Optimization Under Uncertainty

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Many real-world problems require decision-making in the presence of uncertainty. Design optimization methods need to properly account for both aleatory and epistemic uncertainty sources. Our research considers both types of uncertainty within optimization and investigates the following approaches:

  • Robust design optimization (RDO)
  • Reliability-based design optimization (RBDO)
  • Optimization with multi-fidelity models
  • Robust design optimization (RDO)
    • Both the mean and variance of the optimization objective are minimized
    • Constraints are satisfied within specified bounds that account for uncertainty
    • Pareto fronts are constructed to represent the trade-offs between conflicting objectives
    • Applications:
    • Objective function examples: maximize bond quality, maximize part geometry accuracy, minimize part printing time

     

  • Reliability-based design optimization (RBDO)
    • Objective function is optimized such that the reliability with respect to desired performance criterion is above an acceptable threshold
    • Constraints are probabilistic and require calculation of failure probability or reliability index
    • Application: Flight vehicle mission and maneuver optimization
    • Objective function example: minimize mean stress on critical rotorcraft components

  • Reliability-based design optimization (RBDO)
    • Aircraft re-routing optimization under uncertainty
    • Uncertainty in incoming aircraft state (location, heading, speed, etc.), space availability in neighboring airports, radar performance, and communication delays.
    • Support vector regression model is used for constructing the distribution of the key system failure metric.
    • Reliability-based constraint used to ensure that re-routed aircraft land before running out of fuel.

  • Hybrid optimization approach
    • Digital twin approach for damage growth minimization / resilient system operations
    • Application: Damage growth minimization in mechanical components while successfully completing assigned task(s)
    • Generation of an operation-to-load map that defines loading patterns (families) for various operational regimes
    • Parametrization of loading regimes and classification of parameters that define the loading patterns given an operational regime
    • Hybrid approach that combines RDO with RBDO for damage growth minimization under diagnosis and prognosis uncertainty

  • Sensor Placement Optimization with Multi-Fidelity Models
    • Fuses information from models of different fidelities
      • High fidelity model - higher accuracy, computationally expensive
      • Low fidelity model - lower accuracy, computationally cheaper
    • Consider additive, multiplicative, and input correction factors to improve low-fidelity model using high-fidelity model data
    • Optimize collection of high-fidelity model data with the objective of maximizing the information gain (measured using Kullback Leibler divergence)
    • Multi-fidelity model trained with optimal high-fidelity simulations is used for further analysis
    • Application: Sensor placement optimization on rigid panel geometries
    • Objective function examples: Optimize high-fidelity model runs and optimize sensor locations to maximize the information gain regarding the parameters of the multi-fidelity model and to minimize the error between the multi-fidelity model prediction and the experimental observation

Funding

       

Current People

Publications

  1. KapusuzogluB., Sato M., Mahadevan S.,WitherellP., “Process Optimization under Uncertainty for Improving the Bond Quality of Polymer Filaments in Fused Filament Fabrication”, Journal of Manufacturing Science and Engineering, 2020 Aug 18:1-46
  2. Nath, P., Olson, J. D., Mahadevan, S., & Lee, Y.T.T., “Optimization of fused filament fabrication process parameters under uncertainty to maximize part geometry accuracy”,Additive Manufacturing, Vol. 35, 2020.
  3. Zhang, X. and Mahadevan, S., 2017.Aircraft re-routing optimization and performance assessment under uncertainty.Decision Support Systems,96, pp.67-82.
  4. Sisson, W., Mahadevan, S. andSmarslok, B.P., 2020.Optimization of Information Gain in Multi-Fidelity High-Speed Pressure Predictions. InAIAAScitech2020 Forum(p. 0676).
  5. Karve, P. M., Guo, Y.,Kapusuzoglu, B., Mahadevan, S., & Haile, M. A., "Digital twin approach for damage-tolerant mission planning under uncertainty," Engineering Fracture Mechanics, Vol. 225, 2020.