Optimal sensors placement for structural health monitoring based on system identification and interpolation methods

ABSTRACT

Structural health monitoring (SHM) is required before and after major disasters to assess the safety of structures. In the stochastic subspace identification (SSI) method, the accuracy of the calculated frequency and damping ratio depends on the amount of collected data. However, setting sensors on each floor is time-consuming and difficult for high-rise structures. This study proposes an optimal sensor placement (OSP) method that can be used when a structure requires repeated monitoring, in order to reduce the number of sensors required, and to find the higher modal frequencies for the structure. Numerical results based on the dynamic responses of a ten-story shear frame were used to verify the proposed method. In addition, in-situ experiments in the Civil Engineering Research Building of the National Taiwan University were used to demonstrate the feasibility of this method.

KEYWORDS:

• Optimal sensors placement
• stochastic subspace identification
• structural health monitoring
• system identification
• cubic spline interpolation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

A_c : continuous-time state matrix

A_d : discrete-time state matrix

B₂ : input impact matrix

C : damping matrix of structure

C_a : position coefficient matrix

C_c, C_d : output matrix

D_c : direct transmission matrix

E : expected value operator

f_n : n-th modal frequency

$f_n^r$ : n-th reference modal frequency

K: stiffness matrix of structure

M: mass matrix of structure

m: number of modal frequencies

$n_j$ : numbers of group j

O_i : observability matrix

Q, R, S : covariance matrices

$s_j^t$ : data which is clustered to the group j

T : Toeplitz matrix

$\ddot{\mathit{U}}$ : acceleration vectors of structure

${\ddot{\mathit{U}}}^{{ }^t}$ : absolute acceleration of center of mass

$\dot{\mathit{U}}$ : velocity vectors of structure

$\mathit{U}$ : displacement vectors of structure

u : external force input vector

v : measured error

v_k : measured noise

w : simulated disturbance error

w_k : process noise

x_i : data point

x_k : state vector at kΔt time instant

y : measured signal

${\delta }_{pq}$ : Kronecker delta

$\gamma$ : eigenvalue of A_c

$\mathbf{\Psi }$ : eigenvector

λ_i : eigenvalue of i-th mode

α_i : real part of λ_i

β_i : imaginary part of λ_i

${\omega }_i$ : frequency

${\xi }_i$ : damping ratio

${\mu }_j^0$ : the center of groups from initial iteration