Beam dataset for GNN-based VS

Simulated Vibration Response of a Population of Cantilever Beams This dataset contains Opensees finite-element simulations of the dynamic response of cantilever beams. Each sample represents one beam subjected to a prescribed dynamic excitation and includes nodal time histories, applied loads, reduced system matrices, natural frequencies, mode shapes, and structural properties. The code used for the simulation is available at https://github.com/RiccardoFracasso01/Beam_GNN_Virtual_Sensing. This dataset has been used in: "Towards Generalisable Virtual Sensing: A Physics-Informed Graph Neural Network Approach On Cantilever Beams", submitted to the special collection 'Focus on Machine Learning for Structural and Infrastructure Systems' of Machine Learning: Engineering. Dataset organization Each scenario consists of two files: <name>_data.pkl: time histories, structural properties, and system matrices. <name>_meta.pkl: beam parameters, loading metadata, natural frequencies, and mode shapes. Both files are stored as pandas DataFrames, with one row corresponding to one beam realization.Rows correspond to the same realization in both files and share the same system_id. Time sampling Time histories are sampled at 500 Hz (dt = 0.002 s) and contain the final 5 s of each simulation (2500 samples). No time vector is stored: sample k corresponds to t = k / 500 s, for k = 0, ..., 2499. Beam model Each beam is discretized into 30 equally spaced nodes, with node 1 at the clamped base and node 30 at the free end. Adjacent nodes are connected by Timoshenko beam elements with a rectangular cross section. All simulations are performed in OpenseesPy using transient analysis and the Newmark integration scheme. The x-axis coincides with the beam axis, while the y- and z-axes are the two transverse bending directions. Scenarios The following parameters are common to all scenarios: Steel: E = 2.1 × 10¹¹ Pa, ρ = 7860 kg/m³ Modal damping ratio: ζ = 0.008 Rectangular cross section: b = 0.03L, h = 0.01L Tip mass uniformly sampled in [1.275, 1.725] kg Up to 10 simultaneously excited nodes Scenario Number of systems Beam length L (m) Force amplitude (N) Excitation baseline 4000 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] White noise (0–100 Hz) interpL 256 [0.8, 0.9] [40, 80] ∪ [120, 160] White noise (0–100 Hz) extrapL 256 [0.5, 0.7] ∪ [1.0, 1.2] [40, 80] ∪ [120, 160] White noise (0–100 Hz) interpF 256 [0.7, 0.8] ∪ [0.9, 1.0] [80, 120] White noise (0–100 Hz) extrapF 256 [0.7, 0.8] ∪ [0.9, 1.0] [1, 40] ∪ [160, 200] White noise (0–100 Hz) sine 256 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] $F(t) = A \sin(2\pi f t + \phi)$ multisine 256 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] $\displaystyle F(t) = \sum_{i=1}^{3} A_i \sin(2\pi f_i t + \phi_i)$ colored 256 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] $\displaystyle F(s) = H(s)\,W(s),$ \newline$\displaystyle H(s) = \frac{1}{s^2 + 2\zeta_n\omega_n s + \omega_n^2}$ multicolored 256 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] $\displaystyle F(s) = \sum_{i=1}^{3} H_i(s)\,W_i(s),$ \newline$\displaystyle H_i(s) = \frac{1}{s^2 + 2\zeta_{n,i}\omega_{n,i} s + \omega_{n,i}^2}$ shutOff 256 [0.7, 0.8] ∪ [0.9, 1.0] [40, 80] ∪ [120, 160] & $F(t) = \begin{cases} W(t) & 0 \le t \le 2\,\text{s} \\ 0 & 3 \le t \le 5\,\text{s} \end{cases}$ The colored scenario is obtained by passing white noise $W(s)$ through an SDOF filter and using its response as the excitation:$$F(s) = H(s)\,W(s) = \frac{1}{s^2 + 2\zeta_n \omega_n s + \omega_n^2}\,W(s)$$ where $\omega_n = 2\pi f_c$ sets the center frequency and $\zeta_n$ the damping of the SDOF. For multicolored, three of these filters ($f_c = 30, 60, 90$ Hz) are summed. Contents of _data.pkl Each row corresponds to one beam. The columns are detailed in the table below. Column Shape Units Description acc_z (30,2500) m/s² Nodal acceleration in the z direction acc_y (30,2500) m/s² Nodal acceleration in the y direction vel_z (30,2500) m/s Nodal velocity in the z direction vel_y (30,2500) m/s Nodal velocity in the y direction disp_z (30,2500) m Nodal displacement in the z direction disp_y (30,2500) m Nodal displacement in the y direction F (30,2500) N Applied nodal force time history. Non-zero only at excited nodes n_properties (30,2) - Column 1: node position x (m). Column 2: translational support stiffness k_x (N/m), equal to 0 for all systems in this dataset el_properties (29,5) - Per-element properties [A, Iz, Iy, J, μ], where μ = ρA M (29,29) kg Mass matrix C (29,29) Ns/m Damping matrix k (29,29) N/m Stiffness matrix The M, C, K matrices have dimensions (29,29) because the first node is clamped. The row and column corresponding to its constrained translational degree of freedom have been removed. Contents of _meta.pkl Each row corresponds to one beam. The columns are detailed in the table below. Column Units Description E Pa Young's modulus rho kg/m³ Material density L m Beam length b0 m Cross-section width h0 m Cross-section height zeta - Modal damping ratio db - Width taper ratio dh - Height taper ratio l_taper_start m Taper start location L_embedded m Always None in this dataset k_x N/m Always None in this dataset k_r Nm/rad Always None in this dataset m_tip kg Added tip mass n_loads - Number of excited nodes target_nodes - 1-based indices of excited nodes F N Force amplitudes corresponding to target_nodes f0 Hz First five bending natural frequencies mode_shapes - First five bending mode shapes in the excitation direction, evaluated at the 30 beam nodes (5,30)