Prediction method of cyanobacterial blooms spatial-temporal sequence based on deep belief network and fuzzy expert system

Abstract

The process of cyanobacteria bloom in rivers and lakes is a highly non-stationary and non-linear process. The existing cyanobacterial bloom prediction method mainly uses time series model and single intelligent model, but time series model and single intelligent model cannot effectively explain the cyanobacterial bloom generation process, and the prediction accuracy is not high. In view of the above deficiencies, this paper proposes to use the cyanobacteria bloom spatiotemporal sequence data for modeling. Considering the characteristics of large-scale nonlinear trend term and small-scale residual term in the cyanobacteria bloom spatial-temporal sequence, the deep belief networks is used to model and explain the large-scale nonlinear trend term of the cyanobacteria bloom spatiotemporal sequence. Then use the time autocorrelation model and the multivariate spatiotemporal autocorrelation model to model and interpret the small-scale residual term; finally, after superimposing the large-scale nonlinear trend term and the small-scale residual term, the adaptive neuro-fuzzy system model is used to predict the chlorophyll a value of the water. Therefore, a fuzzy spatial and temporal sequence prediction method based on fuzzy expert system is proposed. The model verification results show that compared with the existing time series model and single intelligent model, the method can more fully explain the non-stationary and nonlinear dynamic changes of the cyanobacterial bloom spatial-temporal sequence. It provides a new method for accurately predicting cyanobacteria bloom in rivers and lakes.

Keywords

Cyanobacteria bloom prediction deep belief networks fuzzy expert system spatiotemporal sequence

1 Introduction

With the rapid development of the social economy, agriculture and industry have made rapid progress. The use of a large amount of chemical fertilizers, pesticides, and industrial raw materials has led to excessive nutrients entering the water. It causes the rapid propagation of algae and other plankton in water, the decrease of dissolved oxygen in water, and the massive death of aerobic organisms in water, leading to eutrophication of rivers and lakes. This is already a global problem of water environment [1]. Cyanobacterial blooms are usually caused by “eutrophication of water bodies.” After the cyanobacteria blooms, the color of the water usually shows green or blue. Cyanobacteria bloom is the main problem faced by river and lake water pollution in China. The cyanobacteria bloom seriously affects the aquaculture, the drinking water quality of the basin and other water resources, and has a negative impact on the environment and economy near the basin [2]. Relevant regulatory agencies still lack effective cyanobacterial bloom prediction methods, and can not take effective precautions before the cyanobacteria blooms to reduce the damage of cyanobacteria blooms. Therefore, it is of great significance to effectively prevent the occurrence of cyanobacteria blooms in rivers and lakes by establishing available models to monitor and predict water quality [3, 4].

The growth process of cyanobacteria is complex. It is affected by the physical and chemical conditions of the water, and also affected by external factors such as changes in the natural environment. Therefore, different influencing factors have different effects on the growth and outbreak of cyanobacteria blooms [5, 6]. At present, the prediction of cyanobacteria blooms mainly uses two types of early warning models, namely the mechanism model and the data driven model. The early warning model of water bloom mechanism mainly uses the physiological knowledge of algae growth and reproduction and the physical and chemical changes in water to simulate the content of algae in water. However, the mechanism model needs to consider the ecological process is more cumbersome, and it is necessary to clarify the food chain relationship of algae and the reproductive law of algae, which leads to too many parameters to be determined by the model. Therefore, it is difficult to directly establish a cyanobacterial bloom mechanism model. Among them, Kuang [7], komatsu [8], Wang L L[9], etc. have conducted corresponding research on this. Compared to the mechanistic model, the data-driven model was modeled by using cyanobacterial bloom data. The data-driven model use regression analysis, time series, or intelligent networks to establish an optimal mathematical model between input and output data for cyanobacterial bloom prediction. At the same time, some progress has been made. Wang, XY etc. proposed a hybrid mechanism modeling method based on water bloom mechanism model and data-driven model to predict cyanobacterial blooms [10], and analyzed the cyanobacteria bloom mechanism [11]. BAI X Z etc. proposed a dynamic clustering algorithm based on effectiveness function optimization to achieve cyanobacterial bloom dynamics and small-scale neighborhood optimization prediction [12]. Wang, L etc. proposed a multivariate time series analysis compensation model based on neural network and support vector machine and a nonlinear dynamic model of cyanobacterial growth time-varying system, respectively predicting cyanobacteria blooms [13, 14]. LIU Z W etc. Liu Zaiwen etc. used a variety of intelligent algorithms to study cyanobacteria blooms in Beijing and Taihu Lake [15]. He J etc. realized the monitoring and prediction of water quality through BP neural network combined with GIS [16]. Slawa Bruder etc. proposed a model based on adaptive fuzzy network for algae growth for cyanobacterial bloom prediction [17].

