Time-Domain Condition Indicators

Condition indicators are dimensionless numbers computed directly from the waveform, without any transform to the frequency domain. They answer one question: how impulsive is this signal compared with its own overall level? Because they are ratios, they are largely independent of sensor sensitivity and of the absolute operating level, which makes them robust inputs for classifiers and for simple pass / fail limits.

Four indicators are provided — Shape Factor, Impulse Factor, Margin Factor and Energy Entropy — each in a vs. Time and a vs. RPM form.

Windowing

All four indicators are block quantities: the signal is cut into integration windows and one value is produced per window.

signal → integration window (IntegrationTimeMs) → indicator → one point per window

In the vs. Time form the window length is IntegrationTimeMs and the advance is IntegrationHopMs; when no hop is given the windows are laid end to end without overlap. The time stamp of a window is the geometric centre of its samples. In the vs. RPM form the window is centred on the RPM step crossing, so each point represents the machine state at exactly that speed.

The Indicators

In the formulas below, x_i are the samples inside one window and N is the number of samples in it.

RMS = √( (1/N) Σ x_i² ) peak = max |x_i| mean|x| = (1/N) Σ |x_i|

Shape Factor (dimensionless)

The ratio of the RMS value to the mean rectified value. It describes the shape of the waveform independently of its amplitude: a signal whose energy is concentrated in short excursions has a higher shape factor than one that stays close to its RMS value.

Shape Factor = RMS / mean|x|

Impulse Factor (dimensionless)

The ratio of the peak value to the mean rectified value. This is the classical impulsiveness indicator: it rises as soon as isolated impacts appear on top of an otherwise steady signal, and it rises earlier than the RMS level does, because the mean rectified value hardly moves while the peak grows.

Impulse Factor = peak / mean|x|

Margin Factor (dimensionless, also called clearance factor)

The peak value divided by the square of the mean of the square roots of the absolute samples. The square-root averaging suppresses large samples even more strongly than rectification does, which makes this the most sensitive of the three factors to sparse, high-amplitude impacts — the classical early indicator for rolling-element surface damage.

Margin Factor = peak / ( (1/N) Σ √|x_i| )²

Energy Entropy (0…1)

The window is split into EnergyEntropySubframes sub-frames of equal length (the last one absorbing any remainder). The energy of each sub-frame is normalized into a probability and the Shannon entropy is computed and scaled by its maximum, so the result always lies between 0 and 1:

p_i = E_i / ΣE Energy Entropy = −Σ p_i · log₂(p_i) / log₂(K)

A value near 1 means the energy is spread evenly over the window (stationary operation). A value near 0 means the energy is concentrated in a single sub-frame (a burst, a knock, a switching event).

Reference Values for Common Waveforms

Because all four indicators are closed-form expressions, their values for ideal waveforms are known exactly. These numbers are useful as a sanity check when setting up an analysis.

Waveform	Shape Factor	Impulse Factor	Margin Factor	Energy Entropy
Square wave ±A	1	1	1	1
Sine wave	π / (2√2) ≈ 1.1107	π / 2 ≈ 1.5708	≈ 1.7188	≈ 1 (whole periods)
Constant amplitude, no impacts	low, stable	low, stable	low, stable	near 1
Isolated impacts on a quiet background	rises	rises strongly	rises most strongly	drops

Parameters

Parameter	Default	Applies to	Notes
`AcousticChannel`	0	vs. Time, vs. RPM	Channel index the indicator is computed on
`IntegrationTimeMs`	100 ms (vs. Time) / 170 ms (vs. RPM)	both	Length of the integration window
`IntegrationHopMs`	— (window length)	vs. Time	Advance between windows; if unset the windows do not overlap
`EnergyEntropySubframes`	8	Energy Entropy	Number of sub-frames K; minimum 2
`RpmChannel`	auto	vs. RPM	Tacho channel; the pulse-decoded speed is preferred when available
`RpmStep`	50 rpm	vs. RPM	Width of one speed step
`RpmMin` / `RpmMax`	auto	vs. RPM	Speed range; derived from the speed signal when not given
`SlopeMode`	AutoDetect	vs. RPM	AutoDetect / Runup / Rundown / All

vs. Time and vs. RPM

The vs. Time curve is the working view for a single operating point — it shows when the machine became impulsive. The vs. RPM curve is the working view for a run-up: it shows at which speeds impulsiveness appears, which usually points straight at a resonance or a speed-dependent contact condition. Speed steps for which no full window fits inside the recording remain empty.

Each curve also carries a single value, the mean over all valid points, so an indicator can be used as a scalar test result without further post-processing.

Applications

Early damage detection — margin and impulse factor react to surface damage before the broadband level moves.
End-of-line pass / fail — the single value per recording is a ready-made test result; absolute limits are meaningful because these indicators are closed-form ratios.
Machine-learning inputs — four cheap, sensor-independent features that complement spectral descriptors and add almost no computation cost.
Operating-state segmentation — energy entropy separates steady running from switching, knocking or intermittent loading.

Impulse and margin factor are ratios against a mean value. On a nearly silent signal the denominator becomes very small and the factors can grow without bound; interpret them only where the signal level is well above the noise floor of the measurement chain.

All four indicators follow the standard textbook definitions used in machinery condition monitoring, so values can be compared with published thresholds and with other tooling that implements the same formulas.