CN107153874B - Water quality prediction method and system - Google Patents
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Abstract
The invention provides a water quality prediction method and a system, wherein the method uses a method of combining an ARIMA autoregressive integrated moving average model and a BP neural network to predict water quality time sequence data. The scheme of the invention can predict a large amount of water quality data of a water area to be predicted, has the characteristics of large prediction range, high precision and high speed, and is convenient for multi-water-source supervision, water quality early warning and water pollution treatment.
Description
Technical Field
The invention relates to the technical field of environmental prediction, in particular to a water quality prediction method and system.
Background
At present, water quality prediction is a prerequisite work for realizing flexible management and water pollution prevention of a water system. The water environment of a complex water area has more environmental influence factors, and the establishment of a mathematical model of environmental simulation has the characteristics of uncertainty and complexity just because of the complexity of an environmental system, and simultaneously the application of a prediction method is limited. The environmental problems are complex and various, and the environmental media are of different types, such as the weather factors which can determine the water flow speed, turbidity and the like of rivers, mountains and the like. By using historical data, the nonlinear relation between the environmental variable and the water quality index to be predicted or the change rule of the water quality index to be predicted along with time can be calculated by different prediction methods. At present, the more commonly used prediction methods include 5 categories, such as water quality simulation prediction, neural network model prediction, time series prediction, gray prediction model method, chaos theory-based water quality prediction method and the like.
The seasonal change of the water area is obvious, and is influenced by the double effects of human activities and the hydrological and meteorological conditions, and a plurality of difficulties exist in utilization, so that the water quantity and water quality change conditions of the corresponding watershed need to be monitored in time. The influence factors of the watershed water quality comprise 8 water quality parameters such as PH, Dissolved Oxygen (DO), conductivity (EC), Turbidity (TU), ammonia nitrogen (NH3-N), Chemical Oxygen Demand (COD), Total Phosphorus (TP), Total Nitrogen (TN) and the like, and the parameters can basically meet the water quality prediction requirement at present. The method has important significance for predicting dissolved oxygen, ammonia nitrogen, total phosphorus and total nitrogen in the sewage, no matter pollution treatment and water source management of different watersheds. The collected time series water quality data are utilized to analyze the monitoring data, and model prediction and the like are utilized, so that feasibility is achieved.
In the prior art, Wedding and Cios proposes a method using a combination of radial basis function network (RBF) and Box-Jenkins model; pelikan et al and Ginzburg and Horn propose to improve the accuracy of time series prediction by combining some methods of feedforward neural network; some hybrid models have also emerged, such as methods using a combination of auto-regressive moving average models (ARIMA) and artificial neural networks (ans) applied to time series prediction; chen and Wang constructed a combined model incorporating a seasonal autoregressive synthetic moving average (SARIMA) and support vector machine for seasonal time series model prediction; zhou and Hu propose a mixed modeling and prediction method based on gray color and Box-Jenkins autoregressive moving average model. Tseng et al propose predicting seasonal time series data using a SARIMABP hybrid model that combines a seasonal arima (sarima) model and a back-propagation neural network. Mehdi Khashei et al used a mixed model of ARIMA and ANN to predict time series data.
However, the prior art does not have the beneficial effect of obviously and accurately predicting the water quality, and the prediction result of the prior art is far from reaching the corresponding use standard.
Disclosure of Invention
The present invention overcomes or at least partially solves the above-mentioned problems by providing a water quality prediction method and system that uses a method combining an ARIMA autoregressive integrated moving average model with a BP neural network to predict water quality.
According to an aspect of the present invention, there is provided a water quality prediction method including:
step 1, acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted;
and 2, adding the predicted value of the meteorological factor of the water area to be predicted and the predicted value of the water quality parameter of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
Further, the step 1 further comprises:
training to obtain a water quality linear data prediction model by utilizing an ARIMA autoregressive integral sliding average model based on historical time sequence data of water quality parameters of a water area to be predicted; and acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing the water quality linear data prediction model based on the input data of the water quality parameter of the water area to be predicted.
Further, the step 1 further comprises:
training to obtain a water quality nonlinear data prediction model by utilizing an LM-BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing the water quality nonlinear data prediction model based on input data of the meteorological factors of the water area to be predicted;
further, the step of training to obtain the water quality linear data prediction model by using an ARIMA autoregressive integrated moving average model based on the historical time series data of the water quality parameters of the water area to be predicted further comprises:
judging the stationarity of the time sequence data of the historical meteorological factors of the water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing; calculating coefficients and orders of the ARMA (p, q) autoregressive integral moving average model; and calculating parameters of the ARIMA autoregressive integrated moving average model.
