{
  "method": "CEEMDAN",
  "slug": "ceemdan",
  "title": "CEEMDAN: ensemble averaging with adaptive noise",
  "summary": "CEEMDAN repeatedly estimates components from perturbed signals and updates a shared residual. The noise modes and ensemble averages are algorithmic inputs, not decorative uncertainty bands.",
  "steps": [
    {
      "title": "Generate perturbations",
      "text": "Normalize the input, draw seeded noise, and decompose the noise realizations."
    },
    {
      "title": "Average first IMFs",
      "text": "Apply EMD to each perturbed input and average its first IMF."
    },
    {
      "title": "Update adaptively",
      "text": "Perturb the current residual with the next noise mode, average local means, and extract the next cIMF."
    },
    {
      "title": "Retain the residue",
      "text": "Continue until the stopping criterion, then retain the remaining signal for additive reconstruction."
    }
  ],
  "parameters": [
    {
      "name": "trials",
      "effect": "Number of ensemble members; this small animation uses 8, while DeTime's default is 100."
    },
    {
      "name": "epsilon",
      "effect": "Controls the perturbation scale; this visibility-oriented trace uses 0.04, not the default 0.005."
    },
    {
      "name": "seed and n_jobs",
      "effect": "The trace uses seed 42 and serial execution. Preserve both for reproducibility."
    },
    {
      "name": "primary_period",
      "effect": "Affects DeTime's grouping after the upstream component extraction."
    }
  ],
  "cautions": [
    "Different CEEMDAN variants exist; PyEMD includes the later improved formulation documented by its authors.",
    "An ensemble average does not establish that an IMF is a unique physical component.",
    "Raw DeTime IMF arrays use (mode, time, channel), including a singleton channel for one series."
  ],
  "references": [
    {
      "title": "PyEMD CEEMDAN implementation and reproducibility",
      "url": "https://pyemd.readthedocs.io/en/latest/ceemdan.html"
    },
    {
      "title": "Torres et al. (2011)",
      "url": "https://doi.org/10.1109/ICASSP.2011.5947265"
    },
    {
      "title": "Colominas et al. (2014)",
      "url": "https://doi.org/10.1016/j.bspc.2014.06.009"
    }
  ],
  "trace_kind": "upstream execution trace",
  "trace_note": "Trial inputs, first IMFs, and adaptive local means recorded from EMD-signal 1.10.0; max_imf=3 bounds this upstream teaching run. DeTime's example below exposes the public controls and does not set this internal trace cap.",
  "input_note": "Deterministic synthetic teaching signal; not a benchmark.",
  "example_config": {
    "method": "CEEMDAN",
    "params": {
      "trials": 8,
      "epsilon": 0.04,
      "primary_period": 24
    },
    "seed": 42,
    "n_jobs": 1,
    "backend": "python"
  },
  "checks": {
    "first_ensemble_mean_error": 2.7755575615628914e-17,
    "second_local_mean_error": 8.881784197001252e-16,
    "sum_of_returned_slices_error": 4.440892098500626e-16
  },
  "source_files": [
    "src/detime/methods/ceemdan.py"
  ],
  "frames": 32,
  "duration_ms": 12050,
  "poster_frame": 15,
  "width": 1280,
  "height": 820,
  "artifacts": {
    "gif": {
      "file": "ceemdan.gif",
      "bytes": 1104178,
      "sha256": "356f2cd9d4ffc56bd6447684ef34bcbeeceffdef5a35b3ea3d9c2d84248ccf99"
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    "poster": {
      "file": "ceemdan.png",
      "bytes": 191370,
      "sha256": "ee73513398f425a56e30d75c9fdd7459eeb3ae026f73a6eb9833b8f8edfb387a"
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    "data": {
      "file": "ceemdan.npz",
      "bytes": 60494,
      "sha256": "5f654fae2d8d9e015b88e60d2edff162874eff2b21c43bd8927b318a970e1af6"
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  },
  "source_arrays": {
    "time": [
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    ],
    "input": [
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    ],
    "first_trial_input_and_imf": [
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    ],
    "adaptive_trial_input_and_local_mean": [
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    ],
    "first_running_means": [
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    ],
    "adaptive_running_means": [
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    ],
    "returned_slices": [
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    ]
  },
  "render_provenance": {
    "python_version": "3.12.14",
    "dependencies": {
      "numpy": "2.3.5",
      "scipy": "1.17.0",
      "statsmodels": "0.15.0",
      "matplotlib": "3.10.8",
      "Pillow": "12.3.0",
      "PyWavelets": "1.10.0",
      "EMD-signal": "1.10.0",
      "vmdpy": "0.2",
      "PySDKit": "0.5.0"
    },
    "source_hashes": {
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