Publicado

2016-10-01

Gaussian clarification based on sign function

Clarificación gaussiana basado en la función signo

DOI:

https://doi.org/10.15446/dyna.v83n199.51385

Palabras clave:

Clarification, Fuzzy Logic, Identification, Stochastic Process (en)
Clarificación, Lógica Difusa, Identificación, Proceso Estocástico (es)

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This paper presents a clarification model in the fuzzy sense based on the Membership Inverse Function (MIF), in Control Theory. It is considered as an identification and requires bounded input and output signals. The sign function and its derivative is regarded as a Gaussian function into the mathematical Membership description. Specifically, the sign function considers the difference between the absolute state variable values and its centroid, rather than remaining in the triangle inequality. Therefore, the theoretical result applied in Matlab® using the reference values as an identification process in an Auto Regressive Moving Average (ARMA) (1, 1) model describes the performance. The clarification converging in almost all points of the desired signal depends on the different initial conditions. The convergence obtained by the functional error built by the second probability moment was also used and applied in the same software giving an illustrative description.
Este artículo presenta un modelo de clarificación en el sentido difuso basado en la función de membresía inversa como proceso de identificación para un sistema tipo caja negra con Una Entrada y Una Salida (UEUS). La función signo y su derivada para la función gaussiana, permite la descripción matemática del estado a identificar. Específicamente, la función signo aplica la diferencia entre los valores absolutos de la variable de estado y su centroide, en vez de la desigualdad del triángulo. El resultado teórico estuvo aplicado en Matlab®, usando como valores de referencia a los resultados del modelo Auto-Regresivo de Promedios Móviles (ARPM) (1, 1); permitiendo la clarificación y su convergencia en casi todos los puntos a la señal de referencia con diferentes condiciones iniciales entre ellos. La convergencia de forma ilustrativa se describió por el funcional del error a través del segundo momento de probabilidad usando el mismo software.

Referencias

M. Oussalah, On the compatibility between defuzzification and fuzzy arithmetic operations, Fuzzy Sets and Systems, 128(2), pp. 247-260, 2002.

Saletic., D.Z. and Popovich.,U., On possible constraints in applications of basic defuzzification techniques, Proceeding of the 8th Seminar on neural network applications in electrical engineering, NEUREL, pp. 225-230, 2006.

Jung, S.H., Cho., K.H., Kim., T.G. and Park., K.H., Defuzzification method for multi-shaped output fuzzy sets, Electronics Letters, 30(9), pp. 740-742, 1994.

Jiang., T. and Li., Y., Generalized defuzzification strategies and their parameter learning procedures, IEEE Transactions on Fuzzy Systems, 4(1), pp. 64-71, 1996.

Ma, M., Kandel, A. and Friedman, M., A new approach for defuzzification, Fuzzy Sets and Systems, 111(3), pp. 351-356, 2000.

Runkler, T.A., Extended defuzzification methods and their properties, Proceedings of the 5th IEEE International Conference on Fuzzy Systems, 1, pp. 694-700, 1996.

Liu, F., Wang, J. and Peng, Y., A new approach to parameters identification of fuzzy regression models, Proceedings of the 5th International Conference on Fuzzy Systems and Knowledge Discovery, 1, pp. 127-131, 2008.

Mastorocostas, P. and Theocharis, J., Orthogonal least squares fuzzy modeling of nonlinear dynamical systems, Proceedings of the 6th IEEE International Conference on Fuzzy Systems, 2, pp. 1147-1152, 1997.

Dai, H., Sinha, Naresh, K., Iterative instrumental variable method for robust identification of systems, IEEE Transactions on Industrial Electronics, 42(5), pp. 480-486, 1995.

Yinao, W., Aiqing, R. and Zhihui. Z., The numerical simulation of improving parameter estimation by instrumental variable method, Proceeding of the IEEE International Conference Grey Systems and Intelligent Services (GSIS), pp. 811-815, 2011.

Chen-Sen, O., Naijing, K. and Po-Jen, C., Recursive SVD-Based Least squares algorithm with forgetting factors for neuro-fuzzy modeling, Proceeding of the 14th International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD), pp. 575-580, 2013.

Paleologu, C., Benesty, J. and Ciochina, S., A robust variable forgetting factor recursive least squares algorithm for system identification, IEEE Signal Processing Letters, 15, pp. 597-600, 2008.