The traditional cyanobacterial bloom prediction model using a single water bloom time series data does not reflect the diverse characteristics of cyanobacterial blooms. The formation mechanism of cyanobacteria blooms is complex, and the critical factors for the occurrence of cyanobacterial blooms are still not very clear. Therefore, the multidimensional space-time data of water bloom is used instead of a single water bloom time series data to expand the data dimension. The concentration of chlorophyll a in water has a close correlation with cyanobacterial blooms. When the content of chlorophyll a exceeds the critical point, it can be determined as a cyanobacterial bloom. Therefore, in the cyanobacterial bloom warning, the chlorophyll a concentration is used as a characterization factor for judging whether or not the cyanobacterial bloom is outbreak. In order to solve the problem that the single intelligent model has low generalization ability and low prediction accuracy on non-stationary water bloom spatiotemporal sequence data, and solve the limitation that traditional time series model can not be directly applied to non-stationary nonlinear water bloom spatiotemporal sequence data. In this paper, a hybrid model water bloom prediction method combining deep belief networks, time autocorrelation model, multivariate space-time autocorrelation model and adaptive network-based fuzzy inference system is proposed and applied to the prediction of water bloom spatiotemporal sequence data [18 –21]. The model models the large-scale nonlinear trend and the small-scale residual term separately by intelligent model, time series model and multivariate spatio-temporal sequence model. The large-scale nonlinear trend and the small-scale residual term are superimposed, and then the adaptive fuzzy neural inference system is used to fuse and predict the data, which effectively improves the generalization ability and prediction accuracy of the water bloom spatiotemporal sequence [22, 23].

2 Installing and using the microsoft word template

In this paper, we use the fuzzy expert system based on water bloom spatiotemporal sequence model to predict chlorophyll a. A standard water bloom spatiotemporal sequence can be expressed as: $Z_{i} (t) = μ_{i} (t) + e_{i} (t)$ (1)

Z_i (t) is the actual observation of the spatiotemporal sequence, and μ_i (t) is the large-scale nonlinear trend term, indicating the large-scale nonlinear trend of the spatiotemporal sequence at time t and position i. e_i (t) is a small-scale residual term at time t and position i. The specific model building steps in Fig. 1 are as follows:

Fig.1

Model building step.

2.1 Large-scale nonlinear trend extraction based on deep belief networks

The deep belief networks consists of a multi-layer neural network model consisting of a multi-layer constrained Boltzmann machine (RBM) and a BP neural network, which can effectively represent and train nonlinear spatiotemporal data. The restricted Boltzmann machine consists of a layer of visual neurons v and a layer of hidden neurons h. v is the input layer of the cyanobacterial bloom spatiotemporal sequence, and the h layer neuron output is the characteristic value extracted by the bloom spatial and cyanobacterial temporal sequence. v and h are connected by a neural network weight matrix W and two offset vectors a and b, and the parameter θ = (w, a, b) can be used to represent the parameters of the restricted Boltzmann machine. The restricted Boltzmann machine model is an energy-based model. When the cyanobacterial bloom spatiotemporal sequence is input into the network from the visible layer, the energy function in a given state (v, h) is defined as: $E (v, h) = - h^{T} Wv - a^{T} v - b^{T} h$ (2)

The cyanobacteria bloom time-space sequence is used to train the restricted Boltzmann machine. The purpose is to update the weights and offsets of the neurons in the network to minimize the energy allocated by the network and make the network in the most stable state. The activation probabilities of h and v are as follows: $\begin{matrix} P (h_{j} = 1 | v) = sigmoid (a_{i} + \sum_{i} v_{i} w_{ij}) \\ P (v_{i} = 1 | h) = sigmoid (b_{j} + \sum_{j} h_{j} w_{ij}) \end{matrix}$ (3)

Using the contrastive divergence algorithm as the learning algorithm for limiting the Boltzmann machine, the update amount of the parameter vector θ = (w, a, b) is as follows: $\begin{matrix} Δ w_{ij} = γ (< v_{i} h_{j} >_{0} - < v_{i} h_{j} >_{k}) \\ Δ b_{j} = γ (< h_{j} >_{0} - < h_{j} >_{k}) \\ Δ a_{j} = γ (< v_{i} >_{0} - < v_{i} >_{k}) \end{matrix}$ (4)

γ is the learning rate; <g > ₀ is the expectation of the input data set; <g > _k is the expectation of the data reconstructed by using the contrastive divergence algorithm. The output of the upper layer of the restricted Boltzmann machine is fully trained as the input to the next layer of restricted Boltzmann machines, continuing to train the network. When all the restricted Boltzmann machines are fully trained, then the BP neural network is used as the output. Taking the cyanobacteria bloom time-space sequence as input, the spatiotemporal sequence is input into the deep belief networks in time-space order. Set the appropriate number of hidden layer neurons, the number of training x, the learning rate η₁ of the restricted Boltzmann machine, and the learning rate η₂ of the improved BP network to fully train the network. At this time, the large-scale nonlinear trend term in the water bloom spatiotemporal sequence is extracted by the deep belief networks, and the remaining small-scale residual term of the water bloom spatiotemporal sequence is also obtained.

2.2 Small-scale residual term remodeling

The large-scale nonlinear trend term of the water bloom spatiotemporal sequence contains large-scale nonlinear trend items of chlorophyll a and multivariate spatiotemporal meteorological sequences. At the same time, the small-scale residual term of the water bloom spatiotemporal sequence is obtained. The residual term of the water bloom spatiotemporal sequence contains the small-scale residual term of the chlorophyll a and the multivariate spatiotemporal meteorological sequences. Because the multi-water quality data is single-point data, multivariate meteorological data is multi-point data, and the types of indicators indicated are different, it is necessary to model the two separately. The time autocorrelation model (AR) is used to model the small-scale residuals of chlorophyll a (denoted as e₁ (t)), and the multivariate space-time autocorrelation model (STVAR) is used to model the small-scale residuals of the multivariate spatiotemporal meteorological sequences (denoted as e_n (t)).

