PSI - Issue 64

Maximilian Rohrer et al. / Procedia Structural Integrity 64 (2024) 1256–1263 Rohrer, Moeller, Lenzen / Structural Integrity Procedia 00 (2019) 000 – 000

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The presented work follows a vibration-based output only black box approach. It can be divided into three process oriented parts: The 1 st part data space , contains the type and scope of the sensor network, the quality of the multidimensional field data recorded with it, as well as the spatial and temporal resolution of these. These are, for example, mechanical response variables (accelerations, deformations, temperature fields, etc.), influencing variables (forces, environmental conditions, operational conditions, etc.), but also economic information and costs of the building owners. The 2 nd step data assimilation , includes the robustness of the coupling, evaluation and acquisition methods for large sensor data sets in time and space. The topic of real-time capability of data analysis is included here. The 3 rd part system space , determines the type and quality of the system parameters determined from the data space. The focus is on automated and adaptive control of model building and data evaluation using inverse methods, e.g., system identification. The topic of information reduction to significant variables is important here. The paper is organized as follows. First, selected SHM methods are discussed in section 2. This is followed by a brief introduction to the SP2E method in section 2.4, which is applied to the bridge. Section 3 presents the test structure, the application of the measurement system, and first measurement results for selected environmental and operational conditions. The paper concludes with an outlook on planned experiments.

Nomenclature Models T state space system × 0 undamaged normalization model × undamaged comparison model from learning phase × potentially damaged model from monitoring phase Matrices system matrix of state space system system matrix of feedback state space system ( = − ) feedback gain matrix input matrix of state space system output matrix of state space system feed-through matrix of state space system identity matrix Vectors difference process output vector EOC-vector Δ difference of EOC-vectors ( ) power spectral density vector 2. Methods 2.1. Modeling

Traditional analysis and design methods of structural engineering (e.g. the finite element method (FEM) or boundary element method (BEM)) are generally less suitable for the three paradigms addressed above, as they are not data-oriented or process-oriented. The methodical approaches of model updating address the problem by adapting parameters using optimization methods. However, the reduction to a few significant SHM parameters is ambiguous. In contrast, adaptive methods and models of system and filter theory, used in system identification, are suitable and can methodically and directly capture a fuzzy data stream of the sensor network from the data space for data assimilation in the system space. System identification can be characterized in four steps: The definition of an experiment and its objective, the data acquisition and robust estimation, the reduction of the model parameters and the model validation in a possibly iterative procedure. Numerical methods of linear algebra and parameter optimization are traditionally used here. These are currently being supplemented successfully by data-driven methods (machine