Research on water quality prediction model based on echo state network

Abstract

Using artificial neural network (ANN) to solve the problem of time series water quality prediction has become increasingly mature. In this paper, through the study of leaky-integral echo state neural network (Leaky ESN), combined with the historical water quality data of Dongzhen Reservoir in Fujian Province, a single-day water quality prediction model was constructed, and the Bayesian optimization algorithm was used to realize the automatic optimization of hyper-parameters in the network. On this basis, multi-day prediction models were constructed by further improving the network, which used the historical water quality data of the previous 7 days to predict the water quality of the next 3 days, 5 days and 7 days. Then the prediction models were applied to the water quality prediction of the study. The experimental results show that the single-day prediction model with Bayesian optimization has high accuracy. The multi-day prediction models can also achieve good prediction effect, and have more practical application value. They are more suitable for early warning of water quality.

Keywords

Water quality prediction Leaky ESN hyper-parameters Bayesian optimization alg-orithm single-day prediction multi-day prediction

1. Introduction

Over the years, many surface water bodies have faced a series of problems such as water quality decline, eutrophication and destruction of aquatic ecosystems, resulting in environmental degradation, affecting the orderly development of ecology and endangering the lives and health of residents [1, 2, 3]. However, the water environment monitoring method based on the monitoring point could only obtain the current water quality situation [4, 5], and cannot predict and warn the water environment pollution in advance. Therefore, in order to reduce health risks and control water pollution sources in time, it is necessary to make reliable and accurate water quality prediction in advance.

So far, a large number of scholars have studied various models to predict water quality changes and have achieved certain results [6, 7, 8, 9, 10, 11, 12]. Zhao Jun used the BP neural network to predict the water quality of the Minjiangkou Water Plant [13], and Li Xinxin used the GA-BP neural network to predict the water quality of the construction area [14]. However, the prediction accuracy of these water quality prediction models is generally low, because they can not reflect the time series characteristics of water quality monitoring data. Compared with BP neural network, recurrent neural network (RNN) can describe the internal characteristics of dynamic system [15, 16, 17], so that the system has the ability to adapt to time-varying characteristics. Especially in time series forecasting, RNN can obtain higher prediction accuracy through recursive structure. Echo State Network (ESN) [18] is a new type of RNN, which can greatly reduce the amount of calculation in training and avoid the local minimum in gradient descent to a certain extent. In this paper, we studied the Leaky-integrator echo state network (Leaky ESN), which was an improved ESN [19]. According to the characteristics of water quality factors of Dongzhen Reservoir, Leaky ESN was selected to construct single-day prediction model and multi-day prediction models for Dissolved Oxygen (DO), Ammonia Nitrogen (NH3-N) and Permanganate Index ( $\text{COD}_{\text{Mn}}$ ). The prediction accuracy of each model was compared by experimental results and performance indicators.

2. Leaky ESN principle and evaluation indicator

2.1 Leaky ESN principle

The network structure of Leaky ESN and ESN is exactly the same, and the network is divided into 3 layers: reservoir layer, input layer and output layer. The network structure is shown in Fig. 1.

Figure 1.

ESN structure.

The core of leaky ESN is the reservoir. There are many sparse neurons in the reservoir, and they are randomly connected. With the continuous change of input in the network, these neurons generate a complex dynamic space and internal state information. Finally, using these internal state information and the output weight obtained by training, the required corresponding outputs are linearly combined. The input sequence, state sequence and output sequence in the network are as follows.

$\displaystyle u(t)=[{u_{1}(t),u_{2}(t),\ldots,u_{K}(t)}]^{T}$ (1) $\displaystyle s(t)=[{s_{1}(t),s_{2}(t),\ldots,s_{N}(t)}]^{T}$ (2) $\displaystyle y(t)=[{y_{1}(t),y_{2}(t),\ldots,y_{L}(t)}]^{T}$ (3)

where $u(t)\in R^{K},s(t)\in R^{N},y(t)\in R^{L}$ are the input variables, state variables and output variables of Leaky ESN at time $t$ , respectively. The state update equation of the reservoir is as follows [20].

