An effort has been made to develop concrete compressive strength prediction models with the help of two emerging data mining techniques, namely, Artificial Neural Networks (ANNs) and Genetic Programming (GP). The data for analysis and model development was collected at 28, 56, and 91day curing periods through experiments conducted in the laboratory under standard controlled conditions. The developed models have also been tested on in situ concrete data taken from literature. A comparison of the prediction results obtained using both the models is presented and it can be inferred that the ANN model with the training function LevenbergMarquardt (LM) for the prediction of concrete compressive strength is the best prediction tool.
Conventional concrete is a mixture of cement, water, and coarse and fine aggregates. Supplementary components such as chemical and mineral admixtures may be added to the basic concrete ingredients to enhance its properties in fresh or hardened state. The procedure of selecting appropriate ingredients for concrete and its relative amount with the aim of producing concrete of obligatory strength, workability, and durability as costspinning as possible is termed mix design. The development of tools to find the optimized mix proportions has been the subject of research during the last more than four decades. The aim of any proportioning process is to determine an ample and costeffective material to make up the concrete, which can be used in its fabrication, as near as possible to the chosen properties. The engineering properties of cementbased materials and special concretes depend on various parameters including the nonhomogeneous nature of their components and the intrinsically different properties of various elements and sometimes on the twin and/or contradictory effects of some ingredients on the overall concrete performance. Therefore, a clear understanding of such complex behavior is needed in order to successfully use these materials in various engineered structures. In recent years, many researchers have been working on developing accurate concrete compressive strength prediction models [
The experimental data used for the prediction of concrete compressive strength in the present study have been taken from the research work conducted by Kumar [
Details of proportions for concrete mixes without fly ash.
S. number  Mix designation  W/CM ratio  Mix proportions 
Cement content (C) 

1  MD1  0.53  1 : 1.58 : 3.05  375.00 
2  MD2  0.50  1 : 1.43 : 2.82  400.00 
3  MD3  0.53  1 : 1.54 : 2.99  400.00 
4  MD4  0.47  1 : 1.28 : 2.58  425.00 
5  MD5  0.49  1 : 1.39 : 2.77  425.00 
6  MD6  0.44  1 : 1.14 : 2.35  450.00 
7  MD7  0.47  1 : 1.25 : 2.54  450.00 
8  MD8  0.42  1 : 1.05 : 2.19  475.00 
9  MD9  0.44  1 : 1.19 : 2.46  475.00 
10  MD10  0.53  1 : 1.58 : 3.05  375.00 
11  MD11  0.50  1 : 1.43 : 2.82  400.00 
12  MD12  0.53  1 : 1.54 : 2.99  400.00 
13  MD13  0.47  1 : 1.28 : 2.58  425.00 
14  MD14  0.49  1 : 1.39 : 2.77  425.00 
15  MD15  0.51  1 : 1.51 : 2.95  425.00 
16  MD16  0.44  1 : 1.14 : 2.35  450.00 
17  MD17  0.47  1 : 1.25 : 2.54  450.00 
18  MD18  0.49  1 : 1.37 : 2.73  450.00 
19  MD19  0.42  1 : 1.05 : 2.19  475.00 
20  MD20  0.44  1 : 1.19 : 2.46  475.00 
21  MD21  0.46  1 : 1.23 : 2.51  475.00 
22  MD22  0.52  1 : 1.43 : 2.02  425.00 
23  MD23  0.49  1 : 1.29 : 1.86  450.00 
24  MD24  0.51  1 : 0.391 : 1.9  450.00 
25  MD25  0.46  1 : 1.17 : 1.72  475.00 
26  MD26  0.48  1 : 1.26 : 1.83  475.00 
27  MD27  0.51  1 : 1.39 : 3.26  350.00 
28  MD28  0.54  1 : 1.49 : 3.42  350.00 
29  MD29  0.48  1 : 1.25 : 2.99  375.00 
30  MD30  0.51  1 : 1.35 : 3.19  375.00 
31  MD31  0.45  1 : 1.10 : 2.70  400.00 
32  MD32  0.48  1 : 1.21 : 2.92  400.00 
33  MD33  0.42  1 : 0.98 : 2.47  425.00 
34  MD34  0.45  1 : 1.09 : 2.68  425.00 
35  MD35  0.42  1 : 0.98 : 2.45  450.00 
36  MD36  0.54  1 : 1.49 : 3.42  350.00 
37  MD37  0.51  1 : 1.35 : 3.19  375.00 
38  MD38  0.48  1 : 1.21 : 2.92  400.00 
39  MD39  0.45  1 : 1.09 : 2.68  425.00 
40  MD40  0.42  1 : 0.98 : 2.45  450.00 
41  MD41  0.53  1 : 1.47 : 2.41  375.00 
42  MD42  0.50  1 : 1.32 : 2.21  400.00 
43  MD43  0.53  1 : 1.44 : 2.36  400.00 
44  MD44  0.47  1 : 1.19 : 2.03  425.00 
45  MD45  0.49  1 : 1.29 : 2.18  425.00 
46  MD46  0.44  1 : 1.07 : 1.86  450.00 
47  MD47  0.47  1 : 1.17 : 2.00  450.00 
48  MD48  0.42  1 : 0.95 : 1.68  475.00 
49  MD49  0.44  1 : 1.06 : 1.84  475.00 
Details of compressive strength of concrete mixes without fly ash after curing for 28, 56, and 91 days.
S. number  Mix 
W/CM 
28 d 
56 d 
91 d 

