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Journal of Applied Sciences and Environmental Management
World Bank assisted National Agricultural Research Project (NARP) - University of Port Harcourt
ISSN: 1119-8362
Vol. 9, Num. 1, 2005, pp. 107-113

Journal of Applied Sciences & Environmental Management, Vol. 9, No. 1, 2005, pp. 107-113

Optimal Design of Wastewater Treatment Plant Using Adaptive Simulated Annealing

L.GOVINDARAJAN, S. KRISHNA KUMAR and T. KARUNANITHI

Department of Chemical Engineering,  AnnamalaiUniversity,  Annamalainagar – 608002, INDIA, E-mail: cdl_lln@sancharnet.in

 Code Number: ja05020

ABSTRACT:  This paper deals with the application of Adaptive Simulated Annealing (ASA) for the optimal design of the wastewater treatment plant. The plant consists of a trickling filter, an activated sludge aeration vessel and a secondary clarifier.In this work a successful attempt has been made to use the ASA for optimal design of wastewater treatment plant. ASA based optimal design values have been compared with conventional optimization approaches and has been found to yield the lowest total construction cost of wastewater treatment plant. From this work, it has been found that artificial intelligence based optimization techniques such as adaptive simulated annealing is found to be suitable for the optimal design of wastewater treatment plant. @JASEM 

Several conventional and global optimization techniques had been used for the optimal design of varieties of process engineering problems. The conventional optimization techniques are complex, computationally expensive, and not efficient and in most cases, find local optimum values. These drawbacks of conventional techniques are overcome by adapting a universal technique that could solve all possible optimization problems and should have a higher probability to yield the solutions near enough to global optimum value. There has been an increasing interest recently in the use of artificial intelligence based optimization techniques in solving the design problems.

Artificial intelligence based optimization like simulated annealing, genetic algorithm, differential evolution, evolutionary strategies and evolutionary programming have been used as the replacement for conventional optimization techniques because they overcome the limitations of conventional approaches, due to ease of computation and simplicity in programming (Rao 1996). The objective of this work is to study the efficiency and roubustness of the artificial intelligence based optimization technique for the optimal design of wastewater treatment plant.  In this work adaptive simulated annealing technique has been implemented for the optimal design of wastewater treatment plant.

Wastewater Treatment Plant: Wastewater treatment plant (WTP), considered in this paper, was designed by Mishra et al., 1973 that consists of a trickling filter, an activated sludge aeration vessel and a secondary clarifier as shown in Fig 1.

The principal unit operations in water-treatment plant include coagulation-flocculation, sedimentation and filtration. The performance of each treatment unit affects the efficiency of the subsequent units. Therefore the design decisions should be made with regard to the interactions between various unit operations present in the plant.

Simulated Annealing: Simulated Annealing (SA) is an artificial intelligence based optimization technique that resembles the cooling process of molten metals through annealing. At high temperature, atoms in molten metal can move freely with respect to each another, but as the temperature is reduced, the movement of atoms gets restricted.  The atoms start to get ordered and finally form the crystals having the minimum possible energy.  However, the formation of the crystal mostly depends on the cooling rate. If the temperature is reduced at a very fast rate, the crystalline state may not be achieved at all; instead, the system may end up in a polycrystalline state, which may have a higher energy state than the crystalline state.  Therefore, in order to achieve the absolute minimum energy state, the temperature needs to be reduced at a slow rate. Controlling a temperature-like parameter introduced with the concept of the Boltzmann probability distribution simulates the cooling phenomenon. According to the Boltzmann probability distribution, a system in thermal equilibrium at a temperature T has its energy distributed probabilistically according to P(E) = exp (-E/kT), where k is the Boltzmann constant.  Simulated annealing is a point-by-point method.  The algorithm begins with an initial point and a high temperature T. A second point is created at random in the vicinity of the initial point and the difference in function values (ΔE) at these two points is calculated.  If the second point has a smaller function value, the point is accepted; otherwise the point is accepted with a probability exp (-ΔE/T).  This completes the one iteration of simulated annealing procedure. In the next generation, another point is created at random in neighborhood of current point and Metropolis algorithm is used to accept or reject the point. The algorithm is terminated when a sufficiently small temperature is obtained or a small enough change in function values is found (Deb 1995).

Adaptive Simulated Annealing: Adaptive simulated annealing (ASA) maintains all the advantages of standard simulated annealing algorithm along with improvement in speed of convergence. ASA is also known as the very fast simulated reannealing, is a very efficient version of SA. ASA uses only the value of the cost function in the optimization process and is very simple to program (Ingber, 1989).  The successful working of ASA depends up on three function, those are generating probability density function, acceptance function, and annealing schedule. These three functions are modified in ASA algorithm to improving the convergent speed. The ASA, however, can employ a very fast annealing schedule, as it has self-adaptation ability to re-scale temperature.     

Optimal Design Of Wastewater Treatment Plant: The construction cost and operation cost of the trickling filter, is given by the correlation

 

Where VTF is expressed in ft3 and the last two terms are due to the cost of the recycle pump.

The construction cost and operation cost of the aeration vessel is given by the correlation

where VAS is expressed in million gallons and the last two terms are due to the cost of the pump between the aeration vessel and the trickling filter.

