Adaptive fuzzy system for fuel rod cladding failure in nuclear power plant

Transcription

1 annals of NUCLEAR ENERGY Annals of Nuclear Energy 34 (2007) Technical note Adaptive fuzzy system for fuel rod cladding failure in nuclear power plant Antonio C.F. Guimarães *, Celso M.F. Lapa Instituto de Engenharia Nuclear Divisão de Reatores/CNEN, Ilha do Fundão s/n, , P.O. Box 68550, Rio de Janeiro, Brazil Received 14 July 2006; received in revised form 16 August 2006; accepted 30 November 2006 Available online 1 February 2007 Abstract A new approach to the study of ballooning that causes cladding failure in fuel rods using an adaptive neural fuzzy inference system (ANFIS) is presented in this paper. By mapping input/output patterns describing cladding failure phenomena through average inner cladding temperature and fuel rod gas pressure, ANFIS shows a great potential to modeling this problem in alternative to the traditional approach. A typical pressurized water reactor fuel rod data was used to this application. The results confirm the potential of ANFIS comparatively to experimental calculations. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction Artificial intelligence (AI) approaches and methodologies have been successfully applied to many complex problems related to project, operation and improvement of the safety level in nuclear power plants. In Guimarães (2003a) was used the fuzzy logic methodology to establish inservice inspection priorities for nuclear components. In Guimarães (2003b) was developed a new methodology for the study of flow accelerated corrossion (FAC) phenomenon based on a fuzzy rule system. In Guimarães and Lapa (2004a) were studied the effects analysis fuzzy inference system in nuclear problems using approximate reasoning. In Guimarães and Lapa (2004b) was considered the fuzzy inference system for evaluating and improving nuclear power plant operating performance. Now, loss of coolant of accident (LOCA) in nuclear power plant (NPP) and subsequent straining and ballooning of the cladding with failure from excessive strain or departure from nucleate boiling has motivated the development of a new approach in AI. * Corresponding author. Tel.: ; fax: addresses: tony@ien.gov.br (A.C.F. Guimarães), lapa@ien. gov.br (C.M.F. Lapa). A light water reactor (LWR) fuel rod typically consists of UO2 fuel pellets enclosed in Zircaloy cladding, as shown in the Fig. 1 (Cunningham et al., 2001a). The primary function of the cladding is to contain the fuel column and the radioactive fission products. If the cladding does not crack, rupture, or melt during a reactor transient, the radioactive fission products are contained within the fuel rod. During some reactor transients and hypothetical accidents, however, the cladding may be weakened by a temperature increase, embrittled by oxidation, or over stressed by mechanical interaction with the fuel. These events alone or in combination can cause cracking or rupture of the cladding and release of the radioactive products to the coolant. Furthermore, the rupture or melting of the cladding of one fuel rod can alter the flow of reactor coolant and reduce the cooling of neighboring fuel rods. This event can lead to the loss of a coolable reactor core geometry. More detailed descriptions can be found in Cunningham et al. (2001a). The pressure of the gas in the fuel rod must be known in order to calculate the deformation cladding and the transfer of heat across the fuel-cladding gap. The pressure is a function of the temperature, volume and quantity of gas. Because the temperature is spatially non-uniform, the fuel rod must be divided into several smaller volumes so that /$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi: /j.anucene

