Fully convolutional networks for structural health monitoring through multivariate time series classification

Advanced Modeling and Simulation in Engineering Sciences

Table 2 Adopted random generation rules for the parameters \(\varvec{\eta }^{1sh}_l\) and \(\varvec{\eta }^{1ax}_l\) tuning the frequency and the magnitude of the applied sinusoidal load components in the x (a) and z (b) directions respectively

Parameter	Measurement unit	Adopted random generation rule
(a) x direction
\(f^{sh}\)	Hz	\(\lbrace \texttt {takerand}\left( \left[ 1,2.75,4.5,6.25,8,9.75,11.5,13.25,15\right] \right) \)\(\cdot \left( \texttt {randn}(0,\sqrt{2})\right) \rbrace \)
\(\gamma ^{sh}\)	−	\(\lbrace \gamma ^{dof}_i \cdot \texttt {randn(0,1)} \rbrace \) with \(\gamma ^{dof}_i=\gamma ^{dof}(i)\) and \(\gamma ^{dof}=\left[ 0.13,0.25,0.38,0.50,0.63,0.75,0.88,1.00 \right] \) and i is the dof label
(b) z direction
\(f^{ax}\)	Hz	\(\lbrace \texttt {takerand}\left( \left[ 10,27.5,45,62.5,80,97.5,115,132.5,150\right] \right) \)\(\cdot \left( 2\texttt {randn(0,1)}\right) \rbrace \)
\(\gamma ^{ax}\)	−	\(\lbrace \texttt {randn(0,1)} \rbrace \)

Here, we indicate with randn(\(0,\sigma \)) the sampling from a Gaussian probability distribution \({\mathcal {N}}\left( 0,\sigma ^2\right) \), where \(\sigma ^2\) is its variance, and with takerand\(\left( \left[ {\varvec{v}}\right] \right) \) the uniform sampling from the discrete set of values \(\left[ {\varvec{v}} \right] \)