# Differential Equations Seminar: Dr. Soobum Lee

## Mechanical Engineering, UMBC

Monday, April 16, 2018

11:00 AM - 12:00 PM

11:00 AM - 12:00 PM

Mathematics/Psychology : 401

**Title:**Reliability analysis methods and its applications to reliability-based design optimization in engineering

**Abstract:**The performance of any mechanical system could be highly affected by the sources of uncertainty (e.g., loads, material properties, geometric tolerances). Therefore, it is crucial to discover a design that satisfies the reliability requirements. A commonly used design optimization methodology for engineering systems comprises deterministic modeling and simulation-based design optimization. However, traditional deterministic design optimization (DDO) is not capable of considering design uncertainty. Taking into account for uncertainties could be handled by using a technique so called Reliability-based design optimization (RBDO). Reliability analysis, as the fundamental process in RBDO, evaluates the probability of failure as a probability of a function to reach a defined limit state. RBDO requires reliability analysis to estimate probabilistic design constraints iteratively, and it can be very time consuming because the reliability analysis requires huge number of input data. Hence, efficient reliability analysis is inevitable especially when computationally expensive simulation such as finite element runs is involved. The ultimate purpose for any reliability analysis problem is to increase the efficiency and accuracy of the calculations. There are still clear deficiencies in terms of efficiency and accuracy of the solution methods which is used depending on the nature of the problem (level of nonlinearity and size). The aim of this research is to propose efficient methods for reliability analysis to overcome these shortcomings and apply these techniques to high dimensional RBDO that possibly involves finite element analyses. This seminar introduces dimension reduction (DR) method and an adaptive improved response surface method (AIRSM) in conjunction with a new regression based model. These methods are applied to solve several RBDO problems in engineering field and the performance is compared in terms of efficiency and accuracy.