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Prediction of CBR and resilient modulus of crushed waste rocks using machine learning models

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Abstract

California bearing ratio (CBR) and resilient modulus are critical factors for designing pavements. However, the measurement of CBR and resilient modulus of crushed waste rocks that are widely used for the construction of mine haul roads can be costly and time-consuming which is often prohibitive, especially since service lifetime of haul roads is relatively short. The recent development of machine learning techniques makes it possible to develop more efficient models, but many algorithms exist and it is not always clear which one is better for predicting CBR and resilient modulus. The main objective of this study was therefore to evaluate and compare the performance of multiple models, such as multiple linear regression (MLR), k-nearest neighbors (KNN), decision tree (DT), random forest (RF), multilayer perceptron (MLP), and neuroevolution of augmenting topologies (NEAT) for predicting CBR and resilient modulus of crushed waste rocks. Thirty-nine and 2320 datasets, obtained from a series of CBR and repeated load triaxial tests, were applied to develop CBR and resilient modulus models, respectively. The study of input features and hyperparameters was conducted to determine the optimal architecture of the machine learning models. A comparison study showed that RF models provided better results with coefficient of determination R2 greater than 0.9. NEAT models showed good generalizability and simple structure although their performance was lower than RF models.

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Acknowledgements

This work was carried out with the financial support from FRQNT and the industrial partners of Research Institute on Mines and the Environment (http://irme.ca/). The repeated load triaxial and CBR test equipment used in this study was acquired with a CFI grant.

Funding

Fonds Québécois de la Recherche sur la Nature et les Technologies, 2017-MI-202860, Thomas Pabst

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Authors and Affiliations

  1. Department of Civil, Geological, and Mining Engineering, Polytechnique Montreal, C.P. 6079, Station Centre-Ville, Montréal, QC, H3C 3A7, Canada

    Shengpeng Hao & Thomas Pabst

  2. Research Institute On Mines and Environment (RIME), Montréal, Canada

    Shengpeng Hao & Thomas Pabst

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  1. Shengpeng Hao
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Appendix

Appendix

System configuration and parameters in the NEAT models

Startup parameters

Settings

Definition

Number of generations

30,000

The number of generations to perform for a run

Population size

150

The number of individuals in each generation

Activation function

ReLU

The default activation function attribute assigned to hidden neurons

Activation mutation rate

0.0

The probability that mutation will replace the neuron’s activation function

Bias initial mean

0.0

The mean of the normal/Gaussian distribution

Bias initial standard deviation

1.0

The standard deviation of the normal/Gaussian distribution

Bias max. value

30.0

The maximum allowed bias value

Bias min. value

− 30.0

The minimum allowed bias value

Bias mutation power

0.5

The standard deviation of the zero-centered normal/Gaussian distribution from which a bias value mutation is drawn

Bias mutation rate

0.7

The probability that mutation will change the bias of a neuron by adding a random value

Bias replace rate

0.1

The probability that mutation will replace the bias of a neuron with a newly chosen random value

Compatibility disjoint coefficient

1.0

The coefficient for the disjoint and excess gene counts’ contribution to the network distance

Compatibility weight coefficient

0.5

The coefficient for each weight, bias, or response multiplier difference’s contribution to the network distance (for homologous neurons or connections)

Connection add probability

0.5

The probability that mutation will add a connection between existing neurons

Connection delete probability

0.2

The probability that mutation will delete an existing connection

Enabled default

True

The default enabled attribute of newly created connections

Enabled mutation rate

0.03

The probability that mutation will replace the enabled status of a connection

Feed forward

True

Generated networks will not be allowed to have recurrent connections

Initial connection

Full

Each input neurons are connected to all output neurons

Node add probability

0.3

The probability that mutation will add a new neuron

Node delete probability

0.25

The probability that mutation will delete an existing neuron

Number of hidden neurons

0

The number of hidden neurons to add to each genome in the initial population

Number of input neurons

8 and 3

The number of input neurons, through which the network receives inputs

Number of output neurons

1

The number of output neurons, to which the network delivers outputs

Weight initial mean

0.0

The mean of the normal/Gaussian distribution used to select weight attribute values for new connections

Weight initial standard deviation

1.0

The standard deviation of the normal/Gaussian distribution used to select weight values for new connections

Weight max. value

30.0

The maximum allowed weight value

Weight min. value

− 30.0

The minimum allowed weight value

Weight mutation power

0.5

The standard deviation of the zero-centered normal/Gaussian distribution from which a weight value mutation is drawn

Weight mutation rate

0.8

The probability that mutation will change the weight of a connection by adding a random value

Weight replace rate

0.1

The probability that mutation will replace the weight of a connection with a newly chosen random value

Compatibility threshold

3.0

Individuals whose network distance is less than this threshold are considered to be in the same species

Max. stagnation

20

Species that have not shown improvement in more than this number of generations will be considered stagnant and removed

Species elitism

2

The number of species that will be protected from stagnation; mainly intended to prevent total extinctions caused by all species becoming stagnant before new species arise

Elitism

2

The number of fittest individuals in each species that will be preserved as is from one generation to the next

Survival threshold

0.2

The fraction for each species allowed to reproduce each generation

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Hao, S., Pabst, T. Prediction of CBR and resilient modulus of crushed waste rocks using machine learning models. Acta Geotech. 17, 1383–1402 (2022). https://doi.org/10.1007/s11440-022-01472-1

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