Keywords: FPNN, self organizing, hybrid system, back propagation, concrete compressive strength.

This research presents a novel method of system modelling which is called fuzzy polynomial neural networks (FPNNs). In this paper application of FPNN for approximation of the compressive strength of the concrete is investigated. The implemented FPNN has a hybrid compound architecture that is composed of fuzzy neural networks (FNNs) and polynomial neural networks (PNNs). The FNN viewed as the premise (If-Part) of fuzzy system and the PNN was used as the consequence (Then-Part) of the fuzzy system. A back propagation algorithm and least square estimation are utilized for the tuning of the system in FNN and PNN part of the system, respectively.

The architecture of the proposed model is based on a fuzzy If-Then Macro rule. This macro fuzzy rule is composed of two popular parts: premise(s) and consequence(s). However, in this case, the premise part is a fuzzy neural network that is trained by back propagation algorithm. Moreover, the then-part is a polynomial neural network that is trained by least estimating method. The characteristic of this model is that its structure is of self organizing type and the architecture is formed during the training process [1,2]. In this paper, the main steps of constructing a FPNN for modelling paradigms are explained in detail.

Developed system has been applied to approximate the compressive strength of concrete. In this research, the properties of concrete include fine aggregates (FA), coarse aggregates (CA), water (W), silica fume (SF), super-plasticizer (SP), and cement materials (C). Six different FPNN structures are modelled. These models are trained and tested by collected records, using root means square and correlation coefficient. Finally, these models are compared and evaluated with training and testing pairs. The results of this research show satisfactory models for evaluation of the compressive strength of concrete.

As mentioned above, FPNN models have 6 input variables including concrete mix components (CA, FA, SP, SP, SF, W and C) and one output variable, i.e., compressive strength of concrete. From this point of view, this paper uses more parameters and takes into account two concrete admixtures (SP, SF). The results show that two of developed models (models 3, 5) were rejected because of their poor estimation properties but other models i.e., models 1, 2, 4, 6, in particular the sixth model, have good approximation properties (with RMS=11.6880 and CF=0.8825 for checking records). It has been recognized that with increasing the PD's inputs and orders, the systems approximation performances are improved.

This research has some potential future works. Selection of the best method of the optimization of the proposed system needs further works. Moreover, determination of the kind of polynomials that make better results and the effect of training rated on the system need more efforts.

1

Ivahenko, A.G., "The Group Method of Data Handling: a Rival of Method of Stochastic approximation", Soviet Automatic Control, Vol. 13, No. 3, pp. 43-55 1968.

2

Jang, J.R., "ANFIS: Adaptive-Network-Based Fuzzy Inference System", IEEE Tran. on Systems Man and Cybernetics, Vol. 23, No. 3, pp. 665-685, May-June, 1993. doi:10.1109/21.256541

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