Concurrent multiresponse multifactorial screening of an electrodialysis process of polluted wastewater using robust non-linear Taguchi profiling
Introduction
Water is the ultimate commodity on this planet since life without water cannot exist. It is oxymoron that while water covers 70% of the earth’s surface, a scarce portion of less than 1% is only available for human consumption. This minimal amount is forecasted not to be sustainable to quench the household and farming requirements for a rapidly growing human population in the near future [1,2]. Population migration trends away from arid areas would exacerbate the problem as the planet eco-system warms-up. However, sprouting water-treatment technologies seem to promise opportunities for broader accessibility to potable water [3,4]. Brackish and saline sea water sources are considered for immediate exploitation but wastewater supplies are also not to be overlooked. Desalination and water recycling are at the forefront of treatment options for both purposes: 1) to store drinkable water and 2) to irrigate farms [5,6]. Roughly three quarters of the distributed water is directed to farming. It is foreseeable then that large-scale irrigation operations should draw more engineering attention. There are quite a few engineering options that might be attuned to supply enough water to agricultural land [7]. Highest priority projects to water accessibility are those that align toward reaching ‘Goal 6’ of the United Nations Sustainable Development [48] congruent to disadvantaged human ecosystems. Automatically, in an upward chain-reaction fashion, accomplishing ‘Goal 6’ directly aids in attaining ‘Goal 2’ (zero hunger) [49] by also offering opportunities to cultivate arid land and consequently inching closer to ‘Goal 1’ (Poverty termination) [50]. Engineering solutions based on membrane separation technology – forward or reverse osmosis – seem to be more frequent but their high cost of ownership has not established them as a universal cure-all [8]. In particular, when the feed source is wastewater, issues of biofouling and chemical element adjustment need to be addressed, making reverse osmosis rather an expensive alternative and suitable only for high added-value cultivations. Recently, electrodialysis has been studied as a potentially useful option to treat drainage wastewater and other polluted water bodies for large-scale planting [7]. Developing farming conditions in semi-arid or arid areas around the planet is indispensable. Electrodialysis could aid in this direction by toning down sodium content while balancing soil minerals - calcium, potassium and magnesium - to favorable concentrations for plant growth. For arable crops, readily available soil potassium correlates positively with yield [9]. Moreover, electrodialysis (ED) of wastewater could control outflow water potassium content such that to facilitate the compensation of leached sandy soils, especially when such soils are comprised of little clay and organic matter. A recent study by Abou-Shady [7] brought up the idea of upscaling the ED-tuning of wastewater reserves to right-balancing irrigation water constituents. It was demonstrated how to manipulate four specific ED-process factors in order to promote optimal salinity in complex futuristic large-scale irrigation projects. At the core of that research stands out a key recommendation for the effective use of water qualimetrics (‘aquametrics’) [10] that utilize Taguchi-type screening techniques [11].
Taguchi-type design of experiments (DOE) methods is useful for quick-and-economical, environmentally-friendly, evidence-based screening as well as optimization studies [[12], [13], [14]]. In its backbone, it is the ‘lean-and-agile’ philosophy that has been applied successfully in designing and improving intricate manufacturing processes. It is ‘lean’ because minimizes wasted materials, energy, equipment-availability and man-hours that are required for large-scale industrial trials. It is ‘agile’ because it adapts quickly to the operational demands where Taguchi-methods need to be deployed, thus exploiting any opportunity for rapid discovery. Hidden ‘lean-and-agile’ benefits are also to be reaped indirectly by halving the total experimental effort and duration of the two typical and sequential trial phases; factor screening and parameter design are to be conducted in a single concurrent step [11]. Screening experiments are characterization experiments that require two distinct sequential steps: 1) factor profiling and 2) identification of the strong factors. In the profiling step, the screening dataset is processed in order to quantify - in statistical terms - all factorial influences against one or more characteristics. Once the treatment effects have been quantified, then, the strong influences are selected based on a statistical rule. A statistical processor is used to determine those effects that are greater than a critical value; the one-sided cut-off value corresponds to a preset significance level, α. The identification process is an optimization step because it involves a uni-directional search to locate and select out the strong effect(s), i.e. those effects that perform below a minimum statistical significance constraint. Identification follows the general optimization process that given a set A of k effects ai (1 ≤ i ≤ k) ∀ ai ∈ℜ, and a function ƒ: A→p with statistical significance pi ∈ p ∀ pi ∈ℜ, we seek a subset xo ⊆ A such that f(x0) ≤ f(x) for all x ∈ A subject to the constraint pi < α. Thus, the screening phase leads to a reduction of the initial group of factors. Strong effects are considered for the next phase, which is the parameter optimization. Screening may reduce significantly the amount of experimental work that is to be forwarded to the parameter design phase. But chemical screening is a cost driver that intelligent discovery systems seek to minimize by emphasizing rapid cycle times [15]. Parameter design refines the strong factors that precipitated from the screening phase such that to optimally predict one or more product or process response(s) [16]. Obviously, this tactic of ‘two-in-one’ in Taguchi’s strategy shortens the overall optimization study cycle while lowering materials and energy consumption [12]. There are two economic gains then, one from curtailing trial-related costs and another from making an optimal product that generates less waste while completed in reduced cycle times.
