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

• Applicant: Professor Dr.-Ing. Armin Lenzen
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mechanics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 350257805

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.

• DFG Programme: Research Grants