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Optimal selection of artificial boundary conditions for model update and damage detection

机译：人工边界条件的最佳选择，用于模型更新和损伤检测

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摘要

Sensitivity-based model error localization and damage detection is hindered by the relative differences in modal sensitivity magnitude among updating parameters. The method of artificial boundary conditions is shown to directly address this limitation, resulting in the increase of the number of updating parameters at which errors can be accurately localized. Using a single set of FRF data collected from a modal test, the artificial boundary conditions (ABC) method identifies experimentally the natural frequencies of a structure under test for a variety of different boundary conditions, without having to physically apply the boundary conditions, hence the term "artificial". The parameter-specific optimal ABC sets applied to the finite element model will produce increased sensitivities in the updating parameter, yielding accurate error localization and damage detection solutions. A method is developed for identifying the parameter-specific optimal ABC sets for updating or damage detection, and is based on the QR decomposition with column pivoting. Updating solution residuals, such as magnitude error and false error location, are shown to be minimized when the updating parameter set is limited to those corresponding to the QR pivot columns. The existence of an optimal ABC set for a given updating parameter is shown to be dependent on the number of modes used, and hence the method developed provides a systematic determination of the minimum number of modes required for localization in a given updating parameter. These various concepts are demonstrated on a simple model with simulated test data.
机译：基于灵敏度的模型错误定位和损坏检测受到更新参数之间模态灵敏度幅度的相对差异的阻碍。结果表明，人工边界条件的方法可以直接解决这一局限性，从而导致更新参数的数量增加，可以精确定位错误。人工边界条件（ABC）方法使用从模态测试中收集的一组FRF数据，通过实验确定了待测试结构在多种不同边界条件下的固有频率，而无需物理应用边界条件，因此术语“人工”。应用于有限元模型的特定于参数的最佳ABC集将在更新参数中产生更高的灵敏度，从而产生准确的错误定位和损坏检测解决方案。开发了一种方法，该方法基于带有列旋转的QR分解来识别用于更新或损坏检测的特定于参数的最佳ABC集。当更新参数集仅限于与QR枢轴列相对应的参数时，更新解决方案残差（例如幅度误差和错误误差位置）显示为最小。显示给定更新参数的最佳ABC集的存在取决于所用模式的数量，因此开发的方法可系统确定给定更新参数中定位所需的最小模式数。在具有模拟测试数据的简单模型上演示了这些各种概念。

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