Deeper environmental awareness is to be envisaged in chemical processes. Taguchi methods have been implemented to optimize wastewater treatment with reverse osmosis and to recover heavy metals for quite some time [17,18]. They have been employed to investigate even difficult wastewater treatment cases where there was a need for improving the conditions of a coagulation-flocculation process [19]. Ramping-up processing efficiencies with characterized flocs may also be achieved with Taguchi DOE techniques targeting harsh agro-industrial wastewater treatments [20]. Desalination filtering operations are amenable to Taguchi-type screening and optimization when using modern carbon nanotube membranes [21]. When complex datasets are collected to optimize a forward osmosis process, a combination of Taguchi-type tools and neural networks have proved to be effective [22]. The Taguchi toolbox has been applied successfully in upscaled Fenton-SBR industrial operations that produced wastewater from bamboo treatment [23]. In chemometrics, the classical Taguchi method has been entrusted in optimizing measurement accuracy of UPLC isocyanate [24], optimal mixture settings for enhancing concrete properties [25], Diazinon cloud point extraction [26], and optimized multianalyte determination with biosensors [27].
Technically, Taguchi’s DOE methodology in aquametrics is achieved on two ends. At the frontend, Taguchi methods demand small but structured trials. For this to happen, the DOE framework needs to obey a few predetermined factorial recipes. The experimental recipes rely on the combinatorial rules of fractional factorial designs (FFDs) [28]. The particular Taguchi-type FFD plans belong to the family of orthogonal arrays (OAs) [11]. At the backend, Taguchi methods institute two utilities: 1) the use of the signal-to-noise ratio (SNR) concept in order to compress the collected dataset streaks and 2) the standard deployment of the analysis of variance (ANOVA) to relay statistical significance to the strength of the examined effects. Maximum utilization of the frontend capabilities occurs when a selected OA trial-plan is saturated with tested controlling factors [28]. Saturation locks the requirement for minimum number of experimental runs with respect to the number of the investigated effects. Saturation maximizes the number of effects that are allowed to deliver information given a data-collection OA-plan. To illustrate the importance and ramifications of these aquametrics concepts in screening and optimizing wastewater treatment, in this work, we will take up the interesting four-factor three-response ED-process optimization paradigm of Abou-Shady [7]. We contemplate that it is a unique case as we will explain along because of the nature and the relationships among the selected water characteristics. We will not work out one ‘response-at-a-time’ as it is common in most wastewater treatment studies that employed Taguchi optimization. Instead, it might be useful to generalize the feasibility of the study to a more pragmatic rationale by attempting a concurrent multi-response optimization. The suggested frontend design (L9(34) Taguchi-type OA) in Abou-Shady’s experiments was saturated [7]. It was selected such that to simultaneously screen, optimize and track down the potential influence of non-linearity for each of the tested effects. At saturation point, the constraint for the minimum number of required experiments is n=(2•m)+1; n is the number of trials and m is the number of the examined effects. Furthermore, the experimental design by Abou-Shady [7] featured still another property conducive to rapid, economical and lean-and-green data-generation; experimental recipes were not replicated. By undertaking an unreplicated [29] and saturated OA-scheme, the collected data was ensured to be delivered in low cost, fast turnaround time and minimum material/energy losses [30]. Unfortunately, when designing processes or products by exploiting synchronously the profitable conditions of saturation and unreplication, frontend and backend synchronicity is bound to break down in Taguchi methods. This is because the simultaneous presence of the two conditions eliminates the chance to obtain an estimate for the residual error in ANOVA, since no degrees of freedom for the error are left over [31]. Hence, no statistical inference is possible with ordinary means and no objective sizing of the effects is feasible in such an occurrence. Generally speaking, the “unreplication” condition is inherent to Taguchi methods. The prescribed SNR transformation step will always convert even replicated data to an “unreplicated response” vector form [11,32,33]. Undisputedly, it was recognized that the analysis of the unreplicated factorial experiments was instrumental in discovering in short time those effects that were to play a role behind an intricate landscape in industrial operations [51]. The accompanying comparative study of as many as twenty-four methods attested to such need while concluding to no single ‘all-purpose’ front-runner approach [51]. It definitely encouraged the development of new techniques. Recently, an important study tested leading unreplicated factorial solvers - part of modules of several mainstream software packages [52]; it indicated that benchmarked predictions varied significantly among packages. This justifies the impetus for proposing new unreplicated factorial solvers with robust capabilities. It is a main motivation point for our study. It is the “saturation” condition that may be construed as optional but encouraged from an engineering perspective due to optimal data utilization. As perplexing as it sounds, statistical profiling of an unreplicated-saturated OA-dataset may still be accomplished with specialized handling and data manipulation. Irrespective of the setbacks that may be lurking in interpreting regular Taguchi-type optimization studies [34,35], successful wastewater research has been published as discussed previously, and clearly attesting to that this subject is in demand. One of the purposes of this work is to explore complications on the way to achieving optimal ED-process performance through multi-response multi-factorial non-linear screening/optimization aquametrics [[36], [37], [38]]. Hopefully, some aspects that will be discussed may lay ground for robust and agile ED-process predictions [39,40]. We show how to upgrade the Taguchi analysis for unreplicated-saturated OA ED-trials such that to transcend from the subjective limitations of descriptive statistics to meaningful inferences.
The motivation for the selection of the exploratory desert development project [7] to be re-examined in this work becomes more transparent now. Its principal outlook aligns in accord toward to the general ‘Goal 6’ of the United Nations Sustainable Development [48]. The study by Abou-Shady [7] is unique because it seeks to optimize three different characteristics that all pertain to the behavior of suspended sodium in the feed wastewater. The concurrent screening/optimization of sodium content in three different chemometrical landscapes has not been undertaken before. One characteristic is the percentage of removed sodium cations (ReNa). It characterizes the electrodialysis process itself in a given time interval. It is dependent on the initial sodium cation concentration. It is a process quality index that tracks ED cell performance. The larger the value of the percentage of removed sodium the higher the effectiveness of the ED unit. Being a percentage-based response requires non-conventional handling. Data types in percentage form are distinct for their inherent poor additivity properties in practical situations [41]. This is because intermediate arithmetical operations with percentages are not permitted to exceed the two realistic bounds (0% and 100%). In this specific situation, the SNR transformation [42] is not an appropriate data compressor to be used as in the small and dense dataset of Abou-Shady [7]. Instead, the omega (Ω) conversion method is usually recommended which replaces the quadratic loss in the SNR with the odds ratio in Ω [41]. The formula for Ω then becomes:
Nevertheless, it is known that the omega function is conditionally applicable. This is because the Ω value tends to infinity if measurements approach either of the two bounds. Another noteworthy issue is that for classical SNR transformations (Taguchi-type) to be meaningful, the original (raw) dataset must: 1) be in replicated form and 2) obey normality. For each executed experimental OA-recipe, at least two replicates are necessary to recover a signal (average estimation) and a noise (variability estimation). These two critical conditions are absent in the experimental design of Abou-Shady [7]. It is a main motivation of this work to show how one might circumvent this quandary by proposing an alternative approach which relies on distribution-free statistics. The proposed approach offers simplicity, transparency, robustness and agility in the optimization cycle. Thus, the aim is to aid in deciphering complex, small and dense DOE datasets in ED-optimization studies. In turn, analysis results are pivotal to reliable decision-making for large-scale chemical operations.
