Checking a classical pulse

A classical shock test asks for a pulse of a given shape, peak and duration: a half-sine, a terminal-peak sawtooth or a trapezoid. It is accepted on the measured pulse, point by point against a tolerance envelope drawn around the nominal shape, and as a whole on its velocity change, the area under it. visualdynamics.core.classical_pulse makes that judgment, and plot_pulse_check and the Pulse Check reading on a time history's bar draw it.

The pulse

ClassicalPulse(shape, peak, duration, edge) is the nominal pulse, the peak signed and in SI (m/s²), the duration and edge in seconds.

Shape	Duration	Edge	Nominal velocity change
'half-sine'	the half cycle	none	2AT/π
'sawtooth'	the straight rise	the fall after it; instant if omitted	AT/2
'trapezoid'	rise, top and fall together	the rise and the fall, each; required	A(T − e)

The sawtooth's nominal is AT/2 with the fall taken as instant, as the formula is usually stated. A fall that takes time adds half its length times the peak to the measured change, and the check reports that as it is rather than moving the nominal: a 40 g, 11 ms sawtooth whose fall takes 1.1 ms changes velocity by 93.4 in/s against 84.9, a tenth over before anything else varies.

What it is judged against

Each tolerance is an argument, because the document the test procedure cites decides it. The defaults are this package's starting point, not any one document's figures:

Argument	Default	What it holds
band	0.2	the band either side of the ideal shape on the pulse, and of zero before and after it, as a share of the peak; it holds the measured peak to 0.8 to 1.2 of nominal as well
duration_tolerance	0.1	the measured duration within a tenth of nominal
edge_limit	0.1	the sawtooth's fall, or the trapezoid's rise and fall, no longer than a tenth of the duration
velocity_tolerance	0.2	the velocity change within a fifth of nominal; documents and their revisions differ on this one, so look it up
quiet	2.5	how many durations before and after the pulse are held to the band
window	(0.4, 0.1)	the velocity window, in durations before the pulse starts and after it ends

The envelope is the highest and the lowest of every admissible pulse at each instant, widened by the band: admissible is the shape at any duration inside the duration tolerance and with any edge from instant to the limit. Built that way it agrees with the duration and edge tolerances rather than contradicting them, so a pulse a twentieth long is inside the envelope as well as inside its duration tolerance. At a half-sine's crest the envelope's lower edge, the lowest of the admissible durations less a fifth, sits at 0.785 of the peak, and the peak itself is held to 0.8 apart.

How the measured pulse is read

The pulse is the record's largest excursion in the nominal's direction. Its start, end and edges come from where it crosses a tenth and nine tenths of that peak, walking out from the peak so that noise before and after the pulse is not taken for it: each straight edge extended through its two crossings to zero, and for the half-sine the span between its tenth-of-peak crossings over the share of the duration that span covers. The envelope is placed on the measured start, and every sample from 2.5 durations before it to 2.5 after the latest admissible end is judged.

The velocity change is integrated raw, by the trapezoid rule with nothing removed (filters.integrate with drift_corner=None), over the window from 0.4 nominal durations before the measured start to 0.1 after the measured end. The window is part of the rule: a shaker's compensated pulse, with a shallow pulse of the other sign either side, changes velocity by nothing over the whole record by design, and a mean taken out first would take out exactly the area being measured. The samples have to be evenly spaced, and a record holding a sample that is not a number is refused.

This velocity change is the area under the record across the window: the velocity where the window closes, counted from rest where it opens. The shock check reports a different number under the same name, the span from the lowest velocity to the highest across its window. For a lone pulse of one sign the two agree. An overshoot of the other sign inside the window takes from the area and leaves the span alone, and the part of a compensation pulse that runs into the window counts against the area and not against the span.

check_pulse(history, pulse) returns a PulseCheck with the record and the envelope over the judged span, the samples outside, the velocity across the window, and these readings:

Reading	What it is
measured	the start, end, duration, peak and edges read from the record
outside_count, points	samples outside the envelope, of those judged
peak_ratio, duration_ratio	measured over nominal
velocity_change, nominal_velocity_change, velocity_ratio	the change over the window, the formula's, and the one over the other
envelope_ok, peak_ok, duration_ok, rise_ok, fall_ok, velocity_ok	each part of the judgment
covered	the record reaches across the quiet either side and the velocity window
passed, failures(), describe()	the verdict, what was not met, and both in words

An example

A 40 g, 11 ms sawtooth made the way a shaker makes it: a 40 ms half-sine of the other sign either side, each carrying half its area, so the table starts and ends at rest; the fall takes 1 ms of the 1.1 allowed, and the record carries a noise floor.

from visualdynamics.core.classical_pulse import ClassicalPulse, check_pulse
from visualdynamics.plot import plot_pulse_check
from visualdynamics.units import IN_LBF_S

g = 9.80665
check = check_pulse(history, ClassicalPulse('sawtooth', 40 * g, 0.011))
check.passed                      # True
check.velocity_change / 0.0254    # 91.2 in/s against 84.9
print(check.describe())

plot_pulse_check(history, 'sawtooth', 40 * g, 0.011,
                 unit_system=IN_LBF_S.with_units(acceleration='g'),
                 path='pulse.png')

Every point is inside the envelope, the compensation inside the band either side, and the velocity change is 7.4 % over nominal: the fall's own area, less the tail of the pre-pulse the window takes in.

A 50 g, 11 ms half-sine followed by a fixture ringing at 700 Hz, its first swings at 15 g, is flagged: the pulse is in, and 44 samples after it are outside the band of 10 g, each marked. The velocity change is within a percent of nominal, because only the ringing's first swing falls inside the window. The band after the pulse is where the ringing shows, and it should show somewhere: the test article was excited by it.

In the app

Pulse Check on a time history's bar replaces the trace with the check, for the first selected record (or the object's first acceleration channel), and puts the pulse and its tolerances in the panel beside it: the shape, the peak in the window's units, the duration and edge in milliseconds, and the band, duration, edge-limit and velocity tolerances in percent with the quiet in durations. The edge rows show only for a sawtooth or a trapezoid. Every edit redraws the check. Under the settings the panel lists the measured peak, duration and edges, the velocity change with its distance from nominal, and the samples outside, any value out of its tolerance marked "out", then the verdict. The reading is journaled as its plot_pulse_check call.

A record opens on the half-sine it most resembles (suggest_pulse), rounded, as a place to start. Type the test's own pulse over it: a nominal read off the record being judged would pass whatever the record did.

Where judgment lives

• The tolerances. The defaults are an example; the envelope, the edge limit, the velocity tolerance and the record length are copied from the document the procedure cites, with its revision.
• The window around the pulse. The check reads the velocity change over its window only, so compensation outside it is not counted; a pre-pulse that runs into the window is, as the rule intends.
• A sawtooth at the edge of its fall. A fall at its full allowance spends half of a fifth's velocity tolerance on its own. Under a tenth, the same pulse sits on the edge of its band.
• A flagged record that may be a sensor problem. Integrate the record to velocity over its whole length first: a zero shift or a saturated channel makes the pulse and its velocity change unreliable.