Probabilistic inference, especially in the Bayesian framework, is a foundation for quantifying uncertainties in geophysical inversion applications. However, due to the presence of high-dimensional datasets and the large-scale nature of geophysical inverse problems, the applicability and scalability of probabilistic inference face significant challenges for such applications. This thesis is dedicated to improving the probabilistic inference algorithms' scalability and demonstrating their applicability for large-scale geophysical inversion applications. In this thesis, I delve into three leading applied approaches in computing the Bayesian posterior distribution in geophysical inversion applications: Laplace's approximation, Markov chain Monte Carlo (MCMC), and variational Bayesian inference. The first approach, Laplace's approximation, is the simplest form of approximation for intractable Bayesian posteriors. However, its accuracy relies on the estimation of the posterior covariance matrix. I study the visualization of the misfit landscape in low-dimensional subspace and the low-rank approximations of the covariance for full waveform inversion (FWI). I demonstrate that a non-optimal Hessian's eigenvalues truncation for the low-rank approximation will affect the approximation accuracy of the standard deviation, leading to a biased statistical conclusion. Furthermore, I also demonstrate the propagation of uncertainties within the Bayesian physics-informed neural networks for hypocenter localization applications through this approach. For the MCMC approach, I develop approximate Langevin MCMC algorithms that provide fast sampling at efficient computational costs for large-scale Bayesian FWI; however, this inflates the variance due to asymptotic bias. To account for this asymptotic bias and assess their sample quality, I introduce the kernelized Stein discrepancy (KSD) as a diagnostic tool. When larger computational resources are available, exact MCMC algorithms (i.e., with a Metropolis-Hastings criterion) should be favored for an accurate posterior distribution statistical analysis. For the variational Bayesian inference, I propose a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a deep denoiser through a Plug-and-Play method. I also developed Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD), a novel algorithm to sample the regularized posterior distribution. The PnP-SVGD demonstrates its ability to produce high-resolution, trustworthy samples representative of the subsurface structures for a post-stack seismic inversion application.

Indiana University-Purdue University Indianapolis (IUPUI) / This thesis presents the development, experimentation and validation of a reliable and robust system to monitor the injector pulse generated by an Engine Control Module (ECM) and send the corresponding fueling quantity to the real-time computer in a closed loop Hardware In the Loop (HIL) bench. The system can be easily calibrated for different engine platforms as well. The fueling quantity that is being injected by the injectors is a crucial variable to run closed loop HIL simulation to carry out the performance testing of engine, aftertreatment and other components of the vehicle. This research utilized Field Programmable Gate Arrays (FPGA) and Direct Memory Access (DMA) transfer capability offered by National Instruments (NI) Compact Reconfigurable Input-Output (cRIO) to achieve high speed data acquisition and delivery. The research was conducted in three stages. The first stage was to develop the HIL bench for the research. The second stage was to determine the performance of the system with different threshold methods and different sampling speeds necessary to satisfy the required accuracy of the fueling quantity being monitored. The third stage was to study the error and its variability involved in the injected fueling quantity from pulse to pulse, from injector to injector, between real injector stators and cheaper inductor load cells emulating the injectors, over different operating conditions with full factorial design of experimentation and mixed model Analysis Of Variance (ANOVA). Different thresholds were experimented to find out the best thresholds, the Start of Injection (SOI) threshold and the End of Injection (EOI) threshold that captured the injector “ontime” with best reliability and accuracy. Experimentation has been carried out at various data acquisition rates to find out the optimum speed of data sampling rate, trading off the accuracy of fueling quantity. The experimentation found out the expected error with a system with cheaper solution as well, so that, if a test application is not sensitive to error in fueling quantity, a cheaper solution with lower sampling rate and inductors as load cells can be used. The statistical analysis was carried out at highest available sampling rate on both injectors and inductors with the best threshold method found in previous studies. The result clearly shows the factors that affect the error and the variability in the standard deviations in error; it also shows the relation with the fixed and random factors. The real-time application developed for the HIL bench is capable of monitoring the injector waveform, using any fueling ontime table corresponding to the platform being tested, and delivering the fueling quantity in real-time. The test bench made for this research is also capable of studying injectors of different types with the automated test sequence, without occupying the resource of fully capable closed loop test benches for testing the ECM unctionality.