The second characteristic is the sodium adsorption ratio (SAR). SAR is a water quality trait that quantifies the water suitability which is intended for crop irrigation. Even though it is a single index, SAR delivers complex and crucial information. SAR monitors the soil flocculation status by measuring the balancing act of the soil conditioners. Both, flocculation inhibitors (sodium cations) and promoters (calcium and magnesium ions) tweak soil permeability and hence the water infiltration rate. Furthermore, SAR tracks the aqueous colloid suspension stability status. It is also a standard reliability measure since it diagnoses the sodicity hazard for a farmland. Irrigation water quality is optimal when SAR is minimized and there is a critical value for flocculation.SAR is a ratio quantity. Thus, the discussion regarding the appropriateness of Ω over SNR in ReNa response data above is also pertinent here. It is remarked that SAR is a product (outflow water) characteristic as opposed to ReNa. Also, SAR and ReNa follow opposite response directions in an optimization exercise; the former is minimized and the latter maximized.
The salinity status of the electrodialyzed outflow water may also be expanded to account for all four key (monovalent and divalent) cations. The competing potassium content is thus added in determining the sodium ratio (Na+ ratio):
The Na+ ratio (NaRa) is also a percentage-based quantity that is sought to be minimized just as the SAR. The previous arguments about recommending the Ω-conversion over the SNR-transformation are maintained for this index, too. Similar to the SAR applicability, NaRa reflects water product quality. In the original optimization scheme [7], the ‘smaller-is-better’ expression for the Taguchi-defined SNR data conversion was used for all three examined characteristics (ReNa, SAR, NaRa):
However, ReNa is a ‘larger-is-better’ characteristic and thus the proper Taguchi-defined expression for the SNR data conversion would have been instead:
This article is structured as follows. A methodology is proposed to formulate the concurrent multi-response screening/optimization aquametrics for a wastewater ED-process. The methodology also extends the potential for “two-in-one” combo-solution which is inspired by Taguchi’s main DOE planning strategy but which is restricted to a single response case. This means that it is pursued besides a concurrent multi-response multi-factorial screening-and-optimization solution, the possibility of the influence of non-linearity in the examined effects. On this endeavor, we directly deal with conditions of data “messiness” [43] that Taguchi methods are not tuned to handle. Abou-Shady’s [7] experimental work demonstrated the natural emergence of messiness in the Taguchi-DOE ED-trials. We show the implications of messiness in the Results section where we use modern data fusion techniques for unreplicated-saturated Taguchi-type OA datasets. Messiness brings out the realistic demands in predictions where the phenomena may not really be canned in some parametric modelling [44]. Therefore, we demonstrate the robust, lean and agile screening prediction of ED performance based on ReNA, SAR and NaRa indicators against the four relevant controlling factors [45]. The justification for this new proposal, when compared to the other available published techniques on the subject of the unreplicated factorial analysis [51], relies on accumulating several tangible traits that are not found in the previous approaches. Key features are: the new technique converts constant-free (non-subjectively) and distribution-free (robustly) unreplicated dataset predictions even at the limiting condition of saturation. The former feature is an advantage over the Lenth test [53] and the latter over the half-normal test [47]; they are the two premier tests with great representation in most commercial statistical software packages. But the primary advantage of the new method is that it also delivers distribution-free statistical significance for multi-response unreplicated-saturated OA-datasets. This is in contrast to the leading alternative method, the desirability analysis [54], which instead provides a score estimation in lieu of a significance measure, which would be based on a statistical reference law. Furthermore, in comparison to the desirability analysis, the new method eliminates the (manual) trial-and-error search – a subjective step – which the desirability optimizer depends upon to generate a solution. This would mean discovering an appropriate set of weights to parametrize each of the partaking response functions before succeeding to compute their composite desirability score.
