The safety of water delivery and water quality in the South to North Water Transfer Project of China is important to northern China. Water quality data, flow data and data on factors that influence water quality were collected from 25 May to 26 August, 2013. These data were used to forecast water quality and calculate the relative error when using a genetic algorithm optimized general regression neural network (GA-GRNN) model as well as conventional general regression neural network (GRNN) and genetic algorithm optimized back propagation (GA-BP) models. The GA-GRNN method requires few network parameters and has good network stability, a high learning speed and strong approximation ability. The overall forecasted result of GA-GRNN is the best of three models, of which the root mean square error (RMSE) of every index is nearly the least among three models. The results reveal that the GA-GRNN model is efficient for water quality prediction under normal conditions and it can be used to ensure the security of water delivery and water quality in the South to North Water Transfer Project.

INTRODUCTION

North China is home to more than 25% of China's population and accounts for an even higher share of gross domestic product (GDP) (Berkoff 2003), but the water resources available in this area account for only 6% of the country's total. Water resource problems have been serious in northern China; thus the South to North Water Transfer Project has been put into effect to alleviate such problems. The middle route of the South to North Water Transfer Project originates at the Danjiangkou reservoir to Beijing and aims to deliver 30 million m3 of water to northern China every day. The total length of the main canal, which crosses the North China Plain, would be approximately 1246 km (Liu & Zheng 2002). The safety of water delivery is critical for the project.

Water quality and quantity are both important components of water resources. Water quantity can be guaranteed by the joint control of gates in the main channel of the middle route; however, water quality cannot be effectively managed. Therefore, methods for monitoring and forecasting water quantity were intensely studied to ensure water quality.

A water quality model based on the convection–diffusion equation and water flow continuity equation has been used to forecast water quality in previous studies (Barbagallo et al. 2003). This model has the advantage of being based on physical observations. However, for practical applications, the method requires too many parameters, some of which cannot be determined effectively, and it can take a long time to calculate a result.

A systematic approach is available that has the ability to process large amounts of related data and yield results quickly. This approach has also been widely used for prediction in a wide range of fields. Artificial neural networks are commonly used, are based on a large database and can handle data with complicated relationships (Shen & Bax 2010). Generalized regression neural networks (GRNN) with highly parallel structures have the benefits of requiring few network parameters and having good network stability (Specht 1991). These networks can also be used in the field of water quality prediction.

Under normal conditions, water pollution incidents do not occur in the middle route of the South to North Water Transfer Project. The water quality in the main channel of the middle route is influenced by many external factors, namely water flow, rainfall, air temperature, sunshine hours, wind velocity and average vapor pressure. At the same time, when the quality of water cannot meet the requirements, the gates in the main channel are regulated and the flow is changed to solve the water quality problem. Water quality is influenced by the external factors and also influences the water flow. Thus, water quality is simultaneously affected by both internal and external factors of the water system.

There are three characteristics of GRNN. (1) The data are simultaneously affected by internal and external factors, as is the water quality system described above. (2) The method also functions well in the situation of data deficiency, which is generally the case in water quality monitoring systems. (3) The network is capable of processing unstable data, such as water quality, which is influenced by parameters such as rainfall.

The GRNN model requires only one simple smoothing factor. The larger the smoothing factor is, the smoother the approximation process of the network; the smaller the smoothing parameter is, the stronger the approximation performance of the network (Lu & Bai 2013). Therefore, calculating an ideal smoothing factor is important.

To improve the prediction accuracy of GRNN, the spread of each neuron is treated as an independent variable, and the best value of each spread is found via genetic algorithm (GA) that depends on the degree of impact of the output. Then, a GA-GRNN model is constructed.

