Nonlinear processing of non-Gaussian stochastic and chaotic deterministic time series

It is often assumed that interference or noise signals are Gaussian stochastic processes. Gaussian noise models are appealing as they usually result in noise suppression algorithms that are simple: i.e. linear and closed form. However, such linear techniques may be sub-optimal when the noise process is either a non-Gaussian stochastic process or a chaotic deterministic process. In the event of encountering such noise processes, improvements in noise suppression, relative to the performance of linear methods, may be achievable using nonlinear signal processing techniques. The application of interest for this thesis is maritime surveillance radar, where the main source of interference, termed sea clutter, is widely accepted to be a non-Gaussian stochastic process at high resolutions and/or at low grazing angles. However, evidence has been presented during the last decade which suggests that sea clutter may be better modelled as a chaotic deterministic process. While the debate over which model is more suitable continues, this thesis investigates whether nonlinear processing techniques can be used to improve the performance of maritime surveillance radar, relative to the performance achievable using linear techniques. Linear and nonlinear prediction of chaotic signals, sea clutter data sets, and stochastic surrogate clutter data sets is carried out. Volterra series filter networks and radial basis function networks are used to implement nonlinear predictors. A novel structure for a forward-backward nonlinear predictor, using a radial basis function network, is presented. Prediction results provide evidence to support the view that sea clutter is better modelled as a stochastic process, rather than as a chaotic process. The clutter data sets are shown to have linear predictor functions. Linear and nonlinear predictors are used as the basis of target detection algorithms. The performance of these predictor-detectors, against backgrounds of sea clutter data and against a background of chaotic noise data is evaluated. The detection results show that linear predictor-detectors perform as well as, or better than, nonlinear predictor-detectors against the non-Gaussian clutter backgrounds considered in this thesis, whilst the reverse is true for a background of chaotic noise. An existing, nonlinear inverse, noise cancellation technique, referred to as Broomhead’s filtering technique in this thesis, is re-investigated using a sine wave corrupted by broadband chaotic noise. It is demonstrated that significant improvements can be obtained using this nonlinear inverse technique, relative to results obtained using linear alternatives, despite recent work which suggested otherwise. A novel bandstop filtering approach is applied to Broomhead’s filtering method, which allows the technique to be applied to the cancellation of signals with a band of interest greater than that of a sine wave. This modified Broomhead filtering technique is shown to cancel broadband chaotic noise from a narrowband Gaussian signal better than alternative linear methods. The modified Broomhead filtering technique is shown to only perform as well as, o

