scholarly journals A model-independent tool for evolutionary constrained multi-objective optimization under uncertainty

Author(s):  
Jeremy T. White ◽  
Matthew J. Knowling ◽  
Michael N. Fienen ◽  
Adam Siade ◽  
Otis Rea ◽  
...  
Author(s):  
J. M. Hamel ◽  
S. Azarm

Optimization under uncertainty can be a difficult and computationally expensive problem driven by the need to consider the degrading effects of system variations. Sources of uncertainty that may be reducible in some fashion present a particular challenge because designers must determine how much uncertainty to accept in the final design. Many of the existing approaches for design under input uncertainty require potentially unavailable or unknown information about the uncertainty in a system’s input parameters; such as probability distributions, nominal values or uncertain intervals. These requirements may force designers into arbitrary or even erroneous assumptions about a system’s input uncertainty when attempting to estimate nominal values and/or uncertain intervals for example. These types of assumptions can be especially degrading during the early stages in a design process when limited system information is available. In an effort to address these challenges a new design approach is presented that can produce optimal solutions in the form of upper and lower bounds (which specify uncertain intervals) for all input parameters to a system that possess reducible uncertainty. These solutions provide minimal variation in system objectives for a maximum allowed level of input uncertainty in a multi-objective sense and furthermore guarantee as close to deterministic Pareto optimal performance as possible with respect to the uncertain parameters. The function calls required by this approach are dramatically reduced through the use of a kriging meta-model assisted multi-objective optimization technique performed in two stages. The capabilities of the approach are demonstrated through three example problems of varying complexity.


Author(s):  
Berkcan Kapusuzoglu ◽  
Paromita Nath ◽  
Matthew Sato ◽  
Sankaran Mahadevan ◽  
Paul Witherell

Abstract This work presents a data-driven methodology for multi-objective optimization under uncertainty of process parameters in the fused filament fabrication (FFF) process. The proposed approach optimizes the process parameters with the objectives of minimizing the geometric inaccuracy and maximizing the filament bond quality of the manufactured part. First, experiments are conducted to collect data pertaining to the part quality. Then, Bayesian neural network (BNN) models are constructed to predict the geometric inaccuracy and bond quality as functions of the process parameters. The BNN model captures the model uncertainty caused by the lack of knowledge about model parameters (neuron weights) and the input variability due to the intrinsic randomness in the input parameters. Using the stochastic predictions from these models, different robustness-based design optimization formulations are investigated, wherein process parameters such as nozzle temperature, nozzle speed, and layer thickness are optimized under uncertainty for different multi-objective scenarios. Epistemic uncertainty in the prediction model and the aleatory uncertainty in the input are considered in the optimization. Finally, Pareto surfaces are constructed to estimate the trade-offs between the objectives. Both the BNN models and the effectiveness of the proposed optimization methodology are validated using actual manufacturing of the parts.


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