Integrating model tree and modified stepwise regression in concrete slump prediction and steel fabrication estimating

Publication: Canadian Journal of Civil Engineering
18 June 2021


The model tree algorithm of M5 is integrated with the multiple linear regression technique called modified stepwise regression (MSR), resulting in a new method for modeling complex civil engineering problems. We purposefully chose artificial neural networks (ANN) for comparison against the proposed “M5+MSR” because they fall at the two ends of the model interpretability spectrum in machine learning. This research addresses the critical question of how to balance the trade-off between bias, variance and model complexity in machine learning through contrasting “M5+MSR” against other commonly applied methods. In two application cases (Case 1: concrete workability and Case 2: steel fabrication estimating), the proposed “M5+MSR” gave rise to explainable regression tree models featuring substantially reduced complexities against ANN and model prediction errors comparable to ANN. The resulting “M5+MSR” models consistently outperformed ANN in terms of model overfitting metrics by 19% in Case 1 and 21% in Case 2, thus boasting better learning performances. The proposed new method will potentially find applications in tackling a wide range of complicated engineering problems that entail fitting prediction models based on laboratory or field data.


L’algorithme arborescent modèle de M5 est intégré à la technique de régression linéaire multiple appelée régression séquentielle modifiée (RSM), ce qui donne lieu à une nouvelle méthodologie pour la modélisation de problèmes complexes de génie civil. Nous avons délibérément choisi des réseaux de neurones artificiels (RNA) pour les comparer au « M5+RSM » proposé parce qu’ils se situent aux deux extrémités du spectre d’interprétabilité des modèles dans l’apprentissage machine. Cette recherche aborde la question essentielle à savoir comment trouver un compromis entre le biais, la variance et la complexité du modèle dans l’apprentissage machine en comparant « M5+RSM » à d’autres méthodes couramment appliquées. Dans deux cas d’application (cas 1 : maniabilité du béton et cas 2 : estimation de la fabrication de l’acier), le « M5+RSM » proposé a donné lieu à des modèles d’arbre de régression explicables présentant des complexités considérablement réduites par rapport aux RNA et à des erreurs de prédiction du modèle comparables aux RNA. Dans les deux cas, les modèles « M5+RSM » qui en découlent ont constamment surperformé les RNA en termes de paramètres de dépassement de modèle de 19 % dans le cas 1 et de 21 % dans le cas 2, offrant ainsi de meilleures performances d’apprentissage. La nouvelle méthodologie proposée pourrait trouver des applications pour s’attaquer à un large éventail de problèmes techniques complexes qui impliquent des modèles de prévision d’ajustement basés sur des données de laboratoire ou de terrain. [Traduit par la Rédaction]

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Published In

cover image Canadian Journal of Civil Engineering
Canadian Journal of Civil Engineering
Volume 49Number 4April 2022
Pages: 478 - 486


Received: 16 November 2020
Accepted: 10 June 2021
Published online: 18 June 2021


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Key Words

  1. multiple linear regression
  2. model tree
  3. modified stepwise regression
  4. concrete slump
  5. steel fabrication
  6. estimating


  1. régression linéaire multiple
  2. arbre modèle
  3. régression séquentielle modifiée
  4. affaissement du béton
  5. fabrication de l’acier
  6. estimation



Arash Mohsenijam
Supreme Group, 28169 96 Ave., Acheson, AB T7X 6J7, Canada.
Department of Civil and Environmental Engineering, University of Alberta, 116 St & 85 Ave., Edmonton, AB T6G 2R3, Canada.
Serhii Naumets
Department of Civil and Environmental Engineering, University of Alberta, 116 St & 85 Ave., Edmonton, AB T6G 2R3, Canada.

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