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 Authors : Tjahe Agnes Virginie, Mtopi Fotso Blaise E., Djanna Koffi Francis, Fogue Medard
 Paper ID : IJERTV6IS070311
 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 MultiANFIS Architecture Mounted in Series for the MultiParameters Prediction
Tjahe AgnÃ¨s Virginie
Laboratory of Engineering for Industrial Systems and Environment
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,

Box. 8698 DoualaCameroon
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 article is devoted to the proposed MANFIS (Multioutput Adaptive NeuroFuzzy System) system for the prognostic of failure. It is a system that predicts at short and medium term the evolution of three interdependent parameters with an acceptable accuracy without increasing the complexity of the treatments. The choice of inputs is implemented to improve the performance of the architecture. For this architecture, the cascading of the MANFIS systems is implemented for the incrementation of the horizon of prediction. Research oriented towards the development of prediction systems of the ANFIS type suggests that models with several parameters would be closer to real industrial systems. This is why the prognostic system proposed here allows the prediction of three interdependent parameters. We shall begin the work reported here by presenting the place of prognostic in the maintenance activity. A presentation of features of the predictive system of type MANFIS is proposed. The Lorenz dynamic system is used to illustrate our prediction architecture. A discussion of the distribution of the global architecture error at different horizons of prediction is presented.
Keywords Maintenance; prognostic; choice of inputs; MANFIS in series; multiparameters; 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

[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. 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 [9]. 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, [10] reveal the need for the selection of optimal parameters for the prediction of neurofuzzy systems. The observations above permitted the proposal of a new architecture which uses input parameters considered optimal for the prediction of the evolutions of several interdependent parameters at short and medium interval of time with a satisfactory prediction error.
The rest of this article 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 prognostic in industrial
maintenance and some work aimed at reducing and controlling the error to introduce the need to propose a multi parameters prediction system.
Section 3 presents the NF systems, of the MANFIS and ANFIS types. In section 4 we shall present our proposed MANFIS network and the methodology by which we obtained the results of our work. These results will be analyzed and discussed in Section 5. Section 6 is devoted to the conclusion and definition of future works.

[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].

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 [11]. Formerly the socalled 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 [12] 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. [13] 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 curently 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 [14], [15], and [16] etc. to the curly networks of [17] and [18].
Improved performance and the desire to reduce the
Beside the reduction of the prediction error, [24] and [1] focus their work on controlling prediction error. [24] 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 [25]. 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, [25] developed the MANFIS (Multiple Adaptive NeuroFuzzy Inference System) model. In addition, [26] 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.

Propose a MANFIS system for the prediction of three parameters and the genetic algorithm is associated to improve the performance.
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 applies the selection of inputs to a MANFIS system with three interdependent parameters. The incrementation of the horizon of prediction is done by cascading the proposed MANFIS system.
The work presented here is aimed at proposing a MANFIS system capable of effectively predicting the parameters of a chaotic dynamic system in the short and medium term.


NEUROFUZZY PREDICTION SYSTEM
A. ANFIS Architecture

Effectuates the analysis of some NF architectures and realizes that ANFIS architecture offers a better RMSE.
TABLE I. PERFORMANCE OF SOME NF MODELS [28]
Model
Epochs
RMSE
ANFIS
75
0.0017
NEFPROX
216
0.332
EfuNN
1
0.0140
dmEFuNN
1
0.0042
SONFIN
1
0.0180
Fig. 1. Network structure of ANFIS model [25]
Layer 1. Generates the membership grades:
complexity of prognostic systems led researchers to migrate to hybrid systems such as NF networks [19], [20], [21], [22]
and [23] etc.
O1
i A
i
i B
O1
i
(x) , i=1, 2
( y) , i=1, 2
A
Where
i
and
B
i
can be any membership functions.


PROPOSED SYSTEM FOR THE PREDICTION OF THREE INTERDEPENDENT PARAMETERS
Layer 2. Generates the firing strengths.
In this section we propose a system capable of performing the prediction of three interdependent parameters.
i i A
O2 w
i
(x)
B
i
( y) , i=1, 2
This prediction system could be applicable in cases where the planning of maintenance activities is dependent on three key
Layer 3. Normalizes the firing strengths.
parameters. These parameters being themselves dependent on each other.
i i
O3 w wi , i=1, 2

Structure of our proposed system
MANFIS
w1 w2
Layer 4. Calculates rule outputs based on the consequent parameters.
MANFIS
Xint
Yint Zint
x(t 1) y(t 1) z(t 1)
MANFIS
x(t d)
O4 w f w( p x q y r ) , i=1, 2
i i i i i i
Where, and are the socalled consequential parameters.
Layer 5. Output calculation
2
y(t d)
z(t d)
Fig. 3. Prediction system of three interdependent parameters
For this system, the variable d represents the Horizon
O5
2
i wi fi i1
wi fi
i1
w1 w2
, i=1, 2
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
After this phase, the optimal values of these membership function parameters and consequential parameters are set by a
Variables Xint, Yint and Zint are vectors defined as follows:
Xint [x(t 3) x(t 2) x(t 1) x(t) ]T
hybrid learning algorithm that combines the method of least squares with the backpropagation learning algorithm. Finally,
Yint
[ y(t 3)
y(t 2)y(t 1)
y(t) ]T
the ANFIS output is calculated by means of consequential parameters.
Zint
[z(t 3)
z(t 2)
z(t 1)
z(t) ]T

