Capture of manufacturing uncertainty in turbine blades through probabilistic techniques

Efficient designing of the turbine blades is critical to the performance of an aircraft engine. An area of significant research interest is the capture of manufacturing uncertainty in the shapes of these turbine blades. The available data used for estimation of this manufacturing uncertainty inevitably contains the effects of measurement error/noise. In the present work, we propose the application of Principal Component Analysis (PCA) for de-noising the measurement data and quantifying the underlying manufacturing uncertainty. Once the PCA is performed, a method for dimensionality reduction has been proposed which utilizes prior information available on the variance of measurement error for different measurement types. Numerical studies indicate that approximately 82% of the variation in the measurements from their design values is accounted for by the manufacturing uncertainty, while the remaining 18% variation is filtered out as measurement error

Sparse random Fourier features based interatomic potentials for high entropy alloys

Computational modeling of high entropy alloys (HEA) is challenging given the scalability issues of Density functional theory (DFT) and the non-availability of Interatomic potentials (IP) for molecular dynamics simulations (MD). This work presents a computationally efficient IP for modeling complex elemental interactions present in HEAs. The proposed random features-based IP can accurately model melting behaviour along with various process-related defects. The disordering of atoms during the melting process was simulated. Predicted atomic forces are within 0.08 eV/\unicode{xC5} of corresponding DFT forces. MD simulations predictions of mechanical and thermal properties are within 7$\%$ of the DFT values. High-temperature self-diffusion in the alloy system was investigated using the IP. A novel sparse model is also proposed which reduces the computational cost by 94$\%$ without compromising on the force prediction accuracy

Projection schemes in stochastic finite element analysis

In traditional computational mechanics, it is often assumed that the physical properties of the system under consideration are deterministic. This assumption of determinism forms the basis of most mathematical modeling procedures used to formulate partial differential equations (PDEs) governing the system response. In practice, however, some degree of uncertainty in characterizing virtually any engineering system is inevitable. In a structural system, deterministic characterization of the system properties and its environment may not be desirable due to several reasons, including uncertainty in the material properties due to statistically inhomogeneous microstructure, variations in nominal geometry due to manufacturing tolerances, and uncertainty in loading due to the nondeterministic nature of the operating environment. These uncertainties can be modeled within a probabilistic framework, which leads to PDEs with random coefficients and associated boundary and initial conditions governing the system dynamics. It is implicitly assumed here that uncertainty in the PDE coefficients can be described by random variables or random fields that are constructed using experimental data or stochastic micromechanical analysis