1. Introduction

2. Experimental Design and Analysis

2.3. Adaptive Network Based Fuzzy Inference System

Adaptive Neuro-Fuzzy Inference System (ANFIS), introduced by Jang in 1993 [52], that has gained remarkable attention from researchers, is a hybrid forecasting model that uses both neural networks and fuzzy logic which is a method for generating mapping relationships between inputs and outputs. ANFIS provides highly efficient models for approximation not only in neuro-fuzzy systems but also in various other machine learning techniques. Thus, the shortcomings of neural network black boxes that are unable to explain decisions and the weaknesses of fuzzy logic where learning relies on personal experience can be overcome. In ANFIS, the learning capabilities and relational structure of artificial neural networks are integrated with the decision-making mechanism of fuzzy logic. ANFIS, like artificial neural networks, utilises a training dataset to achieve sample learning of the rule base in the fuzzy logic system. The prediction of mechanical properties of welding using an ANFIS has the advantages of fast modelling and high prediction accuracy, which provides an effective way to solve the problems of difficult prediction models and low prediction accuracy due to the highly nonlinear nature of the welding process. Figure 2 depicts the architecture of ANFIS. It is deduced from Figure 2 that the network consists of three inputs (X₁, X₂, X₃), where each input is organized by 3 membership functions. In addition, the layer containing 27 fuzzy rules and the output layer are useful at building the model. The number of nodes in the first layer can be calculated as the product of 3 (number of inputs) and 3 (number of fuzzy functions) (9). The number of nodes in the other layers (layers 2-4) is linked to the number of fuzzy rules (27). In Figure 2, the basic structure of the ANFIS model is shown. In this example, a five-layer neural network that simulates the operation of a fuzzy inference system as shown in Figure 3 is used. Figure 2 shows the topology of the proposed ANFIS for the hardness yield. Each node in the same layer of the architecture as shown in Figure 2 has a similar function. Square nodes indicate nodes with adjustable parameters, and circular nodes indicate nodes without adjustable parameters. For more details on the implementation of the ANFIS network, it is refered to the literature [22]. ANFIS uses membership functions for several sets while employing the linear functions of Sugeno type for the rule output. Various types of membership functions (MF)are used, such as triangular, trapezoidal, gaussian, and bell functions. For example of Gaussian type of MF, the mathematical equation is:

Figure 2. A framework of ANFIS model with five layers including fuzzy membership layer, fuzzification layer, normalisation layer, defuzzification layer and output layer.

Figure 2. A framework of ANFIS model with five layers including fuzzy membership layer, fuzzification layer, normalisation layer, defuzzification layer and output layer.

Figure 3. Three inputs and one output fuzzy inference system for laser-coated BN/SiC/Ni welds.

Figure 3. Three inputs and one output fuzzy inference system for laser-coated BN/SiC/Ni welds.

$$\mathsf{\mu }\left(\mathrm{x},\mathrm{a},\mathrm{b},\mathrm{c}\right)=\exp \left[-{\left(\frac{\mathit{x}-\mathit{c}}{\mathit{a}}\right)}^2\right]$$

(2)

where Gauss’s one-dimensional graph is the shape of the characteristic symmetric solution “bell curve”, where a is the height of the curve’s peaks, b is the coordinates of the centre of the peaks, and c is called the standard deviation, which characterises the width of the bell shape. ANFIS has done all the five essential processes of fuzzy control, i.e., input layer, membership layer, fuzzification layer, normalisation layer and defuzzification, which constitute an adaptive neuro-fuzzy system by using a learning algorithm of neural networks that automatically extracts rules from the source data of the input and output samples. Its structure of the model was made by merging adaptive network and fuzzy inference system, which functionally inherited the explainability character of the fuzzy inference system and the learning ability of the adaptive network, which is able to modify the parameters of the system according to the a previous knowledge, so as to make the output of the system closer to the real output. The architecture of the neuro-fuzzy model consists of five unique adaptive layers. Takagi and Sugeno proposed the T-S fuzzy model in 1985. The model was later called Sugeno fuzzy model. It is a nonlinear model that expresses the dynamic properties of complex systems and is the most commonly used fuzzy inference model. Figure 3 shows a neural network with five layers in which the ANFIS model was trained. The input values, such as SiC, laser power and travel speed, are converted to fuzzy values by means of a membership function. A example of a simple fuzzy inference system, a first-order model of fuzzy Sugeno that is a typical rule base, which contains two If-Then rules can be expressed as follows

