The neural network is a black box model, and the output results are determined by the input of the model. Therefore, the input factors of the model should first be able to stimulate the problem under study. In other words, the input of the model is the influencing factor of the problem under study. For a complex problem with multi factor coupling, the influencing factors are diverse, and even some factors are factors that have not been noticed in the current research process or can’t be described or verified even if they are noticed. There are scholars established a methane yield prediction model based on lignocellulosic biomass in the process of medium temperature solid anaerobic digestion (SS-AD) using artificial neural networks. Three neural network models were established in this paper. The first model did not make any choice based on the collected data, and took all variables as model inputs; The second model selects the important variables determined in the multiple linear regression as the model input; The third model uses variables that are easy to measure or control as model inputs. The results show that the prediction correlation coefficient (R²) value of model 1 is 0.528, which is not satisfactory. The reason is that too many input variables make the model over fit, and model 2 shows a good prediction effect. The prediction effect of Model 3 is between Model 1 and Model 2, and further experimental data are needed to optimize. In practical projects, it is impossible to input all the influencing factors into the model. Generally, the main factors that affect the output will be selected. Under the condition that the output prediction results are acceptable and can be used for engineering guidance, the fewer input factors selected is the better, and these factors can be directly observed or easily measured and obtained compared with the research problems. This paper is to predict the effluent COD value of IC reactor, so the factors affecting the effluent COD value should be recognized first.

IC reactor is a typical anaerobic reactor, which mainly conducts anaerobic biological reaction. Anaerobic biological reaction mainly depends on the anaerobic digestion of a variety of anaerobic or facultative microorganisms to degrade complex organics and produce biogas with recyclable value. Therefore, the factors affecting the COD value of IC reactor effluent can be studied from the perspective of affecting the anaerobic digestion process. In the above four stages, part of the products in the former stage are the substrates in the later stage, such as volatile fatty acids (VFA). The accumulation of these substances in the reactor affects the balance of the whole reactor. According to the current research, the main factors affecting the operation of IC reactor include water temperature, pH, influent flow, influent COD, influent VFA, etc.

The influence of temperature on anaerobic reaction process is, on the one hand, the influence on microbial activity. Temperature will affect the activity of enzymes in microorganisms and then affect the growth rate of microorganisms themselves and the utilization rate of nutrients; On the other hand, temperature is an important influencing factor of chemical reaction kinetics parameters, which will affect the biochemical reaction speed in the reactor. The effect of temperature on the hydrolysis and acidification stages of the digestion process is not significant, because in the mixed population, there are always some bacteria that are most suitable within the relevant range, while the acetic acid and methane production stages can only be completed by certain specific microorganisms (acetic acid and methane bacteria), which are very sensitive to temperature changes.

pH value not only affects the life activities of anaerobic organisms, but also affects the acid-base balance in the reaction system, thus affecting the biochemical reaction in the reactor (Park et al., 2020). The optimal pH value of methanogens is 6.8–7.2, and the pH value of acid bacteria is higher. The pH value of the anaerobic system is usually maintained between the limits of methanogenesis to prevent the dominant role of acid bacteria leading to the accumulation of VFA. More importantly, pH affects the buffer capacity of the reactor, neutralizes VFA accumulated anywhere in the reactor, so as to prevent the formation of local acid zones in the digestive system and ensure the acid-base balance in the reaction system.

The influent flow will affect the hydraulic conditions and hydraulic retention time in the reactor, thus affecting the state of granular sludge and the sludge water mixing effect in the system, and ultimately affecting the effluent effect. The influent COD load and influent flow rate jointly reflect the volume load of the reactor and have a direct impact on the effluent COD value.

Volatile fatty acids is the intermediate product of anaerobic degradation process and the substrate of methanogenic series reaction. If the substrate is easy to hydrolyze, the acidification fermentation process is a fast process, and the growth rate of methanogens is slower than that of acidic substances. Therefore, excessive organic load will lead to the accumulation of VFA in the reactor. It is generally believed that VFA accumulation is the result of unbalanced digestion reaction. When VFA accumulation occurs in anaerobic system, methanogenic activity will be seriously inhibited, and sludge quality will deteriorate.

In the actual process, the reactor not only takes place in various biological reaction processes, but also takes place in various complex physical and chemical reactions. In addition to the above factors, the characteristics of sewage (mainly referring to the changes in sewage characteristics caused by different papermaking production processes and products), the size and structure of reactors, and the quality of operators will affect the effluent COD value of IC reactors. However, once these factors are determined in the project, their impact on the operation effect of reactors will be basically determined, which can be regarded as the internal characteristics of reactors.

