JAMP  Vol.4 No.4 , April 2016
Recurrence Quantification Analysis of Rough Surfaces Applied to Optical and Speckle Profiles
Abstract: In this paper, Recurrence Quantification Analysis (RQA) is set as a practical nonlinear data tool to establish and compare surface roughness (Ra) through percentage parameters of a dynamical system: Recurrence (%REC), Determinism (%DET) and Laminarity (%LAM). Variations in surface roughness of different machining procedures from a typical metallic casting comparator are obtained from scattering intensity of a laser beam and expressed as changes in the statistics of speckle patterns and profiles optical properties. The application of the analysis (RQA) by Recurrence Plots (RPs), allowed to distinguish between machining procedures, highlighting features that other methods are unable to detect.
Cite this paper: Martinez, O. , Mayorga Cruz, D. , Chavarín, J. and Bustos, E. (2016) Recurrence Quantification Analysis of Rough Surfaces Applied to Optical and Speckle Profiles. Journal of Applied Mathematics and Physics, 4, 720-732. doi: 10.4236/jamp.2016.44083.

[1]   Guerrero, F.E.L., Flores, R.C. and Acosta, M.D. (2003) Caracterización de Superficies Maquinadas por Medio de Parámetros de Rugosidad. Ingenierías, 6, 62-68.

[2]   Ravish, U.K.S., Alva, A., Gangadharan, K.V. and Desai, V. (2011) Recurrence Quantification Analysis to Compare the Machinability of Steels. ARPN Journal of Engineering and Applied Sciences, 6, 8-13.

[3]   Litak, G., Syta, A. and Rusinek, R. (2011) Dynamical Changes during Composite Milling: Recurrence and Multiscale Entropy Analysis. International Journal of Advanced Manufacturing Technology, 56, 445-453.

[4]   Bethencourt, M., Botana, F.J., Calvino, J.J., Marcos, M. and Rodríguez-Chacón, M.A. (1998) Aplicación del Análisis de Fourier al Estudio de Perfiles de Rugosidad de Muestras Erosionadas. Revista de Metalurgia, 34, 7-11.

[5]   Eckmann, J.P., Kamphorst, S.O. and Ruelle, D. (1987) Recurrence Plots of Dynamical Systems. Europhysics Letters, 4, 973-977.

[6]   Webber, C.L. and Zbilut, J.P. (1994) Dynamical Assessment of Physiological Systems and States Using Recurrence Plot Strategies. Journal of Applied Physiology, 76, 965-973.

[7]   Marwan, N. (2003) Encounters with Neighbours—Current Developments of Concepts Based on Recurrence Plots and Their Applications. PhD Thesis, Institute for Physics, University of Potsdam, Potsdam.

[8]   Liu, M. and Hu, Z. (2014) Nonlinear Analysis and Prediction of Time Series in Multiphase Reactors. In: Liu, M., Ed., Springer Briefs in Applied Sciences and Technology, Springer International Publishing, New York, 1-44.

[9]   Pincus, S.M. (1991) Approximate Entropy as a Measure of System Complexity. Proceedings of the National Academy of Sciences of the United States of America, 88, 2297-2301.

[10]   Restrepo, J.N., Shlotthauer, G. and Torres, M.E. (2014) Maximum Approximate Entropy and Threshold: A New Approach for Regularity Changes Detection. Physica A, 409, 97-109.

[11]   Yan, R., Liu, Y. and Gao, R.X. (2012) Permutation Entropy: A Nonlinear Statistical Measure for Status Characterization of Rotary Machines. Mechanical Systems and Signal Processing, 29, 474-484.

[12]   Pérez-Canales, D., álvarez-Ramírez, J., Jáuregui-Correa, J.C., Vela-Martínez, L. and Herrera-Ruiz, G. (2011) Identification of Dynamic Instabilities in Machine Process Using the Approximate Entropy Method. International Journal of Machine Tools & Manufacture, 51, 556-564.

[13]   Pérez-Canales, D., Vela-Martinez, L., Jáuregui-Correa, J.C. and álvarez-Ramírez, J. (2012) Analysis of Entropy Randomness Index for Machining Chatter Detection. International Journal of Machine Tools & Manufacture, 62, 39-45.

[14]   Sherwood, K.F. and Crookall, J.R. (1967-1968) Surface Finish Assessment by an Electrical Capacitance Technique. Proceedings of the Institution of Mechanical Engineers, 182, 344-349.

