Polymorphic uncertainty field quantification in structural analysis with machine learning assistance

This research proposes and evaluates a generalised uncertainty model, the Polymorphic Uncertainty Field, which simultaneously considers two challenges in engineering practices: nearly all uncertainties are spatially dependent, and credibly determining their statistical characteristics is often difficult. Accordingly, two types of polymorphic uncertainty field problems are introduced, i.e., Fuzzy Random Variable Featured and Fuzzy Statistical Moment Featured polymorphic uncertainty fields. By modelling material properties as polymorphic uncertainty fields, the nondeterministic structural static behaviour is investigated. To provide operationally feasible solutions, machine learning-assisted polymorphic uncertainty analyses are developed. A novel supervised machine learning algorithm, Second-order Cone Programming Extended Support Vector Regression (SOCP-X-SVR), is introduced. The hyperplane model construction is carried out in the form of a second-order cone programming problem, with the feature of convexity. The established SOCP-X-SVR hyperplane model replicates the underlying relationships between different quantities of interest in polymorphic uncertainty problems. Then, sampling-based methods and a series of optimization programs are implemented on the established hyperplane models with greatly improved computational efficiency. Through the proposed strategies, sufficient fuzzy-valued statistical information of interest can be effectively and efficiently estimated. In numerical simulations, three engineering structures are thoroughly investigated by considering the proposed polymorphic uncertainty fields. In comparison to the brute-force Monte Carlo Simulation method with limited computational resources, the proposed strategies achieve more comprehensive and reliable estimations of the concerned bounds and significantly improve computational efficiency.