Reliable Identification of Modal Parameters in Vibratory Mechanical Structures under Uncertainty

不确定性下振动机械结构模态参数的可靠识别

• 批准号: 514188140
• 负责人: Professor Dr.-Ing. Michael Hanss
• 金额: --
• 依托单位: Institut für Technische und Numerische Mechanik (ITM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/514188140?language=en
• 关键词: Reliable; Identification; Modal; Parameters; Vibratory

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.

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良振动的强烈敏感性，并要求对其振动特性进行彻底分析，尤其是为了使其鲁棒性和优化。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，这些特性通常包括本征频率、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过程中可能出现的不确定性。但所谓的多态不确定性，即偶然性和认识性的不完全知识，存在于大多数工程系统中。现有的量化不确定性的技术通常依赖于精确的概率不确定性描述，这与贝叶斯观点相反，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得到更可靠的结果，而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结合联合收割机的可能性不确定性量化的理论与完善的方法（实验）模态分析，以开发先进的程序进行必要的预测和推理操作固有的模态测试中的不精确概率的方式。在这样做时，可靠的定量包含的多态性的不确定性发生在模态测试是有保证的，一个忠实的预测的振动特性连同量化的形式的置信度分布的模态参数的相关的不精确性将提供。在这种情况下，统计程序的识别这些置信度分布的模态试验数据应推导出来。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，正问题对应于量化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。反问题是在模态试验过程固有不确定性的条件下，确定模态参数的置信度分布。这两种类型的问题应在本项目中解决，并为他们的解决方案将开发合适的数值实现，提供了一个新的程序，先进的模态测试与鲁棒可靠的不确定性量化。最后，以古典吉他的实验模态分析为例，验证其实用性和计算可行性。