1  MD1  0.53  36.84  40.92  44.52 
2  MD2  0.50  43.13  50.22  51.97 
3  MD3  0.53  38.58  45.51  47.49 
4  MD4  0.47  47.16  51.25  54.27 
5  MD5  0.49  45.05  50.72  52.85 
6  MD6  0.44  49.63  54.48  58.04 
7  MD7  0.47  47.42  51.34  55.30 
8  MD8  0.42  54.01  57.91  60.15 
9  MD9  0.44  50.05  55.72  58.31 
10  MD10  0.53  37.81  43.50  47.55 
11  MD11  0.50  44.11  50.98  52.56 
12  MD12  0.53  40.90  46.56  51.07 
13  MD13  0.47  47.51  52.92  54.47 
14  MD14  0.49  45.30  51.47  53.09 
15  MD15  0.51  42.54  49.05  51.19 
16  MD16  0.44  52.03  56.26  59.19 
17  MD17  0.47  48.74  53.42  55.03 
18  MD18  0.49  46.59  53.21  53.67 
19  MD19  0.42  54.49  58.65  63.07 
20  MD20  0.44  53.06  56.67  62.57 
21  MD21  0.46  49.18  54.04  57.10 
22  MD22  0.52  40.02  46.92  48.48 
23  MD23  0.49  45.25  50.43  53.09 
24  MD24  0.51  42.68  48.54  49.63 
25  MD25  0.46  48.67  53.48  56.50 
26  MD26  0.48  45.52  50.97  53.63 
27  MD27  0.51  39.52  43.31  46.13 
28  MD28  0.54  31.66  37.18  43.92 
29  MD29  0.48  42.73  48.23  52.23 
30  MD30  0.51  40.69  44.46  46.42 
31  MD31  0.45  47.99  52.95  55.51 
32  MD32  0.48  44.89  51.20  53.85 
33  MD33  0.42  51.25  57.55  59.50 
34  MD34  0.45  49.05  54.14  57.35 
35  MD35  0.42  53.69  57.77  59.89 
36  MD36  0.54  36.64  43.46  46.55 
37  MD37  0.51  41.57  46.81  50.04 
38  MD38  0.48  46.22  52.58  53.07 
39  MD39  0.45  50.35  56.02  58.32 
40  MD40  0.42  54.11  58.52  62.28 
41  MD41  0.53  37.30  43.51  46.63 
42  MD42  0.50  44.04  50.53  52.55 
43  MD43  0.53  39.61  46.09  48.17 
44  MD44  0.47  47.37  51.31  54.77 
45  MD45  0.49  44.69  50.69  52.75 
46  MD46  0.44  50.93  55.71  59.05 
47  MD47  0.47  48.08  52.63  55.61 
48  MD48  0.42  54.14  58.21  61.11 
49  MD49  0.44  51.31  56.37  59.51 
Details of proportions for concrete mixes with 0.15 fly ash replacement.
S. number  Mix designation  W/CM ratio  Mix proportions 
Cement content (C) 
Fly ash content (FA) 