$\displaystyle s({t+1})=({1-\alpha})\times s(t)+f({W_{in}\times u({t+1})+W% \times s(t)})$ (4)

The output of the ESN can be obtained from the state of the reservoir. The equation is below.

$\displaystyle{y}({{t}+1})=f_{\textit{out}}({W_{\textit{out}}\times({u({t+1}),s% ({t+1})})})$ (5)

$W_{in},W$ represent input weight matrix and reservoir weight matrix respectively. $\alpha$ is the leaky rate, which can control the degree of retention of internal neurons at the previous moment. The smaller the $\alpha$ is, the slower the state of internal neurons changes, and the short-term memory of the network is stronger. When $\alpha=1$ , it is the traditional ESN. $f(\cdot)$ is the neuron activation function of the reservoir, and the function $\textit{tanh}()$ is usually used. $f_{\textit{out}}()$ is the neuron activation function of the output layer, and the identity function is usually taken.

From the above Eq. (5), the output of the Leaky ESN at each moment can be obtained. Usually the data is linear and feedforward, and the final output sequence can be written as follows.

$\displaystyle Y=W_{\textit{out}}X$ (6)

However, the ultimate goal of network optimization is to make the actual output of the network infinitely approach the expected output, so the network output sequence can be written as the follows.

$\displaystyle Y_{\textit{target}}=W_{\textit{out}}X$ (7)

There are many ways to solve $W_{\textit{out}}$ from Eq. (7). The most stable and reliable one is ridge regression, that is, $W_{\textit{out}}$ can be obtained by the least square method with penalty term [21].

$\displaystyle W_{\textit{out}}=Y_{\textit{target}}X^{T}({XX^{T}+\lambda_{r}I})% ^{-1}$ (8)

Where $\lambda_{r}$ is regularization coefficient and $I$ is diagonal unit matrix.

The Leaky ESN based on ridge regression can improve the prediction accuracy of the nonlinear model. Unlike other networks, it does not need to train all the weight matrix, only the output weight matrix $W_{\textit{out}}$ needs to be trained.

2.2 Evaluation indicator

In order to evaluate the performance of water quality prediction model based on Leaky ESN, this study selected Nash-Sutcliffe Efficiency Coefficient (NSE) and Root-Mean-Square Error (RMSE) to verify the accuracy of the prediction model [22]. The formulas were described as follows.

$\displaystyle\textit{NSE}=1-\frac{\sum_{t=1}^{M}{({{y}(t)-\hat{y}(t)})^{2}}}{% \sum_{t=1}^{M}{({y(t)-\bar{y}(t)})^{2}}},\textit{NSE}\leqslant 1$ (9) $\displaystyle\textit{RMSE}=\sqrt{\frac{1}{M}\sum_{x{t=1}}^{M}{({{y}(t)-\hat{y}% (t)})^{2}}},\textit{RMSE}\geqslant 0$ (10)

where $y(t)$ is the real monitoring data at the $t$ th time. $\hat{y}(t)$ is the predicted data at the $t$ th time. $\bar{y}(t)$ is the average of real monitoring data. $M$ is the total number of monitoring. The NSE value reflects the consistency between the real monitoring data and the predicted data of the model. RMSE reflects the deviation between the real monitoring data and the predicted data. If the NSE value is higher, the RMSE value is smaller, the models would have good quality and high reliability.

