CN108053054B - River water quality prediction method - Google Patents
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Abstract
The invention provides a river water quality prediction method, which comprises the following steps: s1, based on time series test data of the water quality parameters of the target water area, preliminarily predicting initial prediction data of the water quality parameters at a specified time by using an ARIMA prediction model constructed in advance according to historical time series data samples of the water quality parameters, and calculating prediction residual data; and S2, based on the time series test data, the initial prediction data and the prediction residual data, predicting the prediction data of the water quality parameters at the specified time by utilizing a wavelet neural network model which is optimized and constructed in advance according to the historical time series data sample and the ARIMA prediction model through a genetic algorithm. Compared with the traditional water quality prediction method, the method has stronger universality, higher prediction accuracy, higher convergence speed and higher efficiency.
Description
Technical Field
The invention relates to the technical field of environmental prediction, in particular to a river water quality prediction method.
Background
The river water quality prediction is the premise for realizing the flexible management of a river water system and preventing and treating water pollution. The influence factors of the river basin water quality comprise water quality parameters such as pH value, Dissolved Oxygen (DO), conductivity (EC), Turbidity (TU), ammonia nitrogen (NH3-N), Chemical Oxygen Demand (COD), permanganate and the like, and the change prediction of the dissolved oxygen, ammonia nitrogen, total phosphorus and total nitrogen is more beneficial to realizing pollution control and water source management of different basins of the river.
At present, 5 types of common single prediction methods include water quality simulation prediction, neural network model prediction, time sequence prediction, gray prediction model method, chaos theory-based water quality prediction method and the like. In recent years, researchers have also started studying water quality combination prediction models, including water quality prediction models based on a combination of ARIMA and ANN. The water quality prediction method based on ARIMA and ANN mainly comprises the following processing procedures: and taking historical water quality parameter data as input of an ARIMA model, taking obtained residual data as ANN input, and adding an ARIMA predicted value and the output of the ANN to obtain a final prediction result. The relationship between the original data and the residual data is not considered.
However, in the water quality prediction process of each single prediction method, various influence factors of water quality change cannot be considered, and the single treatment means is not enough, so that the prediction result is often not accurate enough, and the prediction performance is not good. The ARIMA and ANN based combined water quality prediction method does not consider the relation between the original data and the residual data, so that the neural network parameters are easy to fall into local optimal values, the prediction effect is poor, and the precision is low.
Disclosure of Invention
In order to overcome the above problems or at least partially solve the above problems, the present invention provides a river water quality prediction method, which is used to effectively improve the universality of a water quality prediction system and improve the accuracy and efficiency of water quality prediction.
The invention provides a river water quality prediction method, which comprises the following steps: s1, based on time series test data of the water quality parameters of the target water area, preliminarily predicting initial prediction data of the water quality parameters at a specified time by using an ARIMA prediction model, and calculating prediction residual data, wherein the ARIMA prediction model is constructed in advance according to historical time series data samples of the water quality parameters; and S2, predicting the prediction data of the water quality parameter at the specified time by using a wavelet neural network model optimized by a genetic algorithm based on the time series test data, the initial prediction data and the prediction residual data, wherein the wavelet neural network model optimized by the genetic algorithm is obtained by optimizing the genetic algorithm in advance according to the historical time series data sample and the ARIMA prediction model.
Wherein the step of constructing the ARIMA prediction model from the historical time-series data samples of the water quality parameter in step S1 further comprises: s11, if the historical time sequence data sample is non-stationary data, smoothing the historical time sequence data by using a difference algorithm to obtain a stationary historical time sequence data sample, and estimating a difference time parameter of the ARIMA prediction model; s12, dividing the stable historical time series data sample into a training sample and a testing sample; s13, estimating an autoregressive item parameter and a moving average item parameter of the ARIMA prediction model by utilizing an autocorrelation function and a partial autocorrelation function based on the training sample; s14, based on the training sample, calculating an ARIMA residual error by using an initial ARIMA prediction model determined by the difference times parameter, the autoregressive item parameter and the moving average item parameter, and carrying out ARIMA residual error detection; s15, if the ARIMA residual error obeys normal distribution with zero mean value and invariable variance, the test sample is used for carrying out significance test on the initial ARIMA prediction model by adopting ARIMA residual error judgment; s16, if the result of the significance test meets the set standard, outputting the initial ARIMA prediction model as the ARIMA prediction model, otherwise, switching to the step S13.
