Proposition of Multi-ANFIS Architecture Mounted in Series for the Multi-Parameters Prediction

Proposition of Multi-ANFIS Architecture Mounted in Series for the Multi-Parameters Prediction

Tjahe Agnès 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 Dschang-Cameroon

Djanna Koffi Francis

Department of Thermal Engineering University Institute of Technology University Of Douala,

1. 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 Médard

   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. Dschang-Cameroon

   AbstractThis article is devoted to the proposed MANFIS (Multi-output Adaptive Neuro-Fuzzy 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; multi-parameters; prediction error

   1. 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

      1. [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 data-driven 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 data-guided approach, several mutations have been observed. We started with the use of Neural Networks (NN), to the NN loops. Today, the data-driven prognostic is based on hybrid systems such as Neuro-Fuzzy (NF) networks. It is for this purpose that the system chosen for the development of our work is an ANFIS (Adaptive Neuro-Fuzzy 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 multi-parameters 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 neuro-fuzzy 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.

   2. PROBLEM DEFINITION

      1. 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 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.

      2. 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].

      3. 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 data-based 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 Neuro-Fuzzy 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.

      1. 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 multi-parameters 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.

   3. NEURO-FUZZY PREDICTION SYSTEM

      A. ANFIS Architecture

      1. 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.

   4. 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

      1. 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 so-called 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

      2. 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.

         1. 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 non-convergent. 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.

         2. 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 (K×3) containing the expected values of the three parameters for the K tests and A the

   5. 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 (K×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

   6. 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 multi-parameter model.

REFERENCES

1. O. E. V. Dragomir, Contribution au pronostic de défaillances par réseau neuro flou : maîtrise de l'erreur de prédiction, Automatique/Robotique. Université de Franche Comté, 2008, France. Français. <tel-00362509>.

2. 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. Université Paris-Est, 2014, English. <NNT: 2014PEST1041>. <tel-01133709>.

3. M. Bengtsson, Condition based maintenance systems technology where is development heading, The 17th

   Conference of Euromaintenance, Spain, Barcelona: Puntex Publicaciones, 2004.

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

5. 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.

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

7. A. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostic implementing condition-based maintenance, Mech Syst Sign Processing. 20, 2006, pp. 1483-1510.

8. R. Gouriveau, M. E. Koujok, N. Zerhouni, Spécification d'un système neuro-flou de prédiction de défaillances à moyen terme, Rencontres Francophones sur la Logique Floue et ses Applications, LFA, 2007. Nîmes, France. <hal-00192060>.

9. J. S. R. Jang, ANFIS: Adaptive-network-based fuzzy inference systems, IEEE Trans. Syst., Man, and Cybern, 23, 1993, pp. 665-685.

10. 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.

11. M. E. Koujok, Contribution au pronostic industriel: intégration de la confiance à un modèle prédictif euro-flou, Automatique/Robotique. Université de Franche-Comté, 2010, Français. <tel-00542230>.

12. ISO 13381-1, 2004: Condition monitoring and diagnostics of machines – prognostics – part1: General guidelines. International Standard ISO.

13. K. Medjaher, A. Mechraoui, N. Zerhouni, Diagnostic et pronostic de défaillances par réseaux bayésiens, Journées Francophone sur les Réseaux Bayésiens, Lyon, France, 2008.

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

15. 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. 378-384.

16. P. Wang, G. Vachtsevanos, Fault prognostic using dynamic wavelet neural networks, Artif Intell for Eng Design Analysis and Manufact. 15, 2001, pp. 349-365.

17. R. Zemouri, D. Racoceanu, N. Zerhouni, Réseaux de neurones récurrents à fonctions de base radiales : RRFR application à la surveillance dynamique, Journal Européen des Systèmes Automatisés. Volume X n°X, 2002.

18. R. Zemouri, Recurrent Radial Basis Function network for time-series prediction, Eng Appl of Artif Intell. 16, 2003, pp. 453-463.

19. Syahputra R., Application of Neuro-Fuzzy Method for Prediction of Vehicle Fuel Consumption, Journal of Theoretical and Applied Information Technology (JATIT), 86(1) , 2016, pp. 138-149.

20. 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].

21. 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. 123-127.

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

23. 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. 573-582.

24. R. Adeline, R. Gouriveau, N. Zerhouni, Pronostic de défaillances: Maîtrise de l'erreur de prédiction, LISMMA, CRAN, ENSTIB. 7ème Conférence Internationale de Mobilisation et Simulation, MOSIM08. Paris, France. 1 (sur CD ROM), 2008, 10 p. <hal-00270725>.

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

26. T. Benmiloud, Multi-output adaptive neuro-fuzzy inference system, in: WSEAS International Conference on Neural Networks, 11, Stevens Point. Proceedings Stevens Point, 2010, pp. 94-98.

27. 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. 616-627.

28. A. Abraham, Neuro Fuzzy Systems: Sate-of-the-Art Modeling Techniques, arXiv preprint cs/0405011, 2004.

29. J. S. R. Jang and C.T. Sun, Neuro-fuzzy modeling and control, Proceedings of the IEEE 83 (3), 1995, pp. 378-406.

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

31. N. A. Sisman-Yilmaz, F. N. Alpaslan and L. Jain, ANFIS unfolded in time for multivariate time series forecasting, Neurocomputing, 61, 2004, pp. 139-168.