# On the estimation of moisture permeability and advection coefficients of a wood fibre material using the optimal experiment design approach

## TL;DR

This paper demonstrates how Optimal Experiment Design (OED) can be used to accurately determine moisture permeability and advection coefficients in wood fibre materials through in-situ measurements and strategic sensor placement.

## Contribution

The study applies OED with Fisher information matrix to optimize experimental conditions for parameter estimation in porous materials, improving accuracy over standard methods.

## Key findings

- Optimal sensor placement improves parameter estimation accuracy.
- Estimated moisture permeability is twice the value from standard methods.
- Advection velocity within the material is approximately 0.01 mm/s.

## Abstract

This paper presents a practical application of the concept of Optimal Experiment Design (OED) for the determination of properties of porous materials with in-situ measurements and an identification method. First, an experimental set-up was presented and used for the measurement of relative humidity within a wood fibre material submitted to single and multiple steps of relative humidity variation. Then, the application of OED enabled to plan the experimental conditions in terms of sensor positioning and boundary conditions out of 20 possible designs. The OED search was performed using the Fisher information matrix and a priori knowledge of the parameters. It ensures to provide the best accuracy of the identification method and thus the estimated parameter. Optimal design results have been found for single steps from the relative humidity phi = 10 to 75%, with one sensor located at the position X between 4 and 6 cm, for the estimation of moisture permeability coefficients, while from phi = 75% to phi = 33%, with one sensor located at X{\deg} = 3 cm, for the estimation of the advection coefficient. The OED has also been applied for the identification of couples of parameters. A sample submitted to multiple relative humidity steps (phi = 10-75-33-75%) with a sensor placed at X{\deg} = 5 cm was found as the best option for determining both properties with the same experiment. These OED parameters have then been used for the determination of moisture permeability and advection coefficients. The estimated moisture permeability coefficients are twice higher than the a priori values obtained using standard methods. The advection parameter corresponds to the mass average velocity of the order of v = 0.01 mm/s within the material and may play an important role on the simulation of moisture front.