2 234 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) temperature in each small volume can be assumed to be uniform. In particular, the fuel rod is divided into a plenum volume and several fuel-cladding gap and fuel void volumes. The temperature of each volume is given by the temperature model, the size of the volume by the deformation model, and the quantity of gases by the fission gas release model (Cunningham et al., 2001a). In the FRAPTRAN code, the internal gas pressure can be calculated by either a static pressure model (which assumes that all volumes inside the fuel rod equilibrate in pressure instantaneously) or by a transient pressure model which takes into account the viscous flow of the gas in the fuel rod. The transient model is an input option. Unless the fuel-cladding gap is small (<25 lm) or closed, the static and transient models give identical results. An integral assessment has been performed of the FRAPTRAN transient fuel behavior code designed to analyze fuel rod thermal and mechanical behavior during a range of transients with fuel burn up to 65 GWd/MTU. This assessment was performed for the US Nuclear Regulatory Commission by Pacific Northwest National Laboratory to quantify the predictive capabilities of FRAPTRAN. The FRAPTRAN predictions are shown to compare satisfactorily to a selected set of experimental data from reactivity-initiated accident (RIA), loss-of-coolant-accident (LOCA), and other transient operating conditions. The assessment was performed by comparing FRAP- TRAN code calculations to data from selected integral irradiation experiments and post irradiation examination programs. In this paper, a new methodology for cladding failure problem, only in LOCA situation, was proposed and the same experimental data used in case of FRAPTRAN analysis were used in our application to estimate the rod internal gas pressure from the cladding temperature. In the following item are presented a few words of traditional computer code FRAPTRAN, for this problem. The ANFIS approach will be described in item Section 3. Development of the system will be presented in Section 4. The results will be presented in Section 5 and the conclusions in Section Words of traditional approach Fig. 1. Schematic of typical LWR fuel rod. The fuel rod analysis program transient (FRAPTRAN) is a FORTRAN language computer code that calculates the transient performance of light water reactor fuel rods during reactor power and coolant transients for hypothetical accidents such as loss-of-coolant accidents (LOCA), anticipated transients without scram, and reactivity-initiated accidents (RIA). FRAPTRAN calculates the temperature and deformation history of a fuel rod as function of time-dependent fuel rod power and coolant boundary conditions. FRAPTRAN is intended to be used as a stand alone code. The phenomena modeled by FRAPTRAN include: (a) heat conduction, (b) heat transfer from cladding to coolant, (c) elastic plastic fuel and cladding deformation, (d) cladding oxidation, and (e) fuel rod gas pressure. FRAP- TRAN was developed from the FRAP-T6 code and incorporates burnup-dependent parameters and corrects errors. Burnup dependent parameters may be initialized from the FRAPCON-3 steady-state single rod fuel performance code. FRAPTRAN is a computer code developed for the US Nuclear Regulatory Commission up to burnup levels of 65 GWd/MTU. FRAPTRAN uses a finite difference heat conduction model for the transient thermal solution, the FRA- CAS-I mechanical model, and the MATPRO (Hohorst, 1990) material properties package. To account for the effects of high burnup, FRAPTRAN uses a new model for UO2 thermal conductivity that incorporates the degradation effects of burnup and a revised model for Zircaloy mechanical properties that accounts for the effect of oxidation and hydrides in addition to irradiation damage. Burnup-dependent fuel rod initial conditions can be obtained from the companion FRAPCON-3 (Berna et al., 1997) steady-state fuel rod performance code. FRAPTRAN was developed from the FRAP-T6 transient code and is intended to replace the FRAP-T6 code. The development approach for FRAPTRAN was to implement applicable existing high-burnup models rather than developing new