Further, the step of training to obtain the water quality nonlinear data prediction model by using the BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted further comprises the following steps:
and repeatedly adjusting and training the weight and the deviation of the BP neural network model by utilizing a back propagation algorithm based on the time series data of the historical meteorological factors of the water area to be predicted, and storing the weight and the deviation of the BP neural network model when the sum of squares of errors of a network output layer is smaller than a threshold value.
Further, before the step 1, the method further comprises: and deleting vacancy values in the historical time sequence data of the water area meteorological factors to be predicted and the historical time sequence data of the water quality parameters of the water area to be predicted.
Further, after the step of calculating the parameters of the ARIMA autoregressive integrated moving average model by the ARIMA autoregressive integrated moving average model, the method further comprises the following steps: and combining error data in the process of establishing the ARIMA autoregressive integral moving average model with the historical meteorological factor time sequence data of the water area to be predicted, and acquiring the predicted value of the meteorological factor of the water area to be predicted by utilizing an LM-BP neural network model.
Further, the step of training to obtain the water quality linear data prediction model by using an ARIMA autoregressive integrated moving average model based on the historical time series data of the water quality parameters of the water area to be predicted further comprises:
s111, judging the stationarity of the time series data of the historical meteorological factors of the water area to be predicted by adopting ADF unit root inspection: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing;
s112, calculating coefficients and orders of the ARMA (p, q) autoregressive integrated moving average model by utilizing an autocorrelation function and a partial autocorrelation function; and calculating the parameters of the ARIMA autoregressive integrated moving average model by using a least square method.
Further, before the step 1, the method further comprises:
s0, preprocessing the data of the historical meteorological factors of the water area to be predicted to obtain at least one of the following values of the main components in the meteorological factors: eigenvalues, contribution rates, and cumulative contribution rates.
According to an aspect of the present invention, there is provided a water quality prediction system including:
the prediction module is used for acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted;
and the superposition module is used for adding the predicted value of the meteorological factors of the water area to be predicted and the predicted value of the water quality parameters of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
The application provides a water quality prediction method and a water quality prediction system, wherein the method uses a method of combining an ARIMA autoregressive integrated moving average model and a BP neural network to predict water quality time sequence data. The scheme of the invention has the advantages of capability of predicting a large amount of water quality data of a water area to be predicted, large prediction range, high precision and high speed, and is convenient for multi-water-source supervision, water quality early warning and water pollution treatment.
Drawings
FIG. 1 is a schematic view of the overall flow of a water quality prediction method according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a water quality prediction method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an overall framework of a water quality prediction system according to an embodiment of the invention;
FIG. 4 is a schematic diagram of an apparatus for water quality prediction method according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
First, the terms with which the present invention appears will be described.
ARIMA autoregressive integrated moving average model: the Model is called Autoregressive Integrated Moving Average Model (ARIMA), and a famous time sequence prediction method was proposed in the early 70 s by bochs (Box) and Jenkins (Jenkins), so it is also called Box-Jenkins Model and bocks-Jenkins method. Wherein ARIMA (p, d, q) is called a differential autoregressive moving average model, AR is autoregressive, and p is an autoregressive term; MA is the moving average, q is the number of terms of the moving average, and d is the number of differences made when the time series becomes stationary. The ARIMA autoregressive integral moving average model is a model established by converting a non-stationary time sequence into a stationary time sequence and then regressing a dependent variable only on a hysteresis value of the dependent variable and a current value and a hysteresis value of a random error term. The ARIMA autoregressive integral moving average model includes a moving average process (MA), an autoregressive process (AR), an autoregressive moving average process (ARMA), and an ARIMA process depending on whether the original sequence is stationary and the part of the regression.
Fig. 1 is a schematic diagram illustrating an overall flow of a water quality prediction method according to an embodiment of the present invention. In general, the method comprises the following steps:
step 1, acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted;
and 2, adding the predicted value of the meteorological factor of the water area to be predicted and the predicted value of the water quality parameter of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
In another embodiment of the present invention, the step 1 further includes:
training to obtain a water quality linear data prediction model by utilizing an ARIMA autoregressive integral sliding average model based on historical time sequence data of water quality parameters of a water area to be predicted; and acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing the water quality linear data prediction model based on the input data of the water quality parameter of the water area to be predicted.