Topics in high dimensional energy forecasting

The forecasting of future energy consumption and generation is now an essential part of power system operation. In networks with high renewable power penetration, forecasts are used to help maintain security of supply and to operate the system efficiently. Historically, uncertainties have always been present in the demand side of the network, they are now also present in the generation side with the growth of weather dependent renewables. Here, we focus on forecasting for wind energy applications at the day(s)- ahead scale. Most of the work developed is for power forecasting, although we also identify an emerging opportunity in access forecasting for offshore operations. Power forecasts are used by traders, power system operators, and asset owners to optimise decision making based on future generation. Several novel methodologies are presented based on post–processing Numerical Weather Predictions (NWP) with measured data, using modern statistical learning techniques; they are linked with the increasingly relevant challenge of dealing with high-dimensional data. The term ‘high-dimensional’ means different things to different people, depending on their background. To statisticians high dimensionaility occurs when the dimensions of the problem are greater than the number of observations, i.e. the classic p >> n problem, an example of which can be found in Chapter 7. In this work we take the more general view that a high dimensional dataset is one with a high number of attributes or features. In wind energy forecasting applications, this can occur in the input and/or output variable space. For example, multivariate forecasting of spatially distributed wind farms can be a potentially very-high dimensional problem, but so is feature engineering using ultra-high resolution NWP in this framework. Most of the work in this thesis is based on various forms of probabilistic forecasting Probabilistic forecasts are essential for risk-management, but also to risk-neutral participants in asymmetrically penalised electricity markets. Uncertainty is always present, it is merely hidden in deterministic, i.e. point, forecasts. This aspect of forecasting has been the subject of a concerted research effort over the last few years in the energy forecasting literature. However, we identify and address gaps in the literature related to dealing with high dimensional data in both the input and output side of the modelling chain. It is not necessarily given that increasing the resolution of the weather forecast increases the skill, and therefore reduces errors associated with the forecast. In fact and when regarding typical average scoring rules, they often perform worse than smoother forecasts from lower-resolution models due to spatial and/or temporal displacement errors. Here, we evaluate the potential of using ultra high resolution weather models for offshore power forecasting, using feature engineering and modern statistical learning techniques. Two methods for creating improved probabilistic wind power forecasts through the use of turbine-level data are proposed. Although standard resolution NWP data is used, high dimensionality is now present in the output variable space; the two methods scale by the number of turbines present in the wind farm, although to a different extent. A methodology for regime-switching multivariate wind power forecasting is also elaborated, with a case study demonstrated on 92 wind balancing mechanism units connected to the GB network. Finally, we look at an emerging topic in energy forecasting: offshore access forecasting. Improving access is a priority in the offshore wind sector, driven by the opportunity to increase revenues, reduce costs, and improve safety at operational wind farms. We describe a novel methodology for producing probabilistic forecasts of access conditions during crew transfers.The forecasting of future energy consumption and generation is now an essential part of power system operation. In networks with high renewable power penetration, forecasts are used to help maintain security of supply and to operate the system efficiently. Historically, uncertainties have always been present in the demand side of the network, they are now also present in the generation side with the growth of weather dependent renewables. Here, we focus on forecasting for wind energy applications at the day(s)- ahead scale. Most of the work developed is for power forecasting, although we also identify an emerging opportunity in access forecasting for offshore operations. Power forecasts are used by traders, power system operators, and asset owners to optimise decision making based on future generation. Several novel methodologies are presented based on post–processing Numerical Weather Predictions (NWP) with measured data, using modern statistical learning techniques; they are linked with the increasingly relevant challenge of dealing with high-dimensional data. The term ‘high-dimensional’ means different things to different people, depending on their background. To statisticians high dimensionaility occurs when the dimensions of the problem are greater than the number of observations, i.e. the classic p >> n problem, an example of which can be found in Chapter 7. In this work we take the more general view that a high dimensional dataset is one with a high number of attributes or features. In wind energy forecasting applications, this can occur in the input and/or output variable space. For example, multivariate forecasting of spatially distributed wind farms can be a potentially very-high dimensional problem, but so is feature engineering using ultra-high resolution NWP in this framework. Most of the work in this thesis is based on various forms of probabilistic forecasting Probabilistic forecasts are essential for risk-management, but also to risk-neutral participants in asymmetrically penalised electricity markets. Uncertainty is always present, it is merely hidden in deterministic, i.e. point, forecasts. This aspect of forecasting has been the subject of a concerted research effort over the last few years in the energy forecasting literature. However, we identify and address gaps in the literature related to dealing with high dimensional data in both the input and output side of the modelling chain. It is not necessarily given that increasing the resolution of the weather forecast increases the skill, and therefore reduces errors associated with the forecast. In fact and when regarding typical average scoring rules, they often perform worse than smoother forecasts from lower-resolution models due to spatial and/or temporal displacement errors. Here, we evaluate the potential of using ultra high resolution weather models for offshore power forecasting, using feature engineering and modern statistical learning techniques. Two methods for creating improved probabilistic wind power forecasts through the use of turbine-level data are proposed. Although standard resolution NWP data is used, high dimensionality is now present in the output variable space; the two methods scale by the number of turbines present in the wind farm, although to a different extent. A methodology for regime-switching multivariate wind power forecasting is also elaborated, with a case study demonstrated on 92 wind balancing mechanism units connected to the GB network. Finally, we look at an emerging topic in energy forecasting: offshore access forecasting. Improving access is a priority in the offshore wind sector, driven by the opportunity to increase revenues, reduce costs, and improve safety at operational wind farms. We describe a novel methodology for producing probabilistic forecasts of access conditions during crew transfers

Learning to forecast: The probabilistic time series forecasting challenge

We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse set of skills in data science and applied statistics. We describe the context and aims of the course, and discuss design parameters like the selection of target variables, the forecast submission process, the evaluation of forecast performance, and the feedback provided to students. Furthermore, we describe empirical properties of students' probabilistic forecasts, as well as some lessons learned on our part

Spatial interpolation of climate data for hydrological and environmental applications

[no abstract

Analyse de la dynamique des peuplements mixtes de sapin baumier et d'épinette rouge après coupe partielle : contraintes et méthodologies statistiques

