ANFIS Based Modeling for Processing Variables’ Effects on Coating Properties in Plasma Spraying Process_____________________________
ANFIS Based Modeling for Processing Variables’ Effects on Coating
Properties in Plasma Spraying Process
Zhenhua Wu*
Department of Engineering
Virginia State University
Petersburg, Virginia, 23806, USA
ABSTRACT
In order to model the effect of processing variables including primary gas flow rate, stand-off distance, powder flow rate, and
arc current on the plasma spraying coating properties including thickness, porosity and micro-hardness, adaptive neural fuzzy
inference system (ANFIS) and neural network based models are proposed to understand the spraying process and estimate
process parameters. In order to overcome the difficulty of small size of sample data, bootstrap method is applied for the
resampling technique and cross validation is applied for the performance evaluation. The ANFIS model and NN model are
compared on the performance metrics of 1) mean square error (MSE), and determination coefficient (R2). The comparisons
illustrated that ANFIS based modeling showed significant superiority than the other approach. This may be due to the fact that
ANFIS combines the strength of NN’s learning capability and fuzzy logic’s knowledge interpretation ability. With this ANFIS
model and identified control rules, feedback control strategy can be effectively implemented to regulate the coating quality in
plasma spraying process.
1. INTRODUCTION
Plasma spraying process is typically for producing thermal barrier coatings (TBCs), which have a very low
thermal conductivity, and a high melting point, thus insulating and protecting underlying super-alloys from exposure
to the high temperatures. In order to operate in the most demanding high-temperature environment of aircraft and
industrial gas-turbine engines, TBCs have complex structure as shown in Figure 1. It comprises of metal and
ceramic multilayers, insulate turbine and combustor engine components from the hot gas stream, and improve the
durability and energy efficiency of these engines [1].
The process of plasma spraying is shown in Figure 2. The plasma spraying gun generates the heat by an
electric arc. A feedstock material is heated and propelled as individual particles or droplets onto a substrate. When
being heated, the material phase is transformed to a plastic or molten state; the molten particles are accelerated by a
compressed gas stream and strike to the substrate. As the sprayed particles hit upon the substrate, they flatten, cool,
and build up layer-by-layer thin splats that conform and adhere to the irregularities of the prepared substrate and to
each other.
Figure 1. Layers of thermal barrier coating on a turbine blade [1].
In the coating process, cracks, pores, and splats on the TBCs need to be controlled, because it results
significantly lower thermal conductivity than the bulk material. The defected microstructure also causes nonlinear
elastic modulus. Qualities on coating properties including thickness, hardness, porosity rate etc. are the control
objective through tuning the processing variables including plasma gas choice, flow rates of plasma gases, size of
nozzle, type of injection, feed rate of powder, feedstock powder particle size distribution, morphology of powder
* Corresponding author: Dr. Zhenhua Wu, Assistant Professor, Email: zwu@vsu.edu, Tel: 804-524-1079, Fax: 804-524-6732
_________________________________________________________________Flexible Automation and Intelligent Manufacturing, FAIM2014
etc. However, this process control is a formidable challenge because of two reasons: 1) the complicate interaction
between the control variables and their effects on the growing of TBCs, the nature of plasma spraying is not fully
understood; and 2) plasma spraying process has the characteristics of short run. Most of the gas-turbine engines are
mass-customized, which results to smaller lot sizes, shorter lead times and less available process data to construct a
control chart. The repeatability of the coating and a coating process is the problem under investigation, but from the
state-of-art on control of plasma spraying, breakthrough has not been reported yet.
Understanding the processing variables’ effects on the coating properties is the very first step to effectively
control the process. Initiated by these, this article aims at identifying of the plasma spraying process. Because of the
difficulty of modeling plasma spraying using classic control theory such as state space approaches, artificial
intelligence based model, specifically ANFIS or NN based model, is applied to identify the pattern between the
processing variable and desired output properties.
Figure 2. Process of plasma spraying process [2].