2.2.1 Establishment of spatial weight matrix for multiple meteorological monitoring points

Use W^(d) to represent the spatial weight matrix, which quantifies the metric spatial adjacency. It also reflects the weight of influence between different regions of the space. The multivariate spatiotemporal meteorological monitoring point is composed of multiple meteorological stations, each with a different distance relationship. The semi-variant function is used to analyze the variation structure in the continuous spatial sequence, and the weight relationship between different sites is constructed. The semi-variant function can calculate spatiotemporal variability and can calculate the range of variation and the dependence of space. The resulting spatial weight matrix is represented by W^(d).

2.2.2 Using the time autocorrelation model (AR) to model the small-scale residual term of the multi-water quality sequence:

For the time series {e₁ (t) } , t = 1, 2, ⋯ , N composed of small-scale residuals of small-scale multivariate water quality sequences, the basic structure of the n-order time autocorrelation model is expressed as:

$\begin{matrix} e_{1} (t) = & ϕ_{1} e_{1} (t - 1) + ϕ_{2} e_{1} (t - 2) + \dots + \\ ϕ_{n} e_{1} (t - n) + ξ (t) \end{matrix}$ (5)

ϕ₁, ϕ₂, ⋯ , ϕ_n is the is the parameter to be estimated in the model; ξ (t) is the white noise sequence with a mean of 0 and a variance of σ²; n is the order of the model; N is the number of data used for modeling; the parameters of the model can be estimated using least squares. Can be expressed as the following equations: $Y = X Φ + ξ (t)$ (6)

In the formula: $\begin{matrix} X = [\begin{matrix} e_{1} (n) & e_{1} (n - 1) & \dots & e_{1} (1) \\ e_{1} (n + 1) & e_{1} (n) & \dots & e_{1} (2) \\ ⋮ & ⋮ & ⋱ & ⋮ \\ e_{1} (N - 1) & e_{1} (N - 2) & \dots & e_{1} (N - n) \end{matrix}], \\ Y = {[\begin{matrix} e_{1} (n + 1) & e_{1} (n + 2) & \dots & e_{1} (N) \end{matrix}]}^{T}, \\ ξ (t) = [\begin{matrix} ξ (n + 1) & ξ (n + 2) & \dots & ξ (N) \end{matrix}]^{T}, \\ Φ = [\begin{matrix} ϕ_{1} & ϕ_{2} & \dots & ϕ_{n} \end{matrix}]^{T} \end{matrix}$ (7)

From this, the least squares estimate of the parameter Φ of the n-order autocorrelation model to be estimated is obtained as: $Φ = (X^{T} X)^{- 1} X^{T} Y$ (8)

2.2.3 Using the multivariate space-time autocorrelation model (STVAR) to model the small-scale residuals of the multivariate spatiotemporal meteorological sequences:

The multivariate spatiotemporal meteorological sequences contains monitoring data for multiple sites, so the small-scale residual term e_n (t) of the multivariate spatiotemporal meteorological sequences is represented as z_ij (t) according to the site relationship. Where i is the space monitoring point label, j is the number of the j th factor in the space monitoring point, and t is the time. The basic structure of the multivariate space-time autoregressive model is: $\begin{matrix} Z (t) = \sum_{k = 1}^{p} \sum_{h = 0}^{1} Φ_{kh} Z (t - k) W_{h}^{(d)} + ɛ (t) \\ = \sum_{k = 1}^{p} Φ_{k 0} Z (t - k) + \sum_{k = 1}^{p} Φ_{k 1} Z (t - k) W_{1}^{(d)} + ɛ (t) \end{matrix}$ (9)

The matrix form of each variable in the model is: $\begin{matrix} Z (t) = [\begin{matrix} z_{11} (t) & z_{12} (t) & \dots & z_{1 N} (t) \\ z_{21} (t) & z_{22} (t) & \dots & z_{2 N} (t) \\ ⋮ & ⋮ & ⋱ & ⋮ \\ z_{M 1} (t) & z_{M 2} (t) & \dots & z_{MN} (t) \end{matrix}] \\ Φ_{kh} = [\begin{matrix} φ_{11 kh} & φ_{12 kh} & \dots & φ_{1 Mkh} \\ φ_{21 kh} & φ_{22 kh} & \dots & φ_{2 Mkh} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ φ_{M 1 kh} & φ_{M 2 kh} & \dots & φ_{MMkh} \end{matrix}] \\ ɛ (t) = [\begin{matrix} ɛ_{11} (t) & ɛ_{12} (t) & \dots & ɛ_{1 N} (t) \\ ɛ_{21} (t) & ɛ_{22} (t) & \dots & ɛ_{2 N} (t) \\ ⋮ & ⋮ & ⋱ & ⋮ \\ ɛ_{M 1} (t) & ɛ_{M 2} (t) & \dots & ɛ_{MN} (t) \end{matrix}] \\ W_{h}^{(d)} = [\begin{matrix} w_{11 h} & w_{12 h} & \dots & w_{1 Nh} \\ w_{21 h} & w_{22 h} & \dots & w_{2 Nh} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ w_{N 1 h} & w_{N 2 h} & \dots & w_{NNh} \end{matrix}] \end{matrix}$ (10)

