CN104699979A - Urban lake and reservoir algal bloom chaos time sequence predication method based on complicated network - Google Patents

Abstract

The invention discloses a method for predicting chaotic time series of algae blooms in urban lakes and reservoirs based on a complex network, and belongs to the technical field of environmental engineering. The present invention tests the chaotic characteristics of the formation process of water blooms in lakes and reservoirs, and provides a prediction method for water blooms based on chaotic time series. The time series of characteristic factors of the bloom generation process with chaotic characteristics, the complex network method is used to construct the statistical characteristic G parameters of the bloom generation process, and the G parameter time series is predicted by the chaotic time series prediction method, so as to realize the multi-factor water bloom generation process Prediction, improve prediction accuracy, provide effective reference for environmental protection departments, and play an important role in the protection and improvement of lake water environment.

Description

Chaotic Time Series Prediction Method of Algae Bloom in Urban Lake Reservoir Based on Complex Network

technical field

The invention relates to a water bloom prediction method, which belongs to the technical field of environmental engineering. Specifically, on the basis of in-depth research on the occurrence mechanism of water blooms, it is tested for its chaotic characteristics, and then combined with the statistical characteristics of complex networks to construct a city A chaotic time series prediction model for algae blooms in lakes and reservoirs to explore an effective way to improve the prediction accuracy of water blooms.

Background technique

With the rapid development of economy and society, water environment problems have become increasingly prominent, among which eutrophication is one of the most common and most influential water environment problems. In recent years, my country's lakes and reservoirs have received excessive plant nutrients such as nitrogen and phosphorus, which has changed the nutrient structure of the water body, caused algae and other aquatic plants to multiply abnormally, caused water quality to deteriorate, water transparency and dissolved oxygen decreased, fish and other The eutrophication of the water body in which a large number of organisms die, which in turn leads to the appearance of algae blooms. The eutrophication of the water body will destroy the aquatic ecosystem, cause algal blooms, release algae toxins, cause higher organisms to rot and die, destroy regional ecological balance, and restrict regional economic development.

Water bloom is a typical manifestation of eutrophication in water bodies, and it is the result of the joint action of nutrient salt factors, environmental factors, biological factors and dynamic factors, and the relationship between various factors is complex.

Because the mechanism of algal blooms is very complicated and there are many influencing factors, its prediction has always been a difficult point in the control and prevention of algal blooms. In recent years, with the deepening of research, many models based on intelligent methods have been applied to water bloom prediction, such as regression models and neural network models.

Among the various prediction methods for water blooms, most of them are based on a single characterization factor such as chlorophyll to describe the phenomenon of water blooms. It is incomplete to describe the phenomenon of algae bloom with a single factor, so the prediction of a single factor is also incomplete for the prediction of algae bloom.

In addition, since the formation process of algae bloom is a complex system, it needs to be described by the analysis method of complex system. The complex network abstracts the interacting entities in the complex system into nodes, and reflects the interaction of the entities in the complex system through the interaction between nodes. Therefore, the complex network can describe the real model as a visible model, and can obtain visible results through mathematical operations, and describe the characteristics of the complex system more completely. Therefore, the complex network can be applied to the modeling of the algal bloom generation process.

In addition, many complex systems often have non-random but seemingly random chaotic characteristics, so the emergence of chaos theory provides a new way of thinking for the study of such highly complex systems. Chaotic time series prediction is an important application field and research hotspot of chaos theory. Its key idea is delay reconstruction, which transforms one-dimensional time series into multi-dimensional phase space by introducing delay time and embedding dimension to reconstruct the motive force system. The reconstructed phase space maintains the original geometry, ie topology, and has the same dynamic properties. In the actual process of water bloom generation, due to the interaction between various characteristic factors, it often has some seemingly random characteristics. Modeling and forecasting of time series.

