توسعه یک استراتژی عملکرد بهینه در یک راکتور دسته ای متوالی (SBR) از طریق بهینه سازی پویای ترکیب عدد صحیح ازدحام ذرات (PSO)

Dynamic optimization in SBRs represents an enormous challenge in order to save time and energy. As the non-convexities presented by these systems limit the application of deterministic techniques, stochastic contributions to meet global optimization become crucial. A PSO algorithm in order to minimize the aeration demand in a SBR was developed. The network size, sequencing and stages duration, were assumed as the decision variables for the dynamic MINLP problem. Two kinds of PSO algorithms (relaxed and mixed-integer) were applied in order to find the best way for taking into account the mixed-integer nature. Stochastic optimization improved the results obtained from a sequential shooting method/NLP, and mixed-integer PSO resulted in the best structure solving the MINLP. Despite that, and in order to assure the most robust and reliable solution, the assessment of both PSO formulations must be considered. PSO results have given an optimal operation policy of easy implementation.

Sequential batch reactor (SBR) represents one of the most important activated sludge technologies for wastewater (WW) treatment. Carbon, nitrogen and phosphorous removal can be carried out simultaneously in this kind of equipment (Artan & Orhon, 2005). The extreme flexibility presented by these systems [feeding pattern and reaction network establishment (Ferrari, Biscaia, & Melo, 2008)] encourages the use of optimal control laws even during its operation at industrial scale. This feature is rarely observed for the rest of WW treatment technologies. Fig. 1 shows an example of a usual SBR process treating continuous WW for carbon and nitrogen removal. Anoxic/aerobic stages, biomass settling, effluent and sludge draw, and some idle time, represent the common phases presented by this instance.

Optimal operation schemes, obtained from deterministic and stochastic techniques, were here developed for a real SBR process in order to minimize the energy consumption (aeration demand) in the equipment. Deterministic optimization results exposed a strong non-convex behaviour for this system demonstrating the unavoidable need of stochastic contributions in order to search for the global optimum. The use of particle swarm optimization allowed improving the obtained results from deterministic techniques with a very reasonable computational cost (no further optimization improvement was needed). In order to solve the constrained dynamic MINLP problem presented in this work and despite higher swarm convergences were obtained with a relaxed PSO formulation, better optimization results were achieved with a mixed-integer particle swarm structure, introducing the MI nature of the inputs at each iteration in the algorithm. The assessment of both PSO formulations should be considered in order to guarantee the most robust and reliable results for this optimization problem. An optimal operation strategy that minimizes the total aeration demand along the SBR process can be easily programmed (switching times) in accordance to PSO results.