Paul Sieber

Last Name

Sieber

First Name

Paul

ORCID

0000-0003-4632-7079

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03890 - Chatzi, Eleni / Chatzi, Eleni

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Publications 1 - 8 of 8

Towards a FRF-based parametric surrogate for guided wave-based evaluation in multiple defect scenarios
Sieber, Paul; Agathos, Konstantinos; Soman, Rohan; et al. (2024)
Proceedings of SPIE ~ Health Monitoring of Structural and Biological Systems XVIII
Ultrasonic Guided Waves (UGWs) are particularly suited for monitoring applications as their high frequency allows them to interact with small defects while traveling long distances. For defect localization in plate struc tures, Lamb waves are generated and exploited in the UGW sense. While data-driven methods, exclusively driven from the collected time series have proven adept for various damage identification tasks, a more refined characterization calls for additional use of physics-based models. In this work, we demonstrate efficient fusion of UGW data with numerical models of plate structures, which are obtained from high-fidelity spectral element simulations. A major bottleneck associated with such a hybrid modeling scheme lies in the excessive computational cost associated with simulations of high–frequency Lamb waves through plate structures. This is due to their short wavelength and short period, which demands a fine discretization in both space and time. To avoid repeated evaluations of prohibitively expensive computational models, model order reduction methods or surrogates can be adopted. A surrogate model should be based on mechanical information, to reduce the amount of training data required. For practical reasons, surrogate models should further be flexible, allowing for assimilation of multiple defect locations, as well as the simulation of more complex geometrical features, such as rivet holes or boundaries. We show steps toward construction of such a surrogate, which draws its construct from the concept of Frequency Response Functions (FRFs), or in other words, the representation of a system in the frequency domain.
Guided waves-based SHM using an ML-based parametric ROM
Sieber, Paul; Agathos, Konstantinos; Soman, Rohan; et al. (2023)
Proceedings of SPIE ~ Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and Transportation XVII
Structural Health Monitoring (SHM) using Ultrasonic Guided Waves (UGWs) offers great potential in detection of minor flaws, due to the employed short wavelengths. A bottleneck in UGWs-based schemes lies in the extensive computational costs for evaluating the associated wave propagation models. Such detailed models form though a necessity to reach higher levels of SHM, e.g. localization and assessment of flaws. Reduced Order Models (ROMs) and surrogate models allow for lowering the substantial numerical costs for SHM applications, especially if they are parameterized with respect to the characteristics of different flaw configurations. Machine Learning (ML) algorithms can be trained for this purpose, however, in the case of black box ML algorithms, this comes with the drawback of the requirement for substantial data availability for the purpose of training. Such, training data, which are typically derived from full order numerical simulations, are computationally costly to obtain. To reduce the amount of training data, known information on the mechanical behavior can be harnessed and inserted into the estimation process. In the present work, a method is introduced that exploits the properties of the interaction of UGWs with flaws in the frequency domain. It can be shown that the frequency domain response is characterized by periodic features that are linked to the flaw location. An ML model based on this knowledge can be trained with less training data. The potential of this approach for damage localization in the context of SHM is illustrated in a simulated example of a composite plate.
Dynamic Response Study of Piezoresistive Ti3C2-MXene Sensor for Structural Impacts
Srivatsa, Shreyas; Sieber, Paul; Hofer, Céline; et al. (2023)
Sensors
MXenes are a new family of two-dimensional (2D) nanomaterials. They are inorganic compounds of metal carbides/nitrides/carbonitrides. Titanium carbide MXene (Ti3 C2 -MXene) was the first 2D nanomaterial reported in the MXene family in 2011. Owing to the good physical properties of Ti3 C2 -MXenes (e.g., conductivity, hydrophilicity, film-forming ability, elasticity) various applications in wearable sensors, energy harvesters, supercapacitors, electronic devices, etc., have been demonstrated. This paper presents the development of a piezoresistive Ti3 C2 -MXene sensor followed by experimental investigations of its dynamic response behavior when subjected to structural impacts. For the experimental investigations, an inclined ball impact test setup is constructed. Stainless steel balls of different masses and radii are used to apply repeatable impacts on a vertical cantilever plate. The Ti3 C2 -MXene sensor is attached to this cantilever plate along with a commercial piezoceramic sensor, and their responses for the structural impacts are compared. It is observed from the experiments that the average response times of the Ti3 C2 -MXene sensor and piezoceramic sensor are 1.28±0.24 μ s and 31.19±24.61 μ s, respectively. The fast response time of the Ti3 C2 -MXene sensor makes it a promising candidate for monitoring structural impacts.
Guided Wave–Based Defect Localization via Parameterized FRF-Based Reduced-Order Models
Sieber, Paul; Agathos, Konstantinos; Soman, Rohan; et al. (2024)
Journal of Engineering Mechanics
