Machine learning aided stochastic analysis for functionally graded structures

Abstract

Functionally graded material (FGM) with a graded profile between two constituent phases, has been prevalently utilized in modern real-life engineering applications, such as mechanical, biomechanical, aerospace, nuclear, military, etc. However, full designability of functionally graded (FG) structures in practical applications is still challenging, due to the inevitable existence of system uncertainties. Therefore, stochastic structural analysis for FG structures appears extremely significant.

This thesis presents a machine learning aided stochastic analysis approach to investigate the static structural reliability and stochastic structural free vibration behaviour for FG frame structure, basing on 3D finite element method (FEM). The uncertain system parameters, which are including the material properties, dimensions of structural members, external loads, as well as the degree of gradation of FGM, can be incorporated within a unified stochastic analysis framework. By extending the traditional support vector machine (SVM), a new kernel-based machine learning technique, namely the extended support vector regression (X-SVR), is proposed for modelling the underpinned relationship between the structural behaviours and the uncertain system inputs. Through the established regression function, the Monte Carlo simulation (MCS) can be conducted with greatly reduced computational costs.

The proposed machine learning aided stochastic analysis framework is capable of providing sufficient statistical information, including the statistical moments (i.e., mean and standard deviation), probability density function (PDF), as well as cumulative distribution function (CDF) for the concerned structural behaviour in an efficient manner. Furthermore, distinctive to the previous generation stochastic uncertainty quantifications, the proposed machine learning aided uncertainty analysis framework is competent to self-optimise and self-update the regression model by constantly adopting the information update regarding the uncertain system inputs. Conceivably, the proposed machine learning aided stochastic analysis framework can be extended to a structural health monitoring (SHM) algorithm during the service-life of the FGM structure. Such unique features have indeed intensified the competitiveness of the proposed analysis framework in the development of smart engineering industry.