In another embodiment of the present invention, the step 1 further includes:
training to obtain a water quality nonlinear data prediction model by utilizing an LM-BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing the water quality nonlinear data prediction model based on input data of the meteorological factors of the water area to be predicted;
in another embodiment of the present invention, the step of training to obtain the water quality linear data prediction model by using an ARIMA autoregressive integrated moving average model based on the historical time series data of the water quality parameters of the water area to be predicted further includes:
judging the stationarity of the time sequence data of the historical meteorological factors of the water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing; calculating coefficients and orders of the ARMA (p, q) autoregressive integral moving average model; and calculating parameters of the ARIMA autoregressive integrated moving average model.
In another embodiment of the present invention, the step of training the nonlinear water quality data prediction model based on the time-series data of the historical meteorological factors of the water area to be predicted by using the BP neural network model further includes:
and repeatedly adjusting and training the weight and the deviation of the BP neural network model by utilizing a back propagation algorithm based on the time series data of the historical meteorological factors of the water area to be predicted, and storing the weight and the deviation of the BP neural network model when the sum of squares of errors of a network output layer is smaller than a threshold value.
In another embodiment of the present invention, a water quality prediction method further includes, before step 1: and deleting vacancy values in the historical time sequence data of the water area meteorological factors to be predicted and the historical time sequence data of the water quality parameters of the water area to be predicted.
In another embodiment of the invention, a water quality prediction method calculates the coefficients and the orders of the ARIMA autoregressive integrated moving average model; the step of calculating the parameters of the ARIMA autoregressive integrated moving average model further comprises the following steps: and combining error data in the process of establishing the ARIMA autoregressive integral moving average model with the historical meteorological factor time sequence data of the water area to be predicted, and acquiring the predicted value of the meteorological factor of the water area to be predicted by utilizing an LM-BP neural network model.
In another embodiment of the present invention, the step of training to obtain the water quality linear data prediction model by using an ARIMA autoregressive integrated moving average model based on the historical time series data of the water quality parameters of the water area to be predicted further includes:
s111, judging the stationarity of the time series data of the historical meteorological factors of the water area to be predicted by adopting ADF unit root inspection: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing;
s112, calculating coefficients and orders of the ARMA (p, q) autoregressive integrated moving average model by utilizing an autocorrelation function and a partial autocorrelation function; and calculating the parameters of the ARIMA autoregressive integrated moving average model by using a least square method.
In another embodiment of the present invention, a water quality prediction method further includes, before step 1:
s0, preprocessing the data of the historical meteorological factors of the water area to be predicted to obtain at least one of the following values of the main components in the meteorological factors: eigenvalues, contribution rates, and cumulative contribution rates.
In another embodiment of the invention, the BP neural network is trained based on a Levenberg-Marquardt algorithm.
In another embodiment of the present invention, a water quality prediction method is provided, as shown in fig. 2.
For collected watershed water quality data to be predicted, the prediction of the water quality data is not easy to be tested by an independent model, because the water quality time sequence data may include characteristics of a plurality of seasonalities and the like, heteroscedasticity or non-Gaussian errors. For time series water quality data: linear and non-linear sequences. Linear data are predicted by using an ARIMA autoregressive integrated moving average model, and for nonlinear data, LM-BP neural network prediction is used to obtain a prediction result finally. And considering that most of the water quality data are nonlinear data, meteorological factors are added into the LM-BP neural network to train the model. The steps of the estimated water quality data time series prediction method are shown in fig. 2.
The method for deleting the vacancy values is adopted to preprocess the water quality data and the meteorological factor data for collected water quality parameters such as PH, Dissolved Oxygen (DO), conductivity (EC), Turbidity (TU), ammonia nitrogen (NH3-N), Chemical Oxygen Demand (COD), Total Phosphorus (TP), Total Nitrogen (TN) and the like of the original water quality data and collected meteorological factors such as air temperature, wind speed, rainfall, atmospheric pressure and the like.
Each variable of the meteorological factors reflects certain information of water quality prediction to different degrees, and indexes have certain correlation with each other, so that the information reflected by the obtained statistical data is overlapped to a certain degree, and redundant information can be eliminated by adopting a principal component analysis technology. And (3) performing data preprocessing on weather factors such as precipitation, temperature, wind speed, humidity, air pressure and the like by adopting principal component analysis to obtain characteristic values, contribution rates and accumulated contribution rates of the principal components. After the multivariate weather factors are subjected to principal component analysis, the weather factor characteristic quantity is extracted, high-dimensional to low-dimensional simplification is realized, the data structure can be simplified, and the prediction efficiency is effectively improved on the premise of ensuring the prediction precision.
