On the density estimation problem for uncertainty propagation with unknown input distributions

TL;DR

This paper introduces new density estimation methods for uncertainty quantification in experiments with unknown input distributions, combining observed and simulated data, and demonstrates their effectiveness through theoretical analysis and practical application.

Contribution

It proposes novel density estimates that integrate observed and simulated data for better uncertainty propagation with unknown inputs.

Findings

Convergence rates of the new estimates are analyzed.

Finite sample performance is validated with simulated data.

Practical application to vibration attenuation system shows usefulness.

Abstract

In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect) simulation model based on estimated input distributions. We analyze the rate of convergence of these estimates. The finite sample size performance of the estimates is illustrated by applying them to simulated data. The practical usefulness of the newly proposed estimates is demonstrated by using them to predict the uncertainty of a lateral vibration attenuation system with piezo-elastic supports.