Probabilistic Active Control of Structures Using a Probabilistic Fuzzy Logic Controller

Document Type : Regular Paper


1 Ph.D. Student, Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Professor, Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

3 Assistant Professor, Faculty of Civil Engineering and Environment, Khavaran Institute of Higher Education of Mashhad, Mashhad, Iran


Because uncertainty is inherent in engineering structures, it is essential to improve the procedures of structural control. The present study focuses on applying a probabilistic fuzzy logic system (PFLS) in active tendons for the covariance response control of buildings. In contrast to an ordinary fuzzy logic system, PFLS integrates the probabilistic theory into a fuzzy logic system that can handle the linguistic and stochastic uncertainties existing in the process. To investigate the proficiency of the proposed controller, a single degree of freedom (SDOF) system and a three-story multiple degree of freedom (MDOF) system with different arrangements of tendons on the floors are considered. The structures are subjected to a random dynamic load modeled using Gaussian white noise, and the modeling parameters such as damping, stiffness, and mass are considered to be random Gaussian samples with a dispersion coefficient of 10%. The results of the proposed intelligent control scheme are compared with those of an uncontrolled structural model and a linear quadratic regulator (LQR) controller model. The numerical results reveal that the probabilistic fuzzy logic controller (PFLC) is more efficient than the LQR controller in decreasing the structural covariance responses. Moreover, the maximum and minimum reductions in displacement responses for the MDOF structures are, respectively, about 36% and 12.5%compared to the LQR controller. It is also showed that the PFLC is more accurate because it includes stochastic uncertainty.


