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 Authors : Tjahe Agnes Virginie, Mtopi Fotso Blaise E., Djanna Koffi Francis, Fogue Medard
 Paper ID : IJERTV6IS070321
 Volume & Issue : Volume 06, Issue 07 (July 2017)
 Published (First Online): 03082017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Proposition of a MANFISPID Hybrid System for the Prediction of Several Interdependent Parameters
Tjahe AgnÃ¨s Virginie
Laboratory of Engineering for Industrial Systems and Environment – LISIE
Department of Mechanical Engineering and Computed Integrated Manufacturing
FOTSO Victor Institute of Technology of Bandjoun University of Dschang P.O. Box. 96 DschangCameroon
Djanna Koffi Francis
Department of Thermal Engineering – University Institute of Technology
University of Douala, P.O. Box. 8698 Douala Cameroon
Mtopi Fotso Blaise E.
Laboratory of Engineering for Industrial Systems and Environment – LISIE Department of Mechanical Engineering and
Computed Integrated Manufacturing FOTSO Victor Institute of Technology of Bandjoun
University of Dschang P.O. Box 96 Dschang Cameroon
Fogue MÃ©dard
Laboratory of Engineering for Industrial Systems and Environment – LISIE Department of Mechanical Engineering and
Computed Integrated Manufacturing FOTSO Victor Institute of Technology of Bandjoun
University of Dschang P.O. Box. DschangCameroon
AbstractThis paper is devoted to the definition of a MANFIS (Multioutput Adaptive NeuroFuzzy System) system combined with PID (Proportional Integral Derivative) regulators for the prognostic of failure. The input selection is implemented to improve the performance of the prediction system. The MANFIS subsystem performs the prediction of three interdependent parameters, and the PID controllers correct for each parameter the prediction error. For the control of the prediction error, we propose PID controllers with optimal parameters remaining constant in the medium term. Research oriented towards the development of neuro fuzzy prediction systems suggests that multiparameter models would be closer to the requirements of real industrial systems. Moreover, it emerges from this work that it is also necessary to improve the accuracy of these prediction systems without necessarily increasing the complexity of the algorithm. This is why the prognostic system proposed here allows the prediction of three interdependent parameters and the control of the prediction error. We will begin the work reported here by presenting the place of the prognostic in the maintenance activity. A presentation of the predictive system of type MANFISPID is carried out. The Lorenz dynamic system is used to illustrate our prediction architecture. The approach for determining the optimal parameters of PID controllers is presented. A comparative analysis of the prediction error distribution of the MANFISPID system and its MANFIS subsystem at different horizons of prediction is also presented
Keywords prognostic; MANFISPID; optimal parameters of PID; prediction Error

INTRODUCTION
Improving reliability has been one of the major challenges facing industrial companies of our time [1]. The anticipation of failures (preventive maintenance) now at the center of maintenance activity allows a real improvement in the availability and reliability of the systems. The implementation of such a maintenance policy requires the provision of adequate resources for monitoring, diagnostics and prediction of the state of the systems [2] [3].
These perpetual challenges have contributed to the development of surveillance systems and the birth of new maintenance concepts. These maintenance concepts increase the autonomy and intelligence of current monitoring systems [4] [5]. These new maintenance concepts thus give a privileged place to the industrial prognostic in the maintenance activity [6]. Today, failures prediction is considered as a research theme [7].
In the field of industrial prognostic, several approaches have been implemented. The datadriven approach is widely used. This approach is used when the modeling of the system is complex and the data collected are reliable. It offers a place of choice to the techniques of artificial intelligence [8].
Concerning prognostic of failure via the dataguided approach, several mutations have been observed. We started with the use of Neural Networks (NN), to the NN loops of [9]. To improve precision, [10] associate a PID controller with the NN loops. Today, the datadriven prognostic is based on hybrid systems such as NeuroFuzzy (NF) networks. It is for this purpose that the system chosen for the development of our work is an ANFIS (Adaptive NeuroFuzzy Inference System) proposed by [11]. Most of
the ANFIS systems developed in the literature focus on the reduction of the prediction error and for others on the control of this error. However, this work reveals the need to develop multiparameters prediction systems. Indeed, the real industrial systems cant be satisfied with the prediction of a single parameter. Furthermore, [12] reveal the need for the selection of optimal parameters for the prediction of neurofuzzy systems. Moreover, the work of [10] reveals that a PID controller could contribute to the improvement of prediction performance without increasing the complexity of the treatment.
We therefore propose a hybrid system consisting initially of a MANFIS subsystem which applies the selection of inputs for the efficient prediction of three interdependent parameters. In a second step, the proposed system also consists of three PID controllers that control the prediction error of each parameter. For the control of the prediction error, we have defined for each PID controller, optimal parameters (Kp, Ki and Kd) remaining constant in the medium term.
The MANFISPID system thus proposed is able to predict the evolution of three parameters while controlling the prediction error. It allows efficient prediction without increasing the complexity of the algorithm.
The rest of this paper is organized as follows: Section 2 is reserved for the definition of the problem. In this section we will start from the position of the prognosis in industrial maintenance and some work to reduce and control the error to introduce the need to propose an efficient multiparameter prediction system.
Section 3 presents the ANFIS and MANFIS systems. In section 4 we present the proposed MANFISPID system and the process of obtaining the optimal parameters of the PID controller (Kp, Ki and Kd) remaining constant in the medium term. These results will be analyzed and discussed in Section 5. Section 6 is devoted to the conclusion and definition of future work.

