PSI - Issue 77

Hugo Mesquita Vasconcelos et al. / Procedia Structural Integrity 77 (2026) 601–610 Hugo Mesquita Vasconcelos/ Structural Integrity Procedia 00 (2026) 000–000

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no more complex then (a+b)+c as the organisation in addition is arbitrary. On the contrary, ax(b+c) requires a non arbitrary organisation of addition and multiplication. Apart from the distributive law being a higher stage, as multiplication is the repeated addition of groups of equal sizes, we can state that in the mathematical domain, the order of hierarchical complexity of the three concepts is: Addition, Multiplication, and Distributive Properties. Commons and Pekker (2008) Through the usage of the MHC, the development throughout the vertical stages gets more proficient, enabling more efficient learning, as shown by Commons and Robinett (2013) or Leite et al. (2023). 2.2. Structuring the Orders of Hierarchical Complexity for Vessel Noise Recognition Identifying which boat type, or class, is passing by a hydrophone solely from the sound wave produced by its hull and/or motor is an understandably complex task. It is straightforward to see that a simpler judgment is to decide whether a recording contains only background or a passing vessel, whereas it is far more demanding to infer speed and direction, or to pinpoint a specific boat, from that same soundwave. To assess the instrumentalization of the MHC learning approach in this domain, it is therefore necessary to define its corresponding Order of Hierarchical Complexity (OHC), or, for the simplicity of the proposed work, just a 3-stage portion of the entire OHC for vessel noise recognition. Although the MHC defines all stages to be able to describe any behaviour, the lowest orders describe pre representational, sensorimotor coordination and simple conditioned responses that precede symbolic categorization. In human development, such capacities emerge from prenatal reflexes and early sensorimotor organization and only later give rise to stable conceptual structures. For the vessel-noise task, an already operating system at Stage 6 (Sentential) is assumed—perceiving acoustic waveforms as “sound” and treating them as meaningful sequences. Following Commons’ general formulation, Stage 7, named Pre-operational, is characterized by simple discriminations; Stage 8, Primary, by basic classifications; Stage 9, Concrete, by coordination of classifications. These definitions do not depend on age, culture, or mechanism; they indicate how tasks increase in order by requiring the non-arbitrary coordination of prior actions, as defined by Commons (2007). On this basis, the 7 th , 8 th and 9 th stages of the OHC for vessel noise recognition are proposed as follows. Stage 7, Pre-operational, corresponds to presence/absence discrimination: determining whether background alone is heard or whether vessel sound is present satisfies Stage 7’s criterion of a single, stable discrimination. Stage 8, Primary, maps to coarse grouping—for example, understanding an underwater noise as a small, medium, or large vessel—since this requires a basic classification that preserves the prior discrimination while introducing group membership. Stage 9, Concrete, maps to class identification, where grouping is refined into a determinate class (e.g., cargo, tanker, passenger), coordinating the earlier classification with additional constraints to resolve near neighbours. This assignment respects the MHC requirement that higher orders are achieved by coordinating and constraining the accomplishments of lower ones rather than by appending arbitrary features. It yields a principled hierarchy for vessel noise recognition that is independent of who or what performs the judgments, and that can be evaluated quantitatively using the same formal criteria that motivate the model defined by Commons (2007) and in accordance with the approach by Commons and Pekker (2008). 2.3. Dataset To determine whether learning through the stages of the MHC yields more efficient learning, a vessel-noise dataset was required for the development and training of the AI models. For this purpose, one of the largest publicly available collections was selected: the Ocean Networks Canada (ONC (2025)) hydrophone recordings from the Strait of Georgia, in which underwater acoustic data are paired with Automatic Identification System (AIS)-based vessel annotations and made accessible by Domingos et al. (2022b). The recordings were initiated in 2017 using an icListen AF hydrophone installed approximately 147 m below sea level. For the present work, the subset covering October 2018 to December 2019 was extracted, yielding 1,593 raw WAV files with a combined duration of 284 hours. The recordings are highly variable in length, with an average of