The rest of this paper is organized as follows: Section 2 surveys related researches on modeling and control of
plasma spraying process, research gap is summarized at the end of this section. Section 3 discusses about the
proposed methodology based on ANFIS modeling, bootstrap and k-fold cross validation (KCV). Section 4 describes
the case study for validating the proposed approach. Section 5 presents the results and discussions. Section 6
concludes the research and outlines the future direction.
2. LITERATURE REVIEW
On the process model, the modeling can be conducted on 1) the relationship between the processing variables
and the in-flight particle states (temperature, velocity and melting states), or 2) the relationship between the
processing variables and the final coating properties. The first kind of models are mainly for the purpose of real time
control of the thermal spraying, since the particle states can be measured in an in-situ way with the in-flight
diagnostics sensors such as DPV 2000® [3], Accuraspray® [3]etc. However, as shown in Figure 2, there still a gap
and uncertainty on the relationship between the particle states and coating deposition structure/properties. On the
second kind of models, the coating properties cannot be measured on-line when spraying. Thus these models cannot
be directly applied on the process since they involves the measurement delay. Current applications have been
conducted on regular regression analysis [4], stepwise regression analysis [5], neural network [6, 7], or fuzzy logic
[7].
From the above literature readings, it is identified that when controlling the thermal spraying processes, the
current literatures lack enough consideration on the modeling and control: How can we involve uncertainty of the
control parameters in the modeling of thermal spraying? Can we generate control rules for modeling the plasma
spraying process? These issues are the research questions which will be addressed in the following sections.
ANFIS Based Modeling for Processing Variables’ Effects on Coating Properties in Plasma Spraying Process_____________________________
3. METHODOLOGIES
3.1. DATA COLLECTION BASED ON DESIGN OF EXPERIMENT
The study starts from data collection with design of experiment (DOE) techniques. DOE permits researchers to
study behaviors under conditions in which independent variables vary simultaneously, so the researchers can
investigate the joint effect of two or more factors on a dependent variable [13]. The DOE also facilitates the study of
interactions, illuminating the effects of different conditions of the experiment on the identifiable subgroups of
subjects participating in the experiment. In reference [8], the authors listed five categories of experimental problem
according to their objectives: 1) treatment comparisons, 2) variable screenings, 3) response surface exploration, 4)
system optimization, and 5) system parameter robustness. This study falls to the categories of 3) and 5). Thus, we
want to apply one of the DOE techniques- response surface methodologies (RSM) for experiment design. It can
cover a wide range of variables with less number of experiments.
After we collect the data with DOE, the model between the processing variables and the coating properties will
be identified with adaptive neuro fuzzy inference system (ANFIS) and neural network (NN) respectively.
3.2. ANFIS BASED MODELING
ANFIS [9] is a class of adaptive networks that functions as a fuzzy-inference system. An ANFIS architecture
with Sugeno-type fuzzy inference is shown in Figure 3.
In this structure, the circle nodes represent fixed nodes and the square nodes represent adaptive nodes. The
square nodes have parameters which can be updated according to the training data and the gradient based learning
procedure.
A1
1 x
A2
B1
n x
B2
Μ Μ
Π
Π
Μ
Ν
Ν
Μ Μ Σ
Layer 1 Layer 2 Layer 3 Layer 4 Layer 5
1 1 w f
n w n w
1 w 1 w
1 x n x
1 x n x
n n w f
f
Figure 3. ANFIS architecture [9].
Layer 1: every node in this layer has the node functionOi1 = μ Ai (x) . Usually μ Ai (x) is chosen as the bell shape
function such as ( )
bi
i
i
Ai
a
x c
x
−
+
=
2
1
μ 1 or ( )
−
= −
2
exp
i
i
Ai a
μ x x c , where { } ai ,bi ,ci is the parameter set.
Parameters in layer are referred to as premise parameters.
