Using fuzzy inference system to model the Earth’s displacement field

Document Type : Research


1 Assistant Professor, Department of Geoscience Engineering, Faculty of surveying, Arak University of Technology, Arak, Iran

2 M.Sc. Student, Department of engineering, Faculty of surveying, Azad University, Ahar branch, Ahar, Iran


Today, by the expansion of geodetic networks and the creation of base points for geodetic applications, the study of the motion of the earth's crust and the study of the activity of faults are the most important tasks of geodesic. With the establishment of satellite positioning systems, the creation of base points in geodetic networks has been substantial. The basic point in creating base points is the estimation and obtaining the velocity field and the displacement of these points in a reference framework. Determining velocity field with the high precision and the displacement of the base points in geodetic networks is of great importance. With the availability of information on the velocity of GPS stations in a geodetic network, one can model the kinematics and dynamics of the earth's crust in that area. In this regard, extensive research on these problems has been conducted around the world.
The main objective of this paper is the use of Fuzzy Inference System (FIS) for modeling the surface displacement field in Iran. The concept and study of fuzzy logic began in 1920, but the fuzzy logic was first used by Lotfizadeh (1921-2017) in 1965 at Berkeley University. FIS can formulate the behavior of a phenomenon in terms of the use of descriptive and empirical rules without the need for an accurate analytical model. The fuzzy inference system is the tool for formulating a process with the help of rules as if-then. The set of these fuzzy rules is called the fuzzy rules base. Argumentation is done using a fuzzy inference system. The fuzzy inference system is generally made up of the following components:
1. Fuzzy, 2. Base rules, 3. Fuzzy Inference Engine, 4. Diffusion.
The process of converting explicit variables into linguistic variables is called fuziation. The inference engine evaluates and deduces the rules using inference algorithms, and after the rules are combined, the output is converted by the divisible unit into an explicit or numerical value. The most common type of fuzzy inference system is the Tacagi-Sugeno fuzzy system.
In this paper, the FIS is used to model the surface displacement field of the Earth's crust in Iran. A fuzzy inference system is a system that uses the rules of the if-then-fuzzy rules to recognize the properties of the phenomenon. Since this system is capable of modeling nonlinear phenomena, in this paper it is used to model the surface variations. For better and more accurate evaluation, the results of the fuzzy inference system were compared with the results of GPS velocity field observations as well as the results of the artificial neural network (ANNs). To do this, 5 test stations have been considered and observations of these 5 stations have not been used in fuzzy network and neural network training. Based on the analysis, the maximum relative error calculated at the 5 test stations for the fuzzy network and the neural network in the eastern component were calculated to be 20.02% and 29.74%, respectively. The results indicate that the fuzzy network has more accuracy than the artificial neural network in speed field modeling.


