Prediction of cement strength using soft computing techniques
Introduction
The standard 28-day compressive strength test is widely used for the characterisation of cement properties [1]. Compressive strength is the most important cement property, inasmuch as it is the main parameter for quality control [2]. It is a long time for the industry to wait for 28 days to get the experimental results for the compressive cement strength (CCS). Therefore, faster determination of CCS is a need for the cement industry and deserves research interest from the researchers.
There are mainly two different ways for CCS determination: (a) accelerated strength test methods and (b) use of mathematical models. The focus in this paper is on the second one. The most widely used mathematical approach in the past is to use simple regression models [1], [2]. CCS depends on many different factors, which are chemical and physical in nature. Analytical models including the statistical ones (e.g., regression analysis) used to describe the effects of these factors on strength can be very complex [3]. Therefore, the use of soft computing techniques seems a promising approach to the CCS prediction problem. In this study, such an attempt is made by employing gene expression programming (GEP) and neural networks (NNs) for the prediction of the compressive strength of Portland composite cement (PCC). In addition to these techniques, stepwise regression analysis is also used to have an idea about the predicting power of these soft computing techniques in comparison to a classical statistical approach.
Soft computing techniques, namely, NNs and fuzzy logic, were already used in the literature for the prediction of CCS. However, the number of published papers on the subject is very small. Akkurt et al. [3] used NNs for the CCS prediction. They also analysed effects of various parameters on the 28-day strength. Fa-Liang [4] applied fuzzy logic to CCS prediction successfully. Other studies made use of regression analysis. Tsivilis and Parissakis [1] and de Siquera Tango [2] applied regression methods for CCS prediction. Interestingly, the number of papers that make use of the regression analysis is also very small. There is no published work in the literature that makes use of genetic programming (GP) approaches on the prediction of CCS. This paper makes such an attempt by using GEP [5] for the prediction of CCS.
In the following sections of this paper, GEP and NNs are briefly described; then, the model construction for GEP and NNs is explained along with the comparison and discussion of the obtained results.
Section snippets
Brief overview of GEP
In this section, a brief overview of GEP is given for motivation. For a detailed explanation of GEP, refer to Ferreira [5].
GP is proposed by Koza [6]. It is a generalization of genetic algorithms (GAs) [7]. The most general form of a solution to a computer-modelled problem is a computer program. GP takes cognizance of this and attempts to use computer programs as its data representation. Similarly to GA, GP needs only the problem to be defined. Then, the program searches for a solution in a
Brief overview of NNs
In this section, a brief presentation of the basic NNs is given for the novice readers. Many different resources are available in the literature for comprehensive explanations on NNs [9], [10], [11].
NNs, also called parallel distributed processing systems (PDPs) and connectionist systems, are intended for modelling the organizational principles of the central nervous system, with the hope that biologically inspired computing capabilities of the NNs will allow the cognitive and sensory tasks
Data collection
The data used in the GEP, NN, and regression analysis are collected from a cement plant located in Adıyaman, Turkey. The data collected are for a 4-month period (data for 104 days of production). The cement strength testing is performed according to European Standard EN 196-1 [15]. The type of cement used in this research was Cem II/B 32.5R European standard EN 197-1 [16]. The format of the data used in this research is explained in Table 1. There are 19 variables that are considered as the
Model construction and analysis using GEP
The experimental data described in Table 1 is used for the modelling of the 28-day CCS of PCC. The major task is to define the hidden function connecting the input variables (d1, d2, d3, …, d18, d19) and output variable (y). This can also be written in the form of the following equation: y=f(d1, d2, d3, …, d18, d19). The function obtained by the GEP algorithm will be used in predicting the 28-day CCS of the PCC. The parameters used in the GEP algorithm are presented in Table 2. The first three
Model construction and analysis using NNs
In this research, the NN suite, which is known as NeuroSolutions, developed by NeuroDimension [17], is used. Seven different NN architectures are used for the CCS prediction of the PCC. These are multilayer perceptron, generalized feedforward, modular network, Jordan/Elman, self-organizing map, principal component analysis, and recurrent network. The experimental data described in Table 1 are also used for modelling the 28-day CCS of the PCC. The major task is to determine best possible weights
Regression analysis
A stepwise regression analysis is also performed to have an idea about the predictive power of the soft computing techniques, in comparison to a classical statistical approach. The experimental data described in Table 1 is used for modelling the 28-day CCS of the PCC. The major task is to determine the multivariable regression equation connecting the input variables (d1, d2, d3, …, d18, d19) to the output variable (y). The obtained equation will be used in predicting 28-day CCS of the PCC. SPSS
Conclusions
In this study, two soft computing techniques, namely, GEP and NN, are applied to the problem of cement strength prediction. Moreover, the stepwise regression analysis is also applied to the problem to have an idea about the predicting power of these soft computing techniques in comparison to a classical statistical approach. The results obtained from our extensive computational tests have shown that soft computing techniques give far better results than the regression analysis. Moreover, GEP
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