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Advances in sensitivity analysis
Reliability Engineering and System Safety 107 (2012) 1–2
Contents lists available at SciVerse ScienceDirect
Reliability Engineering and System Safety journal homepage: www.elsevier.com/locate/ress
Preface
Advances in sensitivity analysis
article info Keywords: Sensitivity analysis Uncertainty analysis Importance measures Metamodelling
abstract This editorial presents the content of the special issue Advances in Sensitivity Analysis that follows the Sixth International Conference on Sensitivity Analysis of Model Output (SAMO 2010). The special issue highlights the state of the art in a field which is rapidly growing and whose importance is more and more recognized by the scientific community at large, as testified by the wide range of theoretical and applied problems addressed in this special issue. & 2012 Published by Elsevier Ltd.
1. Editorial The Sixth International Conference on Sensitivity Analysis of Model Output, SAMO 2010, has been held at Bocconi University in Milan, from July 19 to July 22, 2010. The conference has continued the tradition of the SAMO series, taking place 15 years after the first conference, held in Belgirate in 1995 and followed by Venice (1998), Madrid (2001), Santa Fe (2004), Budapest (2007). The growth in the number of submissions and participants throughout the conference series has been steady and has been consistent in the 2010 edition, with an increase of 40% over the previous years. Sensitivity analysis is nowadays advocated as part of the best practices for model audit and validation by several international bodies and agencies, such as the US Environmental Protection Agency [28] and the European Commission [11]. The fast growth in computing power of these recent years allows analysts to create computer codes that can model a variety of details of the scientific problem of interest. Simultaneously, models become more complex and analysts need methods that provide them with the insights that allow them to fully exploit the modelling efforts, while fully reflecting their state of knowledge. In the recent past, the literature has assisted to the fast growth of sensitivity analysis methods. We can now count on methods that capture a variety of problems, from local methods to nonparametric methods [16], to screening methods [21], to variancebased methods [24], to distribution-based [5]. The research in global sensitivity analysis is also entangled with the literature in metamodelling and response methods, as several of the works in this special issue show. The set of articles here published displays the interdisciplinary nature of sensitivity analysis, with applications ranging from the performance assessment of high level waste repositories to the movement of Antarctic ice. They also show an increase in the rigour with which researchers are considering the sensitivity analysis, because of its key-role in understanding the models’ behavior and in informing decisionmakers about their confidence in model results. 0951-8320/$ - see front matter & 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.ress.2012.09.001
Next, we propose a brief overview of the works in this special issue, listed in alphabetical order. In Allaire and Wilkox [1], a method for variance-based sensitivity analysis that considers the amount of variance reduction that can be achieved for a particular factor is presented. In Annoni and Saltelli [2], variance-based sensitivity analysis designs for partially ordered sets are discussed. Auder et al. [3] address screening and metamodelling of computer codes with functional output. In Baratelli et al. [4], the local and global sensitivity analyses for an evolution model of the Antarctic ice sheet are discussed. Sparse grid interpolation and polynomial chaos expansions in the global sensitivity analysis are addressed in Buzzard [8]. Delenne et al. [9] present an uncertainty analysis for flooding and dam failure risks. Galetakis et al. [12] address production scheduling under uncertainty for a lignite mine. Application of uncertainty and sensitivity methods for an environmental risk assessment model is presented in Garcia-Diaz and Gonzalvez-Zaffrilla [13]. In Dimov et al. [10], Monte Carlo sensitivity analysis for an air pollution model is presented. Hansen et al. [14] and Helton et al. [15] present the uncertainty and global sensitivity analysis methods for nuclear waste repositories. The Morris method is applied by Imron et al. [17] in the sensitivity analysis of a predator–prey model. La Rovere and Vestrucci [18] utilize the Differential [7] and Total Order Importance Measures [6] for the study of a