Sensitivity analysis and dimension reduction of a steam generator model for clogging diagnosis

Abstract Nuclear steam generators are subject to clogging of their internal parts which causes safety issues. Diagnosis methodologies are needed to optimize maintenance operations. Clogging alters the dynamic behaviour of steam generators and particularly the response of the wide range level (WRL – a pressure measurement) to power transients. A numerical model of this phenomenon has previously been developed. Its input variables describe the spatial distribution of clogging and its output is a discretization of the WRL dynamic response. The objective of the present study is to characterize the information about the clogging state of a steam generator that can be inferred from the observation of its WRL response. A methodology based on several statistical techniques is implemented to answer that question. Principal component analysis reveals that clogging alters the WRL response mainly in two distinct ways. Accordingly, the output can be summarized into a vector of dimension 2. A sensitivity analysis is carried out to rank the input variables by magnitude of influence. It has shown that they can be divided into two groups corresponding to the two sides of the steam generator. Finally, sliced inverse regression is used to reduce the input dimension from 16 to 2. A sampling issue that arises when the input dimension is high is addressed. The simplification of the original problem yields a diagnosis methodology based on response surface techniques.

[1]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[2]  Ker-Chau Li,et al.  Sliced Inverse Regression for Dimension Reduction , 1991 .

[3]  Kerby Shedden,et al.  Dimension Reduction for Multivariate Response Data , 2003 .

[4]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[5]  Stefano Tarantola,et al.  Contribution to the sample mean plot for graphical and numerical sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[6]  Ali Gannoun,et al.  Some extensions of multivariate sliced inverse regression , 2007 .

[7]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[8]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[9]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[10]  Bruno Sudret,et al.  Efficient computation of global sensitivity indices using sparse polynomial chaos expansions , 2010, Reliab. Eng. Syst. Saf..

[11]  I. Sobol,et al.  Sensitivity Measures, ANOVA-like Techniques and the Use of Bootstrap , 1997 .

[12]  Brian J. Williams,et al.  Sensitivity analysis when model outputs are functions , 2006, Reliab. Eng. Syst. Saf..

[13]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[14]  I. Sobol.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[15]  R. Cook,et al.  Reweighting to Achieve Elliptically Contoured Covariates in Regression , 1994 .

[16]  L. Petzold.  A description of dassl: a differential/algebraic system solver , 1982 .

[17]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[18]  M. Jansen.  Analysis of variance designs for model output , 1999 .

[19]  Shuangzhe Liu,et al.  Global Sensitivity Analysis: The Primer by Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola , 2008 .

[20]  Clémentine Prieur,et al.  Bias correction for the estimation of sensitivity indices based on random balance designs , 2012, Reliab. Eng. Syst. Saf..

[21]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[22]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[23]  David Makowski,et al.  Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models , 2011, Reliab. Eng. Syst. Saf..

[24]  A. Saltelli,et al.  Reliability Engineering and System Safety , 2008 .

[25]  Olivier Roustant,et al.  Calculations of Sobol indices for the Gaussian process metamodel , 2008, Reliab. Eng. Syst. Saf..

[26]  Jérôme Saracco,et al.  Application of the Bootstrap Approach to the Choice of Dimension and the α Parameter in the SIRα Method , 2008, Commun. Stat. Simul. Comput..

[27]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[28]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[29]  Alexandre Girard,et al.  Estimation of SG TSP Blockage: Innovative Monitoring Through Dynamic Behavior Analysis , 2010 .

[30]  Ker-Chau Li,et al.  On almost Linearity of Low Dimensional Projections from High Dimensional Data , 1993 .

[31]  Ker-Chau Li.  Sliced inverse regression for dimension reduction (with discussion) , 1991 .

[32]  E. Borgonovo.  Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

[33]  K. Shuler,et al.  Nonlinear sensitivity analysis of multiparameter model systems , 1977 .

[34]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[35]  D. Freedman,et al.  Asymptotics of Graphical Projection Pursuit , 1984 .

[36]  I. Jolliffe.  Principal Component Analysis , 2002 .

[37]  Matieyendou Lamboni,et al.  Multivariate global sensitivity analysis for dynamic crop models , 2009 .