We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Urban building energy modeling – A review of a nascent field

Forecasting energy consumption of multi-family residential buildings using support vector regression: Investigating the impact of temporal and spatial monitoring granularity on performance accuracy

http://amirkavousian.com/wp-content/uploads/2015/04/Kavousian_etal_2013_DataDrivenEnergyEfficiency.pdf

Determinants of residential electricity consumption: Using smart meter data to examine the effect of climate, building characteristics, appliance stock, and occupants' behavior

A recent surge of interest in building energy consumption has generated a tremendous amount of energy data, which boosts the data-driven algorithms for broad application throughout the building industry. This article reviews the prevailing data-driven approaches used in building energy analysis under different archetypes and granularities, including those methods for prediction (artificial neural networks, support vector machines, statistical regression, decision tree and genetic algorithm) and those methods for classification (K-mean clustering, self-organizing map and hierarchy clustering). The review results demonstrate that the data-driven approaches have well addressed a large variety of building energy related applications, such as load forecasting and prediction, energy pattern profiling, regional energy-consumption mapping, benchmarking for building stocks, global retrofit strategies and guideline making etc. Significantly, this review refines a few key tasks for modification of the data-driven approaches in the context of application to building energy analysis. The conclusions drawn in this review could facilitate future micro-scale changes of energy use for a particular building through the appropriate retrofit and the inclusion of renewable energy technologies. It also paves an avenue to explore potential in macro-scale energy-reduction with consideration of customer demands. All these will be useful to establish a better long-term strategy for urban sustainability.

A review of data-driven approaches for prediction and classification of building energy consumption

Spatial distribution of urban building energy consumption by end use

Contracted energy flexibility characteristics of communities: Analysis of a control strategy for demand response

The growing demand for energy in urban areas has led to the development of a variety of methodologies for modelling energy in buildings at large scale. However, their accuracy has yet to be thoroughly reviewed. This paper presents a systematic analysis of urban building energy models, that have been validated against measured data, using a singular taxonomy based on key attributes that could influence a model’s accuracy: application, scale, input data, computational method, calibration and validation methods. The analysis showed that the accuracy of urban building energy models is multi-dimensional, considered at a variety of temporal resolutions, spatial resolutions and measures of error, with the results demonstrating that there is no single key attribute that governs it. At the aggregate spatial and annual temporal resolutions, the accuracy, often reported in a single percent error value, can be as low as 1%, while for individual buildings at the annual resolution, the tails of the distribution of errors can reach 1000%. Models using non-calibrated physics-based computational methods were more likely to report overly large errors, while those employing Bayesian calibration consistently reported lower errors at the hourly temporal resolution, demonstrating the positive impact of calibration and in particular the Bayesian approach, on the models’ accuracy. Overall, the review has highlighted that more transparent and consistent reporting of accuracy is necessary and further research is essential for improving the evaluation of accuracy in modelling methodologies, if modern challenges are to be met through emerging applications such as energy systems integration and climate resilience. • Accuracy in Urban Building Energy Modelling is multidimensional in space and time. • No single attribute governs accuracy, rather the collective deficiencies across all. • Errors ranged from 1% at annual aggregate resolutions to 1000% for single buildings. • Bayesian calibration of physics-based models can lead to low hourly measured accuracy. • Measures of error should go beyond textbook statistics to capture dynamic behaviour. 

Bianca Howard

Papers

Spatial distribution of urban building energy consumption by end use

Contracted energy flexibility characteristics of communities: Analysis of a control strategy for demand response

On the accuracy of Urban Building Energy Modelling

Stochastic nonlinear modelling and application of price-based energy flexibility

Current and near-term GHG emissions factors from electricity production for New York State and New York City