Assessing the correlated performance functions of an engineering system via probabilistic analysis

• Joint distribution of performance functions is constructed by copulas.
• Joint failure probabilities are implemented to several engineering system.
• Validation of the proposed approach is performed using bounding methods.

An important issue regarding the use of probabilistic predictions for complex engineering systems is characterising the dependence structure among its correlated performance functions, which are driven by dependent or independent basic random variables. The interrelationship of these performance functions can be attributed to the same random variables and the cross correlation among the input parameters. An assessment of joint failure probability for an engineering system is proposed, which is associated with the correlated performance functions using a copula-based method by conveying the dependence structure of the performance functions. The method is demonstrated with four simple engineering problems, i.e., (a) bivariate distribution in which two predetermined performance functions are associated with each other; (b) pile bearing capacity in which the performance functions are related with the soil internal friction and the compressive strength of a concrete pile; (c) pipe flow in which the performance function of three pipes in a sewer system is assessed with six independent random variables; and (d) retaining wall in which the failure criteria for defining the performance functions include overturning failure about the toe point, sliding failure along the base, and bearing capacity instability considering uncertain soil properties. The computational efficiency is evaluated using the results based on the conventional bounding methods. The joint failure probability expressed by copulas provides a means to obtain the joint probabilities of multiple failure modes, which pave the way for an objective description of the overall failure probability of a practical engineering problem.