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Optimization methods usually obtain the travel direction of the solution by substituting the solutions into the objective function. However, if the solution space is too large, this search method may be time consuming. In order to address this problem, this study incorporated the Taguchi method into the solution space search process of the optimization method, and used the characteristics of the Taguchi method to sequence the effects of the variation of decision variables on the system. Based on the level of effect, this study determined the impact factor of decision variables and the optimal solution for the model. The integration of the Taguchi method and the solution optimization method successfully obtained the optimal solution of the optimization problem, while significantly reducing the solution computing time and enhancing the river water quality. The results suggested that the basin with the greatest water quality improvement effectiveness is the Dahan River. Under the optimal strategy of this study, the severe pollution length was reduced from 18 km to 5 km.

River basin pollution can be classified into four types according to the sources, which are domestic sewage, livestock wastewater, industrial wastewater, and non-point source pollution. If the river flows through a large metropolitan area, the main pollution source will be the domestic sewage. To remedy the domestic sewage pollution, the most effective strategy is the construction of sewerage systems. However, the sewerage system construction period is long, and domestic sewage continues to be discharged without treatment until the entire system is completely constructed. Therefore, besides building the sewerage system, the remediation strategy should also concern the water pollution treatment problem during the construction period.

This study aims to use the verified water quality model, from tens of water pollution remediation strategies or facilities, and integrate a method that can quickly determine the optimal remediation measure combination, in order to reduce the number of operations, and obtain the optimal combination of remediation strategy operations. Previous studies have used the optimization model to obtain the optimal solution. However, in practice, tens of combinations of water pollution remediation measures can result in an enormous solution space. Moreover, the calculation of water quality models is time consuming, thus leading to poor efficiency and infeasibility for field application due to the long solving process. Therefore, this study applies the Taguchi method, which has high efficiency in solving problems, in the optimization model, in order to obtain the influence coefficient of decision variable combinations on the reached targets. Then, the optimal strategy combination is determined according to the influence coefficient. This study takes the Danshui River basin in Taiwan for case analysis. The research process includes four parts: collection of basic data and river remediation strategies, construction of optimization model, input of the Taguchi method, and result analysis.

The Danshui River is the third longest river in Taiwan, running for 158 km and draining a watershed of approximately 2,726 km^{2} (

Danshui River basin range.

RPI trend map of Danshui River basin (RPI: River Pollution Index).

According to the key remediation measures, the rate of household connection in the cities around the Danshui River basin, by the end of 2012, is 70.4% in Taipei City and 49.5% in New Taipei City. There are three main sewage treatment plants, 35 interception stations and 21 onsite treatment facilities in the whole basin. The locations are shown in

Danshui River basin sewage treatment installation distribution diagram.

The total designed capacity and onsite treatment capacity of interception stations in the Danshui River basin, the total household connection capacity, and the total treatment capacity of sewage treatment plants in 2012 are shown in

Comparison of treatment facility and sewage plant capacities.

Item | Flow Rate (m^{3}/day) |
---|---|

Total Interception Capacity | 2,320,184 |

Total Onsite Treatment Capacity | 247,054 |

Household connection capacity in 2012 | 1,174,621 |

Waste water treatment capacity | 1,970,000 |

In practice, the remediation of river water pollution first sets the objectives and period, and then analyzes the effect of remediation strategy, in order to select the optimal strategy combination for attaining the objectives.

In the optimization model solving process, the solution space formed by the decision variables is too large, and the water quality model computation is time consuming, resulting in poor model solving efficiency. Among studies on connecting optimization to simulation models, the speed of optimal solution search is the key factor influencing the overall computing efficiency. In order to improve the computing efficiency, this study uses the Taguchi method and regards the optimization model as a system. The decision variables are experimental parameters, and the objective function is system function. The experimental parameters are changed to obtain the variable parameters for overall function variation, thus accelerating the computational speed for the optimal combination of decision variables, and facilitating the decision-making on the optimal remediation strategy.

This research process includes: (1) determining the key features among domestic sewage—sewage treatment strategy—rivers; (2) developing a river water quality model to simulate river water quality under different strategies; (3) applying the Taguchi method to build an optimization model for selecting optimal strategy. The steps are described below:

The sewer policy of Taiwan is based on a rain and sewage diversion system. Before the household connection is completed, the domestic sewage is discharged to the rivers by the rainwater collection system. On sunny days, the high concentration domestic sewage discharged into rivers in this way deteriorates the river water quality. In order to avoid the direct discharge of high concentration sewage, the current improvement measures, besides promoting household connection, include: (1) special pipes at the drainage end intercepts sewage for onsite treatment before being discharged; (2) the interception facilities intercept the sewage into the main sewer with remaining capacity, and the sewage is delivered to the downstream sewage treatment plant to drain after treatment. The overall regional sewage treatment strategy, including the above two remediation strategies, is illustrated in

Schematic diagram of sewage treatment strategy.

