Task

• 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

Situation

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

Problem

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

Results

• 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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