Abstract
An important segment of the reliability-based optimization problems is to get access to the sensitivity derivatives. However, since the failure probability is not a closed-form function of the input variables, the derivatives are not explicitly computable and rather require a full reliability analysis which is computationally expensive. In this paper, a step-by-step algorithm has been presented to calculate the derivatives of the probability of failure and safety index with respect to the input parameters based on the advanced first-order second-moment (AFOSM) reliability method. The proposed algorithm is then implemented in a spreadsheet using Visual Basic for Application (VBA) programming language. Two geotechnical and structural examples are then presented to examine the program and describe the modeling procedure. The robustness of the proposed method is examined using a Gaussian random perturbation. The capability of the proposed method in the calculation of the sensitivity derivatives of the model uncertainty is explained in a separate section. Finally, the proposed model has been compared to the forward finite difference (FFD) method and the results are validated.
Highlights
Because of aleatory and/or epistemic uncertainties associated with loads and capacity of structures alike, deterministic models fail to provide a sufficiently reliable estimation of design variables [1]
They are mostly based on the implicit algorithms which require cyclic calculations to estimate the derivatives; their performance is limited to specific distribution functions; can only cover the derivatives with respect to the mean or standard deviation of random variables; with any change in the performance function or random variable characteristics, their code should be thoroughly edited [14]
Regardless of the type of distribution function governing the involved random variables, the standard normal form of variables (U), which is commonly used in reliability analysis, is calculated as follows [18]: U
Summary
Because of aleatory and/or epistemic uncertainties associated with loads and capacity of structures alike, deterministic models fail to provide a sufficiently reliable estimation of design variables [1]. Sensitivity analysis demonstrates change(s) in the quantity of response in terms of variations in design variable(s) [10,11,12] This process is necessary since most of the available algorithms for solving the optimization problem need to access derivatives of failure probability with respect to input parameters [13]. They are mostly based on the implicit algorithms which require cyclic calculations to estimate the derivatives; their performance is limited to specific distribution functions; can only cover the derivatives with respect to the mean or standard deviation of random variables; with any change in the performance function or random variable characteristics, their code should be thoroughly edited [14] These limitations have made the structural reliability software packages dependent on utilizing classic methodologies such as finite difference method (FDM) for calculating sensitivity derivatives. The results are compared and validated by forward finite difference (FFD) method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
