.. _sphx_glr_auto_examples_VedEf_optim:

VedEf Operating Window - 5D Parameter Space Exploration
========================================================

This directory contains a comprehensive example for exploring the operating window of a pulsed
plasma torch with 5 design parameters and multiple physics-based constraints.

Overview
--------

The **VedEf** optimization explores 5 design parameters using **ARC002 parameter naming convention**:

- **G_UMAX_OUT** (kV): Generator voltage (High voltage)
- **G_e** (mm): Interelectrode gap distance
- **TP_D_OUT** (mm): Torch outlet diameter
- **G_F** (kHz): PRF - Pulse Frequency
- **G_Ep** (J): Energy per pulse
- **TP_QM** (kg/h): Mass flow rate per torch

All parameters follow the ARC002 parameter registry standard for consistency across
the project and compatibility with experimental specifications.

Files
-----

Integration Layer (Example-Specific)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

- ``1_model_vedef_design_group.py`` - VedEfDesignGroup model definition

  Defines the **VedEfDesignGroup** class that integrates all models for 5D exploration.
  This is the reusable model component containing physics models, constraints, and connections.

- ``1_setup_vedef_problem.py`` - Problem factory function

  Provides **setup_vedef_problem()** convenience function that creates a fully configured
  OpenMDAO Problem with default parameter values. Used by all analysis scripts for consistency.

  **Note:** These are application-specific integration files, not core library components.
  They connect the 5 parameters, 7 physics models/systems, and 10 constraints for this example.

  **Architecture Update (Nov 2025):** Refactored to use:

  - ``HighVoltageGeneratorSystem`` instead of simple HV window ExecComp
  - ``TorchFlowSystem`` instead of separate flow_rate and residence_time ExecComps
  - ``BrownianArcMobilityModel`` for physics-based mobility modeling
  - Explicit intermediate variables (T_0, breakdown_voltage, flow_velocity, etc.)

Main Example
~~~~~~~~~~~~

- ``example_operating_window_5d.py`` - 5D parameter sweep with parallel execution
- ``visualize_operating_window.py`` - Static matplotlib visualization of operating windows
- ``dashboard_operating_window.py`` - Interactive Plotly Dash dashboard
- ``generate_vedef_diagram.py`` - Mermaid diagram generation

Validation and Compliance
~~~~~~~~~~~~~~~~~~~~~~~~~~

- ``validate_arc002_compliance.py`` - Validates parameter names against ARC002 registry

  Checks that all critical design parameters:

  - Are defined in the ARC002 parameter registry
  - Are associated with the correct Equipment_Class (Generator, PlasmaTorch, etc.)
  - Follow the standard naming convention

  **Usage:**

  .. code-block:: bash

     python examples/VedEf_optim/validate_arc002_compliance.py

  **ARC002 Registry Utilities:** ``paroto/validation/arc002.py``

Utilities
~~~~~~~~~

- Uses ``paroto/utils/mermaid_generator.py`` for flowchart generation
- Uses ``paroto/utils/cytoscape_layout.py`` for interactive graph layouts

Physics Models
--------------

New Models Created
~~~~~~~~~~~~~~~~~~

1. Initial Temperature Model (``PulseInitialTemperatureModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Computes the initial gas temperature before each pulse, accounting for:

- **Energy-to-temperature conversion** via sub-model:

  - ``ConstantCpEnergyModel`` (Low fidelity, default)
  - ``CanteraEnergyModel`` (High fidelity, optional)

- Cylindrical thermal diffusion with characteristic time τ = (d_a/2)² / (4α)
- Exponential relaxation between pulses

**Location:** ``paroto/core/models/initial_temperature.py``

**Sub-models:** ``paroto/core/models/energy_to_temperature.py``

**Gallery:** ``examples/gallery/plot_initial_temperature_model_example.py``,
``plot_energy_to_temperature_example.py``

**Validation:** ``paroto/validation/validate_initial_temperature.py``

2. Coverage Model (``ArcCoverageModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Ensures complete gas treatment by the arc, as if the arc was painting the cross-flow gas:

- Constraint: π × e × d_a² / 4 × f ≥ v × S
- Outputs coverage fraction and constraint satisfaction
- Critical for ensuring all gas passes through the thermal treatment zone

**Location:** ``paroto/core/models/coverage.py``

**Gallery:** ``examples/gallery/plot_coverage_model_example.py``

**Validation:** ``paroto/validation/validate_coverage.py``

3. Arc Density Constraint Model (``ArcDensityConstraintModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Limits energy density in the arc volume:

- Constraint: ρ_E = E_p / V_arc < ρ_E_max
- Prevents arc instabilities from excessive energy concentration
- **Note:** Max energy density threshold requires experimental validation

**Location:** ``paroto/core/models/arc_density.py``

**Gallery:** ``examples/gallery/plot_arc_density_model_example.py``

4. Arc Mobility Model (``BrownianArcMobilityModel``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models arc attachment point movement as Brownian motion:

- Affects reignition probability and thermal loading distribution
- Computes RMS displacement, mobility factor, and thermal spread factor
- Based on characteristic velocity and time between pulses

**Location:** ``paroto/core/models/arc_mobility.py``

**Gallery:** ``examples/gallery/plot_mobility_model_example.py``

**Validation:** ``validation/validate_mobility.py``

Existing Systems Integrated
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5. High Voltage Generator System (``HighVoltageGeneratorSystem``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models power electronics constraints:

- Operating window: f × V² × t_pulse / Z ≤ P_max
- Replaces simple ExecComp with full system model
- Outputs: operating_window_power, hv_operating_window_satisfied

**Location:** ``paroto/systems/generator.py``

6. Torch Flow System (``TorchFlowSystem``)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Models gas dynamics:

- Mass conservation: ṁ = ρ × v × S
- Residence time calculation
- Reynolds number and pressure drop
- Replaces simple ExecComps with physics-based flow model

**Location:** ``paroto/systems/torch/flow.py``

Auto-Generated Architecture Diagrams
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The VeDeF example now includes automatic Mermaid diagram generation that introspects
the OpenMDAO problem structure to visualize the complete architecture:

- Run ``generate_auto_diagram.py`` to create diagrams showing actual data flow
- Shows parameters (green), models (blue), intermediates (orange), constraints (red)
- Eliminates manual diagram maintenance - always reflects current implementation

**Script:** ``examples/VedEf_optim/generate_auto_diagram.py``

**Generator:** ``utils/mermaid_generator.py`` - ``generate_problem_graph()`` function



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This is an application-specific OpenMDAO Group for the VedEf operating window example. It integrates all models and constraints for the 5-parameter exploration.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_model_vedef_design_group_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_1_model_vedef_design_group.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">VedEf Design Group for 5-parameter operating window exploration.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates the hierarchical parameter visualization module, showing the 5 primary parameters, models, and 10 constraints in multiple formats: - Hierarchical Mermaid diagram (showing parameter levels and data flow) - NetworkX graph export (for external tools like yEd, Gephi, D3.js)">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_problem_generate_diagram_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_1_problem_generate_diagram.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generate hierarchical visualization for VedEf operating window models.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This module provides the canonical Problem instance for the VedEf operating window example. All analysis and optimization scripts should import and use setup_vedef_problem() to ensure consistency.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_1_setup_vedef_problem_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_1_setup_vedef_problem.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">VedEf Operating Window Problem Setup.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script attempts to find a working set of parameters by: 1. Starting with nominal values 2. Testing individual parameter variations 3. Diagnosing which constraints are violated">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_find_working_params_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_find_working_params.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Find working VedEf parameters through systematic search.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example explores the 5-dimensional parameter space: - V (kV): High voltage - e (mm): Electrode gap distance - d_t (mm): Torch diameter - f (kHz): Pulse frequency - E_p (mJ): Energy per pulse">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_parameter_sweep_5d_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_parameter_sweep_5d.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Example: 5D Operating Window Exploration for VedEf Parameters.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Minimal test to diagnose VedEf model issues.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_simple_test_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_simple_test.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Minimal test to diagnose VedEf model issues.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Smart parameter search for VedEf - targeting power and temperature constraints.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_smart_search_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_smart_search.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Smart parameter search for VedEf - targeting power and temperature constraints.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Search focusing on achieving temperature rise for mobility constraint.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_2_optim_temperature_focused_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_2_optim_temperature_focused.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Search focusing on achieving temperature rise for mobility constraint.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This dashboard provides real-time interactive exploration of the 5D parameter space with constraint visualization and model connectivity graph.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_dashboard_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_dashboard.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Interactive Dash Dashboard for VedEf Operating Window Exploration.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Analyze power constraint violations to find near-feasible operating points.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_power_constraint_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_power_constraint.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Analyze power constraint violations to find near-feasible operating points.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Recommend parameter ranges to achieve 25 kW target power.">

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  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_recommend_parameters_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_recommend_parameters.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Recommend parameter ranges to achieve 25 kW target power.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script loads results from the parameter sweep and creates static matplotlib visualizations showing 2D slices through the 5D parameter space with constraint boundaries.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_3_analysis_visualize_window_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_3_analysis_visualize_window.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Visualization of 5D Operating Window with 2D Slices.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script introspects the problem graph to show: - Nodes organized by hierarchy level - Node types (parameters, models, constraints) - Connections between levels - Graph statistics">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_analyze_problem_graph_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_analyze_problem_graph.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Analyze and visualize the VedEf problem graph structure.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script demonstrates how to use the ARC002 validation utilities to check that a Problem&#x27;s parameters align with the ARC002 parameter registry.">

.. only:: html

  .. image:: /auto_examples/VedEf_optim/images/thumb/sphx_glr_validate_arc002_compliance_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VedEf_optim_validate_arc002_compliance.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Validate VedEf Problem Compliance with ARC002 Parameter Registry.</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/VedEf_optim/1_model_vedef_design_group
   /auto_examples/VedEf_optim/1_problem_generate_diagram
   /auto_examples/VedEf_optim/1_setup_vedef_problem
   /auto_examples/VedEf_optim/2_optim_find_working_params
   /auto_examples/VedEf_optim/2_optim_parameter_sweep_5d
   /auto_examples/VedEf_optim/2_optim_simple_test
   /auto_examples/VedEf_optim/2_optim_smart_search
   /auto_examples/VedEf_optim/2_optim_temperature_focused
   /auto_examples/VedEf_optim/3_analysis_dashboard
   /auto_examples/VedEf_optim/3_analysis_power_constraint
   /auto_examples/VedEf_optim/3_analysis_recommend_parameters
   /auto_examples/VedEf_optim/3_analysis_visualize_window
   /auto_examples/VedEf_optim/analyze_problem_graph
   /auto_examples/VedEf_optim/validate_arc002_compliance