MANFIS Architecture
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 [29].
ANFIS1
y1
x1
ANFIS2
x2 y2
. . . .
. . . .
ANFISm
.
xp ym
Fig. 2. Architecture of the MANFIS network [29]
In this model, the input variables xi (i=1, 2,,p) are independent and the output variables yi (i=1, 2,,p) are functions of the input variables.
For this system, the prediction of the state of the parameters at a given instant takes into account the state of these parameters at the four previous instants. The incrementation of the horizon of prediction is done by cascading the base system.

Training base
For the validation of our system we used the time series of Lorenz. This series of data is chaotic, therefore non periodic and nonconvergent. The time series of Lorentz presents the evolution over time of three interdependent parameters [30]. Although widely used in the field of climate 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
x x1 , x2 ,…, xp
yi fi (x) i , i 1, 2,…, m
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 our prediction system with three interdependent parameters. 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 [31] and taken over by [24].
Consider A the matrix (KÃ—3) containing the expected values of the three parameters for the K tests and A the



RESULTS AND ANALYSIS
Table II presents the RMSE values obtained at different horizons of prediction.
TABLE II. RMSE AT DIFFERENT HORIZONS OF PREDICTION
Horizon of prediction
RMSE test set
t +1
0.0003
t+2
0.0018
t+4
0.0109
t+6
0.0330
t +8
0.0761
t+10
0.1463
t+12
0.468
t+14
0.3766
t+16
0.5310
t+18
0.7019
t+20
0.8802
matrix (KÃ—3) containing the predicted values of the three
parameters for the K tests.
The RMSE between the expected values and the estimated values is calculated by the equation (16). We have tested eleven horizons of prediction (d varying from 1 to 20).
x1 y1 z1
A
(14)
xk yk zk
x1 y1 z1
A
xk yk zk
(15)
Figs. 5 to 7 show a comparative analysis of the predictions obtained by the MANFIS system compared to the test data. Analysis of these curves shows that the selection of
inputs provides acceptable accuracy in the short and medium
k 1, K ,
1 K
2
(16)
term.
K
RMSE
A(k) A(k)
k 1
Horizon of prediction t+12
Y intn You tn
Y int1 You t1
X intn Xou tn
X int1 Xou t1
Data from Lorenz
Import and form data for the training and the test
Generate FIS 1
Generate FIS 2
Generate FIS 3
Training (ANFIS1)
Training (ANFIS2)
Training (ANFIS3)
Form a MANFIS system
10
Test data
MANFIS
9
Vaviable X
8
7
Z intn Zou tn
Z int1 Zou t1
6
5
4
10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+14
Test data
MANFIS
12
11
10
9
Variab le X
8
Repeat d times
7
Use test data for
prediction 6
5

RMSE

Test data vs. MANFIS output plot 4
Fig. 4. Process deployed in the prediction system of three interrelated
parameters
3
2
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+16
Test data
MANFIS
12
11
10
9
Variab le X
8
7
6
5
4
Horizon of prediction t+16
12
Test data
MANFIS
11
10
9
Variab le Y
8
7
6
5
4
3
2
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Fig. 5. Results of prediction of variable X at different horizons of
prediction
3
2
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Fig. 6. Results of prediction of variable Y at different horizons of
prediction
Horizon of prediction t+12
13
12
Test data
11
MANFIS
10
9
Variable Y
8
7
6
5
4
3
2
0 10 20 30 40 50 60 70 80 90 100
Number of samples
Horizon of prediction t+14
34
32 Test data
MANFIS
30
Variab le Y
28
26
24
22
Horizon of prediction t+12
34
Test data
32
MANFIS
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+14
34
Test data
32
MANFIS
30
Variab le Z
28
26
24
20
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+16
Test data
MANFIS
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. 7. Results of prediction of variable Z at different horizons of
prediction


CONCLUSION

The industrial prognostic occupies today a place of choice in industrial maintenance. However, the planning of the maintenance of real industrial systems very often depends on the evolution of several interdependent parameters. This remark proves that the work reported in this paper deals globally with the definition of a prognostic system capable of predicting the evolution of three interdependent parameters.
For the setting up of this system the selection of the inputs and the cascading of the MANFIS systems have been implemented. This cascading allowed the incrementation of the variable time, an important element for the planning of the maintenance activities. The evaluation of the prediction indicators allowed us to conclude that the system offers satisfactory values of the RMSE for short and medium interval of time.
Although we have obtained acceptable prediction accuracy for short and medium term.
This work can be extended along several axes. First we can improve accuracy of prediction system without increasing the complexity of the prediction algorithm. In addition to improving accuracy, we could integrate the operating conditions and the future maintenance actions to this multiparameter model.
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