Traceable signal-processing worksheet

Spectral RMS Integration Worksheet

Combine documented non-overlapping RMS contributions or integrate documented PSD/ASD data over explicit effective bandwidths. The output is the RMS of the entered data—not automatically a machine overall level, ISO acceptance decision or diagnosis.

RMS contributionsPSD integrationASD integrationNo peak-list shortcut

Do not paste a list of displayed peaksA few peak amplitudes do not represent all energy in a frequency band. Do not enter peak, peak-to-peak, max-hold, ESD, mixed-axis, mixed-unit or mixed-record values. Use a documented analyzer export whose scaling and effective integration bandwidth are known.

Measurement identity and scaling

Blank inputs are deliberate. This worksheet cannot infer the analyzer normalization, window correction, complete frequency band or machine acceptance criterion.

Measurement record ID

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Point and direction

Underlying engineering unitEnter the unit of the resulting RMS quantity, not a density suffix.

Intended band start (Hz)

Intended band end (Hz)

Input scaling

Analyzer export and processing record

Documented non-overlapping inputs

Select an input scaling. For density modes, enter the effective integration width belonging to each density value; do not assume that displayed line spacing and noise bandwidth are interchangeable.

Row	Line/band identifier	Value in selected scaling	Effective integration width, Hz
1	Row 1 identifier	Row 1 value	Row 1 effective integration width
2	Row 2 identifier	Row 2 value	Row 2 effective integration width
3	Row 3 identifier	Row 3 value	Row 3 effective integration width
4	Row 4 identifier	Row 4 value	Row 4 effective integration width
5	Row 5 identifier	Row 5 value	Row 5 effective integration width
6	Row 6 identifier	Row 6 value	Row 6 effective integration width
7	Row 7 identifier	Row 7 value	Row 7 effective integration width
8	Row 8 identifier	Row 8 value	Row 8 effective integration width

Evidence gates

The arithmetic can be shown when a gate is incomplete, but the result must not be reported as a reviewed selected-band RMS until all six are documented.

Same channel and quantity. Every row is from the same calibrated channel, point, direction, physical quantity and underlying unit. Same record and condition. Rows belong to the same acquisition and operating condition; averaged records are not mixed without a documented method. Scaling identified. The export is the selected RMS/PSD/ASD type—not peak, peak-to-peak, max-hold, ESD or an unknown analyzer magnitude. Complete intended band. All relevant lines/bands between the declared limits are included, with filters, DC and Nyquist treatment recorded. No overlap or selected-peak shortcut. Rows are mutually non-overlapping and do not double-count leakage, sidebands or previously integrated bands. Analyzer normalization verified. Window, amplitude convention, density normalization and effective integration widths come from the instrument/export documentation.

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RMS of entered data–

Summed mean square–

Rows used–

Largest mean-square share–

Declared intended band–

Input scaling–

Equations and dimensional check

These are public signal-processing relations, not acceptance formulas issued by ISO. They are valid only for correctly scaled, mutually non-overlapping contributions from the declared measurement.

Integrated RMS contributions: x_selected,RMS = sqrt( sum( x_i,RMS^2 ) )

PSD entries: x_selected,RMS = sqrt( sum( G_i * delta_f_i ) )

ASD entries: x_selected,RMS = sqrt( sum( A_i^2 * delta_f_i ) )

G_i has underlying-unit squared per hertz, A_i has underlying-unit per square-root hertz, and delta-f_i is the applicable effective integration width in hertz. Each term therefore has underlying-unit squared; the final square root restores the underlying engineering unit.

Output name: “RMS of entered data” is intentional. It may be described as a selected-band RMS only when the complete declared band and all evidence gates are satisfied. It is not automatically the broadband overall value used by a machine-specific standard.

Published behavior cross-check: the Dewesoft FFT Analyzer V26-1 manual states that its RMS marker sums all FFT lines in a selected band. Its example changes the range from 0–5000 Hz to 0–3800.05 Hz and the RMS changes from 0.9934 to 0.9902. This demonstrates why the selected band and all lines—not a few displayed peaks—matter.

