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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learning (ML)), as the basic methodological steps of ML are in principle directly comparable to system identification (see Brunton and Kutz (2019), Ljung et al. (2020), Strang (2019)). A disadvantage of ML methods is often the lack of physical interpretation options. In contrast, state space models from system theory can be converted into canonical forms, which are then accessible for physical interpretation (Lenzen and Vollmering (2021), Katayama (2005)). Complex nonlinear relations, on the other hand, are typically difficult to describe with state space models, as is a direct stable solution method. ML methods can advantageously map nonlinearities and complex relations between relevant model parameters (see Goodfellow et al. (2016)). Therefore, an automated and data-driven combination of the respective advantages of both methods can be expected to produce results with a high degree of accuracy. 2.2. System Identification System identification of white-box and black-box models is an important distinction for system parametrization. White-box models are based on the constitutive mechanical equations. Since only selected special problems can be solved analytically, numerical approximate solutions (e.g., FE model, BE model) are used. Incorporating the influences of environmental and operational conditions (EOC), non-linearities, variable operating conditions, etc. is complex and time-consuming. Therefore, these models are not directly suitable for real-time capable and process oriented applications. These physically interpretable white box models are contrasted with mathematical black box models, which parameterize a causal transfer from a deterministic and/or stochastic input to an output (e.g., as a state space system). 2.3. Deterministic and Stochastic Black Box Models As black box models are parameterized directly based on measurement data, they have a smaller model order and are in theory real-time capable. The identification based on deterministic excitations (Deterministic Realization, Numerical Algorithms for State Subspace System Identification (N4SID), Multivariable Output Error State Space Algorithm (MOESP) etc.) on large, real structures from civil or mechanical engineering requires complex, cost intensive, difficult to automate and sometimes technically impossible experiments. Ambient noise (e.g., wind, traffic) can be used for most structures during operation for system parametrization with stochastic output-only system identification techniques (e.g., Stochastic Realization, Canonical Correlation Analysis (CCA), covariance/data based Stochastic Subspace Identification (SSI), etc.) as shown in Katayama (2005), Van Overschee and De Moor (1996) and Verhaegen and Verdult (2007). 2.4. State Projection Estimation Error (SP2E) The SP2E method is used to detect and localize damage by Lenzen and Vollmering (2017) & Lenzen et al. (2021). The method is based on linear, time-invariant state space models T . The basis is structural responses of a sensor network applied to a mechanical system. The state space models are realized with the Stochastic Subspace Identification (SSI) (output-only method). The complete state space models T are optimized using 2 / ∞ algorithms.

Figure 1: Block diagram of method SP2E.