.. _sphx_glr_auto_examples_VDEF_optim:

VDEF MDAO Optimization Example
===============================

This folder contains a comprehensive example of using the paroto library for
**Voltage-gap-Distance-Energy-Frequency** (VDEF) optimization in plasma torch design,
using **Multidisciplinary Analysis and Optimization (MDAO)** with OpenMDAO.

Overview
--------

The example demonstrates:

- **Parameter sweep** of plasma torch operating conditions
- **Constraint satisfaction** (25 kW power target, breakdown voltage limits)
- **Parallel execution** using Python multiprocessing (Windows) or MPI (Linux)
- **Data persistence** using SQLite databases
- **Advanced visualization** with pairwise grid (corner plot) analysis

Files
-----

1. example_vdef_mdao.py
~~~~~~~~~~~~~~~~~~~~~~~

Main parameter sweep script that explores the plasma torch design space.

**Features:**

- Uses OpenMDAO's ``TorchDesignGroup`` with physics-based models
- Explores 3D parameter space: **V**\ oltage × gap-**D**\ istance × **F**\ requency
- Computes **E**\ nergy per pulse as output (satisfying power constraint)
- Implements power constraint (25 kW) via balance component
- Tracks convergence status for all evaluations
- Saves results to SQLite database (``parameter_sweep_cases.sql``)

**Usage:**

.. code-block:: bash

   # Run parameter sweep (default: multiprocessing)
   python example_vdef_mdao.py

   # Generate N2 diagram only
   python example_vdef_mdao.py --n2

**Parameters Explored (VDEF):**

- **Voltage** (V): HV voltage: 5 - 80 kV (15 levels)
- **gap** (D): Gap distance: 6 - 30 mm (8 levels)
- **Energy** (E): Energy per pulse (computed output)
- **Frequency** (F): Pulse frequency: 5 - 200 kHz (10 levels)
- **Total evaluations**: 1,200 cases (15 × 8 × 10)

**Outputs:**

- ``parameter_sweep_cases.sql``: SQLite database with all results
- ``parameter_space_visualization.png``: Standard 6-panel visualization
- Console output with convergence statistics

2. analyze_vdef_pairwise.py
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Post-processing script that creates pairwise grid (corner plot) visualization.

**Features:**

- Loads results from SQLite database
- Creates comprehensive pairwise grid showing:

  - All 2D parameter combinations
  - 1D marginal distributions (histograms)
  - Three-way classification: Feasible / Converged-Infeasible / Non-converged

- Eliminates 2D projection ambiguity
- Color-coded by energy per pulse

**Usage:**

.. code-block:: bash

   # Run after example_vdef_mdao.py has generated data
   python analyze_vdef_pairwise.py

**Output:**

- ``pairwise_grid_visualization.png``: Comprehensive corner plot

3. generate_n2_diagram.py
~~~~~~~~~~~~~~~~~~~~~~~~~~

Utility script to generate OpenMDAO N2 diagram showing system architecture.

**Usage:**

.. code-block:: bash

   python generate_n2_diagram.py

**Output:**

- ``n2.html``: Interactive N2 diagram

4. plot_generator_operating_window.py
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Demonstrates automatic constraint boundary exploration for the generator.

**Usage:**

.. code-block:: bash

   python plot_generator_operating_window.py



.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script loads pre-computed parameter sweep results and creates a pairwise grid (corner plot) showing: - All 2D projections of parameter combinations - 1D marginal distributions (histograms) - Three-way classification: Feasible, Converged-Infeasible, Non-converged">

.. only:: html

  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_analyze_vdef_pairwise_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_analyze_vdef_pairwise.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Analysis script: Pairwise grid visualization of parameter space.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to: 1. Set up the problem directly in Python (no STONE config) 2. Use RepetitivePulseBreakdownModel with:    - Pulse duration effects (ionization avalanche kinetics: e + M → e + e + M+)    - Memory effects from repeated pulsing    - Field enhancement factors 3. Explore feasible parameter space with power and breakdown constraints 4. Visualize the solution space 5. Run parameter sweeps in parallel using OpenMDAO&#x27;s DOEDriver">

.. only:: html

  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_example_vdef_mdao_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_example_vdef_mdao.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Example: Direct MDAO problem setup for plasma torch parameter space exploration.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script creates an interactive HTML N2 diagram showing the system architecture and data flow for the plasma torch MDAO problem.">

.. only:: html

  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_generate_n2_diagram_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_generate_n2_diagram.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Generate N2 diagram for the VDEF MDAO example.</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This script loads results from the VDEF parameter sweep and visualizes the generator operating window with actual design points overlaid.">

.. only:: html

  .. image:: /auto_examples/VDEF_optim/images/thumb/sphx_glr_plot_generator_operating_window_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_VDEF_optim_plot_generator_operating_window.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Plot Generator Operating Window from VDEF Parameter Sweep.</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/VDEF_optim/analyze_vdef_pairwise
   /auto_examples/VDEF_optim/example_vdef_mdao
   /auto_examples/VDEF_optim/generate_n2_diagram
   /auto_examples/VDEF_optim/plot_generator_operating_window