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In dieser Arbeit wird der Ansatz der Weltlinienquantenfeldtheorie (WQFT) zur Berechnung von Observablen des klassischen allgemeinen relativistischen Zweikörpersystems vorgestellt. Kompakte Körper wie Schwarze Löcher oder Neutronensterne werden im Rahmen einer effektiven Feldtheorie mit Weltlinienfeldern beschrieben. Die WQFT behandelt alle Weltlinienfelder gleichberechtigt mit dem Gravitationsfeld und ist definiert als die tree-level-Beiträge eines Pfadintegrals auf diesen Feldern. Zuerst wird die effektive feldtheoretische Beschreibung von kompakten Körpern mit Weltlinien und die post-Minkowski'schen Approximation der Streuung dieser Körpern vorgestellt. Die Einbeziehung des Spins wird mit besonderem Augenmerk auf ihre supersymmetrische Beschreibung in Form von antikommutierenden Grassmann-Variablen analysiert. Anschließend wird die WQFT mit einer Diskussion ihrer in-in Schwinger-Keldysh-Formulierung, ihrer Feynman-Regeln und Graphengenerierung sowie ihrer on-shell Einpunktfunktionen vorgestellt. Die Berechnung von Streuobservablen erfordert im Allgemeinen die Auswertung von Multi-Loop-Integralen, und wir analysieren die Zwei-Loop-Integrale, die in der dritten post-Minkowski'schen Ordnung der Weltlinienobservablen auftreten. Schließlich wenden wir uns den Ergebnissen der WQFT zu und beginnen mit der gravitativen Bremsstrahlung bei der Streuung zweier rotierender Körper. Diese Wellenform wird zusammen mit der Strahlungsinformation der Linear- und Drehimpulsflüsse diskutiert. Der gesamte abgestrahlte Drehimpuls führender post-Minkowski'schen Ordnung wird abgeleitet. Wir präsentieren dann die Ergebnisse des konservativen und strahlenden Impulses und des Spin-Kicks bei dritter post-Minkowski'scher Ordnung und quadratischer Ordnung in Spins zusammen mit der Abbildung der ungebundenen Ergebnisse auf einen konservativen (gebundenen) Hamiltonian bei der entsprechenden perturbativen Ordnung. / In this work the worldline quantum field theory (WQFT) approach to computing observables of the classical general relativistic two-body system is presented. Compact bodies such as black holes or neutron stars are described in an effective field theory by worldline fields with spin degrees of freedom efficiently described by anti-commuting Grassmann variables. Novel results of the WQFT include the gravitational bremsstrahlung at second post-Minkowskian order and the impulse and spin kick at third post-Minkowskian order all at quadratic order in spins. Next, the WQFT is presented with a comprehensive discussion of its in-in Schwinger-Keldysh formulation, its Feynman rules and graph generation and its on-shell one-point functions which are directly related to the scattering observables of unbound motion. Here, we present the second post-Minkowskian quadratic-in-spin contributions to its free energy from which the impulse and spin kick may be derived to the corresponding order. The computation of scattering observables requires the evaluation of multi-loop integrals and for the computation of observables at the third post-Minkowskian order we analyze the required two-loop integrals. Our discussion uses retarded propagators which impose causal boundary conditions of the observables. Finally we turn to results of the WQFT starting with the gravitational bremsstrahlung of the scattering of two spinning bodies. This waveform is discussed together with its radiative information of linear and angular momentum fluxes. Lastly we present the conservative and radiative impulse and spin kick at third post-Minkowskian order and quadratic order in spins together with the a conservative Hamiltonian at the corresponding perturbative order. The results obey a generalized Bini-Damour radiation-reaction relation and their conservative parts can be parametrized in terms of a single scalar.

