# active control of high rise building structures using combined fuzzy logic

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1 Active control of high rise building structures using combined Fuzzy logic and Genetic Algorithm(GFLC) Ankit Shrivastava Roll no.:09CE1019 Department of Civil Engineering Indian Institute of Technology, Kharagpur-721302, India E-mail: [email protected] Abstract A critical aspect in the design of civil engineering structures is prevention various damages caused by environmental dynamic loadings (i.e., wind and earthquake).Structural control methods are the most recent strategies for this purpose and Dampers are used to formulate these strategies .They can be classified as active, semi-active, passive, and hybrid control methods. Tuned mass dampers (TMDs) are the oldest structural vibration control devices in existence. Among various type of TMDs Active tuned mass damper (ATMD) has been a popular area of research in recent decades. It stabilize against violent motion caused by harmonic vibrations using computer logic. This paper uses the combined application of Genetic algorithm (GA) and Fuzzy logic control (FLC) to design and optimize the different parameters of the ATMD control for getting the best results in the reduction of the building response under earthquake. This method in short is called GFLC Problem Definition It is found that integration of the Genetic Algorithm GA and FLC for GFLC is highly effective in reduction of the seismically excited buildings. An ATMD system effectively reduces the structural response with the help of external control forces which could be extremely large in the case of massive and large buildings. In order to ensure the structural safety which basically depends on the building displacement response This method uses 1. Genetic Algorithm for tuning the parameters of controller system. 2. Fuzzy controller is used for optimization of the active control of civil engineering structure Structure model The equation of motion of a high rise building structure subjected to a single support seismic excitation g u (t) with active control actions {f} acting on ATMD systems can be written as [M]{ u } + [C]{ u } + [K]{u} = −[M]{r} g u (t) + [D]{f} Eq.-1 1. n is number of stories. 2. Here n × 1 vector {u} designates the relative displacements of each story. 3. m is the number of ATMD systems applied to control the building responses 4. (n+m) × 1 vector {r } is the influence vector representing the displacement 5. (n+m) × n matrices [M] represents the structural mass matrix 6. (n+m) × n matrices [C] represents the Damping matrix and 7. (n+m) × n matrices [K] represents the stiffness matrix 8. m × 1 vector { f } contains the externally applied control forces whose locations are identified through [D] Below genetic algorithm and FLC is discussed for n=11 and m=1 and all other data is provided during discussion in numerical method Genetic Algorithm at work: Now from the above equations it is clear that ATMD consists of three main parameters (related to marked in bold letter above)

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Active control of high rise building structures using combined Fuzzy logic and Genetic Algorithm(GFLC)

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Active control of high rise building structures using combined Fuzzy logic and Genetic Algorithm(GFLC)

Ankit Shrivastava Roll no.:09CE1019

Department of Civil Engineering Indian Institute of Technology, Kharagpur-721302, India

E-mail: [email protected]

Abstract A critical aspect in the design of civil engineering structures is prevention various damages caused by environmental dynamic loadings (i.e., wind and earthquake).Structural control methods are the most recent strategies for this purpose and Dampers are used to formulate these strategies .They can be classified as active, semi-active, passive, and hybrid control methods. Tuned mass dampers (TMDs) are the oldest structural vibration control devices in existence. Among various type of TMDs Active tuned mass damper (ATMD) has been a popular area of research in recent decades. It stabilize against violent motion caused by harmonic vibrations using computer logic. This paper uses the combined application of Genetic algorithm (GA) and Fuzzy logic control (FLC) to design and optimize the different parameters of the ATMD control for getting the best results in the reduction of the building response under earthquake. This method in short is called GFLC

Problem Definition It is found that integration of the Genetic Algorithm GA and FLC for GFLC is highly effective in reduction of the seismically excited buildings. An ATMD system effectively reduces the structural response with the help of external control forces which could be extremely large in the case of massive and large buildings. In order to ensure the structural safety which basically depends on the building displacement response This method uses

1. Genetic Algorithm for tuning the parameters of controller system. 2. Fuzzy controller is used for optimization of the active control of civil engineering structure

Structure model

The equation of motion of a high rise building structure subjected to a single support seismic excitation

gu (t) with active control actions {f} acting on ATMD systems can be written as

[M]{ u } + [C]{ u } + [K]{u} = −[M]{r} gu (t) + [D]{f} Eq.-1

1. n is number of stories. 2. Here n × 1 vector {u} designates the relative displacements of each story. 3. m is the number of ATMD systems applied to control the building responses 4. (n+m) × 1 vector {r } is the influence vector representing the displacement 5. (n+m) × n matrices [M] represents the structural mass matrix 6. (n+m) × n matrices [C] represents the Damping matrix and 7. (n+m) × n matrices [K] represents the stiffness matrix 8. m × 1 vector { f } contains the externally applied control forces whose locations are identified through [D]

Below genetic algorithm and FLC is discussed for n=11 and m=1 and all other data is provided during discussion in numerical method Genetic Algorithm at work: Now from the above equations it is clear that ATMD consists of three main parameters (related to marked in bold letter above) 2

The mass ratio (MATMD = om * TotalM ).

