Task

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

Challenges with Traditional Approaches

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

Our Approach

• Active learning → Feedback on model quality to the DoE.
• Focuses more on dominating bias (systematic) error than on variance (stochastic) error.
• Utilizes powerful local network construction algorithms → HILOMOT.
• Incremental procedure → Measurements can be stopped at any time.

Optimal maximin Latin hypercubes (unsupervised) 

Optimization of Latin Hypercube (LH) Designs

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

Optimization Strategy (Phase 1)

• Initialize with a random LH
• Find the critical points with the minimum distance between them
• Iterate through all critical points (red)
• Attempt to swap with other points (brown) in order to increase the critical distance
• Check all potential swap partners in all dimensions for all critical points
• Iterate until no better partner can be found
• Phase 2, which follows, provides further improvements
   

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 the next measurement point to gather the most information (supervised)
 

HILOMOT-DoE: Active Learning Cycle 

Joint project with

Situation

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

Problem

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

Results

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

Next Chapter: 3. Automatic Input Selection Back to Overview