# A Review of the Artificial Neural Network Models for Water Quality Prediction
## 4 Artificial Neural Networks Models for Water Quality Prediction
[3] pointed out that if more historical data were available [15], ANN models may provide better predictions than a relatively small data set. [PERSON] et al. [41] tested the performance of RNN, GRNN, and MLP in small samples prediction. Results indicated that the error of RNN in test data was less than 10%. Besides, the error of GRNN was lower than MLP. [PERSON] and [PERSON] [55] deleted the missing data directly. Then, discrete wavelet transforms (DWT) with the orthogonal wavelet families was applied to denoise the data measured by proximal sensors. The result indicated that the modeling effect of using TLRN to the data after noise reduction was superior to TLRN, TDNN, and RNN. [PERSON] et al. [12] attempted to use NARX, a dynamic neural network, to model ten-year seasonal water quality data. Then, 42-fold cross-validation was used to divide the data. Results demonstrated that the NARX network outperformed BPNN because it could capture the important dynamic features of TP data. [PERSON] et al. [6] tested the prediction performance of LSTM, BPNN, Online sequential (OS)-ELM in DO, and TP. The results indicated that LSTM was more accurate and generalizable than the above feedforward ANNs. [PERSON] et al. [38] used an improvement of the ESN, namely RESN, to predict the BOD and TP. This new method used the ridge regression algorithm to calculate the output weights to solve the ill-posed problem existing in the ESN. [PERSON] et al. [66] fully preprocessed the acquired water quality data. They firstly imputed, corrected, and denoised the data by using linear interpolation, smoothing which could attenuate high-frequency signals, and moving average filtering techniques. Then, correlation analysis, which belongs to analytical methods, was carried out. The LSTM was adopted for model establishment. Experimental results showed that the prediction accuracy was high and could reach 98.97% and LSTM was suited for long-term prediction. [PERSON] [67] introduced Back-propagation through time (BPTT) to train the SRU model. The main difference between SRU and RNN is the \"cell state\" part added in the hidden layer. They proposed an Improved mean value method to solve the breakpoint phenomenon of the mean value method and the linear interpolation method. Results showed that the prediction error was small, within the range of 1%. [PERSON] et al. [53] converted the irregular data into daily data by using a linear interpolation method and provided a solution to abnormal data identification. They used a fixed threshold method to set the upper and lower threshold ranges and proved that linear interpolation had better robustness than spline interpolation, nearest-neighbor interpolation, and cubic interpolation according to model results when water quality changed dramatically. Results showed that the removal of abnormal data beyond the threshold value could preliminarily improve the data convergence. [PERSON] and [PERSON] [134] decomposed the measured SS data into wavelet components via DWT. The DWT-ANN method could more accurately approximate the peak values, which have lesser distributions compared with non-peak values. [PERSON] et al. [135] applied MLP to forecast daily SS and NO3 without considering missing data. They applied a self-organizing map (SOM), a stratified method, to construct a topological map to visualize the clustered input variables, thereby ensuring that the statistical properties of the subsets were similar. Levenberg-Marquardt algorithm [136; 137; 138; 24; 139] and Bayesian methods were conducted to train the network. Results showed that ANN models could achieve high accuracy. [PERSON] et al. [140] used the SR and AT meteorological data to achieve the WT prediction. They introduced micro-genetic algorithms (u GA), a creep mutation in small populations, to update the weights. [PERSON] et al. [141] reported that the GA-BP algorithm whose relative errors were below 35% was more suitable for TP, TN, and Chl-a prediction than simple multivariate regression analysis.