Rule _i: If x₁ is A_1s, x₂ is B_1s,…, and x_s is C_is; then y_i=f(x₁,x₂,…,x_n) i=1,2,…,M

(3)

where x_i (i=1,2,..,s)is the antecedent input, A_1s, B_1s, and C_1s are membership function and f(x₁,x₂,…,x_s) represents the outputs in the consequent part. Typically y_i=f(x₁,x₂,…,x_s) is a polynomial. The following is a brief description of the Sugeno first-order model with two input variables.

Layer 1: The inputs x₁, x₂, x₃ are fuzzified by means of a membership function, which is transformed to obtain the degree of membership of the linguistic types A1, A2, A3, B1, B2, B3, C1, C2, C3 (e.g., Large, Medium, Small) in the interval [0,1]. The output of layer 1, O_ij, can be expressed as

$$O_{i1}={\mu }_{ij}\left(X_i\right),i=1,\dots ,3,j=1,\dots ,3$$

(4)

where μ_ij is the j^th membership function for the input X_i.

Layer 2: The firing strength of each rule is obtained by multiplying the degrees of membership of each rule;the weight functions wi for the next layer is defined.

O_i2 = wi = µ_Ai(x₁)µ_Bi(x₂) µ_Ci(x₃), i = 1, 2,3

(5)

Layer 3: The firing strength of each rule obtained from layer 2 is normalised to represent the firing weight of that rule in the whole rule base.

$$O{i}_3=\overline{w_i}=\frac{w_i}{\sum _{i=1}^3{w}_i}$$

(6)

Layer 4: The results of a calculated output of a linear combinator of the input functions using normalised weights.

$$\mathrm{O}{\mathrm{i}}_4={\overline{w}}_i{f}_{i}i=1,2,3$$

(7)

Layer 5: The output of the calculation is the sum of the results of the linear combination of the normalized weights of each rule.

$$O_{i5}={\sum }_{i=1}^n{\overline{\mathrm{w}}}_{\mathrm{i}}{f}_i({\mathrm{x}}_{\mathrm{i}})i=1,2,3$$

(8)

In this paper, the parameters in the model are classified into premise and outcome parameters, which are learnt by back propagation algorithm with the least squares calculation. Least squares are used in the forward propagation process to evaluate the subsequent parameters, whereas the backward propagation process updates the premise parameters. There are two important steps in executing an ANFIS model which are training and testing the data. The total number of experimental data to be used in constructing the ANFIS model is 36. In this study, 25 training data and 11 test data are used. The Root Mean Square Error (RMSE) function is employed to examine the performance of the training model by applying it to this network. Its computational formula is as follows:

$$RMSE=\sqrt{\frac{1}{\mathrm{M}}\sum _{i=1}^{\mathrm{M}}({y_i-d_{i)}}^2}$$

(9)

where M is the total number of training sample, d_i is the real output value, and y_i is the ANFIS output value in training algorithms.