Wherein the step of optimizing and constructing the wavelet neural network model by a genetic algorithm according to the historical time series data samples and the ARIMA prediction model in step S2 further comprises: s21, based on the training sample, preliminarily predicting intermediate prediction data by using the ARIMA prediction model, and calculating intermediate residual data; s22, initializing network parameters of the wavelet neural network model by adopting genetic algorithm optimization, and initializing the wavelet neural network model by initializing the learning rate and momentum factor of the wavelet neural network; s23, based on the training sample, the intermediate prediction data and the intermediate residual data, performing forward prediction calculation by using an initialized wavelet neural network model, and performing reverse parameter correction through error judgment and iteration frequency judgment to obtain an initial wavelet neural network model; and S24, testing the prediction accuracy of the initial wavelet neural network model by using the test sample through error judgment, if the accuracy reaches a set standard, outputting the initial wavelet neural network model as the wavelet neural network model, and otherwise, turning to the step S22.
Wherein, in step S22, the step of initializing the network parameters of the wavelet neural network model by using genetic algorithm optimization further includes: s221, randomly obtaining a plurality of wavelet neural network parameter sets to perform population initialization, performing chromosome coding on each wavelet neural network parameter set to obtain a first generation population, wherein each wavelet neural network parameter set corresponds to a chromosome, each chromosome comprises a plurality of genes, and each gene corresponds to a wavelet neural network parameter; s222, calculating the fitness of each chromosome in the first generation population based on the intermediate prediction data and the training samples; s223, selecting the first generation population chromosomes with fitness meeting set requirements, and sequentially performing crossover operation and mutation operation with set probability on the selected chromosomes to respectively obtain a second generation population and a third generation population; s224, selecting chromosomes with fitness meeting set conditions in the third generation population, decoding, and obtaining initial wavelet neural network parameters.
Further, after the step of S224, the method further includes: and adjusting the initial wavelet neural network parameters by using a mean square error method, minimizing an error function, obtaining an error function gradient, and performing back propagation of errors by using the error function gradient to correct the network weight.
Further, before the step of S11, the method further includes: and judging the stationarity of the historical time series data sample by using an ADF (automatic force analysis) unit root test method.
Further, between the steps of S12 and S13, the method further comprises: respectively calculating the AIC values of the AR model, the MA model and the ARMA model based on the difference times parameter, and selecting the model type corresponding to the minimum AIC value as a target ARIMA prediction model; accordingly, the initial ARIMA prediction model is determined from the target ARIMA prediction model, the autoregressive term parameter, and the moving average term parameter.
Further, after the step of initializing the network parameters of the wavelet neural network model by using genetic algorithm optimization in step S22, the method further includes: and further optimizing the network parameters of the wavelet neural network model optimized by the genetic algorithm by adopting a mean square error method.
Further, before the step of outputting the initial wavelet neural network model as the wavelet neural network model in step S24, the method further includes: and evaluating the prediction performance of a combined network model based on the combination of the ARIMA prediction model and the initial wavelet neural network model by using the test sample and adopting one or more of an average absolute error method, a root-mean-square error method and a mean-square error method, and selecting the initial wavelet neural network model corresponding to the combined network model of which the prediction performance meets a given standard.
In step S221, the step of randomly obtaining a plurality of sets of wavelet neural network parameters to perform population initialization further includes: randomly selecting a plurality of arrays as the wavelet neural network parameter set according to the wavelet neural network parameter types, wherein the wavelet neural network parameter types comprise network weights, wavelet expansion and translation factors; and carrying out initialization coding on the plurality of wavelet neural network parameter sets, initializing the cross scale, the selection probability, the cross probability, the mutation probability and the initial population number, and setting the maximum allowable genetic algebra.
Compared with the traditional water quality prediction method, the river water quality prediction method has the advantages of stronger universality, higher prediction accuracy, quicker convergence speed and higher efficiency, and is convenient for multi-water-source supervision, water quality early warning and water pollution treatment.
