2.1 Source of water quality sample data

The experimental data used in this article comes from the aerobic tank part of an A²O method urban sewage treatment simulation device in the laboratory. The schematic diagram of the A²O method urban sewage treatment simulation device is shown in Fig 1, which consists of an inlet tank, anaerobic tank, anoxic tank, aerobic tank, secondary sedimentation tank, effluent tank, and internal and external reflux pipelines.

The main processes occurring in the aerobic pool are nitrification of ammonia nitrogen and oxidative decomposition of organic matter:

Ammonia nitrification: When the sewage enters the aerobic pool, nitrifying bacteria in the sludge undergo nitrification under aerobic conditions to convert ammonia nitrogen in the sewage into nitrate, thereby generating a nitrifying liquid. Subsequently, this nitrifying liquid is directed towards the anoxic pool through internal circulation for further reactions.

The oxidative degradation of organic matter: The oxidation and decomposition of organic matter in the water provide energy for phosphorus-absorbing microorganisms, which then absorb phosphorus from the water. Phosphorus is assimilated into the cellular tissue of these microorganisms and subsequently discharged from the system as phosphorus-rich sludge after undergoing precipitation separation.

The aerobic pool of the A²O method urban sewage treatment simulation device in this study has a volume of 87.56L. To optimize the reduction of urban domestic sewage, glucose and milk powder were selected as carbon sources, while ammonium sulfate ((NH₄)₂SO₄) was chosen as the nitrogen source for sewage allocation. The sewage was prepared with a carbon-nitrogen ratio of 100:5, ensuring that when COD in the sewage is 500mg/L, the nitrogen content remains at 25mg/L. Table 1 presents the specific materials used for sewage preparation.

2.2 Mechanism analysis of COD in aerobic tank effluent

The process of selecting input variables for COD in aerobic tank effluent mainly includes: mechanism analysis of COD in aerobic tank effluent, water quality data collection, and correlation analysis. Firstly, a mechanism analysis is conducted on the COD of the effluent from the aerobic tank of the A²O sewage treatment process to preliminarily determine the types of input variables. At the same time, the selection range of input variables should follow the principle of being able to be collected in real-time by sensors, that is, easy to measure. Then, data collection is carried out based on the preliminarily determined input variables. Finally, correlation analysis is used to adjust and screen the input variables, and finally, the input variables are determined.

The key to analyzing the mechanism of COD in the effluent of aerobic tanks in A²O sewage treatment process lies in how the process efficiently removes organic pollutants from water. In the anaerobic stage, complex organic matter in wastewater is first decomposed into smaller molecules by anaerobic microorganisms. Next, in the anaerobic stage of denitrification reaction, denitrifying bacteria will use nitrate as an electron acceptor for anaerobic respiration, producing nitrogen gas. At the same time, the oxidation-reduction potential (ORP) of wastewater will decrease, and this reaction process will also be accompanied by a certain amount of organic matter degradation, further reducing the COD content. Finally, in the aerobic stage, which is the main stage for COD removal, nitrifying bacteria use dissolved oxygen (DO) to oxidize and decompose the remaining organic matter, converting it into carbon dioxide and water, thereby significantly reducing the COD concentration in water. At the same time, some inorganic salts such as nitrates are also produced, which can affect the electrical conductivity (EC) of wastewater. The high or low water temperature (T) is not conducive to the growth of microorganisms, which in turn affects the rate of reaction.