Contents of the invention

The invention tests the chaotic characteristics of the water bloom generation process in lakes and reservoirs, and provides a water bloom prediction method based on chaotic time series. The time series of characteristic factors of the bloom generation process with chaotic characteristics, the complex network method is used to construct the statistical characteristic G parameters of the bloom generation process, and the G parameter time series is predicted by the chaotic time series prediction method, so as to realize the multi-factor water bloom generation process Prediction, improve prediction accuracy, provide effective reference for environmental protection departments, and play an important role in the protection and improvement of lake water environment.

Among the present invention, the characteristic factor relevant with water bloom phenomenon is divided into two kinds: a kind of is the characteristic factor that influences water bloom to take place, such as total nitrogen, total phosphorus, pH value, dissolved oxygen, temperature, light intensity etc., is called influence below. The other is the characteristic factors that characterize the occurrence of water blooms, such as chlorophyll concentration, algae density, etc., which are called characterization factors below.

The method for predicting the chaotic time series of algae blooms in urban lakes and reservoirs based on the complex network provided by the present invention comprises the following five steps:

Step 1. Inspection of chaotic characteristics of algae bloom generation process in urban lake reservoirs;

1. Selection of water bloom characterization factors;

The water bloom characterization factors include chlorophyll concentration, algae density, etc., wherein the algae density is an indirect measurement factor. In order to improve the reliability and calculation accuracy of the time series, the present invention uses the chlorophyll concentration as the water bloom characterization factor to carry out the chaotic characteristics of the water bloom generation process. test.

2. Phase space reconstruction of chlorophyll time series;

The formation process of algal blooms is the result of the joint action of various factors such as nutrient salt factors, environmental factors, biological factors, etc., showing the characteristics of seemingly random but not random. For the complex system of bloom formation process, the evolution of any component is determined by other components interacting with it. The purpose of phase space reconstruction is to restore the attractor that presents the nonlinear motion law in the process of bloom formation in high-dimensional phase space, so as to mine the hidden information in the evolution process of any component. Therefore, starting from the time series, a set of m-dimensional vectors is constructed to support an embedding space. As long as the embedding space has enough dimensions, the original dynamic form of the complex system of the algae bloom generation process can be restored, and the reconstructed The phase space has similar geometric and information characteristics to the dynamic system of the original bloom formation process.

For a given time series {x(t),t=1,2,...N}, the delay time is τ, the embedding dimension is m, and m<N, the N data in the time series are extended to N -(m-1)τ vectors of m-dimensional phase spaces.

X(t)=(x(t),x(t+τ),…x(t+(m-1)τ)),t=1,…,M,M=N-(m-1)τ

Among them, X(t) is the reconstructed phase space vector, x(t) is the chlorophyll concentration value monitored at different times, t is the sampling time of the time series, and N is the number of samples.

3. Inspection of chaotic characteristics of chlorophyll time series;

Whether the chlorophyll time series can be correctly tested or not has chaotic characteristics will directly determine whether the chaos theory can be used to analyze the chlorophyll time series. This patent adopts the maximum Lyapunov exponent method to determine whether the time series of algae bloom characteristic factors is a chaotic time series. When the index Lyapunov<0, it indicates that the phase volume of the complex dynamical system in the bloom formation process is shrinking and stable in the direction of the corresponding dimension. Conversely, if Lyapunov>0 in a certain direction, it indicates that the phase volume of the complex dynamical system in the process of algal blooms expands and collapses continuously in the direction of the corresponding dimension, and the adjacent trajectories in the attractor become more and more irrelevant, so it cannot Predicting its long-term evolution behavior shows that the evolution of algal blooms presents chaotic characteristics at this time. That is, Lyapunov>0 can exist as a strange attractor in the process of bloom generation, indicating that the process of bloom generation corresponding to the time series has chaotic characteristics.

