Projection Pursuit Evaluation Model of Regional

Water Resour Manage https://doi.org/10.1007/s11269-017-1872-6

Projection Pursuit Evaluation Model of Regional Surface Water Environment Based on Improved Chicken Swarm Optimization Algorithm Dong Liu 1,2,3,4 & Chunlei Liu 1 & Qiang Fu 1 & Tianxiao Li 1 & Muhammad Imran Khan 1 & Song Cui 1 & Muhammad Abrar Faiz 1

Received: 6 September 2016 / Accepted: 5 December 2017 # Springer Science+Business Media B.V., part of Springer Nature 2017

Abstract A Projection Pursuit Evaluation model of surface water environment based on an Improved Chicken Swarm Optimization Algorithm (ICSOA-PPE) is constructed using the ICSOA to optimize the optimal projection direction. Using the Jiansanjiang Administration in Heilongjiang Province, China as an example, 15 subordinate farms were used as an evaluation unit by selecting water quality indexes including CODMn, NH3-N, TP, TN, F− to evaluate the environmental quality of surface water using the ICSOA-PPE model. The results show that the environmental quality of surface water from all farms in this region was generally poor, except for that at the Qinglongshan, Qindeli and Daxing farms. These three farms met the standard for drinking water sources, while the remaining farms failed to reach the standard. By analyzing the relationship between the total amount of chemical fertilizer application per ha, the amount of nitrogen fertilizer application per ha, the amount of phosphate fertilizer application per ha and the environmental quality of the surface water, a conclusion could be reached that the total amount of chemical fertilizer has a substantial effect on water environment. Additionally, the contribution rate of the amount of nitrogen fertilizer application per ha to the organic pollution and the concentration of NH3-N is substantial, and the amount of phosphate fertilizer influences the water environmental quality to some extent. An analysis and comparison of the traversal capacity, the offset capacity and the convergence capacity of the Genetic Algorithm

* Qiang Fu [email protected]

1

School of Water Conservancy & Civil Engineering, Northeast Agricultural University, Harbin, Heilongjiang 150030, China

2

Key Laboratory of Effective Utilization of Agricultural Water Resources of Ministry of Agriculture, Northeast Agricultural University, Harbin, Heilongjiang 150030, China

3

Heilongjiang Provincial Collaborative Innovation Center of Grain production Capacity Improvement, Northeast Agricultural University, Harbin, Heilongjiang 150030, China

4

Key Laboratory of Water-Saving Agriculture of Ordinary University in Heilongjiang Province, Northeast Agricultural University, Harbin, Heilongjiang 150030, China

Liu D. et al.

(GA), the Chicken Swarm Optimization Algorithm (CSOA) and ICSOA reveal that ICSOA is the better optimization algorithm, indicating that the ICSOA-PPE model is logical and reliable. Keywords Water environmental quality . Improved chicken swarm optimization algorithm . Projection pursuit evaluation . Algorithm performance

1 Introduction The water environment is an important component of the ecological environment; it is one of the most complex factors in an environmental system and is closely linked with human production and life (Chen 2001). Human life and industrial and agricultural activities affect the water environment to varying degrees; in turn, the progressive deterioration of the water environmental quality can influence the living conditions of humans. An evaluation of water quality is the most important part of an environmental quality assessment of water, and it is important to perform a water quality assessment to discriminate the main pollutants, understand the water environmental quality and restore water environment. Currently, the primary methods of water quality assessment include the fuzzy artificial neural network (Khaki et al. 2015), health risk assessments (Haque et al. 2016; Nganje et al. 2015), the fuzzy matter-element model (Deng et al. 2015), the fuzzy comprehensive evaluation (Dahiya et al. 2007; Tao et al. 2009), gray relational analysis (Chen et al. 2007), support vector machine (Aryafar et al. 2012) and the Markov model method (Zheng and Han 2016). Each of these methods has their own advantages and disadvantages. In the fuzzy artificial neural network, it is difficult to set parameters, and it is easy to fall into a local minimum; additionally, the fuzzy artificial neural network has a slow convergence rate, poor stability and low resolution (Shao et al. 2010). The health risk assessment method only considers the harm to the human body caused by pollutants as a standard and is unilateral. The fuzzy matter-element model method may not be able to calculate a comprehensive correlative degree because the characteristic value of the matter-element to be calculated exceeds the segment field matterelement (Gong et al. 2015). For the fuzzy comprehensive assessment method, disadvantages in selecting assessment factors, determining weights, choosing operations and other aspects exist (Gong et al. 2015). The resolution of grey relational analysis is low (Li 2005). The support vector machine method requires numerous training samples. For the Markov model, the randomness of the state matrix is strong, and the results are not robust. Projection pursuit (Friedman and Tukey 1974) is a technology of dimensionality reduction that projects high-dimensional data to a low-dimensional space and explores these characteristics according to projection index values that reflect the structures and characteristics of high-dimensional data, opening a path to solve high-dimensional problems using a one-dimensional method (Bachmann et al. 1994). Projection pursuit is a datadriven method that avoids the interference of subjective factors; the results are objective and reasonable, thus attracting widespread attention. Jiang et al. (2015) conducted coherency detection using the projection pursuit theory in the China Southern Power Grid. Pei et al. (2016) constructed a projection pursuit model and used it to evaluate the agricultural drought vulnerability of Sanjiang Plain, China. Demirci et al. (2008) effectively discriminated schizophrenia from healthy persons using projection pursuit based on functional magnetic resonance imaging data. Ghasemi and Zolfonoun (2013) predicted the trace amounts of polycyclic aromatic hydrocarbons in water samples after magnetic solid-phase

