J. Cent. South Univ. (2019) 26: 2906-2914

DOI: https://doi.org/10.1007/s11771-019-4223-3

Neuro-fuzzy systems in determining light weight concrete strength

Seyed Vahid RAZAVI TOSEE¹, Mehdi NIKOO²

1. Department of Civil Engineering, Jundi-Shapur University of Technology, Dezful, Iran;

2. Young Researchers and Elite Club, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: The adaptive neuro-fuzzy inference systems (ANFIS) are widely used in the concrete technology. In this research, the compressive strength of light weight concrete was determined. To this end, the scoria percentage and curing day variables were used as the input parameters, and compressive strength and tensile strength were used as the output parameters. In addition, 100 patterns were used, 70% of which were used for training and 30% were used for testing. To assess the precision of the neuro-fuzzy system, it was compared using two linear regression models. The comparisons were carried out in the training and testing phases. Research results revealed that the neuro-fuzzy systems model offers more potential, flexibility, and precision than the statistical models.

Key words: neuro-fuzzy systems; compressive strength; light weight concrete; linear regression model

Cite this article as: Seyed Vahid RAZAVI TOSEE, Mehdi NIKOO. Neuro-fuzzy systems in determining light weight concrete strength [J]. Journal of Central South University, 2019, 26(10): 2906-2914. DOI: https://doi.org/10.1007/ s11771-019-4223-3.

1 Introduction

The unit weight of light weight concrete (LWC) normally varies between 300 and 2000 kg/m³. Considering the satisfactory mechanical resistance of light weight concrete, it is used in building technologies as it can reduce the building weight. Some of the most common building materials are acoustic planes, floor and roof covering, and roof concrete blocks [1].

TOPCU et al [2] predicted the compressive strength of a concrete specimen mixed with fly ash using the adaptive neuro-fuzzy systems. They used 180 7-, 28- and 90-d concrete samples with 52 mix designs. The input parameters were the curing days, Portland cement, water, sand, crushed stone I (4-8 mm), crushed stone II (8-16 mm), high range water reducing agent replacement ratio, fly ash replacement ratio and CaO. Their findings revealed that the adaptive neuro-fuzzy systems are highly capable of determining the compressive strength of concrete.

ALSHIHRI et al [3] determined the compressive strength of LWC using the artificial neural network (ANN) model. They used 3-, 7-, 14-, and 28-d mix designs in their research and used the feed-forward back propagation and cascade correlation methods to complete the modeling process. They considered different variables such as sand, water/cement ratio, light weight fine aggregate, light weight coarse aggregate, and silica fume to examine the samples. The results revealed that the ANN model satisfactorily estimates the LWC compressive strength. SARIDEMIR et al [4] predicted the long-term effects of GGBFS on the compressive strength of concrete using the artificial neural network model and the fuzzy logic. They used 284 specimens in their research along with variables such as the age of specimen, Portland cement, ground granulated blast furnace slag, water and aggregate contents to measure compressive strength of 3-, 7-, 14-, 28-, 63-, 90-, 119-, 180-, and 365-d specimens. Their findings revealed that the adaptive neuro-fuzzy systems are highly capable of determining the compressive strength of concrete. OZCAN et al [5] compared the artificial neural network and fuzzy logic methods in predicting the compressive strength of microsilica concrete. They used 48 specimens in their research along with the water/cement ratio, three different cement dosages and three partial silica fume replacement ratios. Their findings revealed that the adaptive neuro-fuzzy system is an alternative to the method of predicting microsilica concrete compressive strength.

SLONSKI [6] determined the compressive strength of high-strength concrete (HSC) using the artificial neural network model. They used the artificial neural network, nonlinear regression, and Markov chain models and reported that the Bayesian approach offers more precise results in determining the compressive strength of concrete using the artificial neural network method. MADANDOUST et al [7] studied the compressive strength of the concrete specimens with ultrasonic pulse velocity using the GMGH artificial neural network method. The research parameters included concrete age, water/cement ratio and fine/coarse aggregate ratio. Investigation results revealed that the GMDH neural network is a strong predictor of concrete compressive strength.

