Advanced modeling in Lorentz force eddy current testing

Nowadays, there is an increasing demand on reliable and efficient methods to evaluate materials and components in a nondestructive way. Particularly in the field of aerospace engineering, the components are subject to fulfill high quality and safety standards, which necessitate methods with a high accuracy, repeatability and inspection speed. This work deals with the nondestructive testing method Lorentz force eddy current testing. Unlike traditional eddy current methods, the induction process is based on relative motion between a permanent magnet and the object under test. An integral part of this thesis is the development of a new magnet system with improved characteristics. The proposed design is based on the Halbach principle and is made of Neodymium-Iron-Boron alloys. Besides that, it contains a piece made of highly saturating iron-cobalt. In this sense, it was possible to increase and focus the magnetic flux density in the vicinity of the specimen. The development of a decent optimization strategy allows to determine problem specific magnet designs in dependence on the measurement requirements. In the further course of this thesis, numerical simulations are performed addressing the uncertainty and sensitivity analysis of the system. Therefore, the model parameters are investigated in terms of their statistical properties. The resulting stochastic electromagnetic field problem is solved by means of the generalized polynomial chaos technique in combination with the finite element method. This enabled the identification of most influencing parameters in the system. In the context of the uncertainty analysis, it is observed that the velocity obeys characteristic oscillations. In order to deepen the understanding of this phenomenon, an analytical approach is presented to evaluate the electromagnetic fields and forces while taking into account the resistive and inductive character of the moving conductor. Finally, an alternative Lorentz force eddy current testing system is proposed where the object under test is encompassed by a ring magnet. The working principle is exemplified by theoretical considerations. This work contributes to increase the knowledge and understanding about Lorentz force eddy current testing and intends to advance the current state of the art with new and innovative approaches.In der heutigen Zeit steigt der Bedarf an effizienten und leistungsfähigen Verfahren zur zerstörungsfreien Prüfung von Werkstoffen und Bauteilen rasant an. Besonders in den Bereichen Luft- und Raumfahrttechnik unterliegen die Bauteile hohen Qualitätsstandards im Sinne der Sicherheit. Dies setzt Verfahren mit hoher Genauigkeit, Wiederholbarkeit und Schnelligkeit voraus. Diese Arbeit befasst sich mit der Methode der Lorentzkraft-Wirbelstromprüfung. Im Gegensatz zu klassischen Induktionsverfahren werden die Wirbelströme aufgrund einer Relativbewegung zwischen einem Permanentmagneten und dem Prüfobjekt hervorgerufen. Ein zentraler Gegenstand dieser Arbeit stellt die Entwicklung eines neuen Magnetsystems dar. Dieses basiert auf dem Halbach-Prinzip und besteht neben den bekannten Neodym-Eisen-Bor Legierungen aus einer Eisen-Kobalt-Verbindung mit hoher Sättigungsmagnetisierung. In diesem Sinn war es möglich die magnetische Flussdichte in der Nähe des Prüfkörpers zu fokussieren und zu verstärken. Die Entwicklung einer geeigneten Optimierungsroutine erlaubt die flexible Identifikation der Magnetgeometrie in Abhängigkeit der gestellten Anforderungen. Im weiteren Verlauf wurden numerische Simulationen zur Unsicherheits- und Sensitivitätsanalyse durchgeführt. Im Zuge dessen wurden die Modellparameter hinsichtlich ihrer statistischen Eigenschaften untersucht. Das zugrunde liegende stochastische Feldproblem wurde mit Hilfe der Methode des "Generalized Polynomial Chaos" gelöst. Dies ermöglichte die Identifikation der wichtigsten Einflussgrößen im System. Im Zusammenhang mit der Unsicherheitsanalyse wurden charakteristische Oszillationen der Relativgeschwindigkeit zwischen Permanentmagnet und Prüfkörper beobachtet. Um diese Phänomene besser verstehen zu können, wurde ein analytischer Zugang entwickelt, der die Bestimmung der elektromagnetischen Felder und Lorentzkräfte ermöglicht. Zu guter Letzt wird ein alternatives System zur Lorentzkraft-Wirbelstromprüfung vorgestellt, indem der Prüfkörper von einem Ringmagneten umschlossen ist. Die prinzipielle Funktionsweise des neuen Systems wird mit theoretischen Vorbetrachtungen in Form von analytischen Lösungen aufgezeigt. Die Arbeit vertieft die Kenntnisse über die Lorentzkraft-Wirbelstromprüfung und enthält neue sowie innovative Ansätze, die den Stand der Technik vorantreiben

Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of < 0.1 %, < 1 %, and < 10 %, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions

Low-Temperature Magnetothermodynamics Performance of Tb1-xErxNi2 Laves-Phases Compounds for Designing Composite Refrigerants

