Elsevier

Neurocomputing

Volume 75, Issue 1, 1 January 2012, Pages 219-225
Neurocomputing

Multi-objective learning of white box models with low quality data

https://doi.org/10.1016/j.neucom.2011.02.025Get rights and content

Abstract

Improving energy efficiency in buildings represents one of the main challenges faced by engineers. In fields like lighting control systems, the effect of low quality sensors compromises the control strategy and the emergence of new technologies also degrades the data quality introducing linguistic values. This research analyzes the aforementioned problem and shows that, in the field of lighting control systems, the uncertainty in the measurements gathered from sensors should be considered in the design of control loops. To cope with this kind of problems Hybrid Intelligent methods will be used. Moreover, a method for learning equation-based white box models with this low quality data is proposed. The equation-based models include a representation of the uncertainty inherited in the data. Two different evolutive algorithms are use for learning the models: the well-known NSGA-II genetic algorithm and a multi-objective simulated annealing algorithm hybridized with genetic operators. The performance of both algorithms is found valid to evolve this learning process. This novel approach is evaluated with synthetic problems.

Introduction

Improving energy efficiency represents a big challenge in modern engineering [1], [2], [3], and more specifically, in the field of lighting control systems included in building automation. In a lighting control system, the typical lighting control loop includes a light sensor, the light ballasts and a light controller. The light sensor measures the amount of light in a room, although the measurements lack hysteresis and saturation [2]. Moreover, recent studies show that the measurements obtained from light sensors are highly dependent on the light sensor unit [4]. This meta information in the data gathered from processes is rarely used, and it is mainly related to non-stochastic noise.

In our opinion, learning models using the meta information in the data will result in more robust models and better control design. Hybrid Intelligent methods [5], [6] will be used to cope with this kind of problems. This study shows the presence of such meta information and presents a novel method for learning with this kind of data. The method has been developed for learning equation-based models (hereinafter EB models) but can be easily extended to different models, including neural networks. To evolve the models, two different evolutionary learning strategies have been used: the well-known NSGA-II genetic algorithm [7] and the Multi-Objective simulated annealing hybridized with genetic operators [8] (hereinafter MOSA).

The remainder of this manuscript is as follows. Firstly, the problem description and the uncertainties in real-world problems such as the simulation of lighting control systems are presented. A review of the literature concerned with learning models with low quality data (hereinafter LQD) is then shown. In Section 4 the novel method is described. Section 5 deals with the experimentation and results obtained with the proposal. Finally, some conclusions and future work are outlined.

Section snippets

Low quality data in real-world processes

The aim of lighting control systems is to control the electrical power consumption of the ballasts in the installation so that the luminance complies with the regulations [9]. In these systems, the luminance is measured through light sensors and variables such as the presence of inhabitants are analyzed, as well. However, the relevance of the former is higher as it is used as the feedback in the lighting control loop.

Nevertheless, the output of such sensors is highly dependent on a number of

Algorithms managing low quality data

The need for algorithms capable of facing LQD is a well-known fact in the literature. As analyzed in [10], several studies have presented the decrease in the performance of crisp algorithms as uncertainty in data increases.

On the other hand, [11] analyzes the complex nature of the data sets in order to choose the best Fuzzy Rule Based System. Several measures are proposed to deal with the complexity of the data sets and the Ishibuchi fuzzy hybrid genetic machine learning method is used to test

Learning models with low quality data

As stated in previous sections, data gathered from light sensors is imprecise, behaves with hysteresis and lacks repeatability. Obviously, we can represent this kind of data as non-crisp granules of information (i.e., an interval or a probable radius, etc.), but this approach would introduce higher computational costs and complexity in the model learning process.