1  MDF1  0.45  1 : 0.15 : 1.10 : 2.70  400.00  60.00 
2  MDF2  0.42  1 : 0.15 : 0.98 : 2.46  425.00  63.75 
3  MDF3  0.45  1 : 0.15 : 1.09 : 2.68  425.00  63.75 
4  MDF4  0.47  1 : 0.15 : 1.28 : 2.58  425.00  63.75 
5  MDF5  0.42  1 : 0.15 : 0.98 : 2.45  450.00  67.50 
6  MDF6  0.44  1 : 0.15 : 1.14 : 2.35  450.00  67.50 
7  MDF7  0.47  1 : 0.15 : 1.25 : 2.54  450.00  67.50 
8  MDF8  0.42  1 : 0.15 : 1.05 : 2.19  475.00  71.25 
9  MDF9  0.44  1 : 0.15 : 1.19 : 2.46  475.00  71.25 
10  MDF10  0.45  1 : 0.15 : 1.09 : 2.68  425.00  63.75 
11  MDF11  0.47  1 : 0.15 : 1.28 : 2.58  425.00  63.75 
12  MDF12  0.42  1 : 0.15 : 0.98 : 2.45  450.00  67.50 
13  MDF13  0.44  1 : 0.15 : 1.14 : 2.35  450.00  67.50 
14  MDF14  0.47  1 : 0.15 : 1.25 : 2.54  450.00  67.50 
15  MDF15  0.49  1 : 0.15 : 1.37 : 2.73  450.00  67.50 
16  MDF16  0.42  1 : 0.15 : 1.05 : 2.19  475.00  71.25 
17  MDF17  0.44  1 : 0.15 : 1.19 : 2.46  475.00  71.25 
18  MDF18  0.46  1 : 0.15 : 1.23 : 2.51  475.00  71.25 
19  MDF19  0.47  1 : 0.15 : 1.19 : 2.03  425.00  63.75 
20  MDF20  0.44  1 : 0.15 : 1.07 : 1.86  450.00  67.50 
21  MDF21  0.47  1 : 0.15 : 1.17 : 2.00  450.00  67.50 
22  MDF22  0.49  1 : 0.15 : 1.29 : 1.86  450.00  67.50 
23  MDF23  0.51  1 : 0.15 : 1.39 : 1.98  450.00  67.50 
24  MDF24  0.42  1 : 0.15 : 0.95 : 1.68  475.00  71.25 
25  MDF25  0.44  1 : 0.15 : 1.06 : 1.84  475.00  71.25 
26  MDF26  0.46  1 : 0.15 : 1.17 : 1.72  475.00  71.25 
27  MDF27  0.48  1 : 0.15 : 1.26 : 1.83  475.00  71.25 
Details of compressive strength of concrete mixes with fly ash after curing of 28, 56, and 91 days.
S. number  Mix designation  W/CM 
28 d 
56 d 
91 d 

