Stability analysis of gravity dams under uncertainty using the fuzzy sets theory and a many-objective GA

Uncertainties in the analysis and design parameters of a gravity dam are spread out over the system and make the stability safety factors uncertain too. To analyze the effects of such uncertainties on the dam performance, a conceptual model based on the fuzzy sets theory is introduced here. The input uncertainties are simulated by triangular fuzzy numbers and introduced to the governing equations. To evaluate the extreme values of the dam safety factors, a many objective optimization problem is formed. To solve the problem efficiently, a many-objective genetic algorithm (MOGA) is coupled to the dam stability analysis model. The model is able to estimate all extreme values of the dam safety factors in only one single optimization run. An example gravity dam with and without uncertainty is analyzed respectively by the traditional and the fuzzy approaches. It is found that small input uncertainties can highly influence the analysis responses and, the proposed method can efficiently capture all safety factors uncertainties. For example, the simulations revealed that only± 10% uncertainty in the dam design parameters would lead to about –346 to +146 % uncertainty in the stability safety factors.

[1]  Ali Haghighi,et al.  A fuzzy approach for considering uncertainty in transient analysis of pipe networks , 2012 .

[2]  Ali Haghighi,et al.  Analysis of Transient Flow Caused by Fluctuating Consumptions in Pipe Networks: A Many-Objective Genetic Algorithm Approach , 2015, Water Resources Management.

[3]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[4]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[5]  Guohe Huang,et al.  Fuzzy two-stage non-point source pollution management model for agricultural systems—A case study for the Lake Tai Basin, China , 2013 .

[6]  Michio Sugeno,et al.  Industrial Applications of Fuzzy Control , 1985 .

[7]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[8]  H.-J. Zimmermann.  Fuzzy set theory , 2010 .

[9]  B. Rao,et al.  Efficient Assessment of Structural Reliability in Presence of Random and Fuzzy Uncertainties , 2014 .

[10]  Hans Janssen,et al.  Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence , 2013, Reliab. Eng. Syst. Saf..

[11]  Robert L. Mullen,et al.  Bounds of Structural Response for All Possible Loading Combinations , 1999 .

[12]  Min-Yuan Cheng,et al.  Evolutionary Fuzzy Neural Inference System for Decision Making in Geotechnical Engineering , 2008 .

[13]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[14]  M. Beer,et al.  Approximation Concepts for Fuzzy Structural Analysis , 2014 .

[15]  Ali Haghighi,et al.  Uncertainty analysis of water supply networks using the fuzzy set theory and NSGA-II , 2014, Eng. Appl. Artif. Intell..

[16]  Kyu-Han Kim,et al.  Fuzzy model forecasting of offshore bar-shape profiles under high waves , 2014, Expert Syst. Appl..

[17]  Guohe Huang,et al.  Interval-parameter chance-constrained fuzzy multi-objective programming for water pollution control with sustainable wetland management , 2012 .

[18]  Abraham Kandel,et al.  Fuzzy Expert Systems , 1991 .

[19]  Steven Gray,et al.  Are coastal managers detecting the problem? Assessing stakeholder perception of climate vulnerability using Fuzzy Cognitive Mapping , 2014 .

[20]  Qing Liu,et al.  Fuzzy finite element approach for analysis of fiber-reinforced laminated composite beams , 2004 .

[21]  M. A. Mariño,et al.  Effects of Pipe Roughness Uncertainty on Water Distribution Network Performance During its Operational Period , 2013, Water Resources Management.

[22]  L. Ross,et al.  Spatial modeling of environmental vulnerability of marine finfish aquaculture using GIS-based neuro-fuzzy techniques. , 2011, Marine pollution bulletin.

[23]  M. P. Biswal,et al.  Fuzzy programming approach to multicriteria decision making transportation problem , 1992 .

[24]  Jim W. Hall,et al.  Risk, performance and uncertainty in flood and coastal defence - a review , 2002 .

[25]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[26]  Dongrui Wu,et al.  Fuzzy experts on recreational vessels, a risk modelling approach for marine invasions , 2010 .

[27]  Cv Clemens Verhoosel,et al.  Uncertainty and Reliability Analysis of Fluid-Structure Stability Boundaries , 2009 .

[28]  Eun-Sung Chung,et al.  Robust spatial flood vulnerability assessment for Han River using fuzzy TOPSIS with α-cut level set , 2014, Expert Syst. Appl..

[29]  S. Meysam Mousavi,et al.  An extended compromise ratio model with an application to reservoir flood control operation under an interval-valued intuitionistic fuzzy environment , 2014 .

[30]  Pu Li,et al.  Monte Carlo Simulation–Aided Analytic Hierarchy Process Approach: Case Study of Assessing Preferred Non-Point-Source Pollution Control Best Management Practices , 2013 .

[31]  Bilal M. Ayyub,et al.  Probability, Statistics, and Reliability for Engineers and Scientists , 2003 .