Main Subjects

آزموده اردلان، ع.، وثوقی، ب. و روفیان نایینی، م.، 1390، آنالیز تغییر شکل زمین بر مبنای هندسه ذاتی رویه، تحقیق موردی: آنالیز تغییرشکل شبکة ژئودینامیک کشور در فاصلة زمانی 1999 تا 2005، م. فیزیک زمین و فضا، 37(4)، 125-146.
آزموده اردلان، ع. و روفیان نایینی، م.، 1388، پیشنهادی برای محاسبه مستقیم تانسور کرنش از طریق تغییر در طولها و زوایا، بررسی موردی: محاسبة تغییر شکل شبکة ژئودینامیک کشور، م. فیزیک زمین و فضا، 35(2)، 37-60.
آزموده اردلان، ع. و روفیان نایینی، م.، 1386، برآورد تانسور کرنش در شبکه ژئودینامیک کشور، پایان‌نامه کارشناسی ارشد، پردیس دانشکده‌های فنی دانشگاه تهران.
راست‌بود، ا. و وثوقی، ب.، 1390، مدل‌سازی تغییر شکل سطحی زمین در منطقه برخورد مایل اوراسیا-عربستان در محدوده فلات ایران بر اساس روش المان‌های مرزی، رساله دکتری، دانشگاه صنعتی خواجه نصیر الدین طوسی، تهران
روفیان نایینی، م. و ملکشاهیان، ز.، 1396، آنالیز هندسی تغییر شکل، با استفاده از تلفیق مشاهدات GPS و روش المان محدود غیرخطی بر مبنای درون‌یابی پیوسته بزیر کوبیک، نشریه علمی پژوهشی علوم و فنون نقشه برداری، ۶ (۴)، ۲۹-۳۹.
غفاری رزین، م. ر. و وثوقی، ب.، 1395، برآورد میدان سرعت پوسته زمین با استفاده از شبکه عصبی مصنوعی و درون‌یابی کریژینگ فراگیر (منطقه مورد مطالعه: شبکه ژئودینامیک کشور ایران)، م. فیزیک زمین و فضا، 42(1)، 89-98.
فیضی، ر.، وثوقی، ب. و غفاری رزین، م.ر.، 1398، مدل‌سازی سری‌های زمانی تغییرات محتوای الکترون کلی یونسفر با به‌کارگیری روش عددی سیستم استنتاج عصبی-فازی سازگار مطالعه خاص: ایستگاه دائمی GPS تهران. نشریه علمی پژوهشی علوم و فنون نقشه برداری، ۸(۴)، ۱۰۹-۱۱۹.
کردی، ک.، 1387، آنالیز دوبعدی شبکه ژئودینامیک ایران به‌روش آنالیز رباستنس، پایان‌نامه کارشناسی‌ارشد، دانشگاه صنعتی خواجه نصیرالدین طوسی.
معماریان، ا. و جمور، ی.، 1392، بررسی کارایی شبکه‌های عصبی مصنوعی در تخمین سرعت نقاط ژئودتیک، پایان‌نامه کارشناسی ارشد، دانشگاه آزاد اسلامی واحد اهر، زمستان 1392.
Akyilmaz, O. and Arslan, N., 2008, An experiment of predicting Total Electron Content (TEC) by fuzzy inference systems, Earth, planets and space, 60(9), 967-972.
Bogusz, J., Klos, A., Grzempowski, P. and Kontny, B., 2013, Modelling the velocity field in a regular grid in the area of poland on the basis of the velocities of European permanent stations, Pure and Applied Geophysics, doi: 10.1007/s00024-013-0645-2.
Chen, R., 1991, On the horizontal crustal deformations in Finland, Helsinki, Finish Geodetic Institute.
Djamour,Y., Mousavi, Z., Nankaly, H. and Seddighi, M., 2007, Initial estimates of the velocity field and strains tensor by using Iranian Permanent GPS Network for Geodynamics purposes, The first conferences of the earthquake precursors.
Djamour, Y., Vernant, P., Nankali, H. and Tavakoli, F., 2011, NW Iran-eastern Turkey present-day kinematics: results from the Iranian permanent GPS network. Earth. Planet. Sci. Lett. 307 (1), 27–34.
Fortier, N., Sheppard, J. and Pillai, K., 2012, DOSI: Training artificial neural networks using overlapping swarm intelligence with local credit assignment. In: Soft computing and intelligent systems (SCIS) and 13th international symposium on advanced intelligent systems (ISIS), 1420–1425, doi:10.1109/SCIS-ISIS.2012.6505078.
Grafarend, E. W. and Voosoghi, B., 2003, Intrinsic deformation analysis of the earth’s surface based on displacement fields derived from space geodetic measurements. Case studies: present-day deformation patterns of Europe and of the Mediterranean area (ITRF data sets). J. Geodesy 77(5), 303–326.
Gullu, M., Yilmaz, I., Yilmaz, M. and Turgut, B., 2011, An alternative method for estimating densification point velocity based on back propagation artificial neural networks, Studia Geophysica et Geodaetica, 55(1), 73-86.
