Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

Initial Condition Estimation in Flux Tube Simulations using Machine Learning

Space weather has become an essential field of study as solar flares, coronal mass ejections, and other phenomena can severely impact Earth's life as we know it. The solar wind is threaded by magnetic flux tubes that extend from the solar atmosphere to distances beyond the solar system boundary. As those flux tubes cross the Earth's orbit, it is essential to understand and predict solar phenomena' effects at 1 AU, but the physical parameters linked to the solar wind formation and acceleration processes are not directly observable. Some existing models, such as MULTI-VP, try to fill this gap by predicting the background solar wind's dynamical and thermal properties from chosen magnetograms and using a coronal field reconstruction method. However, these models take a long time, and their performance increases with good initial guesses regarding the simulation's initial conditions. To address this problem, we propose using varied machine learning techniques to obtain good initial guesses that can accelerate MULTI-VP's computational time

Trajectory Learning for Highly Aerobatic Unmanned Aerial Vehicle

The dynamics of fixed wing planes are well understood within the conventional flight envelope. The situation is different in the case of aerobatic maneuvers with a large angle of attack, such as perching and vertical hover. In such maneuvers the airflows around the plane are unpredictable making it difficult to create accurate dynamic models, which would normally be needed for the design of conventional controllers. Yet human RC pilots are able to fly these maneuvers with fixed wing planes. Apprenticeship learning provides a promising solution to the problem of automating highly aerobatic maneuvers. It allows the maneuver to be learned from demonstration flights done by a human RC pilot rather than relying on an accurate dynamics model. The focus of this thesis is on a specific issue in apprenticeship learning, namely how to infer the trajectory the pilot intended to fly from a set of suboptimal demonstration trajectories. Such a trajectory can be used as a target trajectory for an autonomous controller. A trajectory learning algorithm that has shown promising results in automation of aerobatic helicopter flight is applied to a fixed wing UAV platform. The algorithm is tested on two different maneuvers; A straight line of level flight, and a vertical hover maneuver. In the case of both maneuvers the algorithm learned the intended trajectory without prior knowledge about the trajectory. In order to collect training data for the trajectory learning task, an appropriate platform and data acquisition system are needed. This thesis therefore also presents the development of a fixed wing UAV platform for research on automation of aerobatic flight

Stochastische spektrale Methoden zur linearen Bayes'schen Inferenz

Simulation-based control of dynamic systems is of key importance for many areas of science and industry. To ensure the predictive capabilities, simulation models used for predicting control responses have to be calibrated to available observations. Bayesian approaches to make inference from data on unobservable quantities are used because of their consistent, inherent treatment of diverse sources of uncertainties. Spectral approaches to uncertainty quantification have become popular over the last years. However, their combination with Bayesian inference usually employs expensive probabilistic sampling methods. In this work, a family of linear Bayesian approaches is presented which directly results in a representation of the posterior. A specific implementation is discussed which overcomes some of the difficulties that remained unsolved in related approaches. All implementation details are given, and the applicability is demonstrated on some linear and non-linear numerical examples.Die simulationsbasierte Steuerung von dynamischen Systemen stellt eine Schlüsseltechnologie für weite Bereiche von Forschung und Industrie dar. Um die Vorhersagefähigkeiten von Simulationsmodellen sicherzustellen müssen diese auf die verfügbaren Daten kalibriert werden. Bayes'sche Ansätze für die Erzeugung von Rückschlüssen aus Daten auf unbeobachtbare Modellgrößen sind aufgrund ihrer inhärenten Möglichkeiten, Unsicherheiten in den Rückschlussprozess einzubetten, beliebt. Spektrale Methoden für die Quantifizierung von Unsicherheiten sind über die letzten Jahre populär geworden. Allerdings bedingt ihre Kombination mit Bayes'schen Rückschlussmethoden typischerweise den Einsatz von aufwändigen probabilistischen Abtastverfahren. In dieser Arbeit wird eine Familie von linearen Bayes'schen Vorgehensweisen präsentiert, welche direkt die spektrale à posteriori Repräsentation der unsicheren Zielgröße erzeugen. Eine spezifische Implementierung wird vorgestellt, welche einige der Schwierigkeiten der bisher existierenden Ansätze umgeht. Alle Implementierungsdetails hierzu werden beschrieben, und die Anwendbarkeit anhand von verschiedenen linearen und nicht-linearen numerischen Beispielen belegt

