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2023 | OriginalPaper | Chapter

9. Probability Bounds Analysis Applied to Multi-purpose Crew Vehicle Nonlinearity

Authors : Daniel C. Kammer, Paul Blelloch, Joel Sills

Published in: Model Validation and Uncertainty Quantification, Volume 3

Publisher: Springer International Publishing

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Abstract

The Multi-purpose Crew Vehicle (MPCV) Program Orion finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The hybrid parametric variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second-order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value or an interval of response values at a specific probability.

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Footnotes
1
Vehicle bending moments during atmospheric flight are typically dominated by static aeroelastic loads and gust, with buffet playing a secondary role. The uncertainty in buffet responses, therefore, does not reflect an equivalent uncertainty in peak bending moments experienced by the vehicle.
 
2
All levels identified a pair of fairly closely spaced bending modes in the Y-direction, which were not observed in the Z-direction, resulting in 4 Y-bending and 3 Z-bending modes in the frequency range.
 
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Metadata
Title
Probability Bounds Analysis Applied to Multi-purpose Crew Vehicle Nonlinearity
Authors
Daniel C. Kammer
Paul Blelloch
Joel Sills
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-04090-0_9