The use of Lamb waves within a guided wave (GW)–based scheme holds promise toward monitoring and nondestructive evaluation (NDE) of plate structures. Their short wavelength enables interaction with small defects and they can travel long distances, thus offering extensive spatial coverage. In boosting the performance of these schemes for more advanced damage identification tasks, such as precise damage localization and quantification, the fusion of measurement data with models is advantageous. Such a hybrid scheme, which relies on the inclusion of engineering models, is hampered by the short wavelengths of GW-based schemes. Short wavelengths require a fine discretization of numerical models in space and in time, which results in high computational costs. In alleviating this issue, we propose a reduced-order model (ROM) relying on exploitation of the frequency response function (FRF) principle, which is parameterized with respect to the positioning of local defects. Through appropriate coordinate transformations, the surrogate, constructed based on the matching pursuit (MP) algorithm, can exploit the mechanical properties of the wave so that only a small amount of training simulations are needed. The efficacy of the proposed surrogate is demonstrated in a synthetic inverse setting, using a particle swarm optimization (PSO) strategy.
A parametrized Reduced Order Model for rapid evaluation of flaws in Guided Wave testing
Sieber, Paul; Agathos, Konstantinos; Soman, Rohan; et al. (2022)
Structural Health Monitoring 2021: Enabling Next Generation SHM for Cyber-Physical Systems
Data from guided wave propagation in structures, produced by piezoelectric elements, can offer valuable information regarding the possible existence of flaws. Numerical models can be used to complement the attained data for refining the potential for flaw characterization. Unfortunately, evaluation of these models remains computationally expensive, especially for small defects, due to the short wavelength required for detection and, the in turn fine discretization in time and space. This renders realâ€“time simulation infeasible, rendering GWâ€“approaches less attractive for inverse problem formulations, where the forward problem needs to be solved several times. We propose an accelerated computation method, which exploits the properties of guided waves interacting with defects, where an extra band of waves is created, whose phase is differentiated, depending on the location of the flaw (e.g. notch) within the medium. To expedite the actual simulation for the inverse problem, the system is parametrized in terms of the location of the flaw and, in an offline phase, is repeatedly solved to produce snapshots of the systemâ€™s response. The snapshots are used to create a physicsâ€“informed interpolation of the solution of the wave propagation problem for different flaw locations. The gained information is then used in an inverse setting for localising the defect using an evolution strategy as a means to stochastic, derivative-free numerical optimization. The method is demonstrated in simulations of a 2D slice of a thin plate.
Model-based approach to Guided Wave based Damage Detection
Sieber, Paul (2025)
Recent advances in structural engineering have underscored the importance of Structural Health Monitoring (SHM) systems as tools for ensuring safety, extending service life, and reducing the environmental and economic costs of maintenance. In particular, SHM systems based on Ultrasonic Guided Waves (UGWs) have demonstrated significant promise for thin-walled structures, such as plates and shells, where small, incipient flaws may lead to critical failures. Among UGWs, Lamb waves are especially valuable due to their ability to propagate over long distances with low attenuation and to interact sensitively with small defects. Further, wave propagation is influenced by internal anomalies, such as delaminations, allowing for monitoring invisible, subsurface damage. These characteristics, coupled with the availability of low-cost piezoelectric transducers (PZTs) for actuation and sensing, make Lamb wave-based SHM a compelling choice for long-term, in situ monitoring. However, the full exploitation of UGWs in SHM is limited by the challenges associated with interpreting the complex wavefields generated through interactions with damage, boundaries, and material heterogeneities. While high-fidelity numerical models, such as those based on finite or spectral element methods, offer valuable predictive capabilities, they are computationally expensive. The short wavelengths and high frequencies characteristic of UGWs demand fine discretizations in both space and time, which renders traditional simulations infeasible for realtime or large-scale parametric analyses. This thesis addresses this challenge by developing a model-based approach to UGW-based damage detection that leverages surrogate modeling to reduce computational costs without sacrificing physical interpretability. The aim is to create an efficient framework for forward simulations of guided wave propagation that can be used in inverse settings for damage localization and characterization. Central to the proposed framework is the use of Frequency Response Functions (FRFs), which allow for a flexible, frequency-domain representation of the system response and can be adapted to various excitation scenarios. Addressing the limited availability of documented datasets for UGW measurements of complex structures, the thesis begins with an experimental study on a small-scale wind turbine blade subjected to cyclic loading. The experimental campaign provides a high-quality dataset comprising UGW measurements, strain gauge data, and environmental parameters. This dataset is used to evaluate the sensitivity of guided waves to fatigue-induced damage and to benchmark subsequent modeling approaches. The combination of synchronized measurements of strain gauges and UGWs allows for the comparison of different SHM strategies. As the low-frequency excitation of the blade is synchronized with measurements of UGWs, effects of strong ambient vibrations, such as the closing and opening of cracks, can be investigated. Building upon these experimental insights, the first modeling approach developed in this work uses Matching Pursuit (MP) to construct deterministic surrogate models from FRF data. This method enables efficient interpolation between simulated configurations and supports the reconstruction of the full wave