Adjoint Based Design Optimization of Systems With Transient Physics and Probabilistically Modeled Uncertainties

Komahan Boopathy

September 23, 2019 – MK317 – 1:30 PM to 3:30 PM

Committee Members: Dr. Graeme Kennedy, Dr. Brian German, Dr. Marilyn Smith, Dr. Dewey Hodges

The Federal Aviation Authority (FAA) airworthiness certification requires a factor of safety of 1.5 for aircraft structures with human occupancy. Firstly, the inclusion of factor of safety as a certification require-ment is acknowledging of the ubiquitous presence of uncertainties that are beyond the consideration/scope of classical system design process. For aerospace systems, higher factor of safety implies heavier designs with increased operation costs for the entire life cycle of the system. Despite factor of safety stipulations in the design process, systems do fail (a risk concern) or perform in a degraded manner (a robustness concern), partly which is due lack of uncertainty assessments before designing the system. To this end, the fields of uncertainty quantification (UQ) and optimization under uncertainty (OUU) have evolved to rigorously address the effect of uncertainties in the design process. UQ deals with the mathematical representation and propagation of input uncertainties, whereas OUU deals with the mathematical aspects of formulating design/regulatory requirements as objective or constraint functions. Secondly, the mathematical model of physics can also be a contributing factor for unforeseen system behavior. For example, when fixed- and rotary-wing aeromechanical structures are designed without time-dependent analysis of response (by using a static evaluation), the onset of many time dependent adverse effects such as limit cycle oscillations, buffeting, flutter, stall-induced vibration and rotor-shaft whirl can go unpredicted. Arguably, inclusion of time domain within system analysis is as important as uncertainty quantification; thus, time dependent mathematical models of physics along with mathematically modeled uncertain inputs encompass a superior representation of system behavior. The systems designed using such inclusive analyses will emerge better in terms of robustness and reliability. Finally, while performing numerical optimization of large aeromechan-ical systems, gradient-based optimization techniques are computationally efficient compared to techniques that do not use higher order information; thus, an efficient evaluation of gradients is also an important ingredient to the UQ–OUU design process. The time dependent nature of physical analysis necessitates the development of time dependent sensitivity analysis equations. Altogether, a need for incorporation of transient analysis of physics, uncertainty analysis and sensitivity analysis into a common design framework emerges naturally.