1  MDF1  0.45  39.04  47.65  52.20 
2  MDF2  0.42  45.09  50.21  55.75 
3  MDF3  0.45  41.14  48.67  52.69 
4  MDF4  0.47  38.35  43.27  50.42 
5  MDF5  0.42  46.13  51.01  56.51 
6  MDF6  0.44  42.50  49.17  53.11 
7  MDF7  0.47  39.58  44.02  51.07 
8  MDF8  0.42  47.34  52.30  57.70 
9  MDF9  0.44  43.55  49.79  53.79 
10  MDF10  0.45  42.01  49.68  53.39 
11  MDF11  0.47  38.85  44.96  50.50 
12  MDF12  0.42  47.25  51.95  57.17 
13  MDF13  0.44  43.09  50.30  53.67 
14  MDF14  0.47  40.26  45.30  51.62 
15  MDF15  0.49  37.15  44.52  48.08 
16  MDF16  0.42  48.41  53.58  58.19 
17  MDF17  0.44  44.02  51.81  54.12 
18  MDF18  0.46  40.73  45.95  52.10 
19  MDF19  0.47  38.90  43.20  50.50 
20  MDF20  0.44  43.22  49.93  53.62 
21  MDF21  0.47  39.85  44.61  51.42 
22  MDF22  0.49  36.87  41.25  47.30 
23  MDF23  0.51  35.23  40.05  46.11 
24  MDF24  0.42  47.94  53.05  57.82 
25  MDF25  0.44  43.87  50.48  54.38 
26  MDF26  0.46  40.34  45.61  52.39 
27  MDF27  0.48  37.65  42.28  48.55 
An Artificial Neural Network is a network of artificial neurons, which can reveal intricate global performance, determined by the associations between the processing elements and element parameters. In a neural network model, simple nodes, which are called “neurons” or “neurodes” or “processing elements” (PEs) or “units,” are linked jointly to form a network of units, hence called “Artificial Neural Network.”
ANNs consist of the following three major essentials [
Topology: organization and interconnection of a neural network into layers.
Learning: related with the information storage in the network.
Recall: retrieval of information from the network.
A successful application of an ANN for the prediction of compressive strength of concrete needs a good conception of the impact of different internal parameters. For ANN architectures and training of the same, the significant internal parameters include learning rate, initial weights, number of training epochs, number of hidden layers, and number of neurons in every hidden layer and transfer functions for hidden layers and output layers [
In the starting, most of the variants are examined for the network performance optimization. LevenbergMarquardt training (LM) was found to be most suitable for the data patterns for the prediction of concrete compressive strength during trail approach. In the present study, two types of datasets have been taken: dataset 1 has 49 tuples and this dataset is without the substitution of cement with FA and dataset 2 has 27 tuples and this dataset is with 0.15 substitution of cement with FA. Further each dataset is categorized according to the curing time, that is, 28 days, 56 days, and 91 days. The four numbers of input parameters have been engaged, that is, water, cement, coarse aggregate, and fine aggregate, when the output parameter is 28day compressive strength. The five numbers of input parameters have been taken including the 28day compressive strength as input parameter, that is, water, cement, coarse aggregate, fine aggregate, and 28day compressive strength, when the output parameter is 56day compressive strength. The six numbers of input parameters have been used including the 28day compressive strength and 56day compressive strength as input parameters, that is, water, cement, coarse aggregate, fine aggregate, 28day compressive strength, and 56day compressive strength, when the output parameter is 91day compressive strength. For all the experiments in model 1, tansig(
Architecture selected for model 1 (ANN model).
Parameters  Values  Description 

Dataset  Dataset 1: 49 (without fly ash) 
Dataset is of two types. One is without any substitution of cement by fly ash and the second one is with 15% of the cement replaced by fly ash. Dataset 1 is of 49 tuples in total. Dataset 2 is of 27 tuples in total 


Number of input parameters  04 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA)); in case of 05 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA), 28day compressive strength (CS28)); in case of 06 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA), 28day compressive strength (CS28), 56day compressive strength (CS56)). Fly ash (FA) is used with dataset 2 only; all other parameters are the same as dataset 1  When output is 28 days, then the number of input parameters is 04; when output is 56 days, the number of input parameters is 05 as 28day compressive strength is taken as input; when output is 91 days, the number of input parameters is 06 as 28day compressive strength and 56day compressive strength are also taken as input. In dataset 2, FA is replacing 15% of the cement 


Activation function 1  tansig( 



Activation function 2  purelin( 
purelin( 


Performance function  MSE 



Net.trainparam.lr  0.01  Learning rate 


Net.trainfcn  trainlm  LevenbergMarquardt algorithm 


Net.trainparam.epochs  10000  Maximum number of epochs to train 


Net.trainparam.goal  0.000001  Performance goal 


Number of hidden layer neurons  50  — 


Number of output layer neurons  1  — 
Genetic Programming (GP) is a group of instructions and a fitness process to determine how well a machine has performed a particular task. It is a specialization of genetic algorithm (GA) where each node is a computer program. It is a technique used to optimize residents of computer program in line with a suitable site determined by a program’s capability to carry out a prearranged computational condition. The three genetic operations are as follows:
Crossover operates on two programs that are chosen as per their fitness and produces two subprograms. The two random nodes are chosen from each program and then the resultant subtrees are swapped, producing two new programs. These new programs turned into a part of the new generation of programs to be participated further. Population here is increased by 2.
Reproduction: the next important operation is accomplished by copying an elected member from the present generation to the subsequent generation as per the fitness norm. Population here is increased by 1.
Mutation: in GP, mutation becomes a significant operator that provides assortment to the population. One individual is chosen as per the fitness. A subprogram is substituted by another one randomly. The mutant is popped into the new population. Population is then increased by 1.
Koza [
The five numbers of input parameters have been engaged including the 28day compressive strength as input parameter, that is, water, cement, coarse aggregate, fine aggregate, and 28day compressive strength, when the output parameter is 56day compressive strength. The six numbers of input parameters have been used including the 28day compressive strength and 56day compressive strength as input parameters, that is, water, cement, fine aggregate, coarse aggregate, 28day compressive strength, and 56day compressive strength, when the output parameter is 91day compressive strength. The population size (Mu) and the number of children produced (Lamda) have been taken 100 and 150, respectively. The greater the number of generations, the greater the chance of evolving a solution, so the number of generations is taken as 100000 for this model. The values for the parameters crossover rate and mutation rate have been selected as 0.70 and
Architecture selected for model 2 (GP model).
Parameters  Values  Description 