SIDDIQUE et al [8] predicted the compressive strength of self-compacting concrete (SCC) specimens with fly ash using the artificial neural network model. They compared the models developed to predict the 28-d compressive strength of concrete based on the ANN technique. The research variables were cement, sand, coarse aggregate and fly ash. The output parameter was the compressive strength on the 7th, 28th, and 90th d. Their findings indicated that the ANN model offers a considerable potential to determine the compressive strength of concrete. CHENG et al [9] calculated the compressive strength of high-strength concrete using the fuzzy logic and the support vector machines (SVM) model. They used the adaptive neuro-fuzzy method and support vector machines method and found that the ANFIS model offers more precise results than the SVM method. ABOLPOUR et al [10] estimated the compressive strength of concrete using the fuzzy models. They used 1030 specimens and the following input parameters: weight percent of cement, water, blast furnace slag, fly ash, superplasticizer, fine aggregate, coarse aggregate, and age of the concrete. They reported that the fuzzy models used for determining the concrete compressive strength increased the model precision.

DIAB et al [11] predicted the compressive strength of concrete under the long-term impact of sulfate using the neural network model. The inputs in this research were cement content, water/cement ratio, 3CaO·Al₂O₃ (C3A) content, and sulfate concentration. According to their findings, the artificial neural network model could be used to easily predict the compressive strength of concrete specimens of any age with different sulfate concentrations and mix designs. DESHPANDE et al [12] determined the compressive strength of recycled aggregate concrete using the artificial neural network model, non-linear model, and the model tree. The inputs in their research were the cubic meter proportions of cement, natural fine aggregate, natural coarse aggregates, recycled aggregates, admixture and water. They stated that the artificial neural network calculated the concrete compressive strength with high precision.

SKRZYPCZAK et al [13] used an adaptation of the fuzzy method to determine the compressive strength of concrete based on numerical analyses.

The use of artificial neural networks (as intelligent systems) in the concrete technology has increased with the regression and neural network models [14]. Self-organization involves the utilization of neural networks and the genetic algorithm (GA) to determine the compressive strength of concrete systems [15] and mechanical properties of sandcrete materials [16]. In addition, neural networks have been used in determining damages caused by concrete frames [17, 18].

In this paper, first experimental data were produced, and sampling was carried out with respect to scoria percentage and curing day. Afterwards, different models were proposed using the fuzzy theory. To determine the compressive strength of light weight concrete, the artificial neural networks model was used as a proper tool. To assess the neuro-fuzzy system of concern, it was compared two linear regression models. The paper arrangement is illustrated in Figure 1.

Figure 1 Flowchart of research process

2 Adaptive neuro-fuzzy inference system (ANFIS) and regression model

2.1 Adaptive neuro-fuzzy systems

The neuro-fuzzy inference system was introduced by JANG [19], who stated that the adaptive neuro-fuzzy inference system (ANFIS) is a neural network with a performance and function similar to the Takagi-Sugeno inference model. The ANFIS system is a powerful and popular modeling technique that integrates the established artificial neural network learning rules into the transparency of the fuzzy logic theory within the framework of fuzzy networks [20]. In these systems, the membership functions must be adjusted manually after trial and error. The FIS model functions like a white box. In other words, the model designers can discover the way of attaining the model goal. On the other hand, it is possible to learn the rules through artificial neural networks, but these networks function like black boxes in the process of attaining goals [21].

The ANFIS system is recognized as a global assessment system to answer complicated problems. The system consists of a set of adaptive multilayer networks with transitional feedbacks. The system contains input and output variables and Takagi- Sugeno fuzzy rules. The fuzzy logic mechanism of the ANFIS model are described in the following using the “if-then” rule/command for the first-order Sugeno fuzzy model [20].

Rule 1: if x is A₁ and y is B₁, then

f₁=p₁x+q₁y+r₁                            (1)

Rule 2: if x is A₂ and y is B₂, then

f₂=p₂x+q₂y+r₂                                            (2)

The ANFIS framework consists of 5 layers with different functions. However, the layer nodes perform similarly. The ANFIS structure is depicted in Figure 2. As can be seen, the ANFIS structure is composed of five different layers that are explained fully in the following [20].

