Library / Structural dynamics and vibration testing / SDY-32
Structural dynamics and vibration testing
H2 transfer estimate
Frequency response estimate from the output autospectrum Syy divided by the cross-spectrum Sxy.
- Ref
- SDY-32
- Rev
- v1
- Field
- Structural dynamics and vibration testing
- Result
- |H2| [m/N]
The H2 estimate divides the output autospectrum by the cross-spectrum of input against output, H₂ = Syy/Sxy. It is unbiased when the noise is on the input measurement and the output is clean, and it is biased high where noise enters the output. It is the better estimator at resonance for a noisy force channel. This entry returns its magnitude.
Frequency response estimate from the output autospectrum Syy divided by the cross-spectrum Sxy. It is the right choice when the noise is mainly on the input measurement. This entry returns its magnitude.
Calculator
- Real part of H22.25 m/N
- Imaginary part of H2−2.25 m/N
- Phase angle−45 °
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The estimate has magnitude 3.182 m/N.
- H1 and H2 bracket the true response when the noise is on both channels: comparing the two shows how much noise there is.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Syy Output autospectrum | 0.5 to 20 m²/Hz | 0.1768 | 7.071 | 6.894 | +10% | +10 % |
| Re Sxy Real part of the cross-spectrum | −5 to 5 N·m/Hz | 1.671 | 4.5 | 2.829 | +0.2 N·m/Hz | −4.87 % |
| Im Sxy Imaginary part of the cross-spectrum | −5 to 5 N·m/Hz | 1.671 | 4.5 | 2.829 | +0.2 N·m/Hz | +5.12 % |
Sweep of Output autospectrum
| Output autospectrum (m²/Hz) | Magnitude of the H2 estimate (m/N) |
|---|---|
| 0.5 | 0.1768 |
| 2.938 | 1.039 |
| 5.375 | 1.9 |
| 7.813 | 2.762 |
| 10.25 | 3.624 |
| 12.69 | 4.486 |
| 15.13 | 5.347 |
| 17.56 | 6.209 |
| 20 | 7.071 |
Sweep one variable
Variables and how each one contributes
Magnitude of the H2 estimate
What the equation gives you. Everything else feeds it.
Output autospectrum
The averaged output autospectrum, in m²/Hz. More output power raises the H2 estimate and lowers the coherence for the same cross-spectrum. Raising it by 10 % (to 9.9) moves the result by +10 %, from 3.182 to 3.5 m/N.
Real part of the cross-spectrum
The real part of the cross-spectrum Sxy, in N·m/Hz. Changes the magnitude of the cross-spectrum. Raising it by 0.5 (to 2.5) moves the result by −11.7 %, from 3.182 to 2.811 m/N.
Imaginary part of the cross-spectrum
The imaginary part of the cross-spectrum Sxy, in N·m/Hz. Changes the magnitude of the cross-spectrum. Raising it by 0.5 (to −1.5) moves the result by +13.1 %, from 3.182 to 3.6 m/N.
Worked example with the values above
- Cross-spectrum magnitude: |Sₓᵧ| = √(2² + −2²) = 2.8284.
- Divide the output autospectrum 9 by it.
- |H₂| = 3.182 m/N.
Assumptions and limits
- Averaged spectra from the same records, windows and frequency bin, with a stationary, linear system.
- At least several averages are used, because a single unaveraged record gives a coherence of one at every frequency.
Common mistakes
- Using H1 where the force channel is noisy, which biases the peak low, or H2 where the output is noisy.
- Reading frequency response values where the coherence is low.
- Forgetting the 90° and 180° phase changes when converting between receptance, mobility and accelerance.
Statistics and uncertainty
Spectral estimates carry random error that falls as the square root of the number of averages and bias that depends on leakage and noise. Quote the number of averages, and read the coherence before relying on any frequency response value.
Where it is used
- Estimating frequency response functions from impact hammer and shaker tests.
- Converting between displacement, velocity and acceleration responses for modal fitting and coupling.
Maths you need
- Cross-spectrum: the averaged product of one signal and the conjugate of another
- Complex numbers: real and imaginary parts, magnitude and phase
- Frequency response function: output per unit input at each frequency