Step 2, construction of an algae bloom generation identification model based on a complex network;

1. Construct a directed network model for the formation process of water blooms;

Since the water body of lakes and reservoirs is an open and complex system, the existing modeling methods for the formation mechanism of algae blooms cannot accurately and quantitatively describe the relationship between nutrients in the water body and between nutrients and the external environment during the outbreak of algal blooms. . The idea of a complex network is to abstract the interacting entities in a complex system into nodes, and reflect the interaction of entities in a complex system through the interaction between nodes. Therefore, the present invention abstracts the complex water system of lakes and reservoirs into a complex network, and abstracts the main influencing factors affecting the formation of algae blooms into network nodes to form a network point set V (V={v ₁ ,v ₂ ,... ,v _n }), v _i is used to represent the i-th network node, and the total number of network nodes is n; the relationship between the main influencing factors is abstracted into network edges to form an edge set E (E={e ₁ ,e ₂ ,...,e _m }), e _i is used to represent the i-th edge, the total number of edges is m, and all the edges in the edge set E correspond to two nodes in the point set V. This network topology graph composed of the point set V and the edge set E abstracted from the main influencing factors of the lake and reservoir water system and their interrelationships constitutes a directed network model CN=(V,E), which is used to represent algae in the lake and reservoir water body Bloom formation characteristics.

2. Calculate the characteristic parameters of complex networks;

The data characteristics of complex systems are often expressed through the statistical characteristics of their corresponding complex network models. Therefore, the statistical characteristics of complex networks have become the focus of many scholars. At present, the statistical properties that can be calculated mainly include average path length L, node betweenness B _i , clustering coefficient C, shortest distance d _min , etc., where i represents the node number. The complex interaction and degree of interaction between the nonlinear influencing factors on algal blooms can be more completely characterized by the statistical characteristics of the complex network. 3. Construct the G parameters of complex network statistical characteristics in the process of algae bloom generation;

Different characteristic parameters have different roles in the network. In order to characterize the comprehensive characteristics of the algae bloom generation process, a model of the key degree σ of the node is constructed, and the statistical characteristic G parameter of the complex network is calculated, G=f(σ).

Step 3, G parameter time series chaotic characteristics test;

Perform phase space reconstruction on the time series {g(t),t=1,2,…N} of the statistical characteristic G parameters, find the optimal delay time τ and embedding dimension m, where m<N, then the time The N data in the sequence are extended into N-(m-1)τ vectors of m-dimensional phase space,

G(t)=(g(t),g(t+τ),...g(t+(m-1)τ)),t=1,...,M,M=N-(m-1)τ

Among them, G(t) is the reconstructed phase space vector of the G parameter time series, and g(t) is the G parameter time series value acquired at different times.

The maximum Lyapunov exponent is then calculated and the chaotic properties of the G-parameter time series are examined. If the G parameter time series is chaotic, the commonly used local prediction method of chaotic time series can be used to predict the G parameter time series.

Step 4, G parameter time series prediction based on chaotic time series;

Here, the G parameter is the characterization of the overall characteristics of the abstract network corresponding to the complex system of the water bloom generation process. Therefore, the prediction of the G parameter time series can effectively solve the problem that the existing water bloom prediction only targets a single characterization factor. The purpose of comprehensive prediction of water bloom and improve the prediction accuracy.

Here, the essence of the weighted first-order local method is to use the last vector G(M) in the reconstructed phase space as the prediction center point, and use the distance between other vectors and G(M) to fit the first-order Linear fit coefficients. Then, the first-order linear fitting method can be used to approximate the future evolution phase point, and the predicted value of the next evolution phase point can be obtained:

G(M _j+1 )=a+bG(M _j )

Where a, b are first-order linear fitting coefficients, M _j (j=1,2,...,q) represents the sequence number of the jth adjacent point vector that is closer to the prediction starting point G(M), and q is The specified number of sequence vectors that are locally adjacent to the prediction starting point G(M).

The advantages of the present invention are:

1. The present invention proves that the formation process of lake and reservoir water blooms has chaotic characteristics through the inspection of chaotic characteristics, and proposes a method for predicting the time series of water bloom characterization factors based on chaotic time series.

