Modal Measurement and Parameter Identification

The main window consists of a curve information table, the plot area, the combined modal calculation area and the CMIF stability diagram.

A frequency response function (FRF) describes the relationship between the force applied at an excitation point and the vibration at a response point — the vibration fingerprint of the structure. Modal identification from FRFs gives three inherent properties: natural frequencies, damping ratios and mode shapes.

• Resonance avoidance: with the natural frequencies known, operating speed, mounting or stiffness can be changed to keep the excitation frequency away from a natural frequency, reducing fatigue damage and noise.
• Structural optimization: mode shapes show where the structure moves most, giving a quantified basis for ribs, weight reduction or material changes.
• Simulation model validation: test modes are the reference for checking a finite element model and improve confidence in its predictions.
• Root cause of faults: many difficult vibration problems are resonances, and modal data is the strongest evidence in a diagnosis report.

Why each hit has to be checked

Modal tests average several hits to suppress random noise. A single bad hit — especially a double hit where the hammer touches the specimen twice — causes strong ripple in the spectrum. Once it is in the average, the whole batch is contaminated and must be repeated. Traditionally the operator judges each hit by eye, which is hard for beginners. The system scores every hit immediately on four checks — double hit, spectral smoothness, signal-to-noise ratio and clipping — out of 100, and recommends discarding hits below 60.

FRF estimation

In an impact test the force is measured on the hammer channel and the response by accelerometers. Each frame is windowed and transformed by FFT; the FRF H(ω) = A(ω) / F(ω) is estimated from the cross spectrum of response and excitation and the auto spectrum of the excitation. Frames are averaged linearly, so random noise decreases and the curves become smoother as frames are added.

Automatic hammer hit scoring

Scoring thresholds — for example a 5 % second-peak penalty threshold, 6 dB for full ripple deduction and 60 dB for a full signal-to-noise score — are scaled with the sampling parameters, so the criteria remain consistent at different sampling rates and line counts.

Peak half-power method

For each resonance peak, the half-power points 3 dB below the peak (amplitude 1/√2 of the peak) are found on both sides; their frequency difference is the half-power bandwidth Δf and the damping ratio is ζ = Δf / (2 · f₀). The method is quick and intuitive and often serves as a cross-check of more complex methods.

Least-squares complex exponential (LSCE)

LSCE describes the impulse response of the structure (the inverse Fourier transform of the FRF) as a sum of decaying complex exponentials and solves the autoregressive coefficients by least squares, separating all conjugate complex frequencies at once and giving natural frequencies and damping ratios. Solving repeatedly for increasing model order produces a stability diagram: physical modes stay stable in frequency and damping as the order increases, while noise poles drift, so spurious modes can be removed.

MDOF global fitting

For a set of FRFs from several measurement and reference points, a multi-degree-of-freedom rational fraction model is fitted to all curves in the selected band by global least squares, with modal parameters shared across all curves. It suits closely spaced modes that a single curve cannot separate and gives better accuracy and consistency than single-curve methods.

Complex mode indicator function (CMIF)

CMIF performs a singular value decomposition of the FRF matrix at every spectral line. Peaks of the singular values mark mode locations, and the number of significant singular values indicates how many modes coexist. It shows quickly how many modes there are and roughly where, and is used to set the band and order for the stability diagram. It is displayed live with a logarithmic vertical axis.

Modal assurance criterion (MAC)

MAC measures the correlation of two mode-shape vectors: close to 1 for the same mode and close to 0 for different modes. After identification, the MAC matrix has 1 on the diagonal, and off-diagonal values should be small. High off-diagonal values indicate similar shapes and possibly missing or duplicated modes, so the identification settings should be checked.

Universal file format

FRFs are read and written in the UFF dataset 58 format, used in experimental modal analysis for more than thirty years. Exported files can be read directly by mainstream modal post-processing software and vice versa, so data is not locked to one tool chain.

Live mode: acquisition and hit confirmation

Set the sampling rate, number of lines, averaging and force window in the main window, select the hammer channel as the reference and enable the response channels. Click Start and strike the measurement point perpendicular to the surface. After each hit a preview window shows the waveform and spectrum, with the score and deduction reasons. Accept a clean, high-scoring hit to include it in the average; discard a hit marked “double hit at xx ms” or with a low score and strike again. Preview before averaging can be enabled for every hit, and the view can be limited to the hammer signal.

Example: a preview showing a score of 96, “single hit, clean”, means the frame is reliable and can be accepted.

Live mode: open the FRF analysis window

After averaging, open the FRF analysis window and select the live measurement as the data source. The FRFs of all enabled channels are collected, with the hammer as reference and one curve per response channel, colored automatically and listed in the curve table. The magnitude curves and cross spectrum show the resonance peaks.

Import mode: combining several batches

Save the FRFs of each batch as UFF files, preferably named by point number (for example N0001.uff, N0002.uff). Select file import as the data source and select dozens of files at once; they are loaded in file-name order. The curve table lists response and reference points, directions, units and source files, and supports batch swapping of reference and response directions and automatic unit filling. After import, the display range is reset, all curves are overlaid, and the same modal calculation as in live mode can be run.

Display and readout

Six buttons switch between magnitude, phase, real, imaginary, Nyquist and Bode. Two selectors set the vertical axis (linear, logarithmic, dB) and horizontal axis (linear, logarithmic). Click the plot for a cursor showing the frequency and the focus curve value; the up and down arrow keys change the focus curve. Drag to zoom, right-drag to pan, scroll to zoom, and use the context menu to restore the full band.

Modal parameter calculation

Set the frequency range (for example 1000 to 5000 Hz), the resolution and the method. The peak half-power method lists natural frequency and damping for each mode for a quick survey. LSCE and MDOF need a maximum order and a virtual order (for example 30 each); after calculation, the CMIF window draws the stability diagram, where stable poles are candidate modes. Check the natural frequency (Hz), damping (%) and modal stiffness and mass of each mode, then view the MAC matrix: 1 on the diagonal and off-diagonal values well below 1 (for example below 0.1) are normal; higher values call for a review of the identification settings in that band.

Export

Save the FRFs and modal results as UFF or text files for mode shape animation, reports and third-party software.

A demonstration data set of 30 FRFs, acquired with one hammer and sensors placed in batches, in a common unit of g/N, is imported and analyzed. The first three modes in the result table:

Where stable poles line up vertically in the stability diagram there is a real mode. The number of CMIF peaks should match the number of modes in the result table. Once the MAC check passes, the parameters can be used for resonance avoidance and simulation correlation.