To sum up, this paper intends to take factors such as water temperature, influent pH, influent flow, influent COD, and influent VFA as the input factors of the neural network (Liu et al., 2021). However, according to the field treatment of wastewater, the incoming water temperature received by IC reactor is relatively constant, basically between 33 and 36, and the field record value is an integer, which means that the temperature index has only a small fluctuation. Such data input model will affect the learning ability of the model. Therefore, according to the actual situation of the modeling object in this paper, the water temperature factor is not used as the model input. Therefore, the selected input factors are: influent pH, influent flow, influent COD and influent VFA; The output factor is the COD value of reactor effluent.

When the network structure and algorithm are determined, the training samples become the decisive factor of the neural network mapping and generalization ability. However, some literature shows that it is not the more training samples, the better the network training effect and generalization ability, or even the more training samples, the network has learned and cannot converge. Therefore, from the perspective of network training sample set, training samples should have three elements: compactness, ergodicity and compatibility. Therefore, sample pretreatment is generally required.

The input factors selected in this paper are: influent flow, influent COD, influent pH and influent VFA; The output factor is COD value of reactor effluent. According to the field monitoring data, the IC reactor was sampled twice a day at about 9:00 a.m. and 16:00 p.m. respectively. Therefore, in this paper, the sampling data in the morning (influent flow, COD, pH, and VFA) and the sampling data in the afternoon (effluent COD) are combined to form a sample data pair, and the data of 3 months from August to October 2017 are collected, of which 4 days of individual indicators are not recorded, so 88 sample data pairs are obtained. Table 1 shows the range of indicators of IC reactor inlet and outlet water. Due to the large amount of data, Table 2 shows the sorting results of monitoring data in the first 20 days (Vian et al., 2020a).

Because the selected input factors have different units and orders of magnitude, if the original data is directly input into the neural network, the network will be “dominated” by factors with large values, and the internal links between the factors cannot be identified, so the establishment of the network model is meaningless. Therefore, in order to ensure the equal status of each factor before input, it is necessary to normalize the sample data, that is, let each input factor data take value in a unified interval. In this model establishment, the sample data is normalized according to the following formula, as shown in the following formula (1):

In the formula, x_i, x_imax, and x_imin represent the first input data of an input factor and its maximum and minimum values, respectively, and E represents the i-th input data value after normalization. After normalization, the data of each input element will be distributed in the range of (0,1). Similarly, the output of the network should be normalized in the same way.

By analyzing the influence degree of each input variable, we can help identify the possible outliers in the sample set. Pareto diagram for principal component analysis is shown in Figure 2 (Megido et al., 2021).

It can be seen from Figure 2 that the first three principal components account for more than 90% of the explained variance. Therefore, the possible outliers in the sample can be identified by analyzing the two-dimensional principal component background of the first three principal components. MATLAB programming is used to realize the distribution of sample data under the two-dimensional principal component background, and the return of the date corresponding to the specified point can be realized.

After removing the abnormal data, first calculate the Euclidean distance, Markov distance and absolute distance between each sample data after normalization, and then cluster the samples with the shortest distance method, the longest distance method, the center of gravity distance method and the average distance method, and calculate the cophentic correlation coefficient of the samples before and after clustering. The calculation results are shown in Table 3 below:

The cophentic correlation coefficient represents the degree of fitting between the data and the classification structure. The closer the size is to 1, the better the degree of fitting is. Therefore, Mahalanobis distance and barycenter distance are used to cluster the sample data, and a clustering tree is created. The 80 groups of data used for training and simulation have no significant deviation from the sample group.

At present, there is no perfect theoretical guidance for the selection of these parameters. In order to achieve the best prediction effect of the neural network, this paper uses trial calculation to determine the parameters. The basic idea is to adopt the fixed variable method, fix the value of some parameters while changing the value of another parameter, and select the one with the minimum average absolute error of the test sample as the optimal network.

The number of hidden layer nodes is tentatively determined to be 6, and the learning rate and learning error limit are changed in turn. Each case is run for 20 times, and the average value of the 5 operation results with the lowest average absolute error is calculated. The calculation results are shown in Tables 4–7 (Kang et al., 2020).

It can be seen from Tables 4–7 that when the learning rate is set to 0.05 and the learning error limit is set to 0.01, the average absolute error of calculation is the minimum, so it is set as the BP neural network calculation parameter (Anhad et al., 2021). Next, we will consider the optimal number of hidden layer nodes under the operating parameters. The program operation results are shown in Table 8.

It can be seen from Table 8 that when the number of hidden layer nodes is set to 6, the BP neural network established can obtain the best simulation prediction effect. Therefore, the model parameters are selected as follows: learning rate 0.05, learning error limit 0.01, and number of hidden layer nodes 6.