Initial population size  Dataset 1: 49 (without fly ash) 
Dataset is of two types. One is without any substitution of cement by fly ash and the second one is with 0.15 of the cement replaced by fly ash. Dataset 1 is of 49 tuples in total. Dataset 2 is of 27 tuples in total 


Number of input parameters  04 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA)). 05 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA), 28day compressive strength (CS28)), 06 (cement (C), water (W), fine aggregate (sand), coarse aggregate (CA), 28day compressive strength (CS28), 56day compressive strength (CS56)). Fly ash (FA) is used with dataset 2 only; all other parameters are the same as dataset 1  When output is 28 days, then the number of input parameters is 04; when output is 56 days, the number of input parameters is 05 as 28day compressive strength is taken as input; when output is 91 days, the number of input parameters is 06 as 28day compressive strength and 56day compressive strength are also taken as input. In dataset 2, FA is replacing 15% of the cement 


Function set  +, −, 
Set of functions used 


Training percentage  75  — 


Selection method  Tournament  — 


Tournament size of replacement  3  — 


Maximum generations  100000  Maximum number of iterations 


Crossover  0.7  Probability of crossover 


Mutation 

Probability of mutation 


Mu  100  Population size 


Lamda  150  Number of children produced 


Objectives  COD, RMSE  Coefficient of determination, root mean square error 
Namyong et al. [
The objective of the present study was to explore the applicability of the suggested models, that is, model 1 and model 2, for the prediction of concrete compressive strength. This section presents the comparative investigation of results obtained from these approaches and quantitative assessment of the models’ predictive abilities. For model 1, the LM algorithm is used for training, whereas tansigmoid is used as an activation function for evaluating the prediction accuracy parameters. The results, as presented in Table
Results of model 1 (ANN) and model 2 (GP).
Model 1:  Training of the dataset  

Artificial Neural Network (ANN)  Epochs taken  Coefficient of determination ( 
Root mean square error (RMSE)  
Result number  Curing time  
R1 (without fly ash)  28 days  04  0.898  6.9762 
56 days  05  0.998  1.2712  
91 days  03  01  7.3640  
R2 (with 0.15 fly ash)  28 days  05  0.996  3.8809 
56 days  04  01  3.6873  
91 days  04  01  2.2181  


Model 2: Genetic Programming (GP)  


28 days  Not applicable  0.77438  0.01067  
R3 (without fly ash)  56 days  0.99999  0.00550  
91 days  0.99999  0.00644  
28 days  0.93781  0.01415  
R4 (with 0.15 fly ash)  56 days  0.94483  0.00910  
91 days  0.96681  0.00689 
In model 2, the addition is chosen as the linking utility. The values of
From the results, tabulated in Table
Comparison between actual and predicted values of 28 d compressive strength of concrete.
Comparison between actual and predicted values of 56 d compressive strength of concrete.
Comparison between actual and predicted values of 91 d compressive strength of concrete.
Comparison between actual and predicted values of 28 d compressive strength of concrete with FA.
Comparison between actual and predicted values of 56 d compressive strength of concrete with FA.
Comparison between actual and predicted values of 91 d compressive strength of concrete with FA.
It can be clearly observed from these figures that model 1 predicts compressive strength values very near to the experimentally obtained values as compared to model 2 results. To further test the efficacy and reliability of the models, the in situ compressive strength data at curing age of 28 days (as provided in Namyong et al. [
Validation of the proposed model of 28 d compressive strength of concrete with in situ dataset as per [
On the comparative analysis of GP and ANN techniques, used for the prediction of concrete compressive strength without and with FA, it can be concluded that ANN model is the most reliable technique for the purpose. The RMSE values, so obtained, are small enough to indicate that the estimates are most precise and the trained networks supply superior results. According to statistics, if a proposed model gives
The authors declare that there is no conflict of interests regarding the publication of this paper.