The system identification workflow

Before a MIMO vibration test can be controlled, the controller has to know the plant: drive every shaker with known excitation, measure every response, and estimate the FRF matrix between them. A system ID run is that measurement — and the three readings that decide whether it can be trusted: the FRFs themselves, the multiple coherence that says how much of each response the drives account for, and the signal-to-noise that says how far the excitation stood above the ambient.

The walkthrough is the demonstration plate's system ID — four shakers into eight response channels, an ambient recording first and the driven one after — streamed by the controller (generate_plate_sysid.py in the generators repository) to stressdata/plate/sysid_stream.nc4.

Step	In the app	In a script
Import the stream	drag the .nc4 on; answer yes to the question	project.import_file(path)
Say what it is	(the question did) or Set Project Type → System ID	project.project_type = 'System ID'
The FRFs	Compute FRFs in the averaging view — H1	project.compute_frfs(name, 'H1')
Trust, part one	Compute Multiple Coherence	project.compute_multiple_coherence(name)
Trust, part two	PSDs of both phases; select the pair; Ratio (dB)	project.compute_psds(...) twice
Geometry and photos	drag them in, link them	project.add(...), project.link(...)
Report	Generate Report on the bar, the project row selected	project.generate_report('sysid')
Save	Save Project As…	project.save('sysid.vdyn')

In the app, step by step

1. Import the stream, and answer the question

A streamed system ID save is two time streams, a quiet one then a loud one — and at the file level that is indistinguishable from an ordinary run of the same environment. So the app asks rather than guesses: importing a file of that shape poses "Treat this project as a System ID test?", and on yes the two streams take their phase names — Noise Time History for the ambient, Excitation Time History for the driven — told apart by level. (A project already typed System ID is not asked; the streams are named directly. A stop-and-restart run whose two streams are both loud is not asked either.)

2. The FRFs — H1, and why

Compute FRFs in the excitation history's averaging view, method H1: the plant is measured driving through known excitation, so the noise is on the response side, which is exactly the assumption H1 makes. This is the estimator the controller itself uses for the same measurement.

3. Trust, part one: multiple coherence

Multiple Coherence, beside it in the same view, reads how much of each response all the drives together account for, line by line. A dip says the response contains something the drives did not put there — a rattle, ambient bleed, a nonlinearity — at exactly those frequencies, and an FRF line under a coherence dip is a line the control law will be inverting on faith.

4. Trust, part two: the signal-to-noise reading

Compute PSDs of both phases — the ambient borrowing the excitation's frames, since a ratio of densities only exists on shared lines — then select the two PSDs together and choose Ratio (dB) on the bar. The signal-to-noise is a reading of that pair, never a third object: the louder density over the quieter, channel by channel, in decibels. Where the excitation stood 30 dB over the ambient, the FRF there is measurement; where the two densities touch, it is ambient divided by ambient.

5. Geometry, photos, report

Drag the article's geometry in, declare its units, add the setup photographs, link the group. The system ID report binds both recordings with their frames, the excitation and ambient densities side by side, the FRFs and the multiple coherence staged over every channel, the signal-to-noise ratio stage, and the kurtosis of each recording — the record a control run stands on.

The same run, headless

And the script never has to be reconstructed by hand: the console tab along the bottom of the window writes it live as you click — every act of the session as the line that replays it. Expand it, copy the stretch you want, and it runs as-is.

import numpy as np

import visualdynamics

project = visualdynamics.Project('Plate System ID')

# 1. import; a script is never asked, so the type is declared and the
# two phases are named for what they are, quiet first
project.import_file('sysid_stream.nc4')
project.project_type = 'System ID'
histories = sorted(
    (name for name in project.names
     if type(project[name]).__name__ == 'TimeHistory'),
    key=lambda name: float(np.asarray(project[name].ordinate).std()))
project.rename(histories[0], 'Noise Time History')
project.rename(histories[1], 'Excitation Time History')

# 2. geometry, photos, links
geometry = visualdynamics.import_file('geometry.npz')
geometry.define_units('m')
project.add('Geometry', geometry)
project.link(*project.names)
project.set_basis(*project.names)

# 3. the plant, and the two trust readings
project.compute_frfs('Excitation Time History', 'H1')
project.compute_multiple_coherence('Excitation Time History')
project.compute_psds('Excitation Time History')
project['Noise Time History'].averaging = \
    project['Excitation Time History'].averaging
project.compute_psds('Noise Time History')

# 4. report and save
project.generate_report('sysid')
project.export_report(project.report, 'sysid_report.html')
project.save('sysid.vdyn')

Where judgement lives

• The question at import is a question because the file cannot answer it. Two streams, quiet then loud, is also what a stop-and-restart run leaves. The 10 dB gate keeps the obvious non-cases from asking, but the yes is the engineer's.
• Which save to work from. The controller also writes a spectral package — the measured FRFs, coherence and autospectra it computed itself. That imports directly, but it records hardware channel numbers with no units; the stream carries the channel table, so everything computed from it wears real node labels and engineering units and links to the geometry. When both exist, work from the stream and keep the package as the controller's own cross-check.
• A drive with no noise floor reads NaN. The signal-to-noise of a drive channel divides the drive by an ambient that recorded silence, and the honest answer is no ratio rather than infinity. Those lines are simply not drawn, the status line counts the channels it could read, and the report leaves the channel out.
• Coherence near one is necessary, not sufficient. It says the responses are linearly explained by the drives — it does not say the levels were right for the article, which is what the signal-to-noise reading is for. The two together are the case for trusting the plant; neither alone is.