Projection Pursuit Evaluation Model of Regional Surface Water...

extraction using projection pursuit regression. Gupta and Majumdar (2014) applied projection pursuit regression to the nonparametric estimation of the nonlinear long-run money-demand equation. The supervised and unsupervised classifications of hyperspectral imaging data were executed based on a method combining projection pursuit and Markov random field segmentation (Sarkar et al. 2012). Currently, projection pursuit is primarily used in power systems, agriculture, medicine, economy and remote sensing, but usage in water environments is poor. The evaluation grades of each index are incompatible; thus, a comprehensive evaluation of water quality cannot be executed. The Projection Pursuit Evaluation (PPE) model can reasonably and rigorously simplify the high-dimensional evaluation problem of water quality to a one-dimensional pattern, and then, it can be used determine the evaluation intervals of each grade, therefore enabling a synthetic evaluation for the water quality (Wang et al. 2004). The key to using the projection pursuit model is to determine the optimal projection direction. The determination of the optimal projection direction is a complex, high-dimensional nonlinear optimization problem, and the optimization methods commonly used include the Particle Swarm Optimization Algorithm (PSOA) (Berro et al. 2010), the Free Search Algorithm (FSA) (Shao et al. 2010), the Genetic Algorithm (GA) (Espezua et al. 2014), the Ant Colony Algorithm (ACA) (Chen et al. 2008), and the Firefly Algorithm (FA) (Ma et al. 2015). In optimizations, these algorithms cannot always converge to the global optimal solution, and they lack robustness and tend to fall into premature convergence. The Chicken Swarm Optimization Algorithm (CSOA) (Meng et al. 2014) is a stochastic optimization algorithm that optimizes objective functions by simulating the hierarchy in chicken swarms and the movement patterns of chickens in their foraging behavior. Studies (Hafez et al. 2015; Wu et al. 2015) reveal that the CSOA can jump out of local optimization and reach a global optimum with higher probability compared with, e.g., PSO and GA; it also has strong robustness and a high success rate. However, among the high-dimensional optimization problems, the convergence accuracy of CSOA is low, and it is prone to premature convergence. Therefore, the Improved Chicken Swarm Optimization Algorithm (ICSOA) (Wu et al. 2015) that modifies the position update equation of the chicks was proposed. The selflearning coefficient and the part that chicks learn from the group-mate rooster are introduced into the position update equation, effectively avoiding the premature convergence problems of high-dimensional optimization. The objectives of this paper are as follows. (1) Construct a Projection Pursuit Evaluation model of the surface water environment based on the Improved Chicken Swarm Optimization Algorithm (ICSOA-PPE) and evaluate the environmental quality of surface water from each farm in the Jiansanjiang Administration, Heilongjiang Province, China. (2) Analyze the causes of the present situation of the water environment by exploring the relationships among elevation, slope, the total amount of chemical fertilizer application per ha, the amount of nitrogen fertilizer application per ha, the amount of phosphate fertilizer application per ha and water environmental quality. (3) In contrast to ICSOA-PPE, analyze the reasonability and validity of the evaluation methods of water quality, such as the Nemerow Index Method and the Grey Relational Analysis Method. (4) Compare and analyze the performance of GA, CSOA and ICSOA in terms of traversal capacity, offset capacity and convergence capacity.

Liu D. et al.

2 Materials and Methods 2.1 Study Area The Jiansanjiang Administration, which is part of the confluence zone of the Heilongjiang River, the Ussuri River and the Songhua River, is located in northeast Heilongjiang Province. The geographic coordinates are between 46° 49′-48° 12’ N and 132° 31′-134° 32′ E (Lv et al. 2011). The terrain is low and flat. Elevations in mountainous and hilly areas located in the northwest and southeast of the region are 100–611 m; most of the remaining area is a low plain and marsh, and the elevation is 32–100 m. The ground surface slope is small, except for the northwestern and southeastern part of the region; the remaining area is below 5°. There are 15 farms in the Jiansanjiang Administration; the location and administrative division are shown in Fig. 1. Because of the large amount of fertilizer application, the primary pollution type is agricultural non-point source pollution. Because a large quantity of surface water and groundwater is pumped for irrigation, irrigation water is discharged into rivers, lakes and drainage ditches through paddy fields carrying soil nutrients and pollutants. In addition, the process of runoff yield and concentration can also carry pollutants into water bodies. Therefore, the surface water pollution in this area has become increasingly serious, and the water environment conditions are deteriorating. Water environmental quality can be determined macroscopically; the main pollutants can be identified, and the basis for improving water environmental quality can be provided by carrying out an evaluation of the surface water quality.