networked system. Mara and Tarantola [19] discuss variance-based sensitivity indices in the presence of correlated inputs. Millwater et al. [20] discuss a global sensitivity method to assess the regional importance of a random variable. Nagy and Turanyi [22] discuss the uncertainty analysis in a combustion kinetic model. Plischke [23] presents a new method for the estimation of first-order variance-based sensitivity indices. Spiessl et al. [26] apply the extended FAST method [25] for the analysis of a high-level waste repository in clay. Tissot and Prieur [27] discuss the problem of bias reduction in the estimation of sensitivity indices based on random balance designs. Weirs et al. [29] discuss the global sensitivity analysis for hyperbolic conservation laws. A method that ameliorates the
2
Preface / Reliability Engineering and System Safety 107 (2012) 1–2
computation of variance-based sensitivity indices is offered in Wu et al. [30]. Zio and Pedroni [31] address the sensitivity analysis of a model for a thermal-hydraulic passive system using subset simulation and line sampling. Zivanovic [32] discusses the global sensitivity analysis using sparse grid interpolation in application to a transmission line fault detection algorithm. We thank all the authors and reviewers for their efforts. We also thank the editor of Reliability Engineering & System Safety, Prof. Carlos Guedess Soares, for his help and assistance throughout the editorial work associated with this special issue. References [1] Allaire D, Wilkox K. A variance-based sensitivity index function for factor prioritization. Reliability Engineering & System Safety 2012;107:107–14. [2] Annoni P, Bruggemann R, Saltelli A. Random and quasi-random designs in variance-based sensitivity analysis for partially ordered sets. Reliability Engineering & System Safety 2012;107:184–9. [3] Auder B, De Crecy A, Iooss B, Marques M. Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations. Reliability Engineering & System Safety 2012;107:122–31. [4] Baratelli F, Giudici M, Vassena C. A sensitivity analysis for an evolution model of the Antarctic ice sheet. Reliability Engineering & System Safety 2012;107:64–70. [5] Borgonovo E. Measuring uncertainty importance: investigation and comparison of alternative approachesRisk Analysis 2006;26(5):1349–62. [6] Borgonovo E. The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions. European Journal of Operational Research 2010;204:485–95. [7] Borgonovo E, Apostolakis G. A new importance measure for risk-informed decision making. Reliability Engineering & System Safety 2001;72(2):193–212. [8] Buzzard GT. Global sensitivity analysis using sparse grid interpolation and polynomial chaos. Reliability Engineering & System Safety 2012;107:82–9. [9] Delenne C, Cappelaere B, Guinot V. Uncertainty analysis of river flooding and dam failure risks using local sensitivity computations. Reliability Engineering & System Safety 2012;107:171–83. [10] Dimov I, Georgeva R, Ostromsky T. Monte Carlo sensitivity analysis of an Eulerian large-scale air pollution model. Reliability Engineering & System Safety 2012;107:23–8. [11] European-Commission. Impact assessment guidelines. Technical Report 92, 15 January 2009. URL /http://ec.europa.eu/governance/impact/commission_ guidelines/docs/iag_2009_en.pdfS, 51 pp. [12] Galetakis M, Roumpos C, Alevizos G, Vamvuka D. Production scheduling of a lignite mine under quality and reserves uncertainty. Reliability Engineering & System Safety 2012;107:224–30. [13] Garcia-Diaz J, Gonzalvez-Zaffrilla J. Uncertainty and sensitive analysis of environmental model for risk assessments: an industrial case study. Reliability Engineering & System Safety 2012;107:16–22. [14] Hansen C, Helton J, Sallaberry C. Use of replicated Latin hypercube sampling to estimate sampling variance in uncertainty and sensitivity analysis results for the geologic disposal of radioactive waste. Reliability Engineering & System Safety 2012;107:139–48. [15] Helton J, Hansen C, Sallaberry C. Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste
[16]
[17]
[18] [19] [20]
[21] [22]
[23]
[24]
[25] [26]
[27]
[28] [29]
[30]
[31]
[32]
