H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake

Michael Dowglas de Gois Silva; Fábio Roberto  Chavarette

doi:10.59400/jam.v2i2.451

H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake

Michael Dowglas de Gois Silva Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, UNESP-Paulista State University, Ilha Solteira, São Paulo 15385-000, Brasil
Fábio Roberto Chavarette Department of Engineering, Physics and Mathematics, Institute of Chemistry, UNESP-Paulista State Univerity, Araraquara, São Paulo 14800-060, Brasil

Ariticle ID: 451

476 Views, 113 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i2.451

Keywords: shear building; earthquake; wind; H∞ control; MRD; hybrid controller

Abstract

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

References

[1] Tominaga LK, Santoro J, Amaral R. Natural Disasters: Knowing to Prevent, 1st ed (Portuguese). Instituto Geológico; 2009.

[2] Bosse RM. Performance of TMDs in Buildings Subjected to Earthquakes (Portuguese) [Master’s thesis]. Escola de Engenharia da Universidade de São Paulo; 2017.

[3] García-Illescas MA, Alvarez-Icaza L. Model reduction of shear building models: A quantitative approach for master degrees of freedom selection. Engineering Structures. 2019; 179: 512-522. doi: 10.1016/j.engstruct.2018.11.019

[4] Ribeiro M. Numerical and Computational Analysis of a Wind-induced Structural Vibration Control System (Portuguese) [PhD thesis]. Universidade Federal de Juiz de Fora; 2018.

[5] Pandit AR, Biswal KC. Seismic control of multi degree of freedom structure outfitted with sloped bottom tuned liquid damper. Structures. 2020; 25: 229-240. doi: 10.1016/j.istruc.2020.03.009

[6] Chavarette FR, Lima RS de. Nonlinear dynamics, chaos and control of the Hindmarsh-Rose neuron model. Boletim da Sociedade Paranaense de Matemática. 2022; 40: 1-9. doi: 10.5269/bspm.47770

[7] Roefero LGP, Chavarette FR, Mishra LN. Linear Quadratic Regulator Applied to a Magnetorheological Damper Aiming Attenuate Vibration in an Automotive Suspension. Twms Journal of Applied and Engineering Mathematics. 2022; 12: 1189-1201.

[8] Vicente J, Chavarette F, Roefero L. Chaos Control via Mathieu-Van der Pol System and Linear Optimal Control Design with a Non-ideal Excitation and Parametric Uncertainties. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería. 2019; 35. doi: 10.23967/j.rimni.2019.08.001

[9] Bandyopadhyay S, Parulekar YM, Sengupta A, et al. Structure soil structure interaction of conventional and base-isolated building subjected to real earthquake. Structures. 2021; 32: 474-493. doi: 10.1016/j.istruc.2021.03.069

[10] Brasil RMLRF, da Silva MA. Introduction to the Dynamics of Structures for Civil Engineering, 2nd ed (Portuguese). Blucher; 2015.

[11] Paz M, Kim YH. Structural Dynamics. Springer International Publishing; 2019. doi: 10.1007/978-3-319-94743-3

[12] Savi MA. Non-linear Dynamics and Chaos, 2nd ed (Portuguese). E-Papers; 2017.

[13] Chopra AK. Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice Hall; 1995.

[14] Corbani S. Dynamic Elasto-plastic Analysis of Steel Structures Subjected to Random Earthquake Excitation (Portuguese) [Master’s thesis]. Escola Politécnica da Universidade de São Paulo; 2006.

[15] Associação Brasileira de Normas Técnicas. ABNT. NBR 6123. Forces Due to Wind in Buildings (Portuguese). ABNT; 1988.

[16] Carril CFJ. Numerical and Experimental Analysis of the Dynamic Effect of Wind on Metal Lattice Towers for Telecommunications (Portuguese) [PhD thesis]. Escola Politécnica da Universidade de São Paulo; 2000.

[17] Franco M. Direct Along Wind Dynamic Analysis of Tall Structures. Boletim Técnico; 1993.

[18] Associação Brasileira de Normas Técnicas. ABNT. NBR 15421. Design of Earthquake-resistant Structures—Procedure (Portuguese). ABNT; 2006.

[19] Brandão FS. Optimization of Synchronized Dynamic Attenuators for Vibration Control in Buildings Subjected to Seismic Excitation (Portuguese) [Master’s thesis]. Escola de Engenharia da Universidade Federal do Rio Grande do Sul; 2021.