According to the above analysis, the indicators that have a significant impact on COD include pH, ORP, EC, DO, and T. Among them, the pH value will affect the microbial activity in the A²O process, with an ideal pH of 6–9. Within this range, the efficiency of microbial decomposition of organic matter is higher, thereby reducing COD in water quality. When the pH is too low or too high, it will inhibit the activity of microorganisms and reduce the efficiency of COD removal; The value of ORP has a certain impact on the growth of microorganisms. In anaerobic and anaerobic stages, lower ORP helps promote the growth of certain specific microorganisms, which contribute to the decomposition of organic matter and the removal of nitrogen and phosphorus. In the aerobic stage, higher ORP is conducive to the oxidation and decomposition of organic matter, thereby removing COD; EC is an indicator that reflects the ion concentration in water, indirectly reflecting the content of salt and organic matter in wastewater. Excessive EC may indicate a high concentration of organic matter, which may increase the difficulty of COD removal. Meanwhile, high salinity environments may have inhibitory effects on certain microorganisms, affecting the removal of COD; Water temperature affects the activity of microorganisms and the reaction rate of various reactions, thereby affecting the value of COD; In the aerobic stage, an appropriate level of DO can ensure the rate of nitrification reaction and promote the oxidation and decomposition of organic matter, so dissolved oxygen has a significant impact on COD.

In summary, through the mechanism analysis of COD in aerobic tank effluent, the input variables of COD in aerobic tank effluent were preliminarily determined as pH, ORP, EC, T, and DO.

2.3 Collection of water quality sample data

Once the initial selection range of input variables is determined, data collection should be carried out to provide sample data for subsequent correlation analysis and model training. This article uses the A²O method urban sewage treatment simulation device mentioned earlier for data collection, and in order to measure the amount of activated sludge in the aeration tank, MLSS collection is added to the data collection process. After 180 days of experimentation, a total of 500 sets of valid data were obtained, and some sample data (collected in March 2023 in Northeast China) are shown in Table 2.

2.4 Selection of input variables

After the data collection is completed, the next step is to analyze these variables by correlation analysis, which is a statistical analysis method to study the correlation between two or more random variables in the same state. Currently, there are three types of correlation coefficients used to represent the correlation between variables: Pearson correlation coefficient, Spearman correlation coefficient and Kendall correlation coefficient. The correlation coefficient can reflect the direction and degree of the trend of change between two variables. The range of values is [–1,1], with 0 indicating no correlation [17]. Positive values indicate positive correlation and negative values indicate negative correlation. The larger the absolute value of the correlation coefficient, the stronger the correlation. By analyzing the process and historical monitoring dataset of the A²O wastewater treatment process, the conditions for the applicability of the Pearson correlation coefficient were met and the correlation analysis was performed using SPSS software.

Pearson correlation coefficient is a linear correlation coefficient used to measure the linear relationship between two variables [18, 19]. The Pearson correlation coefficient is calculated as follows: (1) Where cov(X,Y) is the covariance of the variable (X,Y), σX and σY are their respective standard deviations.

To verify the correlation between COD and the selected input variables, historical monitoring data covering these parameters were selected for correlation analysis. The correlation analysis is shown in Fig 2, and the correlation coefficients are shown in Table 3.

In order to further verify the rationality of the selected input variables, correlation analysis is conducted between the selected input variables. If the correlation between the selected input variables is strong, it means that there is a lot of duplicate information between the two, and the relevant input variables can be deleted. The correlation coefficients between input variables are shown in Table 4.

According to the analysis results in Table 3, it can be seen that the correlation coefficient between ORP and EC is 0.778, which has a strong correlation, indicating that there is a lot of redundant information between them. At the same time, considering economic and maintenance factors, ORP was removed from the selected input variables, and the final input variables were determined as pH, EC, T, and DO.

2.5 Data normalization

The essence of model training is to find a minimum loss function through a large amount of training data. This study involves multiple variables, which have different physical meanings and dimensions. If normalization is not carried out, it will have a significant impact on the training of the model. Therefore, before inputting sample data into the model, all variables in 500 sets of sample data need to be normalized and scaled to a certain ratio between 0 and 1 [20]. By normalizing, the training time is reduced, the convergence speed of the model is accelerated, and the prediction accuracy of the model is improved. The formula for data normalization is as follows: (2) Where x* is the result of data normalization, x is the sample data, min x is the minimum value in the data, and max x is the maximum value in the data. Since the input data is normalized, the obtained prediction result is also between 0 and 1, so the final prediction result should be de-normalized when output, and the data de-normalized formula is as follows: (3) Where y* is the predicted value after normalization and x* is the predicted value after de-normalization.