When modeling an ARIMA autoregressive integral moving average model, firstly, ADF (automatic dictionary-Fuller) unit root test is adopted to judge the stationarity of data. The water quality data is generally non-stationary data, the data is subjected to d-time difference processing to establish an ARIMA (p, d, q) model, the coefficients and the orders of the ARIMA (p, q) model are judged by adopting an autocorrelation function (ACF) and a partial autocorrelation function (PACF), then the least square method is used for carrying out parameter estimation on the ARIMA autoregressive integral moving average model, whether the ARIMA autoregressive integral moving average model is suitable or not is checked, and the satisfactory ARIMA autoregressive integral moving average model is obtained. And inputting the time series water quality data subjected to the deletion of the vacancy values into an ARIMA autoregressive integrated moving average model, and predicting linear sequence data in the ARIMA autoregressive integrated moving average model.
Error data of the ARIMA autoregressive integral moving average model, namely residual nonlinear sequence data, are combined with weather factor characteristic quantity subjected to principal component analysis to serve as input of the LM-BP neural network model. And the neural network model is established by selecting a BP (back propagation) algorithm and repeatedly adjusting and training the weight and the deviation of the network by using the back propagation algorithm to enable the output vector to be as close as possible to the expected vector, finishing training when the sum of squares of errors of the output layer of the network is less than a specified error, and storing the weight and the deviation of the network. Due to the existence of the nonlinear hidden layer unit, a plurality of minimum points exist in the network, so that the learning process can not be guaranteed to reach the global minimum, and a certain deviation exists between the actual output and the ideal output. The Levenberg-Marguardt (LM) optimization algorithm is adopted to solve the problems of low convergence rate of the learning process, long training time for some complex problems, huge data and the like. The model adopts a three-layer network structure and comprises an input layer, a hidden layer and an output layer. Then, a large amount of water quality data and weather factor data are selected as a sample set to train the network, and the network is trained and tested for many times until a satisfactory network model is obtained.
And finally, adding the ARIMA autoregressive integral moving average model and the LM-BP neural network model result at each time point to be predicted to obtain a water quality prediction result.
The contents of the principal component analysis, the ARIMA autoregressive integrated moving average model and the LM-BP neural network model are respectively described below.
1. A main component analysis step:
certain correlation exists among all factors, information is embedded mutually, information redundancy can be caused by direct use, the calculation complexity is increased, the prediction time is prolonged, and the calculation speed and the prediction efficiency are influenced. Therefore, it is necessary to pre-process these meteorological factors. Principal component analysis is a powerful tool for comprehensively dealing with the problem, and can replace more old variables with fewer new variables on the basis of correlation analysis, and the fewer new variables can retain information reflected by the original variables as much as possible.
For the collected meteorological factors, n samples exist, and each sample has p weather factor variables, so that an n multiplied by p-order data matrix is formed:
a main component analysis step:
(1) standardizing data, namely standardizing the original weather factor data into valid data between [0, 1 ];
(2) calculating a correlation coefficient matrix;
in the formula, rij(i, j ═ 1,2, …, p) of x as original variableiAnd xjThe correlation coefficient between the two is calculated as:
(3) calculating the eigenvalue and eigenvector first solves the equation of 0, λ I-R |, and the eigenvalue λ is usually found by the jacobian methodi(i-1, 2, …, p) and arranged in order of magnitude, i.e. λ1≥λ2≥…≥λpNot less than 0; then, the corresponding characteristic values lambda are respectively obtainediCharacteristic vector e ofi(i ═ 1,2, …, p). Request, rij＝rji，Wherein eijDenotes eiThe jth component of (a).
(4) Calculating principal component contribution rate and accumulated contribution rate
Principal component ziThe contribution rate of (A) is:
the cumulative contribution rate is:
generally, a characteristic value lambda with the accumulated contribution rate of 85-95 percent is taken1,λ2…, the first, the second, …, the m (m is less than or equal to p) th main component corresponding to the lambda m.
(5) The construction of the new sample matrix defines: note x1,x2,…,xpIs an index of a primary variable, z1,z2,…,zmAnd (m is less than or equal to p) is a new variable index, and each sample value of each main component is calculated according to the following two formulas.
