1. Multi-iteration CAE comparison and ranking
In a typical product development program, a single CAE run is rarely the end of the story. Structural topology changes, thickness sweeps, material substitutions, and load-path revisions accumulate across design iterations, and each iteration produces its own set of result files: displacement fields, stress contours, modal frequencies, mass properties, and often dozens of derived metrics. The engineering question is no longer "does this design pass?" but "which of these twenty candidate designs is best, and by how much?" This course addresses that second question systematically — how to compare CAE results across multiple iterations, how to rank candidate designs on a defensible basis, and how to communicate the ranking so that design decisions can be made with confidence.
Why multi-iteration comparison is a distinct engineering problem
Comparing two CAE results is straightforward; comparing twenty is not. Three difficulties dominate. First, result sets are heterogeneous: iteration 3 may report peak von Mises stress at a fillet, iteration 7 may have removed that fillet entirely, and iteration 12 may introduce a new hot spot elsewhere. A naive "minimum peak stress wins" rule silently rewards designs that simply moved the critical location out of the reported scope. Second, metrics have different units, scales, and directions of goodness: mass should be minimized, first natural frequency maximized, and maximum stress minimized, yet all three must be combined into one ranking. Third, results are only comparable if the underlying model, mesh, boundary conditions, and extraction method are consistent; a ranking built on inconsistent baselines is worse than no ranking, because it looks authoritative while being meaningless.
The engineering motivation is therefore economic and organizational as much as technical. Design reviews need a shortlist, not a data dump. Optimization loops need an objective function that reflects real trade-offs. And traceability requirements mean that the ranking must be reproducible: given the same iteration results and the same weighting scheme, any engineer should arrive at the same order.
Scope of the course
The course covers the full comparison-and-ranking workflow for linear static, modal, and lightweight nonlinear CAE studies, using a consistent running example: a bracket-type structural component evaluated across a design space of thickness, rib layout, and material grade. The scope includes:
- Result normalization — extracting a fixed metric set from each iteration's solver output (ODB, result, or CSV), including peak and percentile stress, maximum displacement, first three modal frequencies, mass, and safety factor.
- Baseline and consistency control — verifying that mesh density, element formulation, boundary conditions, and load cases are identical or explicitly reconciled before any comparison is made.
- Multi-criteria ranking — weighted scoring, Pareto dominance, and rank-aggregation methods, with attention to how weighting choices change the outcome.
- Sensitivity and robustness checks — testing whether the top-ranked design remains top-ranked under plausible changes in weighting or load assumptions.
- Reporting — producing a comparison matrix and ranking table that a design review can act on.
Out of scope: detailed solver theory, mesh generation technique, and optimization algorithms themselves. The course treats the solver as a black box that produces result files; the intellectual work is in what happens after the solve.
Key terminology
The following terms are used with fixed meanings throughout the course. Establishing them now prevents the most common source of confusion in multi-iteration work: two engineers using the same word for different quantities.
| Term | Definition used in this course | Typical unit / form |
|---|---|---|
| Iteration | A single, uniquely identified CAE model variant with its own geometry, mesh, and result set. Identified by an ID such as IT-07. |
— |
| Metric | A scalar extracted from an iteration's results that participates in comparison. Must have a defined extraction rule (location, averaging, percentile). | MPa, mm, Hz, kg, — |
| Direction of goodness | Whether a metric should be minimized (cost) or maximized (benefit). | min / max |
| Baseline | The reference iteration against which relative changes are expressed; also the consistency anchor for mesh and BC checks. | Iteration ID |
| Normalized score | A metric rescaled to [0, 1] so that 1 is best, using min–max normalization across the candidate set. | 0–1 |
| Weight | The relative importance assigned to a metric in a weighted-sum ranking; weights sum to 1. | 0–1 |
| Pareto dominance | Design A dominates B if A is at least as good on every metric and strictly better on at least one. | Boolean relation |
| Pareto front | The set of non-dominated iterations; the shortlist from which a final choice is made. | Set of IDs |
| Rank reversal | A change in the ordering of designs caused by a change in weighting, normalization, or candidate set — a warning sign of an unstable ranking. | — |
How the pieces fit together
The figure below shows the relationship between the main objects of the workflow. Iterations feed a metric extraction stage; the extracted metrics are checked for consistency against the baseline; normalized scores and weights feed the ranking; and the ranking is then subjected to a robustness check before it is reported. The dashed path indicates the feedback loop: if the robustness check reveals rank reversal, the weighting or the candidate set is revisited rather than the result being reported as-is.
A worked illustration of the terminology
Consider four candidate iterations of the bracket, with the following extracted metrics (values are illustrative and chosen for teaching, not measured results):
| Iteration | σ_max (MPa, min) | δ_max (mm, min) | f1 (Hz, max) | Mass (kg, min) |
|---|---|---|---|---|
| IT-01 (baseline) | 212 | 0.84 | 96 | 2.40 |
| IT-02 | 178 | 0.91 | 88 | 2.55 |
| IT-03 | 195 | 0.72 | 104 | 2.62 |
| IT-04 | 168 | 0.88 | 91 | 2.71 |
Applying min–max normalization with the stated directions of goodness, IT-04 scores best on stress (1.00) but worst on mass (0.00); IT-03 scores best on displacement and frequency but is mid-pack on stress. No single iteration dominates all others, so the Pareto front contains more than one member — a typical and important outcome. The ranking then depends on weights: with w_stress = 0.5, w_mass = 0.3, w_f1 = 0.2, IT-04 leads; with w_stress = 0.3, w_mass = 0.5, w_f1 = 0.2, IT-03 leads. That sensitivity is exactly what the robustness check is designed to expose, and it is why the course treats weighting as an engineering decision to be documented, not a default setting to be accepted.
With this vocabulary and workflow established, the remaining chapters can move directly into the mechanics: how to define extraction rules that survive geometry changes, how to construct the comparison matrix, how to compute weighted and Pareto rankings, and how to document the result so that it is reproducible in the next design review.