**Table 1.**

*Overview of neural networks applying to sludge bed reactor modeling.*

### **3.2 Neural network modeling**

Although a anaerobic digestion model can be applied, model calibration is difficult and laborious, while errors between model results and measured results still cannot be ignored [26, 27]. The nonlinear regression method shows an empirical relationship between effluent chemical oxygen demand (COD) and operation parameters such as organic load and hydraulic retention time (HRT) [28]. This empirical relation can be treated as a weak artificial neural network (ANN). ANN can effectively model nonlinear systems such as bioreactors for wastewater treatment. ANN is a very powerful computational technique for modeling complex nonlinear relationships [29].

There are a few types of ANNs. **Table 1** shows that the most popular type for granular sludge bed modeling is back propagation (BP). The main difference between various types of ANNs is the network structure and the method for determining the weights and functions for inputs and neurons [29]. **Figure 3** shows the schematic structure of a BP model. In the BP model structure, there is an input layer that is applied for inputting measured data for model training (calibration). An output layer is also required for model results. The selected reactor operation parameters for the input layer and output layer are case-specific. Generally, influent COD and effluent COD are usually applied in an input layer and an output layer to model a wastewater treatment reactor, respectively; pH is not always included. **Table 1** shows the selected parameters for the two layers. In addition, a few layers or a hidden layer is applied to bridge the input layer and output layer. The number of hidden layers in an ANN model is usually determined automatically by a trial and error method, while a single hidden layer network is commonly sufficient for most of the problems [29]. Therefore, three layers are generally applied (**Table 1**). In the structure of an ANN, each layer consists of a few neurons that are shown as circles in **Figure 3**. The connections between neurons in each two nearby layers are usually determined while training the system [29]. The modeled results in the output layer are different from measured data, and the weights are recalculated until the model results that fit the measured results.

**Table 1** shows that BP has been effectively applied to model granular sludgebased reactors. Although these reactors treat different kinds of wastewater, the model results can accurately fit the measured results. However, while reactors are treating the same kind of wastewater, model inputs and output can vary significantly [29, 30, 32]. As a result, different ANN models can be applied to UASB reactors to treat the same kind of wastewater [36–38].

**77**

*Approaches for Modeling Anaerobic Granule-Based Reactors*

able, which challenges the implementation of ADM1 [30].

A bioparticle model can explain biokinetics in a sludge granule. Although a bioparticle model can theoretically be applied for reactor modeling, ANN and models integrating reactor hydrodynamics and ADM1 are much more suitable.

based on a few assumptions. However, neither the layered structure nor the cluster structure of a single granule can model complex substrate degradation in a single granule. The IBM model successfully modeled VFA degradation in a granule and shows a clustered structure. The IBM model is based on accurate relevant anaerobic kinetics and can hopefully model complex substrate degradation in a

The influent COD should be nicely characterized when applying the ADM1 for reactor modeling. The ADM1 requires a detailed characterization of influent organic matter. Nevertheless, such a detailed characterization is generally very

Furthermore, there are 86 parameters in the ADM1. While nonsensitive parameter values can be adopted from the literature, sensitive parameters—which vary significantly—must be calibrated, which is extremely time-consuming and laborious [27]. In addition, the mass of microbial species in bioreactors are not measur-

Calibrating ANN models is easier than ADM1. When the measured variables begin to show differences in the response of ANN models, the model can be retrained using the newer data employed for cross-checking [27]. Numerous applications of ANNs have been successfully utilized in wastewater treatment modeling [38–40]. This is because of the reliable and robust characteristics of ANNs in capturing the nonlinear relationships between variables (multi-input and output)

The other benefit of applying an ANN model for reactor modeling is that an ANN model does not need well-established biokinetics. Currently, the production of extracellular polymeric substances (EPS) is not well understood—a modified ADM1 still cannot effectively model the production of EPS [41]. Therefore, the ANN can be hopefully applied to model the EPS production in an anaerobic sludge bed to provide better effluent quality modeling. Nevertheless, although an ANN model is convenient and reliable in reactor modeling, an applied ANN model cannot explain reactor operation failure because it always treats a bioreac-

ANNs are better and more convenient tools for reactor modeling than the integration of hydrodynamics and ADM1. Nevertheless, a calibrated ADM1 can provide more details regarding reactor operation. A calibrated ADM1 can nicely control reactor operation. An algorithm could be developed for ADM1 calibration considering the difficulty in manual ADM1 calibration and efficient calibration of ANN. These have been successfully achieved [42]. This makes applying ADM1 much easier because parameter calibration is not as difficult as it used to be.

A bioparticle model is beneficial for providing insights into reactions in the inner space of a granule. Anaerobic ammonia oxidation processes are a simple process and have been modeled in an ANAMMOX granule. However, when complex substrates are involved, a model including relevant bioprocesses in a single granule

has not been available. This calls for further research in this field.

A model was established for modeling ANAMMOX process in a single granule

*DOI: http://dx.doi.org/10.5772/intechopen.90201*

**4. Challenges and discussions**

single granule.

difficult [25, 26].

in complex systems.

tor as a black box.

**5. Conclusions**

**Figure 3.** *Schematic view of the structure of BP model.*