Drawings
FIG. 1 is a flow chart of a river water quality prediction method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a process for constructing an ARIMA prediction model according to an embodiment of the present invention;
FIG. 3 is a flowchart of a process for constructing a wavelet neural network model optimized by a genetic algorithm according to an embodiment of the present invention;
FIG. 4 is a schematic structural topology diagram of a wavelet neural network according to an embodiment of the present invention;
FIG. 5 is a flowchart of a wavelet neural network initialization process optimized by a genetic algorithm according to an embodiment of the present invention;
fig. 6 is a flowchart of a wavelet neural network optimized by a genetic algorithm according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As an embodiment of the present invention, this embodiment provides a river water quality prediction method, and referring to fig. 1, is a flowchart of a river water quality prediction method according to an embodiment of the present invention, including:
and S1, based on the time series test data of the water quality parameters of the target water area, preliminarily predicting initial prediction data of the water quality parameters at a specified time by using an ARIMA prediction model, and calculating prediction residual data, wherein the ARIMA prediction model is constructed in advance according to historical time series data samples of the water quality parameters.
It can be understood that, for various water quality parameters of a target water area, 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, a combined prediction model fusing an ARIMA model and a wavelet neural network model optimized by a genetic algorithm is respectively established, and the change of the water quality parameters is predicted by respectively utilizing the corresponding combined prediction model.
And (3) performing prediction calculation on time series test data, namely prediction reference data, of various water quality parameters of the target water area by adopting a combined prediction model of a wavelet neural network optimized by fusing an ARIMA model and a genetic algorithm to obtain a predicted value of the water quality parameters in a specified time period.
The method comprises the steps of firstly initializing time series test data of each water quality parameter to be predicted, namely prediction reference data, inputting test data with the time prior to the initialization into an ARIMA prediction model which is constructed in advance, and outputting prediction data of the ARIMA as initial prediction data. And taking the test data after the time of initialization processing as reference output, comparing the initial prediction data with the reference output, and acquiring the deviation of the initial prediction data and the reference output as prediction residual data.
Before the ARIMA prediction model is utilized, the ARIMA prediction model is constructed, namely the initialization, training and testing process of the ARIMA prediction model is carried out. The method specifically comprises the steps of dividing historical time sequence data of water quality parameters of a preprocessed target water area into a training sample set and a testing sample set, taking part of the historical water quality parameter values as the training sample set to be input into an ARIMA model, taking later-stage water quality parameter values as output, and obtaining a primary optimal model. And (4) checking the trained model by using the test sample set for the primary optimal ARIMA model to obtain an optimal water quality parameter time sequence prediction model based on the ARIMA model.
And S2, predicting the prediction data of the water quality parameter at the specified time by using a wavelet neural network model optimized by a genetic algorithm based on the time series test data, the initial prediction data and the prediction residual data, wherein the wavelet neural network model optimized by the genetic algorithm is obtained by optimizing the genetic algorithm in advance according to the historical time series data sample and the ARIMA prediction model.
It can be understood that after the water quality parameter data is preliminarily predicted by the ARIMA prediction model according to the above steps, the preliminary prediction value is further optimized by using a wavelet neural network model optimized by a genetic algorithm. And (3) taking the initial predicted value output by the ARIMA prediction model, nonlinear residual data obtained by ARIMA prediction and original time sequence test data as the input of a wavelet neural network model optimized by a genetic algorithm, and predicting the data of corresponding water quality parameters. And outputting the predicted data of the final designated time.
It should be understood that before the wavelet neural network model optimized by the genetic algorithm is used for training the wavelet neural network model to further predict the data of the corresponding water quality parameters, the model is constructed according to historical data. Specifically, initial wavelet neural network model parameters are obtained based on a genetic optimization algorithm to carry out initialization setting on the wavelet neural network, then data with the time ahead in the training data are used as input of an ARIMA prediction model to obtain initial prediction data and prediction residual data, the initial prediction data and the prediction residual data are used as input of the initial wavelet neural network together with original training data, and the initial wavelet neural network is trained. And then, using a test sample set for inspection, and finely adjusting network parameters to obtain a wavelet neural network model optimized by an optimal genetic algorithm.
According to the river water quality prediction method provided by the embodiment of the invention, the ARIMA model and genetic algorithm optimization fused wavelet neural network water quality time sequence prediction method is adopted to combine model prediction, and compared with the traditional water quality prediction method, the river water quality prediction method provided by the invention has the advantages of stronger universality, higher prediction accuracy, higher convergence speed and higher efficiency.
Optionally, referring to fig. 2, a further processing step of constructing the ARIMA prediction model according to the historical time series data samples of the water quality parameter in step S1 is a flowchart of a constructing process of the ARIMA prediction model according to an embodiment of the present invention, and includes:
and S11, if the historical time sequence data sample is non-stationary data, smoothing the historical time sequence data by using a difference algorithm to obtain a stationary historical time sequence data sample, and estimating a difference time parameter of the ARIMA prediction model.
