PHX ModelCenter MBE Reduces Complex System Optimization Time by 99% Improve Gas Turbine Design Success with Concept Stage Service Live Estimates
Challenge: Improve Efficiency of System Modeling Optimization under Uncertainty
Georgia Tech's Systems Realization Laboratory conducted a study to improve optimization techniques for real-world systems under uncertainty.1 The practical problem was the optimization of a hydraulic backhoe system with an articulated arm. Such dynamic system simulation involves a large number of variables, requiring substantial time and computer resources for optimization. The mechanical assembly and subsystems are linked, and cannot be easily broken down into independent constitutive elements. Furthermore, arriving at a suitable objective function is complicated by the fact that multiple sub-objectives are possible. Weighting these appropriately is often difficult.
Solution: Optimization in ModelCenter using Kriging Models and Latin-Hypercube Sampling
A Model-Based Engineering (MBE) approach used ModelCenter to integrate modeling tools and improve optimization techniques. The backhoe’s mechanical assembly and subsystems were modeled using the Modelica language and its extensive component libraries. Characteristic values for each part were inserted into the system model from a ProE CAD model of an actual backhoe assembly. Multi-attribute utility theory was used to create a suitable objective function—a utility function—consisting of weightings for critical system attributes. For the backhoe, these were fuel consumption, equipment cost, and dig-track accuracy. These attributes were summed to produce a utility with values from 0 to 1. Weighting was determined subjectively from combinations of attribute values. This utility function easily incorporated into ModelCenter to accurately represent how a customer would rank the integrity of competing alternatives. A sensitivity analysis using Method of Morris screening was used to remove variables with little effect on the attributes. Analysis in ModelCenter evaluated the effect of 92 variables on dig accuracy and fuel consumption. After 3,720 model executions, five design variables (e.g. cylinder bore diameters) and four uncertain variables (e.g. soil cohesion) were optimized by varying the design variables under the influence of the uncertain variables. Using the actual model, an adaptive Kriging surrogate model was built to reduce the time needed to run optimizations. The Kriging model was adaptive because it checked its accuracy against the real model and updated itself as needed. Optimization with uncertainty then proceeded using a Latin Hypercube sampling method to reduce the number of evaluations needed to compute the objective function's expected value.
Benefit: 99% Less Time to Optimize Complex Systems
The MBE approach with ModelCenter provided a computationally feasible optimization methodology for complex, uncertain systems. For an LHS sample size of 10,000, the optimized expected utility was 0.71. Each optimization took about 2 hours to run compared to approximately a week without the adaptive Kriging model.
1 Conigliaro, R.A., Kerzhner, A.A., Paredis, C.J.J., Model-Based Optimization of a Hydraulic Backhoe using Multi-Attribute Utility Theory, SAE International Journal of Materials and Manufacturing, Oct. 2009, Vol. 2, No. 1, 298-309.