*4.3. Corrosivity Category Classification*

When analysing the results of both output layers, represented in each neuron by its corrosion rate value, the neurons were grouped, forming zones mostly corresponding to one type of atmosphere (Table 1). The zones division with different corrosion rates is given in Figure 10. Both C1 and CX categories were filtered out of the dataset due to a lack of consistent data. Thus, the far-left zone corresponds to C2 atmospheres, the left zones to C3, the right zones to C4, and finally, the lower-right end to C5. There is also a transition

between the values so that the C5 are in contact with C4, C4 with C3, etc., demonstrating an optimal training.

**Figure 10.** Corrosion zones according to the environment. (**a**) Corrosion representation (larger circle, more corrosion). (**b**) Corrosivity category representation, according to ISO 9223:2012 standard.

The predicted first-year corrosion rates using SOM trained network were compared with real values. A satisfactory correlation has been obtained (Figure 11), although not all points perfectly matched their counterpoints. The ideal situation would be if the predicted values all lied on the diagonal line. The points tend to be located on the upper side of the graph, meaning that predictions are conservative, and the decisions made based on them can provide greater safety.

**Figure 11.** Predicted first-year corrosion values in micron vs. real first-year corrosion values. The dashed line is the regression line (R<sup>2</sup> = 0.7728). The points situated on the diagonal grey line represent an optimal training.

From the trained network, it is possible to determine the corrosion rate of any situation to be studied. When introducing a new case to the model, it finds the node that most closely resembles its input variables. Thus, the output of the model is the corrosion rate of that node. The uncertainty range is also given, including the minimum and maximum values within each neuron. This can be seen with the following example for a case with the characteristics defined in Table 4.

**Table 4.** Example of model input data.


The case falls into the neuron indicated in Figure 12, which consists of 10 examples.

**Figure 12.** Case study example: the cake portions shown at each node show the contribution of each variable; the larger the size, the greater its final weight.

Table 5 shows all results obtained. Different conclusions can be made by selecting the maximum (Corr\_max), minimum (Corr\_min), and average (Corr\_avg) values of the examples in one single neuron. As a result, when the values with the most or least corrosion occurring within the projects in the neuron are chosen, the optimistic and pessimistic predictions can be obtained. Alternatively, β-distribution is used to determine the 'most probable' rate of Corr\_Zn, using the maximum, minimum, and average values. On the other hand, the category is awarded by the weighted average of the categories in each case. In this case, since all cases are C3, C3 is its category.



Comparing the range given by the model with the range given by the existing standard, it is observed that the latter represents a much higher uncertainty for each corrosivity category. Extending this comparison to the entire study scope, possible model predictions for each category, clustered on similar values and represented by boxplots, can be presented (Figure 13). Although not all categories are equally distributed, they show, in general, narrower intervals.

This study is presented as a possible alternative to the informative procedure of the ISO standard when there is no experimental data available. The results of the informative procedure regarding atmospheric categorisation provide a range of mass losses for each material. The current trend among companies and engineers, when no specific experimental information is available, is to use the highest value of each category to make their decisions. Since corrosion loss values are directly related to the required coating thickness,

the higher the corrosion loss value, the more coating is required. A coating thickness can thus be directly determined by the predicted material's loss.

**Figure 13.** Comparison between each category range offered by the standard using the informative procedure and the possible mean values and uncertainties offered by the model, represented by clustered boxplots on each category.

> The material requirement for coatings can be compared with the largest measurement proposed by the standard in each category and with the value predicted by the model. Following the example above, when using a Zn-coating of 1.6 μm (Corr\_avg) instead of 2.1 μm (maximum in the range given by ISO), a 24% reduction in material's costs is obtained. It is then proposed to carry out this comparison for the rest of the points studied. From a more conservative perspective, comparing the maximum predicted value (Corr\_max) with the maximum proposed by the standard using the informative method can also be used. In this way, uncertainties are also considered. By performing this for all data studied during the evaluation phase, an average saving of 16% in coating material is obtained.