3 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) models, to not substantially change the code structure, to remove no longer needed or used coding, to correct known or found problems in FRAP-T6, and to improve ease of use. To meet these objectives, in addition to changing fuel and cladding models, other changes include deleting dynamic dimensioning and options such as uncertainty analysis, failure analysis, and licensing evaluation models. The ability to accurately calculate the performance of light water reactor (LWR) fuel during irradiation, and during both long-term steady-state and various operational transients and hypothetical accidents, is an objective of the reactor safety research program being conducted by the US Nuclear Regulatory Commission (NRC). To achieve this objective, the NRC has sponsored an extensive program of analytical computer code development and both in-reactor and out-of-reactor experiments to generate the data necessary for development and verification of the computer codes. Provided in volume 1 (Cunningham et al., 2001a) report, there is a description of the FRAPTRAN (Fuel Rod Analysis Program Transient) code developed to calculate the response of single fuel rods to operational transients and hypothetical accidents at burnup levels up to 65 GWd/MTU. The FRAPTRAN code is the successor to the FRAP-T (Fuel Rod Analysis Program-Transient) code series developed in the 1970s and 1980s. FRAPTRAN is also a companion code to the FRAPCON-3 code (Berna et al., 1997) developed to calculate the steady-state high burnup response of a single fuel rod. A major driver for FRAPTRAN was to incorporate new burnup-dependent models and understand and develop a code that could predict cladding strain resulting from transients. The FRAP-T computer code series was developed in the 1970s and 1980s for predicting the performance of LWR fuel rods during operational transients and hypothetical accidents. However, since FRAP-T6 (Siefken et al., 1981; Siefken et al., 1983) was completed, additional experimental data and knowledge of fuel performance have been obtained, thus necessitating an update to the code. In volume 2 (Cunningham et al., 2001b) is the code assessment based on comparisons of code predictions to fuel rod integral performance data up to high burnup (65 GWd/MTU). 3. Description of fuzzy system methodology 3.1. ANFIS This section describes the methodology, which was used to perform the estimated Fuel Rod Gas Pressure. This is a new approach in this type of area. An ANFIS is an fuzzy inference system (FIS) that can be trained with a backpropagation algorithm to model some collection of input/output data. Allowing the system to adapt provides the fuzzy system with the ability to learn the input/output relationships embedded in the collected data. The ANFIS network structure facilitates the computation of a gradient vector that relates the reduction of an error function to a change in the parameters of the FIS. Once this gradient vector is obtained, a number of optimization routines can be applied to reduce the error between the actual and the desired outputs. In the neural network literature, this process is called learning by example (Hines et al., 1997). The ANFIS described here uses the Sugeno-style fuzzy model (also known as the TSK fuzzy model) proposed by Takagi and Sugeno (1985) and Sugeno and Kang (1988). Takagi and Sugeno (1985) proposed to use the following fuzzy IF THEN rules: L ðlþ : IF x 1 is F l 1 and... and x n is F l n ; THEN y l ¼ c l 0 þ cl 1 x1 þ...þ c l n x n ð1þ where F l i are fuzzy sets, c i are real-valued parameters, y l is the system output due to rule L (l), and l = 1,2,...,M. That is, they considered rules whose IF part is fuzzy but whose THEN part is crisp the output is a linear combination of input variables. For a real-valued input vector x =(x 1,...,x n ) T, the output y(x) of Takagi and Sugeno s fuzzy system is a weighted average of the y l s: Y ðxþ ¼ R M l¼1 wl y l = R M l¼1 wl ð2þ Fig. 2. Basic configuration of Takagi and Sugeno s fuzzy system.

4 236 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) where the weight w l implies the overall truth value of the premise of rule L (l) for the input and is calculated as W l ¼ P n i¼1 l Fliðx i Þ ð3þ The configuration of Takagi and Sugeno s fuzzy system is shown in the Fig MatLab ANFIS MATLAB6 s software package and its associated fuzzy logic toolbox (MatLab, 2000) were used to create the adaptive neural fuzzy inference system. MATLAB6 s ANFIS support first-order Sugeno systems have a single output and unity weights for each rule. 4. Development of the system Loss-of-coolant accidents typically occur from full power conditions are initiated with scram, coolant flow is lost, and then eventually coolant flow is restored (reflood and quench). The energy is already present in the fuel at the time of the scram, with a continuing low level of energy deposition in the fuel from decay heat. Another component of energy deposition during the transient, depending on conditions, may be heat generation in the cladding from Zircaloy oxidation. The response of the fuel rods is cladding heatup, while the fuel cools down, and subsequent straining and ballooning of the cladding with failure from either excessive strain or departure from nucleate boiling. Instrumentation during LOCA transient experiments typically consists of cladding outer thermocouples, fuel centerline thermocouples, fuel rod gas pressure (and occasionally plenum temperature), cladding axial elongation, and coolant conditions (temperature, pressure, flow). The database used for this assessment consists of essentially non-irradiated fuel rods. The rods did acquire some minimal burnup during power calibration and decay heat buildup periods prior to the LOCA transients. Post-test examinations may include metrology (diameter and rupture location) and metallography. The typically available data for LOCAs, the assessment of code performance, concentrate on both the thermal and mechanical performance of the test rods. Key parameters for comparison to data are time to rupture, axial location of rupture and ballooning, cladding elongation history, and rod gas pressure history. Three types of the LOCA, named MT-1, MT-4 and MT- 6A, were considered with FRAPTRAN analysis, but only the MT-6A assessment was chosen for our ANFIS application. A principal difference between MT-6A and the other two tests was a redesign of the test train to reduce cladding circumferential temperature gradients and thus induce greater amounts of cladding ballooning and flow blockage. Representative cladding inner surface temperature histories for MT-6A are provided in the Fig. 3, considered as input. A plenum gas pressure history representative for this test is provided in the Fig. 4, considered as output of ANFIS system. The data considered in this analysis were the data obtained fom experimental calculations Input parameter In Figs. 3 and 4, 33 patterns were defined and analyzed with 2.5 s intervals. These values are presented in the Table 1. On defining the input/output data to be mapping with fuzzy inference system (FIS), in the next item, the training, validation and testing data set selection will be presented Training (T), validation (V) and testing data To train the ANFIS, we used the index odd patterns of the entire data set, which resulted in 17 patterns, while for the validation data set, we used the index even patterns, which yielded a total of 16 patterns. Only five patterns found in the training data set were repeated in the validation set (Index odd,even numbers 1, 2, 3, 6 and 17), this being due to a small number of total patterns available. The validation set monitors the fuzzy systems ability to generalize during training (the same principle as cross-validation training in neural network). Each data set, training and Fig. 3. Cladding inner surface temperature for MT-6A ( F Index).