[20] Kanai K. Semi-empirical formula for the seismic characteristics of the ground. Bulletin of the Earthquake Research Institute, University of Tokyo. 1957; 35.

[21] MATLAB 2022 version. Mathworks Company.

[22] Ogata K. Modern Control Engineering (Portuguese), 5th ed. Editora Pearson Prentice Hall; 2010.

[23] Ferreira DC, Chavarette FR, Peruzzi NJ. Linear matrix inequalities control driven for non-ideal power source energy harvesting. Journal of Theoretical and Applied Mechanics. Published online July 23, 2015: 605. doi: 10.15632/jtam-pl.53.3.605

[24] Trofino A, Coutinho DF, Barbosa KA. Improved H2 and H conditions for robust analysis and control synthesis of linear systems. Sba: Controle & Automação Sociedade Brasileira de Automatica. 2005; 16(4): 427-434. doi: 10.1590/s0103-17592005000400004

[25] Boyd S, El Ghaoui L, Feron E, et al. Linear Matrix Inequalities in System and Control Theory. Published online January 1994. doi: 10.1137/1.9781611970777

[26] Palma PHT. Experimental Identification and Active Control of Vibrations Applied to Intelligent Structures (Portuguese) [Master’s thesis]. Universidade Estadual Paulista “Júlio de Mesquita Filho”; 2007.

[27] Peres PLD. H2 Control and H: Characterization by Linear Matrix Inequalities (Portuguese) [PhD thesis]. Universidade Estadual de Campinas; 1997.

[28] Assunção E. Design of robust H2 controllers and H via LMI (Portuguese). In: Class notes from the H2 and H robust controller design discipline via LMI from the electrical engineering postgraduate course at UNESP (Portuguese)—Ilha Solteira. 2019.

[29] Spencer JRBF, Dyke SJ, Sain MK, Carlson JD. Phenomenological model for magnetorheological dampers. Journal of engineering mechanics. 1997; 123(3): 230-238. doi: 10.1061/(ASCE)0733-9399(1997)123:3(230)

[30] Tusset AM, Balthazar JM. On the Chaotic Suppression of Both Ideal and Non-ideal Duffing Based Vibrating Systems, Using a Magnetorheological Damper. Differential Equations and Dynamical Systems. 2012; 21(1-2): 105-121. doi: 10.1007/s12591-012-0128-4

[31] Wolf A, Swift JB, Swinney HL, Vastan JA. Determining Lyapunov exponents from a Time Series. Physica D. 1985; 16: 285-317. doi: 10.1016/0167-2789(85)90011-9

[32] Mohammadi S. Lyaprosen: MATLAB function to calculate Lyapunov exponent. University of Tehran; 2009.

[33] Rosenstein MT, Collins JJ, Deluca CJ. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 1993; 65(1-2): 117-134. doi: 10.1016/0167-2789(93)90009-P

[34] Associação Brasileira de Normas Técnicas. ABNT. NBR 8800. Design of Steel Structures and Mixed Steel and Concrete Building Structures (Portuguese). ABNT; 2008.

[35] Associação Brasileira de Normas Técnicas. ABNT. NBR 6118. Design of Concrete Structures-Procedure (Portuguese). ABNT; 2014.

Published

2024-04-02

How to Cite

de Gois Silva, M. D., & Chavarette, F. R. (2024). H∞ hybrid control and MRD in a steel frame building subjected to excessive vibrations caused by the dynamic action of wind and earthquake. Journal of AppliedMath, 2(2), 451. https://doi.org/10.59400/jam.v2i2.451

Download Citation

Issue

Vol. 2 No. 2 (2024)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

eISSN

2972-4805

Publication Frequency

Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Volume Arrangement

2024

2023

Featured Articles

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana

Masting in GSM network design is one of the most challenging problems in cell planning. The effect of uniform design pattern has been proven geographically to be hexagonal using uniform cell range. In this paper, we present a new uniform greedy semi-regular tessellation model called the octagonal square tessellation model (OSTM) to address the problem of global minimum overlap difference and area. Data from MTN Kumasi-East Ghana was collected and analyzed using the developed model. The original layout for the 0.6 km cell range accounted for an overlap difference of 937.66 m and a total area of 21.41 km² for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km². This is a 59.87% reduction of the original total area. Our solution is shown to be optimal in overlap difference and area for non-uniform cell range.

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.