PROBLEM DEFINITION

Place of prognostic in industrial maintenance
The maintenance applied to an equipment (systems, subsystem or component) contributes to the improvement of the availability and the reliability of the service rendered by this equipment. In addition to the purpose of enabling an asset to fulfill its required function, new requirements of quality, safety and cost must be taken into account. These new requirements make up the new challenges of maintenance and worth its evolution. Indeed, the increase in maintenance costs, the advent of automation and the new requirements of customers demand a high level of flexibility of industrial equipments [13]. Formerly the so called traditional maintenance activity was based on the anomaly detection, the comprehension and identification of the causes of this anomaly (diagnosis) and finally the choice and implementation of an adequate action. However, nowadays, the a posteriori comprehension of a failure gave place to the anticipation of the failure. The
prognostic of failure seems to meet these new maintenance requirements.

Failure prognostic concept
The prognostic is defined by [1] as "an estimate of the duration of operation before failure and the risk of the existence or subsequent appearance of one or more modes of failure". The prognostic is further defined by [7] as a process designed to determine the remaining life of a system. [15] Asserts that the prognosis may also be considered as an estimate of the probability of occurrence of a failure.
The prognostic of failure is based both on the notion of degradation and on the existence of a critical threshold. From a given instant t, the prognostic activity consists first of all in predicting the evolution of the degradation of the system at an instant t + dt. After prediction, the second step of the prognostic consist in evaluating the state of the system according to the predefined referential [8].

Reduction and control of the prediction error
The prognostic of the state of a system being inherently uncertain, it is important to determine measures defining the confidence level of the prognostic system. RMSE (Root Mean Squared Error) is currently used in the literature.
Several works in the literature aim at reducing this error. To improve the performance of databased prognostic systems, we have moved from not curly networks [16], [17], and [18] etc. to the curly networks of
[19] and [20].Improved performance and the desire to reduce the complexity of prognostic systems led researchers to migrate to hybrid systems such as NF networks [21], [22], [23], [24] and [25] etc.
Beside the reduction of the prediction error, [26] and
[1] focus their work on controlling prediction error. [26] Propose a new cost function and a new prediction model composed of two ANFIS systems with four inputs connected in series. [1] Implements the input selection governed by the method of [27]. It seems clear at the end of the analysis of these works that, the prediction of several parameters would be closer to the requirements of real industrial systems.From what is the prediction of several parameters, [27] developed the MANFIS (Multiple Adaptive NeuroFuzzy Inference System) model. In addition, [28] proposed a MANFIS model for the approximation of three sinusoidal functions. However, actual industrial systems exhibit a much more complex evolution than those represented by sinusoidal functions.
[29] Propose a MANFIS system for the prediction of three parameters and the genetic algorithm is associated to improve the performance. [10] Associate the PID with the RRFBR for the control of the prediction error. However, [10] propose for the PID controller combinations of parameters (Kp, Ki and Kd) foreach horizon of prediction. This change in the values of the parameters (Kp, Ki and Kd) at each horizon of prediction seems tedious.
Where pi , qi
parameters.
and ri
are the socalled consequential
It is to improve the accuracy of a multiparameters prediction system without increasing the complexity of the prediction algorithm that, the work proposed in this paper
Layer 5. Output calculation
2
applies the selection of inputs and the PID controller (with constant parameter values in the medium term) to a MANFIS system with three interdependent parameters.
i
O5
2
i1
wi fi
wi fi
i1
w1 w2
i=1, 2
(8)