It can be understood that the ARIMA model considers the prediction index, namely a data sequence formed by various water quality parameter data over 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 influenced by external factors and has a self-changing rule. The ARIMA model can predict linear water quality time series data. According to whether the time series is stable or not and the difference of the parts contained in the regression, the method can be divided into the following steps: autoregressive ar (p) model, moving average ma (q) model, and ARMA (p, q) model.
Since the ARIMA model processes stationary data, in the case where it is known that the historical time-series data samples used for modeling are non-stationary data, the historical time-series data samples are subjected to a differential operation according to a differential algorithm. Assuming that a random sequence { x, t }, t ═ 1,2, … is defined as a unit root process, and if x, t ═ ρ x _ t-1+, t ═ 1,2 … where ρ ═ 1, { } is a stationary sequence (white noise), and E [ ] ═ 0, V () ═ σ ∞, Cov (,) > μ ∞ where τ ═ 1,2 …, then the non-stationary data is processed in a differential form, and the total number of times of difference when stationary data is acquired is the difference number parameter d in the ARIMA (p, d, q) model. AR is autoregressive, p is the autoregressive term, MA is the moving average, and q is the number of terms of the moving average. After the time series data are smoothed, the ARIMA (p, d, q) model is converted into an ARMA (p, q) model.
After the sequence can become a stable sequence after d differences, establishing an ARIMA (p, d, q) model as follows:
wt=φ1wt-1+φ2wt-2+...+φpwt-p++ut+θ1ut-1+θ2ut-2+...+θqut-q;
in the formula, wt,wt-1,wt-2,...,wt-pRepresents time series data phi1,φ2,...,φpCoefficient representing AR, constant, representingSequence data no 0 averaging, ut,ut-1,ut-2,...,ut-qRepresenting a white noise sequence, theta1,θ2,...,θqRepresenting the coefficient of MA.
In one embodiment, between the steps of S12 and S13, the method further comprises: respectively calculating the AIC values of the AR model, the MA model and the ARMA model based on the difference times parameter, and selecting the model type corresponding to the minimum AIC value as a target ARIMA prediction model; accordingly, the initial ARIMA prediction model is determined from the target ARIMA prediction model, the autoregressive term parameter, and the moving average term parameter.
It can be understood that after the non-stationary time series data are subjected to difference processing, difference time parameters of the models are obtained, models of different types of AR, MA and ARMA can be established according to the difference time parameters, in order to select the optimal model type, the AR model, the MA model and the ARMA model are respectively established according to the difference time parameters, AIC values of the models are respectively calculated, and the model type corresponding to the minimum AIC value is selected as the target ARIMA prediction model. And then determining an ARIMA prediction model meeting the standard according to the target ARIMA prediction model.
And S12, dividing the stable historical time series data sample into a training sample and a testing sample.
It can be understood that after the stationary time sequence data is acquired, the stationary time sequence data is divided into two parts, one part is used as a training sample to train the preliminarily established ARIMA model, and the other part is used as a test sample to perform performance test on the trained model.
In one embodiment, after dividing a water quality parameter time series data into a training set and a testing set, the training set data is further normalized, and the data is converted into an interval of [0,1], and the normalization is performed according to the following formula:
in the formula, xiRepresenting raw water quality parameter time series dataNormalized result of (2), XiRepresenting the raw water quality parameter time series data,represents the mean value of time series data of water quality parameters, SiThe standard deviation is indicated.
And S13, estimating the autoregressive term parameter and the moving average term parameter of the ARIMA prediction model by utilizing an autocorrelation function and a partial autocorrelation function based on the training sample.
It is understood that in time series analysis, the autocorrelation function (ACF) and the partial autocorrelation function (PACF) are used to discriminate the coefficients and orders of the ARMA (p, q) model, i.e., the autoregressive term and the moving average term. The range is preliminarily determined. For example, the model parameters are (2,1,3) and (1,0,2), and the corresponding ARIMA models are ARIMA (2,1,3) and ARIMA (1,0, 2). The difference number parameter d obtained according to the above steps may be different, so that it is necessary to determine ARMA (p, q) for model identification, and perform parameter estimation on the model parameter value by using the least square method. 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.