Z (t) represents the M × N dimensional space-time vector at time t, M is the number of factors in the multivariate spatiotemporal meteorological sequences, and N is the number of spatial monitoring points in the multivariate spatiotemporal meteorological sequences. Based on the error term of the model, the log likelihood function of the model is established. Using the log-likelihood function to derive partial derivatives of the model parameters, the following equations are obtained: $\begin{matrix} [\begin{matrix} \frac{\partial ln L}{\partial φ_{11 kh}} = 0 & \frac{\partial ln L}{\partial φ_{12 kh}} = 0 & \dots & \frac{\partial ln L}{\partial φ_{1 Mkh}} = 0 \\ \frac{\partial ln L}{\partial φ_{21 kh}} = 0 & \frac{\partial ln L}{\partial φ_{22 kh}} = 0 & \dots & \frac{\partial ln L}{\partial φ_{2 Mkh}} = 0 \\ ⋮ & ⋮ & ⋱ & ⋮ \\ \frac{\partial ln L}{\partial φ_{M 1 kh}} = 0 & \frac{\partial ln L}{\partial φ_{M 2 kh}} = 0 & \dots & \frac{\partial ln L}{\partial φ_{MMkh}} = 0 \end{matrix}] \\ (k = 0, 1, \dots, p, h = 0, 1) \frac{\partial ln L}{\partial σ^{2}} = 0 \end{matrix}$ (11)

Solve the above equations and obtain the parameters of the demand solution of the multivariate space-time autocorrelation model.

2.3 Superposition of large-scale nonlinear trend term and residuals, and calculation of predicted target area meteorological values

2.3.1 Superposition of large-scale nonlinear trend term prediction values and small-scale residual term prediction values

Firstly, the time autocorrelation model and the multivariate space-time autocorrelation model are used to obtain the small-scale residual term predictions of the multivariate water quality sequence and the multivariate spatiotemporal meteorological sequences. Next, it is superimposed with the predicted large-scale nonlinear trend term of the water bloom spatiotemporal sequence to obtain the predicted value of the future water bloom spatiotemporal sequence after the small-scale residual term correction, namely: ${\hat{Z}}_{i} (t) = {\hat{μ}}_{i} (t) + {\hat{e}}_{i} (t)$ (12)

${\hat{Z}}_{i} (t)$ is the predicted value of the future water bloom spatiotemporal sequence; ${\hat{μ}}_{i} (t)$ is the large-scale nonlinear trend term predictive value; ${\hat{e}}_{i} (t)$ is the small scale residual term predictive value.

2.3.2 The meteorological prediction value of the target area is obtained by the inverse distance weighting method:

The multivariate spatiotemporal meteorological sequences contains N meteorological monitoring points, and the single monitoring points in the target area cannot accurately reflect the meteorological data of the target area monitoring points where the multi-water quality sequence is located. Therefore, it is necessary to calculate the future meteorological data of the target area monitoring point by the values of several surrounding meteorological monitoring points.

Set the distance between the surrounding meteorological monitoring points and the target area to be d_i, and set the meteorological impact of each meteorological monitoring point on the target area to be isotropic. Then the impact of each meteorological monitoring point on the meteorological weather of the target area is only negatively correlated with the distance between them. The inverse distance weighting method is calculated as follows: $z (s_{0}) = \sum_{i = 1}^{N} λ_{i} z (s_{i})$ (13)

z (s₀) indicates the predicted value of the meteorological data of the target area; z (s_i) indicates the predicted value of the meteorological data around the target area; λ_i indicates the weight of the ith meteorological station, and the calculation method of λ_i is as follows: $λ_{i} = d_{i}^{- p} / \sum_{i = 1}^{N} d_{i}^{- p}, \sum_{i = 1}^{N} λ_{i} = 1$ (14)

d₁, d₂, ⋯ , d_N represents the distance between each monitoring point and the target area, p is a power exponential control variable, usually takes 2, and the predicted values of the N monitoring points are multiplied by the influence weights and summed to obtain the meteorological prediction values of the target area.

2.4 Prediction of chlorophyll a value in target waters using Adaptive network-based fuzzy inference system

The adaptive network-based fuzzy inference system (ANFIS) is an organic combination of fuzzy inference system and artificial neural network, which has the advantages of strong neural network learning ability, fast computing speed and rich chain structure [24 –26]. It can use the learning mechanism of neural network to compensate for the shortcomings of fuzzy reasoning. The neural network combined by the two can express human knowledge, has the characteristics of distributed information storage and learning, and can effectively predict nonlinear and non-stationary systems. Figure 2 shows a typical two-input and single-output ANFIS diagram. The structure of ANFIS can be divided into five layers: The fuzzy segmentation layer, the rule inference layer, the fuzzification layer, the defuzzification layer, and the output layer. O_n,i is used to represent the output of the ith node of the nth layer.

Fig.2

Schematic diagram of ANFIS.

The first layer: the fuzzy segmentation layer. The values of the variable input network can be represented using the neurons nodes of this layer, which respectively represent a fuzzy combination, and each fuzzy set is represented by a node function. The output of each node is the degree of membership, which indicates the degree to which the input of the corresponding node belongs to a fuzzy rule. The output function of the ith node is: $O_{1, i} = μ_{A_{i}} (x_{1}), i = 1, 2 or O_{1, i} = μ_{B_{i}} (x_{2}), i = 1, 2$ (15)

The second layer: the rule reasoning layer. The different fuzzy sets are combined to form the corresponding rules, and the if-then rules constitute the rule base. The inference engine maps the input fuzzy set to the output fuzzy set, representing the relationship between the fuzzy input and the fuzzy output. The output of each unit uses the product of all input signals, which reflects the credibility of the rule. The output of each node is: $O_{2, i} = w_{i} = μ_{A_{i}} (x_{1}) \times μ_{B_{i}} (x_{2}), i = 1, 2$ (16)