In this paper, the results of heat capacity measurements performed on the polycrystalline Tb1-xErxNi2 intermetallic compounds with x = 0.25, 0.5 and 0.75 are presented. The Debye temperatures and lattice contributions as well as the magnetic part of the heat capacity were determined and analyzed. The heat capacity measurements reveal that the substitution of Tb atoms for Er atoms leads to a linear reduction of the Curie temperatures in the investigated compounds. The ordering temperatures decrease from 28.3 K for Tb0.25Er0.75Ni2 to 12.9 K for Tb0.75Er0.25Ni2. Heat capacity measurements enabled us to calculate with good approximation the isothermal magnetic entropy ΔSmag and adiabatic temperature changes ΔTad for Tb1-xErxNi2, for the magnetic field value equal to 1 T and 2 T. The optimal molar ratios of individual Tb0.75Er0.25Ni2, Tb0.5Er0.5Ni2 and Tb0.25Er0.75Ni2 components in the final composite were theoretically determined. According to the obtained results, the investigated composites make promising candidates that can find their application as an active body in a magnetic refrigerator performing an Ericsson cycle at low temperatures. Moreover, for the Tb0.5Er0.5Ni2 compound, direct measurements of adiabatic temperature change in the vicinity of the Curie temperature in the magnetic field up to 14 T were performed. The obtained high-field results are compared to the data for the parent TbNi2 and ErNi2 compounds, and their magnetocaloric properties near the Curie temperature are analyzed in the framework of the Landau theory for the second-order phase transitions

Efficient high-resolution TMS mapping of the human motor cortex by nonlinear regression

Transcranial magnetic stimulation (TMS) is a powerful tool to investigate causal structure-function relationships in the human brain. However, a precise delineation of the effectively stimulated neuronal populations is notoriously impeded by the widespread and complex distribution of the induced electric field. Here, we propose a method that allows rapid and feasible cortical localization at the individual subject level. The functional relationship between electric field and behavioral effect is quantified by combining experimental data with numerically modeled fields to identify the cortical origin of the modulated effect. Motor evoked potentials (MEPs) from three finger muscles were recorded for a set of random stimulations around the primary motor area. All induced electric fields were nonlinearly regressed against the elicited MEPs to identify their cortical origin. We could distinguish cortical muscle representation with high spatial resolution and localized them primarily on the crowns and rims of the precentral gyrus. A post-hoc analysis revealed exponential convergence of the method with the number of stimulations, yielding a minimum of about 180 random stimulations to obtain stable results. Establishing a functional link between the modulated effect and the underlying mode of action, the induced electric field, is a fundamental step to fully exploit the potential of TMS. In contrast to previous approaches, the presented protocol is particularly easy to implement, fast to apply, and very robust due to the random coil positioning and therefore is suitable for practical and clinical applications

Magnetocaloric performance of the three-component Ho1-xErxNi2 (x = 0.25, 0.5, 0.75) Laves phases as composite refrigerants

To date, significant efforts have been put into searching for materials with advanced magnetocaloric properties which show promise as refrigerants and permit realization of efficient cooling. The present study, by an example of Ho1−xErxNi2, develops the concept of magnetocaloric efficiency in the rare-earth Laves-phase compounds. Based on the magneto-thermodynamic properties, their potentiality as components of magnetocaloric composites is illustrated. The determined regularities in the behaviour of the heat capacity, magnetic entropy change, and adiabatic temperature change of the system substantiate reaching high magnetocaloric potentials in a desired temperature range. For the Ho1−xErxNi2 solid solutions, we simulate optimal molar ratios and construct the composites used in magnetic refrigerators performing an Ericsson cycle at low temperatures. The tailored magnetocaloric characteristics are designed and efficient procedures for their manufacturing are developed. Our calculations based on the real empirical data are very promising and open avenue to further experimental studies. Systems showing large magnetocaloric effect (MCE) at low temperatures are of importance due to their potential utilization in refrigeration for gas liquefaction

In situ impedance measurements on postmortem porcine brain

The paper presents an experimental study where the distinctness of grey and white matter of an in situ postmortem porcine brain by impedance measurements is investigated. Experimental conditions that would allow to conduct the same experiment on in vivo human brain tissue are replicated