response with a limited number of simulations. The significant speedup of the proposed surrogate enables the calculation of the response surface for different metrics. Applying the surrogate in an inverse setting in combination with Particle Swarm Optimization (PSO) demonstrates the effectiveness of the proposed surrogate for defect localization. In a next step, a stochastic surrogate based on Gaussian Process Regression (GPR) is introduced. This model allows for uncertainty quantification and generalizes more flexibly to scenarios involving defects located between sensors and actuators. Further, this surrogate can be applied in scenarios of anisotropic material behavior, such as Carbon Fiber Reinforced Polymer (CFRP)-plates. Finally, the thesis presents a hybrid surrogate architecture capable of handling multiple defects and arbitrary sensor configurations through a parametric, FRF-based decomposition of the wavefield, relying on ray tracing. This approach retains interpretability and maintains computational efficiency while extending applicability to complex structural configurations. The ray tracing approach enables the extraction of information on different wave packets propagating through the plate. In this sense, the surrogate provides more physical information than common high-fidelity simulations, such as the Finite Element Method (FEM) or Spectral Element Method (SEM). The proposed surrogates are verified against full-order spectral element simulations, which were validated against experimental data. Results demonstrate that the surrogate models achieve a significant reduction in computational time—by several orders of magnitude—while preserving key features of the guided wave response. This allows for the practical implementation of inverse methods, including optimization-based defect localization, in near real-time. By combining physical modeling with machine learning and model reduction techniques, this thesis advances the state of the art in UGW-based SHM. The resulting framework enables efficient simulation and interpretation of guided wave propagation in thin plates and can be extended to broader SHM applications in aerospace, wind energy, and civil infrastructure systems. The methodological contributions provide a foundation for developing intelligent monitoring systems capable of accurate, real-time damage detection and decision support.
Explainable, Flexible, Frequency Response Function-Based Parametric Surrogate for Guided Wave-Based Evaluation in Multiple Defect Scenarios
Sieber, Paul; Soman, Rohan; Ostachowicz, Wieslaw; et al. (2025)
Applied Sciences
Lamb waves offer a series of desirable features for Structural Health Monitoring (SHM) applications, such as the ability to detect small defects, allowing to detect damage at early stages of its evolution. On the downside, their propagation through media with multiple geometrical features results in complicated patterns, which complicate the task of damage detection, thus hindering the realization of their full potential. This is exacerbated by the fact that numerical models for Lamb waves, which could aid in both the prediction and interpretation of such patterns, are computationally expensive. The present paper provides a flexible surrogate to rapidly evaluate the sensor response in scenarios where Lamb waves propagate in plates that include multiple features or defects. To this end, an offline–online ray tracing approach is combined with Frequency Response Functions (FRFs) and transmissibility functions. Each ray is thereby represented either by a parametrized FRFs, if the origin of the ray lies in the actuator, or by a parametrized transmissibility function, if the origin of the ray lies in a feature. By exploiting the mechanical properties of propagating waves, it is possible to minimize the number of training simulations needed for the surrogate, thus avoiding the repeated evaluation of large models. The efficiency of the surrogate is demonstrated numerically, through an example, including different types of features, in particular through holes and notches, which result in both reflection and conversion of incident waves. For most sensor locations, the surrogate achieves an error between 1% and 4%, while providing a computational speedup of three to four orders of magnitude.
Explainable, Flexible, FRF-Based Parametric Surrogate for Guided Wave-Based Evaluation in Multiple Defect Scenarios
Sieber, Paul; Soman, Rohan; Ostachowicz, Wieslaw; et al. (2025)
Preprints
Lamb waves offer a series of desirable features for SHM-applications, such as the ability to detect small defects, allowing to detect damage at early stages of its evolution. On the downside, their propagation through media with multiple geometrical features results in complicated patterns, which complicate the task of damage detection, thus hindering the realization of their full potential. This is exacerbated by the fact that numerical models for Lamb waves, which could aid in both the prediction and interpretation of such patterns, are computationally expensive. The present paper provides a flexible surrogate to rapidly evaluate the sensor response in scenarios where Lamb waves propagate in plates that include multiple features or defects. To this end, an offline-online ray tracing approach is combined with FRF and transmissibility functions. Each ray is thereby represented either by a parametrized FRF, if the origin of the ray lies in the actuator, or by a parametrized transmissibility function, if the origin of the ray lies in a feature. By exploiting the mechanical properties of propagating waves, it is possible to minimize the number of training simulations needed for the surrogate, thus avoiding the repeated evaluation of large models. The efficiency of the surrogate is demonstrated numerically, through an example, including different types of features, in particular through holes and notches, which result in both reflection and conversion of incident waves.

Publications 1 - 8 of 8

Paul Sieber

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