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The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing subdomain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic (also known as single-valued or point) solar forecasts are still far from being standardized, making forecast analysis and comparison difficult. To analyze and compare solar forecasts, the well-established Murphy–Winkler framework for distribution-oriented forecast verification is recommended as a standard practice. This framework examines aspects of forecast quality, such as reliability, resolution, association, or discrimination, and analyzes the joint distribution of forecasts and observations, which contains all time-independent information relevant to verification. To verify forecasts, one can use any graphical display or mathematical/statistical measure to provide insights and summarize the aspects of forecast quality. The majority of graphical methods and accuracy measures known to solar forecasters are specific methods under this general framework. Additionally, measuring the overall skillfulness of forecasters is also of general interest. The use of the root mean square error (RMSE) skill score based on the optimal convex combination of climatology and persistence methods is highly recommended. By standardizing the accuracy measure and reference forecasting method, the RMSE skill score allows—with appropriate caveats—comparison of forecasts made using different models, across different locations and time periods.

In this paper, emphasis is put on the design of a neural network (NN) to model the direct solar irradiance. Since, unfortunately, a neural network is not a statistician-in-a-box, building a NN for a particular problem is a nontrivial task. As a consequence, we argue that in order to properly model the direct solar irradiance, a systematic methodology must be employed. For this purpose, we propose a two-step approach to building the NN model. The first step deals with a probabilistic interpretation of the NN learning by using Bayesian techniques. The Bayesian approach to modeling offers significant advantages over the classical NN learning process. Among others, one can cite (i) automatic complexity control of the NN using all the available data and (ii) selection of the most important input variables. The second step consists of using a new sensitivity analysis-based pruning method in order to infer the optimal NN structure. We show that the combination of the two approaches makes the practical implementation of the Bayesian techniques more reliable. [DOI: 10.1115/1.2210495] Keywords: direct solar irradiance, neural network, Bayesian inference, pruning, sensitivity analysis

This paper deals with the application of Bayesian methods to the estimation of two convective heat-transfer coefficients of a roof-mounted radiant barrier system. As part of an empirical validation of the thermal model of the roofing complex, a parametric sensitivity analysis highlighted the importance of convective coefficients in the thermal behavior of a roofing complex. A parameter estimation method is then used in order to find the values of the coefficients that lead to an improvement of the thermal model. However, instead of using a classical parameter estimation method, we used a Bayesian inference approach to parameter estimation. The aim of the paper is to introduce the basic concepts of this powerful method in this simple two-parameter case. We show that Bayesian methods introduce an explicit treatment of uncertainty in modeling and a corresponding measure of reliability for the conclusions reached. [DOI: 10.1115/1.2188957]

In this paper, we propose a new pruning algorithm to obtain the optimal number of hidden units of a single layer of a fully connected neural network (NN). The technique relies on a global sensitivity analysis of model output. The relevance of the hidden nodes is determined by analysing the Fourier decomposition of the variance of the model output. Each hidden unit is assigned a ratio (the fraction of variance which the unit accounts for) that gives their ranking. This quantitative information therefore leads to a suggestion of the most favorable units to eliminate. Experimental results suggest that the method can be seen as an effective tool available to the user in controlling the complexity in NNs. Index Terms--Feedforward neural networks, Fourier analysis, global sensitivity analysis, pruning, variance decomposition.