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Stochastic finite element model calibration based on frequency responses and bootstrap sampling

机译：基于频率响应和自举采样的随机有限元模型校准

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A new stochastic finite element model calibration framework for estimation of the uncertainty in model parameters and predictions from the measured frequency responses is proposed in this paper. It combines the principles of bootstrapping with the technique of FE model calibration with damping equalization. The challenge for the calibration problem is to find an initial estimate of the parameters that is reasonably close to the global minimum of the deviation between model predictions and measurement data. The idea of model calibration with damping equalization is to formulate the calibration metric as the deviation between the logarithm of the frequency responses of FE model and a test data model found from measurement where the same level of modal damping is imposed on all modes. This formulation gives a smooth metric with a large radius of convergence to the global minimum. In this study, practical suggestions are made to improve the performance of this calibration procedure in dealing with noisy measurements. A dedicated frequency sampling strategy is suggested for measurement of frequency responses in order to improve the estimate of a test data model. The deviation metric at each frequency line is weighted using the signal-to-noise ratio of the measured frequency responses. The solution to the improved calibration procedure with damping equalization is viewed as a starting value for the optimization procedure used for uncertainty quantification. The experimental data is then resampled using the bootstrapping approach and the FE model calibration problem, initiating from the estimated starring value, is solved on each individual resampled dataset to produce uncertainty bounds on the model parameters and predictions. The proposed stochastic model calibration framework is demonstrated on a six degree-of-freedom spring-mass system prior to being applied to a general purpose satellite structure.
机译：本文提出了一种新的随机有限元模型校准框架，用于估计模型参数的不确定性和根据测得的频率响应进行预测。它结合了自举原理和带有阻尼均衡的有限元模型校准技术。校准问题的挑战是找到参数的初始估计值，该估计值合理地接近模型预测和测量数据之间的偏差的全局最小值。使用阻尼均衡进行模型校准的思想是将校准度量公式化为FE模型的频率响应的对数与从测量中找到的测试数据模型之间的偏差，其中对所有模式施加相同水平的模态阻尼。该公式给出了一个平滑的度量，其收敛半径大到全局最小值。在这项研究中，提出了一些实用的建议，以改善此校准程序在处理噪声测量时的性能。建议使用专用的频率采样策略来测量频率响应，以改善测试数据模型的估计。使用测得的频率响应的信噪比对每个频率线上的偏差度量进行加权。带有阻尼均衡的改进校准程序的解决方案被视为用于不确定性量化的优化程序的起始值。然后，使用自举方法对实验数据进行重新采样，并从估计的起始值开始对每个单独的重新采样数据集求解有限元模型校准问题，以产生模型参数和预测的不确定性范围。在将其应用于通用卫星结构之前，在六自由度弹簧质量系统上演示了所提出的随机模型校准框架。

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