2, the present invention is aimed at the deficiency of the single factor prediction method of algae bloom generation process, in conjunction with the relevant statistical theory of complex network, has proposed the comprehensive statistical feature G parameter that adopts multiple characteristic factors as new prediction object, to this abstraction of algae bloom generation process Quantitative description of the complex network of the algae bloom provides the possibility for the multi-factor comprehensive prediction of the algae bloom formation process.

Description of drawings

Fig. 1 is the flow chart of the present invention's method for predicting chaotic time series of algae blooms in urban lakes and reservoirs based on complex networks;

Fig. 2 is a complex network algae bloom formation directed network model affected by comprehensive factors;

Figure 3 is the calculation result of chlorophyll time series statistics;

Figure 4 is the maximum Lyapunov index of the reconstructed chlorophyll time series;

Figure 5 is a comparison of G parameters and chlorophyll in complex network statistical features;

Figure 6 is the statistical calculation result of the G parameter time series;

Figure 7 is the maximum Lyapunov exponent of the G parameter time series after reconstruction;

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings.

The method for predicting the chaotic time series of algae blooms in urban lakes and reservoirs with a complex network provided by the present invention has a process as shown in Figure 1, and the specific steps are as follows:

Step 1. Inspection of chaotic characteristics of algae bloom generation process in urban lake reservoirs;

1. Selection of water bloom characterization factors;

As only chlorophyll can be directly measured among the characterization factors, the chlorophyll concentration is used as the characterization factor of water bloom to test the chaotic characteristics of the bloom formation process.

2. Phase space reconstruction of chlorophyll time series;

The present invention uses the conventional C-C algorithm to reconstruct the phase space of the chlorophyll time series:

Construct statistics based on the C-C algorithm, and determine the optimal delay time τ and the optimal embedding dimension m according to the characteristics of the corresponding statistics obtained through calculation, so that the reconstructed phase space can reflect the original urban lake algae bloom generation process to the greatest extent The dynamic characteristics of the system.

3. Inspection of chaotic characteristics of chlorophyll time series;

The present invention adopts the small amount of data method to calculate the maximum Lyapunov index of the chlorophyll time series after reconstructing the phase space:

First, calculate the distance of each adjacent point pair after the t (t=1,2,...,M)th discrete time step for the M state vectors in the reconstructed phase space, then the maximum Lyapunov exponent can pass through each An estimate of the average divergence rate of a phase point and its nearest neighbors in orbit. Through natural logarithmic transformation, a series of straight lines in which the natural logarithmic value of the distance between each adjacent point pair changes with the discrete time step t can be obtained. The slope of each straight line is roughly equivalent to the maximum Lyapunov exponent, which can be approximated by the least square method Combine the slopes and take the average to find the maximum Lyapunov exponent.

Step 2, construction of an algae bloom generation identification model based on a complex network;

1. Construct a directed network model for the formation process of water blooms;

According to the characteristics of the formation mechanism of water blooms in urban lakes and reservoirs, seven key factors including total phosphorus (TP), total nitrogen (TN), temperature (T), pH value, dissolved oxygen (DO), light (I) and chlorophyll (chl_a) Influencing factors constitute a point set V, and the interrelationships among influencing factors constitute an edge set E, in which the number of nodes n=7 and the number of edges m=14. The directed network model for the formation of algae blooms with complex networks is shown in Figure 2. It can be seen that the formation process of algae blooms is affected by various water factors and meteorological environmental factors in urban lakes and reservoirs, and can be abstracted into a corresponding network model.

2. Calculate the characteristic parameters of complex networks;

According to the directed network model formed by the algae blooms in the complex network, the statistical characteristic parameters of the complex network are calculated according to the conventional formula, and the key parameters such as the average path length L, the node betweenness _Bi , the clustering coefficient C and the shortest distance d _min need to be obtained .

