The use of machine learning in boron-based geopolymers: Function approximation of compressive strength by ANN and GP
Introduction
Boroaluminosilicate (BASG) binder is developed by partially substituting the aluminium atoms with boron within the geopolymer network. Mechanical, physical, and microstructural performance of BASG is characterised in the previous works [3], [4], [5], [6]. The mechanical behaviour of geopolymers, compressive strength, in particular, is influenced by either raw materials or alkaline solution characteristics [2], [15], [18]. Changing the type and chemical composition of these two parts affect the final compressive strength directly. As the first example, the one investigated the role of ground granulated blast furnace slag (GGBS) in the development of the fly ash-based geopolymers [19]. They obtained that addition of only 15% of GGBS to the fly ash contributes to strength development of geopolymers by more than 30 MPa. They maintain that the presence of free calcium ions in the slag might result in enhancement of fly ash dissolution and subsequently raising the strength. As the second instance [11], has investigated the variation in the compressive strength of the fly ash-based geopolymers prepared by sodium compounds with different strength. They employed two types of activators, one sodium hydroxide solution with different molarities and one mixture of sodium hydroxide and sodium silicate with the same molarity. Compressive strength evaluation was carried out in 3, 7, 14, and 28 days of curing. According to the obtained results, mixing sodium silicate with sodium hydroxide resulted in an increase in the compressive strength of the samples in all cases. It is observed that samples with longer curing time are stronger. Therefore, the maximum compressive strength is acquired when a 28-day geopolymer with 16 molar NaOH mixed with Na2SiO3. Authors believed that the addition of sodium silicate to sodium hydroxide led to an increase in dissolution of silicon and aluminium compounds of the raw materials. This can be a reason for strength development due to the incorporation of sodium silicate to the activator.
This work aims to develop a network and a function that are able to model and to predict the compressive strength of BASG based on the certain effective parameters. Despite conventional geopolymers and OPC concrete that have been modelled by the researchers, the literature fails to present a practical model for this new type of construction materials. Hence, attempts for developing a reliable method and formula for the compressive strength of BASG binders are worthwhile and novel. The authors of the current paper have tried to fill the current gap by investigating two methods of machine learning in the compressive strength prediction of boron-based geopolymers. There are different approaches to model the correlation between effective variables and behaviour of geopolymers, ANN [14], genetic algorithm [26], and regression techniques [29] for instance. ANN has recently become very popular among researchers to develop models for behavioural predictions [1], [10], [13], [25], [27], [17]. ANN is a supervised machine learning algorithm that develops a network based on neurons, their communication algorithm and processing. By learning from the latent behavioural information of experimental parameters and results, a network is trained to correlate certain inputs and outputs [28]. The application of ANN in predicting unconfined compressive strength (UCS) of geopolymers was investigated in ref [14]. The input parameters of alkali to binder ratio (A/B), percentage FA (%FA), liquid limit (LL), the concentration (M), Na/Al ratio, Si/Al ratio, plasticity index (PI), and percentage GGBS (%S) in addition to output parameter of 28-day UCS were considered. One hidden layer with a variable number of neurons was adopted for this modelling. Mean square and mean absolute percentage error, as well as the linear correlation coefficient, evaluated the efficiency of the proposed networks. According to the obtained statistical measurements, the optimum performance was relating to a model comprising nine neurons on the hidden layer with a linear correlation coefficient of 0.982, the mean square error of 1.50, and mean absolute percentage error of 8.34%. The sigmoid transfer function for the hidden layer and pure linear transfer function for the output layer was proposed.
Moreover, genetic programming (GP), which is based on the genetic algorithm proposed by Koza [12], is utilised for developing a function to approximate the compressive strength of BASG synthesised from Australian industrial by-products. The application of this method in civil engineering has been recently evaluated in many works [9], [8], [7], [21]. GP is an evolutionary methodology stimulated by biological evolution in order to resolve the problems of correlating independent input to output via nonlinear or linear models. The main utilised operators in the approach are mutation and crossover, which is comprehensively discussed in the literature [12]. The regression evaluation parameter of R-squared in addition to the statistical errors of mean absolute error (MAE), root mean square Error (RMSE), representative area element (RAE), and root relative squared error (RRSE) are extracted in order to evaluate the performance of the model.
Section snippets
Data collection and experiments
The required data for this paper was collected from previous works [3], [4], [5], [6] in addition to certain complementary experiments that are explained in details. Five variables are chosen as input including the percentage of the fly ash (%F), the percentage of the GGBS (%S), as well as the ratio of boron, silicon, and sodium ions in the alkaline solution (B/AA, S/AA, and N/AA respectively). The selected output of this prediction is the compressive strength of BASG samples after 7 days of
ANn
This study employs an MLP algorithm to perform ANN modelling. MLP is a non-linear function approximation algorithm, which is based on a supervised learning process of introduced matrices of features and targets. MATLAB software version R2016 is employed to perform the ANN modelling of compressive strength of the BASG with five input parameters. Multilayer perceptron artificial neural network that was developed first in 1958 [20], was utilised to make a connection between inputs and targets.
ANn
To evaluate the performance of the MLP-ANN certain parameters are considered including coefficient of regression R in addition to statistical characteristics of errors between real targets and modelled outputs. The performance of the network is assessed for training, test, and all data separately. As stated in 8.3, the number of the neurons on the hidden layer varies in 10, 15, and 20. The best performance was attained from 20 of neurons. Therefore, the results of MLP-ANN with one hidden layer
Conclusions
The application of multilayer perceptron artificial neural network and genetic programming in the prediction of the compressive strength of boroaluminosilicate geopolymers, developed from fly ash and slag, has been evaluated. Five influential input parameters including the percentage of the fly ash, the percentage of the slag, in addition to the ratios of boron, silicon and sodium in the alkaline activator were considered for modelling. In the ANN modelling, the best performance, in terms of
Acknowledgment
The authors acknowledge the Australian Research Council for providing funding on a discovery project entitled “Functionally Graded Modelling of Geopolymer and Portland Cement Concretes”.
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