The third layer: the fuzzy layer. The nodes of this layer are represented by N in the figure, and the excitation strength of each rule is normalized. In the rule i, the ratio between w_i and all rules w is: $O_{3, i} = {\bar{w}}_{i} = w_{i} / (w_{1} + w_{2}), i = 1, 2$ (17)

The fourth layer: defuzzification layer. Map the fuzzy output set to an exact output whose output is: $O_{4, i} = {\bar{w}}_{i} f_{i} = {\bar{w}}_{i} (p_{i} x_{1} + q_{i} x_{2} + r_{i}), i = 1, 2$ (18)

Where ${\bar{w}}_{i}$ is the output of the third layer, {p_i, q_i, r_i} is the parameter set of the node;

The fifth layer: the output layer. This layer is labeled with the symbol Σ as a fixed node that calculates the total output of all signals: $O_{5, i} = \sum {\bar{w}}_{i} f_{i} = \sum w_{i} f_{i} / \sum w_{i}, i = 1, 2$ (19)

The algorithm for training ANFIS is a hybrid algorithm combining the least squares algorithm and the backpropagation algorithm, and the back propagation algorithm is used to determine the condition parameters in the neural network. The conditional parameters of the neural network are the center and width of the first-level membership function, and the least squares method is used to correct the center and width of the neural network condition parameters. When network learning, the network error can be calculated according to the actual output value and the target output value, and then the error back propagation can adjust the parameters of the neural network, and the global best advantage of the parameters to be adjusted can be obtained. The adaptive network-based fuzzy inference system is based on the modeling method of the previous data. The membership function and fuzzy rules in the model are obtained through the learning of the previous data. Using the Matlab toolbox to assist in the construction of an adaptive network-based fuzzy inference system, the establishment process mainly requires the following steps:

Construct the initial FIS structure using the genfis1 function:

Calling the genfis1 function, the function uses the mesh segmentation method to generate the FIS structure according to the given data set, and obtains the initial fuzzy inference system matrix fismat and the initial expert rules.

Use the anfis function to build the system:

The training data, the fuzzy inference system matrix, and the training parameters of ANFIS are adjusted. The anfis function is used to train and correct the system. The corrected fuzzy inference system matrix fismat and expert rules are obtained, and the error items of the training set are obtained.

Calculate the output of the FIS:

After obtaining the training and correction system of the training set, the data of the new input system is subjected to fuzzy inference calculation through the evalfis function, and the model output value is obtained after the input data is subjected to fuzzification, fuzzy reasoning and defuzzification. The system output is the concentration value of chlorophyll a.

3 Model instance verification

Take the single-point multi-water quality data collected by a water monitoring station in Jiangsu Province in recent years and the multivariate spatiotemporal meteorological data of three meteorological stations near the target area provided by the China Meteorological Data Network as an example. A total of 1095 sets of spatio-temporal data were obtained in the past 3 years. The data was first screened, missing items were interpolated, and normalized. The specific indicators are shown in Table 1. Select 70% of the front part of the data set, a total of 775 sets of spatiotemporal data as training data, select 30% of the back of the data set, a total of 320 sets of spatiotemporal data as test data;

Table 1
Data indicator

Indicator name Chlorophyll a Dissolved oxygen Total nitrogen Water temperature Wind speed Weather temperature

Indicator unit μg/L mg/L mg/L °C m/s °C

Indicator name	Chlorophyll a	Dissolved oxygen	Total nitrogen	Water temperature	Wind speed	Weather temperature
Indicator unit	μg/L	mg/L	mg/L	°C	m/s	°C

The deep belief networks input data is the water bloom spatiotemporal data of the past time, and the output is the large-scale nonlinear trend term and the small-scale residual term of the extracted chlorophyll a and the multivariate spatiotemporal meteorological data. The input spatio-temporal data is composed of equal-length moving windows that are fixed in length and time-sequentially forward.

In order to prevent the deep belief networks and the spatio-temporal sequence hybrid model from being deformed, to ensure better convergence effect and reduce the calculation amount of the network, it is necessary to normalize the original spatiotemporal data: $z_{i} (t)^{*} = \frac{z_{i} (t) - z_{\min}}{z_{\max} - z_{\min}}$ (20)

z_i (t) is the true value of the single item index of the water bloom spatiotemporal sequence, z_max is the maximum value of the single item index in the water bloom spatiotemporal sequence data, z_min is the minimum value of the single item index of the water bloom spatiotemporal sequence data, and z_i (t) ^* is the index after normalization. Normalize all the water bloom spatiotemporal data, as shown in Fig. 3 is a schematic diagram of partially normalized data.

Fig.3

Partially normalized data.

3.1 Large-scale nonlinear trend extraction based on deep belief networks

Firstly, the deep belief networks is used to extract the non-linear trend term of chlorophyll a from multi-element water quality data. The number of input and output nodes of the model depends on the structure of the input data. The large-scale non-linear trend terms of chlorophyll a at the next moment are extracted from the multi-variate water quality data of the first 6 time points. The input neuron nodes of the model are 24, the output nodes are 1, and the output node represents the future large-scale nonlinear trend term of chlorophyll a at the next moment in the future. The number of two hidden layer nodes in the two-layer deep belief networks is [50 50], the number of iterations is 1000, the learning efficiency η₁ of RBM is 0.03, and the learning efficiency η₂ of BP neural network neurons is 0.5. The large-scale nonlinear trend term of chlorophyll a is extracted by using a deep belief networks. Figure 4 is a schematic diagram of the large-scale nonlinear trend term of chlorophyll a extracted by the model. Similarly, the deep belief networks is used to extract large-scale nonlinear trend items of wind speed and meteorological temperature in the temporal and spatial sequence of water bloom.