3. Construct the G parameter model of the statistical characteristics of the complex network of algal blooms;

In order to better reflect the role of each node in the complex network, the key degree model σ _i' of the constructed node is:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; -</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

In the formula, d _min is the shortest distance calculated from node v _i to chlorophyll a, and λ _i is the node degree, divided into in-degree and out degree B _i is the node betweenness, α ⁺ , α ^- is the weight, the real number ranging from 0 to 1, i represents the node number, i=1,2,...,7.

Considering the influence of the average path length and clustering coefficient on the network, the key degree model of the node is modified twice, and the modified model is:

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; L</span>}}$

In the formula, C _i is the clustering coefficient of node v _i , indicating the degree of coupling between node v _i and other nodes in the complex network, L is the average path length of the network, j=1,2,...,7, β is the weight , a real number ranging from 0 to 1.

Considering that L, B _i , C _i , d _min and σ _i are the key parameters for the complex network characteristics of algae bloom formation, the G parameter model for identification of algae bloom generation is constructed:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span>$

In the formula ^, σ _i represents the product of the key degree model σ _i of node v _i and the specific parameter value of node v _i , that is, σ _i ^, =ci _× σ _i , _ci represents the specific parameter value of node v _i , n is the number of nodes. The specific G parameter model includes several key parameters such as average path length L, node betweenness B _i , clustering coefficient C and shortest distance d _min and a key degree model σ _i .

Step 3, G parameter time series chaotic characteristics test;

Refer to the C-C method in step 1 to reconstruct the state space of the G parameter time series and judge the chaotic properties of the G parameter time series by calculating the maximum Lyapunov exponent.

Step 4, G parameter time series prediction based on chaotic time series;

The weighted first-order local method is used to predict the time series of statistical characteristic G parameters, mainly using the first-order linear fitting coefficients a and b in the first-order linear fitting formula to obtain the prediction of the next evolutionary phase point:

G(M _j+1 )=a+bG(M _j ),j=1,2,…,q

Then the last one-dimensional component in the prediction vector is the predicted value of the G parameter time series sequence.

Example 1:

Step 1. Inspection of chaotic characteristics of algae bloom generation process in urban lake reservoirs;

The data used in the model is the monitoring data of algae blooms under simulated natural conditions in the sun room in 2007. The water samples were collected from Yuyuantan Park in Beijing, which is an important part of the second ring water system in Beijing and has a good representativeness.

The 7 characteristic factors of water bloom in the sun room from June 2007 to August 2007 were monitored, see Table 1 for details.

Table 1 Monitoring list of characteristic factors of water bloom

name pH value illumination temperature total nitrogen Total Phosphorus dissolved oxygen Chlorophyll unit none Lx ℃ mg/L mg/L mg/L mg/L

Among them, chlorophyll is the characterization factor of water bloom, and the other 6 characteristic factors are the influencing factors of water bloom. The monitoring equipment has recorded a total of 1066 groups of water bloom characteristic factor data every 1 hour for 45 days, and reconstructed the phase space of the chlorophyll time series. The calculation results of the statistics are shown in Figure 3, from which the optimal Delay time τ _d =3, embedding window width τ _w =16, m=6 obtained from τ _w =(m-1)τ.

According to the reconstructed phase space, the maximum Lyapunov exponent is calculated, and the result is shown in Figure 4. The calculation results show that the average slope is greater than 0, that is, Lyapunov>0, indicating that the chlorophyll time series has chaotic properties.

Step 2, constructing a G-parameter model of complex network statistical characteristics in the process of bloom generation;

According to the network topology, 109 sets of data in the Sunshine Room in June 2007 were used to calculate the characteristic parameters of the complex network. Among them, the calculation results of the shortest distance between the directed complex network edges and the shortest path between nodes are shown in Tables 2 and 3.

Table 2 The shortest distance for algal blooms to identify directed complex network edges

Table 3 Algae blooms identify the shortest path between nodes in a directed complex network

Combined with the actual data, each parameter in the complex network is analyzed, and the calculation results are shown in Table 4.