Detta arbete har genomförts vid Volvo Construction Equipment i Braås. I nuläget används konventionell spraybågssvetsning med metallpulverfylld rörtråd i produktionen. Ett alternativ som övervägs är att byta till solidtråd. Huvudsyftet med detta arbete har varit att utreda huruvida några utvalda processer med 1.2 mm solidtråd är kapabla att producera ensträngs kälsvetsar som uppfyller av Volvo CE ställda krav: - Minst 3 mm i-mått. - Teoretiskt a-mått mellan 4 och 5.5 mm. - Svetsklass VD enligt Volvo standard STD 181-0004. - Kompatibel med fogföljning via ljusbåge. - Ingen spalt mellan plåtarna tillåten. Arbetet inleddes med en litteraturstudie för att framförallt beskriva svetsparametrars inverkan på svetsens inträngningsprofil och geometri.  Ett stort antal svetsförsök utfördes med konventionell spraybåge samt de vågformsstyrda processerna Fronius PMC och Lincoln Electrics RapidArc. Försöken genomfördes i PA och i PB läge. I PB läget orienterades förbandet dels med gränsytan mellan plåtarna horisontellt och dels vertikalt. Flertalet av försöken genomfördes med svetstraktor. Kompletterande försök genomfördes med svetsrobot. Inträngning och kvalité bedömdes framförallt genom makroprov och syning, men också genom lasermätning. Vid inledande faktorförsök med RapidArc, PMC och konventionell spraybågsprocess användes trådmatningshastighet 13 och 15 m/min i kombination med svetshastighet 55 och 65 cm/min. Försöken visade att i PB läge med horisontell gränsyta kan 3 mm i-mått uppnås med trådmatningshastigheten 13 m/min och svetshastigheten 55 cm/min. Under avslutande svetsförsök med PMC i PB läge med gränsytan vertikalt vid 60 cm/min svetshastighet, pendling och 14.5-15.5 m/min trådmatningshastighet erhölls i-mått avsevärt överstigande 3 mm. Vid svetsförsök i PB läge med solidtråd uppnåddes kraven på 3 mm i-mått och mjuka fattningskanter med ökad svetshastighet jämfört med ett typiskt produktionsfall. I PA läge erhölls mindre skillnad gentemot ett produktionsfall. Genom ytterligare optimering av svetsprocesserna är det dock inte orimligt att svetshastigheterna kan ökas utan försämrade i-mått och fattningskanter. Möjlig kostnadsreducering för tillsatsmaterialet vid övergång till solidtråd är 30-50% beroende på att solidtråden är billigare än metallpulverfylld rörtråd. Ytterligare kostnadsreducering kan erhållas genom förbrukning av mindre mängd tillsatsmaterial. Vid genomförde svetsförsök har mindre mängd tillsatsmaterial tillförts jämfört med typiska produktionsfall.  Både den konventionella spraybågsprocessen och de vågformsstyrda processerna är kapabla att producera de eftersträvade svetsarna med solidtråd. Här måste dock ett ”varnade finger” höjas; vid svetsningen krävs god kontroll av elektrodvinklarna och elektrodens position relativt fogens rot, annars erhålls betydligt sämre resultat. / This thesis has been performed at Volvo Construction Equipment in Braås. Currently, conventional MAG spray transfer with metal cored wire is used in the production. The company is now considering switching from metal cored wire to solid wire. The main purpose of this thesis has been to investigate whether a few selected processes used with 1.2 mm solid wire are capable of producing single pass fillet welds that conform to the following requirements set by Volvo CE: - Minimum i-dimension 3 mm. - Theoretical throat thickness between 4 and 5.5 mm. - Weld class VD according to Volvo standard STD 181-0004. - Compatible with Through Arc Seam Tracking. - No gap between the plates is allowed. A literature study was performed primarily in order to describe the influence of weld parameters on the weld and penetration profile. A large number of weld trials were performed with conventional spray transfer and the two waveform controlled processes Fronius PMC and Lincoln Electrics RapidArc. The weld trials were performed in the weld positions PA and PB. For PB the joint root was orientated both horizontally and vertically. For the majority of trials a weld tractor was used. Complementary trials were performed by a robot. Weld testing consisted primarily of macro etch testing and visual inspection but also laser scanning. The initial trials with RapidArc, PMC and conventional spray transfer were performed with the wire feed speeds 13 and 15 m/min in combination with the travel speeds 55 and 65 cm/min. The trials showed that when using weld position PB with a horizontal joint root, 3 mm i-dimension can be achieved by using wire feed speed 13 m/min and travel speed 55 cm/min. Final trials with PMC were