The new sample matrix is then:
and calculating a characteristic value to obtain a characteristic vector, and taking the characteristic vector and the nonlinear water quality time sequence data as the input of the LM-BP neural network.
ARIMA autoregressive integrated moving average model
The Model is called Autoregressive Integrated Moving Average Model (ARIMA), and a famous time sequence prediction method was proposed in the early 70 s by bochs (Box) and Jenkins (Jenkins), so it is also called Box-Jenkins Model and bocks-Jenkins method. Wherein ARIMA (p, d, q) is called a differential autoregressive moving average model, AR is autoregressive, and p is an autoregressive term; MA is the moving average, q is the number of terms of the moving average, and d is the number of differences made when the time series becomes stationary. The ARIMA autoregressive integral moving average model is a model established by converting a non-stationary time sequence into a stationary time sequence and then regressing a dependent variable only on a hysteresis value of the dependent variable and a current value and a hysteresis value of a random error term. The ARIMA autoregressive integrated moving average model includes a moving average process (MA), an autoregressive process (AR), an autoregressive moving average process (ARIMA), and an ARIMA process depending on whether the original sequence is stationary and the part of the regression. The ARIMA is the most common method in the current time sequence analysis, and is a process of firstly extracting information such as long-term trend, fixed period and the like through differential operation, and then converting a non-stationary sequence into a stationary sequence and then analyzing the stationary sequence.
The ARIMA autoregressive integral moving average model regards a data sequence formed by the prediction index along with the time as a random sequence, and the dependency relationship of the group of random variables reflects the time continuity of the original data, which is not only influenced by external factors, but also has a self-changing rule. The ARIMA autoregressive integrated moving average model can predict linear water quality time series data.
The establishing of the ARIMA time sequence model comprises four steps:
(1) smooth processing of data
When modeling an ARIMA autoregressive integral moving average model, firstly, ADF (automatic dictionary-Fuller) unit root test is adopted to judge the stationarity of data. The non-stationary data is processed in a differential mode, and the difference frequency is the order d in an ARIMA (p, d, q) model. After the time series data are smoothed, the ARIMA (p, d, q) model is converted into an ARIMA (p, q) model.
Establishing an ARIMA (p, d, p) model when the sequence can become a stable sequence after d differences:
wt＝φ1wt-1+φ2wt-2+…+φpwt-p+δ+ut+θ1ut-1+θ2ut-2+…+θqut-q
w represents time-series data, δ is a constant, indicating that the series data is not 0-averaged, and ut is a white noise series.
(2) Model identification
In time series analysis, the coefficients and orders of the ARIMA (p, q) model are discriminated using autocorrelation function (ACF), partial autocorrelation function (PACF). An autocorrelation function (ACF) describes a linear correlation between a time series observation and its past observations. A partial autocorrelation function (PACF) describes a linear correlation between a time series observation and its past observations given an intermediate observation.
(3) Parameter estimation
After the order of the time series analysis model is determined, the ARIMA autoregressive integrated moving average model is subjected to parameter estimation by using a least square method.
(4) Model validation
Verifying whether the parameter estimation values of the fitted time series model have significance and verifying whether the residual sequence of the fitted time series model is a white noise sequence, namely, an independence test of the residual sequence.
LM-BP neural network algorithm
The modeling is to select a BP neural network model of an LM algorithm, then select a large amount of water quality data and weather factor data as samples to train the network, and train and test for many times until a satisfactory network model is obtained. Because the water quality index prediction has a complex input and output nonlinear implicit relation, a useful model can be obtained only through a large amount of sample learning and training. And (3) using the meteorological factors and nonlinear water quality time sequence data subjected to dimensionality reduction by using a principal component analysis technology as input of a neural network. According to the data processing characteristics of the neural network, normalization processing needs to be performed on input data.