Table 4 The parameter values of the complex network for identification of algae bloom generation

Using the constructed statistical characteristic G parameter model, combined with actual data, the characteristic G parameter time series was calculated, and compared with the chlorophyll time series, the results are shown in Figure 5. It can be seen from Figure 5 that there is a clear correlation between the statistical characteristic G parameter of algae bloom formation and the value of chlorophyll a that characterizes the formation of water bloom. It shows that the statistical characteristic G parameters can well reflect the formation process of algae blooms, and at the same time provide more abundant information than chlorophyll. The change of the characteristic G parameter is ahead of the change of chlorophyll. It can be seen from the analysis that the numerical model of the statistical characteristic G parameter of the complex network formed by the water bloom can better reflect the formation of the water bloom, and can quickly identify the phenomenon of water bloom and Algal bloom trends. When the content of the key factors affecting the outbreak of algal blooms in the water body changes or has a tendency to change, due to the lag in the change of chlorophyll a, it cannot quickly reflect the outbreak of algal blooms. However, through the calculation of the G parameter model , can quickly identify the changes and trends of chlorophyll a in water bodies, thus providing a reliable guarantee for relevant departments to take preventive and control measures in time.

Step 3, G parameter time series chaotic characteristics test;

Phase space reconstruction was performed on the statistical characteristic G parameter time series of 605 sets of data from June to July 2007. The calculated statistics and the maximum Lyapunov exponent are shown in Figure 6 and Figure 7.

The Lyapunov exponent is greater than 0, indicating that the complex network statistical characteristic G parameter time series has chaotic properties.

Step 4, G parameter time series prediction based on chaotic time series;

The weighted first-order local method is used to predict the statistical characteristic G parameters, and the predicted results are compared with the actual values. The results are shown in Table 5.

Table 5 Comparison of predicted value and measured value of statistical characteristic parameter G

There is a slight error between the predicted results and the measured values. This shows that the time prediction method based on chaos theory has a good prediction effect in the prediction of water bloom outbreaks. Through the time series prediction of complex network characteristic G parameters, the history of single variable prediction of water bloom outbreaks has been changed, and the system prediction has been realized. .

Claims (4)