3. Experimental Results and Discussion

3.2. Microstructure of the Weld Zone for Laser-Coated NB/SiC/Ni Welds by Laser Cladding

A magnified 2000X SEM picture of the microstructures in the cross-section of each of the laser-coated NB/SiC/Ni weld can be seen in Figure 3, which shows that the molten zone of the weld is characterised by various sizes of grains. During the laser cladding process, different forms of carbides and precipitates are generated in the composite coatings due to the differences in the carbide, nitride and nickel content of the molten pool. There are large white areas and small black areas in the melting zone, whereas in the lower hardness areas, coarse crystalline with plate-like grains grows, while in the higher hardness areas, the particles are fine with white carbide structure. Unfortunately, this study has failed to avoid partial dissolution of silicon carbide on the molten pool. This is due to the different temperature gradient of the melt pool between the white and dark zones, which affects the corresponding structure of the solidification zone by cladding welds. In addition, Table 2 lists the EDS results for the typical areas labelled Tests 4, 9, 13 and 14 in Figure 3. The powder is pre-positioned on the substrate by laser cladding where the powder is melt-mixed with the substrate. The SEM micrographs of the laser coatings are shown in Figure 3a labeled Test 4, where large grains can be seen, with plate-like coarse grains growing within the weld zone, along with crystalline structures of Si particles at the grain boundaries. The chemical compositions of the BN/SiC/Ni welds obtained by EDS are listed in Table 3. In EDS, the elements O and Fe are higher, C is lower, and Ni and Si are even lower. The cross-section of the cladding zone shown in Figure 3b indicated Test9 contains obvious black dissolved Si dendrites, no pores and cracks, and irregularly distributed aggregates in the lower-left region, while the white region contains fine precipitated carbides and the lower-right region has some incompletely melted Si. The thickness of the melt layer is about 4-6 µm, which is much smaller than the thicknesses produced by the other fractions. Comparing Figure 3a with Table 2, it is clear that Figure 3b is harder. Furthermore, the EDS analysis shows that Figure 4b has less Si and C elements while more O and Ni elements than Figure 4a. This is due to the different temperature gradients in the melt pool, which affects the solidification time during deposits thereby resulting in different corresponding structures. As shown in Figure 3c, the grain growth is complete, but some of the black particles have not melted and accumulated at the grain boundaries, where pin-like eutectic crystals can be seen in the grains, as shown in the white part of the SEM micrograph. Typical areas labelled Test 13 in Figure 4c and the EDS results are shown in Table 3. An analysis of the distribution of elements in the melting zone by X-ray diffraction shows that the white areas are rich in O and Fe, while C, Si and Ni are less abundant, mainly iron oxide (Fe₂O₃), h-BN, γ-(Ni, Fe), B₄C and iron silicide (Fe₂Si) [12]. As shown in Figure 3d, most of the plate-like carbides and a few unmelted SiC and BN particles are clearly visible in the zone, which contains iron clusters in grey colour and precipitated carbides when melted. It is the hardest of the 18 groups. Table 3 analyses of test 14 using EDS. The analysis of test 14 by EDS is shown in Table 2. In the molten region, O decreases to 5,250% and Ni increases to 1.050, while the remaining elements show little change, which is not evidenced by the EDS analysis. Therefore, it seems to be necessary to use the microstructure of the molten zone as a support for the results.

Figure 4. Comparison of signal-to-noise ratio and microhardness with a standard deviation of laser-coated NB/SiC/ Ni welds.

Figure 4. Comparison of signal-to-noise ratio and microhardness with a standard deviation of laser-coated NB/SiC/ Ni welds.

Figure 5. shows the distribution of microhardness values for BN/SiC/Ni welds with tests 4, 9, 13 and 14, including the melting zone, the heat affected zone and the matrix.

Figure 5. shows the distribution of microhardness values for BN/SiC/Ni welds with tests 4, 9, 13 and 14, including the melting zone, the heat affected zone and the matrix.

Figure 6. SEM microstructures of various tests in the deposits by laser cladding including (a) trial4;( b) trial9; (c) trial13; (d) trial14.

Figure 6. SEM microstructures of various tests in the deposits by laser cladding including (a) trial4;( b) trial9; (c) trial13; (d) trial14.

Figure 7. The elemental intensity of the EDS surface analysis with Figure 6 in a laser-coated weld.

Figure 7. The elemental intensity of the EDS surface analysis with Figure 6 in a laser-coated weld.