5 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) Fig. 4. Plenum gas pressure for MT-6A (MPa Index). Table 1 Values of temperatures (F) and plenum gas pressure (MPa) Index Elapsed time (s) Inner temperature of cladding (F) Fuel rod gas pressure (Mpa) Table 2 All patterns used for training and validation of the ANFIS Index odd,even Temp (T odd) (F) Fuel rod gas pressure (T odd) validation, contained the maximum and minimum data value for each data pattern in the entire data set. It is important to cover the entire span of a fuel rod gas pressure s actuation range so that values will be covered in the membership functions domain. Testing of the system was performed with the entire data set, which consisted of 33 patterns. In the Table 2 are presented the training (T) and validation (V) data for this application. In the Figs. 5 and 6, the training and validation data output are presented graphically ANFIS structure and training Temp (V even) (F) Fuel rod gas pressure (V even) In this part, it will be described how the fuzzy inference system (FIS) was developed. MATLAB s software package and its associated fuzzy logic toolbox were used to create the ANFIS based on the data set defined before. MAT- LAB s ANFIS supports first-order Sugeno systems that have single output and unity weights for each rule. The ANFIS is developed by using a training data set that contains the desired input/output data pairs of the system to be modeled and a validation data set that checks the generalization capability of the resulting FIS. The FIS parameters with minimum validation set error are chosen as optimal. In the Fig. 7, the FIS Sugeno is presented schematically. After the performance of some test with MATLAB s simulator the use of five gauss memberships functions was

6 238 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) Fig. 5. Training data set for ANFIS (MPa Index odd ) Fig. 6. Validation data set for ANFIS (MPa Index even ). Fig. 7. Sugeno fuzzy inference system. found to be optimal. In the Fig. 8, these five membership functions are plotted. 5. Results Measured time to rupture for the MT-6A rods was between 58 and 64 s, while FRAPTAN predicted time to rupture was 40 s (Cunningham et al., 2001b). The ANFIS predicted and measured gas pressure histories are compared in the Fig. 9. Note that each point in the axe index has 2.5 s, which means that time to rupture rods was between 25 and 30 in the ANFIS predicted. In general, good agreement was obtained between the ANFIS prediction and the experimental data for rod gas pressure and time to failure. In the Table 1 the Index or Elapsed Time in seconds can be seen with an interval of 2.5 s for each point of Index. In the Table 2, the Index odd (Temp (T) and Fuel Rod Gas Pressure (T) where T means Training) and Index even (Temp (V) and Fuel Rod Gas Pressure (V) where V means Validation) are presented together as Index odd, even and represent a new index for odd and

