Transient landing dynamics analysis for a lunar lander with random and interval fields

Abstract

This paper presents an objective comparison of random fields and interval fields to propagate spatial uncertainty, based on a finite element model of a lunar lander. The impulse based substructuring method is used to improve the analysis efficiency. The spatially uncertain input parameters are modeled by both random fields and interval fields. The objective of this work is to compare the applicability of both approaches in an early design stage under scarce information regarding the occurring spatial parameter variability. Focus is on the definition of the input side of the problem under this scarce knowledge, as well as the interpretation of the analysis outcome.To obtain an objective comparison between both approaches, the gradients in the interval field are tuned towards the gradients present in the random field. The result shows a very similar dependence and correlation structure between the local properties for both approaches. Furthermore, through the transient dynamic estimation, it is shown that the response ranges that are predicted by the interval field and random field are very close to each 1 other.

Application of interval field method to the stability analysis of slopes in presence of uncertainties

“…In probability theory, random fields are generally used to quantify the uncertainty of a spatially uncertain parameter, in which the quantity at arbitrary location x ∈ Ω ⊂ R n d is considered as a random variable with a probability distribution, where x is the spatial coordinate in n d dimensions in the physical model domain Ω. Different from the random field model, the interval field model employs bounds, namely a pair of upper and lower bounds, to describe the spatial uncertainty, which can efficiently perform uncertainty analysis based on limited information (Chen et al, 2020). For specific problems, how to represent the interval field is the basis of simulation calculations.…”

Uncertainty propagation with B-spline based interval field decomposition method in boundary value problems

“…Jiang et al [26] investigated the dynamic responses of a vibration system with multiple degrees of freedom subjected to time-varying external loads, modelled as an interval process. Chen et al [27] studied the dynamic response of a simplified dynamic finite element model of a lunar lander with its Young's modulus modelled as a 1D interval field. Although these studies demonstrate that interval field formulations can be effectively integrated into systems and account for crisp output bounds, few can directly work with Partial Differential equations (PDEs) in boundary value problems, typically requiring a discretised system equation.…”

B-spline based interval field decomposition method

“…Another set of basis functions is defined in the framework of the so-called Local interval field decomposition (LIFD) introduced by Imholz et al [22,23], where a set of piecewise second-order polynomial functions serve as basis functions with constraints on their bounds as well as maximum gradient as a measure of spatial dependency. Chen et al [24] modified these basis functions into non-negative polynomials on their supports. However, the LIFD method has its limitations.…”