Recent advancements in Lorentz force eddy current testing

Lorentz Force Eddy Current Testing (LET) is a non-destructive testing technique based on induced eddy currents due to relative motion between a permanent magnet and a conductive, non-ferromagnetic device under test which has been recently introduced. The Lorentz force acting on the magnet is measured and perturbations in conductivity change the Lorentz force profile along the conductor. The permanent magnet is placed in a lift-off distance above the specimen moving with a constant velocity relative to the magnet. The design of the magnet is the most crucial element to improve the technique. Therefore, we present new developments in LET: the optimization of an innovative magnetic structure enhancing the Lorentz force and an uncertainty analysis to identify most important sources of variance. Futhermore, in a defect depth study a detection limit for LET was determined. A new cylindrical magnetic Halbach structure has been designed to concentrate and magnify the magnetic field below the structure. For internal defects a multi-objective, non-linear optimization to maximize the defect response of the drag force is performed. The optimized magnet shape depends on the geometrical parameters of the experimental setup and therefore the optimal shape is highly problem-specific. Secondly, we investigate the uncertainties in our existing experimental setup quantified by a non-intrusive polynomial chaos expansion to determine the impact of multiple unknown input parameters. The experimentally determined statistics of velocity, magnetic remanence of the permanent magnet, conductivity of the specimen and the lift-off distance are modeled as uniform and beta-distributed random variables. The numerically predicted force profiles were validated by experiments. The included analysis of variance of the Lorentz force enables the enhancement of defect detection capability. Finally, experiments with a specimen containing a quasi-infinite crack were performed. By variation of the defect depth a detection limit for LET for drag- and lift-force components of the Lorentz force was determined. It showed the compatibility of LET compared with traditional eddy current testing

A principled approach to conductivity uncertainty analysis in electric field calculations

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems

Motion-induced eddy current testing of composite materials

Modern composite materials are gaining more and more importance in mechanical engineering. Due to the complex structure of most of these materials, traditional NDT methods do not satisfy the measurement requirements. In this paper we address the capabilities and limitations of the non-destructive testing method of motion-induced eddy currents for (non-ferromagnetic) composite materials. The specimen moves with constant velocity through a magnetic field, which is created by a fixed permanent magnet. The interaction of induced eddy currents and the primary magnetic field re-sults in the Lorentz force acting on the specimen. Due to the third Newton law, the reaction force acts on the magnet system itself and is measured in all three spatial dimensions. Every force component has a characteristic profile for a certain defect-free specimen. Anomalies in the specimen affect the eddy currents due to variations of local conductivity. These deviations influence the measured force profiles from which the location, size and type of the defect in the specimen may be determined. Two types of magnet systems have been applied: a cylindrical magnet and a radial Halbach array with a ferromagnetic disc. The cylindrical magnet produces a dipole-like field, whereas the Halbach array with the additional disc creates a field concentrated right below the magnet system. Experiments show, that the Halbach array is very well suited for thin speci-mens. The defect response signal is higher due to the stronger eddy currents caused by the focused magnetic field. Two different types of composite materials have been experimentally tested: Carbon fiber reinforced plastic (CFRP) and glass laminate aluminum reinforced epoxy (GLARE). For CFRP four samples were fabricated, whereas one was tested. For GLARE two samples were used with defects in different depth

Lions at the Gates: Trans-disciplinary Design of an Early Warning System to Improve Human-Lion Coexistence

Across Africa, lions (Panthera leo) are heavily persecuted in anthropogenic landscapes. Trans-disciplinary research and virtual boundaries (geofences) programmed into GPS-tracking transmitters offer new opportunities to improve coexistence. During a 24-month pilot study (2016–2018), we alerted communities about approaching lions, issuing 1,017 alerts to four villages and 19 cattle posts. Alerts reflected geofence breaches of nine lions (2,941 monitoring days) moving between Botswana's Okavango Delta and adjacent agro-pastoral communities. Daily alert system costs per lion were US$18.54, or$5,460.24 per GPS deployment (n = 13). Alert-responsive livestock owners mainly responded by night-kraaling of cattle (68.9%), significantly reducing their losses (by $124.61 annually), whereas losses of control group and non-responsive livestock owners remained high ($317.93 annually). Community satisfaction with alerts (91.8%) was higher than for compensation of losses (24.3%). Study lions spent 26.3% of time monitored in geofenced community areas, but accounted for 31.0% of conflict. Manual alert distribution proved challenging, static geofences did not appropriately reflect human safety or the environment's strong seasonality that influenced cattle predation risk, and tracking units with on-board alert functions often failed or under-recorded geofence breaches by 27.9%. These insufficiencies prompted the design of a versatile and autonomous lion alert platform with automated, dynamic geofencing. We co-designed this prototype platform with community input, thereby incorporating user feedback. We outline a flexible approach that recognizes conflict complexity and user community heterogeneity. Here, we describe the evolution of an innovative Information and Communication Technologies-based (ICT) alert system that enables instant data processing and community participation through interactive interfaces on different devices. We highlight the importance of a trans-disciplinary co-design and development process focussing on community engagement while synthesizing expertise from ethnography, ecology, and socio-informatics. We discuss the bio-geographic, social, and technological variables that influence alert system efficacy and outline opportunities for wider application in promoting coexistence and conservation