Reliable Identification of Modal Parameters in Vibratory Mechanical Structures under Uncertainty

现代标准要求工程中的振动机械结构保持耐用，而成本和效率的趋势要求这些结构变得更轻。这些要求经常导致结构对不良振动的强烈敏感性，并要求对其振动特性进行彻底的分析，尤其是为了加固和优化它们。模态分析是一门旨在研究、预测和识别这些特性的工程学科，这些特性通常包括特征频率、模态振型和模态阻尼比。然而，模态分析的一个共同缺点是忽略了在其过程中可能出现的不确定性。但所谓的多态不确定性，即对选择性和认识性的不完全认识，存在于大多数工程系统中。现有的不确定性量化技术通常依赖于精确的概率不确定性描述，这与贝叶斯的观点相反，在多态不确定性的情况下是不合理的。当代研究表明，使用不精确概率的方法可以导致更可靠的结果，可能性理论是描述它们的有效框架。因此，拟议项目的目标是巧妙地将可能性不确定性量化理论与成熟的（实验）模态分析方法结合起来，以便开发先进的程序，以非精确概率方式执行模态测试固有的基本预测和推理操作。这样，就保证了模态测试中出现的多态不确定性的可靠定量包含，并将提供振动特性的忠实预测以及模态参数置信度分布形式的相关不精度的量化。在这种情况下，应导出从模态试验数据中识别这些置信分布的统计程序。除了不确定性建模的关键任务外，还必须解决两类问题：正问题和逆问题。在模态分析中，正演问题对应于对由实际模型参数或边界条件的不确定性引起的有限元建模系统的不确定振动特性进行量化。反问题涉及在模态试验过程固有不确定性下确定已识别模态参数的置信分布。这两种类型的问题都将在本项目中得到解决，并将为它们的解决方案开发合适的数值实现，提供一种具有鲁棒可靠的不确定性量化的先进模态测试新程序。最后，以古典吉他的实验模态分析为例，保证其实际性能和计算可行性。

Modern standards require vibratory mechanical structures in engineering to remain durable, whereas cost and efficiency trends necessitate those to become lighter. These demands frequently result in a strong sensitivity of the structures to undesirable vibrations and call for a thorough analysis of their vibrational characteristics, not least in order to robustify and optimize them. Modal analysis is an engineering discipline aimed at studying, predicting and identifying these characteristics, which generally include eigenfrequencies, mode shapes and modal damping ratios. A common shortcoming of modal analysis, however, is the disregard of uncertainties that may occur in its process. But so-called polymorphic uncertainty, i.e. incomplete knowledge of aleatory and epistemic nature, is present in most engineering systems. And existing techniques for the quantification of uncertainty commonly rely on precise probabilistic uncertainty descriptions, which, contrary to the Bayesian view, are arguably unjustified in cases of polymorphic uncertainty. Contemporary research suggests that approaches using imprecise probabilities can lead to more reliable results, and possibility theory is an efficient framework for their description. Therefore, the goal of the proposed project is to smartly combine the theory of possibilistic uncertainty quantification with the well-established methodology of (experimental) modal analysis in order to develop advanced procedures for performing the essential predictive and inferential operations inherent to modal testing in an imprecise-probabilistic manner. In doing so, a reliable quantitative inclusion of the polymorphic uncertainty occurring in modal testing is guaranteed and a faithful prediction of the vibrational characteristics together with a quantification of the associated imprecision in form of confidence distributions for the modal parameters will be provided. In this context, a statistical procedure for the identification of these confidence distributions from data of modal testing shall be derived. Besides the critical task of uncertainty modeling, two classes of problems must be tackled: forward and inverse problems. In modal analysis, the forward problem corresponds to quantifying the uncertain vibrational characteristics of a finite-element-modeled system, induced by uncertainty about the actual model parameters or boundary conditions. Inverse problems are concerned with determining confidence distributions for the identified modal parameters under the process-inherent uncertainty of modal testing. Both types of problems shall be addressed in this project and suitable numerical implementations for their solutions will be developed, providing a new procedure of advanced modal testing with robustly reliable uncertainty quantification. Finally, the procedures shall exemplarily be applied to the experimental modal analysis of a classical guitar to ensure their practical performance and computational feasibility.