Date of Completion


Embargo Period



reliability analysis, reliability-based design optimization, interval uncertainty, turbomachinery bladed disk, vibration localization

Major Advisor

Dr. Jiong Tang

Associate Advisor

Dr. Xu Chen

Associate Advisor

Dr. Horea Ilies

Associate Advisor

Dr. Ying Li

Associate Advisor

Dr. Julian Norato

Field of Study

Mechanical Engineering


Doctor of Philosophy

Open Access

Open Access


This study presents novel reliability-based design optimization (RBDO) methods with mixture of random and interval uncertainties. While conventional second-order reliability method (SORM) contains three types of errors, novel SORM proposed in this study avoids the other two types of error by describing the quadratic failure surface with the linear combination of noncentral chi-square variables and using the linear combination of probability of failure estimation. Sensitivity analysis on the developed SORM is then performed for more accurate RBDO. As an alternative to analytic RBDO, sampling-based RBDO is used in case when gradients of performance functions are not available. In this study, interval uncertainty is newly incorporated into existing sampling-based RBDO, since distribution of random uncertainty may not be always identified. Sensitivity-based interval analysis method is developed, which is integrated into optimization framework. It is demonstrated in numerical example that the proposed method efficiently converges to optimum design within a few design cycles. The RBDO approach is further applied to turbomachinery bladed disk, whose dynamic response is very sensitive to presence of uncertainties when interblade coupling is weak. Multi-objective optimization method is developed for optimal piezoelectric circuitry design to simultaneously achieve delocalization of vibration modes and vibration suppression, which is integrated into the host bladed disk structure. Since piezoelectric material cannot withstand the high temperatures, this method is limited to fan blades that is operated at mild temperatures. Alternatively, this study develops the mathematical framework of reliability-oriented optimal design for bladed disk throughout modification of geometry/material properties of blades utilizing intentional mistuning technique, which is applicable to both compressor blades and high pressure turbine blades that are operated at severe temperatures. Both random uncertainty of blades and interval uncertainty of disk connections are considered. It is demonstrated in case studies that durability and reliability in bladed disk can be achieved using the proposed methods.