The modeling steps of the water quality nonlinear time series data prediction model are as follows:
(1) the statistical analysis determines a prediction object and an influence factor thereof, and carries out principal component analysis on the influence factor, and a few irrelevant factors are used for substitution;
(2) carrying out normalization processing on the data;
(3) establishing a three-layer network prediction model which comprises an input layer, a hidden layer and an output layer;
(4) training an LM-BP neural network by using a sample set to train an initial network;
(5) testing by using the residual samples to obtain a network prediction model;
the LM algorithm is a fast algorithm utilizing a standard numerical optimization technology, is a combination of a gradient descent method and a Gaussian-Newton method, is an improved form of the Gaussian-Newton method, and has the local convergence of the Gaussian-Newton method and the global characteristic of the gradient descent method. The standard LM-BP algorithm is:
let the error objective function be:
wherein
aij＝tij-yij (2)
Is a network error vector, vi(x) Is an error vector. By newton method:
then:
although Newton method has the advantage of rapid convergence, the Hessian matrix F cannot be guaranteed in each iteration calculation2(x) All are reversible, then J can be usedT(x) J (x) + S (x) approximately replacing F2(x) Wherein J (x) is a Jacobian (Jacobian) matrix of a (x).Is the error matrix of a (x).
It can be demonstrated that:
when the solution is close to the extreme point:
S(x)＝0 (7)
then:
Δ(x)＝-[JT(x)J(x)]-1JT(x)a(x) (8)
the formula (8) is modified to include both the Gaussian-Newton method and the mixed form of the gradient descent method. The formula is as follows:
Δ(x)＝-[JT(x)J(x)+IU]-1·JT(x)a(x) (9)
wherein I is a unit matrix, U is a proportionality coefficient, and if U is close to 0, it is a Gaussian-Newton method, and if U is larger, it is a gradient descent methodA common adjustment strategy is to start the algorithm with U taking a small positive value, if one step cannot reduce the value of the error objective function f (x), then U is multiplied by a step factor θ larger than 1, i.e. U ═ U θ, and if one step yields a smaller f (x), then U is divided by θ in the next step, i.e. U ═ U/θ.
The LM algorithm can enable the BP neural network model to be converged more quickly, and an effective prediction result is obtained.
In fig. 3, a schematic diagram of an overall framework of a water quality prediction system in an embodiment is shown. In its entirety, comprising:
the prediction module A1 is used for acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted;
and the superposition module A2 is used for adding the predicted value of the meteorological factors of the water area to be predicted and the predicted value of the water quality parameters of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
In another embodiment of the present invention, a water quality prediction system, the prediction module is further configured to: training to obtain a water quality linear data prediction model by utilizing an ARIMA autoregressive integral sliding average model based on historical time sequence data of water quality parameters of a water area to be predicted; acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing the water quality linear data prediction model based on input data of the water quality parameter of the water area to be predicted; training to obtain a water quality nonlinear data prediction model by utilizing an LM-BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; and acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing the water quality nonlinear data prediction model based on input data of the meteorological factors of the water area to be predicted.
In another embodiment of the present invention, a water quality prediction system, the prediction module is further configured to:
judging the stationarity of the time sequence data of the historical meteorological factors of the water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing; calculating coefficients and orders of the ARMA (p, q) autoregressive integral moving average model; and calculating parameters of the ARIMA autoregressive integrated moving average model.
In another embodiment of the present invention, a water quality prediction system, the prediction module is further configured to: based on the time series data of the historical meteorological factors of the water area to be predicted, the weight and the deviation of the BP neural network model are adjusted and trained repeatedly by using a back propagation algorithm,
and when the sum of squares of the errors of the network output layer is smaller than a threshold value, storing the weight and the deviation of the BP neural network model.
In another embodiment of the present invention, a water quality prediction system, the prediction module is further configured to: and deleting vacancy values in the historical time sequence data of the water area meteorological factors to be predicted and the historical time sequence data of the water quality parameters of the water area to be predicted.
In another embodiment of the present invention, the prediction module is further configured to obtain the predicted value of the meteorological factors of the water area to be predicted by using an LM-BP neural network model in combination with the historical time series data of the meteorological factors of the water area to be predicted, based on error data in the process of establishing the ARIMA autoregressive integrated moving average model.
In another embodiment of the present invention, a water quality prediction system, the prediction module is further configured to: adopting ADF unit root inspection to judge the stationarity of the time series data of the historical meteorological factors of the water area to be predicted: establishing an ARIMA autoregressive integrated moving average model after d times of difference processing; calculating the coefficient and the order of the ARIMA autoregressive integrated moving average model by utilizing an autocorrelation function and a partial autocorrelation function; and calculating the parameters of the ARIMA autoregressive integrated moving average model by using a least square method.
In another embodiment of the present invention, the prediction module is further configured to perform data preprocessing on historical meteorological factors of a water area to be predicted, so as to obtain at least one of the following values of principal components in each meteorological factor: eigenvalues, contribution rates, and cumulative contribution rates.