repository at Yucca Mountain, Nevada. Reliability Engineering & System Safety 2012;107:44–63. Helton JC. Uncertainty and sensitivity analyses techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering & System Safety 1993;42(2–3):327–67. Imron M, Gergs A, Berger U. Structure and sensitivity analysis of individualbased predator–prey models. Reliability Engineering & System Safety 2012;107:71–81. La Rovere S, Vestrucci P. Investigation of the structure of a networked system. Reliability Engineering & System Safety 2012;107:214–23. Mara T, Tarantola S. Variance-based sensitivity indices for models with dependent inputs. Reliability Engineering & System Safety 2012;107:115–21. Millwater H, Singh G, Cortina M. Development of a localized probabilistic sensitivity method to determine random variable regional importance. Reliability Engineering & System Safety 2012;107:3–15. Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics 1991;33(2):161–74. Nagy T, Turanyi T. Determination of the uncertainty domain of the Arrhenius parameters needed for the investigation of combustion kinetic models. Reliability Engineering & System Safety 2012;107:29–34. Plischke E. An adaptive correlation ratio method using the cumulative sum of the reordered output. Reliability Engineering & System Safety 2012;107: 149–56. Saltelli A, Tarantola S. On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposalJournal of the American Statistical Association 2002;97(459):702–9. Saltelli A, Tarantola S, Chan K. A quantitative, model independent method for global sensitivity analysis of model output. Technometrics 1999;41:39–56. Spiessl S, Becker D, Ruebel A. EFAST analysis applied to a PA model for a generic HLW repository in clay. Reliability Engineering & System Safety 2012;107:190–204. Tissot JY, Prieur C. Bias correction for the estimation of sensitivity indices based on random balance designs. Reliability Engineering & System Safety 2012;107:205–13. US EPA. Guidance on the development, evaluation, and application of environmental models, March 2009. Weirs G, Kamm J, Swiler L, Tarantola S, Ratto M, Adams B, et al. Sensitivity analysis techniques applied to a system of hyperbolic conservation laws. Reliability Engineering & System Safety 2012;107:157–70. Wu Q-L, Cournede P-H, Mathieu A. An efficient computational method for global sensitivity analysis and its application to tree growth modelling. Reliability Engineering & System Safety 2012;107:35–43. Zio E, Pedroni N. Monte Carlo simulation-based sensitivity analysis of the model of a thermal-hydraulic passive system. Reliability Engineering & System Safety 2012;107:90–106. Zivanovic R. Global sensitivity analysis of transmission line fault-locating algorithms using sparse grid regression. Reliability Engineering & System Safety 2012;107:132–8.
Emanuele Borgonovo ELEUSI Research Center, Bocconi University, Milan, Italy
Stefano Tarantola Joint Research Centre of the European Commission, Ispra, Italy
Contents lists available at SciVerse ScienceDirect
Reliability Engineering and System Safety journal homepage: www.elsevier.com/locate/ress
Preface
Advances in sensitivity analysis
article info Keywords: Sensitivity analysis Uncertainty analysis Importance measures Metamodelling
abstract This editorial presents the content of the special issue Advances in Sensitivity Analysis that follows the Sixth International Conference on Sensitivity Analysis of Model Output (SAMO 2010). The special issue highlights the state of the art in a field which is rapidly growing and whose importance is more and more recognized by the scientific community at large, as testified by the wide range of theoretical and applied problems addressed in this special issue. & 2012 Published by Elsevier Ltd.
1. Editorial The Sixth International Conference on Sensitivity Analysis of Model Output, SAMO 2010, has been held at Bocconi University in Milan, from July 19 to July 22, 2010. The conference has continued the tradition of the SAMO series, taking place 15 years after the first conference, held in Belgirate in 1995 and followed by Venice (1998), Madrid (2001), Santa Fe (2004), Budapest (2007). The growth in the number of submissions and participants throughout the conference series has been steady and has been consistent in the 2010 edition, with an increase of 40% over the previous years. Sensitivity analysis is nowadays advocated as part of the best practices for model audit and validation by several international bodies and agencies, such as the US Environmental Protection Agency [28] and the European Commission [11]. The fast growth in computing power of these recent years allows analysts to create computer codes that can model a variety of details of the scientific problem of interest. Simultaneously, models become more complex and analysts need methods that provide them with the insights that allow them to fully exploit the modelling efforts, while fully reflecting their state of knowledge. In the recent past, the literature has assisted to the fast growth of sensitivity analysis methods. We can now count on methods that capture a variety of problems, from local methods to nonparametric methods [16], to screening methods [21], to variancebased methods [24], to distribution-based [5]. The research in global sensitivity analysis is also entangled with the literature in metamodelling and response methods, as several of the works in this special issue show. The set of articles here published displays the interdisciplinary nature of sensitivity analysis, with applications ranging from the performance assessment of high level waste repositories to the movement of Antarctic ice. They also show an increase in the rigour with which researchers are considering the sensitivity analysis, because of its key-role in understanding the models’ behavior and in informing decisionmakers about their confidence in model results. 