3. Sample datasets and data processing

3.1 Sample datasets

The sample set selected in this study is the monitoring data of water quality indicators of Dongzhen Reservoir in Fujian Province in the past three years from 2018 to 2020. A total of 1077 water quality indicators are sampled, and the sampling period is once a day. The statistics of each water quality factor (TEMP denoted water temperature, PH denoted potential of hydrogen, DO denoted Dissolved Oxygen, EC denoted Electric Conductivity, TUB denoted Turbidity, NH3-N denoted Ammonia Nitrogen, $\text{COD}_{\text{Mn}}$ denoted Permanganate Index, TP denoted total phosphorus, TN denoted total nitrogen, Chl denoted Chlorophyll, BGA denoted Blue-green algae) are briefly introduced below as Table 1.

Table 1
Statistical table of water quality factor

	TEMP	PH	DO	EC	TUB	NH3-N	$\text{COD}_{\text{Mn}}$	TP	TN	Chl	BGA
Max	32.10	10.11	10.84	75.0	24.7	0.31	5.50	0.04	1.26	58.8	57231
Avg	23.42	7.68	7.95	54.5	7.27	0.08	2.46	0.017	0.73	13.7	14078
Min	12.60	6.04	4.39	41.2	0.30	0.02	0.95	0.002	0.29	2.7	116

Owing to the complexity of water quality and many parameters affecting water quality, it is necessary to construct a model for each indicator to complete the comprehensive water quality forecast. In this study, only three factors (DO, NH3-N and $\text{COD}_{\text{Mn}}$ ) that have great influence on water quality change are selected for modeling. We can build models for other factors using the same method in the future.

3.2 Data preprocessing

Because of sensor errors, transmission errors and other reasons, abnormal and missing data will appear in online monitoring of big data. These abnormal and missing data need to be detected and repaired, otherwise it will seriously affect the effective construction of water quality prediction model. In order to ensure the accuracy of the model, outliers and missing values were repaired and filled in this study, and the missing data in sample datasets were filled by linear interpolation in SPASS tools [23].

3.3 Data normalized processing

The inconsistency of dimensional and dimensional units among water quality indicators will interfere with the results of data analysis. Therefore, before modeling, it is necessary to normalize each indicator for comprehensive comparison purpose [24]. When all factors are in the same order of magnitude, some low-value features can be avoided to be submerged. It is particularly emphasized that the training data and test data need to be normalized respectively to ensure the prediction effect of the model and prevent the influence of test data on the prediction accuracy of the model. The method is as follows.

$\displaystyle{x}^{\prime}_{i}=\frac{x_{i}-\min({x_{i}})}{\max({x_{i}})-\min({x% _{i}})}({i=1,2,\cdots n})$ (11)

Where $\min({x_{i}})$ and $\max({x_{i}})$ represent the minimum and maximum of the $i$ th indicator of the training data set and the test data set, respectively. The normalized values are all in the range of 0–1.

4. Construction of water quality prediction model based on Leaky ESN

4.1 Single-day prediction model

Single-day prediction model based on Leay ESN acturally uses the historical data of the previous day to predict the water quality of the next day. The parameters in the training process include the size of the reservoir (i.e. N), the sparsity of the reservoir (SD), the spectral radius coefficient (SR), the input scale (IS), the regularization coefficient (Reg) and the leaky rate ${\alpha}$ . The main four parameters are N, SR, Reg and ${\alpha}$ . To ensure the accuracy of the prediction model, the selection of hyper-parameters is particularly important. It is more reliable and efficient to train the model by automatic hyper-parameter tuning than by empirical parameter tuning [25]. At present, the automatic hyper-parameter optimization algorithm which are commonly used include Bayesian optimization, random search and grid search. In this study, Bayesian optimization algorithm was used for hyper-parameter optimization [26]. Since the internal connection of the reservior is random, the noise of the reservior state obtained from the initial input sequences will be relatively large. Therefore, this study used some data (e.g. m) to initialize the state of the reservior to reduce the impact of noise. The training process is below.