Fig. 4 is a block diagram showing the structure of the water quality prediction method according to the embodiment of the present application.
Referring to fig. 4, the test apparatus of the water quality prediction method includes: a processor (processor)401, a memory (memory)402, a communication Interface (Communications Interface)403, and a bus 404;
wherein the content of the first and second substances,
the processor 401, the memory 402 and the communication interface 403 complete mutual communication through the bus 404;
the communication interface 403 is used for information transmission between the test equipment and communication equipment of the water quality prediction method;
the processor 401 is configured to call the program instructions in the memory 402 to execute the methods provided by the above-mentioned method embodiments, for example, including: step 1, acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; and 2, adding the predicted value of the meteorological factor of the water area to be predicted and the predicted value of the water quality parameter of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
The present embodiment discloses a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the method provided by the above-mentioned method embodiments, for example, comprising: step 1, acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; and 2, adding the predicted value of the meteorological factor of the water area to be predicted and the predicted value of the water quality parameter of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
The present embodiments provide a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the methods provided by the above method embodiments, for example, including: step 1, acquiring a predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time series data of the historical meteorological factors of the water area to be predicted; and 2, adding the predicted value of the meteorological factor of the water area to be predicted and the predicted value of the water quality parameter of the water area to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above-described embodiments of the water quality prediction method, such as the apparatus, are merely illustrative, where the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
The invention relates to a water quality time series prediction method based on a BP neural network and an ARIMA autoregressive integral moving average model, which is characterized in that collected basin water quality parameter time series data to be predicted and weather factor data are preprocessed, missing data in historical data are deleted, and main component analysis is carried out on weather factor data for dimension reduction; dividing preprocessed watershed water quality parameter time series data to be predicted into a training sample set and a testing sample set, taking water quality parameter values of a plurality of continuous unit times before the training sample set as an ARIMA autoregressive integral sliding average model input, taking the water quality parameter values of the next unit time as an output, and inspecting the trained model by using the testing sample set for the ARIMA autoregressive integral sliding average model to obtain a water quality parameter time series prediction model based on the ARIMA autoregressive integral sliding average model; the method comprises the following steps of training an LM-BP neural network model by taking nonlinear data left after passing through an ARIMA autoregressive integral moving average model and weather factor data subjected to principal component analysis as input of the BP neural network model, and testing a sample set to obtain a proper BP neural network model; and finally, predicting the new water quality parameter time sequence data by using an ARIMA autoregressive integrated moving average model and a BP neural network model, and adding values of the prediction result at each time point to be predicted to obtain a more accurate prediction result.
The water quality time series prediction method based on the LM-BP neural network and the ARIMA autoregressive integrated moving average model can be applied to prediction of water quality parameters such as PH, Dissolved Oxygen (DO), conductivity (EC), Turbidity (TU), ammonia nitrogen (NH3-N), Chemical Oxygen Demand (COD), Total Phosphorus (TP), Total Nitrogen (TN) and the like of different watersheds, and is high in prediction precision, wide in range and good in robustness.
Finally, the method of the present application is only a preferred embodiment and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A water quality prediction method is characterized by comprising the following steps:
step 1, acquiring a first predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a second predicted value of the water quality parameter of the water area to be predicted by utilizing a BP neural network model based on the time sequence data of the historical meteorological factors of the water area to be predicted and the time sequence data of the historical water quality parameter of the water area to be predicted;
step 2, adding the first predicted value of the water area water quality parameter to be predicted and the second predicted value of the water area water quality parameter to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted;
wherein the step 1 further comprises:
training to obtain a water quality linear data prediction model by utilizing an ARIMA autoregressive integral sliding average model based on historical time sequence data of water quality parameters of a water area to be predicted; based on input data of water quality parameters of a water area to be predicted, acquiring first predicted values of the water quality parameters of the water area to be predicted by using the water quality linear data prediction model;
wherein the step 1 further comprises:
training to obtain a water quality nonlinear data prediction model by utilizing an LM-BP neural network model based on historical time sequence data of water quality parameters of a water area to be predicted; acquiring a second predicted value of the water quality parameter of the water area to be predicted by using the water quality nonlinear data prediction model based on input data of the water area meteorological factor time series data to be predicted;
the step of training to obtain the water quality linear data prediction model by using an ARIMA autoregressive integrated moving average model based on the historical time sequence data of the water quality parameters of the water area to be predicted further comprises the following steps:
judging the stationarity of historical time sequence data of water quality parameters of a water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing; calculating coefficients and orders of the ARIMA (p, q) autoregressive integrated moving average model; calculating parameters of the ARIMA autoregressive integrated moving average model;
wherein p is an autoregressive term; MA is the moving average, q is the number of terms of the moving average, and d is the number of differences made when the time series becomes stationary.
