Library / Structural dynamics and vibration testing / SDY-31
Structural dynamics and vibration testing
H1 transfer estimate
Frequency response estimate from the cross-spectrum Syx of input and output divided by the input autospectrum Sxx.
- Ref
- SDY-31
- Rev
- v1
- Field
- Structural dynamics and vibration testing
- Result
- |H1| [m/N]
The H1 estimate is the cross-spectrum of output against input divided by the input autospectrum, H₁ = Syx/Sxx. It is unbiased when there is no noise on the input and the output noise is uncorrelated with the input, and it is biased low where noise enters the force channel. This entry gives its magnitude; the derived values give its real and imaginary parts and phase.
Frequency response estimate from the cross-spectrum Syx of input and output divided by the input autospectrum Sxx. It is the right choice when the input is clean and the output carries the noise. This entry returns its magnitude.
Calculator
- Real part of H12 m/N
- Imaginary part of H12 m/N
- Phase angle45 °
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 2.828 m/N and phase 45°.
- Pair H1 with the coherence: where the coherence drops, treat the value as unreliable.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Sxx Input autospectrum | 0.1 to 5 N²/Hz | 0.5657 | 28.28 | 27.72 | +10% | −9.09 % |
| Re Syx Real part of the cross-spectrum | −5 to 5 m·N/Hz | 2 | 5.385 | 3.385 | +0.2 m·N/Hz | +5.12 % |
| Im Syx Imaginary part of the cross-spectrum | −5 to 5 m·N/Hz | 2 | 5.385 | 3.385 | +0.2 m·N/Hz | +5.12 % |
Sweep of Input autospectrum
| Input autospectrum (N²/Hz) | Magnitude of the H1 estimate (m/N) |
|---|---|
| 0.1 | 28.28 |
| 0.7125 | 3.97 |
| 1.325 | 2.135 |
| 1.938 | 1.46 |
| 2.55 | 1.109 |
| 3.163 | 0.8944 |
| 3.775 | 0.7493 |
| 4.388 | 0.6447 |
| 5 | 0.5657 |
Sweep one variable
Variables and how each one contributes
Magnitude of the H1 estimate
What the equation gives you. Everything else feeds it.
Real part of the cross-spectrum
The real part of the averaged cross-spectrum of output against input at one frequency, in m·N/Hz. Raises the magnitude of the estimate. Raising it by 0.5 (to 2.5) moves the result by +13.2 %, from 2.828 to 3.202 m/N.
Imaginary part of the cross-spectrum
The imaginary part of the cross-spectrum, in m·N/Hz. It sets the phase of the estimate. Raises the magnitude of the estimate. Raising it by 0.5 (to 2.5) moves the result by +13.2 %, from 2.828 to 3.202 m/N.
Input autospectrum
The averaged input autospectrum, in N²/Hz. It must be positive. A larger input spectrum lowers the estimate. Raising it by 10 % (to 1.1) moves the result by −9.09 %, from 2.828 to 2.571 m/N.
Worked example with the values above
- Cross-spectrum magnitude: |Sᵧₓ| = √(2² + 2²) = 2.8284.
- Divide by the input autospectrum 1.
- |H₁| = 2.8284 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