(1)
Set the number of output and input neurons of the training dataset to 1, that is, L $=$ K $=$ 1, and the reservior capacity is between 50 and 300.
(2)
The training set $({u(t),t=1,2,\cdots,{n}})$ is input into the network through $W_{in}$ . For each input, a reservior state can be obtained through Eq. (4), and finally the state matrix $S=(s_{1}({i}),\linebreak s_{2}({i}),\cdots,s_{N}({i}))({i=m,m+1,\cdots,n})$ is obtained.
(3)
Using the least square method of ridge regression, $W_{\textit{out}}$ is obtained from the output $y(k)(k=1,2,\linebreak\cdots,n-m+1)$ of the training set and the state matrix $S$ of the reservior according to Eq. (8). At this time, The model has been trained.
(4)
Input the data from the test set into the trained model to obtain each predicted output.

Finally, RMSE and NSE are used to validate the prediction model.
4.2 Muti-day prediction model

Single-day prediction model can only predict the water quality data of the next day. In practical engineering applications and environmental monitoring, it is often necessary to predict the changes of each water quality factor in the next few days so as to meet the needs of early warning of water quality. Therefore, this study improved the model on the basis of Leaky ESN, so as to achieve the prediction of multi-day water quality changes with historical data, and constructed the models of DO, NH ${}_{3}$ -N and $\text{COD}_{\text{Mn}}$ to predict the water quality parameters of the next 3 days, 5 days and 7 days. Because the Bayesian optimization algorithm has less iterations and faster speed, it is still selected in the multi-day prediction model to realize automatic hyper-parameter optimization. The model training process is as follows.

(1)
Initializes $W_{in}$ and $W$ randomly, and the sparsity of $W$ is between 1% and 5%. Because the dimension of the reservior state matrix $S$ is relatively high, it is initialized to 0 before training. The reservoir capacity is between 50 and 500, the spectral radius coefficient is between 0.1 and 2, the leaky rate is between 1e-3 and 1, and the regularization coefficient is between 1e7 and 1e1.
(2)
The biggest difference from the single-day prediction model is the adjustment of input and output. The input of the training data set is changed to $u(t)=[{u(i),u({i+1}),\ldots,u({i+d})}]^{T},(d=6,t=\linebreak 1,2,\cdots,n,i=t)$ . Each matrix $u(t)$ is input into the network through $W_{in}({N\times({1+d})})$ . The state of the reservior at the next moment $t+1$ is obtained by each $u(t)$ and the state $s(t)$ of the current reservior through Eq. (4). The final state matrix of the reservoir is $S=({s_{1}({i}),s_{2}({i}),\cdots,s_{N}({i})})({i=m,m+1,\cdots,n})$ .
(3)
From the output matrix $y(k)=[{y(i),y({i+1}),\ldots,y({i+d})}]^{T}({d}$ take 3, 5, 7, respectively, ${k}=1,2,\cdots,{n}-{m}+1,{i}={k})$ of the training set and the state matrix $S$ obtained by step (2), $W_{\textit{out}}$ of each model is obtained according to Eq. (8). At this time, the 3-day, 5-day and 7-day prediction models based on Leaky ESN are trained.
(4)
Input the data from the test set into the model trained in step 3, and the prediction output of each model can be obtained by Eq. (5).

Finally, RMSE and NSE are used to verify the effect of each prediction model.