Figure 2 Simple structure of adaptive fuzzy system [20]

Layer 1: This layer is in charge of the fuzzification of the input attribute values into 0 to 1. Values such as the membership functions are defined for the i-th node in this layer [20]:

                               (3)

where x is the i-th node input and A_i is the language label of the function.

Layer 2: Each command is a node in ANFIS that uses the product to find the adaptive factor, w_i. The input signals are multiplied in this layer to produce the output shown in Eq. (4) [20].

                    (4)

Layer 3: Membership values are normalized in this layer. Equation (5) shows the formulation of the output severity for the i-th node in this layer [20].

                        (5)

Layer 4: This layer establishes a link between the input and output values as shown in Eq. (6) [20].

                        (6)

where is the output of layer 3, and {p_i, q_i, r_i} is a parameter set [20].

Layer 5: This layer is known as the de- fuzzification layer. It is composed of a node and concludes the previous node input signals to yield a single value. In this layer, each output command is added to the input layer. The overall input to this layer is calculated using Eq. (7) [20].

                      (7)

2.2 Multiple linear regression model

One of the statistical models used in this research was the multiple linear regression model, in which two or several independent variables considerably influence the dependent variable. The equation for this model is written as Eq. (9) [22].

      (8)

In Eq. (8), y is the dependent variable; x₁, x₂, … are the independent variables; a₁, a₂, a₃, … are the regression coefficients [22].

3 Material and method

3.1 Introducing research data

In this paper, 5% to 100% of scoria was obtained from Tabriz City, Iran. The scoria percentage was multiplied by 5 to obtain the sand and gravel contents required for the concrete. Scoria is a grayish white substance with open and closed pores, a rough surface and angular particles. The specific density of the aggregates is less than 1 g/cm³ based on the porosity of the substance. This type of scoria is formed by the accumulation of volcanic ashes, a slight temperature decrease and bubbles resulting from the gas and vapor emissions [1]. Table 1 presents the properties of the research data [1].

Table 1 Properties of input and output research parameters [1]

To examine the research parameters, a hundred 15 cm×30 cm lightweight concrete specimens were built, and their compressive strength and tensile strength were measured [1].

3.2 Methodology

The research model was the adaptive neuro- fuzzy inference system, and a separate model was used for each of the concrete compressive strength and tensile strength output variables. The properties of these two systems are listed in Table 2. The membership functions of each input are depicted in Figures 3 and 4.

The input parameters of these networks were the curing day, S_q and scoria percentage, S_a, and the output parameters of each system were light weight concrete compressive strength and tensile strength. Among the 100 data patterns, 70% were used for training and 30% were used for testing. The analytical results of the training and testing phases with the ANFIS model are listed in Table 2, and Table 3 presents the mean absolute error (MAE),age absolute error (AAE), root mean square error (RMSE), mean square error (MSE), the convergence coefficient (R²), and the slope of the straight line.

Table 2 Properties of adaptive neuro-fuzzy inference system for compressive strength and tensile strength of light weight concrete

Figure 3 Membership function of scoria percentage (S_a) as input parameter

Figure 4 Membership function of curing day (S_q) as input parameter

According to Table 3, the ANFIS model determines the LWC compressive and tensile strength with satisfactory precision. Figures 5-8 present the results of the best model.

3.3 Validation

In this paper, various linear regression models of the research input and output variables were studied in MiniTab. The best multiple linear and non-linear regression models matching the LWC compressive and tensile strength data are shown in Eqs. (9) and (10). Table 4 also shows the statistical criteria results.

y₁=146.83-0.139x₁+0.795x₂             (9)

y₂=17.888-0.0323x₁+0.0909x₂           (10)

In Eq. (9), y₁, x₁, x₂ and y₂ denote the compressive strength, scoria percentage, curing days, and tensile strength, respectively. In the multiple linear regression model, the R² coefficient for the lightweight concrete strength parameters in the training and testing phases is determined using Table 4 based on the model requirements. The results are shown in Figures 9-12.

In this paper, various linear regression models of the input and output variables were studied in MiniTab 17. The most appropriate linear regression coefficients for compressive and tensile strength are presented in Table 4, which shows the R² coefficient and straight line slope values of the linear regression model in the training and testing phases.

