<p>Uncertainty analysis is of great use both for calculating outputs that are more akin to real<br> flight, and for optimization to more robust shapes. However, implementation of uncertainty<br> has been a longstanding challenge in the field of aerodynamics due to the computational cost<br> of simulations. Geometric uncertainty in particular is often left unexplored in favor of uncer-<br> tainties in freestream parameters, turbulence models, or computational error. Therefore, this<br> work proposes a method of geometric uncertainty analysis for aerodynamic shapes that miti-<br> gates the barriers to its feasible computation. The process takes a two- or three-dimensional<br> shape and utilizes a combination of multifidelity meshes and Gaussian process regression<br> (GPR) surrogates in a multifidelity Monte Carlo (MFMC) algorithm. Multifidelity meshes<br> allow for finer sampling with a given budget, making the surrogates more accurate. GPR<br> surrogates are made practical to use by parameterizing major factors in geometric uncer-<br> tainty with only four variables in 2-D and five in 3-D. In both cases, two parameters control<br> the heights of steps that occur on the top and bottom of airfoils where leading and trailing<br> edge devices are attached. Two more parameters control the height and length of waves<br> that can occur in an ideally smooth shape during manufacturing. A fifth parameter controls<br> the depth of span-wise skin buckling waves along a 3-D wing. Parameters are defined to<br> be uniformly distributed with a maximum size of 0.4 mm and 0.15 mm for steps and waves<br> to remain within common manufacturing tolerances. The analysis chain is demonstrated<br> with two test cases. The first, the RAE2822 airfoil, uses transonic freestream parameters<br> set by the ADODG Benchmark Case 2. The results show a mean drag of nearly 10 counts<br> above the deterministic case with fixed lift, and a 2 count increase for a fixed angle of attack<br> version of the case. Each case also has small variations in lift and angle of attack of about<br> 0.5 counts and 0.08◦, respectively. Variances for each of the three tracked outputs show that<br> more variability is possible, and even likely. The ONERA M6 transonic wing, popular due<br> to the extensive experimental data available for computational validation, is the second test<br> case. Variation is found to be less substantial here, with a mean drag increase of 0.5 counts,<br> and a mean lift increase of 0.1 counts. Furthermore, the MFMC algorithm enables accurate<br> results with only a few hours of wall time in addition to GPR training. </p>

<p dir="ltr">For turbocharged engine simulation analysis, manufacturer-provided data are typically used to predict the mass flow and efficiency of the turbine. To create a turbine map, physical tests are performed in labs at various turbine speeds and expansion ratios. These tests can be very expensive and time-consuming. Current testing methods can have limitations that result in errors in the turbine map. As such, only a modest set of data can be generated, all of which have to be interpolated and extrapolated to create a smooth surface that can then be used for simulation analysis.</p><p><br></p><p dir="ltr">The current method used by the manufacturer is a physics-informed polynomial regression model that depends on the Blade Speed Ratio (BSR ) in the polynomial function to model the efficiency and MFP. This method is memory-consuming and provides a lower-than-desired accuracy. This model is decades old and must be updated with new state-of-the-art Machine Learning models to be more competitive. Currently, CTT is facing up to +/-2% error in most turbine maps for efficiency and MFP and the aim is to decrease the error to 0.5% while interpolating the data points in the available region. The current model also extrapolates data to regions where experimental data cannot be measured. Physical tests cannot validate this extrapolation and can only be evaluated using CFD analysis.</p><p><br></p><p dir="ltr">The thesis focuses on investigating different AI techniques to increase the accuracy of the model for interpolation and evaluating the models for extrapolation. The data was made available by CTT. The available data consisted of various turbine parameters including ER, turbine speeds, efficiency, and MFP which were considered significant in turbine modeling. The AI models developed contained the above 4 parameters where ER and turbine speeds are predictors and, efficiency and MFP are the response. Multiple supervised ML models such as SVM, GPR, LMANN, BRANN, and GBPNN were developed and evaluated. From the above 5 ML models, BRANN performed the best achieving an error of 0.5% across multiple turbines for efficiency and MFP. The same model was used to demonstrate extrapolation, where the model gave unreliable predictions. Additional data points were inputted in the training data set at the far end of the testing regions which greatly increased the overall look of the map.</p><p><br></p><p dir="ltr">An additional contribution presented here is to completely predict an expansion ratio line and evaluate with CTT test data points where the model performed with an accuracy of over 95%. Since physical testing in a lab is expensive and time-consuming, another goal of the project was to reduce the number of data points provided for ANN model training. Furthermore, strategically reducing the data points is of utmost importance as some data points play a major role in the training of ANN and can greatly affect the model's overall accuracy. Up to 50% of the data points were removed for training inputs and it was found that BRANN was able to predict a satisfactory turbine map while reducing 20% of the overall data points at various regions.</p>