GA-GRNN has been uses in some fields, such as three-dimensional aerodynamic optimization design (Yao et al. 2012), inter-characteristics analysis (Lee et al. 2011) and the streams of nitrogen composition (Li et al. 2008). In order to test and verify the adaptability of water quality forecasting using GA-GRNN, compared with GRNN and GA optimized back propagation (GA-BP). GRNN has the similar model structure with GA-GRNN, but the parameters of it cannot be adjusted according to different indices; back propagation (BP) is the most widely used way to adjust connection weights in the artificial neural network iteratively in order to minimize the error. (Yao 1999). GA-BP uses GA to optimize its parameters, but its model structure cannot reflect the link between internal and external factors. The infection of structure and parameters in model can be analyzed from this comparison

The present paper aims to forecast water quality under normal conditions, in which large-scale water pollution events do not occur. After using the water quality data from the middle route of the South to North Water Transfer Project and comparing three systematic approaches, namely, GRNN, GA-BP and GA-GRNN, it was found that GA-GRNN has good network stability, high learning speed and strong approximation ability. This paper verifies that the systematic method of GA-GRNN can be used to forecast water quality under normal conditions, and it can help ensure the safety of water delivery in the middle route of the South to North Water Transfer Project in China.

DATA ACQUISITION

Water quality data were collected by the Hydrology and Water Resources Survey Bureau of Hebei Province in the Beijing Shijiazhuang section of the middle route of the South to North Water Transfer Project. Data used in this paper were collected once a day during a temporary operation period as well as a period from 25 May to 26 August, 2013, 94 data points in total. Water was collected and tested at the Huinanzhuang pumping station, which is the only large pumping station in the main channel of the middle route of the South to North Water Transfer Project. The pumping station is the key to the artesian flow and pressurized delivery of mass water in the Beijing section. This station is also a key infrastructure component of the main line of the middle route of the South to North Water Transfer Project.

Eleven indices, namely water temperature, conductivity, pH, dissolved oxygen, turbidity, ammonia nitrogen, permanganate index, dissolved organic matter, total phosphorus, total nitrogen and chlorophyll content, were used to indicate the water quality. These indices were measured using automatic water quality detection equipment located at the Huinanzhuang pumping station. The water quality data are shown in Table 1.

Table 1

Water quality data

ParametersRangeUnit
Water temperature 21.8–30.5 °C 
Conductivity 457–781 us/cm 
pH 7.7–8.3  
Dissolved oxygen 7.8–11.3 mg/L 
Turbidity 0.1–4.1 NTU 
Ammonia nitrogen 0–0.1 mg/L 
Permanganate index 2–3.4 mg/L 
Dissolved organic matter 4–14.2 mg/L 
Total phosphorus 0.02–0.03 mg/L 
Total nitrogen 2.03–4.03 mg/L 
Chlorophyll content 3.73–15 μg/L 
ParametersRangeUnit
Water temperature 21.8–30.5 °C 
Conductivity 457–781 us/cm 
pH 7.7–8.3  
Dissolved oxygen 7.8–11.3 mg/L 
Turbidity 0.1–4.1 NTU 
Ammonia nitrogen 0–0.1 mg/L 
Permanganate index 2–3.4 mg/L 
Dissolved organic matter 4–14.2 mg/L 
Total phosphorus 0.02–0.03 mg/L 
Total nitrogen 2.03–4.03 mg/L 
Chlorophyll content 3.73–15 μg/L 

We postulate that there are six factors influencing water quality in the main channel of the middle route: water flow, rainfall, air temperature, sunshine hours, wind velocity and average vapor pressure. Water flow data were collected during the temporary operation period of the Beijing-Shijiazhuang section of the middle route. The meteorological data were collected by the national meteorological station. The data collected for the factors that influence water quality are shown in Table 2.

