PD Results

Key Results

Full results and analysis are available in the accompanying paper (currently in press).

Design Space Coverage

While just a few existing models claim substantial coverage of the considered design space, the overall coverage reaches 94.9%. The cumulative coverage histogram shows that almost 65% of the design points are predicted by at least two overlapping models. At the same time, an exponential decay of overlap-powered confidence is present, and only 10.9% of the design space is covered by at least eight overlapping models.

Claimed coverage of the design space of randomly packed beds with the counts of overlapping models

Model Validity (Post-Consensus)

After cross-validation and consensus alignment, model validity scores can be grouped in three tiers. Design points with low validity score ($v_{i,k}^{(m)}<0.2$) should generally be considered unreliable, and those with high validity score ($v_{i,k}^{(m)}>0.8$) are reliable. The consensual coverage histogram indicated that less than 45% of the considered models are in strong agreement with the overall consensus and that about 12% of models consistently produce outlying data. No definite correlation between model characteristics (e.g., claimed validity range, publication year, breadth of input parameters) and agreement with consensus was observed so far.

Consensual coverage of the source models after alignment adjustment

Blind Spots

The binned distribution of the validity scores $v_{i,k}$ for the considered design space differs drastically from the model-based consensual coverage because it is affected by a density check that heavily penalizes the validity score at design points with low overlap of the source models. Logarithmic penalization halves the validity of points supported by only two models and reduces validity to one third for points supported solely by a single model. This emphasizes the existence of gaps in pressure drop correlations in the design space of randomly packed beds, even when operating with a consensual model.

Consensual coverage of the design space after model alignment adjustment

 

A set of definitions for blind spots heavily depends on penalty threshold $\theta$ that can be adjusted in cross_validation.py. For example, at $\theta=5$ the detected gaps are as follows:

Size	Confidence	Gap definition
7.6%	97.2%	$1.12\le D/D_p<28.4$, $0.8<\phi_s\le 0.95$, $0.02<U_s\le 0.5$.$
6.4%	90.1%	$1.92\le D/D_p<39.87$, $\phi_s\le0.8$, $\varepsilon\le0.67$, $0.03<U_s\le0.28$
4.6%	95.2%	$9.88\le D/D_p<67.98$, $\phi_s>0.8$, $U_s>0.58$
3.4%	97.1%	$67.98\le D/D_p<271.4$, $\phi_s>0.8$, $U_s>0.23$
3.3%	86.5%	$28.55\le D/D_p<189.41$, $\phi_s\le0.8$, $\varepsilon\le0.67$, $U_s>0.66$