← All 31 animations

Variational mode decomposition

Variational mode decomposition

Property Value
Method VMD
Input mode univariate
Trend shape (96,)
Notebook execution ran
Reconstruction RMSE 0.00000000

Notebook example metric: root mean square of input - (trend + season + residual) over all samples and channels. This checks additive bookkeeping; it is not a forecast error or a component-recovery score. The separate teaching input and intermediate arrays for the animation are linked below.

How it works

Method maturity: stable. Implementation: native-backed.

VMD alternates between frequency-domain mode updates and spectral-energy centers. DeTime's grouping into trend and season is a separate step after this optimization.

VMD: Prepare the spectrum; Update a mode; Update its center; Reconstruct and group

Deterministic synthetic teaching signal; not a benchmark.

Open GIF · Static PNG · Source arrays (NPZ) · Trace metadata

Follow the four steps

1. Prepare the spectrum

Mirror the signal, compute its FFT, and retain the positive-frequency representation.

2. Update a mode

Fit the remaining spectrum with a bandwidth penalty around the current center frequency.

3. Update its center

Use the mode's positive-frequency energy to update its center, then repeat across modes.

4. Reconstruct and group

Complete the conjugate spectrum, invert the FFT, crop the mirrored margins, and group modes.

Parameters that change the result

Parameter Effect on the computation
K Number of modes; the demonstration uses 3.
alpha Penalizes spectral spread around each center; the demonstration uses 1500.
tau Dual-update step; zero permits noise slack and does not enforce an exact sum of modes.
init / tol Initialization and convergence tolerance affect the computed solution.

What this animation computes

Captured vmdpy 0.2 loop arrays without changing solver updates; intermediate time-domain modes use its conjugate-completion and mirror-cropping convention.

Interpretation

  • The animation captures the optional vmdpy path; the native path has its own implementation and iteration control.
  • Center frequencies shown here are raw solver frequencies in cycles/sample, not DeTime's converted metadata field.
  • VMD modes need a grouping rule before being named trend or season; frequency ordering is not a physical-source guarantee.

Try the method

Use this configuration with DecompositionConfig and decompose. The animation generator supplies the teaching input and records intermediate arrays.

{
  "method": "VMD",
  "params": {
    "K": 3,
    "alpha": 1500.0,
    "tau": 0.0,
    "init": 1,
    "tol": 1e-07,
    "primary_period": 24
  },
  "backend": "python"
}

See the configuration reference for the full interface and optional dependencies.

Sources and reproduction

Regenerate this animation with python scripts/generate_method_animations.py --methods VMD. The reproduction guide explains the environment, numerical checks, coverage manifest, and how to inspect the stored arrays.

Code

case = CASES["VMD"]
run_gallery_case("VMD")

Output

VMD: Variational mode decomposition integrated into the common workflow layer.
status: ran
input mode: univariate
trend shape: (96,)
backend: native
reconstruction RMSE: 0.00000000

Decomposition Plot

VMD decomposition