Table 2

Data of factors that influence water quality

ParametersRangeUnit
Water flow 10.8–13.5 m³/s 
Rainfall 0–84.2 mm 
Air temperature 19.0–31.7 °C 
Sunshine hours 0–14.1 
Wind velocity 1–4.1 m/s 
Average vapor pressure 7.3–33.9 hpa 
ParametersRangeUnit
Water flow 10.8–13.5 m³/s 
Rainfall 0–84.2 mm 
Air temperature 19.0–31.7 °C 
Sunshine hours 0–14.1 
Wind velocity 1–4.1 m/s 
Average vapor pressure 7.3–33.9 hpa 

METHODS

The GRNN consists of four layers, including the input layer, hidden layer, summation layer and output layer. The input layer is fully connected to the pattern layer, where each unit represents a training pattern and its output is a measure of the distance of the input from the stored patterns. Each pattern layer unit is connected to the two neurons in the summation layer: the S-summation neuron and the D-summation neuron (Kim & Lee 2005).

The theory of GRNN is based on non-linear regression analysis (Specht 1991). Using regression analysis of a non-independent variable y related to independent variable x, the y corresponding to the greatest probability value can be calculated. Assume that f(X, y) represents the joint probability density function of a random vector x and a random scalar variable y and that the value of x is X. is the predicted output of variable y on the condition that X is the input of variable x, and the conditional mean of y given X is given by 
formula
1
, which represents the predicted density function, was deduced by using the Parzen kernel non-parametric estimation based on sample data , and is given by 
formula
2
where Xi and Yi are sample observations of variable x and variable y, respectively; n is the sample size; p is the dimension of variable x; and σ is the spread factor of the Gaussian function called the smooth factor.
By using instead of f(X, y) in Equation (1) and interchanging the order of integration and summation, the predicted output of variable y is given by 
formula
3
As , Equation (3) will be obtained by performing the indicated integrations: 
formula
4
We can conclude that the predicted output is the weighted value of the dependent variable values of all training samples and the weight factor is . When the value of σ is large enough, the predicted output is approximately equal to the average value of all dependent variables. In contrast, when the value of σ trends to 0, the predicted output will be close to the training samples. In such circumstances, the generalization ability of the network analysis is weakened. When input variables x are included in samples, the process will predict accurate results, but if the input variables are not included in the samples, the net predictive results will be inaccurate.

It can be concluded that the appropriateness of the value of σ is closely related to the accuracy of the model. To obtain a more accurate model, a GA is used to optimize the value of σ. In the GA, a fitness function maps the error between the output of the GRNN and the desired output of the GRNN. The most appropriate value of σ will be found through continuously generating a new population. For convenience, a GRNN model optimized by GA is expressed as a GA-GRNN model.

Based on the way that using GA to optimize the value of σ mentioned above, the steps of this model are as follows:

  • (1)

    Normalize the original data to meet the requirements of the model.

  • (2)

    Based on the way of real code and the scale of population, the initial population P(t) is generated randomly, meanwhile the value of t is set to 0.

  • (3)

    The parameters of GRNN are obtained after decoding the chromosome in GA, then use GRNN to predict the output of training samples.

  • (4)
    The error between the output of GRNN and the actual value is calculated, then the fitness function (Equation (5)) is used to transform it to the fitness value: 
    formula
    5
    where is the output of GRNN corresponding to index j of the training data i, and is the actual value corresponding to index j of training data i.
  • (5)

    The optimal preservation strategy is adopted, followed by the evaluation of the individual fitness value.

  • (6)

    The process is terminated once the precision requirements are met, otherwise, go to the next step.

  • (7)

    The process is terminated once t reaches the maximum generation, otherwise, go to the next step.

  • (8)

    A new population P(t+1) is generated after selection, crossover and mutation operations, then go to step 3.

The flow chart of this model is depicted in Figure 1. The GA-GRNN model would be built after the above training process finished, then use the test samples to test this model.

Figure 1

The flow chart of GA-GRNN.

Figure 1

The flow chart of GA-GRNN.

RESULTS AND DISCUSSION

For each water quality datum and the data of factors that influence water quality, three types of models were constructed, including GRNN, GA-BP and GA-GRNN. These data were collected once a day by the Hydrology and Water Resources Survey Bureau of Hebei Province from May 25 to August 26, 2013, and divided into 94 sets. Sets 1 through 90, which include the data from May 25 to August 22, 2013, were used to train the network of three models. Sets 91 through 94, which are the data from August 23 to August 26, 2013, were used to test the network.

