فاطمه سعادتمند

In all engineering problems, the existence of random parameters such as section dimensions, construction error, load values, properties and strength of materials is inevitable. Thus, ignoring these uncertainties, especially in optimal designs can lead to catastrophic results and fatal failures. Therefore, it is better to perform optimization process by considering the probability of system failure, which is done by defining one or more probabilistic constraints and calculating the system reliability for them based on the values obtained from the optimization loop. Over the years, a variety of methods have been developed and used to calculate and eva‎luate reliability. One of these methods is to use first-order reliability methods. In this research, a detailed review of first-order reliability methods has been attempted in two general categories of methods based on calculating reliability index and methods based on performance function eva‎luation along with commonly used examples and benchmark limit state functions that have been studied in various studies. Then, a review of different optimization methods based on reliability has been done. Finally, inspired by the various methods of calculating reliability, in order to increase the speed and accuracy of convergence of first-order methods especially in Reliability-based design optimization with highly nonlinear constraints, two new methods based on modified chaos control and adaptive step length selection are presented. The first proposed method is a two-stage method in which in the first step, the type of performance function in each iteration is determined based on the new conditions introduced in this study. These conditions are presented by considering the normal gradient vector, the location vector, and the angle between each in three consecutive iterations. Then, an initial step length and therefore a new point corresponding to the type of function detected is calculated. In the second step, the calculated point is eva‎luated by another condition, which is the angle between two normal negative gradient vectors. If this condition is satisfied, this new iteration is accepted, otherwise, by modifying the step length, the new iterative point in the present iteration is computed until the relevant condition is satisfied. The second proposed method is a simple method that does not need to identify the type of performance function. In this method, only one condition based on the angle between the normal location vector and the negative normal gradient vector in two consecutive iterations is introduced, which will be discussed in detail in the relevant chapter. The step length control parameter starts from the unity in the first iteration and is modified in each iteration based on the mentioned condition. The proposed relationship to modify the parameter control and, consequently, the step length is also an exponential function that provides a fast and efficient process for the proposed algorithm. The accuracy, speed and efficiency of the proposed methods in mathematical and structural fields in reliability assessment as well as in design optimization based on reliability have been studied and the results are compared with up-to-date and recently developed methods. The results indicate that the above proposed methods are efficient approaches with high convergence rate and acceptable accuracy to solve engineering problems related to reliability and are able to provide competitive performance in Reliability-based design optimization with strictly nonlinear probabilistic constraints.

قابليت اعتماد مرتبه اول , شاخص قابليت اعتماد , بهينه سازي براساس قابليت اعتماد , قيود غيرخطي شديد

first-order reliability method , reliability index , reliability-based design optimization , highly nonlinear constraints

Fatemeh Saadatmand

Dr. Majid Ilchi Ghazaan