Damage Localization and State Space Identification Based on Noisy Observations, H-infinity Estimation Theory and Subspace Methods during Lifetime of Non-Stationary, Mechanical Structures using Ambient Excitation

在最近的研究中，基于Krein空间的H-无穷估计理论，提出了一种新的损伤定位和状态识别方法，称为状态投影估计误差(SP2E)。这种估计理论在结构动力学、损伤定位和状态识别方面是未知的。SP2E既不使用平衡方程、物质定律、运动学，也不使用化学过程模型。相反，它是由黑匣子的系统理论识别(反问题)来定义的。它的基础是与耦合状态空间模型(过程模型)相关的多维Popov函数的因式分解。在这里，理论上应用了倾斜投影，这导致了一个明确的损伤指示器。原则上，SP2E方法允许(硬)实时分析。估计误差过程(损伤指示器)的平均功率被用于面向应用的损伤定位。这种方法已经在实验室实验中得到了多次验证，其中机械结构受到环境激励的激励。基于所描述的非常积极的研究结果，SP2E新方法在理论和应用上都应该是先进的。基于Krein空间的H无穷估计既允许确定性激励，也允许随机激励。环境激励有利于大型结构的系统识别和损伤识别。噪声观测仅在SP2E中使用，因为应用的多维、面向过程的建模方法不需要先验激励知识。该项目将H-无穷大理论引入损伤定位和状态空间识别。在这里，在其他主题中，混合H-2/H-无穷大估计方法和平方根方法被考虑。这里可以期待巨大的理论进步，因为这些方法在损伤定位和状态空间识别方面是全新的。一个重要的项目细节是SP2E方法的理论进展及其实验验证。其中，在存在干扰影响以及环境和操作条件的情况下，验证了损伤定位的质量。所开发的理论首先在实验室实验中得到了验证。在接下来的长期实验中，是在开放的研究领域进行的。这里，在损伤局部化的框架下，考虑了环境条件(如可变激励(风)、温度)的变化对数值识别的结构行为的连续影响。从工业应用的角度，实现了在大型结构(如桥梁、风力发电厂)上的初步实验。

In recent studies, a new method for damage localisation and state identification, called State Projection Estimation Error (SP2E), has been derived with the help of Krein space based H-infinity estimation theory. This estimation theory is unknown in structural dynamics, damage localisation and state identification. Neither balance equations, material laws, kinematics nor chemical process models are used in SP2E. Instead, it is defined by a system theoretical identification of a black box (inverse problem). Its foundation is the factorization of a multidimensional popov function in connection with a coupled state space model (process model). Here, the oblique projection is applied theoretically, which leads to an explicit damage indicator. In principal, the method SP2E allows (hard) real-time analyses. The average power of an estimation error process (damage indicator) is used application-oriented for damage localisation. This approach has been verified in laboratory experiments multiple times, in which a mechanical structure was excited by ambient excitation. Based on the described very positive research results, the new method SP2E shall be advanced in theory and application. Krein space based H-infinity estimation allows both deterministic and stochastic excitation. Ambient excitation is advantageous in system and damage identification of large-scale structures. Noisy observations are used only in SP2E, because a priori excitation knowledge is unnecessary for the applied multidimensional, process-oriented modelling approach. The intended project introduces H-infinity theory to damage localisation and state space identification. Here, among other topics mixed H-2/H-infinity estimation approaches and Square Root methods are considered. Huge theoretical progress can be expected here, because those approaches are completely new in damage localisation and state space identification. An important project detail is the theoretical advancement of the method SP2E and its experimental validation. Therein the quality of damage localisation is validated in the presence of disturbance influences and environmental and operational conditions. The developed theories are verified in laboratory experiments first. In the following long-term experiments are conducted at open research areas. Here, the continuous influence of changing environmental conditions (e.g. variable excitation (wind), temperature) to numerically identified structural behaviour is taken into account and studied in the frame of damage localisation. In view of industrial applications, preliminary experiments at large-scale structures (e.g. bridges, wind energy plants) are realised.