2.2 Data Resources During the ponding period in May 2016, 15 representative sampling points were selected, and the positions of the sampling points are shown in Fig. 1. Three water samples were obtained at each point; then, the concentrations of CODMn, NH3-N, TP, and TN, F− were measured using a Hach DR 2800 Spectrophotometer manufactured by Hach Company in Loveland, Colorado, USA, and the average concentrations of three water samples at each point are used to represent the concentration at this point. The average concentrations of several sampling points were used to represent the concentrations of some farms according to the positional relationship between the sampling points and farms. The concrete corresponding relationship and concentration diagrams of each index in every farm are shown in Fig. 2. Twelve years (2004–2015) of data were sorted into the total amount of chemical fertilizer application per ha, the amount of nitrogen fertilizer application per ha, and the amount of phosphate fertilizer application per ha from the Statistical Yearbook of Jiansanjiang Administration; the data from 2015 were prolonged according to changes in the data laws from 2004 to 2014. Overproof analysis of several water quality indexes is supported by these data.

2.3 Projection Pursuit Evaluation Model The basic modeling steps of the PPE model are as follows (FU et al. 2003). Step 1:

Data preprocessing. Let the standard sample that is set for each grade be {x∗(i, j)|i = 1~m, j = 1~n}, where x∗(i, j) is the value of the ith grade of the jth index, and m and n represent the number of grades and indexes, respectively. To eliminate the dimension of each index and unified variation ranges, the normalization method is adopted as follows.

Projection Pursuit Evaluation Model of Regional Surface Water...

Fig. 1 Location of study area and the administrative division of the Jiansanjiang administration

For the index when the high value represents serious pollution: xði; jÞ ¼

x* ði; jÞ−xmin ð jÞ xmax ð jÞ−xmin ð jÞ

ð1Þ

For the index when the low value represents serious pollution: xði; jÞ ¼

xmax ð jÞ−x* ði; jÞ xmax ð jÞ−xmin ð jÞ

ð2Þ

where xmax(j)、xmin(j) are the maximum and minimum values of the jth index in the standard sample set, respectively, and x(i, j) is the index value after normalization. Step 2:

Construction of the projection index function. The n dimensional data {x∗(i, j)|j = 1~n} can be synthesized to the projection value z(i) with one dimension using a = {a(1), a(2), a(3), ⋯, a(n)} as the projection direction, as follows:

n

zðiÞ ¼ ∑ að jÞxði; jÞ ði ¼ 1∼mÞ

ð3Þ

j¼1

where a is a unit vector. The projection index function is defined as follows: QðaÞ ¼ S z Dz

ð4Þ

Liu D. et al.

Fig. 2 Relationship of the sampling points and farms: a farm might contain several sampling points, and the average concentrations of these sampling points represent the concentration of the farm; Concentration of water quality indexes at each farm of the Jiansanjiang Administration: the 5 bars represent 5 indexes, and the height of the bar reflects the concentration magnitude

where Sz and Dz are the standard deviation and local kernel density of z(i), respectively.

Sz ¼

m

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi um u ∑ ðzðiÞ−E ðzÞÞ2 t

m

i¼1

m−1

Dz ¼ ∑ ∑ ðR−rði; jÞÞ⋅uðR−rði; jÞÞ

ð5Þ

ð6Þ

i¼1 j¼1

Here, E(z) is the expectation of {z(i) | i = 1~m}; R is the window radius of Dz that can be determined experimentally (Friedman and Tukey 1974); r(i, j) is determined by r(i, j) = |z(i) − z(j)|; and u(t) is a unit step function, u(t) = 1 when t ≥ 0, otherwise u(t) = 0.

Projection Pursuit Evaluation Model of Regional Surface Water...

Step 3:

Optimization of the projection index function Q(a). The optimal projection direction can maximally expose the feature structure of high-dimensional data and can be estimated by optimizing the projection index function. 8 < Max : QðaÞ ¼ S z ⋅Dz p

2 : s:t: ∑ a ð jÞ ¼ 1

ð7Þ

j¼1

Step 4:

Grade Evaluation. The normalization sequence x(i, j) and optimal projection direction a∗ determined through Step 3 are introduced into Eq. (3) to calculate the projection values of each standard grade. The PPE model y∗ = f(z∗) is constructed according to the grades and corresponding projection values. The normalized sample set is evaluated, and the projection values z(i) are calculated, introducing z(i) into y∗ = f(z∗) to obtain the grades for each sample.

