4. Metamodeling

For CFD, FEM, and Look-up Tables.

 

Benefits of Local Model Network Architecture

• Distinction between rule premises (if…) and rule consequents (then…)
• Easy to interpret
• Well suited for high-dimensional input spaces
• Gained knowledge about premises and consequents can be used for DoE designs

Artificial Example

AiF Project in cooperation with the Institute of Fluid- and Thermodynamics

(AiF: Arbeitsgemeinschaft industrieller Forschungsvereinigungen)

• Problem: New EU regulation requires higher degree of efficiency for ventilators
  => Most existing ventilators will be prohibited
  => New efficient dimensioning and optimization strategies required
• Computational Fluid Dynamic (CFD) models fulfill accuracy requirements, but:
  - Many evaluations necessary for optimization
  - Computationally very expensive
  => Economically unviable!
• Approach to solving the problem:
  - Metamodel: Model of the CFD model
  - CFD model generates data set
  - Local model network (LMN) is used

Local Model Network Advantages for the AiF Project Tasks

System Identification

• Automatic model complexity determination saves data for the training
  - Akaike’s corrected information criterion (AICc) instead of validation data
• Deterministic training procedure (no initialization required)

Design of Experiments

• Active learning strategy
  - Structure of LMN is utilized to determine future CFD simulations
• Exploitation of separation between linear and nonlinear effects

Optimization

• Local quadratic models can be used
• Very likely to find global optimum of the LMN
  - M local models => M reasonable initialization points

Construction of Centrifugal Fan

Computational fluid dynamics (CFD) simulations utilized (~4 hours per simulation)

• Target values
  - Pressure curve and efficiency curve
• Design parameters
  - Number of blades, inner and outer diameter, several angles, etc.

Two Metamodeling Approaches

1. Direct Metamodeling

• 10 inputs: Geometric parameters and volume flow.
• 2 outputs: Efficiency and pressure.

2. Indirect Metamodeling via Characteristic Curves

• 9 inputs: Geometric parameters.
• 3 or 4 outputs: Characteristic parameters of efficiency and pressure curves.

Characteristic Curve Model

• 3 or 4 inputs: Characteristic parameters (metamodel outputs).
• 2 outputs: Efficiency and pressure.

CFD (black line), Indirect (MIMO, blue line), Indirect (multiple MISO, green line), Direct (red line)

Next Chapter: 5. Nonlinear Dynamic Models     Back to Overview