Memory based mould growth model using real-world datasets

We propose an adapted VTT model using dynamically varying threshold humidities for growth activation based on memory of recent conditions. Optimal thresholds, and the extent to which previous conditions can affect thresholds, is determined via machine learning approaches using data and mould survey results from residential properties. Additionally, we determine if an explicit condensation weighting improves the model.


Introduction
Smart monitoring has been suggested as a means for identifying properties at risk of mould [1].Multiple deterministic mould growth prediction models are available, notably VTT, WUFI Mold Index and the ANSI/ASHRAE 160 [2][3][4].These models were developed by fitting growth rates to results found from mould grown in various stable laboratory configurations of temperature, relative humidity ( ) and surface material. Amongst the most prominent of models, the VTT model maps temperature and levels to a continuously  adjusting 'mould index' which describes the growth rate.For smaller than a critical relative humidity  () growth rates decrease steadily to zero, whereas growth increases up to a maximum for .In mould  >=  biology, this is due to growth activation only being possible when the surrounding environment is moist enough for osmosis to occur through permeable cell wall membranes [6].However, the has been found to vary  significantly across studies, depending heavily on environmental conditions and the material mould is grown on [7].Since indoor environments can be highly dynamic and possess varied surfaces (for example ceramic tiling, plasterboard and soft fabric in furnishings like carpets and curtains), determining a generally applicable for  indoor risk prediction presents a challenge.
In this work we first seek to identify an optimal static value.We then consider whether model  performance can be improved by allowing this value to vary dynamically based on previous conditions.Rooms monitored in UK residential properties supply environmental data for the model.Ground truth of mould growth is established through resident completed surveys.We assess model performance by converting survey and model results into binary predictions about the existence of mould using threshold based approaches.

Methodology
In the VTT model a non-static value has been partially introduced.Here is described as being 80% for   temperatures greater than 20 degrees Celsius, and temperature driven when .However, does   < 20  not go below 79% in the regime, which is higher than reported thresholds in other studies [8,9]. < 20 Indeed, the VTT model results were trained exclusively on wooden surfaces kept in stable laboratory conditions.Noting that in the VTT model growth rates do not decline in the 6 to 24 hour period following conditions becoming unfavorable, and only decrease slowly after that, we propose mould has memory, with previously favourable conditions enabling a lower . This memory can be encoded as: where f is a function of the Memory retained at time t.We propose that f be a polynomial with form: The coefficients of f will be determined utilising a learning approach.In the case Memory is found to have no effect then B=C=0.In any case, A represents a constant multiplicative adjustment to , yielding a refined  By following a similar approach to [5], which performed regression analysis on different parameters of VTT by evaluating the model risk prediction against self reported occurrences of mould according to resident surveys, we seek to find optimal values for A, B , C. We will also consider results across differing degrees of memory loss L. Models will be assessed using multiple performance metrics (balanced accuracy, sensitivity, precision).

Additionally, condensation (
) may be favourable for mould growth [10].This could be through a  = 100% combination of liquid water quenching spores as well as the mechanical disturbance causing spores to become airborne and so able to colonise new sites.Condensation effects were not explored in the VTT model.Whilst permanently submerging spores in liquid water inhibits aeration, preventing growth [6], condensation may not completely blanket a surface.This paper seeks to quantify any additional favorability of condensation by immediately elevating the VTT mould index to the maximum whenever condensation occurs.

Conclusion
This work outlines a means for identifying a generally relevant critical humidity threshold for activation of new mould growth indoors, if one exists.Using regression analysis on real-world property data we consider whether encoding an effective memory based adjustment to this threshold improves performance in residential environments.Additionally, condensation effects are discussed.The emergence of IoT monitoring devices makes the above prescriptions relevant to a growing body of datasets.

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Corresponding author.+447572156765.tom@homelink.co The Author(s).This is an open access article distributed under the terms of the Creative Commons Attribution Licence (CC-BY) 4.0 https://creativecommons.org/licenses/by/4.0,which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.DOI: 10.14293/ICMB230050 2nd International Conference on Moisture in Buildings (ICMB23), online, 3-4 July 2023 =0representative for all time.The Memory function is a time weighted function of previous growth rates: () = ℎ=0  ∑ ( − ℎ) • (ℎ),where g is a function of growth rates at time t, N the number of historic hours to remember growth for and w(h) is a weighting applied to growth from h hours ago.There are multiple possible implementations of w but we consider the following: equal time weighting, L=1 represents a linear decrease with time, and L>1 represents exponentially increasing penalisation for older times.Larger L implies quicker memory loss.The function g describing growth rates is as per the VTT model for both scenarios and .Whilst the  >=   <  VTT model depends on multiple parameters, selection of specific ones means it can effectively be reduced to a function of one variable, .Then,   , where M depends on L  ' (  ) ∝  −  −  2