[15]   Blessing, G.V. and Eitzen, E.D. (1998) Surface Roughness Sensed by Ultrasound. Surface Topography, 1, 143-158.

[16]   Sosa Correa, W.O., Sierra, M., Parra Vargas, C.A. and Salcedo, L.A. (2006) Análisis de Rugosidad por Microscopía de Fuerza Atómica (AFM) y Software SPIP Aplicado a Superficies Vítreas. Revista Colombiana de Física, 38, 826-829.

[17]   Peña Sierra, R., Romero-Paredes, R.G. and águila Rodríguez, G. (2001) Estudio de la Morfología Superficial e índice de Refracción en Películas Nanométricas de Silicio Poroso. Superficies y Vacío, 13, 92-96.

[18]   Sherrington, I. and Smith, E.H. (1988) Modern Measurement Techniques in Surface Metrology: Part I. Stylus Instruments, Electron Microscopy and Non-Optical Comparators. Wear, 125, 271-288.

[19]   Sherrington, I. and Smith, E.H. (1988) Modern Measurement Techniques in Surface Metrology: Part II. Optical Instruments. Wear, 125, 289-308.

[20]   Sampaio, A.L., Lobao, D.C., Nunes, L.C.S., Dos Santos, P.A.M., Silva, L. and Huguenin, J.A.O. (2011) Hurst Exponent Determination for Digital Speckle Patterns in Roughness Control of Metallic Surfaces. Optics and Lasers in Engineering, 49, 32-35.

[21]   Marbán, A., Sarmiento-Martínez, O., Mayorga-Cruz, D., Menchaca, C. and Uruchurtu, J. (2010) Polymer Surface Roughness Determination throughout the Hurst Analysis from Optical Signal Measurements. Journal of Materials Science and Engineering, 4, 26-31.

[22]   Menchaca, C., Nava, J.C., Valdéz, S., Sarmiento-Martínez, O. and Uruchurtu, J. (2010) Gamma-Irradiated Nylon Roughness as Function of Dose and Time by the Hurst and Fractal Dimension Analysis. Journal of Materials Science and Engineering, 4, 50-58.

[23]   Elias, J. and Rajesh, V.G. (2010) Detection of Chatter in Turning Using Recurrence Plot Analysis of Input Current, Vibration of Tool and Speckle Image of Machined Surface. International Journal of Production Technology and Management (IJPTM), 1, 56-64.

[24]   Mhalsekar, S.D., Rao, S.S. and Gangadharan K.V. (2010) Investigation on Feasibility of Recurrence Quantification Analysis for Detecting Flank Wear in Face Milling. International Journal of Engineering, Science and Technology, 2, 23-38.


[26]   Takens, F. (1993) Detecting Nonlinearities in Stationary Time Series. International Journal of Bifurcation and Chaos, 3, 241-256.

[27]   Cazares Ibáñez, E.A. (2005) Estudio de sistemas caóticos y su relación con el fenómeno de corrosión por picadura en un sustrato metálico en presencia de iones cloruro y sulfato. PhD Thesis, Facultad de Química, UNAM, México, D.F.

[28]   Fraser, A.M. and Swinney, H.L. (1986) Independent Coordinates for Strange Attractors from Mutual Information. Physical Review A, 33, 1134-1140.

[29]   Kennel, M.B., Brown, R. and Abarbanel, H.D.I. (1992) Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction. Physical Review A, 45, 3403-3411.


[31]   Grassberger, P. and Procaccia, I. (1983) Estimation of Kolmogorov Entropy from a Chaotic SIGNAL. Physical Review A, 28, 2591-2593.

[32]   Schouten, J.C., Takens, F. and Van den Bleek, C.M. (1994) Maximum-Likelihood Estimation of the Entropy of an Attractor. Physical Review E, 49, 126-129.

[33]   Schouten, J.C., Takens, F. and Van den Bleek, C.M. (1994) Estimation of the Dimension of a Noisy Attractor. Physical Review E, 50, 1851-1861.



[36]   Shinkel, S. Dimigen, O. and Marwan, N. (2008) Selection of Recurrence Threshold for Signal Detection. The European Physical Journal Special Topics, 164, 45-53.

[37]   Zbilut, J.P., Thomasson, N. and Webber, C.L. (2002) Recurrence Quantification Analysis as a Tool for Exploration of Nonstationary Cardiac Signals. Medical Engineering & Physics, 24, 53-60.