Auto Power Spectrum (APS) Analysis

The auto power spectrum transforms a time waveform to the frequency domain and computes the squared magnitude of each spectral line. The result is a quantitative curve of energy against frequency. Compared with the time waveform, it shows fault frequencies, resonance peaks and the background noise level directly. It is the most basic and most frequently used frequency-domain tool in condition monitoring, product inspection and fault diagnosis.

The analysis is integrated in the real-time test window. During acquisition every frame passes through windowing, FFT, power correction, averaging and unit conversion, and the spectrum updates as the test runs, without offline processing.

The same curve settings also provide the linear spectrum, power spectral density (PSD), cross power spectrum, coherence, frequency response function (FRF), auto- and cross-correlation, probability distribution, octave spectra, sound pressure level and other curve types, 20 in total. They share the same acquisition, windowing and averaging settings, so they can be compared in parallel.

The auto power spectrum turns vibration into quantified engineering values.

• Quantitative results: each line reads in engineering units, peak or RMS (g, mm/s, µm), and can be compared line by line with a limit.
• Energy-consistent readings: built-in window power and amplitude correction keep the total signal energy the same before and after windowing, so readings can be used in reports and acceptance.
• Averaging suppresses random interference: random noise cancels out over several averages while stable periodic fault components remain, so weak early faults appear sooner.
• Several quantities from one acquisition: acceleration, velocity and displacement spectra from the same frame meet the evaluation basis of different standards without repeating the test.
• Repeatable records: spectra export to Excel for inspection reports, trend records and fault comparisons.

All steps run automatically on every frame.

Gxx(f) = |X(f)|² × Kp, where Kp = n / Σw²(i) is the window power correction factor

Windowing: why and which window

FFT analysis uses a finite record, which truncates the signal and spreads energy into neighboring lines (leakage). Peaks read too low and false side lobes rise. A window weights the record with a smooth curve that tapers to zero at both ends and suppresses the discontinuity.

When the window changes, the software recalculates three factors automatically: amplitude correction (single-tone peak), power correction (total energy) and the equivalent noise bandwidth, ENBW (for example 1.5 for Hanning and about 3.77 for flat top). All later scaling uses them.

Averaging: bringing stable components forward

Random interference fluctuates strongly from frame to frame, while fault frequencies appear at the same line in every frame. Averaging several power spectra line by line cancels random components and keeps stable ones, so the noise floor drops.

Linear: Āk = Ak / k + Āk−1 × (1 − 1/k) Exponential: Ā = Anew / N + Ā × (1 − 1/N)

Amplitude scales and velocity or displacement spectra

The same power spectrum can be displayed in eight scales, covering peak, RMS, squared and density forms. EU is the engineering unit of the channel, for example g or m/s² for an acceleration channel.

Velocity and displacement spectra are obtained by integrating the acceleration spectrum line by line in the frequency domain:

V(f) = A(f) / (2πf) D(f) = A(f) / (2πf)² × 1000 (mm)

The conversion recognizes the channel unit (13 units, including g, m/s², mm/s² and in/s²), normalizes it and outputs velocity in m/s peak and displacement in mm peak. One acceleration measurement therefore supports the usual practice of evaluating high frequencies by acceleration, mid frequencies by velocity and low frequencies by displacement, without changing sensors.

Set the analysis parameters and window

1. Select the sampling rate (for example 5120 Hz) and the number of spectral lines (for example 800). The software shows the frequency resolution (2.5 Hz) and the frame period.
2. Select the window: Hanning for general vibration analysis, flat top for precise amplitude calibration, force/exponential for impact tests.
3. After a window change, the software recalculates the correction factors and resets the average.

Configure the curve and averaging

1. Right-click the graph area and open the curve display settings.
2. Select the auto power spectrum curve type and the channels to display.
3. Select the scale: EUpk for general use, EUrms for report evaluation, or the velocity or displacement spectrum for low-frequency evaluation.
4. Enable averaging and set the mode and count (linear averaging, 10 averages, is recommended for steady tests). Confirm with automatic axis adjustment.
5. Click Start for real-time spectrum analysis. Use Restart Average to clear and accumulate again.

Read and export

1. Move the cursor to read the value at the target frequency. The Y axis label includes the scale, for example “Power spectrum EUpk (g)”.
2. Enable peak marking to capture the largest peak and its frequency automatically.
3. Right-click the graph and save as Excel: all visible curves, with the frequency column, axis units, time stamp and curve names, are written to a worksheet. Text and BMP image export are also available.

Interpreting spectra

• Peak frequency identifies the source: match peaks to running speed, bearing characteristic frequencies and gear mesh frequencies.
• Peak height indicates severity: compare the reading with the limit (ISO 20816 zones for velocity spectra).
• The noise floor indicates the signal-to-noise ratio: the lower it is after averaging, the easier weak faults are to find. If it stays high, check grounding and sensor mounting first.
• Trends show deterioration: export spectra regularly under the same conditions and compare peak drift and new lines; trends often appear before an absolute alarm.