NEUROFUZZY PREDICTION SYSTEM

ANFIS Architecture
[30] Effectuates the analysis of some NF architectures and realizes that ANFIS architecture offers a better RMSE.TABLE I. PERFORMANCE OF SOME NF MODELS [30]
Model
Epochs
RMSE
ANFIS
75
0.0017
NEFPROX
216
0.332
EfuNN
1
0.0140
dmEFuNN
1
0.0042
SONFIN
1
0.0180
After this phase, the optimal values of these membership function parameters and consequential parameters are set by a hybrid learning algorithm that combines the method of least squares with the backpropagation learning algorithm. Finally, the ANFIS output is calculated by means of consequential parameters.

MANFIS Architecture
The ANFIS architecture is similar to the new MANFIS system proposed in this paper. Indeed, the MANFIS architecture can be considered as an aggregation of several ANFIS [31].
Fig. 1. Network structure of ANFIS model [27]
Layer 1. Generates the membership grades:
y1
ANFIS1
x1
ANFIS2
x2 y2
. . . .
. . . .
xp
ANFISm
Epochs
RMSE
.
ym
Fig. 2. Architecture of the MANFIS network [31]
In this model, the input variables xi (i=1, 2,,p) are
i A
O1
i
O1
(x) , i=1, 2
( y) , i=1, 2
(3)
(4)
independent and the output variables yi (i=1, 2,,p) are functions of the input variables.
i B i
i
i
Where A and B can be any membership functions.
x x1 , x2 ,…, xp
yi fi (x) i , i 1, 2,…, m
(9)
(10)
Layer 2. Generates the firing strengths.
i i A
O2 w
i
(x)
B
i
( y) , i=1, 2
(5)


MANFISPID SYSTEM FOR THE
Layer 3. Normalizes the firing strengths.
PREDICTION OF THREE
i i
O3 w
wi w1 w2
, i=1, 2
(6)
INTERDEPENDENT PARAMETERS
In this section, we propose a MANFISPID system
Layer 4. Calculates rule outputs based on the consequent parameters.
capable of performing the prediction of three interdependent parameters. This system consists of two
i i i i i i
O4 w f w( p x q y r ) i=1, 2
(7)
subsystems. The MANFIS subsystem performs the prediction of three interdependent parameters, and the PID controllers (with constant parameters) perform the control of prediction error for each parameter (X, Y and Z).

Structure of the MANFIS subsystem
MANFIS
MANFIS
MANFIS
Xint Yint Zint
MANFIS
x'(t 1)
y'(t 1)
z'(t 1)
x'(t d)
y'(t d )
z'(t d )
Fig. 3. MANFIS prediction subsystem of three interdependent
parameters
For this subsystem, the variable d represents the horizon of prediction. For each of the input variables (X, Y, Z), the components chosen as inputs are those corresponding to the four previous instants to the instant of prediction. Input Variables Xint, Yint and Zint are vectors defined as follows:
Fig. 4. MANFISPID system
Unlike the PID controller proposed by [10], the particularity of the PID controllers proposed here is that they keep constant, parameter values Kp, Ki and Kd in the
Xint
[x(t 3)
x(t 2)
x(t 1)
x(t) ]T
(11)
medium term.
Consider the variable X, the control of the prediction
Yint [ y(t 3)
Zint [z(t 3)
y(t 2)
z(t 2)
y(t 1)
z(t 1)
y(t) ]T
z(t) ]T
(13)
error can be written:
(12)
t
x1(t)
For this subsystem, the prediction of the state of the
x(t 1) x'(t 1) KPx1(t) Ki 0 x1( )d Kd t
(14)
parameters at a given instant takes into account the state of these parameters at the four previous instants. The
With
x1(t) the prediction error for the horizon t+1
t
incrementation of the horizon of prediction is done by
By induction, at the horizon t + d we can also write:
cascading the bse system.