Fig.4

Large-scale nonlinear trend term of chlorophyll a.

3.2 Small-scale residual term remodeling

3.2.1 Establishment of spatial weight matrix for multiple meteorological monitoring points

There are 3 meteorological monitoring points (site 1, site 2, site 3) near the target area. By extracting the large-scale nonlinear trend term of the water bloom spatiotemporal sequence, the small-scale trend term of the water bloom spatiotemporal sequence can be obtained. The total small-scale trend term contains the small-scale trend items of the multivariate spatiotemporal meteorological sequences, and Fig. 5 is a schematic diagram of some small-scale trend term. After measuring, the distance relationship between the stations is shown in Table 2:

Fig.5

Small scale trend item.

Table 2

Distance relationship between meteorological stations

Site relationship	Site 1 – Site 2	Site 1 – Site 3	Site 2 – Site 3
Distance	152.4 km	145.8 km	181.5 km

A spatial influence weight matrix between the three sites is established by the distance relationship between the three sites. Where w_ij is the weight of the impact of Site i on Site j, so a 3 × 3 spatial weight matrix is established: $W^{(d)} = [\begin{matrix} 0 & 0.4361 & 0.4518 \\ 0.5325 & 0 & 0.4699 \\ 0.4642 & 0.4125 & 0 \end{matrix}]$ (21)

The following is a remodeling of small-scale trend items in the temporal and spatial sequence of water blooms.

3.2.2 Using the time autocorrelation model (AR) to model the small-scale residual term of the multi-water quality sequence:

The stability of the water bloom spatiotemporal sequence is tested, and the small-scale residual term fluctuates around the mean 0, which is a stationary process. Next, we use the 4-order time autocorrelation model to model. The model structure is: $e (t) = ϕ_{1} e (t - 1) + ϕ_{2} e (t - 2) + ϕ_{4} e (t - 4) + ξ (t)$ (22)

Using the least squares estimation method to estimate the model parameters, we can conclude that the parameters ϕ₁, ϕ₂, ϕ₃, ϕ₄ of the 4-order time autocorrelation model are shown in Table 3.

Table 3

Time autocorrelation model parameters

Parameter	ϕ ₁	ϕ ₂	ϕ ₃	ϕ ₄
Estimated value	0.696	– 0.0443	– 0.464	0.302

Obtain a small-scale residual term model of chlorophyll a to explain the trend of future small-scale residuals;

Using the multivariate space-time autocorrelation model (STVAR) to model the small-scale residuals of the multivariate spatiotemporal meteorological sequences:

z_ij (t) represents the small-scale residual term of the multivariate spatiotemporal meteorological sequences, where i represents the spatial monitoring point label and j represents the jth influencing factor in the spatial monitoring point i.

The multivariate spatiotemporal meteorological sequences contains 3 spatial monitoring points, each of which contains 2 meteorological factors, namely meteorological temperature and wind speed. Therefore, in the multivariate space-time autocorrelation modelM = 2, N = 3, the correlation order is p = 2. A small-scale residual term model of the multivariate spatiotemporal meteorological data is obtained to explain its future small-scale residual term trend.

3.3 Superposition of large-scale terms and residuals, and calculation of predicted target area meteorological values

After obtaining the large-scale nonlinear trend term and the small-scale residual term model of the water bloom spatiotemporal sequence, the values of the future large-scale nonlinear trend term and the small-scale residual term are predicted respectively. The two parts are superimposed, and the small-scale residual term is used to correct the large-scale nonlinear trend term to obtain the predicted value of the future water bloom spatiotemporal sequence.

The predicted multi-water quality data in the temporal and spatial sequence of the water bloom is the predicted value of the target area, and the multivariate spatiotemporal meteorological data is the predicted value of the monitoring points around the target area. The weight of the meteorological site and the target area needs to be further calculated to obtain the meteorological prediction value of the target area. The weight relationship between the meteorological site and the target area is obtained by the distance between the three stations and the target area. As shown in Table 4;

Table 4
Site and target water distance and weight relationship

Site name Site 1 Site 2 Site 3

Distance 77.8 km 112.5 km 94.2 km

Weight relationship λ₁= 0.463 λ₂= 0.221 λ₃= 0.316

Site name	Site 1	Site 2	Site 3
Distance	77.8 km	112.5 km	94.2 km
Weight relationship	λ₁= 0.463	λ₂= 0.221	λ₃= 0.316

And use the inverse distance weighted to calculate the predicted value of the meteorological data of the target area.

3.4 Adaptive network-based fuzzy inference system prediction of target area chlorophyll a

Through the above steps, the predicted values of chlorophyll a and meteorological data of the target area are obtained. Meteorological conditions have an important influence on the formation of cyanobacteria blooms. Therefore, an adaptive network-based fuzzy inference system is used to fuse chlorophyll a and meteorological data to predict the future direction of chlorophyll a.