1. The method for predicting chaotic time series of algae blooms in urban lakes and reservoirs based on complex networks, characterized in that: comprising the following steps, Step 1. Inspection of chaotic characteristics of algae bloom generation process in urban lake reservoirs; Using chlorophyll concentration as the characterization factor of water bloom to test the chaotic characteristics of the process of water bloom formation; For a given time series {x(t),t=1,2,...N}, the delay time is τ, the embedding dimension is m, and m<N, the N data in the time series are extended to N -(m-1)τ vectors of m-dimensional phase spaces: X(t)=(x(t),x(t+τ),…x(t+(m-1)τ)),t=1,…,M,M=N-(m-1)τ Among them, X(t) is the reconstructed phase space vector, x(t) is the chlorophyll concentration value monitored at different times, t is the sampling time of the time series, and N is the number of samples; The maximum Lyapunov exponent method is used to judge whether the time series of the characteristic factors of algae blooms is a chaotic time series. When the index Lyapunov<0, it indicates that the phase volume of the complex dynamic system in the process of algae bloom formation is shrinking and stable in the direction of the corresponding dimension; Conversely, if Lyapunov>0 in a certain direction, it indicates that the evolution of the bloom generation process presents chaotic characteristics; Step 2, construction of an algae bloom generation identification model based on a complex network; (1) Construct the directed network model of the bloom formation process; The complex water system of lakes and reservoirs is abstracted into a complex network, and the main factors affecting the formation of algae blooms are abstracted into network nodes to form a network point set V(V={v ₁ ,v ₂ ,...,v _n } ), v _i is used to represent the i-th network node, and the total number of network nodes is n; the relationship between the main influencing factors is abstracted into network edges to form an edge set E (E={e ₁ ,e ₂ ,... ,e _m }), e _i is used to represent the i-th edge, the total number of edges is m, and all the edges in the edge set E correspond to two nodes in the point set V; The network topology diagram composed of the point set V and the edge set E abstracted from the main influencing factors and their interrelationships constitutes a directed network model CN=(V,E), which is used to represent the formation characteristics of algal blooms in lakes and reservoirs; (2) Calculate complex network characteristic parameters; The characteristic parameters of the complex network include average path length L, node betweenness B _i , clustering coefficient C and shortest distance d _min , where i represents the node number; (3) Construct the G parameters of the complex network statistical characteristics of the bloom formation process; Step 3, G parameter time series chaotic characteristics test; Perform phase space reconstruction on the time series of G parameters {g(t),t=1,2,…N}, find the optimal delay time τ and embedding dimension m, where m<N, then the time series can be The N data of are extended into N-(m-1)τ vectors of m-dimensional phase space, G(t)=(g(t),g(t+τ),...g(t+(m-1)τ)),t=1,...,M,M=N-(m-1)τ Among them, G(t) is the reconstructed phase space vector of the G parameter time series, and g(t) is the G parameter time series value acquired at different times. Then calculate the maximum Lyapunov exponent, and check the chaotic characteristics of the G parameter time series; if the G parameter time series is chaotic, use the commonly used local prediction method of the chaotic time series to predict the G parameter time series; Step 4, G parameter time series prediction based on chaotic time series; The weighted first-order local method used for G-parameter time series forecasting. 2. The method for predicting chaotic time series of algae blooms in urban lakes and reservoirs based on complex network according to claim 1, characterized in that: the weighted first-order local method in step 4 is to reconstruct the last vector G in the phase space (M) as the prediction center point, use the distance between other vectors and G(M) to fit the first-order linear fitting coefficient; use the first-order linear fitting method to approach the future evolution phase point, and get the next evolution phase The predicted value of the point: G(M _j+1 )=a+bG(M _j ) Where a, b are first-order linear fitting coefficients, M _j represents the sequence number of the jth adjacent point vector that is closer to the prediction starting point G(M), j=1,2,...,q, q is The specified number of sequence vectors that are locally adjacent to the prediction starting point G(M). 3. The method for predicting chaotic time series of algae blooms in urban lakes and reservoirs based on complex network according to claim 1, characterized in that: said point set V comprises 7 key influencing factors, which are respectively total phosphorus TP, total nitrogen TN, temperature T, pH value, dissolved oxygen DO, light I, chlorophyll chl_a. 4. the method for predicting the chaotic time series of algae blooms in urban lakes and reservoirs based on complex network according to claim 1, characterized in that: build the complex network statistical characteristic G parameter model of the bloom generation process, specifically: First construct the criticality model σ _i' of the node as: ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; +</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{<span\; class="notranslate">\; -</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; -</span>}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$ In the formula, d _min is the shortest distance calculated from node v _i to chlorophyll a, and λ _i is the node degree, divided into in-degree and out degree B _i is the node betweenness, α ⁺ , α _- is the weight, the value range is a real number from 0 to 1, i represents the node number, i=1,2,...,7; Considering the influence of the average path length and clustering coefficient on the network, the key degree model of the node is modified twice, and the modified model is: ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; L</span>}}$ In the formula, C _i is the clustering coefficient of node v _i , indicating the degree of coupling between node v _i and other nodes in the complex network, L is the average path length of the network, j=1,2,...,7, β is the weight , a real number ranging from 0 to 1; Considering that L, B _i , C _i , d _min and σ _i are the key parameters for the complex network characteristics of algae bloom formation, the G parameter model for identification of algae bloom generation is constructed: $\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span>$ In the formula, σ _i ' represents the product of the key degree model σ _i of node v _i and the specific parameter value of node v _i , that is, σ _i '= _ci ×σ _i , _ci represents the specific parameter value of node v _i , n is the number of nodes; the specific G parameter model includes average path length L, node betweenness B _i , clustering coefficient C, shortest distance d _min , and criticality model σ _i .