In Taiwan, there is no domestically developed river water quality model, and all the above models are adopted from foreign experiences. The commonly used water quality models include WASP, QUAL2K, and SWMM. In terms of the Danshui River basin, in order to unify the water quality model tool, the Environmental Protection Administration (EPA) adopted WASP as the main model for simulating the Danshui River water quality. Since then, numerous studies have used WASP as the tool for Danshui River basin. This study uses the Danshui River model built by Chen

The Taguchi method is a quality engineering proposed by Genichi Taguchi. The method includes off-line and on-line quality engineering and MTS (Mahalanobis-Taguchi System). This study uses off-line quality engineering method, which aims to improve R&D, design and production technology for solving optimization problem. The purposes are to obtain the optimal improvement measures, including functional evaluation of quality, determination of specifications (tolerance), parameter design and tolerance design [

Orthogonal arrays and S/N ratios are two main components of the Taguchi method. An orthogonal array is used to reduce testing time/cost. If an experiment has 15 control factors with two levels, all possible

The smaller-the-better (STB) type:

The larger-the-better (LTB) type:

The nominal-the-better (NTB) type:

The solving process proposed by this study is to build the optimization model first, and then determine the number of system parameters and level. The level of parameters is changed according to the orthogonal arrays of the Taguchi method, and the system is simulated repeatedly. Finally, the sensitivity of parameters to the system and the optimal solution of system are obtained. The solving process is shown in

Solving process of this study.

The objective function of this optimization model is set as the minimum average RPI of the entire Danshui River basin; the purpose of which is to optimize the remediation strategy for the lower river pollution level. The decision variables are the strategies of various treatment facilities, and the constraints are the limitations of treatment facility strategies (the total interception capacity of interception stations along main sewer does not exceed the remaining capacity of the main sewer and the onsite treatment capacity does not exceed the designed capacity). The amount of sewage received by various treatment facilities is the amount of domestic sewage in the corresponding sewage collection area. The total flow of main sewer does not exceed the treatment capacity of sewage treatment plant. The basin pollution concentration is the computing result of WASP water quality model. The optimization model is expressed as follows:
_{ijk}_{ij}_{ij}

Equation (4) is the objective function Z, representing basin-wide minimum average PRI, _{i}_{i}_{i}_{i}

Equations (5) and (6) show the flow rate and water quality at the _{ijk}_{ij}_{ij}

Equation (7) is the amount of domestic sewage of the _{ij}_{ij}

In Equation (8), Σ_{ijk}_{ij}_{kT}_{kT}

In Equation (9), _{T} is the treatment capacity of the

The decision variable of this study is the facility operating strategy _{ij}_{ij}

When the number of system parameters and operating strategies are determined, the number of repeated simulations and the values of parameters in each simulation can be determined according to the orthogonal array of the Taguchi method. This study selects 31 system parameters and each parameter has two operating strategies. The optimum parameter combination can be obtained according to the simulation result of only 32 repeated system simulations. In comparison to general optimization, which needs to find the optimal solution among 2^{31} = 2,147,483,648 permutations, the Taguchi method can shorten the computation time greatly. The 31 system parameters selected by this study are indicated as codes A,B~AE, while 1 means that the operating strategy is 100%, 2 means that the operating strategy is 0%. For example, the value of parameter A in the first strategy combination is 1, meaning that the operating strategy of parameter A in the strategy combination is 100%, and so forth. The parameters in various strategy permutations are shown in

The basin-wide average water quality of each simulation is determined after 32 simulations. The basin-wide average water quality under the same operating strategy value of the same facility is calculated. Finally, the values under different strategies are subtracted to obtain the influence coefficient of the facility (system parameters), as shown in

System simulation parameter permutations.

Strategy Parameter | No. 1 | No. 2 | No. 3 | No. 4 | No. 5 | No. 6 | No. 7 | No. 8 | No. 9 | No. 10 | No. 11 | No. 12 | No. 13 | No. 14 | No. 15 | No. 16 | No. 17 | No. 18 | No. 19 | No. 20 | No. 21 | No. 22 | No. 23 | No. 24 | No. 25 | No. 26 | No. 27 | No. 28 | No. 29 | No. 30 | No. 31 | No. 32 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Danshui River water pollution remediation strategy simulation results- Dahan River BOD_{5} concentration.

Danshui River water pollution remediation strategy simulation results- Dahan River BOD_{5} concentration.

System impact factors.