Machine learning tools for pattern recognition in polar climate science

This thesis explores the application of two novel machine learning approaches to the study of polar climate, with particular focus on Arctic sea ice. The first technique, complex networks, is based on an unsupervised learning approach which is able to exploit spatio-temporal patterns of variability within geospatial time series data sets. The second, Gaussian Process Regression (GPR), is a supervised learning Bayesian inference approach which establishes a principled framework for learning functional relationships between pairs of observation points, through updating prior uncertainty in the presence of new information. These methods are applied to a variety of problems facing the polar climate community at present, although each problem can be considered as an individual component of the wider problem relating to Arctic sea ice predictability. In the first instance, the complex networks methodology is combined with GPR in order to produce skilful seasonal forecasts of pan-Arctic and regional September sea ice extents, with up to 3 months lead time. De-trended forecast skills of 0.53, 0.62, and 0.81 are achieved at 3-, 2- and 1-month lead time respectively, as well as generally highest regional predictive skill ($> 0.30$) in the Pacific sectors of the Arctic, although the ability to skilfully predict many of these regions may be changing over time. Subsequently, the GPR approach is used to combine observations from CryoSat-2, Sentinel-3A and Sentinel-3B satellite radar altimeters, in order to produce daily pan-Arctic estimates of radar freeboard, as well as uncertainty, across the 2018--2019 winter season. The empirical Bayes numerical optimisation technique is also used to derive auxiliary properties relating to the radar freeboard, including its spatial and temporal (de-)correlation length scales, allowing daily pan-Arctic maps of these fields to be generated as well. The estimated daily freeboards are consistent to CryoSat-2 and Sentinel-3 to within $< 1$ mm (standard deviations $< 6$ cm) across the 2018--2019 season, and furthermore, cross-validation experiments show that prediction errors are generally $\leq 4$ mm across the same period. Finally, the complex networks approach is used to evaluate the presence of the winter Arctic Oscillation (AO) to summer sea ice teleconnection within 31 coupled climate models participating in phase 6 of the World Climate Research Programme Coupled Model Intercomparison Project (CMIP6). Two global metrics are used to compare patterns of variability between observations and models: the Adjusted Rand Index and a network distance metric. CMIP6 models generally over-estimate the magnitude of sea-level pressure variability over the north-western Pacific Ocean, and under-estimate the variability over the north Africa and southern Europe, while they also under-estimate the importance of regions such as the Beaufort, East Siberian and Laptev seas in explaining pan-Arctic summer sea ice area variability. They also under-estimate the degree of covariance between the winter AO and summer sea ice in key regions such as the East Siberian Sea and Canada basin, which may hinder their ability to make skilful seasonal to inter-annual predictions of summer sea ice

The 8th International Conference on Time Series and Forecasting

The aim of ITISE 2022 is to create a friendly environment that could lead to the establishment or strengthening of scientific collaborations and exchanges among attendees. Therefore, ITISE 2022 is soliciting high-quality original research papers (including significant works-in-progress) on any aspect time series analysis and forecasting, in order to motivating the generation and use of new knowledge, computational techniques and methods on forecasting in a wide range of fields

Development of numerical and data models for the support of digital twins in offshore wind engineering

