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Heyer, Torsten

Horlacher, Hans-B.

Stamm, Juergen

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Hydraulic Engineering Repository

Conference Paper, Published VersionHeyer, Torsten; Horlacher, Hans-B.; Stamm, JuergenReliability Analysis of River Levees Using LogisticRegression Models – Abilities and LimitationsZur Verfügung gestellt in Kooperation mit/Provided in Cooperation with:Kuratorium für Forschung im Küsteningenieurwesen (KFKI)Verfügbar unter/Available at: https://hdl.handle.net/20.500.11970/109693Vorgeschlagene Zitierweise/Suggested citation:Heyer, Torsten; Horlacher, Hans-B.; Stamm, Juergen (2012): Reliability Analysis of RiverLevees Using Logistic Regression Models – Abilities and Limitations. In: Hagen, S.; Chopra,M.; Madani, K.; Medeiros, S.; Wang, D. (Hg.): ICHE 2012. Proceedings of the 10thInternational Conference on Hydroscience & Engineering, November 4-8, 2012, Orlando,USA.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 392     RELIABILITY ANALYSIS OF RIVER LEVEES USING LOGISTIC REGRESSION MODELS – ABILITIES AND LIMITATIONS   Torsten Heyer1, Hans-B. Horlacher2, and Juergen Stamm3   Flood risk assessment is an essential part of modern flood risk management. For riverine areas that are mainly protected by levees, the inundation risk derives from the possibility of their failure. Using the basic product formula (occurrence probability of an event ×  (negative) consequences) for the quantification of risk, the numeric expression of the reliability of a levee or levee system is an essential necessity. Logistic regression models, as proposed e. g. in Heyer et al. (2010), allow the computation of failure probabilities for individual levee sections considering local loadings and properties. Based on the local failure probabilities of individual levee sections, the total failure probability of different levee states (failing of one or more sections) can be determined. As the use of logistic regression models is still rather uncommon in civil engineering, their basic approach and data requirements are briefly explained within this paper, followed by a discussion of the advantages and disadvantages associated with their application. Logistic regression is a statistical modelling approach used in multivariate data analysis. Although it has been widely used in the field of medicine, social science or economics, it is not well known in engineering. The application of logistic regression is preferable whenever dependencies between several factors and observed events are undoubted, but the processes leading to the observation are uncertain. Regression models generally aim for the prediction of the outcome of a dependent variable (response variable), Y, given a set of influencing factors, Xk (eq. 1). Although not compulsory, logistic regression is often used when the response variable Y has binary realisations (e.g. "failure"/"non-failure",) and metric and non-metric parameters X need to be combined.  ( )1 2 0,1, , , kX X X Y⇒  (1) The links between the considered regression parameters X and a dependent value P(z), which represents the occurrence probability of the event Y(1), is shown schematically in Figure 1.  Figure 1 Logistic function and threshold for failure prediction                                                  1 Research Associate, Institute of Hydraulic Engineering and Technical Hydromechanics, Technische Universitaet Dresden, Dresden, D-01062, Germany (torsten.heyer@tu-dresden.de) 2 Emeritus Professor, Institute of Hydraulic Engineering and Technical Hydromechanics, Technische Universitaet Dresden, Dresden, D-01062, Germany (hans-b.horlacher@tu-dresden.de) 3 Professor, Institute of Hydraulic Engineering and Technical Hydromechanics, Technische Universitaet Dresden, Dresden, D-01062, Germany (juergen.stamm@tu-dresden.de) 1 2 kX ,X ,...,X  z  y 1P(z) =  linear link link logistic ( ).11 nf n n zP P ze−= = +( )01kn i niiz xβ β== + ⋅∑The 10th Int.  Conf. on Hydroscience and Engineering (ICHE-2012), Nov. 4 – Nov. 7, Orlando, USA 393 where nz  Logit value for the nth observation 0β  Constant iβ  Regression coefficient of parameter Xi nix  Value of parameter Xi for the nth observation   Figure 2 Logistic function and defined threshold for failure prediction  While the values for xni are results of observations and surveys, the values of 0 1, , , kβ β β  are determined through model calibration (maximum likelihood approach), using a training data set that includes information on cases (e. g. failed levee sections) and non-cases (e. g. non-failed levee sections). Thus, data availability and the selection of relevant regression parameters are essential requirements for the formulation and applicability of logistic regression models in general. The logistic regression models used for the prediction of levee failure (levee failure logit model), which we developed, is based on a dataset of 661 observations from levees of the “Vereinigte Mulde” river in Saxony/Germany, containing data on 48 failed levee sections. In the model setup phase, 24 parameters (hydraulic, biological, mechanical, geometrical, soil mechanical, structural; 11 metric and 13 non-metric) were statistically tested regarding their effect on levee failure. Although the logit models that were applied to the training data set showed (by nature) a high hit ratio (prediction meets observation) and a reasonable interpretability from the engineer’s point of view, mathematical shortcomings (e. g. model overfitting) and the necessity of enhanced model validation became obvious. A detailed statistical analysis identified significant interactions between the regression parameters used. In attendance to this, a principal component analysis was conducted with the aim of reducing the number of regression parameters and minimizing correlation effects within the model. The transferability and predictability of levee failure logit models were tested by Salmon (2011) for levees along the “Isère Amont” river in France. This work showed that the original logit model performed considerably worse when applied to the test data set from the “Isère Amont”. However, by merging these datasets and recalibrating the model based on this training sample, an acceptable hit ratio for the datasets from both rivers could be achieved. Motivated by these findings the ongoing research focuses on gathering and analyzing more data from other rivers. Considering their advantages (e. g. observation-based, applicable even with limited data available, updatable, combination of metric and non-metric parameters, ability to explicitly account for inhomogeneities, etc.) and disadvantages (e. g. not process-based, fixed fragility curves), levee failure logit models can be seen as an enhancement relative to existing approaches.  REFERENCES Heyer, T., Horlacher, H.-B. and Stamm, J. (2010) “Multicriteria Stability Analysis of River Embankments Based on Past Experience”, Proceedings of 1st European Congress of the IAHR, Edinburgh. Salmon, A. (2011) “Zuverlässigkeitsbewertung von Flussdeichen – Angewandte Methoden in Frankreich und Vergleich mit dem logistischen Regressionsmodell des IWD”, Master thesis, Technische Universität Dresden, Dresden. 

Reliability Analysis of River Levees Using Logistic Regression Models – Abilities and Limitations

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Reliability Analysis of River Levees Using Logistic Regression Models – Abilities and Limitations

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