Step 1: Mode Shape Extraction
Extract and normalize mode shapes from acceleration data using RMS averaging
Mode Shape Matrix
The extracted mode shapes are summarized in the mode shape matrix $\boldsymbol{\Phi}$, where each column represents a mode:
where $\phi_{i,j}$ represents the normalized mode shape component at floor $i$ for mode $j$. The matrix is normalized such that the maximum absolute value in each column is 1.0. The actual numerical values are displayed in the individual mode analyses below.
Methodology
The workflow assumes a single dominant mode during each forced-vibration record:
- RMS ratios: floor accelerations are converted to relative modal amplitudes via \( \phi_j/\phi_3 \approx a_j/a_3 \).
- Sign consistency: correlations with the roof response enforce in- / out-of-phase behavior.
- Instantaneous shapes: every time sample produces a normalized acceleration vector aligned with the reference shape.
- Cleaning filters: low-amplitude or off-shape samples are discarded (reference floor <5% of max, global response <2%, or cosine <0.95).
- Statistics: the remaining samples feed the Gaussian and time-variation plots; raw (unfiltered) moments are logged for traceability.
Mode 1 Analysis
Mode 2 Analysis
Mode 3 Analysis
Statistical Analysis Summary
Key Metrics
The visualizations above show four key analyses for each mode:
Reference shape from RMS ratios, normalized to max amplitude of 1.0 and aligned with the roof motion.
Computed both for the raw scatter and the filtered set; reported CVs correspond to the used (filtered) samples.
Bounds of the filtered instantaneous shapes. Raw limits are logged in the console for comparison.
Grouped averages of the retained samples (1-second bins) contrasted against the reference modal amplitudes.
What If We Skip the Filters?
The cleaning stage is optional but strongly recommended. Without removing low-energy and off-shape samples, coefficients of variation can exceed 40%, Gaussians span both signs, and the time-variation plot becomes dominated by noise. A dedicated summary of the raw, unfiltered analysis is available below.