Table 2
Hyper-parameters and error values of single-day prediction model

Water quality factors hyper-parameters RMSE NSE

N SR ${\alpha}$ Reg

DO 300 0.8 0.3 1e-5 1.0e-3 0.997

$\text{NH}_{3}$ -N 100 0.9 0.3 1e-6 4.9e-4 0.961

$\text{COD}_{\text{Mn}}$ 300 1.25 0.4 1e-2 1.2e-3 0.975

Table 3
Hyper-parameters and error values of muti-day prediction model

Water quality factors Hyper-parameters Indicators d $+$ 3 d $+$ 5 d $+$ 7

N SR ${\alpha}$ Reg

DO 60 0.6 0.5 1e-2 RMSE 0.036 0.040 0.051

NSE 0.963 0.954 0.928

$\text{NH}_{3}$ -N 100 1.1 0.5 1e-2 RMSE 0.008 0.009 0.011

NSE 0.837 0.794 0.705

$\text{COD}_{\text{Mn}}$ 50 0.75 0.4 1e-2 RMSE 0.034 0.037 0.044

NSE 0.894 0.871 0.822

Figure 2.
Water quality prediction results (DO, $\text{NH}_{3}$ -N and $\text{COD}_{\text{Mn}}$ ) of single-day prediction model.

Figure 3.
Water quality prediction results (DO, $\text{NH}_{3}$ -N and $\text{COD}_{\text{Mn}}$ ) of 3-day prediction model.

Figure 4.
Water quality prediction results (DO, $\text{NH}_{3}$ -N and $\text{COD}_{\text{Mn}}$ ) of 5-day prediction model.

Figure 5.
Water quality prediction results (DO, $\text{NH}_{3}$ -N and $\text{COD}_{\text{Mn}}$ ) of 7-day prediction model.

5. Results and analysis of precision

Water quality factors	hyper-parameters	RMSE	NSE
	N	SR	${\alpha}$	Reg
DO	300	0.8	0.3	1e-5	1.0e-3	0.997
$\text{NH}_{3}$ -N	100	0.9	0.3	1e-6	4.9e-4	0.961
$\text{COD}_{\text{Mn}}$	300	1.25	0.4	1e-2	1.2e-3	0.975

Water quality factors	Hyper-parameters	Indicators	d $+$ 3	d $+$ 5	d $+$ 7
	N	SR	${\alpha}$	Reg
DO	60	0.6	0.5	1e-2	RMSE	0.036	0.040	0.051
					NSE	0.963	0.954	0.928
$\text{NH}_{3}$ -N	100	1.1	0.5	1e-2	RMSE	0.008	0.009	0.011
					NSE	0.837	0.794	0.705
$\text{COD}_{\text{Mn}}$	50	0.75	0.4	1e-2	RMSE	0.034	0.037	0.044
					NSE	0.894	0.871	0.822

5.1 Analysis of single-day prediction results

The results of prediction demonstrated that there is a good fit between the real monitoring value and the predicted value of the model. The forecasting accuracy can be reflected from the evaluation indicators. The error value of the Leaky ESN model constructed by Bayesian optimization algorithm for the prediction of each water quality indicator is shown in Table 2, and the forecasting effect is shown in Fig. 2 (where DO represents dissolved oxygen, $\text{NH}_{3}$ -N represents ammonia nitrogen, $\text{COD}_{\text{Mn}}$ represents permanganate index, N represents the capacity of the reservoir, SR represents the spectral radius coefficient, ${\alpha}$ represents the leaky rate, and Reg represents the regularization coefficient).

5.2 Analysis of muti-day prediction results

The results in Table 2 show that the NSE values of each water quality parameter obtained from the single-day forecasting model are all above 0.96, and the reliability of the model is very high. The hyper-parameter values of the improved forecasting models and the comparison of the evaluation indicators of these models are shown in Table 3 (DO represents dissolved oxygen, $\text{NH}_{3}$ -N represents ammonia nitrogen, $\text{COD}_{\text{Mn}}$ represents permanganate index, N represents the capacity of the reservoir, SR represents the spectral radius coefficient, ${\alpha}$ represents the leaky rate, and Reg represents the regularization coefficient, d $+$ 3 represents the data change after 3 days of prediction, d $+$ 5 represents the data change after 5 days of prediction, d $+$ 7 represents the data change after 7 days of prediction).

The effect of each water quality parameter predicted by the 3-day prediction model, 5-day prediction model and 7-day prediction model are shown in Figs 3 to 5.

