Correction: Neural network based active control of base isolated structure considering isolator nonlinearity

A Correction on
Neural network based active control of base isolated structure considering isolator nonlinearity

by Ghanemi NE, Abdeddaim M, Ounis A and Basili M (2025). Front. Built Environ. 11:1630131. doi: 10.3389/fbuil.2025.1630131

Equation (10) in Section 2 - Mathematical model, was erroneously given as:

$d=\left\{\begin{array}{c}0\\ 0\\ ⋮\\ 0\\ 0\\ 1\end{array}\right\}$, $H=\left\{\begin{array}{c}1\\ 0\\ ⋮\\ 0\\ 0\\ -1\end{array}\right\}$

The correct equation is:

$d=\left\{\begin{array}{c}0\\ 0\\ ⋮\\ 0\\ 0\\ 1\end{array}\right\}$, $H=\left\{\begin{array}{c}1\\ 0\\ ⋮\\ 0\\ 0\\ 0\end{array}\right\}$

Equation (13) in Section 2 - Mathematical model, was erroneously given as:

$B=\left[\begin{array}{cc}-M^{-1}d& -E\\ 0& 0\end{array}\right]$

The correct equation is:

$B=\left[\begin{array}{ccc}-M^{-1}H& M^{-1}d& -r\\ 0& 0& 0\end{array}\right]$

The published article stated:

[$u\left(t\right)={\left[f_u\left(t\right)\ddot{x_g}\left(t\right)\right]}^T$ is the input vector collecting the ATMD force and the seismic acceleration.]

A correction has been made to the section Section 2 - Mathematical model:

“[$u\left(t\right)={\left[f_{NL}\left(t\right)f_u\left(t\right){\ddot{x}}_g\left(t\right)\right]}^T$ is the input vector collecting the nonlinear component of the restoring force, the force ATMD force and the seismic acceleration.]”

The original article has been updated.

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