3.1 Convolutional neural networks

Convolutional neural network (CNN) is a feedforward neural network with convolutional operation and deep structure. CNN is usually composed of input layer, convolutional layer, pooling layer, fully connected layer, and output layer. Convolutional layers are specialized for data processing, used to filter input data and extract useful information, and use convolutions of different sizes to check the data for convolution [21, 22]. A pooling layer is periodically inserted between consecutive convolution layers to gradually reduce the spatial size of the data body and effectively prevent overfitting. Finally, the training results are obtained through fully connected layers and output layers. A one-dimensional CNN can extract corresponding features of time series. Water quality data belongs to time series; Therefore, one-dimensional CNN networks are applied to feature extraction of wastewater quality data. The process of multidimensional matrix processing for time series data is as follows:

Convolution layer: The preprocessed sewage water quality data is used as input, and the feature matrix is generated by convolution operation. (4) Where: conv is the convolution operation in CNN network; and are the input and output of the convolution process, respectively; l is the length of the sewage water quality data sequence, i and j represent the processing position in the convolution process. is the weight of the convolution layer; is the bias of the convolutional layer. (5) Where and are the input and output of the activation function respectively; f is the nonlinear activation function Relu.

Pooling layer: The pooling operation is performed on the obtained feature matrix. (6) The pooling function represents the pooling operation; represents the output after the pooling layer.

In this paper, the feature vectors obtained by the CNN network convolution operation are input into the subsequent BiLSTM network layers for time-related feature extraction.

3.2 Long Short-Term Memory Neural Networks

Long Short-Term Memory Neural Network (LSTM) is a special type of Recurrent Neural Network (RNN) that has good performance in processing time series data [23, 24]. However, RNN has a long-term dependency problem. When the input time series data is too long, RNN cannot effectively learn long-distance dependency relationships. To solve this problem, researchers combined gating functions and hidden states to propose LSTM [25]. LSTM introduces a "gate" mechanism to control the flow and loss of features, solving the long-term dependency problem of RNN and effectively avoiding problems such as gradient disappearance and explosion [26]. Fig 3 shows the basic structure of LSTM, and the relevant formulas of LSTM are as follows:

1. 1. A forget gate is a hidden cell state in an LSTM that determines the extent to which the previous time’s cell state is retained for the current time.

(7)

1. 2. The input gate determines how much of the network’s input at the current time is saved to the unit state.

(8)(9)

1. 3. The update of the storage unit involves discarding unnecessary information and adding new information learned by the network at the current moment.

(10)

1. 4. Calculate the output gate and the hidden layer state at the current time

(11)(12)

where, f, i, C, o and h are the outputs of the forget gate, input gate, cell state, output layer and hidden node, respectively. σ and tanh are the sigmoid activation function and the hyperbolic tangent function, respectively. W and b denote the corresponding weight coefficient matrix and bias, respectively.

3.3 Bi-directional Long Short-Term Memory Neural Networks

Bidirectional Long Short-Term Memory Neural Network (BiLSTM) is an optimization and improvement of LSTM, and is a neural network with a powerful architecture. It is formed by combining forward LSTM and backward LSTM, rather than simply increasing the depth of the model through stacking. The hidden state h_t of BiLSTM at the current time t includes forward hidden state h_t−1 and backward hidden state h_t+1. Traditional LSTM can only process data in one direction, so BiLSTM combines reverse LSTM to capture important features that traditional LSTM may miss and fully consider past and future information [27, 28]. Therefore, BiLSTM greatly expands the amount of information available in neural networks, improving the utilization of sample data and prediction accuracy. The structure of BiLSTM is shown in Fig 4.

Where and represent the outputs of the forward LSTM and reverse LSTM hidden layers, respectively. The BiLSTM layer generates an output vector Y, where each element is computed as follows. (13) Where the σ function is used to couple sequences and , and the final output of BiLSTM is represented as Y = [y₁,y₂,⋯,y_t].

