Smart sensing of the axial power and offset in NPPs using GMDH method
Introduction
Group method of data handling (GMDH) as a tool for forecasting future trends has been used in various fields. Zhang et al., 2012, Khemchandani and Jayadeva & Chandra, S., 2009, for example, used GMDH for financial time series forecasting. Huang and Shih (2002), on the other hand, applied GMDH to enhance the performance of fuzzy modeling for short-term load forecast applications. It has also been used for the identification of physical laws, short-term and long-term stepwise forecasting, etc. (Ivakhnenko and Ivakhnenko, 1995, Madala and Ivakhnenko, 1994). This paper will describe how the GMDH can be used for predicting some of the most important control parameters in nuclear power plant (NPP) systems. In this work, GMDH is also applied for the first time to the whole reactor core.
The status of NPP conditions must be checked to avoid initial events which can eventually lead to accidents such as loss of coolant accident (LOCA) and steam generator tube rupture (SGTR). In particular, axial power distribution and Axial Offset (AO) are very important data for operators of an NPP. To monitor in-core power distributions in pressurized water reactors (PWRs), the axial power profile reconstruction using in-core detector signals is essential. Currently, the Core Operating Limit Supervisory System (COLSS) uses fifth-order Fourier series expansion to reconstruct axial power shapes, which is known to have relatively large errors for the saddle, top- and bottom-skewed shapes (Park and Shin, 2014). Operators usually use the COLSS to understand the real core state in order to take appropriate action. The fifth-order Fourier series is widely used to reconstruct power distribution corresponding to in-core neutron detectors. In et al. (1991) used the cubic spline synthesis for OPR1000/APR1400 NPP. A stochastic method, the alternating conditional expectation algorithm was applied by Lee et al. (1999). In addition, Park and Shin (2014) used the GMDH algorithm to reconstruct 20-node axial fuel power shapes from five in-core detector power measurements. They used axial power as an input and output of the GMDH method. However, they focused on the fuel assembly level calculations instead of the core level calculations.
Moreover, any change in control rod position can affect the time-space xenon oscillation which in turn induces large local power peaking. Axial offset (AO) is a key parameter which is usually used to state three-dimensional core power peaking, in the form of a practical parameter. Here, the GMDH is adopted and employed as an efficient method to predict axial power and the AO of the reactor core as well as fuel assemblies at different core conditions. Although the AO can be calculated after the axial power has been reconstructed, we propose to directly predict the AO from the detector signals so as to avoid the impacts of the possible biases in the reconstructed axial power shape. In addition, by using the in-core detector signals instead of the ex-core detector signals to predict the AO, it is expected the results can be more precise and accurate, which is a great potential advantage for the core protection and monitoring systems that might improve the operation margin. Although the AO is an integral parameter, there is no information loss since the AO is treated as an additional independent parameter besides the axial power distribution.
Among all kinds of soft-computing methods, the GMDH is a heuristic self-organizing modeling technology. The GMDH algorithm was first introduced and applied by (Ivakhnenko, 1970) to solve high-order regression polynomials. As stated earlier, the GMDH has a wide range of applications, but the basic idea which is hidden in such methods is to build a multilayer feedforward network structure. Starting from the input layer, new candidate models are generated in every layer. New candidate models can be made by combining two models of the previous layer. Finally, utilizing some external criteria, the middle candidate models can be evaluated and selected (Ivakhnenko, 1976, Sarychev, 1990, Xiao et al., 2009). Our main goal in this paper is to find an optimum relation between the in-core detector signals and the dependent variables, the axial power and the AO.
Section snippets
Definition of axial offset in a NPP
Local power peaking factor has two main components, the radial and axial power peaking factors. Radial power peaking can be flattened by loading pattern optimization while the axial power peaking factor continues to change by perturbation caused by control rod movement. The AO is routinely used to present core power peaking. It is defined asWhere state the fraction of thermal power generated in the top and bottom of the reactor core, respectively. In other words,
Outline of GMDH algorithm
The GMDH includes sorting, which indicates a sequential testing of models taken out of a set of candidate models according to a specified criterion. Most of the GMDH algorithms employ polynomial basis functions. General connections between input and output variables can be found in the form of a functional Volterra series, whose discrete analog is known as the Kolmogorov-Gabor polynomial (Madala and Ivakhnenko, 1994)where
Developed method
To adopt and apply the GMDH algorithm for AO prediction, one can rewrite Eq. (4) as belowwhere is power in the axial direction, are the polynomial coefficients, and is the measured detector signal. Here, a multilayered GMDH is used in which an optimal solution (optimum structure) can be found by an iterative approach. Fig. 6 demonstrates a typical multilayered Ivakhnekov GMDH algorithm. Fig. 6 also shows the
Core axial power test case
To verify the developed software, the axial power and AO of the reactor core using “CORE_Dataset” is considered. Fig. 10, Fig. 11, Fig. 12 show the predicted axial power for the beginning of the cycle (BOC), middle of the cycle (MOC) and end of the cycle (EOC), respectively. The GMDH results compared with those of the spline method and reference values. The presented errors in Fig. 10, Fig. 11, Fig. 12 are the difference between the GMDH predicted values and the reference values. The maximum
Conclusion
The investigation carried out in this paper supplied an intuition into the way the GMDH deals with axial power and AO prediction. Previously, the GMDH method is used for axial power reconstruction of the fuel assembly. Our study extends the application of GMDH to the whole reactor core and the prediction of the AO of both the fuel assembly and the core. Considering the recent progress in computer science, the application of GMDH, a complex but nonlinear fitting method, in reconstructing the
Acknowledgement
This research was supported by the project (L17S018000) by Korea Hydro & Nuclear Power Co. Ltd.
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2020, Nuclear Engineering and TechnologyCitation Excerpt :GMDH was utilized in many applications such as semiconductor manufacturing [23], recognition of medical image of blood vessels [24], fault identification [25], fluid flow simulations [26], and many more. For nuclear applications, GMDH was used for different purposes such as predicting the break size in loss of coolant accidents [27], heat transfer applications [28], reactor power shaping and sensing [29,30], and monitoring and fault diagnosis in steam generators and thermal systems [31,32]. In this section, the GMDH method implemented in this study is described in detail, followed by a brief description of the other metamodelling techniques used for comparison with GMDH performance.