performed in weld position PB with a vertical joint root using wire feed speeds 14.5-15.5 m/min, a travel speed of 60 cm/min and weaving resulting in i-dimensions much greater than 3 mm being achieved. Using solid wire in weld position PB, welds with 3 mm i-dimension and good wetting of the toes were produced with increased travel speed compared to a typical production case. However, in weld position PA less difference was obtained compared to a typical production case. By further optimizing the weld processes it is not unlikely that the travel speeds can be increased while maintaining the i-dimension and good wetting of the toes. A possible cost reduction for the filler material is 30-50% because solid wire is cheaper than metal cored wire. Using less filler material will result in additional cost reductions. During performed weld trials less filler material was used compared to current production scenarios. Both the conventional spray transfer process and the waveform controlled processes are capable of producing the desired welds with solid wire. However, a cautionary tale must be told: when welding, good control of the electrode angles and position relative to the joint root is needed otherwise much worse results will be obtained.

[ES] La estandarización de la Quinta Generación de redes móviles o 5G, ha concluido este año 2020. No obstante, en el año 2014 cuando la ITU empezó el proceso de estandarización IMT-2020, una de las principales interrogantes era cuál sería la forma de onda sobre la cual se construiría la capa física de esta nueva generación de tecnologías. El 3GPP se comprometió a entregar una tecnología candidata al proceso IMT-2020, y es así como dentro de este proceso de deliberación se presentaron varias formas de onda candidatas, las cuales fueron evaluadas en varios aspectos hasta que en el año 2016 el 3GPP tomó una decisión, continuar con CP-OFDM (utilizada en 4G) con numerología flexible. Una vez decidida la forma de onda, el proceso de estandarización continuó afinando la estructura de la trama, y todos los aspectos intrínsecos de la misma. Esta tesis acompañó y participó de todo este proceso. Para empezar, en esta disertación se evaluaron las principales formas de onda candidatas al 5G. Es así que se realizó un análisis teórico de cada forma de onda, destacando sus fortalezas y debilidades, tanto a nivel de implementación como de rendimiento. Posteriormente, se llevó a cabo una implementación real en una plataforma Software Defined Radio de tres de las formas de onda más prometedoras (CP-OFDM, UFMC y OQAM-FBMC), lo que permitió evaluar su rendimiento en términos de la tasa de error por bit, así como la complejidad de su implementación. Esta tesis ha propuesto también el uso de una solución armonizada como forma de onda para el 5G y sostiene que sigue siendo una opción viable para sistemas beyond 5G. Dado que ninguna de las forma de onda candidatas era capaz de cumplir por sí misma con todos los requisitos del 5G, en lugar de elegir una única forma de onda se propuso construir un transceptor que fuese capaz de construir todas las principales formas de onda candidatas (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). Esto se consiguió identificando los bloques comunes entre las formas de onda, para luego integrarlos junto con el resto de bloques indispensables para cada forma de onda. La motivación para esta solución era tener una capa física que fuese capaz de cumplir con todos los aspectos del 5G, seleccionando siempre la mejor forma de onda según el escenario. Esta propuesta fue evaluada en términos de complejidad, y los resultados se compararon con la complejidad de cada forma de onda. La decisión de continuar con CP-OFDM con numerología flexible como forma de onda para el 5G se puede considerar también como una solución armonizada, ya que al cambiar el prefijo cíclico y el número de subportadoras, cambian también las prestaciones del sistema. En esta tesis se evaluaron todas las numerologías propuestas por el 3GPP sobre cada uno de los modelos de canal descritos para el 5G (y considerados válidos para sistemas beyond 5G), teniendo en cuenta factores como la movilidad de los equipos de usuario y la frecuencia de operación; para esto se utilizó un simulador de capa física del 3GPP, al que se hicieron las debidas adaptaciones con el fin de evaluar el rendimiento de las numerologías en términos de la tasa de error por bloque. Finalmente, se presenta un bosquejo de lo que podría llegar a ser la Sexta Generación de redes móviles o 6G, con el objetivo