2.4 Chicken Swarm Optimization Algorithm (1) Standard Chicken Swarm Optimization Algorithm The CSOA follows four hypotheses. Hypothesis 1:

There is more than one subgroup in the whole chicken swarm. Each subgroup comprises one rooster and at least one hen while the remaining are chicks. Hypothesis 2: Divide all chickens into three types, including roosters, hens and chicks, according to the fitness values. Individuals with the best fitness value are defined as roosters, and each of them leads a subgroup. The individuals that have the worst fitness values are designed as chicks, and the remaining are hens. The hens randomly choose subgroups to live within; chicks choose hens randomly and establish a mother-child relationship with the hens. Hypothesis 3: The hierarchical order, affiliation and mother-child relationship remain invariant once they are established and are only updated after a specific number of iterations. Hypothesis 4: All individuals in a subgroup follow the only rooster to look for food. Roosters have priority for food followed by the hens and then the chicks. During optimization, each individual represents a solution to the optimization problem. Assume N is the number of the whole chicken swarm, the position xi, j(t) indicates the value of the ith individual in the jth dimension in the tth iteration. There are three types of chickens in the whole chicken swarm, and the position update equation differs with different chicken species. The position update equation of roosters is as follows:    xi; j ðt þ 1Þ ¼ xi; j ðt Þ⋅ 1 þ Randn 0; σ2

ð8Þ

Liu D. et al.

σ2 ¼

8
15

≤ 0.15 ≤ 0.5 ≤ 0.625 ≤ 0.75 ≤ 0.875 ≤1 ≤ 1.125 ≤ 1.25 ≤ 1.375 ≤ 1.5 ≤2 >2

≤ 0.02 ≤ 0.1 ≤ 0.125 ≤ 0.15 ≤ 0.175 ≤ 0.2 ≤ 0.225 ≤ 0.25 ≤ 0.275 ≤ 0.3 ≤ 0.4 >0.4

≤ 0.2 ≤ 0.5 ≤ 0.625 ≤ 0.75 ≤ 0.875 ≤1 ≤ 1.125 ≤ 1.25 ≤ 1.375 ≤ 1.5 ≤2 >2

≤1 ≤1 ≤1 ≤1 ≤1 ≤1 ≤ 1.125 ≤ 1.25 ≤ 1.375 ≤ 1.5 ≤ 1.5 >1.5

Projection Pursuit Evaluation Model of Regional Surface Water... Table 2 Classification standards of water quality evaluation Grade

Fitting values

Fitting values

Fitting values

I II III-1 III-2 III-3 III-4

[0, 1] (1, 2] (2, 2.25] (2.25, 2.5] (2.5, 2.75] (2.75, 3]

IV-1 IV-2 IV-3 IV-4 V Worse V

(3, 3.25] (3.25, 3.5] (3.5, 3.75] (3.75, 4] (4, 5] >5

As shown in Fig. 4, the water environmental quality in the Jiansanjiang Administration is poor in general. Except for the Farm Qinglongshan, the Farm Qindeli and the Farm Daxing, the grades of water environmental quality of the remaining farms are higher than III-4 and do not meet the standard for a drinking water source. Water environmental quality appears to have spatial distribution characteristics, namely, the water environmental quality of farms in the central region is worse and that at the remaining farms is better. This finding is related to the total amount of fertilizer application per ha, the amount of nitrogen fertilizer application per ha, and the amount of phosphate fertilizer application per ha. Then, the spatial correlation coefficients between the amount of chemical fertilizer application and projection value sequences, CODMn, NH3-N, TP, TN sequences are calculated as shown in Table 3.

Fig. 4 Partition of the environmental quality of each farm

Liu D. et al. Table 3 Spatial correlation coefficients between the amount sequences of chemistry fertilizer application and each index

Total amount of chemistry fertilizer application The amount of nitrogen fertilizer application The amount of phosphate fertilizer application

Projection value series

CODMn

NH3 -N

TP

TN

0.547873 0.163211 0.212365

0.215159 0.320168 0.191313

0.378555 0.535932 –

0.460268 – 0.224553

0.578473 0.1972565 –

As Table 3 shows, the coefficients between the total amount of chemical fertilizer application per ha and projection value sequences, CODMn, NH3-N, TP, and TN, are positive and relatively strong, indicating that the total amount of chemical fertilizer has a great effect on water environmental quality and the concentrations of each index. The coefficients between the amount of nitrogen fertilizer application per ha and projection value sequences, CODMn, NH3-N, and TN, are positive, and the coefficients between the amount of nitrogen fertilizer application per ha and CODMn and NH3-N sequences are high, indicating that the contribution rate to the organic pollution and the concentration of NH3-N is high. There is a positive correlation between the amount of phosphate fertilizer application per ha and the projected value sequences, CODMn, and TP sequences, revealing that the amount of phosphate fertilizer application per ha influence the water environmental quality to some extent. Furthermore, the elevation of the farms located in the northwest region is high, and the ground surface slope is great; thus, the flow velocity and the update speed of water bodies is large, and the pollutants are not easily retained. The central region is located in the hinterland of the Sanjiang Plain and has a low elevation, small slope, and slow catchment speed; thus, contaminates tend to remain. This is also one of the reasons that water environmental quality presents spatial distribution characteristics.

