Treating Uncertainties to Generate a Robust Design of Gas Turbine Disk Using L Moments and Scarce Samples Including Outliers
TL;DR: This work proposes using L moments to model the spread of data and shows that the proposed approach works better than the classical robust design formulation.
Abstract: Uncertainties in the input variables are inevitable in any design process. As a consequence, the output responses are also uncertain. Robust design is one of the sought after approach to treat such uncertainties for controlling the variation in the output responses, while maximizing the mean performance. Variation is modeled by a measure of data spread. Often, the details of the uncertainties in the input space are not available readily and they are usually characterized from scarce sample realizations. In addition, there could also be outliers in the realizations. These will increase the error in the measure of spread of the output response. Hence, it is desirable that an approach that is insensitive to outliers but can characterize the spread of data is developed for robust design. In this work we propose using L moments to model the spread of data. The classical robust design formulation is reformulated using the second L moment (l2). The proposed approach is demonstrated on a turbine disk design with 17 design and random variables. The details of the uncertainties are not known. A DoE of 200 samples is used and at each DoE point, we propagate the uncertainties using scarce samples, which include outliers. Robust design is performed and it is shown that the proposed approach works better than the classical robust design formulation.
TL;DR: L-moment ratio diagram that uses higher order L-moments is adopted to choose the appropriate distribution, for uncertainty quantification and the probabilistic estimates obtained are found to be less sensitive to the extremes in the data, compared to the results obtained from the conventional moments approach.
Abstract: Sampling-based uncertainty quantification demands large data. Hence, when the available sample is scarce, it is customary to assume a distribution and estimate its moments from scarce data, to characterize the uncertainties. Nonetheless, inaccurate assumption about the distribution leads to flawed decisions. In addition, extremes, if present in the scarce data, are prone to be classified as outliers and neglected which leads to wrong estimation of the moments. Therefore, it is desirable to develop a method that is (i) distribution independent or allows distribution identification with scarce samples and (ii) accounts for the extremes in data and yet be insensitive or less sensitive to moments estimation. We propose using L-moments to develop a distribution-independent, robust moment estimation approach to characterize the uncertainty and propagate it through the system model. L-moment ratio diagram that uses higher order L-moments is adopted to choose the appropriate distribution, for uncertainty quantification. This allows for better characterization of the output distribution and the probabilistic estimates obtained using L-moments are found to be less sensitive to the extremes in the data, compared to the results obtained from the conventional moments approach. The efficacy of the proposed approach is demonstrated on conventional distributions covering all types of tails and several engineering examples. Engineering examples include a sheet metal manufacturing process, 7 variable speed reducer, and probabilistic fatigue life estimation.