Applying particle swarm optimization algorithm for tuning a neuro-fuzzy inference system for sensor monitoring M.V. Oliveira a, * , R. Schirru b a Divisa ˜o de Instrumentaça ˜o e Confiabilidade Humana, Instituto de Engenharia Nuclear, CNEN, Rua He´lio de Almeida, 75 Caixa Postal 68550, Cidade Universita ´ria, 21945-970 Rio de Janeiro, Brazil b Laborato ´rio de Monitoraça ˜o de Processos, Programa de Engenharia Nuclear, UFRJ, Av. Brigadeiro Tronpowski s/n, Caixa Postal 68509, Cidade Universita ´ria, 21945-970 Rio de Janeiro, Brazil Keywords: Signal validation Particle swarm optimization Neuro-fuzzy system abstract A neuro-fuzzy inference system (ANFIS) tuned by particle swarm optimization (PSO) algorithm has been developed for monitoring the relevant sensor in a nuclear power plant (NPP) using the information of other sensors. The antecedent parameters of the ANFIS that estimates the relevant sensor signal are optimized by a PSO algorithm and consequent parameters use a least-squares algorithm. The proposed methodology to monitor sensor output signals was demonstrated through the estimation of the nuclear power value in a pressurized water reactor using as input to the ANFIS six other correlated signals. The obtained results are compared to two similar ANFIS using one gradient descendent (GD) and other ge- netic algorithm (GA), as antecedent parameters’ training algorithm. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Sensor signals from many different measurement locations in a nuclear power plant are used in operation and control of the plant. The optimal control and safe operation of a complex dynamic system such as a nuclear power plant are dependent on the validity of sensors providing information about the process state. The operator usually interprets the data based on experience and knowledge of the system and makes a decision about whether the results suggest a faulty instrument or a corrective measure is un- necessary. This decision may be crucial during an emergency when an operator has to deal simultaneously with numerous signals or a critical measurement on which the system stability is dependent. Signal validation can be defined as the identification of faulty process measurements and subsequent production of an estimate for the variable being measured. Redundant sensors are often used for signal validation in critical parts of plant control systems to ensure the required degree of safety. The hardware redundant sensor methodology increases the cost of the whole system. To achieve substantial savings on hard- ware redundancy, and, at same time, to meet the requirements of reliable and accurate sensor measurements many signal validation systems based on analytical redundancy have been proposed. The state-of-art methodologies for signal validation using analytical redundancy range from the emerging techniques based on artificial intelligence (AI) to conventional parity space methods. The AI-based methods include petri nets, neural networks, fuzzy inference system, and other knowledge-based techniques. Artificial neuro-fuzzy inference systems have been applied in different nuclear fields (Guimara ˜es et al., 2006; Guimara ˜es and Lapa, 2007). Many studies (Hines et al., 1997; Na,1999; Na and Oh, 2002) on signal validation using artificial neuro-fuzzy inference system have been realized recently. Most of them (Hines et al., 1997; Na, 1999) use a gradient descendent technique for optimizing the antecedent parameters and a least means square method for the consequent parameters of the ANFIS. More recently (Na and Oh, 2002), an optimization technique based on genetic algorithm was proposed for training the parameters in the antecedent part of a fuzzy system. In this work, we suggest to use particle swarm optimization technique for training the antecedent parameters of a fuzzy inference system. The proposed methodology to monitor sensor output signals was demonstrated through the estimation of the nuclear power value in a pressurized water reactor using as input to the ANFIS six other correlated signals. The results obtained from the tests are compared with similar ANFIS based on gradient descendent and genetic algorithm techniques for training the antecedent parameters. 2. Adaptive neuro-fuzzy inference system An ANFIS is an FIS that can be trained to model some collection of input/output data. The training process allows the system to adjust its parameters to learn the input/output relationships embedded in the collected data. * Corresponding author. Tel.: þ55 21 2173 3846; fax: þ55 21 2173 3836. E-mail addresses: mvitor@ien.gov.br (M.V. Oliveira), schirru@lmp.ufrj.br (R. Schirru). Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene Progress in Nuclear Energy 51 (2009) 177–183 Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene 0149-1970/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.pnucene.2008.03.007