General regression neural network

In the GRNN model, training data were normalized by a Premnmx Function (Equation (6)). 
formula
6
Then the normalized training sample was cross-validated by K-fold function, where the original sample was divided into K sub-samples, one of which used to test this model, and the others for further training. This process would be repeated K times before the mean value was calculated. Here the value of K was set to 10. The iteration method is used to search for the proper value of spread (σ). The experimental spread range was increased from 0.1 to 2 in increments of 0.1. When the relative error between the forecasted output, based on training data, and desired output is the lowest, the most appropriate value of σ will be found.

The GRNN model forecasted the output based on testing data. Then, the error between forecasted output and desired output was calculated. The absolute value of relative error, is depicted in Table 3. The GRNN process is complete when the predicted result is mapped to the data before normalization.

Table 3

The absolute value of relative error in the GRNN model

Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 2.2 3.6 2.3 14.8 88.8 0.0 16.5 21.9 12.5 8.5 38.6 
Test data 2 2.5 4.1 1.7 6.1 67.2 0.1 13.5 8.6 10.6 14.5 30.6 
Test data 3 3.2 1.5 0.4 1.1 56.5 0.2 3.5 0.8 4.6 21.4 28.0 
Test data 4 0.9 0.9 1.9 8.5 72.1 0.3 10.3 18.6 3.6 23.6 38.6 
Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 2.2 3.6 2.3 14.8 88.8 0.0 16.5 21.9 12.5 8.5 38.6 
Test data 2 2.5 4.1 1.7 6.1 67.2 0.1 13.5 8.6 10.6 14.5 30.6 
Test data 3 3.2 1.5 0.4 1.1 56.5 0.2 3.5 0.8 4.6 21.4 28.0 
Test data 4 0.9 0.9 1.9 8.5 72.1 0.3 10.3 18.6 3.6 23.6 38.6 

Genetic algorithm optimized back propagation

In the GA-BP model, the training data were used by the GA to optimize the weighted values w1 and w2 and the thresholds b1 and b2 in the BP neural network after the training data were normalized with the Premnmx Function. Where roulette-wheel selection, two-point crossover type, and uniform mutation operator were used in selection, crossover and mutation operation respectively. The probabilities for the crossover and mutation operators were 0.4 and 0.1, respectively, and the maximum generation number was set to 100.

The BP model forecasted the output based on testing data and mapped the predicted result to the data before normalization. Then, the absolute value of relative error between the forecasted output and desired output was calculated, and the relative error, which is depicted in Table 4, reflects the quality of the model.

Table 4

The absolute value of relative error in the BP model

Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 0.4 9.0 1.2 13.2 91.3 0.3 11.6 12.6 9.0 4.3 41.0 
Test data 2 1.9 5.4 0.8 7.9 48.0 0.5 6.2 16.5 5.3 14.2 39.1 
Test data 3 2.3 11.5 1.4 0.5 62.5 0.4 1.3 9.0 2.5 21.2 49.5 
Test data 4 3.0 15.8 1.9 8.0 62.8 0.4 5.7 2.7 3.3 9.0 49.7 
Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 0.4 9.0 1.2 13.2 91.3 0.3 11.6 12.6 9.0 4.3 41.0 
Test data 2 1.9 5.4 0.8 7.9 48.0 0.5 6.2 16.5 5.3 14.2 39.1 
Test data 3 2.3 11.5 1.4 0.5 62.5 0.4 1.3 9.0 2.5 21.2 49.5 
Test data 4 3.0 15.8 1.9 8.0 62.8 0.4 5.7 2.7 3.3 9.0 49.7 

Genetic algorithm optimized general regression neural network

In the GA-GRNN model, the GA was applied to optimize the GRNN model, and the value of σ that is the most appropriate for each factor was found through the dynamic GA. In the GA, the fitness function reflects the relative error between the forecasted output based on training data and the desired output. Where roulette-wheel selection, two-point crossover type, and uniform mutation operator were used in selection, crossover and mutation operation, respectively. The probabilities for the crossover and mutation operators were 0.8 and 0.2, and the maximum generation number was set to 100. The GA-GRNN process is complete when the predicted result is mapped to the data before normalization.

