Optimal Design of Magnetorheological Damper Based on Tuning Bouc-Wen Model Parameters Using Hybrid Algorithms


This paper presents a useful approach to optimally design magnetorheological (MR) dampers used in structural buildings. To fulfill this aim, damper parameters are regarded as the design variables whose values can be obtained through an optimization process. To improve the quality of searching for the optimum parameters of MR dampers, charged system search (CSS) and grey wolf (GW) algorithms, two of the most widely utilized meta-heuristic algorithms, are used together, and hybrid CSS-GW is presented. To show the authenticity and robustness of the new algorithm in solving optimization problems, some benchmark test functions are tested, at first. Then, an eleven-story benchmark building equipped with 3 MR dampers is considered to get the optimum design of the MR damper using the hybrid CSS-GW. Results show that the developed hybrid algorithm can successfully figure out the optimum parameters of the MR dampers.

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A, B, C, D, and h :

State matrixes of the system

\(\overrightarrow{A}\;\rm{and}\;\overrightarrow{C}\) :

Coefficient vectors in the GWO

\(\mathcal{C}\) :

Damping system matrix

c 0 :

Viscous damping of the MR damper at high velocities

c 1 :

Viscous damping of the MR damper at low velocities

\(\left\| {d_i^c(t)} \right\|\) :

Norm drift of the controlled building

\(\left\| {d_i^u(t)} \right\|\) :

Norm drift of the uncontrolled building


Vector of ones

F j :

Resultant force acting on the jth charged particle


Control force

\(\mathcal{K}\) :

Stiffness system matrix

k a :

Acceleration coefficients of the CSS algorithm

k v :

Velocity coefficients of the CSS algorithm

k 0 :

Stiffness of the MR damper at high velocities

k 1 :

Accumulator stiffness of the MR damper

m :

Number of control devices

\(\mathcal{M}\) :

Mass system matrix

n :

Number of degrees of freedoms

N :

total number of charged particles

p ij :

Probability of moving each CP towards the others

q i :

Magnitude of the charge for each CP in CSS

r ij :

separation distance between any two charged particle

rand j :

random number uniformly distributed in the range (0,1)

r⃗ 1 and r⃗ 2 :

Random vectors in the range [0, 1]

u :

First order output filter

v :

Input voltage of the MR damper

W best :

Best objective function values

W i :

Fitness of the agent i

W worst :

Worst objective function values

X i :

Position of the ith charged particles

R⃗ p(pt):

Position vector of the victim


Displacement vector of building

x 0 :

Initial deflection of the accumulator gas spring

z :

Hysteresis component of Bouc-Wen model

Z :

State vector of the system

α :

The fittest solution in the GWO


Scaling value for the Bouc-Wen model

β :

The second best solution in the GWO

δ :

The third best solution in the GWO

γ d, β d and A :

Hysteresis shape parameters of the Bouc-Wen model

ε :

Small positive number

I :

Location vector of the control forces


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Correspondence to Bahman Farahmand Azar.

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Azar, B.F., Veladi, H., Talatahari, S. et al. Optimal Design of Magnetorheological Damper Based on Tuning Bouc-Wen Model Parameters Using Hybrid Algorithms. KSCE J Civ Eng 24, 867–878 (2020). https://doi.org/10.1007/s12205-020-0988-z

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  • Optimum design
  • Magnetorheological damper
  • Optimum parameters
  • Grey wolf algorithm
  • Charged system search algorithm
  • Hybrid algorithms