Layer 2: every node in this layer is circle node labeled Π which multiplies the incoming signals (
wi = μ Ai (x)×μBi (y)) and sends out the product.
Layer 3: every node in this layer is circle node labeled N. The ith node calculates the ratio of ith rule’s firing
strength to sum of all rules’ firing strengths:
n
i
i w w
w w
+ +
=
1 Λ
.
Layer 4: every node in this layer is a square node with node function ( ) Oi = wi fi = wi pi x + qi y + ri 4 , { } pi , qi , ri
is the parameter set, parameter sets are referred as consequence parameters.
Layer 5: the single node in this layer is a circle node labeled Σ which computes the overall output as the
summation of all incoming signals, Σ
=Σ = Σ
i i
i i i
i
i i f
w f
O5 w f
1 .
_________________________________________________________________Flexible Automation and Intelligent Manufacturing, FAIM2014
In the neuro-fuzzy inference system, it requires two major types of learning: structure learning is used first to
find the appropriate structure and fuzzy logic rules of a neuro-fuzzy system; and parameter learning is then used to
fine-tune the parameters [10]. Identification of fuzzy rule is the most important aspects in design of fuzzy inference
system. Construction of fuzzy logic rules from numerical data consists of two procedures: 1) fuzzy partitioning of
the input spaces and/or out spaces; and 2) identification of a fuzzy logic rules for each fuzzy subspaces. Parameters
learning methods: gradient descent-based learning algorithms (e.g. error back propagation algorithm), reinforcement
learning and approximate least square estimator (LSE) etc.
For the detail of construction of ANFIS and learning algorithms to tune the structure and parameters, the
readers can refer to [9, 10].
3.3. NN BASED MODELING
The goal of neural network modeling was to predict the outputs of coating properties using a function of the
inputs, which were processing variables that would act upon the output. Desired network architectures were built
containing a few hidden layers and hidden nodes for a good prediction of the coating properties. In the neural
network modeling process, two aspects of information need to be decided: (1) the neural network’s topology
including input variables and output variables, number of neurons in each layer, types of neuron functions in each
layer; and (2) weights and biases with learning and training functions used in the neural network model [11]. The
input was propagated forward through the network to compute the output value. The error is calculated based on the
difference between the calculated output value and the desired value. In order to get the mean square error (MSE)
between the actual and desired output values as close as possible to zero, back propagation algorithm was applied by
adjusting the weights and biases associated with each link of the network [12]. During the backward pass, the error
terms were computed when the hidden units and the weights and biases were updated. The output was then
compared to the desired output and the MSE was computed. If the error was zero or close to preset values, the
network training process stopped. Otherwise desired weights and biases would be searched with different learning
and training functions such as gradient descent algorithm etc. [12].
After deciding the NN topology and training the NN weights and biases, the network model is completely
determined, and the outputOUTp , as the predicted coating properties, can be expressed by a function f (X,W,B)of
the input data [ ]T
X = x1,Λ , xm , network parameters weights vector [ ] W H H H H m 2 1 2 1 = λ1,Λ ,λ ;β11,Λ ,β ;γ 11,Λ ,γ , and
biases vector [ ] 11, , 1 ; 21, , 2 ; 31 1 2 B = b Λ b H b Λ b H b . The scalars H1 and H2 denote the number of nodes in hidden layers
1 and 2 of the network, respectively. g1(x) , g2 (x) and g3 (x), are neuron functions attached to nodes in hidden
layer1, layer2 and output layer. The neural network can be interpreted as a parametric nonlinear regression ofOUT
on X . OUTp can be calculated as equation
( )
+
+
= = Σ Σ Σ +
= = =
3
1
2
1
1
1
3 2 1
2
2
2
1
1
2 2 1 1 1 OUT f X,w g g g x b b b
H
h
h
H
h
h
m
i
p λh βh h γ h i i . For the detail of construction of NN
model and learning algorithms, the readers can refer to [11, 12].
