Artificial neural network which can be identified as the data processing systems, are algorithms simulating the functioning of the biologic neurons. An Adaptive Neuro-Fuzzy Inference System (ANFIS) is a hybrid predictive model which uses both of neural network and fuzzy logic to generate mapping relationship between inputs and outputs . The structure of this model consists of five layers in which each layer is constructed by several nodes. As in a neural network, in an ANFIS structure the inputs of each layer are gained by the nodes from pervious layer. Figure 1b describes an ANFIS structure. It can be inferred from figure 1b that the network includes m inputs (X1…Xm), which each one consists of n Membership Functions (MFs). Moreover, a layer with R fuzzy rules and also an output layers are contributed to construction of this model. Number of nodes in first layer can be calculated as the product of m as number of inputs and n as number MFs (N=m.n). The number of nodes in other layers (layer 2-4) relates to number of fuzzy rules (R).The layers of an ANFIS model can be summarized as follows:Figure 2:
Structure of adaptive neuro-fuzzy inference system graphene is a monoatomic layer of carbon atoms in a honeycomb lattice [1,6]. It is one of the strongest materials ever used with tensile strengths over 130 GP making it 200 times as strong as steel .The unique chemical structure of Graphene has been attractive for biologists and biomedical properties .
First layer: Fuzzification layer
In this layer crisp inputs transforms to linguistic type Aij (such as bad, middle, good) by using membership functions. The output of this layer can be expressed as:
Where μij is the jth membership function for the input Xi. Several types of MFs are used, for example, triangular, trapezoidal and generalized bell function. In this study, the Triangular and Gaussian functions were selected for ultimate tensile strength and elongation respectively. The mathematical equations for Triangular and Gaussian type of membership function are expressed as equations 2 and 3 respectively:
Where a and b vary the width of the curve and c locates the center of the curve. The parameter b should be positive. These parameters are named as premise parameters.
Second layer: Product layer
Third layer: Normalized layer
Fourth layer: Defuzzification
Fifth layer: Output layer (for further details refer to reference 4)
The Root Mean Square Error (RMSE) function is applied to this network for inspection of trained model performances. It can be calculated by following equation:
Where, M is the total number of training sample, Sz is the real output value, and Yz is the ANFIS output value in training .
In order to correlate the relationship between input parameters and responses, this model has been employed. The first step is to identify the input (e.g., laser power, powder feeding rate, carrier gas flow rate, etc). And output (e.g., catchment efficiency and clad height or weight) parameters of the process. These parameters can be either quantitative or qualitative depending on the research objectives. To this end, researchers rely on either experimental or simulation works (or a combination of both) to optimize the laser cladding process.
Laser cladding has a great potential to benefit these cutting-edge technologies, as laser deposition techniques can provide a revolutionary technique for making micro structure fabrication. Optomec Inc., is a company in the USA, has advanced a new process for making micro coating on substrates which is in the range of 10 to 50μm.
The laser cladding process has drawn great attention both from researchers and users. Consequently with the advent of artificial intelligent system especially ANFIS. We strongly believe that optimizing the laser cladding process for hybrid alloys of graphene/metallic material will significantly improve the characterization of response parameters. Moreover, ANFIS model can be applied to generate mapping relationship between process factors and responses. Also, it will estimate the output parameters with maximum accuracy. In other words, the main advantages of the ANFIS scheme are: computationally efficient, well-adaptable with optimization and adaptive techniques. To use the effect of input parameters on the outputs, MATLAB (ANFIS toolbox) can be used. Furthermore, the effect of process factors (processing inputs) on the outputs can be studied through plots derived out of models developed in ANFIS simulation.