The construction cost and operation cost of the secondary clarifier is given by the correlation

Totaling the costs of the individual process subsystems and allowing 40% in excess for engineering fees and ancillary costs estimated the total construction cost of the system. Mathematically the total construction cost is given by the equation

 

Optimization Problem Formulation: The objective function for optimal design of wastewater treatment plant is given by

Subject to the equality constraints

 

There are 26 design equations and 51 variables of which 16 variables are specified.  Thus there are 9 variables free for the optimal design purposes. In this work the variables selected for the optimal design are α10, α11, α12, α21,

RESULTS AND DISCUSSION

Adaptive Simulated Annealing (ASA) based optimal design value of wastewater treatment plant has been furnished in Table 1. The computation time required to obtain these optimal design values is in the order of 3 s in P-III 500 MHz processor. Table 1 indicates that maximum specific growth rate k=2.4 is the feasible region to operate the wastewater treatment plant from the results of the system operated at various k values such as 0.48, 2.4 and 4.8. The reason for selecting k=2.4 as the feasible region is that it the plant can be designed and operated at the minimum total construction cost for the waste water treatment plant that including the operating cost. A further decrease in k to a 0.24, the system acts like an infeasible one. The system was computed with two different regions of X12, such as unbounded region and bounded value with the maximum of 1x105. From both cases we are getting minimum CT value for unbounded region with k= 2.4 day -1.

From Table 2 shows the optimal design values of wastewater treatment plant at different initial vector values with the condition of X2r unbounded and k= 2.4 day -1.  The minimum total construction cost CT of WTP was found to be $ 151400 (case-3).  The optimal design component values such as depth, cross-sectional area and volumetric flow rates for the equipment present in WTP have been furnished in Table 3 (case-3).

Comparison Of Asa Based Optimal Design Values With Other Optimization Techniques: ASA based optimal design value obtained for the wastewater treatment problem has been compared with the optimization approaches used in the previous investigations. The optimal synthesis of WTP using a simplex pattern approach had been studied (Mishra et al., 1973). The cost obtained 2,15,095 with 02r <105 and k=2.4 as the plant operating conditions. The same problem was also solved by using generalized reduced gradient (G.R.G) method (Himmlebalu, 1976). The total construction cost obtained by was  $ 2,43,841 with upper bound constraint on the recycle sludge concentration of 1×105 PPM. Modified random search was also used for the optimal design of WTP (Wang and Luus, 1977). The total construction cost obtained was $ 1,55,000 and 1,66,409, with two regions of recycle sludge concentration as unbounded region and maximum of 9.1×104 respectively.  The hybrid technique of integrated control random search was also used for the design of WTP (Banga and Long, 1981). The total construction cost obtained was $1,57,902 and 1,70,902, with two regions of recycle sludge concentration as unbounded region and maximum of 1×105 respectively. The wastewater treatment system synthesis had been also solved by using continuous search method (Nishida and Power, 1983). The total construction cost was found to be $ 1,68,132, with the recycle sludge concentration as 1×10 5 and structural parameter value k=2.4. Table 4 shows that minimum value of CT for the WTP by various optimization techniques and ASA. For most of the cases CT minimum is obtained at the condition of k=2.4 day-1 and X2r unbounded, ASA results obtained in this work also favors the condition previously established by the other approaches but reaches a new low total construction cost value of $ 1,51,400 and 1,61,200.00 with the plant parameters of X2r unbounded and 02r<105   respectivelyfor k=2.4. The value obtained by ASA has been found to be a stable from the sensitivity analysis done for the problem considered in this work.

Conclusion: The wastewater treatment plant considered in this study had been solved by using conventional optimization techniques in previous investigations including the simplex search, modified random search algorithm, generalized reduced gradient method, and a hybrid technique of using integrated control random search. But these techniques have their own limitations like requirement of complex mathematical analysis, difficulties in the problem formulation.  In this paper, a successful attempt has been made to apply the adaptive simulated annealing technique for the optimal design of wastewater treatment plant. The results have been compared with conventional optimization approaches to establish the superiority of ASA. From this work artificial intelligence based optimization technique such as adaptive simulated annealing is found to be suitable for the optimal design of wastewater treatment plant and ASA based methodology can also be extended for the real time optimization problems.   

Acknowledgements:  The authors wish to express their gratitude for the support extended by the authorities of Annamalai University, Annamalai Nagar, India in carrying out the research work.

REFERENCES

  • Banga, J R; Long, J C (1981). Integrated Controlled Random search: Application to a Waste water Treatment Plant Model. IChemE Symposium Series, Technical report.100: 183-192.
  • Deb K (1995). Optimization for Engineering Design: Algorithms and Examples, Prentice Hall of India private Limited, New Delhi.
  • Himmelblau, D M (1976). Optimal Design via Structural Parameters and Non Linear Programming. Engineering Optimization, 2: 17-27.
  • Ingber, L (1989). Very fast simulated re-annealing, Mathl Comput.  Modelling, 12: 967-973 
  • Mishra, P N ; Fan, L T; Ericksson, L E (1973). Biological Wastewater Treatment System
  • Design,  Part I.   Canad. Jour. Chem. Engng., 51: 604-701.
  • Nishid; Powers J (1983). On the Computational Technique of Optimal Synthesis Problem using Synthesis Structure Parameters. Technical report. Carnegie- Mellon university, U.S.A.
  • Rao S S (1996). Engineering Optimization: Theory and Practice New Age International Limited , New Delhi.
  • Wang, B C; Luus, R (1977). Optimization of Non Uni-model Systems, Inter. Jour. Num. Method.  Engng. 11: 1235 – 1250.

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