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Methods for Structural Reliability Analysis 97


             Compared with other models, ANN modeling necessitates the use of all vari-
           ables that influence the failure of a pipe. Higher degree of nonlinearity can be
           taken into consideration by ANN models. Because these models basically depend
           on actual data parameters, a limitation may be the lack of data utilities possess.
           An increased level of skill and training is also required in order to develop the
           complex networks in ANN models (Clair and Sinha, 2012).
             Fuzzy logic models use engineering judgment and professional experience in
           order to predict pipes’ deterioration processes. This type of model is often used
           when data is scarce and observations and model criteria are expressed in vague or
           “fuzzy” terms. This technique implements expert opinions. A high level of skill is
           required in constructing the rule set and deciding the defuzzification process for a
           reliable output.
             Kleiner et al. (2005) proposed a fuzzy Markov deterioration process to predict
           the future condition of CI pipes. The fuzzy set techniques help to incorporate the
           imprecision and subjectivity of the data. Rajani and Tesfamariam (2007) applied
           a fuzzy set theory for consideration of uncertainties to estimate the structural
           capacity of aging CI water mains. Fares and Zayed (2010) developed a hierarchi-
           cal fuzzy expert system to determine the risk-of-failure of water mains. The
           system consists of 16 risk-of-failure factors within four main categories: environ-
           mental, physical, operational, and post failure.
             Compared with other deterioration models, fuzzy logic models necessitate the
           use of fuzzy logic-based techniques that possess the ability to incorporate engi-
           neering judgment to predict pipe deterioration. Fuzzy logic models are used for
           systems that are subject to uncertainties, ambiguities, and contradictions. The pri-
           mary limitation for fuzzy logic models is the challenges that exist in constructing
           a fuzzy rule set, selecting a membership function, and determining a defuzzifica-
           tion process (Clair and Sinha, 2012).
             Heuristic models are rare and limited in nature, but can illustrate how method-
           ologies incorporate engineering knowledge in the determination of deterioration
           rates. This technique is a structured way of capturing expert opinions. A limita-
           tion of using engineering knowledge is the inconsistency in the expert judgments
           from individual to individual and/or lack of personal experience in making the
           judgments. However, model capabilities can be improved by considering addi-
           tional expert knowledge and opinions (Clair and Sinha, 2012).
             Watson (2004) proposed a Bayesian methodology that combines engineering
           knowledge with recorded failure data to establish failure rates. This hierarchical
           model works to combine information from various sources of data. Al-Barqawi
           and Zayed (2008) presented an integrated model utilizing an analytic hierarchy
           process (AHP) and ANN. The AHP is first utilized to assign weights and assess
           the current condition of a water main based on physical, environmental, and oper-
           ational factors. Then an ANN, which is trained with the available data set,
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