Datacentric Similarity Matching of Emergent Stigmergic Clustering to Fractional Factorial Vectoring: A Case for Leaner-and-Greener Wastewater Recycling

Water scarcity is a challenging global risk. Urban wastewater treatment technologies, which utilize processes based on single-stage ultrafiltration (UF) or nanofiltration (NF), have the potential to offer lean-and-green cost-effective solutions. Robustifying the effectiveness of water treatment is a complex multidimensional characteristic problem. In this study, a non-linear Taguchi-type orthogonal-array (OA) sampler is enriched with an emergent stigmergic clustering procedure to conduct the screening/optimization of multiple UF/NF aquametric performance metrics. The stochastic solver employs the Databionic swarm intelligence routine to classify the resulting multi-response dataset. Next, a cluster separation measure, the Davies–Bouldin index, is used to evaluate input and output relationships. The self-organized bionic-classifier data-partition appropriateness is matched for signatures between the emergent stigmergic clustering memberships and the OA factorial vector sequences. To illustrate the proposed methodology, recently-published multi-response multifactorial L9(34) OA-planned experiments from two interesting UF-/NF-membrane processes are examined. In the study, seven UF-membrane process characteristics and six NF-membrane process characteristics are tested (1) in relationship to four controlling factors and (2) to synchronously evaluate individual factorial curvatures. The results are compared with other ordinary clustering methods and their performances are discussed. The unsupervised robust bionic prediction reveals that the permeate flux influences both the UF-/NF-membrane process performances. For the UF process and a three-cluster model, the Davies–Bouldin index was minimized at values of 1.89 and 1.27 for the centroid and medoid centrotypes, respectively. For the NF process and a two-cluster model, the Davies–Bouldin index was minimized for both centrotypes at values close to 0.4, which was fairly close to the self-validation value. The advantage of this proposed data-centric engineering scheme relies on its emergent and self-organized clustering capability, which retraces its appropriateness to the fractional factorial rigid structure and, hence, it may become useful for screening and optimizing small-data wastewater operating conditions.