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，而成本和效率趋势要求这些结构变得更轻。这些要求经常导致结构对不希望的振动非常敏感，需要对其振动特性进行彻底的分析，尤其是为了增强和优化它们。模态分析是一门工程学科，旨在研究、预测和识别这些特征，通常包括固有频率、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其过程中可能出现的不确定性。但是，在大多数工程系统中都存在所谓的多态不确定性，即对不确定性和认识性的不完全认识。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，与贝叶斯观点相反，在多态不确定性的情况下，这种描述是不合理的。当代研究表明，使用不精确概率的方法可以产生更可靠的结果，而可能性理论是描述这些结果的有效框架。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(实验)模式分析的成熟方法相结合，以便开发高级程序，以不精确-概率的方式执行模式测试固有的基本预测和推理操作。在这样做时，将保证可靠地定量包含在模态测试中发生的多态不确定性，并且将提供振动特性的真实预测以及以模态参数的置信度分布的形式的相关不精确度的量化。在这种情况下，应推导出从模态试验数据中识别这些置信度分布的统计程序。除了不确定性建模的关键任务外，还必须解决两类问题：正问题和反问题。在模态分析中，正问题对应于量化有限元建模系统的不确定振动特性，该不确定振动特性是由实际模型参数或边界条件的不确定性引起的。反问题涉及在过程中确定识别的模态参数的置信度分布--模态试验的固有不确定性。这两种类型的问题都将在本项目中解决，并将为它们的解决方案开发合适的数值实现，从而提供一种具有稳健可靠的不确定度量化的先进模式试验的新程序。最后，将这些程序示范应用于古典吉他的实验模态分析，以确保它们的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.