An efficient approach for high-fidelity modeling incorporating contour-based sampling and uncertainty

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Crowley, Daniel R.
Mavris, Dimitri N.
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During the design process for an aerospace vehicle, decision-makers must have an accurate understanding of how each choice will affect the vehicle and its performance. This understanding is based on experiments and, increasingly often, computer models. In general, as a computer model captures a greater number of phenomena, its results become more accurate for a broader range of problems. This improved accuracy typically comes at the cost of significantly increased computational expense per analysis. Although rapid analysis tools have been developed that are sufficient for many design efforts, those tools may not be accurate enough for revolutionary concepts subject to grueling flight conditions such as transonic or supersonic flight and extreme angles of attack. At such conditions, the simplifying assumptions of the rapid tools no longer hold. Accurate analysis of such concepts would require models that do not make those simplifying assumptions, with the corresponding increases in computational effort per analysis. As computational costs rise, exploration of the design space can become exceedingly expensive. If this expense cannot be reduced, decision-makers would be forced to choose between a thorough exploration of the design space using inaccurate models, or the analysis of a sparse set of options using accurate models. This problem is exacerbated as the number of free parameters increases, limiting the number of trades that can be investigated in a given time. In the face of limited resources, it can become critically important that only the most useful experiments be performed, which raises multiple questions: how can the most useful experiments be identified, and how can experimental results be used in the most effective manner? This research effort focuses on identifying and applying techniques which could address these questions. The demonstration problem for this effort was the modeling of a reusable booster vehicle, which would be subject to a wide range of flight conditions while returning to its launch site after staging. Contour-based sampling, an adaptive sampling technique, seeks cases that will improve the prediction accuracy of surrogate models for particular ranges of the responses of interest. In the case of the reusable booster, contour-based sampling was used to emphasize configurations with small pitching moments; the broad design space included many configurations which produced uncontrollable aerodynamic moments for at least one flight condition. By emphasizing designs that were likely to trim over the entire trajectory, contour-based sampling improves the predictive accuracy of surrogate models for such designs while minimizing the number of analyses required. The simplified models mentioned above, although less accurate for extreme flight conditions, can still be useful for analyzing performance at more common flight conditions. The simplified models may also offer insight into trends in the response behavior. Data from these simplified models can be combined with more accurate results to produce useful surrogate models with better accuracy than the simplified models but at less cost than if only expensive analyses were used. Of the data fusion techniques evaluated, Ghoreyshi cokriging was found to be the most effective for the problem at hand. Lastly, uncertainty present in the data was found to negatively affect predictive accuracy of surrogate models. Most surrogate modeling techniques neglect uncertainty in the data and treat all cases as deterministic. This is plausible, especially for data produced by computer analyses which are assumed to be perfectly repeatable and thus truly deterministic. However, a number of sources of uncertainty, such as solver iteration or surrogate model prediction accuracy, can introduce noise to the data. If these sources of uncertainty could be captured and incorporated when surrogate models are trained, the resulting surrogate models would be less susceptible to that noise and correspondingly have better predictive accuracy. This was accomplished in the present effort by capturing the uncertainty information via nuggets added to the Kriging model. By combining these techniques, surrogate models could be created which exhibited better predictive accuracy while selecting the most informative experiments possible. This significantly reduced the computational effort expended compared to a more standard approach using space-filling samples and data from a single source. The relative contributions of each technique were identified, and observations were made pertaining to the most effective way to apply the separate and combined methods.
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