And S14, calculating an ARIMA residual error and carrying out ARIMA residual error detection by using an initial ARIMA prediction model determined by the difference times parameter, the autoregressive item parameter and the moving average item parameter based on the training sample.
It can be understood that, according to the above steps, a water quality parameter time series data training sample is input into an ARIMA model, data stationarity is detected according to ADF, d-time difference is carried out, an autocorrelation graph and a partial correlation graph are observed, and the model is identified. The prediction result of the ARIMA model is set asOriginal time series ytAnd predicting the resultResidual error of (a) is etNamely:
the non-linear relation in the original time sequence is implicit in the residual sequence etIn (j), i.e.:
et=f(et-1,et-2,...,et-n)+t;
wherein, { et,et-1,et-2,...,et-nDenotes a prediction residual sequence,tindicating a random error.
And S15, if the ARIMA residual error obeys normal distribution with zero mean value and invariable variance, carrying out significance test on the initial ARIMA prediction model by using the test sample and adopting ARIMA residual error judgment.
It is understood that when training the established model according to the above steps, the ARIMA residual follows a normal distribution with zero mean and constant variance as a termination condition. When the residual meets the criterion, the trained model is trained using the test sample. Inputting a test sample into an ARIMA model, and verifying whether a residual sequence of the fitted time sequence model is a white noise sequence or not by judging whether a model subjected to residual error detection and training meets a significance standard or not, namely performing independence detection on the residual sequence.
S16, if the result of the significance test meets the set standard, outputting the initial ARIMA prediction model as the ARIMA prediction model, otherwise, switching to the step S13.
It can be understood that, when it is known from the above judgment that the prediction error is normal distribution with a mean value of zero and a variance of a constant, that is, normal distribution with zero mean value and unchanged variance is obeyed, the established model is judged to satisfy the significance test standard, data is subjected to inverse normalization processing to obtain residual sequence data and prediction data, the tested ARIMA prediction model is output, and the model establishment is completed.
In one embodiment, before the step of S11, the method further includes: and judging the stationarity of the historical time series data sample by using an ADF (automatic force analysis) unit root test method.
Under the condition of uncertain stability of the water quality parameter data, stability inspection needs to be performed on input data, namely the water quality parameter data, including training sample data and test sample data during model building and test data for water quality parameter prediction by using an ADF (automatic document feeder) unit root inspection method. For the embodiment, the stability of the historical time series data sample is firstly judged by using an ADF (automatic document feeder) unit root test method.
Optionally, referring to fig. 3, as a further processing step of constructing the wavelet neural network model by genetic algorithm optimization according to the historical time series data samples and the ARIMA prediction model in step S2, a flowchart of a process for constructing the wavelet neural network model by genetic algorithm optimization according to an embodiment of the present invention includes:
and S21, preliminarily predicting intermediate prediction data by using the ARIMA prediction model based on the training samples, and calculating intermediate residual data.
Wavelet Neural Networks (WNNs) are networks based on an error-back propagation neural network topology, similar to BP neural networks. In the wavelet neural network, the error is propagated reversely while the signal is propagated forwards, except that the transfer function of the hidden layer node of the wavelet neural network is the wavelet basis function. The WNN comprises three parts, namely an input layer, an output layer and a hidden layer, and the topological structure of the WNN is shown in FIG. 4 and is a structural topological schematic diagram of a wavelet neural network according to an embodiment of the invention. The wavelet neural network of the embodiment of the invention adopts a single hidden layer structure, and hidden layer nodes select a Morlet wavelet function as a transfer function according to the processed signal properties.
x1,x2,...,xkIs an input parameter of WNN; y is the predicted output value; w is aijAnd wjkIs the network connection weight value. When the input water quality parameter sample sequence is xiWhen (1, 2.. k), the hidden layer output is:
wherein h (j) is the output of the jth node of the hidden layer, wijA connection weight value representing the input layer and the hidden layerjAs a wavelet basis function hjScaling factor of bjIs hjTranslation factor of, MjIs a wavelet basis function.
The wavelet basis function adopted in this embodiment is a Morlet mother wavelet basis function, and the formula is:
in the formula, x represents an input of the transfer function, and y represents an output of the transfer function.
The wavelet neural network output layer calculation formula is as follows:
in the formula, wikRepresenting the network connection weight value from the hidden layer to the output layer; h (i) the output of the ith node of the hidden layer is shown, m is the number of nodes of the hidden layer, and n is the number of nodes of the output layer.