3.4 Surface Water Quality Evaluation Method Comparison To verify the accuracy of the evaluation results, the Single Index Evaluation Method (SIEM), the Nemerow Index Method (NIM) (Ji et al. 2016) and the Grey Relational Analysis Method (GRAM) (Chen et al. 2007), the Projection Pursuit Evaluation model based on the Genetic Algorithm (GA-PPE) and the Projection Pursuit Evaluation model based on the Chicken Swarm Optimization Algorithm (CSOA-PPE) are used to evaluate the environmental quality of surface water of 15 farms. Then, the results are compared with ICSOA-PPE. By comparison, it’s found that the evaluation results of GA-PPE and CSOA-PPE are consistent with those of ICSOA-PPE, therefore, only ICSOA-PPE is displayed. The evaluation results are as shown in Table 4. (1) It can be seen from the evaluation results of SIEM in Table 4 that the concentrations of some water quality indexes are high at each farm, including TP and TN followed by CODMn and NH3-N, indicating that the eutrophication degree is high in the study area. This result is closely related to the industrial structure in the study area in which agricultural production is the main fraction. According to the data of the amount and area of chemical fertilizer application in the Jiansanjiang Administration in 2004– 2015, the total amount of chemical fertilizer application per ha is calculated (pure amount, the same below) (144.0328, 146.7327, 134.6402, 164.5235, 160.2002, 164.1707, 170.3581, 187.4615, 189.5645, 186.9779, 181.0189, 205.5191). Data

Projection Pursuit Evaluation Model of Regional Surface Water... Table 4 Comparison of water quality evaluation results Farm

CODMn

NH3 -N

TP

TN

F−

NIM

GRAM

ICSOA-PPE

Chuangye Hongwei Shengli 859 Qianfeng Erdaohe Qianshao Yalvhe Qindeli Nongjiang Qinglongshan Honghe Qianjin Qixing Daxing

IV-4 IV-1 V V IV-1 IV-1 IV-4 V V IV-4 V IV-4 V V IV-4

III-2 IV-4 III-4 II III-3 III-3 III-3 III-4 I III-2 I I Worse V III-4 II

Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V III-3 Worse V IV-2 III-4 Worse V V III-4

Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V III-2 Worse V Worse V Worse V Worse V

I I I I I I I I I I I I I I I

Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V Worse V

III-3 III-4 IV-3 III-1 III-1 IV-1 III-4 IV-2 III-4 III-3 III-4 IV-1 IV-1 IV-1 IV-2

IV-2 IV-3 V V IV-4 IV-4 IV-1 IV-4 III-1 IV-3 II IV-2 Worse V IV-3 III-4

promulgated by the Ministry of Agriculture of the People’s Republic of China shows that the total amount of chemical fertilizer application per ha in China is 328.5 kg, and the global average is 120 kg. According to the Statistical Yearbook of Heilongjiang Province, the total amount of chemical fertilizer application per ha is 158.7 kg. According to the calculation results, the total amount of chemical fertilizer application per ha in the Jiansanjiang Administration is more than 120 kg annually and shows a rising trend, with an average increase of 5.4702 kg/a. After 2009, the total amount of chemical fertilizer application per ha exceeded 157.5 kg. Although the total amount of chemical fertilizer application per ha is below the national average, it is higher than the global average and is higher than the average in the Heilongjiang Province in recent years. A high amount of chemical fertilizer application and low utilization rate combined with a vast area of paddy fields and a high degree of water exchange among irrigation and drainage in the paddy fields lead to increasing losses of water and soil. Fertilizers included in drainage water are discharged into the rivers, lakes and other water bodies, causing serious agricultural non-point source pollution. This is the main reason that the concentrations of indexes such as TN, CODMn and NH3-N are too high in the Jiansanjiang Administration. (2) We can see that the evaluation results of NIM, GRAM and ICSOA-PPE are not consistent. The reasons may be as follows: 1) NIM neglects the weights of pollution factors in water quality assessments and only considers the primary pollution factor and the average effect of all pollution factors. NIM excessively highlights the primary factor, which may lead to the high composite score. For example, the grade of CODMn at the Farm Qinglongshan is V, and its score is 10, the grade of TP is IV-2, and it score is 4.5, and the grade of TN is III-2, and its score is 2. The grades of the other two indexes are I, and they scored a 0. The comprehensive score reaches 7.44614, which is too high. Under the conditions in which a high concentration exists, the evaluation result of NIM must be carefully considered. 2) The resolution of the evaluation results of GRAM is not high, and the Farm Qixing and the Farm Qianjin are cited to illustrate the phenomenon. As shown in Fig. 2, concentrations of NH3-N and TN at the Farm Qiqing are far lower than those at the Farm Qianjin, but the evaluation results of GRAM are consistent. It is not beneficial to improve discriminability.

Liu D. et al.