3.3. Effect of Designing with Ternary SiC/BN/Ni Mixtures on Hardness Yields

In order to solve the problem of the mixture ratio of three materials using mixture design, it effectively controls the mixture properties of lased cladding. The effects of the three mixture powders, including SiC, BN, and Ni alloys, are considered in turn to determine the relationships between the hardness and the variables and to determine the nature of the hardness. For a better visualization of the effect each component in the three SiC, BN, and Ni blends, the various hypsographic maps using a mixture design are shown in Figure 4, which shows how the three factors (SiC, BN, and Ni) affect the hardness SiC, BN, and Ni response of the clads that yield a desirable value. Figure 4 shows the region of the ternary contour plot which gives an insight into the appropriate proportioning of the three component mixtures of SiC, BN and Ni on the welds of the cladding. As shown in Figure 4a, the triangular response surface to show the effect of SiC, BN, and Ni at fixed control factors and levels for the laser cladding are generated by a linear mixture. The response plots show that hardness is highest with 100% increase in SiC which is decreased slightly with increase in BN. That is, there is a tendency for the upper-left region to have higher hardness, while the lower-right region has lower hardness. Similarity, the plots in Figure 4b show the response surface with contour plots for the effect of SiC, BN, and Ni that are generated by a linear mixture. It displays a contour plot of the hardness using a linear mixture, where the red areas have higher hardness values while the blue areas have lower hardness values. Clearly, the optimum zone of 70–90 wt% SiC 10–30 wt% BN and 10–20 wt% Ni gives the desirable zone for the mixture design. However, the decrease in hardness is due to the addition of proper amounts of Ni element into the WC/Ni/Co blend, but this hardness increases when the amount of SiC powder increases. In summary, there are graphically shown contour areas of linear mixtures which show the desired value of 606HV and a mixture of 67% SiC, 17% BN and 17% Ni was picked. In the triangular contour plot, the area of red highlights is ideal for individual powder components and mixture powder components on the pattern of hardness, which has a greater impact on the expected output for different combinations of mixture components than the other highlight areas.

Figure 8. Triangular contour plots for three powder mixed effects with a linear mixture, accounting for the effect of individual and mixture powder components including SiC, BN, and Ni alloys for the hardness. (a) three-dimensional surface plot. (b) contour plot of predicted hardness.

Figure 8. Triangular contour plots for three powder mixed effects with a linear mixture, accounting for the effect of individual and mixture powder components including SiC, BN, and Ni alloys for the hardness. (a) three-dimensional surface plot. (b) contour plot of predicted hardness.

3.5. Confirm Run and Their Optimization on the Hardness Properties

Three repetitions of each test were carried out in different areas of the melting zone in order to estimate the optimum performance of the welds for all the tests. Table 2 lists the results and the S/N ratios obtained using the formulae that fulfils the “ larger-the-better” property. Table 4 shows the computation of the response of the S/N ratio in the orthogonal array experiment using mean value analysis. Clearly, the larger S/N ratio indicates better performance of the laser-coated BM/SiC/BN welds. That is, the higher the S/N ratio, the more important the factor is. As shown in Figure 4, the optimal value for each factor was derived from the maximum S/N value for each level of the factor. The optimal setting for the factorial levels is A₂B₂C₃D₁E₁F₂G₃H₃. The optimal parameters for the sputtering process are: substrate of #45 steel, 15wt%BN, 70wt%SiC, 0wt%Ni, laser power of 2400W, carrier gas of 1600 mL/min, travel speed of 6 mm/s, and stand-off distance of 50 mm. Of all the 18 sets of orthogonal array experiments, we choose the 9th group with a pessimistic colour, which is better in the first nine sets, and the 14th group with a dark-blue colour, which is better in the last nine sets, which are compared with the optimal group with a brown colour. As shown in Figure 6, the higher the hardness, the closer it is to the right side of the chart. Using a Gaussian plot, the thinnest solid curve shown on the right side of Figure 6 indicates the best test, which produces the greatest hardness with very little deviation. It is evident that the optimum setting of the control factors is remarkably robust to variability, which demonstrates that reproducibility is good.

Figure 9. Comparison of probability density for the five trials in the orthogonal table with trial 9, trial 14 and the optimal trial.

Figure 9. Comparison of probability density for the five trials in the orthogonal table with trial 9, trial 14 and the optimal trial.

4. Results and Discussion

5. Concluding Remarks

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