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On the optimality of harmonic excitation as input signals for the characterization of parameters in coupled piezoelectric and poroelastic problems

机译：关于谐波激励作为输入信号的最优性，以表征压电和多孔弹性耦合参数

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摘要

In this work we provide theoretical and numerical results regarding optimal designs of experiments with an emphasis on coupled problems like piezoelectrics and poroelastics. The work is motivated by the need of identifying parameters for complex problems from measured data, where it is a priori not clear which data are to choose. We assume a harmonic excitation of the systems and measurements related to different excitation frequencies. Results of optimal experimental designs under harmonic excitations are reviewed and adapted correspondingly, e.g., the D-optimality criterion is extended to the case of multiple fields. The manuscript at hand further reviews techniques to identify parameters and their statistical properties and discusses the previously derived theory for two examples, one coming from piezoelectricity, the other from poroelasticity. For these examples, it is analytically shown that they fit to the previously presented theory. Numerical results discussing the optimal choice of the fields to measure and finding the optimal excitation frequencies finalize this work.
机译：在这项工作中，我们提供有关最佳实验设计的理论和数值结果，重点是压电和多孔弹性等耦合问题。这项工作的动机是需要从测量的数据中识别出复杂问题的参数，而先验不清楚要选择哪些数据。我们假设系统的谐波激​​励和与不同激励频率有关的测量值。对谐波激励下最佳实验设计的结果进行了审查和相应调整，例如D优化准则扩展到了多个领域的情况。手稿进一步回顾了识别参数及其统计特性的技术，并针对两个示例讨论了先前得出的理论，其中一个来自压电性，另一个来自多孔弹性。对于这些示例，通过分析表明它们符合先前提出的理论。讨论测量场的最佳选择并找到最佳激励频率的数值结果完成了这项工作。

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