3.4. BOOTSTRAP AND K-FOLD CROSS VALIDATION
The dataset available with DOE techniques usually represents a finite-sized sample set from a population with
an unknown probability distribution. The traditional methods for training and testing ANFIS or neural network
model call for splitting the dataset into a training subset and a testing subset. The training data subset is used to
calculate the weights of the network and the test data subset is used to assess the performance of the model. When
the size of the available data is small, the simple training–test data splitting method is not effective. Even with a
large size data, the performance of the model cannot be estimated on all future samples presented to the network if a
simple training–test data splitting method is used. This is clearly impossible unless the underlying probability
distribution that the training samples are drawn from is exactly equal to the probability distribution from which the
future samples are drawn. There are a number of schemes for addressing this problem and the most suitable for the
size of dataset used in this study, are bootstrap [13] and k-fold cross validation (KCV) [13].
3.4.1. BOOTSTRAP
The bootstrap methods provide a direct computational way of assessing uncertainty, by sampling from the
training data [13]. Suppose that we have a model that fits to a set of training data. We denote the training set by
ANFIS Based Modeling for Processing Variables’ Effects on Coating Properties in Plasma Spraying Process_____________________________
( ) Z = z1, z2 ,Λ , zN where ( ) zi = xi , yi . Bootstrap approach will randomly draw datasets with replacement from the
training data by B times, each sample the same size as the original training set. This operation will produce B
bootstrap datasets, Then the model will be refitted to each of the bootstrap datasets, and examine the behavior of the
fits over the B replications. Suppose ( * )
s zb is any quantity computed from the data Z, for example, the prediction at
some input point. That estimation can be thought of as a Monte-Carlo estimate of the quantity under sampling from
the empirical distribution function F
ˆ for the data ( ) z1, z2 ,Λ , zN . Evaluate the bootstrap replication corresponding to
each bootstrap sample: s(zb ),b 1, , B
θˆ* = * = Λ . Estimate the standard error ( * )
ˆθ
seB by the sample standard error of
the B replicates ( ) ( ( ) ( ))
− •
−
= Σ=
B
b
B b
B
se
1
* * * 2
ˆ
ˆ
1
1
ˆ θ θ θ , e r e h ( ) ( ) Σ=
• = −
B
b
B b
1
* 1 *
ˆ
θˆ θ .
3.4.2. K-FOLD CROSS VALIDATION
KCV randomly divides the available data into k equal size and mutually exclusive partitions (or folds). For a k-fold
cross validation k neural networks are trained with a different fold used each time for the validation, while the
other k
−1 folds are used for the training. The choice of k influences the ratio of data used for training and validating
with an optimal value of k in the range 5–10. The performance obtained using a KCV procedure is less biased than
the one obtained using a simple training–validating data splitting method. The KCV procedure requires that the
number of data samples is a multiple of the number of folds. Five-fold cross validation was used in this study. The
available data was randomly partitioned into five mutually exclusive groups. The partition pairs were used to train
five prediction models. Figure 4 illustrates the implemented five-cross validation procedure. All the five ANFIS/NN
models have the same architecture but differ by the values for their network connection weight vectors.
Figure 4. ANFIS training and testing using five-fold cross validation procedure.
The mean squared prediction error is calculated for each model as = 1 (d (i)− d (i))2 , n = 1,Λ ,5
N
MSPE n pn
te
n ,
where dn is the vector of actual coating property values used during the testing of model n, d pn is the vector of
coating property values predicted by network n, and Nte = 5 is the number of data used for network testing. The
s a d e n i f e d s i ) E V C ( r o r r e n o i t a d i l a v s s o r c Σ=
=
5
1 5
1
n
CVE MSPEn .
4. CASE STUDY AND RESULTS
In order to illustrate the proposed modeling and validation approach on plasma spraying, a case study was
developed on the data was collected by previous studies [4]. The following processing variables of plasma spraying
were taken into consideration: primary gas flow rate (G), stand-off distance (D), powder flow rate (P), and arc
current (A). The responses considered were thickness (Th), porosity (Pr), and micro-hardness (H) of the coatings.