Structure of the MANFISPID system and
x(t d) x'(t d) KPxd (t) Ki
0 xd ( )d Kd
xd (t)
(t)
(15)
determination of the optimal parameters Kp, Ki and Kd of the PID controllers
For the MANFISPID system, the prediction errors
x1(t) , y1 (t) and z1(t) are respectively calculated between
With xd (t) the prediction error for the horizon t+d
t
The command com11 delivered by the PID1 controller to predict the state of the variable X at instant t+1 can be written as:
the values x '(t) , y '(t) and z '(t) predicted by the MANFIS
com K
(t) K
( )d K
x1(t)
(16)
subsystem and the real values x(t) , y(t) and z(t) . The controllers PID1, PID2 and PID3 respectively deliver the
11 P x1
i 0 x1
d t
commands com11, com21 and com31 capable of adjusting the predictions of the MANFIS subsystem. The control of the
com11 x(t 1) x'(t 1)
(17)
prediction error thus performed allows us to obtain x(t 1) ,
y(t 1) and z(t 1) .
Similarly, the command com1d delivered by the PID1
controller at time t+d can be written:
com1d x(t d) x'(t d)
(18)
Ideally,
x(t d) x(t d)
This implies that:
com1d x(t d) x'(t d)
(20)
Considering the previous expressions, there are constant and optimal values Kp, Ki and Kd satisfying the following equation system:
The RMSE between the expected values and the estimated values is calculated by the equation (24).
x1 y1 z1
t x1 (t)
A
(22)
com11 KP x1 (t) Ki x1 ( )d Kd
0 t
xk yk zk
t xd (t)
(21)
com1d KP xd (t) Ki 0 xd ( )d Kd
(t)
x1
y1
z1
A
(23)
xk yk zk
The resolution of this system of equation allows us to find the optimal parameters Kp, Ki and Kd to obtain optimal PID controls. These parameters remain unchanged up to the horizon t+d. The same approach is applied to the variable Y and Z.

Training base
For the validation of our system we used the time series of Lorenz. This series of data is chaotic, therefore nonperiodic and nonconvergent. The time series of Lorentz presents the evolution over time of three interdependent parameters [32]. Although widely used in the field of climatic predictions, we have found it interesting to validate our system whose application is in the field of industrial maintenance.

Prediction Methodology Implemented
The prediction methodology begins with the formation of 150 training data and 100 test data. The data of each of the parameters X, Y and Z are arranged in the form of five column matrices (the four inputs and the desired output) and n rows (n being the size of the training / test set). These data are used for the generation of fuzzy inference systems and the training of three ANFIS systems, each for the prediction of one of the three parameters. The symbiosis of the three systems allowed us to form a MANFIS subsystem. The MANFIS subsystem performs
RMSE
K
1 K A(k) A(k) 2
k 1
(24)
the prediction by delivering the values x'(t d) , y '(t d)
and
z'(t d). To this system is associated the controllers PID1,
PID2 and PID3 who issue the commands respectively com1d, com2d and com3d. Commands com1d, com2d and com3d are applied to the values previously predicted by the MANFIS subsystem to give respectively x(t d) , y(t d) and
z(t d) . These values thus constitute the prediction effectuated by the MANFISPID system.
The cascade of the previously formed system makes it
possible to increment the horizon of prediction. The variable d corresponds to this horizon of prediction. This cascading is inspired by the work of [33] and taken over by [26].
Consider A , the matrix (KÃ—3) containing the expected values of the three parameters for the K tests and A , the matrix (KÃ—3) containing the predicted values of the three parameters for the K tests.
Fig. 5. Process deployed in the MANFISPID prediction system