3.4 Attention mechanism

Attention mechanism originates from the investigation of human vision [29]. For instance, our visual system usually tends to focus on the parts of the image that are helpful for judgment, while ignoring irrelevant information. Different variables have different impacts on the main variable, and important variables contain more critical information, which has a greater impact on the main variable [30]. However, traditional neural networks cannot distinguish the importance of variables, resulting in the inability to highlight important features during model training. Therefore, attention mechanism is introduced for optimization. The attention mechanism assigns different weights based on different features, that is, assigns higher weights to key information, reduces or ignores irrelevant information through weight differentiation, amplifies important information needed, improves processing efficiency and model prediction accuracy. The formula for attention mechanism is as follows: (14) (15) (16) Where v, U and W represent the learnable network parameters, q is the query vector, s(x_i, q) is the attention scoring function, and α_i is the attention distribution.

For the input [x₁,x₂⋯x_N]of the Attention layer, the correlation between the query vector and each input x is calculated through the attention scoring function s(x_i, q) to obtain a score, and then these scores are normalized using the softmax function to obtain a series of attention distributions [α₁,α₂⋯α_N]. Finally, the input information is weighted and summed according to the attention distribution to obtain the output sequence att(X,q). The structure of the attention mechanism is shown in Fig 5.

3.5 CNN-BiLSTM-Attention algorithm model

In this paper, a CNN-BiLSTM-Attention algorithm model is proposed and applied to soft-measurement prediction of COD values of effluent from aerobic zone of A²O wastewater treatment process. First, the input data are preprocessed, next, Conv1D is used to perform convolution operation on the data to extract the local features of the data. Then, BiLSTM serializes the extracted local features. Meanwhile, during the training process, Dropout layer is utilized to randomly reject some features to improve the robustness of the model. On this basis, the attention mechanism is introduced to weight the sequence data, and different weights are assigned according to the importance of the sequence data. Finally, the predicted values in the test set are output, and the error analysis is given and the model is saved. The flow chart of the model is shown in Fig 6.

3.6 Model performance metrics

In order to test the performance of the CNN-BiLSTM-Attention hybrid model, three indexes, root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²), were used to evaluate the CNN-BiLSTM-Attention hybrid model. RMSE reflects the degree of deviation between the true value and the predicted value, and MAE represents the average absolute error between the true value and the predicted value. The smaller the RMSE and MAE are, the closer the predicted value is to the true value and the better the prediction effect is, while R² represents the degree of fit, and the closer it is to 1, the better the fitting ability of the data is. The formula for RMSE, MAE, MAPE, and R² is as follows: (17) (18) (19) (20) Where m is the number of samples in the water quality sample data, y_i is the actual COD value, is the predicted COD value, RMSE is the mean square error, MAE is the mean absolute error, R² is the coefficient of determination, and MAPE is the average absolute percentage error.

4.1 Experimental environment

In this paper, the deep learning framework Keras is applied to build the environment required for simulation experiments. The specific environment parameters are: CPU, AMD Ryzen 7 4800H; GPU, NVIDIA GeForce GTX 1650; RAM, 16GB; Operating system, windows 11, 64-bit;keras version 2.8.0; tensorflow version 2.8.0; python version 3.9.

4.2 Model parameter setting

In this study, GridSearchCV from scikit-learn library is used to find the best combination of hyperparameters, which provides a convenient interface to define hyperparameter grids, instantiate models, perform cross-validation and performance evaluation. Considering the grid search method in this paper, we define several key hyperparameters, including learning rate, batch size, dropout rate, CNN layer number and convolution kernel parameter, BiLSTM layer number and cell number. At the same time, a reasonable search space is set for each hyperparameter to cover the best possible configuration, as shown in Table 5.

During grid search, cross validation is used to evaluate the performance of the model. Cross validation divides the dataset into multiple subsets, and then uses each subset as the test set and the remaining subsets as the training set for model training and validation. This process will be repeated multiple times, each time using a different subset as the test set. Finally, calculate the average of all validation results as the performance indicator for this hyperparameter combination. Through multiple experimental analyses, the optimal values of these parameters were obtained, as shown in Table 6.

