Fuzzy Expected Value Analysis of an Industrial Grinding Process

• Fuzzy expected value model (FEVM) is adopted to carry out the uncertainty analysis.
• Determination of uncertain Pareto region based on risk appetite
• Novel approach to conduct parametric sensitivity
• Demonstration on a real life industrial case study

Uncertainty in parameters, which are assumed to be known and do not change their values during the course of deterministic optimization, can have a great impact on the outcome of an optimization study. Investigations on the development and application of optimization approaches that can accommodate such kind of uncertainty in parameters during the course of optimization are, therefore, necessitated. One of the methods to overcome such situations is to assume uncertain parameters as fuzzy variables, when distribution information for uncertain parameters are not available, and solve an equivalent deterministic formulation by transforming the original uncertain formulation. Expected value model (EVM) is one such method which converts the uncertain optimization formulation into a deterministic problem using expected values of the objective functions and constraints based on fuzzy credibility theory. In this work, an industrial grinding model has been adapted under the credibility theory based fuzzy framework to handle several uncertain parameters and shown how the presence of uncertainty leads to an operating zone of varied risk appetite of a decision maker by defining the entire frontier of the uncertain solution region. The deterministic multi-objective optimization model has been taken from the published work [1] and several modifications due to uncertainty in the parameters are carried out on this. The resultant deterministic equivalent of the multi-objective fuzzy uncertain optimization problem has been solved using Fuzzy Expected Nondominated Sorting Genetic Algorithms II (FENSGA-II). Unlike the two-stage stochastic programming (TSSP) approach, a very popular approach to handle uncertainty during optimization, the generic fuzzy approach does not give rise to the situation of unmanageable explosion in problem size with the increase in number of uncertain parameters.

“The Pareto optimal fronts for the industrial grinding process can be observed in the figure given below for different shapes of triangular fuzzy functions for the uncertain parameters. If the shape of the triangular fuzzy functions are scalene in nature and generated by allowing deviations 15% on the lower side and 5% on the higher side with respect to their nominal values, the Pareto front is observed to shift towards the downward direction with respect to the deterministic PO front obtained using the nominal values of the uncertain parameters (shown as “certain”). Similarly, if the widths of triangular fuzzy functions are 5% (lower side) and 15% (upper side) other way, Pareto front shifts towards upward direction and gives us the better throughput and mid-size fraction values”.Figure optionsDownload as PowerPoint slide