0951-8320/$ - see front matter & 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.ress.2012.09.001
Next, we propose a brief overview of the works in this special issue, listed in alphabetical order. In Allaire and Wilkox [1], a method for variance-based sensitivity analysis that considers the amount of variance reduction that can be achieved for a particular factor is presented. In Annoni and Saltelli [2], variance-based sensitivity analysis designs for partially ordered sets are discussed. Auder et al. [3] address screening and metamodelling of computer codes with functional output. In Baratelli et al. [4], the local and global sensitivity analyses for an evolution model of the Antarctic ice sheet are discussed. Sparse grid interpolation and polynomial chaos expansions in the global sensitivity analysis are addressed in Buzzard [8]. Delenne et al. [9] present an uncertainty analysis for flooding and dam failure risks. Galetakis et al. [12] address production scheduling under uncertainty for a lignite mine. Application of uncertainty and sensitivity methods for an environmental risk assessment model is presented in Garcia-Diaz and Gonzalvez-Zaffrilla [13]. In Dimov et al. [10], Monte Carlo sensitivity analysis for an air pollution model is presented. Hansen et al. [14] and Helton et al. [15] present the uncertainty and global sensitivity analysis methods for nuclear waste repositories. The Morris method is applied by Imron et al. [17] in the sensitivity analysis of a predator–prey model. La Rovere and Vestrucci [18] utilize the Differential [7] and Total Order Importance Measures [6] for the study of a networked system. Mara and Tarantola [19] discuss variance-based sensitivity indices in the presence of correlated inputs. Millwater et al. [20] discuss a global sensitivity method to assess the regional importance of a random variable. Nagy and Turanyi [22] discuss the uncertainty analysis in a combustion kinetic model. Plischke [23] presents a new method for the estimation of first-order variance-based sensitivity indices. Spiessl et al. [26] apply the extended FAST method [25] for the analysis of a high-level waste repository in clay. Tissot and Prieur [27] discuss the problem of bias reduction in the estimation of sensitivity indices based on random balance designs. Weirs et al. [29] discuss the global sensitivity analysis for hyperbolic conservation laws. A method that ameliorates the
2
Preface / Reliability Engineering and System Safety 107 (2012) 1–2
computation of variance-based sensitivity indices is offered in Wu et al. [30]. Zio and Pedroni [31] address the sensitivity analysis of a model for a thermal-hydraulic passive system using subset simulation and line sampling. Zivanovic [32] discusses the global sensitivity analysis using sparse grid interpolation in application to a transmission line fault detection algorithm. We thank all the authors and reviewers for their efforts. We also thank the editor of Reliability Engineering & System Safety, Prof. Carlos Guedess Soares, for his help and assistance throughout the editorial work associated with this special issue. References [1] Allaire D, Wilkox K. A variance-based sensitivity index function for factor prioritization. Reliability Engineering & System Safety 2012;107:107–14. [2] Annoni P, Bruggemann R, Saltelli A. Random and quasi-random designs in variance-based sensitivity analysis for partially ordered sets. Reliability Engineering & System Safety 2012;107:184–9. [3] Auder B, De Crecy A, Iooss B, Marques M. Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations. Reliability Engineering & System Safety 2012;107:122–31. [4] Baratelli F, Giudici M, Vassena C. A sensitivity analysis for an evolution model of the Antarctic ice sheet. Reliability Engineering & System Safety 2012;107:64–70. [5] Borgonovo E. Measuring uncertainty importance: investigation and comparison of alternative approachesRisk Analysis 2006;26(5):1349–62. [6] Borgonovo E. The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions. European Journal of Operational Research 2010;204:485–95. [7] Borgonovo E, Apostolakis G. A new importance measure for risk-informed decision making. Reliability Engineering & System Safety 2001;72(2):193–212. [8] Buzzard GT. Global sensitivity analysis using sparse grid interpolation and polynomial chaos. Reliability Engineering & System Safety 2012;107:82–9. [9] Delenne C, Cappelaere B, Guinot V. Uncertainty analysis of river flooding and dam failure risks using local sensitivity computations. Reliability Engineering & System Safety 2012;107:171–83. [10] Dimov I, Georgeva R, Ostromsky T. Monte Carlo sensitivity analysis of an Eulerian large-scale air pollution model. Reliability Engineering & System Safety 2012;107:23–8. [11] European-Commission. Impact assessment guidelines. Technical Report 92, 15 January 2009. URL /http://ec.europa.eu/governance/impact/commission_ guidelines/docs/iag_2009_en.pdfS, 51 pp. [12] Galetakis M, Roumpos C, Alevizos G, Vamvuka D. Production scheduling of a lignite mine under quality and reserves uncertainty. Reliability Engineering & System Safety 2012;107:224–30. [13] Garcia-Diaz J, Gonzalvez-Zaffrilla J. Uncertainty and sensitive analysis of environmental model for risk assessments: an industrial case study. Reliability Engineering & System Safety 2012;107:16–22. [14] Hansen C, Helton J, Sallaberry C. Use of replicated Latin hypercube sampling to estimate sampling variance in uncertainty and sensitivity analysis results for the geologic disposal of radioactive waste. Reliability Engineering & System Safety 2012;107:139–48. [15] Helton J, Hansen C, Sallaberry C. Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste
[16]
[17]
[18] [19] [20]
[21] [22]
[23]
[24]
[25] [26]
[27]
[28] [29]
[30]
[31]
[32]
repository at Yucca Mountain, Nevada. Reliability Engineering & System Safety 2012;107:44–63. Helton JC. Uncertainty and sensitivity analyses techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering & System Safety 1993;42(2–3):327–67. Imron M, Gergs A, Berger U. Structure and sensitivity analysis of individualbased predator–prey models. Reliability Engineering & System Safety 2012;107:71–81. La Rovere S, Vestrucci P. Investigation of the structure of a networked system. Reliability Engineering & System Safety 2012;107:214–23. Mara T, Tarantola S. Variance-based sensitivity indices for models with dependent inputs. Reliability Engineering & System Safety 2012;107:115–21. Millwater H, Singh G, Cortina M. Development of a localized probabilistic sensitivity method to determine random variable regional importance. Reliability Engineering & System Safety 2012;107:3–15. Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics 1991;33(2):161–74. Nagy T, Turanyi T. Determination of the uncertainty domain of the Arrhenius parameters needed for the investigation of combustion kinetic models. Reliability Engineering & System Safety 2012;107:29–34. Plischke E. An adaptive correlation ratio method using the cumulative sum of the reordered output. Reliability Engineering & System Safety 2012;107: 149–56. Saltelli A, Tarantola S. On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposalJournal of the American Statistical Association 2002;97(459):702–9. Saltelli A, Tarantola S, Chan K. A quantitative, model independent method for global sensitivity analysis of model output. Technometrics 1999;41:39–56. Spiessl S, Becker D, Ruebel A. EFAST analysis applied to a PA model for a generic HLW repository in clay. Reliability Engineering & System Safety 2012;107:190–204. Tissot JY, Prieur C. Bias correction for the estimation of sensitivity indices based on random balance designs. Reliability Engineering & System Safety 2012;107:205–13. US EPA. Guidance on the development, evaluation, and application of environmental models, March 2009. Weirs G, Kamm J, Swiler L, Tarantola S, Ratto M, Adams B, et al. Sensitivity analysis techniques applied to a system of hyperbolic conservation laws. Reliability Engineering & System Safety 2012;107:157–70. Wu Q-L, Cournede P-H, Mathieu A. An efficient computational method for global sensitivity analysis and its application to tree growth modelling. Reliability Engineering & System Safety 2012;107:35–43. Zio E, Pedroni N. Monte Carlo simulation-based sensitivity analysis of the model of a thermal-hydraulic passive system. Reliability Engineering & System Safety 2012;107:90–106. Zivanovic R. Global sensitivity analysis of transmission line fault-locating algorithms using sparse grid regression. Reliability Engineering & System Safety 2012;107:132–8.
Emanuele Borgonovo ELEUSI Research Center, Bocconi University, Milan, Italy
Stefano Tarantola Joint Research Centre of the European Commission, Ispra, Italy