After the ARIMA prediction model meeting the standard conditions is constructed according to the above embodiment, the construction of a wavelet neural network model for genetic optimization using the ARIMA prediction model is required. When the wavelet neural network model is constructed, the original water quality parameter time series data, namely the training samples, the intermediate prediction data preliminarily predicted by the ARIMA prediction model and the intermediate residual data obtained by calculation are used as network input, so that the training samples are input into the constructed ARIMA prediction model in step S21, and the intermediate prediction data and the intermediate residual data are obtained through preliminary prediction.
And S22, initializing the network parameters of the wavelet neural network model by adopting genetic algorithm optimization, and initializing the wavelet neural network model by initializing the learning rate and momentum factor of the wavelet neural network.
It can be understood that, when the wavelet neural network model is constructed, the structure and parameters of the network model need to be initialized. Specifically, when network parameters are initialized, a genetic optimization algorithm is adopted, and the optimal parameters are selected as the initialized network parameters of the wavelet neural network model. And simultaneously, the initial learning rate and the momentum factor of the wavelet neural network model are set, so that the initial setting of the wavelet neural network model is realized.
And S23, based on the training sample, the intermediate prediction data and the intermediate residual data, performing forward prediction calculation by using the initialized wavelet neural network model, and performing reverse parameter correction through error judgment and iteration number judgment to obtain the initial wavelet neural network model.
It can be understood that, after the intermediate prediction data and the intermediate residual data are obtained according to the training data and the constructed ARIMA prediction model in the above steps and the network parameters of the wavelet neural network are initialized by using the genetic optimization algorithm, the training sample, the intermediate prediction data and the intermediate residual data are used as the input of the initial wavelet neural network, and the forward prediction calculation of the input data is performed to obtain the prediction result.
The later data in the training sample is compared with the prediction result to calculate the deviation. And when the deviation is not within the set error range, simultaneously judging whether the iteration times exceed the maximum set times, if not, performing reverse propagation of the error, correcting the network parameters, predicting a new training sample of the model after the parameters are corrected until the predicted deviation is within the set range, and outputting the network model of the current parameters as an initial wavelet neural network model.
And S24, testing the prediction accuracy of the initial wavelet neural network model by using the test sample through error judgment, if the accuracy reaches a set standard, outputting the initial wavelet neural network model as the wavelet neural network model, and otherwise, turning to the step S22.
It can be understood that after the initial wavelet neural network model is built according to the above steps, the initial network model is also required to be tested by using a test sample to check whether the performance of the initial network model meets the set standard. Specifically, the test sample is used as the input of a combined test model formed by combining the ARIMA prediction model and the initial wavelet neural network model, and a prediction result is output through the prediction calculation of the combined test model.
And meanwhile, comparing the prediction result with the actual data with later time in the test sample to obtain the prediction deviation, and judging whether the combined test model is effective or not by judging whether the prediction deviation meets the set deviation standard or not. If the set deviation standard is met, the test sample is effective, and the combined test model is output as a final prediction model. If the set deviation standard cannot be reached, the combined test model is invalid for the test sample, the combined test model is presumed not to be representative, the step S22 is returned, and the combined model construction process is repeated until the combined model meeting the requirements is obtained.
Further, after the step of initializing the network parameters of the wavelet neural network model by using genetic algorithm optimization in step S22, the method further includes: and further optimizing the network parameters of the wavelet neural network model optimized by the genetic algorithm by adopting a mean square error method.
Further, before the step of outputting the initial wavelet neural network model as the wavelet neural network model in step S24, the method further includes: and evaluating the prediction performance of a combined network model based on the combination of the ARIMA prediction model and the initial wavelet neural network model by using the test sample and adopting one or more of an average absolute error method, a root-mean-square error method and a mean-square error method, and selecting the initial wavelet neural network model corresponding to the combined network model of which the prediction performance meets a given standard.
It can be understood that, after the prediction accuracy of the initial wavelet neural network model is determined to reach the set standard according to the above embodiment, in order to further verify the effectiveness of the model, one or more of Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Square Error (MSE) are used to evaluate the prediction performance of the model, and if any error is within the set range, the model is considered to be an effective prediction model.