Des éléments de la dynamique des peuplements mixtes de sapin baumier et d’épinette rouge après coupe partielle ont été étudiés sur une base statistique, afin de déterminer dans quelle mesure ils pourraient contribuer au phénomène de raréfaction de l’épinette rouge. L’étude visait principalement à identifier les changements structurels et à quantifier la croissance tant à l’échelle du peuplement que des tiges individuelles. Pour ce faire, les données de deux dispositifs de suivi ont été utilisées : l’Aire d’observation de la rivière Ouareau (Parc national du Mont-Tremblant) et la Forêt expérimentale du lac Édouard (Parc national de la Mauricie). Chacun de ces dispositifs disposent d’un réseau de placettes permanentes dont les mesures s’étendent sur un horizon de plus de 50 ans après une coupe partielle. Des méthodologies statistiques ont été proposées afin de formuler des inférences statistiques adaptées à la nature des données disponibles. L’analyse de la croissance s’est faite à partir d’un modèle linéaire incluant des effets aléatoires (à l’échelle de la tige individuelle) et d’un modèle non linéaire comportant une structure de covariance (à l’échelle du peuplement) afin de tenir compte de l’hétéroscédasticité des données et de l’autocorrélation des erreurs. Les changements structurels ont été analysés à l’aide d’un modèle linéaire généralisé puisque la variable dépendante n’était pas une variable continue, mais plutôt une fréquence. Pour tenir compte de l’effet dû aux placettes, des effets aléatoires ont été ajoutés au modèle. Finalement, une matrice de transition à deux niveaux a été construite sur la base de distributions discrètes dont les paramètres sont estimés par la méthode du maximum de vraisemblance. L’utilisation de distributions discrètes offre ainsi des résultats plus cohérents par rapport à l’approche traditionnelle. À l’échelle des tiges individuelles, les résultats de ces analyses démontrent que les différences quant à la croissance en diamètre sont relativement faibles. Le recrutement et la mortalité sont en fait des facteurs beaucoup plus importants dans l’évolution de ces peuplements après coupe partielle. À l’échelle du peuplement, ils induisent une variabilité importante dans l’évolution de la surface terrière du sapin baumier, de sorte que l’épinette rouge apparaît comme une essence beaucoup plus stable. La durée et l’importance de l’ouverture de la canopée après coupe partielle sont des éléments critiques qui déterminent l’abondance du recrutement du sapin baumier. Pour maintenir la proportion d’épinette rouge et une distribution diamétrale irrégulière, les coupes partielles de faible intensité comme le jardinage par pied d’arbre sont indiquées

Spatio-temporal prediction of wind fields

Short-term wind and wind power forecasts are required for the reliable and economic operation of power systems with significant wind power penetration. This thesis presents new statistical techniques for producing forecasts at multiple locations using spatiotemporal information. Forecast horizons of up to 6 hours are considered for which statistical methods outperform physical models in general. Several methods for producing hourly wind speed and direction forecasts from 1 to 6 hours ahead are presented in addition to a method for producing five-minute-ahead probabilistic wind power forecasts. The former have applications in areas such as energy trading and defining reserve requirements, and the latter in power system balancing and wind farm control. Spatio-temporal information is captured by vector autoregressive (VAR) models that incorporate wind direction by modelling the wind time series using complex numbers. In a further development, the VAR coefficients are replaced with coefficient functions in order to capture the dependence of the predictor on external variables, such as the time of year or wind direction. The complex-valued approach is found to produce accurate speed predictions, and the conditional predictors offer improved performance with little additional computational cost. Two non-linear algorithms have been developed for wind forecasting. In the first, the predictor is derived from an ensemble of particle swarm optimised candidate solutions. This approach is low cost and requires very little training data but fails to capitalise on spatial information. The second approach uses kernelised forms of popular linear algorithms which are shown to produce more accurate forecasts than their linear equivalents for multi-step-ahead prediction. Finally, very-short-term wind power forecasting is considered. Five-minute-ahead parametric probabilistic forecasts are produced by modelling the predictive distribution as logit-normal and forecasting its parameters using a sparse-VAR (sVAR) approach. Development of the sVAR is motivated by the desire to produce forecasts on a large spatial scale, i.e. hundreds of locations, which is critical during periods of high instantaneous wind penetration.Short-term wind and wind power forecasts are required for the reliable and economic operation of power systems with significant wind power penetration. This thesis presents new statistical techniques for producing forecasts at multiple locations using spatiotemporal information. Forecast horizons of up to 6 hours are considered for which statistical methods outperform physical models in general. Several methods for producing hourly wind speed and direction forecasts from 1 to 6 hours ahead are presented in addition to a method for producing five-minute-ahead probabilistic wind power forecasts. The former have applications in areas such as energy trading and defining reserve requirements, and the latter in power system balancing and wind farm control. Spatio-temporal information is captured by vector autoregressive (VAR) models that incorporate wind direction by modelling the wind time series using complex numbers. In a further development, the VAR coefficients are replaced with coefficient functions in order to capture the dependence of the predictor on external variables, such as the time of year or wind direction. The complex-valued approach is found to produce accurate speed predictions, and the conditional predictors offer improved performance with little additional computational cost. Two non-linear algorithms have been developed for wind forecasting. In the first, the predictor is derived from an ensemble of particle swarm optimised candidate solutions. This approach is low cost and requires very little training data but fails to capitalise on spatial information. The second approach uses kernelised forms of popular linear algorithms which are shown to produce more accurate forecasts than their linear equivalents for multi-step-ahead prediction. Finally, very-short-term wind power forecasting is considered. Five-minute-ahead parametric probabilistic forecasts are produced by modelling the predictive distribution as logit-normal and forecasting its parameters using a sparse-VAR (sVAR) approach. Development of the sVAR is motivated by the desire to produce forecasts on a large spatial scale, i.e. hundreds of locations, which is critical during periods of high instantaneous wind penetration