3.5 Performance analysis of the Optimization Algorithm GA, CSOA and ICSOA, are used to optimize the projection direction of the PPE model of the surface water environment. The performance of the three optimization algorithms are analyzed and compared regarding traversal capacity, offset capacity and convergence capacity (Liu et al. 2016). (1) Traversal capacity To determine the optimal solution and to avoid falling into local optimization, an intelligent optimization algorithm should maintain the diversity of the samples. This ability is called traversal capacity, which can be evaluated by the variety of samples, and the variety of samples can be reflected by the same sample probability in each iteration, as in Eq. (15): ω¼

X d¼0  100% C 2N

ð15Þ

where d is the Euclidean distance of two samples (d = 0 indicates that the two samples are the same); Xd = 0 represents the number of samples for which the Euclidean distances are 0 in a iteration; and N is the number of samples in a iteration, this value is 50 in this study; C 2N is the combinatorial number. The diversity of the samples of GA, CSOA and ICSOA is shown in Fig. 5. As shown in Fig. 5a, the probability of the same samples of GA is 0–0.45%, indicating that GA has a higher diversity of samples and that the traversal capacity is strong. However, the ability to search a region emphatically is weak, and the convergence speed may be inhibited. As shown in Fig. 5b, the peak of the proportion curve of the same samples of CSOA occurs in the 18th iteration, and the values increase after 70 iterations, indicating that the traversal capacity is weak in the two periods. Fig. 5c shows that many peaks occur in the proportion curve of the same samples of ICSOA, illustrating that ICSOA constantly maintains the diversity of the samples to avoid local convergence. ICSOA can search certain regions emphatically and increase the convergence speed. (2) Offset capacity The largest difference between intelligent optimization algorithms and simple random searching algorithms is that intelligent optimization algorithms can execute the next search specifically based on the information obtained from the previous search. The blindness of the search can be reduced, and the search process can accelerate. This ability of intelligent optimization algorithms to stress searching is called offset ability. The mean value of samples can characterize the offset capacity of an intelligent optimization algorithm: Eð f ðSÞÞ=Eð f ðUÞÞ > 1

ð16Þ

where S represents the random sampling variables of intelligent optimization algorithms. U represents the random variables that are uniformly sampled in the feasible solution. The sampling step size used in this study was 2. The offset capacity for GA is 0.9981 and for CSOA is 1.0135, which is smaller than that for ICSOA 1.2046. This finding illustrates that the offset capacity for ICSOA is stronger than that of the other algorithms and that ICSOA can search certain areas frequently; thus, it is beneficial to find the global optimum for ICSOA.

Projection Pursuit Evaluation Model of Regional Surface Water... 0.5

14

(a) Probability(%)

Probability(%)

0.3 0.2

10

0.1 0

(b)

12

0.4

8 6

4 2

0

20

40

60

80

0

100

0

20

40

16

80

100

(c)

14 Probability(%)

60 Iteration

Iteration

12 10

8 6 4 2

0

0

20

40

60

80

100

Iteration

Fig. 5 Traversal capacity of G0041 (a), CSOA (b) and ICSOA (c)

(3) Convergence capacity The convergence of GA, CSOA and ICSOA is shown in Fig. 6. GA reaches an optimal solution in the 68th iteration, with an optimal value of 2149.6008. CSOA obtains the optimal solution in the 62nd iteration, with an optimal value of 2154.8854. ICSOA presents an optimal solution in the 57th iteration, with an optimal value of 2155.1206. It can be seen that ICSOA can converge to the global optimum faster than the other two algorithms and then avoid falling into local optimization. In summary, ICSOA is much better than GA and CSOA in terms of traversal capacity, offset capacity and convergence capacity, and it can obtain the better global optimum. 2200 GA ICSOA CSOA

2000

Fitness

1800 1600 1400 1200 1000 800

10

20

30

40

50

Iteration

Fig. 6 Convergence ability of GA, CSOA and ICSOA

60

70

80

90

100

Liu D. et al.

Therefore, the optimal projection direction optimized by ICSOA is most reasonable and may expose data structure features to the greatest extent; thus, the reliability of the ICSOA-PPE model is verified.