Compared with the above prediction results, it can be concluded that with the increase of time, the RMSE value of all models will increase, and the NSE value will decrease. This is in line with the model prediction accuracy will decrease with time series. From the multi-day prediction results of three water quality parameters, the prediction accuracy of DO is the highest, and the NSE value can still reach 0.928 after 7 days. Even $\text{NH}_{3}$ with the worst prediction effect, the NSE value was above 0.7 after 7 days. Overall, these models have good quality, high reliability and good applicability.

6. Conclusions

In this paper, the single-day and multi-day forecasting models based on ridge regression Leaky ESN were constructed to predict the water quality parameters of DO, $\text{NH}_{3}$ -N and $\text{COD}_{\text{Mn}}$ in Dongzhen Reservoir. The comparison between the predicted results and the real monitoring values shows that the models both have good prediction effect, good stability and reliability. Therefore, all the models established in this paper are applicable to the water quality change warning and prediction system. However, in the practical application process, due to the continuous updating of water quality data, the models also need to be dynamically adjusted. And this paper does not build the models for other water quality factors. Therefore, it is necessary to continue to study the Leaky ESN based on online learning, and further optimize the models to improve the network identification and prediction accuracy of training samples. Then the members of the research group will continue to build forecasting models for other water quality indicators. In addition, LSTM neural network modeling can be considered to compare the accuracy and generalization ability of various models.

Footnotes

Acknowledgements

Key R & D projects in Hebei Province “Study on watershed water quality prediction method based on measured and remote sensing data of water environment” under Grant 21370103D.

Key R & D projects in Hebei Province “Research and demonstration of multi-source remote sensing monitoring and early warning technology for typical ecological disasters of Hebei Province coastal” under Grant 21373301D.

Key R & D projects in Hebei Province “Unmanned Airborne Multispectral Joint Hyperspectral Monitoring and Early Warning Technology for Marine Ecological Disasters and Environmental Pollution” under Grant 19273301D.

General project of Hebei Natural Science Foundation “Study on the mechanism of marine low frequency variation triggered by the cascade process of upper ocean kinetic energy” under Grant D2019407046.

National key R & D projects “Study on Frequent Ecological Disasters Causes and Monitoring and Early Warning System in Qinhuangdao Sea Area” under Grant 2019YFC1407903.

Research on Social Sciences Development in Hebei Province “Research on the Construction of River Basin Water Quality Prediction Information System in Hebei Province” under Grant 20210201445.

Research on Social Sciences Development in Hebei Province “Red-tide Monitoring Information System Construction in Hebei coastal waters” under Grant 20200302075.

Hebei Agricultural Data Intelligent Perception and Application Technology Innovation Center, HebeiQinhuangdao, 066004.

References

Wang

Cui

, et al. Research and application of human health water quality standard characteristic parameters. Environmental science. 2021; 34(7): 1553-1561.

Adyasari

Pratama

Teguh

, et al. Anthropogenic impact on Indonesian coastal water and ecosystems: Current status and future opportunities. Marine Pollution Bulletin. 2021; 171: 112689.

Madhav

Ahamad

Singh

, et al. Water pollutants: sources and impact on the environment and human health. Sensors in Water Pollutants Monitoring: Role of Material. Springer, Singapore. 2020; 43-62.

Krishna

Sarath

Kumaraswamy

, et al. Iot based water parameter monitoring system. In 2020 5th International Conference on Communication and Electronics Systems (ICCES). in IEEE Access. 2020 Jun; pp. 1299-1303.

Nandakumar

Sangeeth

Thomson

, et al. Real time water contamination monitor using cloud, IOT and embedded platforms. In 2020 International Conference on Smart Electronics and Communication (ICOSEC). in IEEE Access. 2020 Sep; pp. 854-858.

Al-Sulttani

Al-Mukhtar

Roomi

, et al. Proposition of new ensemble data-intelligence models for surface water quality prediction. in IEEE Access. 2021; 9: 108527-108541.

