Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly efficient and accurate methods of mapping input-output relationships to investigate complex models. There is substantial potential to increase the efficacy of the method regarding the selected sampling scheme. We examine state-of-the-art sampling schemes categorized in space-filling-optimal designs such as Latin Hypercube sampling and L1-optimal sampling and compare their empirical performance against standard random sampling. The analysis was performed in the context of L1 minimization using the least-angle regression algorithm to fit the GPCE regression models. Due to the random nature of the sampling schemes, we compared different sampling approaches using statistical stability measures and evaluated the success rates to construct a surrogate model with relative errors of <0.1\%, <1\%, and <10\%, respectively. The sampling schemes are thoroughly investigated by evaluating the y of surrogate models constructed for various distinct test cases, which represent different problem classes covering low, medium and high dimensional problems. Finally, the sampling schemes are tested on an application example to estimate the sensitivity of the self-impedance of a probe that is used to measure the impedance of biological tissues at different frequencies. We observed strong differences in the convergence properties of the methods between the analyzed test functions

Pygpc: A sensitivity and uncertainty analysis toolbox for Python

We present a novel Python package for the uncertainty and sensitivity analysis of computational models. The mathematical background is based on the non-intrusive generalized polynomial chaos method allowing one to treat the investigated models as black box systems, without interfering with their legacy code. Pygpc is optimized to analyze models with complex and possibly discontinuous transfer functions that are computationally costly to evaluate. The toolbox determines the uncertainty of multiple quantities of interest in parallel, given the uncertainties of the system parameters and inputs. It also yields gradient-based sensitivity measures and Sobol indices to reveal the relative importance of model parameters

Effect of contact pressure on porcine postmortem brain tissue impedance

In this experimental study we demonstrate the influence of contact pressure on porcine postmortem brain tissue impedance using a movable electrode array and a load cell. We show that the variation of the contact pressure between the tissue and the measurement probe leads to a coefficient of variation in the measured impedance of under 3%. Its influence can therefore be neglected in the investigated use case. Further, we fit the measured impedances to an equivalent circuit model and compare the resistance of grey and white matter brain tissue based on the model parameters