UQ and AI: data fusion, inverse identification, and multiscale uncertainty propagation in aerospace components

A key requirement for engineering designs is that they offer good performance across a range of uncertain conditions while exhibiting an admissibly low probability of failure. In order to design components that offer good performance across a range of uncertain conditions, it is necessary to take account of the effect of the uncertainties associated with a candidate design. Uncertainty Quantification (UQ) methods are statistical methods that may be used to quantify the effect of the uncertainties inherent in a system on its performance. This thesis expands the envelope of UQ methods for the design of aerospace components, supporting the integration of UQ methods in product development by addressing four industrial challenges. Firstly, a method for propagating uncertainty through computational models in a hierachy of scales is described that is based on probabilistic equivalence and Non-Intrusive Polynomial Chaos (NIPC). This problem is relevant to the design of aerospace components as the computational models used to evaluate candidate designs are typically multiscale. This method was then extended to develop a formulation for inverse identification, where the probability distributions for the material properties of a coupon are deduced from measurements of its response. We demonstrate how probabilistic equivalence and the Maximum Entropy Principle (MEP) may be used to leverage data from simulations with scarce experimental data- with the intention of making this stage of product design less expensive and time consuming. The third contribution of this thesis is to develop two novel meta-modelling strategies to promote the wider exploration of the design space during the conceptual design phase. Design Space Exploration (DSE) in this phase is crucial as decisions made at the early, conceptual stages of an aircraft design can restrict the range of alternative designs available at later stages in the design process, despite limited quantitative knowledge of the interaction between requirements being available at this stage. A histogram interpolation algorithm is presented that allows the designer to interactively explore the design space with a model-free formulation, while a meta-model based on Knowledge Based Neural Networks (KBaNNs) is proposed in which the outputs of a high-level, inexpensive computer code are informed by the outputs of a neural network, in this way addressing the criticism of neural networks that they are purely data-driven and operate as black boxes. The final challenge addressed by this thesis is how to iteratively improve a meta-model by expanding the dataset used to train it. Given the reliance of UQ methods on meta-models this is an important challenge. This thesis proposes an adaptive learning algorithm for Support Vector Machine (SVM) metamodels, which are used to approximate an unknown function. In particular, we apply the adaptive learning algorithm to test cases in reliability analysis.Open Acces

A probabilistic framework for source localization in anisotropic composite using transfer learning based multi-fidelity physics informed neural network (mfPINN)

The practical application of data-driven frameworks like deep neural network in acoustic emission (AE) source localization is impeded due to the collection of significant clean data from the field. The utility of the such framework is governed by data collected from the site and/or laboratory experiment. The noise, experimental cost and time consuming in the collection of data further worsen the scenario. To address the issue, this work proposes to use a novel multi-fidelity physics-informed neural network (mfPINN). The proposed framework is best suited for the problems like AE source detection, where the governing physics is known in an approximate sense (low-fidelity model), and one has access to only sparse data measured from the experiment (highfidelity data). This work further extends the governing equation of AE source detection to the probabilistic framework to account for the uncertainty that lies in the sensor measurement. The mfPINN fuses the data-driven and physics-informed deep learning architectures using transfer learning. The results obtained from the data-driven artificial neural network (ANN) and physicsinformed neural network (PINN) are also presented to illustrate the requirement of a multifidelity framework using transfer learning. In the presence of measurement uncertainties, the proposed method is verified with an experimental procedure that contains the carbon-fiberreinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers. The results conclude that the proposed technique based on a probabilistic framework can provide a reliable estimation of AE source location with confidence intervals by taking measurement uncertainties into account

Reversible GANs for Memory-efficient Image-to-Image Translation

The Pix2pix and CycleGAN losses have vastly improved the qualitative and quantitative visual quality of results in image-to-image translation tasks. We extend this framework by exploring approximately invertible architectures which are well suited to these losses. These architectures are approximately invertible by design and thus partially satisfy cycle-consistency before training even begins. Furthermore, since invertible architectures have constant memory complexity in depth, these models can be built arbitrarily deep. We are able to demonstrate superior quantitative output on the Cityscapes and Maps datasets at near constant memory budget

Disentangled Multi-Fidelity Deep Bayesian Active Learning

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), that learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency. Our code is available at https://github.com/Rose-STL-Lab/Multi-Fidelity-Deep-Active-Learning

Multi-fidelity wavelet neural operator with application to uncertainty quantification

Operator learning frameworks, because of their ability to learn nonlinear maps between two infinite dimensional functional spaces and utilization of neural networks in doing so, have recently emerged as one of the more pertinent areas in the field of applied machine learning. Although these frameworks are extremely capable when it comes to modeling complex phenomena, they require an extensive amount of data for successful training which is often not available or is too expensive. However, this issue can be alleviated with the use of multi-fidelity learning, where a model is trained by making use of a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. To this end, we develop a new framework based on the wavelet neural operator which is capable of learning from a multi-fidelity dataset. The developed model's excellent learning capabilities are demonstrated by solving different problems which require effective correlation learning between the two fidelities for surrogate construction. Furthermore, we also assess the application of the developed framework for uncertainty quantification. The results obtained from this work illustrate the excellent performance of the proposed framework