Model development and surface analysis of a bio-chemical process
Introduction
Soil contamination is a problem of national concern that is responsible for degradation of human health and environment [1]. The contamination has rapidly increased in last few decades as a result of waste and wastewater discharged from anthropogenic sources [2]. The methods such as the ion exchange, precipitation, reverse osmosis and evaporation (physio-chemical methods) can be applied for decontaminating however, these methods require a lot of resources and thus expensive to implement. However, phytoremediation, a technique involving bio-chemical mechanisms (adsorption, transport, accumulation and translocation; Fig. 1[3]) has gained wide acceptance in remediating the contaminants from the soil using vegetation.
It has advantage of being economical and also environment friendly. Phytoremediation works on principle of natural processes occurring in plant and therefore it is not dependent on any external resources and is easy and reasonably inexpensive to implement. For the phytoremediation on metal contaminated soils, the quantification of the relationship between the metal-tolerant plant species and chemical properties of soil is vital.
The use of spinach for phytoremediation of metal-contaminated soils has been reported in previous studies [4], [5], [6]. Experimentally it has been found that, the removal efficiency of heavy metals varies with the metal ion concentration and plant density. There is a risk in this method that, with this removal, there is a certain amount of accumulation of heavy metals in root as well as shoot of plants [7], [8]. Any relationship between removal efficiency and accumulation in roots, shoots along with plant density and concentration will be of prime interest in evaluating the risk and design of bio-remediation measures for contaminated soils [8]. In this context, the quantification of the relationships based on the statistical response surface methodology (RSM) can be applied. However, the mechanism of the formulation of models using RSM methodology is based on the prior assumptions such as the form of the model, residual and data correlation assumptions, etc. These models are built on the training data and not tested for the testing data beyond the input range in a realistic condition. Therefore, this induces the ambiguity in prediction ability of the model on the testing samples. Alternatively, the artificial intelligence (AI) approach of genetic programming (GP) in formulating the decision support models can be applied. This AI approach works on the optimization and genetic algorithm principle and its mechanism supports to evolve the mathematical models [9], [10], [11], [12], [13] explicitly from the given data. The decision support model can also suggest the precise selection of shoot and root properties for the maximizing the lead removal efficiency. Past quantitative studies [14], [15], [16] involving the applications of GP in modelling of systems have reported that the performance of the GP models depends the architect (objective function, parameter settings and complexity measure) selected.
Therefore, the present work will explore the ability of the artificial intelligence approach of genetic programming (GP) based on the two new architects in formulating the decision support models for % removal efficiency of lead. The two new architects of GP are defined by the two new objective functions. One objective function to be investigated is the structural risk minimization principle (SRM) while the other is Akaike information criterion (AIC). The complexity measures based on the minimum order of the polynomial and the number of nodes will be used in the penalty term of these two objective functions. The procedure involving the experimentation planning and the modelling procedure of the % removal efficiency with respect to the four inputs is shown in Fig. 2. The % removal efficiency of lead is summarized statistically from laboratory experiments [8]. The rest of the procedure involves the settings of the architects of GP, models formulation, models analysis and validation and the surface analysis to find any physical interpretation from it.
Section snippets
Phytoremediation chemical process for measuring % removal efficiency of lead
The complete set-up including the experimental procedure for evaluating % removal efficiency of lead and other plant properties are kept the same as those mentioned in the work by [8]. Soil selected in their study was mainly sand (59%) and considerable clay content (11%). It has organic content of 0.72%. Spinach (Spinacia oleracea) was selected as plant for conducting phytoremediation in contaminated soil with lead. Spinach is native to central and southwestern Asia and can grow to a height of
Artificial intelligence approach with polynomial and number of nodes complexity measure in objective functions SRM and AIC respectively
In this work, the two architects of artificial intelligence approach of genetic programming (GP) [21] are proposed and applied on the data shown in Table 2. The mechanism of the two architects is same as that of the GP except the difference in use of the objective functions. The implementation of GP (Fig. 4) involves the settings of functional and terminal, that are essentially responsible for evolving the functional expressions/explicit/decision support models based on the data [21]. The
Performance analysis of lead removal efficiency models formed from both the versions of GP
In this section, the performance analysis for both the versions of the GP based lead removal efficiency models is done based on the actual data (Table 2) using the error metrics given in Appendix A (Eqs. (A3) and (A4)).
Table 4 shows the three performance measures of the both the versions of the GP based lead removal efficiency models. It is clear that the models formed from the GP using SRM objective function (order of polynomial as complexity) in its architect have performed better on both the
2-D and 3-D surface analysis on the GP based lead removal efficiency model
This section implements the surface analysis based on the parametric and sensitivity procedure of the models formulated from GP architect using SRM function. The details of the implementation of the procedure are kept the same as discussed in Panda et al. [15]. 2-D plots (Fig. 6) illustrates that the lead removal efficiency increases linearly with an increase in values for the number of planted spinach, root accumulation and sampling time. The highest non-linear variation and interaction
Conclusions
This work highlights the motivation behind investigating the role of the phytoremediation process in removal of lead contaminant from the soil. In this context, a comprehensive study based on phytoremediation experiments and numerical modelling is conducted. The experimental work evaluates the lead removal efficiency from the soil based on the inputs such as the number of planted spinach, the sampling time (days), the shoot and root accumulation. Further, the numerical modelling is performed by
Acknowledgement
This study was supported by Shantou University Scientific Research Funded Project (Grant No. NTF 16002). The authors also gratefully acknowledge the financial supports from the Macau Science and Technology Development Fund (FDCT) (Codes: 125/2014/A3 and 011/2013/A1), the National Natural Science Foundation of China (Grant no. 51508585) and the University of Macau Research Fund (MYRG2015-00112-FST and MYRG2014-00175-FST).
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