2. The method of claim 1, wherein the step of training a water quality nonlinear data prediction model based on the historical meteorological factor time series data of the water area to be predicted and the historical water quality parameter time series data of the water area to be predicted by using a BP neural network model further comprises:
and repeatedly adjusting and training the weight and the deviation of the BP neural network model by using a back propagation algorithm based on the historical meteorological factor time series data of the water area to be predicted and the historical water quality parameter time series data of the water area to be predicted, and storing the weight and the deviation of the BP neural network model when the sum of squares of errors of a network output layer is smaller than a threshold value.
3. The method of any of claims 1 or 2, wherein step 1 is preceded by: and deleting vacancy values in the historical time sequence data of the water area meteorological factors to be predicted and the historical time sequence data of the water quality parameters of the water area to be predicted.
4. The method of claim 1, wherein the step of calculating parameters of the ARIMA autoregressive integrated moving average model by an ARIMA autoregressive integrated moving average model further comprises: and acquiring a second predicted value of the water quality parameter of the water area to be predicted by combining error data in the ARIMA autoregressive integral moving average model building process with the historical meteorological factor time sequence data of the water area to be predicted and utilizing an LM-BP neural network model.
5. The method as claimed in claim 1, wherein the step of training the linear data prediction model of water quality by using an ARIMA autoregressive integrated moving average model based on the historical time series data of water quality parameters to be predicted further comprises:
s111, adopting ADF unit root inspection to judge the stationarity of the historical time sequence data of the water quality parameters of the water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing;
s112, calculating the coefficient and the order of the ARIMA (p, q) autoregressive integrated moving average model by utilizing an autocorrelation function and a partial autocorrelation function; and calculating the parameters of the ARIMA autoregressive integrated moving average model by using a least square method.
6. The method of claim 1, wherein step 1 is preceded by:
s0, preprocessing the data of the historical meteorological factors of the water area to be predicted to obtain at least one of the following values of the main components in the meteorological factors: eigenvalues, contribution rates, and cumulative contribution rates.
7. A water quality prediction method system is characterized by comprising:
the prediction module is used for acquiring a first predicted value of the water quality parameter of the water area to be predicted by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of the water quality parameter of the water area to be predicted; acquiring a second predicted value of the meteorological factors of the water area to be predicted by utilizing a BP neural network model based on the time sequence data of the historical meteorological factors of the water area to be predicted and the time sequence data of the historical water quality parameters of the water area to be predicted;
the superposition module is used for adding the first predicted value of the water area water quality parameter to be predicted and the second predicted value of the water area water quality parameter to be predicted at each time point to be predicted to obtain a water quality prediction result of the water area to be predicted;
the prediction module is further used for training to obtain a water quality linear data prediction model by utilizing an ARIMA autoregressive integrated sliding average model based on historical time sequence data of water quality parameters of a water area to be predicted; based on input data of water quality parameters of a water area to be predicted, acquiring first predicted values of the water quality parameters of the water area to be predicted by using the water quality linear data prediction model;
the prediction module is further used for training to obtain a water quality nonlinear data prediction model by utilizing an LM-BP neural network model based on historical time sequence data of water quality parameters of a water area to be predicted; acquiring a second predicted value of the water quality parameter of the water area to be predicted by using the water quality nonlinear data prediction model based on input data of the water area meteorological factor time series data to be predicted;
the method for obtaining the water quality linear data prediction model through training based on the historical time sequence data of the water quality parameters of the water area to be predicted and by utilizing an ARIMA autoregressive integrated moving average model specifically comprises the following steps:
judging the stationarity of historical time sequence data of water quality parameters of a water area to be predicted: establishing an ARIMA (p, d, q) autoregressive integrated moving average model after d times of difference processing; calculating coefficients and orders of the ARIMA (p, q) autoregressive integrated moving average model; calculating parameters of the ARIMA autoregressive integrated moving average model;
wherein p is an autoregressive term; MA is the moving average, q is the number of terms of the moving average, and d is the number of differences made when the time series becomes stationary.
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