For the first 775 sets of multivariate spatiotemporal meteorological data, the inverse distance weighting method is used to calculate the meteorological data of the target area. Combined with the 775 chlorophyll a data, the training data of 775 sets of adaptive neuro-fuzzy systems are formed;

The meteorological temperature and the wind value and the previous chlorophyll a value in the meteorological data were used as model inputs, and the model output is the predicted value of the future chlorophyll a. The number of membership functions of the input variable is set to 5, 7, 3, and the membership function setting type is a trigonometric function;

The initial FIS structure is generated, and the initial fuzzy inference system matrix and initial expert rules are obtained, and 5 * 7 *3 = 105 initial expert rules are obtained;

Use MATLAB’s ANFIS toolbox training model to set the model training times to 300. The FIS editor and the fuzzy inference rules after training are shown in Fig. 6. The square root error of the trained model is 0.0518.

By inputting the multivariate water quality data and meteorological data calculated in the above multiple steps into the trained adaptive network-based fuzzy inference system, the output value of the system can be obtained. As shown in Fig. 6, when the weather temperature is 0.359, the wind power value is 0.318, and the chlorophyll a value is 0.297, the value of the future chlorophyll a obtained by the system is 0.285.

Fig.6

FIS editor and fuzzy inference rules.

After obtaining the water bloom spatiotemporal sequence prediction model based on fuzzy expert system, 775 sets of spatiotemporal data are used as training data to train the spatiotemporal sequence hybrid model. The model was tested and verified using 320 sets of spatiotemporal data. The comparison between predicted and actual values is shown in Fig. 7.

Fig.7

Comparison between predicted and actual values.

As can be seen from Fig. 7, the predicted value and the actual value change trend are basically the same. After calculation, the root mean square error of the 320 sets of predicted values is 1.74%. Compared with the results of the traditional deep belief networks and the time autocorrelation model, the results are shown in Table 5, indicating that the prediction method has higher precision. Therefore, the cyanobacterial bloom spatial-temporal sequence prediction method based on the fuzzy expert system can effectively predict the chlorophyll a and indirectly predict the cyanobacteria bloom.

Table 5

Comparison of prediction results

Model type	DBN	DBN+STVAR+ANFIS	AR
RMSE	1.87%	1.74%	2.17%

4 Results and discussion

Aiming at the problem that the traditional single intelligent model and time series model can not deal with the spatio-temporal series of cyanobacterial blooms well, this paper proposes a prediction method of cyanobacterial blooms spatio-temporal series based on fuzzy expert system.

Firstly, the large-scale nonlinear trend term of cyanobacterial bloom spatial-temporal sequence is extracted by deep belief network, and the small-scale residual term of cyanobacterial blooms spatial and temporal sequence is obtained. Next, the time autocorrelation model and the multivariate space-time autocorrelation model are used to model and interpret the small-scale residuals of the multivariate water quality data and the multivariate spatiotemporal meteorological data. It is used to superimpose large-scale nonlinear trend items to make more accurate predictions of future water bloom spatiotemporal sequences. The small-scale residual term is used to superimpose the large-scale nonlinear trend term to predict the future water bloom spatiotemporal sequence more accurately. Then use the inverse distance weighting method to obtain the meteorological data of the target area. Finally, an adaptive network-based fuzzy inference system is used to predict the trend of the chlorophyll a concentration value in the future target region. The fuzzy temporal space-time sequence prediction model based on fuzzy expert system can overcome the shortcomings of time series model and single intelligent model, and can simulate the generation process of cyanobacterial blooms from multiple angles and multiple factors.

The experimental results show that the prediction results of the cyanobacterial bloom spatial-temporal sequence prediction model based on fuzzy expert system are closer to the actual trend of chlorophyll a in the future, which is more consistent with the actual generation of cyanobacteria blooms. Therefore, it is verified that the model proposed in this paper has certain reference value.

Footnotes

Acknowledgments

The authors acknowledge the National Natural Science Foundation of China (Grant: 61703008), the National Natural Science Foundation of China (Grant: 61802010). Support Project of High-level Teachers in Beijing Municipal Universities in the Period of 13th Five-year Plan (Grant: CIT&TCD201804014). Those supports are gratefully acknowledged

References

, Zha

, Li

, et al., Eutrophication of Lake Waters in China: Cost, Causes, and Control, Environmental Management 45(4) (2010), 662–668.

Paerl

H.W.

and Otten

T.G.

, Harmful Cyanobacterial Blooms: Causes, Consequences, and Controls, Microbial Ecology 65(4) (2013), 995–1010.

Miao

, Ze

, Jian-Peng

, et al., Impact of Agricultural Non-point Source Pollution in Eutrophic Water Body of Taihu Lake, Environmental Science & Technology 33(10) (2010), 106–111.

Liu

Z.W.

, Lu

S.Y.

, Wang

X.Y.

, et al., Forecast methods for algal bloom in rivers and lakes, Water Resources Protection 24(5) (2008), 42–47.

Qin

B.Q.

, Yang

G.J.

, Ma

J.R.

, et al., Dynamics of variability and mechanism of harmful cyanobacteria bloom in Lake Taihu, China (in Chinese), Chin Sci Bull 61(7) (2016), 759–770.

Miao

, Li

and Yu

G.J.

, Analysis of phytoplankton chlorophyll-a concentration in summer and autumn in Chaohu Lake and the impact factors of cyanobacterial blooms, Journal of Biology 28(2) (2011), 54–57.

Kuang

and Lee

, Physical hydrography and algal bloom transport in Hong Kong waters, China Ocean Engineering 19(4) (2005), 539–556.

Komatsu

, Fukushima

and Shiraishi

, Modeling of P-dynamics and algal growth in a stratified reservoir— mechanisms of P-cycle in water and interaction between overlying water and sediment, Ecological Modelling 197(3-4) (2006), 331–349.

