A Model-Based Damage Identification using Guided Ultrasonic Wave Propagation in Fiber Metal Laminates

[EN] Fiber metal laminates (FML) are lightweight hybrid structural materials that combine the ductile properties of metal with high specific stiffness of fiber reinforced plastics. These advantages led to a dramatic increase in such materials for aeronautical structures over the last few years. One of the most common and vulnerable defects in FML is impact-related delamination, often invisible to the human eye. Guided ultrasonic waves (GUW) show high potential for monitoring structural integrity and damage detection in thin-walled structures by using the physical phenomena of wave propagation interacting with the defects. The focus of this research project is on describing an inverse solution for the detection and characterization of defect in FML. Model-based damage analysis utilizes an accurate finite element model (FEM) of GUW interaction with the damage. The FEM is developed by the project partners from mechanics at Helmut-Schmidt-University in Hamburg, Germany, and will be treated as a black-box for further analysis. A Bayesian approach (Markov chain Monte Carlo) is employed to characterize the damage and quantify its uncertainties. This inference problem in a stochastic framework requires a very large number of forward solves. Therefore, a profound investigation is carried out on different reduced-order modeling (ROM) methods in order to apply a suitable technique that significantly improves the computational efficiency. The proposed method is well illustrated on a simpler case study for the damage detection, localization and characterization using 2D elastic wave equation. The damage in this case is modeled as a reduction in the wave propagation velocity. The inference problem utilizes a parameterized projection-based ROM coupled with a surrogate model instead of the underlying high-dimensional model.This research is funded by the Deutsche Forschungsgemeinschaft Research Unit 3022 under Grant No. LO1436/12-1.Bellam Muralidhar, NK.; Lorenz, D. (2022). A Model-Based Damage Identification using Guided Ultrasonic Wave Propagation in Fiber Metal Laminates. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 36-45. https://doi.org/10.4995/YIC2021.2021.12684OCS364

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution

Damage Identification in Fiber Metal Laminates using Bayesian Analysis with Model Order Reduction

Fiber metal laminates (FML) are composite structures consisting of metals and fiber reinforced plastics (FRP) which have experienced an increasing interest as the choice of materials in aerospace and automobile industries. Due to a sophisticated built up of the material, not only the design and production of such structures is challenging but also its damage detection. This research work focuses on damage identification in FML with guided ultrasonic waves (GUW) through an inverse approach based on the Bayesian paradigm. As the Bayesian inference approach involves multiple queries of the underlying system, a parameterized reduced-order model (ROM) is used to closely approximate the solution with considerably less computational cost. The signals measured by the embedded sensors and the ROM forecasts are employed for the localization and characterization of damage in FML. In this paper, a Markov Chain Monte-Carlo (MCMC) based Metropolis-Hastings (MH) algorithm and an Ensemble Kalman filtering (EnKF) technique are deployed to identify the damage. Numerical tests illustrate the approaches and the results are compared in regard to accuracy and efficiency. It is found that both methods are successful in multivariate characterization of the damage with a high accuracy and were also able to quantify their associated uncertainties. The EnKF distinguishes itself with the MCMC-MH algorithm in the matter of computational efficiency. In this application of identifying the damage, the EnKF is approximately thrice faster than the MCMC-MH

Ultraschallüberwachung von Faser-Metall-Laminaten mit integrierten Sensoren: Modellbasierte Schadens Analyse

Structural health monitoring (SHM) with in-situ piezoelectric sensing elements based on guided ultrasonic waves (GUW) is an international research object. However, SHM approaches are hardly addressed for fiber metal laminates (FML). This research presents a model-based damage analysis using GUW and methodologies to localize, characterize and quantify damage parameters in FML. In this work, a two-dimensional elasticity-based finite element model for GUW excitation and sensing has been developed for various damage configurations and validated through numerical experiments. The damage detection by GUW measurements is an inverse problem, with questions of solvability, uniqueness of solution, and sensitivity to measurement disturbances. Strong regularizers can help with certain ill-posed problems, but they only provide a point estimate of the damage parameter. Due to the inherent uncertainties in the application, this research followed a broader approach of Bayesian inference that offers the solution for an inverse problem by modeling the unknown parameters as a random variable and describing it by means of its probability distribution. The damage identification procedure involves the computation of the underlying high fidelity (HiFi) model several thousand times making the simulation cost prohibitively high. Therefore, an efficient adaptive parametric model order reduction method that accelerated the underlying HiFi model by several folds was employed. The resulting reduced-order models that could swiftly simulate the wave propagation with a close approximation of the HiFi solution are further exploited by the Bayesian inference methods to identify different damage configurations of the FML. A very limited amount of in-situ sensor measurements is required to estimate the damage parameters of FML. The algorithms are capable of inferring the position, length and stiffness of the damage parameters along with their associated uncertainties.Structural Health Monitoring (SHM) mit in-situ piezoelektrischen Sensorelementen basierend auf geführten Ultraschallwellen (GUW) ist ein internationaler Forschungsgegenstand. Allerdings werden SHM-Ansätze für Faser-Metall-Laminate (FML) kaum berücksichtigt. In dieser Arbeit werden eine modellbasierte Schadensanalyse mit GUW und Methoden zur Lokalisierung, Charakterisierung und Quantifizierung von Schadensparametern in FML vorgestellt. In dieser Arbeit wurde ein zweidimensionales, auf Elastizität basierendes Finite-Elemente-Modell für GUW-Anregung und -Sensorik für verschiedene Schadenskonfigurationen entwickelt und durch numerische Experimente validiert. Die Schadenserkennung durch GUW-Messungen ist ein inverses Problem, bei dem sich Fragen der Lösbarkeit, der Eindeutigkeit der Lösung und der Empfindlichkeit gegenüber Messstörungen stellen. Starke Regularisierer können bei bestimmten schlecht gestellten Problemen helfen, aber sie liefern nur eine Punktschätzung des Schadensparameters. Aufgrund der inhärenten Unsicherheiten in der Anwendung verfolgte diese Forschung einen breiteren Ansatz der Bayes'schen Inferenz, der die Lösung für ein inverses Problem bietet, indem er die unbekannten Parameter als Zufallsvariable modelliert und sie durch ihre Wahrscheinlichkeitsverteilung beschreibt. Bei der Schadensidentifizierung muss das zugrunde liegende High-Fidelity-Modell (HiFi) mehrere tausend Mal berechnet werden, was die Simulationskosten prohibitiv hoch macht. Daher wurde ein effizientes adaptives parametrisches Modellordnungsreduktionsverfahren eingesetzt, das das zugrunde liegende HiFi-Modell um ein Vielfaches beschleunigt. Die daraus resultierenden Modelle mit reduzierter Ordnung, die die Wellenausbreitung mit einer guten Annäherung an die HiFi-Lösung schnell simulieren können, werden von den Bayes'schen Schlussfolgerungsmethoden weiter genutzt, um verschiedene Schadenskonfigurationen der FML zu identifizieren. Für die Schätzung der Schadensparameter von FML ist eine sehr begrenzte Anzahl von In-situ-Sensormessungen erforderlich. Die Algorithmen sind in der Lage, die Position, Länge und Steifigkeit der Schädigungsparameter zusammen mit den zugehörigen Unsicherheiten abzuleiten