4 Conclusions (1) Optimal projection direction is optimized by ICSOA, and the ICSOA-PPE model of water environmental assessment is constructed. The ICSOA-PPE model solves the incompatible problem of water environmental quality comprehensive evaluation. (2) By comparing and analyzing the evaluation results of NIM, GRAM and ICSOA-PPE, a conclusion can be drawn that NIM highlights the largest pollution factor excessively and its evaluation results are high; the resolution of GRAM is low; the ICSOA-PPE model can obtain the optimal projection direction and then objectively determine the degree of influence that indicates water quality. The ICSOA-PPE model evaluation results are reasonable and reliable. (3) According to the evaluation results from the ICSOA-PPE model, the farms in the Jiansanjiang Administration do not reach the standard for drinking water sources, except for the Farm Qinglongshan, the Farm Qindeli and the Farm Daxing. This result indicates that water pollution is serious and that the water environment situation is bleak. The situation couples the action results of the high amount of chemical fertilizers application and the high elevation. The total amount of chemical fertilizer application per ha exerts a greater influence on the water environmental quality than the other studied parameters. The amount of nitrogen fertilizer application per ha has a great effect on organic pollution and NH3-N concentration. The amount of phosphate fertilizer application per ha influences the water environmental quality to some degree. (4) Compared with GA and CSOA, ICSOA has advantages in traversal capacity, offset capacity and convergence capacity, and it can obtain a better global optimum. Therefore, the optimal projection direction optimized by ICSOA is reasonable, making the water environment classification more reasonable. (5) The determination of local window radius and the constructive mode of the projection index function affect the optimal projection direction and influence the results of the evaluation. Further studies must be performed to determine the window radius and the constructive mode of the projection index function using a scientific and rational method. In addition, predicting the water environmental quality based on the collection of the time series of water quality is the direction of further study.

Acknowledgements This study is supported by the National Natural Science Foundation of China (No.51579044, No.41071053, No.51479032), National Key R&D Program of China (No.2017YFC0406002), Natural Science Foundation of Heilongjiang Province (No.E2017007), Science and Technology Program of Water Conservancy of Heilongjiang Province (No.201319, No.201501, No.201503). Novelty

1. An composite evaluation model of surface water environment named ICSOA-PPE is proposed. 2. Compared with NIM and GRAM, the ICSOA-PPE model can objectively reflect the water environmental quality.

Projection Pursuit Evaluation Model of Regional Surface Water...

3. ICSOA is superior to GA and CSOA in traversal capacity, offset capacity and convergence capacity, and it can obtain a better global optimum.

4. The spatial variation characteristic of surface water environment and the possible causes are analyzed.

References Aryafar A, Gholami R, Rooki R, Doulati Ardejani F (2012) Heavy metal pollution assessment using support vector machine in the Shur River, Sarcheshmeh copper mine, Iran. Environ Earth Sci 67(4):1191–1199. https://doi.org/10.1007/s12665-012-1565-7 Bachmann CM, Musman SA, Luong D, Schultz A (1994) Unsupervised BCM projection pursuit algorithms for classification of simulated radar presentations. Neural Netw 7(4):709–728. https://doi.org/10.1016/08936080(94)90047-7 Berro A, Larabi Marie-Sainte S, Ruiz-Gazen A (2010) Genetic algorithms and particle swarm optimization for exploratory projection pursuit. Ann Math Artif Intell 60(1-2):153–178. https://doi.org/10.1007/s10472- 0109211-0 Chen XH (2001) Water environment assessment and planning. SUN Yat-sen University Press, Guangzhou Chen J, Zhu JM, Wang ZY, Liu XH, Zhang XL (2007) Application of Grey relational analysis in water quality evaluation. J Grey Syst 19(1):99–106 Chen GZ, Wang JQ, Li CJ (2008) Solving the optimization of projection pursuit model using improved ant Colony algorithm. In: Fourth International Conference on Natural Computation pp 521–525. doi: https://doi. org/10.1109/ICNC.2008.582 Dahiya S, Singh B, Gaur S, Garg VK, Kushwaha HS (2007) Analysis of groundwater quality using fuzzy synthetic evaluation. J Hazard Mater 147(3):938–946. https://doi.org/10.1016/j.jhazmat.2007.01.119 Demirci O, Clark VP, Calhoun VD (2008) A projection pursuit algorithm to classify individuals using fMRI data: application to schizophrenia. NeuroImage 39(4):1774–1782. https://doi.org/10.1016/j. neuroimage.2007.10.012 Deng XJ, YP X, Han LF, ZH Y, Yang MN, Pan GB (2015) Assessment of river health based on an improved entropy-based fuzzy matter-element model in the Taihu plain, China. Ecol Indic 57:85–95. https://doi. org/10.1016/j.ecolind.2015.04.020 Espezua S, Villanueva E, Maciel CD (2014) Towards an efficient genetic algorithm optimizer for sequential projection pursuit. Neurocomputing 123:40–48. https://doi.org/10.1016/j. neucom.2012.09.045 Friedman JH, Tukey JW (1974) A projection pursuit algorithm for exploratory data analysis. IEEE Trans Comput 23(9):881–890. https://doi.org/10.1109/T- C.1974.224051 Fu Q, Xie YG, Wei ZM (2003) Application of projection pursuit evaluation model based on real-coded accelerating genetic algorithm in evaluating wetland soil quality variations in the Sanjiang plain, China. Pedosphere 13(3):249–256 Ghasemi JB, Zolfonoun E (2013) Simultaneous spectrophotometric determination of trace amount of polycyclic aromatic hydrocarbons in water samples after magnetic solid-phase extraction by using projection pursuit regression. Environ Monit Assess 185(3):2297–2305. https://doi.org/10.1007/s10661-012-2709-7 Gong YC, Zhang Y, Ding F, Hao J, Wang H, Zhang D (2015) Projection pursuit model for assessment of groundwater quality based on firefly algorithm. J China Univ Min Technol 44(3):566–572 Gupta R, Majumdar A (2014) Reconsidering the welfare cost of inflation in the US: a nonparametric estimation of the nonlinear long-run money-demand equation using projection pursuit regressions. Empir Econ 46(4): 1221–1240. https://doi.org/10.1007/s00181-013 -0721-6 Hafez AI, Zawbaa HM, Emary E, Mahmoud HA (2015) An innovative approach for feature selection based on chicken swarm optimization. In: international conference on soft computing and pattern recognition, IEEE. Vol 2. Pp 269-279 Haque MM, Al Attas HA, Hassan MA (2016) Health risk assessment of trace elements in drinking water from Najran City, southwestern Saudi Arabia. Arab J Geosci 9(6):1–12. https://doi.org/10.1007/ s12517-016-2501-z Ji XL, Dahlgren RA, Zhang M (2016) Comparison of seven water quality assessment methods for the characterization and management of highly impaired river systems. Environ Monit Assess 188(1):1–16 Jiang T, Jia HJ, Yuan HY, Zhou N (2015) Projection pursuit: a general methodology of wide-area coherency detection in bulk power grid. IEEE Trans Power Syst 31(4):1–11 Khaki M, Yusoff I, Islami N (2015) Application of the artificial neural network and neuro-fuzzy system for assessment of groundwater quality. CLEAN – Soil, Air, Water 43(4):551–560. https://doi.org/10.1002 /clen.201400267 Li RZ (2005) Progress and trend analysis of theoretical methodology of water quality assessment. J Hefei Univ Technol 28(4):369–373

