1. Introduction
2. Installation
3. Getting Started
4. Modules
5. Examples
6. Contributing
7. License
8. Acknowledgments

OTAF (Open Tolerance Analysis Framework) is a research oriented library designed to perform statistical tolerance analysis of mechanical assemblies. It can be used for iso- and over- constrained rigid mechanical assemblies, without large displacements. It allows for the semi-automatic construction a System of Constraints (SOC)-based assembly model, given a minimal representation of the assembly and its components as well as hypotheses.

This model can then be used to perform statistical tolerance analysis, by modeling defects as random variables, and estimating the probability of non assembly using different estimation techniques.

These codes have been developed during a PhD called TRIP (ToleRance analysis with Imprecise Probabilities), where the defect distributions are modelled using imprecise probabilities, and the notebooks, (once currated) will be from the examples in the paper.

Key use cases include:

• Construction of a SOC Model: Automatically construct the linear problem modeling the assembly.
• Modeling Manufacturing Deviations: Analyze the effects of geometric and dimensional variations.
• Probability of Failure Estimation: Use advanced statistical tools to quantify and mitigate risks (Monte Carlo, FORM, SORM, GLD).
• Imprecise Probability of Failure Estimation: Apply methods developed in an upcoming paper [COMING SOON] to model the space of possible defects.

• Only Rigid Transformations: Only rigid defects (translations and rotations) are modeled.
• Limited Feature Types: Currently supports only planar and cylindrical features.
• No Tools for Tolerance Allocation: Users must implement this on their own after generating the SOC model.
• Not Production-Ready: Apart from SOC model construction, the rest of the program is in an alpha stage and may remain so. Use at your discretion.

Do this inside of a virtual environment or conda :

# Clone the repository
git clone https://github.com/Kramer84/otaf.git

# Navigate to the project directory
cd otaf

# Install the package
pip install .

# Install the package with documentation build dependencies
pip install .[docs]

The following Python libraries are required:

• Base: joblib, beartype
• Scientific: numpy, scipy, sympy
• Uncertainty Quantification: openturns
• Visualization: matplotlib, trimesh
• Machine Learning: torch, torcheval, scikit-learn
• Geometry: triangle, pytransform3d[all]

The AssemblyDataProcessor takes as an input a minimal representation of the assembly in the form of a dictionary, that needs to be constructed manually. Some specific notation choices have been made on how to represent features and assemblies. Parts are always represented by a sequence of numbers, surfaces always by a sequence of lowercase letter, and points on the surface always as the same sequence as for the surface in uppercase and an identifying sequence of numbers after it.

So for Part number 123 on surface abc and point ABC321 can be written like this : P123abcABC321

The point with index 0 is always the origin point of the feature! This notation is kinda arbitrary, and may be updated if something better is proposed.

The system data dictionary may look like this :

system_data = {
    "PARTS" : {
        '1' : {
            "a" : {
                "FRAME": RP1a, # Array of size 3x3 with each component being the x,y,z unit vectors for the local frame of the surface (x positive outwards for planar features)
                "POINTS": {'A0' : P1A0, 'A1' : P1A1, 'A2' : P1A2}, # Dictionary mapping point names to the coordinate as numpy array
                "TYPE": "plane", # Type of the feature
                "INTERACTIONS": ['P2a'], # The other feature this feature is interacting with
                "CONSTRAINTS_D": ["PERFECT"], # We can constrain the defect vector D to be 0 so there is no defect modelled on this feature
                "CONSTRAINTS_G": ["FLOATING"], # We can constrain components on the gap vector G at the feature level
            },
        ...
        ...
        },
        '2' : {
            "a" : {
                "FRAME": RP2a,
                "POINTS": {'A0' : P2A0, 'A1' : P2A1, 'A2' : P2A2},
                "TYPE": "plane",
                "INTERACTIONS": ['P1a'],
                "CONSTRAINTS_D": ["PERFECT"], # In this modelization, only defects on the right side
                "CONSTRAINTS_G": ["FLOATING"],
            },
        ...
        ...
        }
    },
    "LOOPS": {
        "COMPATIBILITY": {
            "L0": "P1cC0 -> P2cC0 -> P2aA0 -> P1aA0", #Minimal representation of the compatibility loops
            "L1": "P1cC0 -> P2cC0 -> P2bB0 -> P1bB0",
        },
    },
    "GLOBAL_CONSTRAINTS": "2D_NZ",
}

Information about the different values that the keys can take refer to the source code in constants.py.

Visit the OTAF Documentation for detailed guides, examples, and API references.

TO COMPILE THE DOCUMENTATION LOCALLY INSTALL PACKAGE WITH [docs] FLAG, THEN:

sudo apt install pandoc

sphinx-apidoc -o docs/source src/otaf

cd docs/

make clean
make html

OTAF is modular and extensible, with the following key components:

• assembly_modeling: Base classes for mechanical assemblies. MOST IMPORTANT MODULE
• geometry: Geometric functions for validating geometry, point clouds, etc.
• optimization: Tools for solving SOC optimization with diverse approaches.
• sampling: Sampling distributions of defects or defect parameters.
• distribution: Modeling distributions based on assembly_modeling objects and other specialized tools.
• surrogate: Experimental methods to create surrogate models for the SOC.
• uncertainty: Methods for reliability analyses and failure probability estimation.

Explore the source code for a complete overview.

Explore the NOTEBOOKS/ directory for scripts demonstrating OTAF's capabilities. THE NOTEBOOKS HAVE YET TO BE CLEANED UP

We welcome contributions! Whether you're reporting a bug, suggesting a feature, or submitting a pull request, your help is appreciated. There is still significant work to do to support a broader variety of cases. As the product of three years of PhD research, some parts of the code may not yet be fully optimized for adding new feature types or handling form defects. Legacy code for experimental tools, such as neural network-based surrogate models, may also require further refinement.

This project is licensed under the GNU General Public License v3.0 (GPLv3). For details, see the LICENSE file.

This work is supported by the French National Research Agency (ANR) under the project "Analyse des tolérances avec les probabilités imprécises" (ANR-21-CE46-0009). The goal is to develop new formalisms for tolerance analysis based on imprecise probabilities, bridging the gap between theory and industrial applications.