RESULT AND ANALYSIS
Table 2 presents the different values of the Kp, Ki and Kd parameters obtained for each of the three variables. The integration parameter Ki being zero, we have PD type controllers (Proportional Derivative).
TABLE II. VALUES OF OPTIMAL PARAMETERS KP, KI AND
KD FROM HORIZON t+1 TO t+20
Kp
Ki
Kd
Variable X
1.1019
0
0.1183
Variable Y
1.1901
0
0.1784
Variable Z
0.8907
0
1.1165
A comparative analysis of the performance of the
0.9
0.8
0.7
0.6
RMSE
0.5
0.4
0.3
0.2
0.1
0
MANFIS
MANFISPID
0 2 4 6 8 10 12 14 16 18 20
Horizons of prediction
Fig. 6. Evolution of RMSE at different horizons of prediction
Figs. 7 to 9 show the results of the prediction
MANFISPID prediction system and its MANFIS subsystem is presented in Table 3 and Figure 6. This analysis shows a real decrease in the RMSE of the MANFISPID system compared to the RMSE of the MANFIS subsystem. We can see that the PD controller increases the prediction performances without requiring the variation of the values of the parameters Kp, Ki and Kd with the horizon of prediction.
TABLE III. COMPARATIVE ANALYSIS OF PID MANFIS SYSTEM PERFORMANCE COMPARED TO ITS SUBSYSTEM MANFIS
obtained for the three variables at different horizons of prediction for the MANFISPID system and its MANFIS subsystem. A relative but perceptible increase in prediction is observed for variables X and Y by the MANFISPID system. On the other hand, the MANFISPID system provides an excellent improvement in the prediction performance for the variable Z.
Horizon of prediction t+12
Test data
MANFIS
MANFISPID
10
9
Variab le X
8
7
6
5
Horizon of prediction
Prediction System
RMSE test set
t+1
MANFIS
0.0003
MANFISPID
0.0001
t+2
MANFIS
0.0018
MANFISPID
0.0010
t+4
MANFIS
0.0109
MANFISPID
0.0047
t+6
MANFIS
0.0330
MANFISPID
0.0170
t+8
MANFIS
0.0761
MANFISPID
0.0475
t+10
MANFIS
0.1463
MANFISPID
0.0960
t+12
MANFIS
0.2468
MANFISPID
0.1765
t+14
MANFIS
0.3766
MANFISPID
0.1561
t+16
MANFIS
0.5310
MANFISPID
0.3147
t+18
MANFIS
0.7019
MANFISPID
0.5545
t+20
MANFIS
0.8802
MANFISPID
0.6274
4
10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+14
11
Test data
MANFIS MANFISPID
10
9
Variab le X
8
7
6
5
4
Horizon of prediction t+14
Test data
MANFIS MANFISPID
34
32
Variab le Y
30
28
26
24
22
3
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+16
11
20
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+16
14
10 Test data
MANFIS
9
MANFISPID
Variab le X
8
7
6
5
4
0
10
20
30
40
50
60
70
80 9
0 100 2
0
10
20
30
40
50
70
80
90
100
Number of samples
Number of samples
3
12 Test data
MANFIS
10 MANFISPID
Variable Y
8
6
4
60
Fig. 7. Results of prediction of variable X at different horizons of
prediction
Fig. 8. Results of the prediction of variable Y at different horizons of
prediction
Horizon of prediction t+12
14
12
10
Test data MANFIS MANFISPID
Horizon of prediction t+12
34
32 Test data
MANFIS
30 MANFISPID
Variab le Y
Variab le Z
8 28
6 26
24
4
2
0 10 20 30 40 50 60 70 80 90 100
Number of samples
22
20
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+14
34
Test data
32
MANFIS
MANFISPID
30
Variab le Z
28
26
24
22
20
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+16
Test data
MANFIS MANFISPID
34
32
30
Variab le Z
28
26
24
22
20
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Fig. 9. Results of prediction of the variable Z at different horizons of
prediction