4.3 Model performance and analysis

In order to verify the performance of the CNN-BiLSTM-Attention algorithm model, this paper divides 20% of the 500 sample data after data normalization into the test set and 80% into the training set, and trains and tests the model, the model training results are shown in Fig 7. Meanwhile, evaluate the performance of the model using RMSE, MAE, MAPE, and R².

It can be seen from Fig 7 that the model can capture the inherent law of the data well, with high prediction accuracy, small error between the predicted value and the true value, and fast convergence speed.

4.4 Comparative validation of different models

In order to further verify the performance of CNN-BiLSTM-Attention model, CNN-BiLSTM-Attention model was compared with other models (CNN-LSTM-Attention, CNN-BiLSTM, CNN-LSTM, LSTM, RNN, BP).The comparison of COD prediction results is shown in Fig 8, and RMSE, MAE, MAPE, and R² of each model structure are shown in Table 7.

From Fig 8 and Table 7, it can be concluded that the prediction accuracy of the CNN-BiLSTM-Attention model is higher than that of other models. In terms of RMSE, the CNN-BiLSTM-Attention model decreased by 17.18%, 23.19%, 40.36%, 53.44%, 63.24%, 64.64%, 57.17%, 56.06%, and 64.57% compared to the other nine models, respectively. In terms of MAE, the CNN-BiLSTM-Attention model reduced by 18.61%, 22.63%, 45.95%, 51.07%, 58.38%, and 62.16% compared to the other nine models, respectively. In terms of MAPE, the CNN-BiLSTM-Attention model decreased by 5.13%, 6.35%, 9.66%, 20.85%, 27.90%, 29.28%, 24.15%, 23.83%, and 28.78% compared to the other nine models, respectively. In R ² In terms of performance, the CNN-BiLSTM-Attention model has improved by 1.17%, 1.92%, 3.62%, 7.26%, 13.85%, 16.14%, 9.54%, 10.03%, and 12.70% compared to the other nine models, respectively. Through model comparison, the accuracy of the proposed CNN-BiLSTM-Attention model for COD prediction has been further verified, and its performance is superior to other models.

4.5 Wilcoxon signed-rank test

In order to consolidate the conclusions of the comparative verification of different models in this chapter, we conducted a non parametric statistical test, namely Wilcoxon signed rank test, on the proposed CNN-BiLSTM-Attention model and CNN-LSTM-Attention model, and CNN-BiLSTM model and CNN-LSTM model. the null hypothesis is these four models are similar, that is, combining convolutional neural networks, bidirectional long short-term memory, and attention mechanisms did not improve the accuracy of soft measurement. Therefore, the soft measurement results of the four models mentioned above are very similar or identical. In Table 8, the average, standard deviation, maximum, and minimum values of various performance evaluation indicators for the four models are presented. The CNN-BiLSTM-Attention model was compared pairwise with other models. According to the Wilcoxon signed rank test, it can be concluded from this table that after 10 independent runs, RMSE of CNN-BiLSTM-Attention model The mean values of MAE, MAPE, and R² are all superior to other models. In Table 9, the positive and negative ranks of each pair of error measures corresponding to the CNN-BiLSTM-Attention model and other models are presented. Further evaluate and analyze the tests in Table 10 based on the descriptive statistical data presented in Tables 8 and 9.

The Wilcoxon signed rank test shows significant differences among the four models mentioned above, with Z-values of the test statistic being -2.312, -2.452, -2.617, -2.121, -3.332, -3.134, -3.421, -3.109, -3.501, -3.683, -3.603, and -3.555, respectively. From Asymp.Sig.(2-tailed) can infer the relationship between the CNN-BiLSTM-Attention model and the CNN-LSTM-Attention model, RMSE is 0.020, MAE is 0.014, MAPE is 0.008, R² is 0.033. The CNN-BiLSTM-Attention Model and CNN-BiLSTM All indicators between CNN-LSTM are 0. Based on the results of Wilcoxon’s signed-rank test, we reject the null hypothesis, the CNN-BiLSTM-Attention model differs significantly from other models.