PWR's xenon oscillation control through a fuzzy expert system automatically designed by means of genetic programming
Introduction
Since axial oriented oscillations are the most unstable in a pressurized water reactor (PWR) core [5], and control rods are generally moved in that direction, axial oscillations control has been an important task in the nuclear reactors operation. Axial xenon oscillation is a highly non-linear phenomenon, strongly influenced by the changes in the neutron absorption, that may occur due to soluble boron concentration or control rods position changes. Minor variations in such absorption may lead to an axial xenon oscillation.
Controlling the axial xenon oscillations through the use of axial offsets have been successfully proposed by Shimazu [7], [8]. In his work, he proposed a continuous guidance procedure for xenon oscillation control, based on the axial offsets of xenon (AOx), iodine (AOi) and power (AOp). More recently, Na [4], successfully proposed a neuro-fuzzy approach.
Recently, the successful applications of genetic programming (GP) [3]—a powerful evolutionary computation (EC) technique—in control systems design [1], [2] has been motivating its use.
In the present work, we propose the use of GP to automatically find a set of fuzzy rules, which can effectively control the axial xenon oscillation. The main idea of the proposed approach is to have the GP playing the role of an expert, finding a good fuzzy strategy, which can effectively control the axial xenon oscillations.
Section snippets
Axial xenon oscillation model
In PWR's, axial xenon oscillations are induced when the neutron flux or the power are disturbed. Changing the absorption cross-section, principally through control rods position changes generally controls such transient.
In this work, we have used a two-point xenon oscillation model, which employs the non-linear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation with non-linear power reactivity feedback, successfully proposed by Onega and Kisner [5].
Control model
A method for controlling such axial xenon oscillations, proposed by Shimazu [7] has considered the axial offsets of power, xenon and iodine concentrations:Shimazu [7] has demonstrate that axial xenon oscillations can be avoided whenBy this principle we can proceed the control by estimating the moment when AOi and AOx will intercept each other and then, adjusting
Genetic modeling
Genetic programming [3] is a powerful search technique which belongs to the class of the evolutionary algorithms. Inspired by the Darwin's theory, these algorithm works by simulating the evolution of structures by means of fitness-based natural selection and genetic operators, such as reproduction, crossover and mutation. In GP individuals are computer programs, generally represented as trees. In this work, the trees represent a fuzzy controller, in which if–then rules, encoded into trees, as
Application and results
The above described approach was implemented by using a constrained genetic programming toolkit, adequate to manipulate syntactically and semantically restricted structures such as fuzzy rule bases.
Using a population of 1000 individuals, and typical crossover and mutation rates, we have found the best structure after 295 generations, as shown on Table 1. Such best controller has used 103 rules, including repetitions. Only 10 different rule were found.
A rule that appears N times in the fuzzy
Conclusions
The main role for an human expert in designing a fuzzy controller lays in correctly choose the combinations of rules able to keep the process to be controlled under acceptable limits. This aim demands a reasonable knowledge of the process.
In nuclear engineering such knowledge often is not present in a manageable way, and in some situation it do not even exist. In some cases the presence of a human expert is not possible.
Artificial intelligence hybrid techniques come to fill this lack out. This
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New monitoring procedure of axial xenon oscillation in large pressurized water reactors
2019, Annals of Nuclear EnergyCitation Excerpt :Some researchers have already discussed on this matter (R. Domingos et al., 2003). Domingos et al. investigated the use of the three axial offsets concept in Genetic Programming (GP) to design a fuzzy expert system to control axial xenon oscillations (Domingos et al., 2003). One of our main authors investigate the usage of the three axial offsets concept in Westinghouse type PWRs (Deswandri, 2012).
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2015, Annals of Nuclear EnergyCitation Excerpt :Control systems are designed to limit the amplitude of both types of oscillation and to stabilize the state of the reactor near a chosen steady state. Since the discovery of the problems posed by xenon instabilities in nuclear power reactors, a lot of work has been carried out and analyzed extensively for PWRs until now (Randall and John, 1958; Stacey, 1970; Onega and Kisner, 1978; Christie and Poncelet, 1973; Bauer and Poncelet, 1974; El-Bassioni and Poncelet, 1974; Chae, 1979; Moon and Han, 1982; Cho and Grossman, 1983; Song et al., 1995; Sutton and Aviles, 1996; Song and Cho, 1999; Jeong and Choi, 2000; Domingos et al., 2003; Marseguerra et al., 2003; Shimazu, 2004; Boroushaki et al., 2004; Doshi and Obaidurrahman, 2006; Shimazu, 2007; Reddy et al., 2008; Gabor et al., 2011). The demand to construct larger nuclear power reactors brought the problem of the out-of-phase or spatial xenon oscillations.
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