CONCLUSION
The industrial prognostic occupies today a place of choice in industrial maintenance. However, planning for the maintenance of real industrial systems very often depends on the evolution of several interdependent parameters. Moreover, the improvement of the performances of the prediction systems without increasing the complexity of the algorithm proves to be a major challenge in the field of industrial prognostic. It is strong from these remarks that, the work reported in this paper deals globally with the definition of a prognostic system capable of effectively predicting the evolution of three interdependent parameters. This system combines the neuralfuzzy network of the MANFIS type with PID controllers. These controllers have the particularity of keeping constant parameter values with several horizons of prediction.
The definition of the MANFISPID system proposed in this paper requires the definition of its MANFIS subsystem which implements the selection of inputs for the improvement of the prediction of three interdependent parameters. Three regulators of the PID type with constant gain values are associated with this prediction subsystem. The purpose of these controllers is to control the prediction error. The cascading of the prediction systems allowed the time variable to be incremented, an important element in the planning of maintenance activities.
The approach of obtaining the values of gains remaining constant at several horizons of prediction is presented. A comparative analysis of the RMSE of the MANFISPID system and its MANFIS subsystem is carried out. The representation of the predictions of the three variables is also performed at different horizons of prediction. The analysis of these different results reveals that the MANFISPID system offers better performance than its MANFIS subsystem. This improvement in the performance of the MANFISPID system is due to the control of the prediction error.
This work can be extended along several axes. In order to better meet the requirements of industrial systems, it will be possible to integrate the operating conditions and the future maintenance actions with this multiparameter prediction model.
REFERENCES

O. E. V. Dragomir, Contribution au pronostic de dÃ©faillances par rÃ©seau neuro flou : maÃ®trise de l'erreur de prÃ©diction, Automatique/Robotique. UniversitÃ© de Franche ComtÃ©, 2008, France. FranÃ§ais. <tel00362509>.

W. Sammouri, Data mining of temporal sequences for the prediction of infrequent failure events: application on oating train data for predictive maintenance, Signal and Image processing. UniversitÃ© ParisEst, 2014, English. <NNT: 2014PEST1041>. <tel 01133709>.

M. Bengtsson, Condition based maintenance systems technology where is development heading, The 17th Conference of Euromaintenance, Spain, Barcelona: Puntex Publicaciones, 2004.

M. H. Karray, B. MorelloChebel and N. Zerhouni, Towards a maintenance semantic architecture, In The Fourth World Congress on Engineering Asset Management. Athens, 2009.

M. Lewandowski and S. Oelker, Towards autonomous control in maintenance and spare part logistics challenges and opportunities for preacting maintenance concepts, Procedia Technology 15, 2014, pp. 333 340.

J. Lee, J. Ni, D. Djurdjanovic, H. Qiu, H. Liao, Intelligent prognostics tools and emaintenance, Computers in Industry – Special issue: Emaintenance archive Vol. 57 Issue 6, 2006.

A. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostic implementing conditionbased maintenance, Mech Syst Sign Processing. 20, 2006, pp. 14831510.

R. Gouriveau, M. E. Koujok, N. Zerhouni, SpÃ©cification d'un systÃ¨me neuroflou de prÃ©diction de dÃ©faillances Ã moyen terme, Rencontres Francophones sur la Logique Floue et ses Applications, LFA, 2007. NÃ®mes, France. <hal00192060>.

R. Zemouri, D. Racoceanu, N. Zerhouni, Recurrent Radial Basis Function network for timeseries prediction, Engin.Appl. of Artificial Intelligence, vol. 16, 2003, pp.453463.

R. Zemouri, R. Gouriveau, P. C. Patic, Combining a recurrent neural network and a PID controller for prognostic purpose: A way to improve the accuracy of predictions, WSEAS TRANSACTIONS
on SYSTEMS and CONTRO. Issue 5, Volume 5, May 2010, pp 353371, 2010.

J. S. R. Jang, ANFIS: Adaptivenetworkbased fuzzy inference systems, IEEE Trans. Syst., Man, and Cybern, 23, 1993, pp. 665 685.

S. Kara, S. Dasb, P. K. Ghoshb, Applications of neuro fuzzy systems: A brief review and future outline, Appl. Soft Comput. 15, 2014, pp. 243259.

ISO 133811, 2004: Condition monitoring and diagnostics of machines – prognostics – part1: General guidelines. International Standard ISO.

K. Medjaher, A. Mechraoui, N. Zerhouni, Diagnostic et pronostic de dÃ©faillances par rÃ©seaux bayÃ©siens, JournÃ©es Francophone sur les RÃ©seaux BayÃ©siens, Lyon, France, 2008.