Error on title page. Date of award is 2022.As offshore wind farms grow there is a continued demand for reduced costs. Maintenance costs and downtime can be reduced through greater information on the asset in relation to its operational loads and structural resistance to damage and so there is an increasing interest in digital twin technologies. Through digital twins, an operational asset can be replicated computationally, thus providing more information. Modelling these aspects requires a wide variety of models in different fields. To advance the feasibility of digital twin technology this thesis aims to develop the multi-disciplinary set of modelling domains which help form the basis of future digital twins. Throughout this work, results have been validated against operational data recorded from sensors on offshore structures. This has provided value and confidence to the results as it shows how well the mix of state-of-the art models compare to real world engineering systems. This research presents a portfolio of five research areas which have been published in a mix of peer-reviewed journal articles and conference papers. These areas are: 1) A computational fluid dynamics (CFD) model of an offshore wind farm conducted using a modified solver in the opensource software. This work implements actuator disk turbine models and uses Reynolds averaged Naiver Stokes approaches to represent the turbulence. This investigates the impact of modelling choices and demonstrates the impact of varied model parameters. The results are compared to operational site data and the modelling errors are quantified. There is good agreement between the models and site data. 2) An expansion on traditional CFD approaches through incorporating machine learning (ML). These ML models are used to approximate the results of the CFD and thereby allow for further analysis which retains the fidelity of CFD at comparatively negligible computational cost. The results are compared to operational site data and the errors at each step are quantified for validation. 3) A time-series forecasting of weather variables based on past measured data. A novel approach for forecasting time-series is developed and compared to two existing methods: Markov-Chains and Gradient Boosting. While this new method is more complex and requires more time to train, it has the desirable feature of incorporating seasonality at multiple timescales and thus providing a more representative time-series. 4) An investigation of the change in modal parameters in an offshore wind jacket structure from damages or from changing operational conditions. In this work the detailed design model of the structure from Ramboll is used. This section relates the measurable modal parameters to the operational condition through a modelling approach. 5) A study conducted using accelerometer data from an Offshore Substation located in a wind farm site. Operational data from 12 accelerometers is used to investigate the efficacy of several potential sensor layouts and therefore to quantify the consequence of placement decisions. The results of these developments are an overall improvement in the modelling approaches necessary towards the realisation of digital twins as well as useful development in each of the component areas. Both areas related to wind loading as well as structural dynamics have been related to operational data. The validation of this link between the measured and the modelled domains facilitates operators and those in maintenance in gaining more information and greater insights into the conditions of their assets.As offshore wind farms grow there is a continued demand for reduced costs. Maintenance costs and downtime can be reduced through greater information on the asset in relation to its operational loads and structural resistance to damage and so there is an increasing interest in digital twin technologies. Through digital twins, an operational asset can be replicated computationally, thus providing more information. Modelling these aspects requires a wide variety of models in different fields. To advance the feasibility of digital twin technology this thesis aims to develop the multi-disciplinary set of modelling domains which help form the basis of future digital twins. Throughout this work, results have been validated against operational data recorded from sensors on offshore structures. This has provided value and confidence to the results as it shows how well the mix of state-of-the art models compare to real world engineering systems. This research presents a portfolio of five research areas which have been published in a mix of peer-reviewed journal articles and conference papers. These areas are: 1) A computational fluid dynamics (CFD) model of an offshore wind farm conducted using a modified solver in the opensource software. This work implements actuator disk turbine models and uses Reynolds averaged Naiver Stokes approaches to represent the turbulence. This investigates the impact of modelling choices and demonstrates the impact of varied model parameters. The results are compared to operational site data and the modelling errors are quantified. There is good agreement between the models and site data. 2) An expansion on traditional CFD approaches through incorporating machine learning (ML). These ML models are used to approximate the results of the CFD and thereby allow for further analysis which retains the fidelity of CFD at comparatively negligible computational cost. The results are compared to operational site data and the errors at each step are quantified for validation. 3) A time-series forecasting of weather variables based on past measured data. A novel approach for forecasting time-series is developed and compared to two existing methods: Markov-Chains and Gradient Boosting. While this new method is more complex and requires more time to train, it has the desirable feature of incorporating seasonality at multiple timescales and thus providing a more representative time-series. 4) An investigation of the change in modal parameters in an offshore wind jacket structure from damages or from changing operational conditions. In this work the detailed design model of the structure from Ramboll is used. This section relates the measurable modal parameters to the operational condition through a modelling approach. 5) A study conducted using accelerometer data from an Offshore Substation located in a wind farm site. Operational data from 12 accelerometers is used to investigate the efficacy of several potential sensor layouts and therefore to quantify the consequence of placement decisions. The results of these developments are an overall improvement in the modelling approaches necessary towards the realisation of digital twins as well as useful development in each of the component areas. Both areas related to wind loading as well as structural dynamics have been related to operational data. The validation of this link between the measured and the modelled domains facilitates operators and those in maintenance in gaining more information and greater insights into the conditions of their assets

Renewable Energy Resource Assessment and Forecasting

In recent years, several projects and studies have been launched towards the development and use of new methodologies, in order to assess, monitor, and support clean forms of energy. Accurate estimation of the available energy potential is of primary importance, but is not always easy to achieve. The present Special Issue on ‘Renewable Energy Resource Assessment and Forecasting’ aims to provide a holistic approach to the above issues, by presenting multidisciplinary methodologies and tools that are able to support research projects and meet today’s technical, socio-economic, and decision-making needs. In particular, research papers, reviews, and case studies on the following subjects are presented: wind, wave and solar energy; biofuels; resource assessment of combined renewable energy forms; numerical models for renewable energy forecasting; integrated forecasted systems; energy for buildings; sustainable development; resource analysis tools and statistical models; extreme value analysis and forecasting for renewable energy resources

Proceedings of the 35th International Workshop on Statistical Modelling : July 20- 24, 2020 Bilbao, Basque Country, Spain

466 p.The InternationalWorkshop on Statistical Modelling (IWSM) is a reference workshop in promoting statistical modelling, applications of Statistics for researchers, academics and industrialist in a broad sense. Unfortunately, the global COVID-19 pandemic has not allowed holding the 35th edition of the IWSM in Bilbao in July 2020. Despite the situation and following the spirit of the Workshop and the Statistical Modelling Society, we are delighted to bring you the proceedings book of extended abstracts