.. _auto_curve_derivative_exceeds_threshold:

*DETECT SIGN CHANGES BASED ON 3RD DERIVATIVE SIGN CHANGE*
=========================================================

Computes the n-th order derivative of a curve and detects sign changes where the derivative magnitude exceeds a threshold ratio, flagging inflection-like events. Use this worker to identify significant curvature transitions or instability points in time-history or load-displacement data.

When to use
-----------

Classification: **process**.

Tagged: ``3rd_derivative``, ``curve_analysis``, ``derivative``, ``inflection``, ``sign_change``, ``threshold``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve
     - curve
     - vector
     - —
     - 
     - Input X-Y curve (e.g. time-history or load-displacement) on which the derivative analysis is performed; provide as a two-column vector [x, y].
   * - Order
     - order
     - scalar
     - 3
     - 
     - Derivative order to compute before checking the sign-change threshold; defaults to 3 (third derivative), leave at default for standard inflection detection.
   * - Ratio
     - ratio
     - scalar
     - 0.75
     - 
     - Fractional threshold (0–1) relative to the derivative's peak magnitude; a sign change is only flagged when the local derivative exceeds this ratio — defaults to 0.75, increase to suppress minor fluctuations.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - curve_derivative_exceeds_threshold_output_1
     - curve_derivative_exceeds_threshold_output_1
     - string
     - String result reporting the detected sign-change locations or status flags where the n-th order derivative exceeded the specified ratio threshold.

Disciplines
-----------

- data.curve.transform
- data.signal_processing

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curve_derivative_exceeds_threshold <https://www.d3view.com/api/workflow/example?id=curve_derivative_exceeds_threshold>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_derivative_exceeds_threshold</code>. Schema hash: <code>0c586adf129a</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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