To further illustrate the above embodiments, the following wavelet neural network modeling flow is provided:
first, a genetic algorithm optimized wavelet neural network (GA-WNN) model is applied to residual sequences { etAnd an original water quality parameter time series data ytAnd prediction of ARIMAThree input sequences are predicted, and the result of combined prediction by using ARIMA and GA-WNN models is set asThen:
in the formula (I), the compound is shown in the specification,indicates the combined prediction result, ytRepresenting time series data of the original water quality parameter, etWhich represents the prediction residual data, is represented,representing the initial prediction of the ARIMA model.
Residual sequence data, prediction data and original water quality parameter time sequence data which are predicted by the ARIMA model are normalized and used as input of wavelet nerve.
And optimizing the expansion factor, the translation factor and the connection weight of the wavelet by using a genetic algorithm to obtain the optimal network parameters.
And giving initial values to the learning rate and the momentum factor of the wavelet neural network, and optimizing the scaling factor, the translation factor and the connection weight again by using a mean square error method.
And adjusting network parameters to enable the error function to reach a minimum value, and performing error back propagation by using the gradient value of the error function. If the error function is smaller than a preset certain precision value or reaches the maximum iteration number, calculating the output of the hidden layer and the output layer, and stopping the network learning process, otherwise, returning to the step of giving initial values to the wavelet neural network learning rate and the momentum factor to execute the steps circularly until the error function meets the set precision.
And evaluating the prediction performance of the model by using the average absolute error (MAE), the Root Mean Square Error (RMSE) and the Mean Square Error (MSE), and storing the network parameters to obtain the network model.
And verifying the prediction of the combined model by using the test set to obtain a prediction result.
Optionally, the step of optimizing by using a genetic algorithm and initializing the network parameters of the wavelet neural network model in step S22 refers to fig. 5, which is a flowchart of a wavelet neural network initialization process optimized by using a genetic algorithm according to an embodiment of the present invention, and includes:
s221, randomly obtaining a plurality of wavelet neural network parameter sets to perform population initialization, performing chromosome coding on each wavelet neural network parameter set to obtain a first generation population, wherein each wavelet neural network parameter set corresponds to a chromosome, each chromosome comprises a plurality of genes, and each gene corresponds to a wavelet neural network parameter;
s222, calculating the fitness of each chromosome in the first generation population based on the intermediate prediction data and the training samples;
s223, selecting the first generation population chromosomes with fitness meeting set requirements, and sequentially performing crossover operation and mutation operation with set probability on the selected chromosomes to respectively obtain a second generation population and a third generation population;
s224, selecting chromosomes with fitness meeting set conditions in the third generation population, decoding, and obtaining initial wavelet neural network parameters.
It should be understood that the Genetic Algorithm (GA) is a calculation model of a biological evolution process simulating natural selection and Genetic mechanism of darwinian biological evolution theory, and is a method for obtaining an optimal solution by simulating a natural evolution process, and has an advantage in that a local optimal solution can be avoided, thereby extracting important influence factors. The WNN network flow optimized by the genetic algorithm is shown in fig. 6, which is a flow chart of the genetic algorithm optimized wavelet neural network according to the embodiment of the present invention.
In one embodiment, the step of randomly acquiring a plurality of wavelet neural network parameter sets for population initialization in step S221 further includes: randomly selecting a plurality of arrays as the wavelet neural network parameter set according to the wavelet neural network parameter types, wherein the wavelet neural network parameter types comprise network weights, wavelet expansion and translation factors; and carrying out initialization coding on the plurality of wavelet neural network parameter sets, initializing the cross scale, the selection probability, the cross probability, the mutation probability and the initial population number, and setting the maximum allowable genetic algebra.
The WNN parameters are optimized by adopting a genetic algorithm, so that the initial value sensitivity of the gradient descent method parameters can be better overcome, the local minimum and the oscillation effect are easy to generate, and the globally optimal network parameters are obtained. The steps are implemented according to the following flow:
initializing population and encoding network parameters. Randomly selecting P wavelet neural network parameter sets as P chromosomes PiThe wavelet neural network parameters, i.e., weights and scale factors, are initially encoded (i.e., 1, 2.., n). Initializing cross scale, selecting probability, cross probability and mutation probability, calling a genetic initialization function to randomly initialize population number, and setting genetic algebra Gen.
The population number is a set constant, and represents the number of initial session parameter sets, for example, 30 populations are selected. A combination of 30 such solutions.
