Results and code checks
What the unity values mean, how they were computed for the training data, and what a surrogate prediction can and cannot tell you.
Unity in one sentence
Unity is the ratio of a calculated stress to the allowable stress. Below 1.0 the element passes that check. Above 1.0 it does not. The tools report two unities for every element, and the larger of the two at the worst element is the governing unity for the design.
How the training labels were computed
The strength model was trained on unities computed from Abaqus results, element by element, for the operating condition of a gas pipeline under ASME B31.8. The basis was:
| Item | Value used |
|---|---|
| Pipe grade | X65, SMYS 65,300 psi |
| Design factors | hoop 0.5, longitudinal 0.8, combined 0.9 |
| Corrosion allowance | 0.118 in, removed from the wall for all checks |
| Manufacturing tolerance | 0.14 in, also removed for the combined check |
| Elbow wall thinning | 10 % of nominal wall |
| Stress intensification | 1.0 in and out of plane |
| Hoop stress | thin-wall or thick-wall formula depending on the diameter-to-thickness ratio |
Coatings were not modelled as load-bearing. Defaults such as a 0.024 in composite coating with no concrete coating were used and have a minor effect on the result.
Longitudinal unity
Axial stress from the section force plus bending stress from the two bending moments, combined as the resultant moment over the section modulus. The larger magnitude of tension-side and compression-side stress is divided by 0.8 × SMYS.
Combined unity
Von Mises equivalent stress from the longitudinal stress, the hoop stress from internal minus external pressure, and the torsional shear stress, on the wall reduced by corrosion allowance and manufacturing tolerance. The larger of the two fibre values is divided by 0.9 × SMYS.
Reading a result
- Governing unity is the highest unity anywhere on the jumper, and which check produced it.
- Governing element is where that maximum sits, numbered from hub 1. The profile chart shades elbows, so you can see whether the peak is in a bend or a straight run.
- Location in the design tool groups elements into hub 1, left shoulder, belly, right shoulder and hub 2. Where the maximum sits suggests what to change: hub-governed designs usually want more flexible legs; belly-governed designs want a shorter belly or more clearance.
What a prediction is
The tools do not run a finite-element analysis. They return what a neural network trained on a large campaign of finite-element results predicts for your inputs.
- On held-out simulations inside the training ranges, the strength model’s root-mean-square error is about 0.07 unity (validation MSE 4.9×10⁻³), as published in the ISOPE 2026 paper. Typical unities range from 0.5 to 2.5.
- That accuracy applies inside the training ranges. Outside them, errors grow in ways the validation numbers do not describe.
- The model has seen only the M-shape topology, the 90° 5D bends and the code basis above. Other materials, design factors, conditions such as hydrotest, or other jumper shapes are out of scope.
DeepUnity is research software for screening and early design. Verify the governing case of any design you take forward with a code-compliant finite-element analysis by a qualified engineer.