Avoiding Flutter: Analyzing Uncertainty Methods

Engineerblogger
March 9, 2012

Image: Charbel Farhat, University of Colorado, Boulder.

Aircrafts are designed and tested to avoid flutter, an instability that can occur due to aerodynamic, structural, and inertial forces. Predicting how an aircraft will respond if it encounters flutter conditions can involve analyses with multiple iterations, thousands of variables, and fine mesh finite-element and computational fluid dynamics-based models. Many sources of uncertainty exist, not only structurally, with differences between "as planned" and "as built," but also "as flown" when aerodynamically interacting with random forces of nature.

Though desirable, traditional uncertainty analysis (UA) is often not performed during aircraft flutter analysis for transonic flight due to the expense of the intensive computing resources that are required. New methods for predicting flutter instabilities, which use reduced computing resources while maintaining accuracy, have been found in techniques not traditionally used for UA. Under a NASA SBIR program, Systems Technology, Inc., Hawthorne, CA, has demonstrated the feasibility of using reduced order models (ROMs) of a verified AGARD wing with two methods: Design of Experiments Coupled to Response Surface Methods (DOE/RSM) and Mu Analysis.

Simpler Models Verified by Monte Carlo

Full nonlinear aeroelastic models of aircraft containing uncertainty parameters can be mathematically decomposed into compact linear forms that contain essential dynamics characteristics. Analyzing ROMs using traditional stochastic Monte Carlo techniques is much faster than with the full models. But Brian Danowsky, senior research engineer for the study, says another important advantage of using ROMs is that linear methods can be used to predict dynamic responses and system behavior rather than having to perform full simulations or sacrifice accuracy.

Traditional MC simulations from the ROMs generated in the study predicted accurate flutter stability points matching known experimental values for this wing, validating the ROMs, and serving as a basis of comparison for two further linear techniques.

DOE/RSM Reduces Inputs

Flutter stability points could be generated quickly by a combination of DOE and RSM. DOE identifies and selects only the most important input parameter values for the linear ROMs that maximize the information provided from the system's output. Sensitivity analysis of response surfaces generated by those input parameters using RSM can then rapidly arrive at the desired predictions.

The technique predicted accurate flutter stability points that agreed with those predicted by the benchmark MC method and the known nominal values for the wing model. The results were obtained with computational run times, two orders of magnitude faster than direct MC.

One disadvantage of this technique is that it assumes a relationship between the model output and its input parameters, so its results depend upon the quality of the inputs. The direct MC method, which tests random values within the range of all possible values, does not. Another disadvantage, Danowsky warns, is that if the form of the relationship is properly chosen, it provides results quickly, but if it is not, the results may be misleading.

Mu Guarantees Stability

The more abstract Mu Analysis, primarily developed in the 1980s and periodically favored by the aerospace industry, is a mathematical method that measures the robustness of a system with uncertainties without having to estimate probabilities or distributions and does not require multiple simulations.

Generally, it involves the small-gain theorem and interconnected closed-loop feedback systems of stable operators subject to perturbations. "Given a bound and parameters with their own bounds, this method provides a mathematically guaranteed robust stability point, which is extremely valuable," says Danowsky.

Mu Analysis produced accurate flutter bounds agreeing with the benchmark MC method, but required much longer run times. The study contained a high-order stability parameter that has since been integrated into the main model differently, improving the run times and demonstrating the need for further benchmarking.

This study has demonstrated that it is possible to reduce the size of the Mu Analysis problem to get more accurate results much faster, Danowsky says. Results were so encouraging with this technique that NASA awarded a Phase 2 study to enhance Mu Analysis techniques, currently underway in mid-2011.

Studies like these that expand our understanding of uncertainties are helping aerospace and other industries decide where to spend resources for improving prediction capabilities. This will not only lead to quicker, more efficient analysis, but ultimately, improved safety.

Source: ASME