For the final analysis of the models, the best state of each model was selected. As a result, the ANFIS and LR models were selected as the best models. Tables 3 and 4 present the resulting concrete strength values.

Table 3 Results of statistical criteria for LWC compressive and tensile strength in ANFIS

Figure 5 Experimental and calculated values of LWC compressive strength using ANFIS model in training phase

Figure 6 Experimental and calculated values of LWC compressive strength using ANFIS model in testing phase

According to the line equations fitted to the calculated and observed values of each model and the respective coefficients of determination, the statistical results are listed in Table 4. As suggested by these results, the adaptive neuro-fuzzy systems yield more precise LWC strength values than the multiple linear regression model (Figures 13-16).

Figure 7 Experimental and calculated values of LWC tensile strength using ANFIS model in training phase

Figure 8 Experimental and calculated values of LWC tensile strength using ANFIS model in testing phase

4 Conclusions

1) The results of the proposed method on the structure of artificial neural network showed that the fuzzy system works successfully.

2) In the best ANFIS model to determine compressive strength of light-weight concrete, R² coefficient in training and testing stages are 0.9894 and 0.9798 respectively. Also the slopes of straight line in this model, in both steps, are 0.9861 and 1.0199, which shows that this model has high accuracy. In this model, the statistical parameters of AAE, RMSE, MSE and MAE have small values of 2.70, 4.95, 24.47 and 4.26, respectively, in the testing stage, which indicates that this model has small error.

Table 4 Results of statistical criteria of linear regression model for LWC compressive and tensile strength

Figure 9 Experimental and calculated LWC compressive strength values obtained using linear regression model in training phase

Figure 10 Experimental and calculated LWC compressive strength values obtained using linear regression model in testing phase

Figure 11 Experimental and calculated LWC tensile strength values obtained using linear regression model in training phase

Figure 12 Experimental and calculated LWC tensile strength values obtained using linear regression model in testing phase

Figure 13 LWC compressive strength values resulted from different models in training phase

Figure 14 LWC compressive strength values resulting from different models in testing phase

3) In the best ANFIS model to determine tensile strength of light-weight concrete, R² coefficient in training and testing stages has the values of 0.983 and 0.9652 respectively. Also the slopes of straight line in this model, in both stages, are 0.983 and 1.0246, showing that this model has high accuracy. In this model, the statistical parameters of AAE, RMSE, MSE, and MAE have small values of 3.65, 0.81, 0.66 and 0.68 respectively in the testing stage, which indicates that this model has small error.

Figure 15 LWC compressive tensile values resulted from different models in training phase

Figure 16 LWC tensile strength values resulted from different models in testing phase

4) The statistical model used in this research is a multiple linear regression used to determine compressive and tensile strength of light-weight concrete. In this model, the R² coefficient in training and testing stages has the values of 0.484 and 0.4307 respectively for compressive strength, and the values of 0.4769 and 0.4211 for tensile strength.

5) To evaluate the adaptive neuro-fuzzy inference system, its model was compared to multiple linear regression model. The results showed that the ANFIS model for determining the strength of light-weight concrete, is more accurate and flexible in comparison to the multiple regression model.

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(Edited by ZHENG Yu-tong)

中文导读

神经模糊系统确定轻量化混凝土强度

摘要：目前，自适应神经模糊推理系统(ANFIS)在混凝土技术中得到了广泛的应用。本研究利用神经模糊系统确定了轻量化混凝土的抗压强度。以废渣百分率和固化天数作为网络的输入参数，以抗压强度和抗拉强度作为输出参数。实验选用了100个模式，其中70%用于训练，30%用于测试。为了评估神经模糊系统的精度，比较了神经模糊系统和统计模型(LR)两种线性回归模型的训练和测试阶段。结果表明，神经模糊系统模型比统计模型具有更大的潜力、适应性性和精度。

关键词：神经模糊系统；抗压强度；轻量化混凝土；线性回归模型

Received date: 2018-03-04; Accepted date: 2018-12-11

Corresponding author: Seyed Vahid RAZAVI TOSEE, PhD; Tel: +989183886109; E-mail: vahidrazaviii@gmail.com; ORCID: 0000- 0002-8036-9478