Regularization methods commonly used in mathematics are introduced to CMCM method. Theapplicability is verified through a numerical example, and then the noise robustness ofCMCM method is discussed based on the application conditions. Results indicate thatproper regularization can solve the ill-conditioned model updating problems, but need tojudge the solvability conditions: discrete Picard conditions. In addition, for the sameupdating object, less CMCM equations will have better robustness.
3. This thesis extends the CMCM method to update the boundary conditions ofconstraint and piles. Because of the lack of modal shapes near the boundary, onlyfrequencies are used in the updating procedure, which can avoid the influence of shapeerrors of the upper nodes. And also, multi-steps mehod is used to update the wholestructre (including the boundary and the superstructure), which can avoid theill-conditioned problem. Numerical and experimental examples verified the feasibility ofthe method.
4. Experimental study of a steel jacket scale model is conducted. Model updatingresults verified the practicability of the methods proposed in the thesis.
To some extent, this thesis solved the difficult problems of model updating faced inthe practical applicating and advanced the CMCM method form the theory level to theenginering applicating level. The multi-steps updating method based on sensitivitygrading presented in this thesis is also applicable to other method and has greatersignificance.
引文
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[2] Hu, S.-L.J., Li, H., and Wang, S. Cross-model cross-mode method for model updating.Mechanical Systems and Signal Processing,2007,21(4):1690~1703
[3] Huajun Li, Junrong Wang, Sau-Lon James Hu. Using incomplete modal data for damagedetection in offshore jacket structures. Ocean Engineering,2008,25:1793~1799
[4] Hu, S.-L.J., Li, H. Simultaneous mass, damping, and stiffness updating for dynamic systems.AIAA Journal,2007,45(10):2529~2537
[5] Junrong Wang, Huajun Li, Ping Li, S.-L James Hu. Using Modal Frequencies for DamageAssessment in Offshore Jacket Structures. ISOPE-2010. Beijing
[6]王俊荣.海洋平台结构物损伤检测与模型修正方法研究.[博士学位论文].青岛：中国海洋大学,2009
[7]刘福顺.非比例阻尼条件下海洋平台模型修正与损伤诊断方法研究.[博士学位论文].青岛：中国海洋大学,2008
[8]张敏.固定式海洋结构模型转换与动力特性研究.[博士学位论文].青岛：中国海洋大学,2010
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