This study is based on the national river cross-sectional water quality monitoring dataset, the location of water quality monitoring points ( Figure 1 ), where the Yangtze River and Huaihe River basins are the most abundant river water resources, and the basin area of about 1.27 million square kilometers. It is also based on the river flows through Henan, Jiangsu, Hubei, Zhejiang, Hunan, Fujian, and other provinces and autonomous regions, affecting more than 250 million residents. Therefore, it isof great strategic importance to monitor the water quality of domestic rivers and protect the water quality safety of rivers. At the same time, the data and information obtained from monitoring can also provide a scientific basis for pollution source control, environmental planning, etc.

The dataset used in this paper is the monthly data of water quality monitoring at each river cross-section nationwide from January to December 2021 ( Table 1 ). The monitoring dataset consists of seven parameter features, including dissolved oxygen, temperature, turbidity, ammonia nitrogen, permanganate index, ph, and total dissolved solid.

According to China’s Surface Water Environmental Quality Standard (GB3838-2002), water quality in the dataset was divided into six different categories, including I, II, III, IV, V, and poor V ( Table 2 ). Considering that there are no standard limits forturbidity and total dissolved solid of river cross-section water quality, the standard limits for turbidity and total dissolved solid of drinking water were used in the evaluation process. Water quality responds to the impact of industry, agriculture, and other sources of river water pollution along the river on water quality.

GRA is a method for assessing the degree of interaction between indicators through geometric similarity between them (Zhang et al., 2021), and it takes a leveling treatment of the indicators. Sutadian et al. proposed a subjectively empowered method for calculating the correlation of indicators (Sasikumar et al., 2022). Miao, C et al. also introduced an objectively assigned indicator correlation calculation (Xu et al., 2020). However, their method only considers the influence of a single factor on the correlation of indicators rather than considering subjective and objective factors together. Hence, the results often do not accurately reflect the correlation between indicators. To compensate for this deficiency, the ACGRA method was proposed in this paper. The calculation process and equation are as follows:

Set the parent indicator X ₀(i)={x ₀(1),x ₀(2),…,x ₀(i)} , where X ₀(i) denotes the water quality category of the first i water quality data of X ₀, and x ₀ (i) is for the water quality category of the i water quality data. Then set the subindex X _j (i)={x _j (1),x _j (2),…,x _j (i)} , where X _j (i) represents the first i water quality data of X_j , and x_j (i) indicates the i water quality data of X_j . Set the parent indicator X ₀(i)={x ₀(1),x ₀(2),…,x ₀(i)} , where X ₀(i) denotes the water quality category of the first i water quality data of X ₀, and x ₀(i) is for the water quality category of the i water quality data. Then, set the subindex X _j (i)={x _j (1),x _j (2),…,x _j (i)} , where X j (i) represents the first i water quality data of X_j , and x_j (i) indicates the i water quality data of X_j . Thedata are normalized, where X_j (i) is the normalized value of the subindex.

Determine the number of grey-off contacts, where s _j (i) is the PSO-MSVM coefficient between the subindex and the parent index. In addition, Δ _max  and Δ _min  are the maximum and minimum values of X ₀(i) and X _j (i)^' absolute difference, respectively, and ρ is the difference coefficient, which is usually set to 0.5 (Zavareh et al., 2021).

Calculate weight. First, the hierarchical structure was constructed for the research problem, after which the comparison matrix Q=(q _jl ) _n×n was obtained using the 1-9 level scaling method (Coffey and Claudio, 2021), and then the comparison matrix was calculated using Eq. (3) to obtain subjective weights α _j as follows:

The amount of information C _j for each attribute can be computed using Eq. (4), where σ _j denotes the standard deviation of each indicator, and r _ij is the correlation coefficient of the i indicator data with the jcategory.

The objective weight β _j of each attribute can be determined by Eq. (5) as:

Eq. (6) was used to calculate the combination weights ω _j

Eq. (7) was employed to compute the index correlation r(j) .

An SVM is a binary classifier that can only distinguish between two different water quality categories. There are currently two methods for SVMs to solve multi-classification problems, including one-to-over (OVR) (Abe, 2015) and one-to-one (OVO) (El Mamoun et al., 2019). OVR is the synthesis of multiple categorical solution problems into a single optimization solution problem that seeks to be solved in one go. However, it is not often used due to its high computational complexity, difficulty in implementation, and low accuracy. In this paper, OVO was applied to solve the multi-classification problem. It is to design a hyperplane between any two classes of samples to construct k ( k − 1 ) 2 classifiers. When classifying the unknown samples, the classifier takes a vote, and the final category with the most votes is the category of the unknown samples.

The choice of SVM parameters and the quality of the kernel function have a great impact on the performance of the SVM model (Haixiang et al., 2017). Table 3 provides the commonly used kernel functions and their corresponding parameters. Given that the kernel function chosen in this paper is the radial basis kernel function, the optimal values of parameters C and r should be considered to obtain accurate evaluation results. In this paper, we use particle swarm algorithm to optimize SVM parameters, so as to further improve its water quality assessment accuracy.