Medel, J.J. and Zagaceta, M.T., Estimación-identificación como filtro digital integrado: descripción e implementación recursiva. Rev. Mex. Fis., 56(1), pp. 1-8, 2010.

Ding, F., Liu, G. and Liu., X.P., Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE Transactions on Automatic Control, 55(8), pp. 1976-1981, 2010.

Chang, S.L. and Ogunfunmi, T., Stochastic gradient based on 3rd order Volterra system identification by nonlinear Wiener adaptive algorithm, IEE Proceedings of the Vision, Image and Signal Processing, 150(2), pp. 90-98, 2003.

Bershad, N.J., Celka, P. and Vesin, J., Stochastic analysis of gradient adaptive identification of nonlinear systems with memory for Gaussian data and noisy input and output measurements, IEEE Transactions on Signal Processing, 47(3), pp. 675-689, 1999.

Wei, C.L., Tsai, J.S.H., Guo, S.M. and Shieh., L.S., Universal predictive Kalman filter based on fault estimator and tracker for sampled-data non-linear time-varying systems, Control Theory & Applications, IET, 5(1), pp. 203-220, 2011.

Chafaa, K., Ghanai, M. and Benmahammed, K., Fuzzy modeling using Kalman filter, Control Theory & Applications, IET, 1(1), pp. 58-64, 2007.

Medel, J.J. y García, C.V., Estimación de parámetros usando la deconvolución y la pseudo-inversa: descripción e implementación recursiva. Rev. Mex. Fis., 56(1), pp. 54-60, 2010.

Erdogmus, D., Hild., K.E., Principe, J.C., Lazaro, M. and Santamaria, I., Adaptive blind deconvolution of linear channels using Renyi's entropy with Parzen window estimation, IEEE Transactions on Signal Processing, 52(6), pp. 1489-1498, 2004.

Chen, L. and Kim-Hui, Y., A soft double regularization approach to parametric blind image deconvolution, IEEE Transactions on Image Processing, 14(5), pp. 624-633, 2005.

Depeyrot, M., Linear System identification using real-time deconvolution, IEEE Transactions on Computers, C-1(12), pp. 1139- 1145, 1970.

Meng-Xin, L., Cheng-dong, W. and Feng, J., A vision-based inspection system using fuzzy rough neural network method, Proceeding of the International Conference on Machine Learning and Cybernetics, pp. 3228-3232, 2006.

Sivanandam, S.N., Deepa, S.N. and Sumathi, S., Introduction to Fuzzy logic using MATLAB®, Springer, pp. 95 – 108, 2007.

Nguyen, H.T., Prasad, N.R., Walker., C.L. and Walker, E.A., A 1st course in Fuzzy and neural Control, (Chapman and Hall/CRC, (2002), Ed. 1, pp. 120-123.

Kosinski, W., Evolutionary algorithm determining defuzzyfication operators, Engineering Applications of Artificial Intelligence, 20(5), pp. 619-627, 2007.

Urbanski, K. and Wasowski, J., Fuzzy measurement theory, Measurements, 41(4), pp. 391-402, 2008.

Jang, J.S.R., Sun, C.T. and Mizutani, E., Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence, Prentice-Hall, 1997, pp. 24 - 28.

Shin, Y.C. and Xu, C., Intelligent systems: modeling, optimization, and control. Section 2.1.3. CRC Press, 2008.

Slotine, J.J. and Li, W., Applied nonlinear control, Prentice-Hall, 1991, 1, pp. 290-306.

Shtessel, Y., Edwards, C., Fridman, L. and Levant, A., Sliding Mode control and observation, Control Engineering, Birkhäuser, pp. 18-19, 2013.

Velásquez-Henao, J.D. and Branch-Bedoya, J.W., Examples in the classroom: Pattern classification using the R language, DYNA, 79(173), pp. 81-88, 2012.

Velásquez-Henao, J. D., Rueda-Mejía, V.M. and Franco-Cardona, J.D. Electricity demand forecasting using a SARIMA- multiplicative single neuron hybrid model, DYNA, 80(180), pp. 4-8, 2013.

Roy-Chowdhury, S. and Pedrycz, W., A survey of defuzzification strategies, Int. J. Intel. Syst, pp. 679-695, 2001.

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[1]
“Clarificación gaussiana basado en la función signo”, DYNA, vol. 83, no. 199, pp. 225–228, Oct. 2016, doi: 10.15446/dyna.v83n199.51385.

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