Primary gas flow rate was varied between 7.866×10
−4 and 11.8×10
−4 m3/s. The stand-off distances to create the
coatings were kept in between 0.150 and 0.200 m. The powder flow rate was varied between 3.775×10
−3 and
7.7550×10
−3 kg/s. The range for arc current was considered from 400 to 500 A. Three levels were considered for
each of the input parameters. The ranges of the input parameters had been decided based on the manufacturer’s
recommendation, as those could be machine-dependent. Experiments had been conducted to generate input–output
data using a 3 MB Sulzer Metco plasma spray setup. Low-carbon (C-20) steel was taken as the substrate material,
and Ni–5 wt% Al alloy powder (450 NS, Sulzer Metco) had been used as the coating material. The plasma spraying
_________________________________________________________________Flexible Automation and Intelligent Manufacturing, FAIM2014
trials had been designed using a central composite design (CCD) based RSM methodology and the collected data is
as Table 1.
Table 1. Central composite design of experiments with measured responses [4].
Processing Variables Coating Properties
G (m3/s ×10
−4) D (m) P (kg/s ×10
−3) A (ampere) Th (μm) Pr (%) H (Hv 100)
7.866 0.15 3.775 400 705 11.2 236.1
11.8 0.15 3.775 400 780 11.1 180.9
7.866 0.2 3.775 400 737 6.94 251.9
11.8 0.2 3.775 400 790 8.69 201.9
7.866 0.15 7.755 400 670 8.16 254.5
11.8 0.15 7.755 400 905 9.65 185.1
7.866 0.2 7.755 400 417 8.89 248.8
11.8 0.2 7.755 400 580 10.8 208.4
7.866 0.15 3.775 500 487 7.29 220.9
11.8 0.15 3.775 500 910 8.93 184.0
7.866 0.2 3.775 500 157 9.27 260.3
11.8 0.2 3.775 500 90 10.3 228.5
7.866 0.15 7.755 500 243 7.11 156.8
11.8 0.15 7.755 500 180 8.71 205.4
7.866 0.2 7.755 500 207 9.54 238.9
11.8 0.2 7.755 500 87 8.98 201.0
7.866 0.175 5.662 450 180 8.47 198.0
11.8 0.175 5.662 450 450 11.4 189.8
9.833 0.15 5.662 450 180 10.5 166.2
9.833 0.2 5.662 450 107 9.9 174.3
9.833 0.175 3.775 450 73 10.2 144.8
9.833 0.175 7.755 450 103 7.61 158.5
9.833 0.175 5.662 400 73 11.8 146.5
9.833 0.175 5.662 500 437 11.7 210.4
9.833 0.175 5.662 450 83 10.5 188.2
4.1 RESULTS AND DISCUSSIONS
With the data collected in Table 1, the proposed modeling approaches were conducted. Section 4 will present
the results and discussions.
Further goodness-of-fit statistics for the model predictions in arithmetic scale were performed by using statistical
parameters such as the determination coefficient R2 and MSE.
a) Determination coefficient- R2 : ( ) ( )
= − Σ − Σ −
= =
N
i
i
N
i
R yi y y y
1
2
1
2 2
1 ˆ . The R2 is a value between 0 and 1, and
it is a measure of correlation between the predicted and the measured values, thus determining accuracy of the
fitting model (the higher R2 , the higher accuracy).
) b : ) E S M ( r o r r E e r a u q S n a e M ( ) Σ=
= −
n
t
yt yt et
n
MSE
1
2
arg
1 . The yt is actual value in the t th production run, the
yt arget is target value. The smaller the MSE is, the better the modeling result is.
The ANFIS based models were compared with NN models on performances of MSE and R2 with bootstrap
strategy. In these comparisons, the NN models are four-layer forward with the 4-60-60-1(neurons in each layer)
structure. The weights and biases as well as the neuron parameters are trained with the back propagation approaches.
