Multi-objective optimization of some process parameters of a lab-scale thickener using grey relational analysis

Identifying the influential priority of the factors governing PHB production by activated sludge with integration of uniform design and grey relational analysis

“…Therefore, the input four operating factors and the output variables were normalized to have the same order for the reduction of error. The following three equations were used for the normalization [23,26]:…”

“…Here, n value of 0.5 was taken for calculation because it is generally adopted in most studies [23]. Finally, the grey relational grade was determined as the average value of all grey relational coefficients, which represents the influential priority of a factor on the entire system.…”

“…It is capable of producing samples with high representation in the studied experimental domain and accommodating the largest possible number of levels for each factor [18], thus effective evaluation of multiple parameters can be achieved at limited number of experiments [20]. On the other hand, grey relational analysis is well known for its capability of finding out complicated interrelationships among multiple factors and variables at minimal data required [21][22][23]. In grey relational analysis, the influential degree of a compared series on the reference series is represented by the relative distance between them in an imaging grey space, thus prior assumption about the distribution type is not needed [24].…”

The influence of parameters variability on biomass selection for energy use

“…In these cases, no single best alternative exists [20]. Grey relational analysis classifies different input sequences by determining the grey relational grade (GRG) [21]. Higher GRG values indicate better alternatives.…”

Biomass Fuel and Combustion Conditions Selection in a Fixed Bed Combustor

“…Moreover, GRA enables the processing of variables with different attributes, scales, and units. Thus, this method is more versatile than other decision tools [17]. Another characteristic of GRA is the ability to work with variables that are optimized in opposite directions [18].…”