The GA-GRNN model forecasted the output based on testing data and mapped the predicted result to the data before normalization. The absolute value of relative error between forecasted output and desired output was calculated, and the relative error is depicted in Table 5.

Table 5

The absolute value of relative error in the GA-GRNN model

Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 1.6 1.6 2.0 8.2 85.6 0.2 9.6 10.3 4.3 5.0 45.6 
Test data 2 0.2 0.3 2.5 8.6 62.6 0.2 7.2 0.8 6.0 9.5 42.1 
Test data 3 2.8 0.9 1.8 6.2 45.5 0.4 4.5 9.5 1.0 7.8 42.6 
Test data 4 2.4 0.3 2.3 2.3 60.6 0.3 6.6 8.9 1.1 5.9 41.7 
Water temperature (%)Conductivity (%)pH (%)Dissolved oxygen (%)Turbidity (%)Ammonia nitrogen (%)Permanganate index (%)Dissolved organic matter (%)Total phosphorus (%)Total nitrogen (%)Chlorophyll content (%)
Test data 1 1.6 1.6 2.0 8.2 85.6 0.2 9.6 10.3 4.3 5.0 45.6 
Test data 2 0.2 0.3 2.5 8.6 62.6 0.2 7.2 0.8 6.0 9.5 42.1 
Test data 3 2.8 0.9 1.8 6.2 45.5 0.4 4.5 9.5 1.0 7.8 42.6 
Test data 4 2.4 0.3 2.3 2.3 60.6 0.3 6.6 8.9 1.1 5.9 41.7 

Analysis

Comparing the forecasted results of the three models, we found that the forecasting accuracy of indices of turbidity and chlorophyll content is poor in all three models. According to prior research on turbidity (Bustamante et al. 2009) and chlorophyll content (Filella & Penuelas 1994), the indices of turbidity and chlorophyll content are influenced by many factors. Some of these factors cannot be accurately measured through conventional detection methods, and others are unstable. However, the values of turbidity and chlorophyll content are affected by the water collection process. As a corollary, the indices of turbidity and chlorophyll content cannot be accurately forecasted by these three models; thus, when analyzing the accuracy of the models, these indices were not taken into consideration.

Analyzing the absolute value of relative errors of GRNN, we found that 21 absolute values of relative prediction errors are < 5%, four are between 5 and 10%, eight are in the range of 10 to 20% and the other three are over 20%. Analyzing GA-BP, we found that 18 absolute values of relative prediction errors are less than 5%, 10 are between 5 and 10%, seven are in the range of 10 to 20% and one is over 20%. In the GA-GRNN model, 23 absolute values of relative prediction errors are less than 5%, 12 are between 5 and 10% and only one is over 10%.

Using the RMSE (root mean square error) which is depicted in Equation (3) to evaluate the model quality of nine indices, namely water temperature, conductivity, pH, dissolved oxygen, ammonia nitrogen, permanganate index, dissolved organic matter, total phosphorus and total nitrogen. The RMSE of each index of the three models is shown in Table 6. 
formula
7
Table 6

