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2. Design of Experiments (DoE)


  • Where to measure in order to optimally improve a model?

Difficulty with Traditional Approaches

  • Unsupervised → Good for initialization.
  • Whole measurement plan is designed a priori.
  • Model quality is either
    - not considered at all (space filling designs, etc.) or
    - only variance component is optimized (D-optimal, etc.).

Our Approach

  • Active learning → Feedback of model quality to DoE.
  • Focus rather on dominating bias (systematic) error than on variance (stochastic) error.
  • Utilizes powerful local network construction algorithms → HILOMOT.
  • Incremental procedure → Measurement can be stopped anytime.

Optimal maximin latin hypercubes (unsupervised)


Optimization of Latin Hypercube (LH) Designs

  • LH not necessarily space filling → Optimization required. Here: maximin or Φp.
  • Goal: Maximization of the critical points (closest to each other).
  • Implementation: Deterministic optimization strategy.

Optimization Strategy (Phase 1)

  • Initialize with random LH
  • Find critical points with minimal distance to each other
  • Go through all critical points (red)
  • Try to swap with other points (brown)  in order to increase critical distance
  • Check all potential swapping partners in all dimensions for all critical points
  • Iterate until no improving partner can be found anymore
  • Subsequent phase 2 improves further

Example: 5 points / 2 dimensions


LH Optimization for 100 Points (Phase 1: Improving Critical Points)


LH Optimization for 100 Points (Phase 2: Further Improvements)



Optimization of next measurement point to gather most information (supervised)


HILOMOT-DoE: Active Learning Cycle



Joint project with f29_b01




  • Increasing degrees of freedom.
  • More potential for optimization.


  • Cost and engine test stand times overwhelming.
  • Individual approaches become tedious.
  • Advanced systematic procedures required.


  • Sophisticated models intertwined with DoE (active learning).
  • Much faster engine measurement/calibration times.
  • Flexible trade-off between model accuracy and required engine test stand times.

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