*by Neeraj Shandilya ^{1+}, Tom Ligthart^{2}, Imelda van Voorde^{3}, Burkhard Stahlmecke^{4}, Simon Clavaguera^{5}, *Yaobo

*Ding*

^{6}and Henk Goede^{1+}Bayesian Belief Networks (BBN) represent a branch of Bayesian modelling where the probability distributions are generally expressed in discrete form and solved analytically.* BBN are expected to be advantageous in the forecasting of next-generation nanomaterials because they can handle missing data, facilitate the learning of causal relationships between variables and show good prediction accuracy also with smaller sample sizes; they also consist of formal rules that can be updated when new information becomes available. *,**

Here we describe the FNN-BBN Shredding Model, which was developed within the framework of FNN, to forecast potential airborne releases of nanomaterials during shredding of nano-enabled product/composite. It combines the effect of material related (blue coloured nodes) and shredding process related variables (green coloured nodes) through a set of intermediate variables (white coloured nodes) to calculate nanomaterial release in terms of discrete distributions of number, size, mass and composition of released particles (individual, aggregated or agglomerated or embedded/associated within the matrix).

**Download the model:** FNN_BBN_Shredding_model.zip

**How to use the model?**

The model works with the Genie 2.1 software- a graphical interface that runs on Windows, OSX and Linux. The software can be downloaded without cost for academic teaching and research use at the following page: https://download.bayesfusion.com/files.html?category=Academia. To open the model, go to ** File** option and click

**. Choose the file “**

*Open Network***”.**

*FNN BBN Shredding model.xdsl***NOTE**: The details about each variable can be retrieved by bringing the cursor on yellow post-it sign at the right side of the bottom of the corresponding node (shown encircled below).

**Example case**

To illustrate how the FNN-BBN model works, an experimental study (Raynor et al., 2012) is shown below as an example. This experimental study involved the shredding of a commercial product- 18CPP091 Forte Nanocomposite manufactured by Noble Polymers (Grand Rapids, Michigan, USA) which was composed of polypropylene resin reinforced with approximately 5%, by mass of montmorillonite nanoclay. During the experiment, the shredding was performed using a 4 kW small scale industrial grade shredder (Cumberland Engineering Corp., South Attleboro, Mass.). The released particles concentration measurements were taken adjacent to the shredder i.e. negligible distance between the source and measurement probe.

In **step 1**, determine the value of each input variable (both material and process related) and then assign it to one of its state in which it lies, as shown in the table below for example.

Values of input variables and the states to which they are assigned

Material related input variable |
Experimental value |
Process related input variable |
Experimental value |

Hardness composite |
State 2: 5-6 mohs | Primary or secondary shredder |
Primary |

Nano object size |
State 1: <10 nm | Number of shafts |
State 1: Single |

Isotropy composite |
State 1: Isotropic | Width of knives |
State 2: 2-5 cm |

Toughness composite |
State 1: Tough | Number of teeth |
State 2: 1-7 |

Brittleness composite |
State 2: Ductile | Sieve used |
State 1: Yes |

Particles nano in composite |
State 2: 1-10 % | Input size |
State 4: >10×10 cm^{2} |

Affinity nanomaterial in matrix |
State 4: Chemically completely inbound | Output size |
State 1: <1×1 cm^{2} |

Dispersion state |
State 1: Well dispersed |

In **step 2**, set the probabilities to 100% for the states in which the input variable values were assigned earlier. This can be done one by one in the following way:

- Right click on any input variable node (for example
*Hardness composite*). A dialogue box pops up.

2. Click on ** Set Evidence** in the dialogue box.

3. Click state 2: ** mohs_5_6**. Consequently, the question mark changes to an arrow sign at the right side of the bottom of the node (shown encircled below). This signifies that the probability of state 2 is set at 100% for

*Hardness composite*.

4. Follow the same procedure for each input variable.

5. Once done for all input variables, the arrow sign should appear as indicated earlier for each input variable node.

In **step 3**, update the model by clicking on the yellow coloured ‘lightning sign’ in the menu bar.

The result corresponding to each output variable is shown in the form of bar charts. The model predicts that there is a probability of 73% that the number of released particles would be less than 10^{3} g^{-1} in the present experimental case. Moreover, their size mode occurs at less than 100 nm with a probability of 49%. There is 88% probability that their mass would be less than 10 µg/kg.

**Author Information**

- TNO Utrechtseweg 48, 3704 HE Zeist, Netherlands
- TNO Princetonlaan 6, 3584 CB Utrecht, Netherlands
- TNO Oude Waalsdorperweg 63, 2597 AK The Hague, Netherlands
- IUTA Bliersheimer Straße 58-60, 47229 Duisburg, Germany
- Univ. Grenoble Alpes, F-38000 Grenoble, France; Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA), LITEN, NanoSafety Platform, F-38054 Grenoble, France
- Institute for Work and Health (IST), Universities of Lausanne and Geneva, Route de la Coniche 2, 1066, Epalinges, Switzerland

*+ corresponding authors contact information:*

*Neeraj Shandilya – neeraj.shandilya@tno.nl*

*Henk Goede – henk.goede@tno.nl*

**References**

* Uusitalo L. Advantages and challenges of Bayesian networks in environmental modelling. Ecological modelling 2 0 3 ( 2 0 0 7 ) 312–318

** Wiesner MR, Bottero JY. A risk forecasting process for nanostructured materials, and nanomanufacturing. Proceedings of the French Academy of Sciences; 2011.