Separate time-record crest factor

Crest factor requires an absolute instantaneous peak and RMS from the same time record, channel, unit, band and filter. A magnitude-only spectrum does not contain the phase/time history needed to reconstruct the waveform peak.

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Crest-faktor–

FormelCF = |peak| / RMS

No diagnostic thresholdThis worksheet does not label a crest factor “normal,” identify a bearing fault or set an alarm. Interpretation depends on sensor bandwidth, filtering, operating condition, signal type and a validated diagnostic procedure.

Source and standards boundary

ID	Kilde	Verified public information	Use on this page
S1	ISO 18431-1:2005, Edition 1; Cor 1:2009	Published. Last confirmed in 2019; the official lifecycle shows systematic review/close of review and “to be revised.” Its public abstract covers transformations and physical units and warns that signal type must be identified correctly, especially in frequency-domain analysis.	Signal-type and units boundary only; no protected transformation or clause is reproduced.
S2	ISO 18431-2:2004, Edition 1; Cor 1:2008	Published. Last confirmed in 2019 and currently shown at stage 90.60 under review. The public abstract covers rectangular, Hanning and flat-top time windows before DFT analysis.	Windowing context only; no protected correction coefficient is inferred.
S3	ISO 13373-1:2002, Edition 1	Published and confirmed in 2024. The public scope covers general vibration measurement and data-collection procedures for machinery condition monitoring.	Measurement-record context, not the source of the arithmetic.
S4	ISO 13373-2:2016, Edition 2	Published and confirmed in 2021; the official lifecycle currently shows systematic review. Its public scope covers processing, analysis and presentation of vibration data in time and frequency domains.	Processing context, not an ISO acceptance threshold.
S5	Dewesoft FFT Analyzer Solution User Manual V26-1	Public full manual: pp. 20–21 explain window noise bandwidth; pp. 42–43 distinguish Linear, Power, PSD and ASD units/scaling; p. 54 states that the RMS marker sums every FFT line in the selected band.	Public implementation evidence for scaling distinctions, effective bandwidth and the published band-RMS behavior.

NEEDS_LICENSED_SOURCEThe exact normative transformations, window definitions/corrections and machinery-monitoring procedures in ISO 18431-1, ISO 18431-2 and ISO 13373 are protected. Their official cards verify lifecycle and public scope only. This worksheet does not invent clauses, tolerances, acceptance zones or an ISO “overall vibration” formula.

Corrections made in this audit

Selected peaks are no longer called an overall level

The former calculator accepted ten unlabeled amplitudes and applied RSS without frequencies, bandwidths, spectrum normalization or proof that the intended band was complete. The replacement labels the result as the RMS of entered data and requires measurement identity, scaling, band and processing evidence.

RMS, PSD and ASD are separated

The former page treated any same-unit amplitudes as interchangeable. The replacement has three explicit formulas and requires effective integration widths for density values. Peak, peak-to-peak, max-hold, ESD and unknown analyzer magnitudes are rejected by scope.

Peak-to-RMS conversion was removed

Dividing a peak by the square root of two is valid for a sinusoid, not an arbitrary vibration waveform or peak list. The replacement performs no peak-to-RMS conversion.

Crest factor no longer comes from a spectral peak

The former calculator divided an optional peak by the RSS of selected spectral entries and labeled values above four as a bearing-fault indication. Crest factor is now isolated to a same-record time-domain peak/RMS pair and has no diagnostic threshold.

Input integrity and traceability were rebuilt

Decimal point and decimal comma are accepted separately. Mixed separators, negative values, incomplete rows, invalid bands, non-finite calculations and density values without bandwidth are rejected. Defaults, presets, auto-calculation, browser history, clipboard export and external formula rendering were removed.

ISO claims are bounded to public evidence

The visible equations are identified as public signal-processing relations rather than ISO acceptance formulas. Official lifecycle cards and the public Dewesoft manual are linked, while protected details remain explicitly NEEDS_LICENSED_SOURCE.