Marcelo Espinoza

Short-term load forecasting, profile identification, and customer segmentation: a methodology based on periodic time series

Results from a project in cooperation with the Belgian National Grid Operator ELIA are presented in this paper. Starting from a set of 245 time series, each one corresponding to four years of measurements from a HV-LV substation, individual modeling using Periodic Time Series yields satisfactory results for short-term forecasting or simulation purposes. In addition, we use the stationarity properties of the estimated models to identify typical daily customer profiles. As each one of the 245 substations can be represented by its unique daily profile, it is possible to cluster the 245 profiles in order to obtain a segmentation of the original sample in different classes of customer profiles. This methodology provides a unified framework for the forecasting and clustering problems.

Electric Load Forecasting

This article illustrates the application of a nonlinear system identification technique to the problem of STLF. Five NARX models are estimated using fixed-size LS-SVM, and two of the models are later modified into AR-NARX structures following the exploration of the residuals. The forecasting performance, assessed for different load series, is satisfactory. The MSE levels on the test data are below 3% in most cases. The models estimated with fixed-size LS-SVM give better results than a linear model estimated with the same variables and also better than a standard LS-SVM in dual space estimated using only the last 1000 data points. Furthermore, the good performance of the fixed-size LS-SVM is obtained based on a subset of M = 1000 initial support vectors, representing a small fraction of the available sample. Further research on a more dedicated definition of the initial input variables (for example, incorporation of external variables to reflect industrial activity, use of explicit seasonal information) might lead to further improvements and the extension toward other types of load series.

Fixed-size Least Squares Support Vector Machines: A Large Scale Application in Electrical Load Forecasting

Based on the Nyström approximation and the primal-dual formulation of the least squares support vector machines, it becomes possible to apply a nonlinear model to a large scale regression problem. This is done by using a sparse approximation of the nonlinear mapping induced by the kernel matrix, with an active selection of support vectors based on quadratic Renyi entropy criteria. The methodology is applied to the case of load forecasting as an example of a real-life large scale problem in industry. The forecasting performance, over ten different load series, shows satisfactory results when the sparse representation is built with less than 3% of the available sample.

Kernel based partially linear models and nonlinear identification

In this note, we propose partially linear models with least squares support vector machines (LS-SVMs) for nonlinear ARX models. We illustrate how full black-box models can be improved when prior information about model structure is available. A real-life example, based on the Silverbox benchmark data, shows significant improvements in the generalization ability of the structured model with respect to the full black-box model, reflected also by a reduction in the effective number of parameters.

Glycemia Prediction in Critically Ill Patients Using an Adaptive Modeling Approach

Background: Strict blood glucose control by applying nurse-driven protocols is common nowadays in intensive care units (ICUs). Implementation of a predictive control system can potentially reduce the workload for medical staff but requires a model for accurately predicting the glycemia signal within a certain time horizon. Methods: GlucoDay (A. Menarini Diagnostics, Italy) data coming from 19 critically ill patients (from a surgical ICU) are used to estimate the initial ICU “minimal” model (based on data of the first 24 hours) and to reestimate the model as new measurements are obtained. The reestimation is performed every hour or every 4 hours. For both approaches the optimal size of the data set for each reestimation is determined. Results: The prediction error that is obtained when applying the 1-hour reestimation strategy is significantly smaller than when the model is reestimated only every 4 hours (p < 0.001). The optimal size of the data set to be considered in each reestimation process of the ICU minimal model is found to be 4 hours. The obtained average “mean percentage error” is 7.6% (SD 3.1%) and 14.6% (SD 7.0%) when the model is reestimated every hour and 4 hours, respectively. Conclusions: Implementation of the ICU minimal model in the appropriate reestimation process results in clinically acceptable prediction errors. Therefore, the model is able to predict glycemia trends of patients admitted to the surgical ICU and can potentially be used in a predictive control system.

Bankruptcy prediction with least squares support vector machine classifiers

Classification algorithms like linear discriminant analysis and logistic regression are popular linear techniques for modelling and predicting corporate distress. These techniques aim at finding an optimal linear combination of explanatory input variables, such as, e.g., solvency and liquidity ratios, in order to analyse, model and predict corporate default risk. Recently, performant kernel based nonlinear classification techniques, like support vector machines, least squares support vector machines and kernel fisher discriminant analysis, have been developed. Basically, these methods map the inputs first in a nonlinear way to a high dimensional kernel-induced feature space, in which a linear classifier is constructed in the second step. Practical expressions are obtained in the so-called dual space by application of Mercers theorem. In this paper, we explain the relations between linear and nonlinear kernel based classification and illustrate their performance on predicting bankruptcy of mid-cap firms in Belgium and the Netherlands.

Load forecasting using fixed-size least squares support vector machines

Based on the Nystrom approximation and the primal-dual formulation of Least Squares Support Vector Machines (LS-SVM), it becomes possible to apply a nonlinear model to a large scale regression problem. This is done by using a sparse approximation of the nonlinear mapping induced by the kernel matrix, with an active selection of support vectors based on quadratic Renyi entropy criteria. The methodology is applied to the case of load forecasting as an example of a real-life large scale problem in industry, for the case of 24-hours ahead predictions. The results are reported for different number of initial support vectors, which cover between 1% and 4% of the entire sample, with satisfactory results.

A minimal model for glycemia control in critically ill patients.

In this paper we propose a modified minimal model to be used for glycemia control in critically ill patients. For various reasons the Bergman minimal model is widely used to describe glucose and insulin dynamics. However, since this model is mostly valid in a rather restrictive setting, it might not be suitable to be used in a model predictive controller. Simulations show that the new model exhibits a similar glycemia behaviour but clinically more realistic insulin kinetics. Therefore it is potentially more suitable for glycemia control. The designed model is also estimated on a set of critically ill patients giving promising results

Primal-Dual Monotone Kernel Regression

This paper considers the estimation of monotone nonlinear regression functions based on Support Vector Machines (SVMs), Least Squares SVMs (LS-SVMs) and other kernel machines. It illustrates how to employ the primal-dual optimization framework characterizing LS-SVMs in order to derive a globally optimal one-stage estimator for monotone regression. As a practical application, this letter considers the smooth estimation of the cumulative distribution functions (cdf), which leads to a kernel regressor that incorporates a Kolmogorov–Smirnoff discrepancy measure, a Tikhonov based regularization scheme and a monotonicity constraint.

Least squares support vector machines and primal space estimation

In this paper a methodology for estimation in kernel-induced feature spaces is presented, making a link between the primal-dual formulation of least squares support vector machines (LS-SVM) and classical statistical inference techniques in order to perform linear regression in primal space. This is done by computing a finite dimensional approximation of the kernel-induced feature space mapping by using the Nystrom technique in primal space. Additionally, the methodology can be applied for a fixed-size formulation using active selection of the support vectors with entropy maximization in order to obtain a sparse approximation. Examples for different cases show good results.