Main Subjects

[1] Zadeh, L. A. (1995). “Discussion: Probability Theory and Fuzzy Logic are Complementary Rather than Competitive.” Technometrics 37(3):271-276.
[2] Liu, Z., Li, H.X. (2005). “A Probabilistic Fuzzy Logic System for Modeling and Control.” IEEE Transactions on Fuzzy System 13(6): 848-859.
[3] Zhang, G., Li, H.X. (2012). “An Efficient Configuration for Probabilistic Fuzzy Logic System.” IEEE Transactions on Fuzzy System 20(5):898-909.
[4] Zadeh, L.A. (1965). “Fuzzy set.” Information and Control 8(3):338–353.
[5] Karnik, N.N., Mendel, J.M. (2001). “Centroid of a type-2 Fuzzy Set.” Information Science 132(1-4):195-220.
[6] Zadeh, L.A. (1975). “The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I.” Information Science 8(3):199-249.
[7] Karnik, N.N., Mendel, J.M. (1998). “Type-2 Fuzzy Logic Systems: Type-reduction.” IEEE International Conference on Systems, San Diego, CA, October. 2:2046-205.
[8] Karnik, N.N., Mendel, J.M. (1998). “Introduction to Type-2 Fuzzy Logic Systems.” IEEE International Conference on Fuzzy Systems Proceeding, Anchorage, May, 2:915-920.
[9] Karnik, N.N., Mendel, J.M., Liang, Q. (1999). “Type-2 Fuzzy Logic Systems.” IEEE Transactions on Fuzzy systems 7(6):643-658.
[10] Mendel, J.M., John, R.I.B. (2002). “Type-2 Fuzzy Sets Made Simple.” IEEE Transactions on Fuzzy Systems 10(2):117-127.
[11] Liang, Q., Mendel, J.M. (2000). “Interval Type-2 Fuzzy Logic Systems: Theory and Design.” IEEE Transactions on Fuzzy systems 8(5):535-550.
[12] Mendel, J.M., John, R.I.B., Liu, F. (2006). “Interval Type-2 Fuzzy Logic Systems Made Simple.” IEEE Transactions on Fuzzy system 14(6):808–821.
[13] Mendel, J.M. (2007). “Advances in Type-2 Fuzzy Sets and Systems.” Information Sciences 177(1):84-110.
[14] Li, L., Lin, W.H., Liu, H. (2006). “Type-2 Fuzzy Logic Approach for Short-Term Traffic Forecasting.” IEEE Proceedings- Intelligent Transport Systems 153(1):33-40.
[15] Al-Dawod, M., Naghdy, F., Samali, B., Kwok, K. (1999). “Active Control of Wind Excited Structures Using Fuzzy Logic.” IEEE International Conference on Fuzzy Systems, Seoul, Aug, 72-77.
[16] Al-Dawod, M., Samali, B., Naghdy, F., Kwok, K. (2001). “Active Control of along Wind Response of Tall Building using a Fuzzy Controller.” Engineering Structures 23(11):1512-1522.
[17] Al-Dawod, M., Samali, B., Li, J. (2006). “Experimental Verification of an Active Mass Driver System on a Five-Storey Model using a Fuzzy Controller.” Structural Control and Health Monitoring 13(5):917-43.
[18] Samali, B., Al-Dawod, M. (2003). “Performance of a Five-Storey Benchmark Model Using an Active Tuned Mass Damper and a Fuzzy Controller.” Engineering Structures 25(13):1597-1610.
[19] Samali, B., Al-Dawod, M., Kwok, K., Naghdy, F. (2004). “Active Control of Cross Wind Response of 76-Story Tall Building Using a Fuzzy Controller.” Journal of Engineering Mechanics 130(4).
[20] Pourzeynali, S., Lavasani, H.H., Modarayi, A.H. (2007). “Active Control of High rise Building Structures Using Fuzzy Logic and Genetic Algorithms.” Engineering Structures 29(3):346-357.
[21] Shariatmadar, H., Golnargesi, S., Akbarzadeh-T, M.R. (2014). “Vibration Control of Buildings Using ATMD against Earthquake Excitations through Interval Type-2 Fuzzy Logic Controller.” Asian Journal of Civil Engineering (Bhrc) 15(3):321-338.
[22] Golnargesi, S., Shariatmadar, H., M. Razavi, H. (2018). “Seismic Control of Buildings with Active Tuned Mass Damper through Interval Type-2 Fuzzy Logic Controller Including Soil-Structure Interaction.” Asian Journal of Civil Engineering 19:177-188.
[23] Zabihi Samani, M., Ghanooni-Bagha, M. (2019).”The Effect of Intelligent Semi-Active Thermal Exchange-Fuzzy Inference System in Structural Seismic Rehabilitation.” Journal of Rehabilitation in Civil Engineering 7,1: 49-69. https://10.22075/JRCE.2018.11513.1189
[24] Laviolette, M., Seaman, J.W. (1994). “Unity and Diversity of Fuzziness from a Probability Viewpoint.” IEEE Transactions on Fuzzy systems 2(1):38–42.
[25] Loginov, V.J. (1966). “Probability Treatment of Zadeh Membership Functions and Their Use in Pattern Recognition.” Engineering Cybernetics 468-69.
[26] Liang, P., Song, F. (1996). “What does a Probabilistic Interpretation of Fuzzy Sets Mean?” IEEE Transactions on Fuzzy systems 4(2):200–205.
[27] Meghdadi, A.H., Akbarzadeh-T., M.R. (2001). “Probabilistic Fuzzy Logic and Probabilistic Fuzzy Systems.” 10th IEEE International Conference on Fuzzy Systems 2:1127–1130.
[28] Colubi, A., Fernandez-Garcia, C., Gil, M.A. (2003). “Simulation of random Fuzzy Variables: an Empirical Approach to Statistical/Probabilistic Studies with Fuzzy Experimental Data.” IEEE Transactions on Fuzzy systems 10(3):384–390.
[29] Zhang, Y., Liu, Z., Wang, Y. (2009). “A three-Dimensional Probabilistic Fuzzy Control System for Network Queue Management.” Journal of Control Theory and Applications 7:29-34.
[30] Liu, Z., Li, H.X. (2009). “Probabilistic Fuzzy Logic System: a Tool to Process Stochastic and Imprecise Information.” IEEE International Conference on Fuzzy Systems, Jeju Island, 848-853.
[31] Li, H.X., Liu, Z. (2009). “A Probabilistic Fuzzy Logic System: Learning in the Stochastic Environment with Incomplete Dynamics.” IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, 383-388.
[32] Zhang, G., Li, H.X., Gan, M. (2012). “Design a Wind Speed Prediction Model Using Probabilistic Fuzzy System.” IEEE Transactions on Industrial Informatics 8(4):819-827.
[33] Huang, W.J., Li, Y.H., Xu, K.K. (2019). “The General Probabilistic Fuzzy Set for Modeling and its Application in EMG Robots” Journal of Intelligent and Fuzzy Systems 37(2):2087-2100.
[34] Shaheen, O., El-Nagar, A.M., El-Bardini, M., El-Rabaie, N.M. (2019). “Stable Adaptive Probabilistic Takagi-Sugeno-Kang Fuzzy Controller for Dynamic Systems with Uncertainties.” Journal of ISA Transactions 98:271-283.
[35] Nguyen, L. (2020). “Integrating the Probabilistic Uncertainty to Fuzzy Systems in Fuzzy Natural Logic.” International  Conference on Knowledge and Systems Engineering, 142-146.
[36] Chung, L.L., Reinhorn, A.M., Soong, T.T. (1988). “Experiments on Active Control of Seismic Structures.” Journal of Engineering Mechanics 114(2).
[37] Chung, L.L., Lin, R.C., Soong, T.T., Reinhorn, A. M. (1989). “Experimental Study of Active Control for MDOF Seismic Structures.” Journal of Engineering Mechanics 115(8)1609-1627.
[38] Spencer Jr, B.F., Sain, M.K., Won, C.H., Kaspari, D.C., Sain, P.M. (1994). “Reliability- Based measures of Structural Control Robustness.” Structural Safety 15(1-2):111-129.
[39] Suhardjo, J., Spencer Jr, B.F., Sain, M.K. (1990). “Feedback-Feedforward Control of Structures Under Seismic Excitation.” Structural Safety 8(1-4) 69-89.
[40] Hotz, A., Skelton, R.E. (1987). “Covariance Control Theory.” International Journal of Control 46:13-32.
[41] Robinson, W. (2012). “A Pneumatic Semi-Active Control Methodology for Vibration Control of Air Spring Based Suspension Systems.” Graduate Theses and Dissertations, Iowa State University.
[42] Skelton, R.E. (1988). “Dynamic Systems Control: Linear System Analysis and Synthesis.” Wiley, New York.
[43] Nigdeli, S.M., Boduroglu, M.H. (2010). “Active Tendons for Seismic Control of Buildings.” International Journal  of Civil and Environmental Engineering 4(8):267- 273.