## 5 Conclusions  
As water resources are rendered scarce, ultrafiltration (UF) and nanofiltration (NF) membranes facilitate the development of sustainable separation solutions. Moreover,  
Figure 16: Databionic swarm clustering solution (k = 3) for individual factorial vectors to evaluate cluster separability (within a factor) using mean silhouette measure estimates for the reduced-schedule nanofiltration process characteristics (IBM SPSS v.29): (**A**) membrane type, (**B**) cross-flow velocity, (**C**) temperature and (**D**) transmembrane pressure.  
Figure 17: Databionic swarm clustering solution (k = 2) to evaluate cluster separability using mean silhouette estimates for the reduced-schedule nanofiltration process characteristics (IBM SPSS v.29).  
there are lean-and-green incentives for single-stage filtration processes in treating urban wastewater. The screening and optimization of single-stage UF-/NF-membrane wastewater processes require the tailored design of the operations by taking in account several aspects that range from customization of the treatment unit to the condition of the incoming wastewater volumes as well as the functionality of the selected membranes in specific operating conditions, namely the mass transfer properties and solute rejection. In realistic circumstances, process customization success is subject to a holistic comprehension of the separation dynamics that involve selected structural membrane properties and their physicochemical interactions with the wastewater medium. Taguchi-type methods may be employed for quick and economical studies that intend to improve the filtration performance for a single process characteristic. However, to screen and optimize physicochemical separation processes, Taguchi-type orthogonal array sampling recipes are still useful in generating small multi-characteristic non-linear datasets, even when the collected responses are described by different measurement scales and data types. In spite of the availability of various statistical multivariate techniques to handle the multifactorial multi-response problem, there is a great interest for unsupervised algorithmic solvers.  
The approach that was tested in this work attempted to firstly cluster the gathered multi-response dataset and then try to directly match the stochastic signature of the clustered members to the factorial vector sequences in the orthogonal array in a naive backtracking exercise. The technique was applied on recently published multi-characteristic multifactorial data for a single-stage urban wastewater operation that involved as many as seven UF-membrane process characteristics and six NF-membrane process characteristics. The investigated controlling factors were the (1) membrane type, (2) cross-flow velocity, (3) temperature and (4) transmembrane pressure. The data analysis part was inherently demanding because the generated dataset was constructed based on the restrictive Taguchi-type L\({}_{9}\)(3\({}^{4}\)) OA; the factorial screening, effect curvatures and parameter optimization were expected to be explained by only nine observations per process characteristic. The Databionic swarm intelligence classifier was implemented to complete the cluster identification task. Minimization of the Davies-Bouldin similarity measure revealed the more influential controlling factors by contrasting the appropriateness of the configuration of the cluster identification vector to the factorial-setting vector pattern. It was found that the membrane type in both filtration setups was the controlling factor that predominantly influenced their respective groups of the UF-/NF-membrane process characteristics. Future work could reconcile the bionic solver predictions of the two processes by making use of unsupervised stochastic comparison treatments.