Leveraging Statistical and Machine Learning Approaches for Engineering Design under Uncertainties

Research Context:

The utilization of computational models has revolutionised the engineering design process, offering engineers greater efficiency, accuracy, and confidence. However, the omnipresence of uncertainty in engineering design presents formidable challenges, necessitating innovative methodologies to address and manage uncertainty effectively.

For example, the finite element method (FEM) stands as a cornerstone in numerical engineering, providing a robust framework for modelling complex systems. However, its deterministic nature inherently limits its capacity to account for uncertainties inherent in real-world engineering problems. Consequently, traditional FEM struggles to reliably analyse systems when confronted with uncertainty.

To address this limitation, researchers have amalgamated conventional FEM with other methodologies, giving rise to innovative approaches like the Stochastic Finite Element Method (SFEM). SFEM enables the analysis of systems characterized by random variations and uncertain parameters, expanding the applicability of FEM in uncertain environments. Additionally, Monte Carlo simulation (MCS) emerges as a versatile technique for solving FEM with uncertainties.

However, the computational demands of MCS often hinder its practical implementation for real engineering systems.

A promising solution to this computational bottleneck involves leveraging surrogate models, which offer faster computation times compared to traditional simulators. By replacing the costly simulator with a surrogate model, engineers can efficiently analyse uncertainties and facilitate subsequent analyses. Nonetheless, in this transition, the contribution of uncertainties inherent in the surrogate model to simulation output uncertainties is frequently overlooked.

Recent advancements in the field have highlighted the efficacy of a Bayesian inferential framework for characterizing and propagating uncertainties. This framework provides a systematic methodology for addressing uncertainties, offering a probabilistic solution to both boundary value and initial value problems. Moreover, it naturally incorporates various types of uncertainties encountered in computer simulations, making it a versatile and comprehensive approach to uncertainty quantification in engineering design.

Aims and Objectives:

This Ph.D. project seeks to develop novel statistical and machine learning methods to enhance computational engineering design, enabling the quantification and propagation of uncertainties throughout the design process. By adopting a Bayesian inferential framework, the aim is to integrate different sources of information, including model predictions and experimental data, to achieve optimal uncertainty quantification.

Research methodology:

Develop advanced statistical and machine learning techniques, such as Gaussian Processes, to address both the forward simulation and inverse inference problems in computational engineering design.

Investigate physics-informed machine learning approaches to augment the predictive capability of probabilistic surrogate models, ensuring robustness and reliability in design predictions.

Tackle practical challenges associated with uncertainty quantification in engineering design, including the management of mixed epistemic and aleatory uncertainties, heterogeneous data integration, and the incorporation of multiphysics models. EPSRC alignment: Engineering Physical sciences