COMPARISON OF STRUCTURAL RELIABILITY PROBLEM FORMULATIONS

• DOI: https://doi.org/10.22533/at.ed.3174252421105

• Palavras-chave: Confiabilidade Estrutural, Índice de Confiabilidade, Método GRG, Processo de Monte Carlo

• Keywords: Structural Reliability, Reliability Index, GRG Method, Monte Carlo Process.

• Abstract:

  The classic formulation of structural reliability problems, such as that used in the GRG (Generalized Reduced Gradient) and FORM (First Order Reliability Method) methods, is defined as an optimization problem, where the random variables are the design variables, the reliability index is the objective function and the equality constraint is given by the performance function, calculated as the safety margin. The reliability index can be defined as the smallest distance, in the space of reduced variables, between the performance function and the origin of the system. So the reliability problem is usually formulated as: determine the design variables (random variables) that minimize the objective function (reliability index) subject to the equality constraint (safety margin). As the objective function is the distance from the project to the origin, in the space of the reduced variables, it doesn't matter in the equation whether these variables have positive or negative values. This can cause problems for the solution, as the sign of these variables significantly interferes with the calculation of the probability of failure of the model being analyzed. Examples will be shown where this formulation is not valid. The paper concludes that the most appropriate formulations are those based on defining the reliability index as the ratio between the mean and standard deviation of the performance function. Formulations such as the Monte Carlo (MC) process use this definition and therefore do not affect the results obtained and are more reliable, especially in more complex problems with a significant number of random variables. Examples using the GRG method and the Monte Carlo process will be presented and the discrepancies between the GRG method and the coherent results given by the Monte Carlo process in some classical problems will be shown. Suggestions for future studies will also be presented.