Liu D. et al. Liu D, Hu YX, Fu Q, Imran KM (2016) Optimizing channel cross-section based on cat swarm optimization. Water Sci Technol Water Supply 16(1):219–228. https://doi.org/10.2166/ws.2015.128 Lv P, Liu D, Zhao FF (2011) Comprehensive evaluation of water resources carrying capacity in Jiansanjiang branch bureau. Adv Mater Res 204-210:834–837. https://doi.org/10.4028/www.scientific.net/AMR.204210.834 Ma Y, Zhao YX, LG W, He YX, Yang XS (2015) Navigability analysis of magnetic map with projecting pursuitbased selection method by using firefly algorithm. Neurocomputing 159(1):288–297. https://doi.org/10.1016 /j.neucom.2015. 01.028 Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. In: Tan Y, Shi YH, Coello CAC (eds) Advances in swarm intelligence: 5th international conference, ICSI 2014, Hefei, China, October 17–20, 2014, proceedings. Part I. Springer International Publishing, Cham, pp 86–94. https://doi.org/10.1007/978-3-319-11857- 4_10 Nganje TN, Hursthouse AS, Edet A, Stirling D, Adamu CI (2015) Assessment of the health risk, aesthetic and agricultural quality of rainwater, surface water and groundwater in the shale bedrock areas, southeastern Nigeria. Water Qual Expo Health 7(2):153–178. https://doi.org/10.1007/ s12403-014-0136-4 Pei W, Fu Q, Liu D, Li TX, Cheng K (2016) Assessing agricultural drought vulnerability in the Sanjiang plain based on an improved projection pursuit model. Nat Hazards 82(1):683–701. https://doi.org/10.1007/ s11069-016-2213-4 Sarkar A, Vulimiri A, Paul S, Iqbal J, Banerjee A, Chatterjee R, Ray SS (2012) Unsupervised and supervised classification of hyperspectral imaging data using projection pursuit and Markov random field segmentation. Int J Remote Sens 33(18):5799–5818. https://doi.org/10.1080/ 01431161.2012.670959 Shao L, Zhou XD, Yang FT, Han J (2010) Projection pursuit model for comprehensive evaluation of water quality based on free search. China Environ Sci 30(12):1708–1714 Tao L, Cai SM, Yang HD, Wang XL, SJ W, Ren XY (2009) Fuzzy comprehensive-quantifying assessment in analysis of water quality: a case study in Lake Honghu, China. Environ Eng Sci 26(2):451–458. https://doi. org/10.1089/ees.2007.0270 Wang SJ, Yang ZF, Ding J (2004) Projection pursuit cluster model and its application in water quality assessment. J Environ Sci 16(6):994–995 Wu, DH Kong F, Gao WZ, Shen YX (2015) Improved chicken swarm optimization. In: The 5th Annual IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems pp 681–686. doi: https://doi.org/10.1109/CYBER.2015.7288023 Xiong P, Lou WG (2016) Determination and analysis of reasonable value of key parameter in projection pursuit clustering modelling. Comput Eng Appl 52(9):50–55 Zheng Y, Han F (2016) Markov chain Monte Carlo (MCMC) uncertainty analysis for watershed water quality modeling and management. Stoch Env Res Risk A 30(1):293–308. https://doi.org/10.1007/ s00477-0151091-8