P. Wang, G. Vachtsevanos, Fault prognosis using dynamic wavelet neural networks, in: Maintenance and Reliability Conference, 1999.

S. Zhang, R. Ganesan, Multivariable trend analysis using neural networks for intelligent diagnostics of rotating machinery, J Eng for Gas Turbines and Power. 119, 1997, pp. 378384.

P. Wang, G. Vachtsevanos, Fault prognostic using dynamic wavelet neural networks, Artif Intell for Eng Design Analysis and Manufact. 15, 2001, pp. 349365.

R. Zemouri, D. Racoceanu, N. Zerhouni, RÃ©seaux de neurones rÃ©currents Ã fonctions de base radiales : RRFR application Ã la surveillance dynamique, Journal EuropÃ©en des SystÃ¨mes AutomatisÃ©s. Volume X nÂ°X, 2002.

R. Zemouri, Recurrent Radial Basis Function network for time series prediction, Eng Appl of Artif Intell. 16, 2003, pp. 453463.

R. Syahputra, Application of neurofuzzy method for prediction of vehicle fuel consumption, Journal of Theoretical and Applied Information Technology (JATIT), 86(1), 2016, pp. 138149.

E. O. Dragomir, F. Dragomir, V. Stefan, E. Minca, Adaptive neuro fuzzy inference systems as a strategy for predicting and controling the energy produced from renewable sources, Energies, 8, 2015, pp. 1304713061. [Google Scholar] [CrossRef].

N. Ashiyani, and T. M. V. Suryanarayana, Adaptive Neuro Fuzzy Inference System (ANFIS) for prediction of groundwater quality Index in Matar Taluka and Nadiad Taluka, International Journal of Science and Research (IJSR), Vol. 4 Issue 9, 2015, pp. 123127.

R. E. Silvaa, R. Gouriveaua, S. JemeÃ¯a, D. Hissela, L. Boulonc, K. Agbossouc, S. N. Yousfi, Proton exchange membrane fuel cell degradation prediction based on Adaptive NeuroFuzzy Inference Systems, International Journal of Hydrogen Energy, Vol. 39, Issue 21, 2014, pp. 1112811144.

H. Wang, R. Hong, J. Chen, M. Tang, Intelligent health evaluation method of slewing bearing adopting multiple types of signals from monitoring system, International Journal of Engineering (IJE), TRANSACTIONS A: Basics Vol. 28, No. 4, 2015, pp. 573582.

R. Adeline, R. Gouriveau, N. Zerhouni, Pronostic de dÃ©faillances: MaÃ®trise de l'erreur de prÃ©diction, LISMMA, CRAN, ENSTIB. 7Ã¨me ConfÃ©rence Internationale de Mobilisation et Simulation, MOSIM08. Paris, France. 1 (sur CD ROM), 2008, 10 p. <hal 00270725>.

J. S. R. Jang, C. T. Suni and E. Mizutani, Neurofuzzy and soft computing: a computational approach to learning and machine intelligence, New York: Prentice Hall, 1997.

T. Benmiloud, Multioutput adaptive neurofuzzy inference system, in: WSEAS International Conference on Neural Networks, 11, Stevens Point. Proceedings Stevens Point, 2010, pp. 9498.

V. Nayak, Y. P. Banjare and M. F. Qureshi, Genetically Optimized Multiple ANFIS Based Discovery and Optimization of Catalytic Materials, International Journal of Innovative Research in Science, Engineering and Technology. Vol. 4, Issue 2, 2015, pp. 616627.

A. Abraham, Neuro Fuzzy Systems: SateoftheArt Modeling Techniques, arXiv preprint cs/0405011, 2004.

J. S. R. Jang and C.T. Sun, Neurofuzzy modeling and control, Proceedings of the IEEE 83 (3), 1995, pp. 378406.

E. N. Lorenz, Empirical orthogonal functions and statistical weather prediction, Sci. Rep. No. 1, Statist. Forecasting Proj. Dept. Meteor., MIT, 1956.

N. A. SismanYilmaz, F. N. Alpaslan and L. Jain, ANFIS unfolded in time for multivariate time series forecasting, Neurocomputing, 61, 2004, pp. 139168.