# Inverse Parametric Uncertain Identification using Polynomial Chaos and high-order Moment Matching benchmarked on a Wet Friction Clutch

## TL;DR

This paper introduces an efficient inverse method combining Polynomial Chaos and moment matching for identifying probabilistic models of system parameters, demonstrated on a wet clutch system, improving accuracy and reducing computational effort.

## Contribution

It presents a novel inverse uncertainty identification approach using high-order moments and polynomial chaos, significantly reducing simulation costs and increasing model accuracy.

## Key findings

- Achieved a tenfold reduction in required simulations.
- Improved log-likelihood by approximately 4%.
- Enhanced accuracy of output probability density estimation by up to 47%.

## Abstract

A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of experiments. To perform maximum likelihood estimation, the output probability density function is required. Forward propagation of input uncertainty is established combining Polynomial Chaos and moment matching. High-order moments of the output distribution are estimated using the generalized Polynomial Chaos framework. Next, a maximum entropy parametric distribution is matched with the estimated moments. This method is numerically very attractive due to reduced forward sampling and deterministic nature of the propagation strategy. The methodology is applied on a wet clutch system for which certain model variables are considered as stochastic. The number of required model simulations to achieve the same accuracy as the brute force methodologies is decreased by one order of magnitude. The probability model identified with the high order estimates resulted into a true log-likelihood increase of about 4% since the accuracy of the estimated output probability density function could be improved up to 47%.