The summarization of the results is as below Tables 2 and 3. In these two tables, the data was re-sampled for 50
times. In each sampling, 20 sets of data (80 percent of data) were used for modeling, and 5 sets of data (20 percent
of data) were used for validation. We can see that ANFIS has better R2 and MSE performances than NN on the
modeling stage.
ANFIS Based Modeling for Processing Variables’ Effects on Coating Properties in Plasma Spraying Process_____________________________
Table 2. Comparison on the R2 through bootstrap on thickness, porosity, and micro-hardness.
Thickness Porosity Micro-hardness
Model Validate Model Validate Model Validate
ANFIS 1 mean:0.57
se: 0.3308
1 mean: 0.42
se: 0.362
1 mean: 0.47
se: 0.351
NN 0.84 mean: 0.512
se: 0.3265
0.867 mean: 0.52
se:0.31
0.887 mean: 0.56
se:0.373
Table 3. Comparison on the MSE through bootstrap on thickness, porosity, and micro-hardness.
Thickness Porosity Micro-hardness
Model Validate Model Validate Model Validate
ANFIS 0.005 mean: 8.09e4
se: 8.99e4
0.005 mean: 23.67
se: 19.15
1.3e-5 mean:1.02e4
se:1.1e4
NN 1.94e3 mean: 1.82e5
se: 1.03e5
0.32 mean: 89.50
se: 10.24
127.14 mean: 4.12e4
se: 5.99e3
The regression plots for the ANFIS modeling results on (a) thickness, (b) porosity and (c) micro-hardness are
illustrated as below Figure 5 (a) to (c). Figure 6 (a) to (c) are the regression plots for NN modeling.
(a) R2=1 (b) R2=1 (c) R2=1
Figure 5. Regression plots for the ANFIS modeling on (a) thickness, (b) porosity and (c) micro-hardness.
(a) R2=0.84 (b) R2=0.86 (c) R2=0.88
Figure 6. Regression plots for the NN modeling on (a) thickness, (b) porosity and (c) micro-hardness.
The ANFIS based modeling was compared with NN based approach on cross validation performances of MSE.
The summarization of the results is as below Table 4.
Table 4. Comparison on the CVE performance on thickness, porosity, and micro-hardness.
Thickness Porosity Micro-hardness
ANFIS 1.32e5 51.99 2.16e4
NN 1.22e5 4.09 1.95e3
_________________________________________________________________Flexible Automation and Intelligent Manufacturing, FAIM2014
From these tables and figures, we see that ANFIS achieved the better results on modeling the effects of processing
parameters on the final coating properties. In this stage, the dataset size is relatively larger than the validation stage
(80% vs 20%). However, in the validation stage, NN shows better performance. This may be caused due to the
uncertainty in the model since there are only 5 pieces of data for validation. Neural network and fuzzy logic are two
complimentary techniques. NN can learn from data and feedback, while lacking understands of the knowledge or
pattern. Also, it is difficult to develop an insight about the meaning associated with each neuron and each weight.
Fuzzy logic is easy to be understood in that it uses the linguistic variables and the structure of “IF-THEN” rules.
However, fuzzy logic is short of learning capability. ANFIS combines advantage of these two techniques.
4.2. ANFIS Model Rules between Processing Variables and Coating Properties
As mentioned in Section 3.2, identification of fuzzy rule is the most important aspects in design of fuzzy
inference system. ANFIS models also identified rules between processing variables and coating properties. In Figure
7, the surface views about these rules are illustrated. Due to the page limitation, only the model rules between
coating properties and processing variables of G and D are presented here.
(a) (b) (c)
Figure 7. Surface views of the rules of the ANFIS models on (a) thickness, (b) porosity and (c) micro-hardness.
