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首页> 外文期刊>Advances in Adaptive Data Analysis >SPARSE APPROXIMATION AND FIT OF INTRADAY LOAD CURVES IN A HIGH DIMENSIONAL FRAMEWORK
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SPARSE APPROXIMATION AND FIT OF INTRADAY LOAD CURVES IN A HIGH DIMENSIONAL FRAMEWORK

机译：高维框架中日负荷曲线的稀疏近似和拟合

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摘要

An important perspective in electric consumption obviously is the forecasting. A crucial step in the forecasting process is the modeling. It is commonly admitted that many variables are influential for the prediction in this context. On the other hand, a prediction, to be robust and efficient, has necessarily to rely on a small number of well chosen predictors. We are typically in a situation where sparse multidimensional modeling can bring an essential input, and this paper is an attempt to prove it. In this perspective, we shall address the question of providing a sparse representation of the intraday load curves, with good approximation properties. One difficulty is that we have here a large set of potential predictors among climate variables and shape "patterns", and even if high dimensional sparse methods have clearly as objective to select among a large number of covariates, they are especially efficient when the predictors are not too correlated. So our task is twofold: first we need to operate a preselection of the predictors, and then use an appropriate sparse method. The first part and especially when shape patterns are concerned is not simple. We solve this aspect using a pre-processing in three steps process. We first provide a sparse modeling of the intraday load curves as functions of the time. Then, using the sparse representation of each load curve, we define clusters of consumption, which yield finally typical profiles, the group centroids or patterns of consumption. Then we investigate the modeling of the intraday load curves using both exogenous climate variables and endogenous consumption variables as previously designed. We exhibit, as a result, sparse models relying just on few variables and also characterized by very good approximation performances. We end by explaining how sparse approximation is a first step towards clustering. The sparse approximation is here obtained by performing a robust and simple algorithm, LOLA, presented at the end of the paper.
机译：耗电量的一个重要方面显然是预测。预测过程中的关键步骤是建模。通常认为，在这种情况下，许多变量对预测有影响。另一方面，预测要鲁棒和有效，就必须依赖少数精心选择的预测器。通常情况下，稀疏多维建模可以带来必要的输入，本文试图证明这一点。从这个角度来看，我们将解决以下问题：提供具有良好近似特性的日内负荷曲线的稀疏表示。一个困难在于，我们在气候变量和形状“模式”中拥有大量潜在的预测变量，即使高维稀疏方法显然具有在众多协变量中进行选择的目标，但当预测变量为不太相关。因此，我们的任务是双重的：首先，我们需要对预测变量进行预选择，然后使用适当的稀疏方法。第一部分，尤其是在涉及形状图案时，并不简单。我们通过三步预处理来解决这一方面。我们首先提供日内负荷曲线随时间变化的稀疏模型。然后，使用每个负载曲线的稀疏表示，我们定义了消耗簇，这些簇最终产生了典型的轮廓，组质心或消耗模式。然后，我们使用先前设计的外源气候变量和内源消耗变量研究日内负荷曲线的模型。结果，我们展示了仅依赖少量变量的稀疏模型，并且还具有非常好的近似性能。最后，我们将说明稀疏近似是如何实现聚类的第一步。稀疏近似值是通过执行本文末尾提出的鲁棒且简单的算法LOLA获得的。

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