Structural and reliability analyses of ships with fuzzy and random variables

The reliability analysis of existing structures requires engineers to model two types of uncertainty, cognitive and noncognitive types. The objective of this study is to reexamine structural analysis and reliability assessment methods by considering the cognitive and noncognitive uncertainties.; The noncognitive uncertainty of a variable can be described by a probability mass or density function (PMF or PDF). Moment or simulation methods can be used for structural reliability analysis. A methodology based on the ultimate strength assessment module for hull-girder bending of ships was developed using the advanced second moment (ASM) method and simulation with variance reduction techniques. This methodology demonstrates the structural reliability assessment of hull-girder bending by considering its strength parameters as random variables in a non-closed performance function using ASM and simulation methods. The methodology can also be applied to closed-form performance functions. It is also suitable for developing the structural strength and loads for hull-girder bending as individual modules.; The cognitive uncertainty of a variable can be described by a membership function as used in defining fuzzy sets. Two approaches that are based on the displacement method for structural analysis are proposed: (1) fuzzy arithmetic approach, and (2) permutations approach. The first approach only obtains approximate solutions. The second approach produces the exact solution but requires more computing time. The behavior of fundamental structural systems was investigated, and the results based on the second approach showed that if the modulus of elasticity is a triangular fuzzy number, the member forces can be either fuzzy numbers or crisp values depending on the structural system type. Modified fuzzy division and subtraction were also proposed for solving simultaneous equations using fuzzy arithmetic.; The combined effect of both cognitive and noncognitive uncertainties for a variable in structural and reliability analyses was modeled using a proposed fuzzy-random PDF. The variable is assumed to have a fuzzy mean and a non-fuzzy standard deviation. The fuzzy-random PDF is defined as the marginal density function of the multiplication of its normalized membership function and its random distribution. Relationships for the means and variances among the fuzzy-random distribution, normalized membership function, and random distribution were developed. Moments method and discrete method were proposed for dealing with the fuzzy-random PDF.; Reliability analysis that accounts for both types of uncertainties showed that the permutations method provides upper and lower bounds on reliability estimates, whereas the fuzzy-random PDF approach provides an average estimate.