The frequency ratio (KATMD = MATMD ×ω2

×β)

TMD Damping ratio ,ξ

In order to design the ATMD system these parameters should be optimized to get maximum reduction in structural dynamic response .Thus parameterized scaling functions and membership functions are adopted by Genetic algorithm. In Genetic Algorithm the above are the parameters to be decided and the fitness function here considered is

1

1

11

i

i

i

i

ii

GA

P

UR

CRP

F

Eq-2

iCR and iUR are the controlled and uncontrolled peak value displacement responses of the top story building and

iP is the Weighting coefficient for i considered earthquakes. The crossover and Mutation probability are taken

80% and 85% respectively for the concerned example

om = MATMD/ TotalM = 3%, β = 1.2 and ξ = 7%

Fuzzy logic controller at work FLC is designed to evaluate the active control force in an ATMD controller system based on getting the maximum reduction in displacement response of the building’s top story. In design of the FLC system the building’s top story displacement and velocity responses are considered as the feedback to the FLC. Different parameters in the FLC system [ATMD damping ratio, frequency ratio, mass ratio, overlap parameters in membership functions (input and output parameters)] are optimized using the GA optimizer to get the maximum reduction in the building response. The following is the block diagram for FLC

Note: Details of How FLC is used will be discussed in Numerical study with example

Fig.2. : FLC component

Fig.1

. 3

Fig.3. Building under vibration 4

Numerical Study For the numerical study, an 11-story realistic building is chosen, which is modeled as a shear frame, and the problem is solved in state space. The structure is considered as a linear system and 2-D motion is considered. The structural properties are provided in Table 1. The ATMD system is considered to be mounted on the top floor of the building, and the active control force is exerted utilizing a hydraulic actuator. The maximum displacement response of the top story of the building due to earthquake excitation is taken as objective of the optimization problem, which should be minimized. Therefore, this maximum displacement response is used in the fitness function In this study Matlab Simulink with Fuzzy Toolbox is used. The fuzzy logic control system of the structural system uses displacement of a storey (here it is the top floor) and its velocity as the input variables, use their membership functions (below) optimized in GA and takes decision based on the rules (defined in Table 2) giving controller force as output(u).

Below are the considered Mebership functions (optimized by GA) and the rules for this example

The fuzzy input and output variables’ membership function abbreviations used to define the fuzzy space are: LP =Large and Positive; P = Positive; Z = Zero; N = Negative; LN= Large and Negative (for input variable); and PL = Positive and Large; PM = Positive and Medium; PS = Positive and Small; ZR = Zero; NL = Negative and Large; NM = Negative and Medium; NS = Negative and Small (for output variable). The fuzzy controller will couple the point-valued MAX–MIN fuzzy inference engine product rule to combine the membership values for each rule and the center of area (COA) defuzzifier scheme to obtain the

crisp value.

Fig.3. Fig.4. 5

The values of weighing coefficient optimized by GA is given in above table

Result:

The results of controlled displacement response of the example building top story due to the earthquake Calculated by the TMD, LQR, and GFLC systems are compared with the corresponding uncontrolled ones. Thus an average designed GFLC system is more effective than others

Table 4 6

Summary This paper focuses on the combined application of genetic algorithms and a fuzzy logic controller (GFLC) for the reduction of the high rise building responses subjected to earthquake excitations using the ATMD control system. A fuzzy logic controller (FLC) is designed for evaluating the active control force in an ATMD controller system based on getting the maximum reduction in displacement response of the building’s top story. In the design of the FLC system the building’s top story displacement and velocity responses are considered as the feedback to the FLC. Different parameters in the FLC system are optimized using the GA optimizer to obtain the maximum reduction in the building response .For the numerical study, an 11-story realistic shear building is chosen and the problem is solved in state space. The optimum values of the ATMD mass, damping, and frequency ratios are obtained (by the GA optimizer) to be about 3%, 7%, and 1.2 finally using FLC controlled/uncontrolled ratio it is being found that GFLC method is much better Future directions As with increase in urban population and lack of space more and more high rise buildings will be preferred so for those to be earthquake resistance GFLC is required is required to be more accurate and more easily adoptable for different situations with decreasing its scope of limitations. Following things can be done to make this possible.

1. Both the structure and Damper model considered in this study are linear one; this provides a further scope to study this problem using a nonlinear model for TMD as well as for structure.

2. The frame model considered here is two-dimensional, which can be further studied to include 3-D structure model.

3. Further scope, also includes studying the possibility of constructing Active TMD which requires less power and energy with fast and more accurate computation as for now it is difficult to say that it may work during the earthquake of very high intensity.

4. Further study of this method for stability of MDoF Structure in future is also a better option Reference

S. Pourzeynali_, H.H. Lavasani, A.H. Modarayi Department of Civil Engineering, Faculty of Engineering, The University of Guilan, Rasht, Islamic Republic of Iran

M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi World Academy of Science, Engineering and Technology 80 2011

Rahmi GUCLU Yildiz Technical University, Faculty of Mechanical Engineering, Besiktas, Istanbul-TURKEY e-mail: [email protected]