Rank | Impact Factor | Facility | Rank | Impact Factor | Facility |
---|---|---|---|---|---|

1 | 0.1248 | X | 17 | 0.0037 | A |

2 | 0.0993 | I | 18 | 0.0030 | M |

3 | 0.0343 | Q | 19 | 0.0023 | Y |

4 | 0.0258 | AC | 20 | 0.0020 | U |

5 | 0.0238 | T | 21 | 0.0018 | F |

6 | 0.0198 | AA | 22 | 0.0017 | V |

7 | 0.0164 | L | 23 | 0.0016 | Z |

8 | 0.0104 | B | 24 | 0.0012 | S |

9 | 0.0086 | E | 25 | 0.0012 | O |

10 | 0.0082 | R | 26 | 0.0011 | J |

11 | 0.0069 | P | 27 | 0.0011 | G |

12 | 0.0047 | H | 28 | 0.0010 | N |

13 | 0.0043 | D | 29 | 0.0009 | AE |

14 | 0.0041 | C | 30 | 0.0008 | AD |

15 | 0.0040 | K | 31 | 0.0002 | W |

16 | 0.0038 | AB |

The analyzed optimal solution can be determined according to the impact factor and the remaining capacity of system; the result is shown in _{5} concentration and RPI, as shown in

Optimal solution of optimization model.

Rank | Faculity | Creek | Current Condition | Simulation Result | Rank | Faculity | Creek | Current Condition | Simulation Result |
---|---|---|---|---|---|---|---|---|---|

1 | X | Dahan | 10% | 100% | 17 | A | Xindian | 31% | 0% |

2 | I | Dahan | 24% | 100% | 18 | M | Dahan | 26% | 0% |

3 | Q | Dahan | 100% | 100% | 19 | Y | Dahan | 68% | 100% |

4 | AC | Dahan | 56% | 100% | 20 | U | Dahan | 0% | 0% |

5 | T | Keelung | 42% | 100% | 21 | F | Dahan | 5% | 0% |

6 | AA | Dahan | 41% | 100% | 22 | V | Keelung | 47% | 100% |

7 | L | Dahan | 12% | 100% | 23 | Z | Dahan | 100% | 100% |

8 | B | Xindian | 35% | 0% | 24 | S | Xindian | 26% | 0% |

9 | E | Dahan | 16% | 100% | 25 | O | Dahan | 100% | 100% |

10 | R | Xindian | 77% | 0% | 26 | J | Keelung | 47% | 0% |

11 | P | Dahan | 100% | 100% | 27 | G | Dahan | 19% | 0% |

12 | H | Dahan | 64% | 0% | 28 | N | Dahan | 22% | 0% |

13 | D | Xindian | 83% | 0% | 29 | AE | Xindian | 5% | 0% |

14 | C | Xindian | 19% | 0% | 30 | AD | Keelung | 49% | 0% |

15 | K | Dahan | 0% | 0% | 31 | W | Keelung | 23% | 100% |

16 | AB | Keelung | 38% | 100% |

Danshui River water pollution remediation strategy simulation results- Dahan River BOD_{5} concentration.

Danshui River water pollution remediation strategy simulation results- Dahan River RPI.

Danshui River water pollution remediation strategy simulation results—Xindian Creek BOD_{5} concentration.

Danshui River water pollution remediation strategy simulation results—Xindian Creek RPI.

Danshui River water pollution remediation strategy simulation results—Keelung River BOD_{5} concentration.

Danshui River water pollution remediation strategy simulation results—Keelung River RPI.

The optimal strategy combination of this study and current condition are compared in

Comparison between optimal strategy combination and current condition.

Tributary | Q(CMD) | Number of Operating Facilities | Rate of Household Connection | ||
---|---|---|---|---|---|

Current Condition | Simulation Result | Current Condition | Simulation Result | ||

Dahan River | 474,842 | 796,700 | 28 | 23 | 25.1% |

Hsindian Creek | 298,251 | 39,700 | 11 | 4 | 36.7% |

Keelung River | 237,378 | 203,080 | 14 | 12 | 69.1% |

Total | 1,010,471 | 1,039,480 | 53 | 39 | -- |

This study incorporated the Taguchi method into the optimization model for solution. According to the sequence of influence of parameters on the system and the limitation of optimization model system capacity, the optimal solution of the optimization problem was determined. The model computing time was shortened greatly.

The facility influence weights were obtained using the Taguchi method, and the optimum combination was screened according to the remaining capacity. The result suggested that the simulation result of this study is better than the current condition, and the Dahan River is the basin with the highest water quality improvement effectiveness. Under the optimal strategy of this study, the severe pollution length was shortened from about 18 km to about 5 km.

According to the comparison between simulation result and the rate of household connection of basins, the basin water quality improvement effectiveness was proportional to the river pollution condition, and inversely proportional to the rate of household connection of basins.

This study used two operating strategies for strategy configuration. Future studies can increase the operating strategies, from the On (100%) and Off (0%) strategies to operating altitudes of different openings, allowing the facilities to be used more flexibly and effectively.

Study conception and design: Tsung-Ming Yang

Acquisition of data: Chih-Chiang Chiu, Hsin-Ju Wang

Analysis and interpretation of data: Tsung-Ming Yang, Nien-Sheng Hsu

Drafting of manuscript: Chih-Chiang Chiu, Hsin-Ju Wang

Critical revision: Nien-Sheng Hsu

The authors declare no conflict of interest.