Lord of the rubber rings, the trilogy

Bram De Jaegher

Lord of the rubber rings, the trilogy

Bram De Jaegher

Electrodialysis

Electrodialysis

Electrodialysis fouling

Electrodialysis fouling

Previously: mechanistic model ED

Prominent fouling factors

Foulant props.

Salt concentration

Crossflow velocity

Current

pH

Membrane props.

Quiz intermezzo

Part 1: The internship of the ring

Experimental factors

Foulant props.

Salt concentration

Crossflow velocity

Current

pH

Membrane props.

Experiments: reality vs. expectations

My design

Experiments: reality vs. expectations

My design

Experiments: reality vs. expectations

Expected experiments

Experiments: reality vs. expectations

My design

Expected experiments

Experiments: reality vs. expectations

Experiments performed

Experiments: reality vs. expectations

My design

Expected experiments

Experiments performed

Experiments: reality vs. expectations

What I can actually use

Experiments: reality vs. expectations

My design

Expected experiments

Experiments performed

What I can actually use

What went wrong?

bolt

bolt

Bolt and nut adapted from: www.freepik.com

Experimental results

exp

Temperature compensation

$$R_{20} = 0.889 \cdot 10^{A/B}\, R\, $$

with,

$$ A = 1.37\,(T-20) + 8.36\cdot 10^{-4} (T-20)^2 $$

$$ B = 109 + T $$

Part 2: The return of the neural ODE

Neural differential equations

$$\frac{d \mathbf{R}(t)}{dt} = f(\mathbf{R}(t),\, v,\, i, \, C_e)$$

NeuralODE

Loss function

$$ L = \sum^N_{j=1} \left( \mathbf{R}_j - \hat{\mathbf{R}}_j \right)^2 + \lambda \, \sum^M_{k=1} \left| w_k \right| $$

The data is split in a Training and Test set

Cross-validation

NeuralODE

$$ \epsilon_{CV} = \frac{1}{K} \sum^K_{l=1} \left( \mathbf{R}_l - \hat{\mathbf{R}}_l \right)^2 $$

NeuralODE

Model testing

Mapping the initial fouling rate is easy

Extrapolation

Part 3: The two models (2020)

Lord of the rubber rings, the trilogy

Bram De Jaegher