. Hybrid decision tree-based machine learning models for short-term water quality prediction. Chemosphere. 2020; 249: 126169.

Ahmed

Othman

Afan

, et al. Machine learning methods for better water quality prediction. Journal of Hydrology. 2019; 578: 124084.

Aldhyani

Al-Yaari

Alkahtani

, et al. Water quality prediction using artificial intelligence algorithms. Applied Bionics and Biomechanics. 2020 Dec 30; 2020.

10.

Zhou

Wang

Xiao

, et al. Water quality prediction method based on IGRA and LSTM. Water. 2018; 10(9): 1148.

11.

Chen

Zhou

, et al. Comparative analysis of surface water quality prediction performance and identification of key water parameters using different machine learning models based on big data. Water Research. 2020; 171: 115454.

12.

Noori

Kalin

Isik

. Water quality prediction using SWAT-ANN coupled approach. Journal of Hydrology. 2020; 590: 125220.

13.

Zhao

Zhang

Xie

, et al. Water quality simulation of Minjiang estuary waterworks based on BP artificial neural network. Environmental Science and Technology. 2020; 43(S1): 198-203.

14.

Zheng

Yang

, et al. Prediction and early warning model of water quality in construction area based on GA-BP neural network. Journal of Chongqing Jiaotong University (Natural science edition). 2020; 39(12): 106-110.

15.

Apaydin

Feizi

Sattari

, et al. Comparative analysis of recurrent neural network architectures for reservoir inflow forecasting. Water. 2020; 12(5): 1500.

16.

Sha

Zhang

, et al. RNN-based subway passenger flow rolling prediction. in IEEE Access. 2020; 8(2020): 15232-15240.

17.

Wei

Zhang

Yang

, et al. Machine learning for pore-water pressure time-series prediction: Application of recurrent neural networks. Geoscience Frontiers. 2021; 12(1): 453-467.

18.

Jaeger

. The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. Bonn, Germany: German National Research Center for Information Technology GMD Technical Report. 2001; 148(34): 13.

19.

Jaeger

, et al. Optimization and applications of echo state networks with leaky-integrator neurons. Neural Networks. 2007; 20(3): 335-352.

20.

Lukoševičius

. A practical guide to applying echo state networks. Neural networks: Tricks of the trade. Springer, Berlin, Heidelberg. 2012; 659-686.

21.

Zhao

Zhang

, et al. Water quality prediction in the waste water treatment process based on ridge regression echo state network. IOP Conference Series: Materials Science and Engineering. IOP Publishing. 2018; 435(1): 012025.

22.

Zhou

. Real-time probabilistic forecasting of river water quality under data missing situation: Deep learning plus post-processing techniques. Journal of Hydrology. 2020; 589: 125164.

23.

Vieira

. Introduction to real world statistics: With step-by-step SPSS instructions. Routledge; 2017.

24.

Folorunso

Aibinu

Kolo

, et al. Effects of data normalization on water quality Model in a recirculatory aquaculture system Using artificial neural network. I-manager’s Journal on Pattern Recognition. 2018; 5(3): 21.

25.

Feurer

Hutter

. Hyperparameter optimization. Automated machine learning. Springer, Cham. 2019; 3-33.

26.

Chen

Zhang

, et al. Hyperparameter optimization for machine learning models based on Bayesian optimization. Journal of Electronic Science and Technology. 2019; 17(1): 26-40.

Research on water quality prediction model based on echo state network

Abstract

Keywords

1. Introduction

2. Leaky ESN principle and evaluation indicator

2.1 Leaky ESN principle

3.1 Sample datasets

Table 1 Statistical table of water quality factor

3.3 Data normalized processing

4.1 Single-day prediction model

5.1 Analysis of single-day prediction results

5.2 Analysis of muti-day prediction results

6. Conclusions

Footnotes

Acknowledgements

References

Table 1
Statistical table of water quality factor