Optimal representation of multi-dimensional random fields with a moderate number of samples: Application to stochastic mechanics

• A methodology called FQ-IDCVT for optimal sampling of random functions is discussed.
• This paper focuses on the extension of FQ-IDCVT to multi-dimensional random fields.
• FQ-IDCVT can be applied to non-Gaussian, non-homogeneous, multi-dimensional fields.
• Technique demonstrated on a 2D plane-stress problem with random Young’s modulus.
• Sensitivity analysis performed to determine accuracy and limits of applicability.

A significant amount of problems and applications in stochastic mechanics and engineering involve multi-dimensional random functions. The probabilistic analysis of these problems is usually computationally very expensive if a brute-force Monte Carlo method is used. Thus, a technique for the optimal selection of a moderate number of samples effectively representing the entire space of sample realizations is of paramount importance. Functional Quantization is a novel technique that has been proven to provide optimal approximations of random functions using a predetermined number of representative samples. The methodology is very easy to implement and it has been shown to work effectively for stationary and non-stationary one-dimensional random functions. This paper discusses the application of the Functional Quantization approach to the domain of multi-dimensional random functions and the applicability is demonstrated for the case of a 2D non-Gaussian field and a two-dimensional panel with uncertain Young modulus under plane stress.