The life cycle of technical structures - infrastructures, buildings, facilities - includes planning (design) ,use, maintenance and upkeep (maintenance) aswell as rescheduling or subsequent utilization (recycling). The maintenance phase, which is the focus of this project, is the most time-consuming but also the most cost-intensive.

In the design phase of technical structures, the finite element method (FEM) is a recognized engineering-oriented planning and modelling tool. Due to the principles involved, very complex calculation models are used here in order to achieve the most accurate results possible.

In the maintenance phase of technical structures, observations and measurements on the technical constructions can be used to gather new information during use, which enables model validation. Based on this, future-oriented, resource and capital-saving, model-oriented, plannable use, maintenance and upkeep can be carried out.

Unfortunately, the high model complexity and parameter diversity of the FEM is not directly suitable for incorporating the necessary, unambiguous, consistent and possibly real-time capable model adaptation to the new measured information on the technical condition.

Fault-tolerant parameter estimators with adaptable parameters based on fuzzy observations for damage localization and condition identification can be used very advantageously to model mechanical structures in the maintenance phase. It should be emphasized that the multisensory process-oriented modeling used in this research project can only be carried out by measuring the structural response without knowledge of an ambient excitation of the mechanical structure. In particular, the H∞ estimators in Krein space are used here, which are unknown in structural dynamics, damage localization and state identification and were originally developed in mathematically oriented robust control theory - within the framework of modern methods of linear algebra and optimization.

This research project aims to further develop new approaches of process-oriented modeling ('State Projection Estimation Error' - SP2E) for damage and system identification of a mechanical structure - based on the H∞ estimation and control theory and projections in the state space - during the use phase and taking into account disturbance variables (environmental and operating conditions, etc.), which have been proven to be very successful in laboratory tests. Finally, the theoretical methods and transient models developed by the applicant are to be verified experimentally under real operating conditions on exposed structures - e.g. bridges and wind turbines - in order to enable real damage localization and condition identification as well as safety and service life analyses.

Using the Krein space based H∞ estimation theory, a new procedure for damage localization and state identification called State Projection Estimation Error (SP2E) was developed in previous studies. Krein space based estimators are not known in structural dynamics, damage localization and state identification. The SP2E method does not use balance equations, material laws, kinematic formulations or chemical process models, but solves an inverse problem (system-theoretical black box). The basis is the decomposition of a multidimensional Popov function in conjunction with a coupled state space model as a process model. Using the algebraic method of oblique projections, a unique parameter can be theoretically derived in the state space as a damage indicator and localizer.

In principle, the method is (hard) real-time capable.

In an engineering-oriented manner, a process estimation error performance is selected as an indicator and evaluation measure for damage localization. The SP2E method has been prototypically tested several times in laboratory tests on a real mechanical system under ambient excitation with very good results. Against this very positive background, the new SP2E method is to be further developed and investigated in theory and application.

The H∞ estimators used enable the theoretical treatment of both deterministic and stochastic structural excitations. Ambient excitation is very advantageous for system and damage identification of large mechanical structures. From a methodological point of view, it should be emphasized that the multisensory, process-oriented modeling used can only be carried out by measuring the structural response without knowledge of the excitation of the mechanical structure.

In the planned project, the H∞ theory will be introduced and validated in damage localization and condition identification. Among other things, approaches for the application of mixed H-2/H∞ estimation methods and square-root methods will be investigated. Major developments are expected, as these are new in damage localization and condition identification.

A central component of the project is the theoretical further development of the SP2E method and its experimental verification. This involves validating the quality of damage localization under interference, environmental and operating conditions. It will start with laboratory tests. Building on this, long-term tests are carried out on an outdoor test facility. Here, the influence of continuously changing environmental conditions (e.g. change of excitation (wind), temperature) on the numerically identified structural behaviour for damage localization must be taken into account. Furthermore, in preparation for industrial applications, pilot studies are carried out on complex structures (e.g. bridges, wind turbines).

Accelerations were measured in the direction of the weak axis at the cantilever tip. The excitation was ambient.