5. CONCLUSIONS AND FUTURE DIRECTIONS
In order to identify the effect of processing variables, including (primary gas flow rate, stand-off distance,
powder flow rate, and arc current), on the coating properties including (thickness, porosity and micro-hardness),
ANFIS and NN based models were to understand the process and to estimate process parameters. On the modeling
performance, we saw that ANFIS indeed improved the performance than 1) multiple variable regression and 2)
neural network on MSE and R2. This may be due to the fact that ANFIS combines the strength of NN’s learning
capability and fuzzy logic’s knowledge interpretation ability.
For future research, further investigations from the following aspects are suggested:
1) The models that we developed in this research are all multi-input single-output (MISO) models. Further
research will extend the plasma spraying models to multi-input multi-output (MIMO) model.
2) Integrate the proposed modeling approaches with effective feedback control algorithms to regulate the plasma
spraying process.
REFERENCES
[1] Nitin P. Padture, Maurice Gell, Eric H. Jordan, “Thermal Barrier Coatings for Gas-Turbine Engine Applications”,
Science, 2002: Vol. 296, no. 5566 pp. 280–284.
[2] Maria Oksa, Erja Turunen, Tomi Suhonen, Tommi Varis and Simo-Pekka Hannula, Optimization and Characterization of
High Velocity Oxy-fuel Sprayed Coatings: Techniques, Materials, and Applications, Coatings, 2011, 1, 17–52.
[3] Georg Mauer, Robert Vaßen, Detlev Stover, “Comparison and Applications of DPV-2000 and Accuraspray-g3 Diagnostic
Systems”, JTTEE5 16:414–424.
[4] Somak Datta, Dilip Kumar Pratihar, Partha Pratim Bandyopadhyay, “Modeling of plasma spray coating process using
statistical regression analysis”, Int J Adv Manuf Technol (2013) 65:967–980.
[5] J.F. Li, H.L. Liao, C.X. Ding, C. Coddet, “Optimizing the plasma spray process parameters of yttria stabilized zirconia
coatings using a uniform design of experiments”, Journal of Materials Processing Technology 160 (2005) 34–42.
[6] Sofiane Guessasma, Ghislain Montavon, Patrick Gougeon, Christian Coddet, “Designing expert system using neural
computation in view of the control of plasma spray processes”, Materials and Design 24 (2003) 497–502.
ANFIS Based Modeling for Processing Variables’ Effects on Coating Properties in Plasma Spraying Process_____________________________
[7] Abdoul-Fatah Kanta, Ghislain Montavon, Michel Vardelle, Marie-Pierre Planche, Christopher C. Berndt, and Christian
Coddet, “Artificial Neural Networks vs. Fuzzy Logic: Simple Tools to Predict and Control Complex Processes—Application
to Plasma Spray Processes”, JTTEE5 17:365–376.
[8] Wu, C.F.J. and Hamada, M.S. (2009) Experiments: Planning, Analysis, and Optimization. Wiley, NY.
[9] J.S.R. Jang, ANFIS: Adaptive-Network-Based Fuzzy Inference System, IEEE Trans. Systems, Man, Cybernetics,
23(5/6):665–685, 1993.
[10] J. Kim, N. Kasabov, HyFIS: Adaptive Neuro-fuzzy Inference Systems and Their Application to Nonlinear Dynamical
Systems, Neural Networks12 (1999) 1301–1319.
[11] Zhenhua Wu, Sheng Hu, Fujie Zhou “Prediction of Stress Intensity Factors in Pavement Cracking with Neural Networks
based on Semi-analytical FEA”, Expert Systems with Applications, 41, 1021–1030, 2014.
[12] White, H., Wooldridge, J., Gallant, A.R., Hornik, K., & Stinchcombe, M. (1992). Artificial neural networks: approximation
and learning theory. Blackwell Publishers, Cambridge, MA.
[13] Trevor Hastie, Robert Tibshirani, Jerome Friedman, (2001).The Elements of Statistical Learning: Data Mining, Inference,
and Prediction, 2nd edition, Springer.