Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Macropores generated during shrinkage in two paddy soils using X-ray micro-computed tomography

Soil shrinkage curve represents a decrease of total porosity or an increase of bulk density with water loss. However, our knowledge of the dynamics of pores and their geometry during soil shrinkage is scarce, partially due to lack of reliable methods for determining soil pores in relation to change in soil water. This study aimed to investigate the dynamics of macropores (>30 mu m) of paddy soils during shrinkage. Two, paddy soils, which were sampled from one paddy field cultivated for 20 years (YPF) and the other one for over 100 years (OPF), represented difference in crack geometry in the field. Macropore parameters (volume, connectivity, and orientation of pores) and soil shrinkage parameters were determined on the same undisturbed soil cores by X-ray microtomography and shrinkage curve, respectively. Macroporosity was on average four times larger in the YPF than in the OPF whereas the shrinkage capacity was lower in the YPF as compared to the OPF (0.09 vs. 0.15 COLE). Soil shrinkage increased the volume of pores by 3.7% in the YPF and by 1.6% in the OPF as well as their connectivity. The formation of macropores occurred mostly in the proportional shrinkage phase. As a result, the slope of the proportional shrinkage phase was smaller in the YPF (0.65) than in the OPF (0.89). New macropores were cracks and extended pre-existing pores in the range of 225-1215 pm size without any preferential orientation. This work provides image evidences that in paddy soils with high shrinkage capacity more macropores are generated in the soil presenting a smaller proportional shrinkage slope. (C) 2015 Elsevier B.V. All rights reserved.