The application of uncertainty analysis for the prediction of aeroelastic stability, using probabilistic and non-probabilistic methodologies, is considered in this chapter. Initially, a background to aeroelasticity and possible instabilities, in particular “flutter,” that can occur in aircraft is given along with the consideration of why Uncertainty Quantification (UQ) is becoming an important issue to the aerospace industry. The Polynomial Chaos Expansion method and the Fuzzy Analysis for UQ are then introduced and a range of different random and quasi-random sampling techniques as well as methods for surrogate modeling are discussed. The implementation of these methods is demonstrated for the prediction of the effects that variations in the structural mass, resembling variations in the fuel load, have on the aeroelastic behavior of the Semi-Span Super-Sonic Transport wind-tunnel model (S4T). A numerical model of the aircraft is investigated using an eigenvalue analysis and a series of linear flutter analyses for a range of subsonic and supersonic speeds. It is shown how the Probability Density Functions (PDF) of the resulting critical flutter speeds can be determined efficiently using both UQ approaches and how the membership functions of the aeroelastic system outputs can be obtained accurately using a Kriging predictor.
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Advanced virtual modelling and simulation in engineering is the way forward in the creation of physical prototypes right-at-the-first-time, leveraging the recent developments in Computer-Aided-Engineering (CAE) tools and numerical methods as well as the ever increasing power in computer systems. Nowadays, engineers in aerospace industries are able to design and de-risk virtual prototypes earlier in the product development cycle, using modelling and simulation tools of higher fidelity e.g. Computational Fluid Dynamics methods and nonlinear structural Finite Element analysis. As a result, it is becoming increasingly common to perform multi-disciplinary analyses by combining two or more separate disciplines and leading to robust design of products. Another key feature of modern design and certification process is the lack of reliance upon experimental testing to validate computational models, since there is a greater confidence in the accuracy of the aerodynamic and structural predictions coming from numerical testing.
However, aircraft operate inevitably in an uncertain world and despite the advanced manufacturing methods, there will always be a certain tolerance in every component and joint in an aircraft. Aerospace structures also degrade during their lifetime and are subjected to uncertain aerodynamic and ground loads. The traditional approach to aircraft design is to include a safety factor for every aspect of the design, leading to over-designed, and thus overweight, aircraft that are inefficient in terms of performance, manufacturing cost and environmental impact. The knowledge in the field of modelling and predicting the responses of aircraft is constantly enhanced and uncertainty modelling is considered as a modern tool that increases confidence to designs by providing engineering insight. Although, it is impossible to investigate the effects of uncertainty and variation through brute force computation as there are far too many uncertain parameters to consider and the resulting computational requirements would be enormous.
Consequently, in recent years, there has been an increased interest in developing efficient uncertainty-based methods that enable a statistical approach to be applied to the deterministic formulations required for aircraft design (e.g. Pettit, 2004). Such approaches can be divided into probabilistic and non-probabilistic methods, depending upon whether the variation of the input parameters (e.g. Young’s Modulus or atmospheric temperature) are known as an interval (min/max) or as a probability distribution function (PDF) (Beran et al., 2006; Catravete et al., 2008; Kuttenkeuler & Ringertz, 1998). A range of methods, including Polynomial Chaos Expansion, Interval and Fuzzy Arithmetic approaches have been proven as reliable and efficient tools for investigation of uncertainty analysis in engineering problems (Georgiou et al., 2012; Manan & Cooper, 2009; Khodaparast et al., 2010). However, there are still concerns of how to deal with large number of uncertain parameters.