Wang

L.L.

, Dai

H.C.

and Cai

Q.H.

, Numerical predicting of velocity and chl-a in Xiangxi river and correlativity Research, Journal of Basic Science and Engineering 17(5) (2009), 652–658.

10.

Xiaoyi

, Junyang

, Yan

, et al., Research on hybrid mechanism modeling of algal bloom formation in urban lakes and reservoirs, Ecological Modelling 332 (2016), 67–73.

11.

Wang

X.Y.

, Tang

L.N.

, Liu

Z.W.

, et al., Formation mechanism of cyanobacteria bloom in urban lake reservoir,– , CIESC Journal 63(5) (2012), 1492–1497.

12.

Bai

X.Z.

, Zhang

H.Y.

, Wang

X.Y.

, et al., Dynamic clustering based on nearest neighbors for predicting of cyanobacteria bloom in lakes and reservoirs, Bulletin of Soil and Water Conservation 4 (2017), 161–165.

13.

, Nonlinear information data mining based on time series for fractional differential operators, Chaos 29 (2019), 013114. DOI: 10.1063/1.5085430.

14.

, Wu

, Wang

and Zou

, Evaluation of Developer Efficiency Based on Improved DEA Model, Wireless Personal Communications 102(4) (2018), 3843–3849.

15.

, Wang

and Zou

, Sewage information monitoring system based on wireless sensor, Desalination and water treatment 121 (2018), 73–83.

16.

, Jin

J.L.

, et al., Hazard Evaluation of Chaohu Lake Water Bloom Based on BP and GIS, Water Resources and Power 29(5) (2011), 34–36.

17.

Bruder

, Babbar-Sebens

, Tedesco

, et al., Use of fuzzy logic models for prediction of taste and odor compounds in algal bloom-affected inland water bodies, Environmental Monitoring and Assessment 186(3) (2014), 1525–1545.

18.

Yao

J.Y.

, Xu

J.P.

, Wang

X.Y.

, et al., Research on algal bloom prediction based on deep learning, Computers and Applied Chemistry 32(10) (2015), 1265–1268.

19.

Zhao

, Wang

J.Q.

and Deng

, Spatial-temporal autocorrelation model of road network based on travelling time, Journal of Central South University (Science and Technology) 43(10) (2012), 4114–4122.

20.

Bruder

, Babbar-Sebens

, Tedesco

, et al., Use of fuzzy logic models for prediction of taste and odor compounds in algal bloom-affected inland water bodies, Environmental Monitoring and Assessment 186(3) (2014), 1525–1545.

21.

Yang

, Qi

, et al., Wind power prediction based on adaptive neuro-fuzzy inference system, Electrical Measurement & Instrumentation 52(14) (2015), 6–10.

22.

Wang

S.B.

, Wang

J.D.

and Chen

H.Y.

, STARMA-network model of space-time series prediction, Application Research of Computers 31(8) (2014), 2315–2319.

23.

G.C.

, Dai

W.J.

, Yang

G.X.

and Liu

, Application of Space-Time Auto-Regressive Model in Dam Deformation Analysis, Geomatics and Information Science of Wuhan Univers 40(7) (2015), 877–893.

24.

Krishnaraj

, Elhoseny

, Thenmozhi

, Selim

Mahmoud M.

and Shankar

, Deep learning model for real-time image compression in Internet of Underwater Things (IoUT), Journal of Real-Time Image Processing, (2019). In Press DOI: 10.1007/s11554-019-00879-6.

25.

Elhoseny

and Shankar

, Optimal Bilateral Filter and Convolutional Neural Network based Denoising Method of Medical Image Measurements, Measurement 143 (2019), 125–135.

26.

Shankar

, Elhoseny

, Lakshmanaprabu

S.K.

, Ilayaraja

, Vidhyavathi

R.M.

and Alkhambashi

, Optimal feature level fusion based ANFIS classifier for brain MRI image classification, Concurrency and Computation: Practice and Experience, 2018. DOI: 10.1002/cpe.4887.

Prediction method of cyanobacterial blooms spatial-temporal sequence based on deep belief network and fuzzy expert system

Abstract

Keywords

1 Introduction

2 Installing and using the microsoft word template

2.2.1 Establishment of spatial weight matrix for multiple meteorological monitoring points

2.2.2 Using the time autocorrelation model (AR) to model the small-scale residual term of the multi-water quality sequence:

2.3.1 Superposition of large-scale nonlinear trend term prediction values and small-scale residual term prediction values

Table 1 Data indicator Indicator name Chlorophyll a Dissolved oxygen Total nitrogen Water temperature Wind speed Weather temperature Indicator unit μg/L mg/L mg/L °C m/s °C

3.2.1 Establishment of spatial weight matrix for multiple meteorological monitoring points

Table 4 Site and target water distance and weight relationship Site name Site 1 Site 2 Site 3 Distance 77.8 km 112.5 km 94.2 km Weight relationship λ1= 0.463 λ2= 0.221 λ3= 0.316

Footnotes

Acknowledgments

References

Table 1
Data indicator

Indicator name Chlorophyll a Dissolved oxygen Total nitrogen Water temperature Wind speed Weather temperature

Indicator unit μg/L mg/L mg/L °C m/s °C

Table 4
Site and target water distance and weight relationship

Site name Site 1 Site 2 Site 3

Distance 77.8 km 112.5 km 94.2 km

Weight relationship λ₁= 0.463 λ₂= 0.221 λ₃= 0.316