de entender las nuevas aplicaciones que podrían ser utilizadas en un futuro, así como sus necesidades. Completado el estudio llevado a cabo en esta tesis, se puede afirmar que como se propuso desde un principio la solución, tanto para el 5G como para beyond 5G, la solución es la armonización de las formas de onda. De los resultados obtenidos se puede corroborar que una solución armonizada permite alcanzar un ahorro computacional entre el 25-40% para el transmisor y del 15-25% para el receptor. Además, fue posible identificar qué numerología CP-OFDM es la más adecuada para cada escenario, lo que permitiría optimizar el diseño y despliegue de las redes 5G. Esto abriría la puerta a hacer lo mismo con el 6G, ya que en esta tesis se considera que será necesario abrir nuevamente el debate sobre cuál es la forma de onda adecuada para esta nueva generación de tecnologías, y se plantea que el camino a seguir es optar por una solución armonizada con distintas formas de onda, en lugar de solo una como sucede con el 5G. / [CA] L'estandardització de la Quinta Generació de xarxes mòbils o 5G, ha conclòs enguany 2020. No obstant això, l'any 2014 quan la ITU va començar el procés d'estandardització IMT-2020, uns dels principals interrogants era quina seria la forma d'onda sobre la qual es construiria la capa física d'esta nova generació de tecnologies. El 3GPP es va comprometre a entregar una tecnologia candidata al procés IMT-2020, i és així com dins d'este procés de deliberació es van presentar diverses formes d'onda candidates, les quals van ser avaluades en diversos aspectes fins que l'any 2016 el 3GPP va prendre una decisió, continuar amb CP-OFDM (utilitzada en 4G) amb numerología flexible. Una vegada decidida la forma d'onda, el procés d'estandardització va continuar afinant la frame structure (no se m'ocorre nom en espanyol), i tots els aspectes intrínsecs de la mateixa. Esta tesi va acompanyar i va participar de tot este procés. Per a començar, en esta dissertació es van avaluar les principals formes d'onda candidates al 5G. És així que es va realitzar una anàlisi teòrica de cada forma d'onda, destacant les seues fortaleses i debilitats, tant a nivell d'implementació com de rendiment. Posteriorment, es va dur a terme una implementació real en una plataforma Software Defined Radio de tres de les formes d'onda més prometedores (CP-OFDM, UFMC i OQAM-FBMC), la qual cosa va permetre avaluar el seu rendiment en termes de la taxa d'error per bit, així com la complexitat de la seua implementació. Esta tesi ha proposat també l'ús d'una solució harmonitzada com a forma d'onda per al 5G i sosté que continua sent una opció viable per a sistemes beyond 5G. Atés que cap de les forma d'onda candidates era capaç de complir per si mateixa amb tots els requeriments del 5G, en compte de triar una única forma d'onda es va proposar construir un transceptor que fóra capaç de construir totes les principals formes d'onda candidates (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). Açò es va aconseguir identificant els blocs comuns entre les formes d'onda, per a després integrar-los junt amb la resta de blocs indispensables per a cada forma d'onda. La motivació per a esta solució era tindre una capa física que fóra capaç de complir amb tots els aspectes del 5G, seleccionant sempre la millor forma d'onda segons l'escenari. Esta proposta va ser avaluada en termes de complexitat, i els resultats es van comparar amb la complexitat de cada forma d'onda. La decisió de continuar amb CP-OFDM amb numerología flexible com a forma d'onda per al 5G es pot considerar també com una solució harmonitzada, ja que al canviar el prefix cíclic i el número de subportadores, canvien també les prestacions del sistema. En esta tesi es van avaluar totes les numerologías propostes pel 3GPP sobre cada un dels models de canal descrits per al 5G (i considerats vàlids per a sistemes beyond 5G), tenint en compte factors com la mobilitat dels equips d'usuari i la freqüència d'operació; per a açò es va utilitzar un simulador de capa física del 3GPP, a què es van fer les degudes adaptacions a fi d'avaluar el rendiment de les numerologías en termes de la taxa d'error per bloc. Finalment, es presenta un esbós del que podria arribar a ser la Sexta Generació de xarxes mòbils o 6G, amb l'objectiu d'entendre les noves aplicacions que podrien ser utilitzades en un futur, així com les seues necessitats. Completat l'estudi dut a terme en esta tesi, es pot afirmar que com es va proposar des d'un principi la solució, tant per al 5G com per