Sensor location in concrete slabs with various layout of opening using modified ‘FEMS-COMAC’ approach


Two-way concrete slabs are widely used around the world for the construction of many types of infrastructures and common buildings. The optimal sensor placement (OSP) in slabs with various opening positions is the most important issue in structural health monitoring (SHM) to increase reliability. In this study, a novel approach of OSP was evaluated to obtain the number and placement of sensors using examination of the closed loop performance. The nonlinear finite element (NFE) was used to discretize the mechanism behavior of slab. Multi-Objective Optimization based on the coordinate modal assurance criterion (COMAC) and cost considerations was considered in the optimization processes. All of the analysis, discretization and optimization process was designed and developed as a novel approach in Matlab by the author under the name ‘FEMS-COMAC’ (FEM analysis of slab with COMAC). The points in the finite element method (FEM) mesh were classified as line by line information along the slab. The OSP in each line was optimized according to the objective function. The slabs with various width, thickness, aspect ratio and opening position were selected as case studies. The results of the OSP using the COMAC algorithm around the slab openings were compared with the novel ‘FEMS-COMAC’ method. The statistical analysis according Mann-Whitney criteria shows that there were significant differences between them in some of the case studies (mean P-value=0.54).

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B :

Length of the bay of slab (longer side)

C eff :

Effective damping coefficient eff


Coordinate modal assurance criterion

D :

The slab flexural rigidity


Degree of freedom

E :

Modulus of elasticity for plane stress analysis

EI :

Effective independence


Finite element method


FEM analysis of slab with COMAC


Eigenvalue vector product

f :

Natural frequency


Natural frequency of freely

f num :

Numerical natural frequency num

f anal :

Analytical natural frequency anal


Fiber bragg grating


Genetic algorithm


Kinetic energy

G :

Shear modulus

M :



Modal assurance criterion


Mode shape summation plot


Modal analysis


Mean absolute error

N :

Number of observations


Nonlinear finite element


Nonlinear time history analysis


Optimal sensor placement

Q x :

Shearing forces parallel to z axis

Q y :

Shearing forces perpendicular to x and y axes y

R 2 :

Correlation coefficient


Reinforced concrete


Root mean square error


Structural health monitoring


Simply supported


Slab with opening No. 1


Slab with opening No. 2


Slab with opening No. 3


Slab with opening No. 4


Slab with opening No. 5


Slab without opening

u :

Displacements in x direction

v :

Displacements in y direction

w :

Displacements in z direction

W :

length of the span of slab (smaller side)

α :

Numerical correction factor

γ :

Shear strain

γ max :

Maximum shear strain max

ε :


ζ :

damping ratio

θ :


ρ :


λ :

Dimensionless natural frequency factor

μ :

Mass density per unit area of slab

υ :

Poisson’s ratio of the concrete

σ :


φ i :

Eigenvector of mode i, comprising only the measured degrees of freedom

φ j :

Corresponding experimental eigenvector of mode j

φ T :

Transpose of φ

χ :

Curvature along directions


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Vosoughifar, H., Manafi, P. Sensor location in concrete slabs with various layout of opening using modified ‘FEMS-COMAC’ approach. Earthq. Eng. Eng. Vib. 19, 205–222 (2020).

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  • two-way concrete slabs
  • openings
  • OSP
  • MAC