7 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) Fig. 8. Membership function of input variable temperature. Fig. 9. Comparison of measured and predicted plenum gas pressure for MT-6A (Mpa Index). even data set used in ANFIS. And then, the Index in the Fig. 9 is the same Index used in the Fig. 4, when all data sets are considered. Now, if rupture is found between 25 and 30, we only have to multiply this number there by 2.5 to find the appropriate time to rupture in seconds. 6. Conclusion A fuzzy inference system using ANFIS was presented in this article to predict the Fuel Rod Gas Pressure history from Cladding Inner Surface Temperatures history for Loss-of-Coolant accident simulation. Experimental results for this temperature were used for predicted pressure. The results of this study have shown that the prediction system using an ANFIS is very pratical and simple. For illustration effects to application ANFIS methodology, only one data set, specific to measured cladding inner surface temperature data at elevations of 90 in., was considered. Experimental data were collected for six elevations. Future developments will be considering all elevations and other feasible predictions to compare with experimental results. Acknowledgements This research has been supported by the National Council for Scientific and Technological Development (CNPq), a foundation linked to the Ministry of Science and Technology (MCT), to support Brazilian research. Grant number: /

8 240 A.C.F. Guimarães, C.M.F. Lapa / Annals of Nuclear Energy 34 (2007) References Berna, G.A. et al., FRAPCON-3: a computer code for the calculation of steady-state, thermal mechanical behavior of oxide fuel rods for high burnup. NUREG/CR-6534 (PNNL-11513), vol. 2, Pacific Northwest National Laboratory, Richland, Washington. Cunningham, M.E., Beyer, C.E., Medvedev, P.G., Berna, G.A., FRAPTAN: A Computer Code for the Transient Analysis of Oxide Fuel Rod, NUREG/CR 6739, vol. 1, US Nuclear Regulatory Commission. Cunningham, M.E., Beyer, C.E., Panisko, F.E., Medvedev, P.G., Berna, G.A, Scott, H.H., FRAPTRAN: Integral Assessment, NUREG/CR 6739, vol. 2, US Nuclear Regulatory Commission. Guimarães, A.C.F., 2003a. The use of fuzzy logic methodology to establish inservice inspection priorities for nuclear components. Progress in Nuclear Energy 42 3, Guimarães, A.C.F., 2003b. A new methodology for the study of FAC phenomenon based on a fuzzy rule system. Annals of Nuclear Energy 30 7, Guimarães, A.C.F., Lapa, C.M.F., 2004a. Effects analysis fuzzy inference system in nuclear problems using approximate reasoning. Annals of Nuclear Energy 31 1, Guimarães, A.C.F., Lapa, C.M.F., 2004b. Fuzzy inference system for evaluating and improving nuclear power plant operating performance. Annals of Nuclear Energy 31 3, Hines, J.W., Wrest, D.J., Uhrig, R.E., Signal validation using an adaptive neural fuzzy inference system. Nuclear Technology 119, Hohorst, J.K., SCDAP/RELAP5/MOD2 Code Manual, vol. 4: MATPRO A Library of Materials Properties for Light Water- Reactor Accident Analysis. NUREG/CR-5273 (EGG-2555), vol. 4, EG&G Idaho, Inc., Idaho Falls, Idaho. MatLab 6, User s Guide of the Fuzzy Logic Toolbox. Siefken, L.J. et al., FRAP-T6: A Computer Code for the Transient Analysis of Oxide Fuel Rods. NUREG/CR-2148 (EGG-2104), EG&G Idaho, Inc., Idaho Falls, Idaho. Siefken, L.J. et al., FRAP-T6: A Computer Code for the Transient Analysis of Oxide Fuel Rods. NUREG/CR-2148 Addendum (EGG Addendum), EG&G Idaho, Inc., Idaho Falls, Idaho. Sugeno, M., Kang, G.T., Structure identification of fuzzy models. Fuzzy Sets and System 28, 15. Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems Man and Cybernetics SMC-15 (1),