The new method does not involve regression coefficients, hence it is computationally simpler. Therefore, it produces no residuals. Moreover, residuals are extremely sensitive to outliers. If appearing in small datasets, outliers become particularly risky. Still, residual analysis requires inspecting for independence of errors (autocorrelation effect) which is a non-relative condition in the proposed method. Since regression methods implicate mean estimators during the data fitting process, the characteristic 0% breakdown point of the method is ominously present. On the other hand, our method uses rank-sums (median estimator), which protects the data reduction process to a breakdown point of 50% [55]; it provides the maximum possible protection as a clear technique advantage. Summarizing, our technique is simpler and more robust from other alternative profilers/optimizers; this might be a desirable amelioration according to the Occam’s Razor principle.
Section snippets
A brief description of the wastewater electrodialysis experiments
Abou-Shady’s design selection is a saturated (three-level) non-linear Taguchi-type (L9(34)) orthogonal array [7]. The unreplicated-saturated L9(34) OA has been featured as a preferred trial planner in non-linear screening/optimization in diverse areas of studies that involve complex chemometrics [[56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70]]. Parenthetically, the methodology is construed to be extended for non-linear effects also tested in four or
Preliminary data analysis
The three water characteristics generate parallel and probably overlapping information in tracking the wastewater treatment performance. Therefore, the ED-process efficiency (ReNa) and the two water quality indices (SAR and NaRa) should be tested for possible correlations between them. If they found to significantly correlate with each other, then, some of them should be eliminated from further modelling consideration. They would merely provide redundant information. The three possible
Discussion
The concurrent optimization of the wastewater ED-process may be assessed by reviewing the individual behaviors against the respective (ordinary) main effects plots (Part D - Supplementary Material). Briefly, the DF-effect plays the predominant role in all three screenings. Since NaRa and SAR are ought to be both minimized, we see that this could be conveniently achieved because their behavior appears to be linear. The suggested optimal dilute flow is located in the lower endpoint, at the value
Conclusions
Managing to extract water for household and irrigation needs from polluted wastewater pools is a major modern environmental challenge. Special engineering methods are needed to be adapted each time to the particular kind of local water demands in order to ensure adequate water supply. One of the most promising chemical processes to assist such plans is electrodialysis. For optimum feed recovery, sophisticated optimization methodologies are necessitated to deal with the complexity of the
CRediT authorship contribution statement
George J. Besseris: Conceptualization, Methodology, Formal analysis, Data curation, Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We thank the Editor in Chief and the three reviewers for their critical comments that led to the improvement of this work.
References (74)
Recycling of polluted wastewater for agriculture purpose using electrodialysis: perspective for large scale application
Chem. Eng. J.
(2017)- et al.
Cost of speed: a practical approach to evaluate a screening method from a Bayesian perspective
Chemometr. Intell. Lab. Syst.
(2016) - et al.
Lowering manufacturing cost of material by formulating it through statistical modeling and design
Chemometr. Intell. Lab. Syst.
(1995) - et al.
Heavy metals recovery from industrial wastewater using Taguchi method
Chem. Eng. J.
(2007) - et al.
Employing the Taguchi method to obtain the optimum conditions of coagulation-flocculation process in tannery wastewater treatment
Chem. Eng. J.
(2010) - et al.
Coagulation-flocculation treatment of high-strength agro-industrial wastewater using natural Cassia obtusifolia seed gum: treatment efficiencies and flocs characterization
Chem. Eng. J.
(2014) - et al.
Salty water desalination using carbon nanotubes membrane
Chem. Eng. J.
(2011) - et al.
Determination of optimum condition in forward osmosis using a combined Taguchi-neural approach
Chem. Eng. Res. Des.
(2016) - et al.
Combined Fenton-SBR process for bamboo industry wastewater treatment
Chem. Eng. J.
(2013) - et al.
A TOPSIS-based Taguchi optimization to determine optimal mixture proportions of the high strength self-compacting concrete
Chemometr. Intell. Lab. Syst.
(2013)