The RMSE of each index in three models

Water temperature (°C)Conductivity (μg/cm)pHDissolved oxygen (mg/L)Ammonia nitrogen (mg/L)Permanganate index (mg/L)Dissolved organic matter (mg/L)Total phosphorus (mg/L)Total nitrogen (mg/L)
GRNN 0.65 16.19 0.14 0.86 0.03 0.30 1.17 0.61 0.38 
GA-BP 0.59 65.44 0.11 0.82 0.05 0.18 1.03 0.44 0.29 
GA-GRNN 0.55 5.32 0.17 0.65 0.02 0.18 0.70 0.31 0.16 
Water temperature (°C)Conductivity (μg/cm)pHDissolved oxygen (mg/L)Ammonia nitrogen (mg/L)Permanganate index (mg/L)Dissolved organic matter (mg/L)Total phosphorus (mg/L)Total nitrogen (mg/L)
GRNN 0.65 16.19 0.14 0.86 0.03 0.30 1.17 0.61 0.38 
GA-BP 0.59 65.44 0.11 0.82 0.05 0.18 1.03 0.44 0.29 
GA-GRNN 0.55 5.32 0.17 0.65 0.02 0.18 0.70 0.31 0.16 

It is illustrated that the RMSE of every index in GA-GRNN is nearly the least in three models, which shows GA-GRNN is the most appropriate among three models for this case. The model quality of GRNN is the worst, although the convergence rate of it is high, and the forecasting results can be obtained quickly. For the GA-BP model, in most instances, the forecasted results are acceptable. However, with regard to forecasting the index of conductivity, the result is quite good in the GRNN, whereas the result is unsatisfactory in the GA-GRNN. According to previous studies on GA-BP (Huang et al. 2009), the model becomes unstable when data are highly variable.

Comparing the GRNN model and the GA-GRNN model, we can see that the forecasted effect of the GA-GRNN is better than that of the GRNN. Therefore, the GA is needed for the process of searching for the proper value of spread in the GRNN. Comparing the GA-BP model and the GA-GRNN model, we can see that although both use a GA to optimize the parameters, the GA-GRNN's forecasted effect is better than that of the GA-BP. The BP requires a large number of data to be trained; thus, the GRNN model is more suitable than the BP when the amount of available data is limited.

On the one hand, the GRNN has the ability to map nonlinear data and is capable of processing unstable data; thus, the GRNN functions well in situations of data deficiency. On the other hand, using the GA to optimize parameters can improve the forecasting effect. As a corollary, using the GA-GRNN to forecast water quality under normal conditions, meaning that large-scale water pollution events do not occur, is feasible and effective.

CONCLUSIONS

This paper focuses on whether a GA-GRNN model can be used to forecast water quality under normal conditions. In the middle route of the South to North Water Transfer Project in China, which has stable water quality due to its design, water quality can be measured continuously and the indices that influence water quality are measurable. The data, which were acquired from the middle route of the South to North Water Transfer Project, were used to test and verify our hypothesis, and the conclusions are as follows:

  • (1)

    Compared with the BP or other models, the GRNN requires fewer network parameters and has good network stability, high learning speed and strong approximation ability; thus, it is more suitable for water quality prediction.

  • (2)

    The GA can increase the forecasting performance of the GRNN by searching for the best value of spread for each factor.

  • (3)

    The dimension of the matrix in the calculation of the GA-GRNN is far less than that of the GA-BP; thus, the forecasting speed of the GA-GRNN is faster.

In summary, the GA-GRNN method is efficient for water quality prediction under normal conditions. This paper verifies the feasibility of water quality forecasting using a systematic approach, providing a new concept of water quality forecasting for practical uses. So the methodology can be used to predict water quality accurately and quickly in normal conditions which is often overlooked but actually important. When applied to the South to North Water Transfer Project, the prediction system is able to obtain water quality of the next few days within ten minutes, hence specific methods can be utilized to improve water quality in the case of possible substandard situations. Therefore this paper plays an important role in the water security of the South to North Water Transfer Project.

ACKNOWLEDGEMENTS

The authors thank the referees and the editor for their valuable comment and suggestions on improvement of this paper. This work is supported by the National Science and Technology Major Special Project (No. 2012ZX07205005) and the National Natural Science Foundation of China (No. 51379150 and No. 51439006).

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