a beyond 5G, la solució és l'harmonització de les formes d'onda. dels resultats obtinguts es pot corroborar que una solució harmonitzada permet aconseguir un estalvi computacional entre el 25-40% per al transmissor i del 15-25% per al receptor. A més, va ser possible identificar què numerología CP-OFDM és la més adequada per a cada escenari, la qual cosa permetria optimitzar el disseny i desplegament de les xarxes 5G. Açò obriria la porta a fer el mateix amb el 6G, ja que en esta tesi es considera que serà necessari obrir novament el debat sobre quina és la forma d’onda adequada per a esta nova generació de tecnologies, i es planteja que el camí que s’ha de seguir és optar per una solució harmonitzada amb distintes formes d’onda, en compte de només una com succeïx amb el 5G. / [EN] The standardization of the Fifth Generation of mobile networks or 5G is still ongoing, although the first releases of the standard were completed two years ago and several 5G networks are up and running in several countries around the globe. However, in 2014 when the ITU began the IMT-2020 standardization process, one of the main questions was which would be the waveform to be used on the physical layer of this new generation of technologies. The 3GPP committed to submit a candidate technology to the IMT-2020 process, and that is how within this deliberation process several candidate waveforms were presented. After a thorough evaluation regarding several aspects, in 2016 the 3GPP decided to continue with CP-OFDM (used in 4G) but including, as a novelty, the use of a flexible numerology. Once the waveform was decided, the standardization process continued to fine-tune the frame structure and all the intrinsic aspects of it. This thesis accompanied and participated in this entire process. To begin with, this dissertation evaluates the main 5G candidate waveforms. Therefore, a theoretical analysis of each waveform is carried out, highlighting its strengths and weaknesses, both at the implementation and performance levels. Subsequently, a real implementation on a Software Defined Radio platform of three of the most promising waveforms (CP-OFDM, UFMC, and OQAM-FBMC) is presented, which allows evaluating their performance in terms of bit error rate, as well as the complexity of its implementation. This thesis also proposes the use of a harmonized solution as a waveform for 5G and argues that it remains a viable option for systems beyond 5G. Since none of the candidate waveforms was capable of meeting on its own with all the requirements for 5G, instead of choosing a single waveform, this thesis proposes to build a transceiver capable of building all the main waveforms candidates (CP-OFDM, P-OFDM, UFMC, QAM-FBMC, OQAM-FBMC). This is achieved by identifying the common blocks between the waveforms and then integrating them with the rest of the essential blocks for each waveform. The motivation for this solution is to have a physical layer that is capable of complying with all aspects of beyond 5G technologies, always selecting the best waveform according to the scenario. This proposal is evaluated in terms of complexity, and the results are compared with the complexity of each waveform. The decision to continue with CP-OFDM with flexible numerology as a waveform for 5G can also be considered as a harmonized solution, since changing the cyclic prefix and the number of subcarriers, changes also the performance of the system. In this thesis, all the numerologies proposed by the 3GPP are evaluated on each of the channel models described for 5G (and considered valid for beyond 5G systems), taking into account factors such as the mobility of the user equipment and the operating frequency. For this, a 3GPP physical layer simulator is used, and proper adaptations are made in order to evaluate the performance of the numerologies in terms of the block error rate. Finally, a sketch of what could become the Sixth Generation of mobile networks or 6G is presented, with the aim of understanding the new applications that could be used in the future, as well as their needs. After the completion of the study carried out in this thesis, it can be said that, as stated from the beginning, for both 5G and beyond 5G systems, the solution is the waveform harmonization. From the results obtained, it can be corroborated that a harmonized solution allows achieving computational savings between 25-40% for the transmitter and 15-25% for the receiver. In addition, it is possible to identify which CP-OFDM numerology is the most appropriate for each scenario, which would allow optimizing the design and deployment of 5G networks. This would open the door to doing the same with 6G, i.e., a harmonized solution with different waveforms, instead of just one as in 5G. / Flores De Valgas Torres, FJ. (2020). Study on Air Interface Variants and their Harmonization for Beyond 5G Systems [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/164442