Jang, J. S., 1993, ANFIS: adaptive-network-based fuzzy inference system. IEEE transactions on systems, man, and cybernetics, 23(3), 665-685.
Malekshahian, Z. and Raoofian Naeeni, M., 2018, Deformation analysis of Iran Plateau using intrinsic geometry approach and C1 finite element interpolation of GPS observations, Journal of Geodynamics, 119, 47-61.
Mars, P., Chen, J. R. and Nambiar, R., 1996, Learning algorithms: theory and applications in signal processing, Control and Communications, CRC Press, Boca Raton, Florida.
Moghtased-Azar, K. and Grafarend, E. W., 2009, Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects. J.Geodesy 83(5), 431–454.
Moghtased-Azar, K. and Zaletnyik, P., 2009, Crustal velocity field modeling with neural network and polynomials, in: Sideris, M.G., (Ed.), Observing our changing Earth, International Association of Geodesy Symposia, 133, 809-816.
Mashhadi Hossainali, M., 2006, A comprehensive approach to the analysis of the 3Dkinematics of deformation, Ph.D. thesis, Geodesy, Darmstadt, University of Darmstadt.
Ratnam, D. V., Vindhya, G. and Dabbakuti, J. K., 2017, Ionospheric forecasting model using fuzzy logic-based gradient descent method, Geodesy and Geodynamics, 8(5), 305-310.
Schalkoff, R. J., 1997, Artificial neural networks. Vol. 1. New York: McGraw-Hill.
Segal, P. and Matthews, M. V., 1988, Displacement calculations from geodetic data and the testing of geophysical deformation models, Joural of Geophysical Research, 93, 14954-14966.
Takagi, T. and Sugeno, M., 1985, Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 15(1), 116-132.
Terada, T. and Miyabe, N., 1929, Deformation of earth crust in Kiranasai District and its relation to the orographic feature. Bull Earth Res Inst 7, 223–241.
Van Gorp, S., Masson, F. and Chéry, J., 2006, The use of Kriging to interpolate GPS velocity field and its application to the Arabia-Eurasia collision zone, Geophysical Research Abstracts, 8, 02120.
Vernant, Ph., Nilforoushan, F., Chery, J., Bayera, R., Djamour, Y., Massona, F., Nankali, H., Ritza, J.F., Sedighi, M. and Tavakoli, F. 2004a, Deciphering oblique shortening of central Alborz in Iran using geodetic data." Earth and Planetary Science Letters 223, 177-185.
Vernant, Ph., Nilforoushan, F., Hatzfeld, D., Abassi, M.R., Vigny, C., Masson, F., Nankali, H. R., Martinod, J., Ashtiani, A., Bayer, R., Tavakoli, F. and Chery, J., 2004b, Present-day crustal deformation and plate kinematics in the Middle East constrained by GPS measurements in Iran and northern Oman, Geophys. J. Int., 157, 381-398.
Voosoghi, B., 2000, Intrinsic deformation analysis of the earth surface based on 3-D displacement fields derived from space geodetic measurements, PhD Thesis, Department of Geodesy and Geoinformatics, Stuttgart University.
Yakubu, I., Ziggah, Y. Y. and Asafo-Agyei, D., 2017, Appraisal of ANN and ANFIS for Predicting Vertical Total Electron Content (VTEC) in the Ionosphere for GPS Observations, Ghana Mining Journal, 17(2), 12-16.
Yilmaz, M., 2013, Artificial neural networks pruning approach for geodetic velocity field determination, BCG-Boletim de Ciências Geodésicas.
Zadeh, L. A., 1996, Fuzzy sets”. Information and control. 8, 338-353.
Zarifi, Z., Nilfouroushan, F. and Raeesi, M., 2013, Crustal stress Map of Iran: insight from seismic and geodetic computations, Pure and Applied Geophysics, 171(7), 1219-1236.
Zhang, J. R., Zhang, J., Lok, T. and Lyu, M., 2007, A hybrid particle swarm optimization–back-propagation algorithm for feed forward neural network training, Applied Mathematics and Computation, 185, 1026–1037.