Conversely, we will assume that the data set used for learning the models contains imprecise crisp values only. Besides, we will

Experiments and results

To test our proposal five different synthetic problems are proposed. The formulas for generating the data sets are presented in Table 1. The input variables {x0,…,x3} evolve with the time. The formulates {f1,f2,f3} are intended to deal with regression problems, while {f4, f5} represent time series problems. For each problem two data sets of 100 examples each are generated: the precise and the imprecise data sets. The former is obtained directly from the equations, while the latter is obtained

Conclusions

This study proposes learning EB models to deal with LQD. The EB models include a representation of the uncertainty and evaluating a model generates a fuzzy value. The learning of models is defined as a multi-objective problem using Fuzzy fitness functions and two evolutionary learning strategies are proposed. The proposal has been analyzed with synthetic problems. The results show that the uncertainty representation in the EB models learned with the two evolutionary heuristic techniques keeps

José R. Villar obtained his Engineering degree at the University of Oviedo (1992) and his PhD at the University of León (2002). He had worked for several engineering companies between 1992 and 1998. In 1998 he became an Assistant Professor with the Electric and Electronic Department at the University of León. In 2004 he became an Assistant Professor with the Computer Science Department at the University of Oviedo. Since 2008, he is an Associate Professor with this department. He had

References (20)

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José R. Villar obtained his Engineering degree at the University of Oviedo (1992) and his PhD at the University of León (2002). He had worked for several engineering companies between 1992 and 1998. In 1998 he became an Assistant Professor with the Electric and Electronic Department at the University of León. In 2004 he became an Assistant Professor with the Computer Science Department at the University of Oviedo. Since 2008, he is an Associate Professor with this department. He had participated in several research projects and contracts with public and private funding and had published contributions in indexed international journals and ranked conferences as well as several book chapters. He is a member of the IEEE Systems, Man & Cybernetics Chapter Society Spanish Chapter. His research interests are focussed in Genetic Fuzzy Systems, Meta-heuristics and Low Quality Data processing.

Alba Berzosa obtained her Computer Science Engineering Degree at the University of Burgos in 2007. Since 2009 she is working with the Artificial Intelligence and Applied Electronics at the Instituto Tecnológico de Castilla y León. She is the co-author of several contributions to ranked international conferences. Her research interests are focused in Genetic Fuzzy Systems, Meta-heuristics and Low Quality Data processing.

Enrique A. de la Cal Marín received the MSc and PhD degrees in computer science from the University of Oviedo, Oviedo, Spain, in 1995 and 2003,respectively. Previously, during 1995 was contracted like predoctoral researcher in CSIC Daza Valdes Research Institute. In 1996 he is contracted like associated professor in Oviedo University. Currently, he is Professor with the Department of Computer Sciences, the University of Oviedo. His research interests are in the fields of fuzzy-rule-based systems, soft computing industrial problems modeling, energy efficiency, automatic trading, genetic algorithms, and genetic programming.

Dr. Javier Sedano is an expert in the development of electronic systems – hardware – industrial projects and production-systems acquisition and control systems, “also in the design of connectionless models for the identification and modeling of dynamic systems”. He has directed and participated in many research and development projects for the development of prototypes in pre-competitive projects, competitive and industrial research. He is the head of the group of Artificial Intelligent and Electronic Applied at the Instituto Tecnológico de Castilla y León. Also, he is part of the Applied Computational Intelligence Group at the University of Burgos, a few years working on projects and publications related to artificial intelligence and system modeling. It also collaborates in the organization of international scientific conferences, program committees and organization. He is a member of the IEEE Systems, Man & Cybernetics Chapter Society Spanish Chapter. It has some international publications, book chapters and participating in conference, as well as records of software and industrial patents.

Marco A. Garcia Tamargo has a degree in Computer Engineering from the University of Oviedo, and PhD from the same university. He has worked in a private company developing and implementing Urban Traffic Control Systems. Since 1996 he works as Associate Professor at the University of Oviedo. His main areas of research so far has been the Traffic Control Systems, Distributed Systems, Multiagent Systems and Intelligent Systems for Risk Assessment based on data mining.

This research has been funded by the Spanish Ministry of Science and Innovation, under project TIN2008-06681-C06-04, and by the ITCL project CONSOCO.

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