Society is going through a change to be more sustainable, and one big step in that process is to convert the power grid from convectional power generation to increased part of renewable energy sources. Renewable energy sources often require power electronics such as converters to connect to the power grid, and power electronics can cause interference in the grid. This development in Sweden and rest of the Nordic countries is driven by the large increase of load based on power electronics. To maintain a stable power grid, it is essential to detect disturbances through measurement techniques adapted to the challenges that may arise.   The measurement techniques in the Swedish power grid have historically been based on power quality meters and RMS-based measurements, and this thesis focuses on the disturbances that RMS-based measurements may fail to detect. The objective is to compare the RMS-based measurements techniques available in the power grid with waveform measurement techniques developed to see how they could detect disturbances in the power grid. The first research question pertains to the characteristic frequency bandwidths within which a power system typically operates, and what frequency bandwidths a system could have with a significant amount of power electronics installed. The second research question concerns the measurement techniques.   This work consists of four main parts: bandwidth analysis of control systems for voltage source converter, RMS vs waveform detection techniques, interaction between converter and voltage perturbation, and realistic phenomena studies. The bandwidth analysis aims to determine the frequency range expected in future power systems, which in turn informs the minimum detection capabilities required for measurement techniques. This was achieved through calculations involving the control loops of converters, including the inner current control loop, outer control loop, and phase locked loop. Bode diagrams were generated for each control loop, with variables manipulated, and the short circuit ratio adjusted to determine the bandwidth of the control loop.   The RMS vs waveform detection techniques  phase was central to the study, involving simulations imitating various phenomena that could occur in the power grid. This was accomplished using two ideal sources and examining their interactions. The simulations included frequency perturbations, amplitude perturbations, and added oscillations apparent at sub-synchronous, super-synchronous, and high super-synchronous frequencies. Simulation results were presented for both RMS and waveform based defection techniques, simulating different reporting rates to mimic real measurement tools.   The third and fourth parts involved validating the RMS vs waveform detection techniques  results using real-case simulations. An HVDC model was employed to simulate the effects of voltage perturbation and observe the coupling over frequency mechanism. The same HVDC model was also used to simulate phenomena occurring in weak grids. Additionally, a wind park model was utilized to simulate the induction generator effect phenomena.   The findings reveal that the bandwidth of a power system undergoes significant expansion as the proportion of power electronics increases in the grid. Specifically, analysis of converter indicates a shift from under 50 Hz to several kHz in systems dominated by synchronous generators versus those dominated by power electronics. To effectively detect higher frequency oscillations within the grid, waveform measurement tools become essential, as classical RMS measurement tools are inadequate for capturing oscillations originating from power electronics. As power systems evolve towards dominance by power electronics, it becomes imperative to develop measurement systems capable of accurately detecting high frequency oscillations.   The recommendation of this thesis is to invest in waveform measurement tools alongside the already existing RMS-based ones to enhance the detection of disturbances, particularly those with super synchronous frequencies, addressing future power grid challenges.