PSO is a population-based intelligent optimization stochastic search algorithm (Lu et al., 2022). First, the initialized particle swarm is generated as a solution in the feasible space. Then, the search iterations continue among the particles to continuously modify the feasible solutions and finally find the global optimal solution G _bt (Hameed et al., 2017). The particles will be updated in each search iteration by the local optimal solution P _bt and the global optimal solution G _bt ( Figure 2 ). The calculation steps are as follows:

First, set the initial value of the particle swarm and the maximum number of iterations T _max . Assuming that the particle swarm is iteratively searched in an n-dimensional space, the position of the j particle is denoted by Z _j ={z _j1,z _j2,…,z _jm } , and the velocity of the j particle is represented by V _j ={v _j1,v _j2,…,v _jm } .

Second, after finding P _bt and G _bt , the velocity of the j particle is updated by the following two equations:

where ω is the inertia weight. Further, c ₁ and c ₂, as well as r ₁ and r ₂ are learning factors and arbitrary numbers in the range of [0,1], respectively.

The third section is related to iterative search termination conditions. There are two conditions for terminating the iteration; the first one is that the precision is less than the set error value and the particle swarm converges, thus the iteration can be stopped, and the second one is that the number of iterations reaches the set maximum number of iterations T _max .

Finally, the optimal parameters obtained after the iterations are used to build a water quality assessment model.

When c ₁ is larger than c ₂, it leads to a part of particles being trapped in the local search, eventually leading to the inability to find the global optimal solution. Therefore, the value of c ₁ is taken as 1.6, and the value of c ₂ is taken as 2 in the model of this paper. Although when ω is larger, the global search capability is stronger, the algorithm is extremely prone to fall into local extremes when ω>1.2. Thus, to enable the particles to detect globally better regions in the early stage, while ensuring the convergence of the algorithm to the global optimal solution in the later stage, a linear decreasing weight strategy was chosen with the following equation:

where t represents the number of current iterations.

The flow of the water quality assessment method based on ACGRA and PSO-MSVM is shown in Figure 3 . To make full use of the correlation between water quality information, the features were selected from the water quality information using the method in Section 3.1, and the water quality assessment model was built using the method in Section 3.2.

The specific steps of the river water quality assessment are as follows:

Accuracy, precision, recall, and RMSE criteria were used to evaluate the performance of the model. Accuracy is defined as:

Precision is defined as:

Recall is defined as:

where TP, TN, FP, and FN represent the true case, false positive case, true negative case, and false negative case, respectively.

RMSE is defined as:

where k is the number of samples, Y_i and Y i ' are the actual and evaluated values of the samples, respectively.

In this paper, different correlation analysis methods were employed to calculate the direct correlation between water quality and other water quality indicators, and the results are presented in Table 4 .

Based on data in Table 4 , ACGRA fully considers the effect of subjective and objective weights on the correlation between water quality and other water quality indicators compared to the single weighted grey correlation analysis used in the literature literature (Sasikumar et al., 2022) and literature (Xu et al., 2020).

To further verify the effectiveness of ACGRA, four water quality indicators with high correlation with water quality ( Table 4 ) were selected as the input features of the PSO-MSVM-based water quality assessment model, and the model errors are provided in Table 5 .

The results of water quality assessment using features obtained by weighted grey relational analysis are better compared to previous research literature (Zhang et al., 2022b) using features obtained by equal-weighted grey relational analysis for water quality assessment ( Table 5 ). Compared to the improved GRA algorithm in studies by literature (Sasikumar et al., 2022) and literature (Xu et al., 2020), the RMSE is smaller when selecting the characteristic variables with ACGRA. This indicates that ACGRA can make full use of the correlation between water quality indicators and can effectively improve the accuracy of river water quality assessment.

In this paper, radial basis function (Rbf) is selected as the kernel function of SVM model. In order to verify the effectiveness of the Rbf, it is compared with the Linear Kernel (Linear) and Polynomial Kernel (Poly), and the results are shown in Figure 4 .

As can be seen from Figure 4A , when the kernel function is Rbf, the accuracy, accuracy and recall rate of the model are all higher than those of the other two types of kernel functions, and the RMSE of the three types of kernel functions is shown in Figure 4B . The results show that the model can evaluate water quality more accurately when radial basis function is selected as kernel function.

The choice of SVM parameters had a great influence on the effectiveness of water quality assessment models, thus the particle swarm algorithm was used to optimize the SVM so as to obtain the best parameters.

To verify the effectiveness of the PSO algorithm, it was compared with the multi-classification SVM model optimized by the multi-classification SVM and genetic algorithm ( Figure 5 ).

As shown in Figure 5A , the multi-classification SVM model using PSO has higher accuracy, precision, and recall and lower RMSE ( Figure 5B ). Based on the results, the particle swarm algorithm could better optimize the multi-classification SVM algorithm and effectively improved the performance of the water quality assessment model.

In this paper, the initial particle population and the maximum number of iterations were set to 300 and 300, respectively, and the learning factors c ₁ =1.6 and c _{2 =} 2. _A river water quality assessment model based on PSO-MSVM was developed using water quality indicators such as dissolved oxygen, temperature, turbidity, ammonia nitrogen, permanganate index, ph, and total dissolved solid of the river.

To verify the effectiveness of PSO-MSVM, it is compared with the PSO-DT and PSO-MLP algorithm models, and the results are illustrated in Figure 6 .

Based on data in Figure 6A , the PSO-MSVM model has higher accuracy, precision, and recall compared to the other two algorithms, and the RMSEs of the three methods are displayed in Figure 6B . The results demonstrate that the PSO-MSVM model is more accurate in assessing river water quality.