A population is a combination of various parameter values that make the overall network energy function, i.e., the minimum error function, whereas a population is composed of a certain number of individuals that are genetically encoded. Each individual is actually a chromosome-bearing entity. Mapping from phenotype to genotype, i.e. encoding, needs to be done at the outset. The chromosome is a defined number, for example, real number coding is used for coding parameters, and an initialization function is called in a genetic algorithm packet; a gene is each network parameter in each set of network parameters.
Then, calculating fitness value, and determining the fitness value of the individual corresponding to each chromosome according to the training result. The fitness value is calculated by a fitness function as follows:
wherein V represents the fitness value of the ith individual,indicating the desired output value, y, of the ith output nodeiThe actual output value of the ith node is represented, and L represents the training sample length.
And calculating a fitness value V according to the fitness function, and storing N individuals with the maximum V values.
Then, selection, crossover and mutation operations are performed. The purpose of the selection operation is to select more excellent individuals that can be inherited by the next generation, so that the most suitable individual is directly inherited to the next generation, but the diversity of the population is maintained as much as possible, so that local optimality is avoided. By adopting the fitness proportion method, the selection probability of the individuals is proportional to the fitness value of the individuals, and the individuals with high fitness values copy more individuals in the filial generation, so that the individuals with the maximum fitness are ensured to be reserved. The selection probability calculation is performed as follows:
in the formula, PsIndicates the selection probability, VnDenotes the fitness, V, of the nth individualiThe fitness of the ith individual is represented, L represents the length of the training sample, and N represents the number of the selected optimal individuals.
The crossing is a process of randomly selecting a pair of chromosomes by setting the crossing probability and exchanging partial genes of the chromosomes to obtain two brand new individuals, and the individuals without crossing operation are directly copied to obtain a second generation population. The mutation is to randomly change a certain position in a chromosome by setting the mutation probability so as to generate a new individual, and the mutated individual forms a third generation population.
And finally, taking the population genetic algebra exceeding a preset value as a termination condition, decoding the obtained optimal coding individual, converting the optimal coding individual into an optimized wavelet network connection weight and a telescopic translation scale, otherwise, returning to the step of fitness calculation, and circularly executing the steps until the set standard is met.
In another embodiment, after the step of S224, the method further includes: and adjusting the initial wavelet neural network parameters by using a mean square error method, minimizing an error function, obtaining an error function gradient, and performing back propagation of errors by using the error function gradient to correct the network weight.
It can be understood that the weighting w of the wavelet neural network is completed by using a genetic algorithmij、wjkAnd wavelet expansion and translation factor aj、bjAfter the optimization is completed, the network parameters are adjusted by using a mean square error method to enable the error function F to reach the minimum value, the gradient of the error function F is obtained, and then the error is reversely propagated by using the gradient value. With a network parameter wijAnd ajFor example, the adjustment formula is as follows:
in the formula, F represents an error function,andbefore being adjusted respectivelyAnd the adjusted weights between the input layer nodes and the hidden layer nodes,anda balance factor before and after adjustment, η is the net learning rate, L represents the training sample length,indicating the desired output value, y, of the ith output nodeiRepresenting the actual output value of the ith node.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (8)
1. A river water quality prediction method is characterized by comprising the following steps:
s1, based on time series test data of the water quality parameters of the target water area, preliminarily predicting initial prediction data of the water quality parameters at a specified time by using an ARIMA prediction model, and calculating prediction residual data, wherein the ARIMA prediction model is constructed in advance according to historical time series data samples of the water quality parameters;
s2, predicting the prediction data of the water quality parameters at the specified time by utilizing a wavelet neural network model optimized by a genetic algorithm based on the time series test data, the initial prediction data and the prediction residual data, wherein the wavelet neural network model optimized by the genetic algorithm is obtained by optimizing the genetic algorithm in advance according to the historical time series data sample and the ARIMA prediction model;
wherein the step of constructing the ARIMA prediction model from the historical time-series data samples of the water quality parameter in step S1 further comprises:
s11, if the historical time sequence data sample is non-stationary data, smoothing the historical time sequence data by using a difference algorithm to obtain a stationary historical time sequence data sample, and estimating a difference time parameter of the ARIMA prediction model;
s12, dividing the stable historical time series data sample into a training sample and a testing sample;
s13, estimating an autoregressive item parameter and a moving average item parameter of the ARIMA prediction model by utilizing an autocorrelation function and a partial autocorrelation function based on the training sample;
s14, based on the training sample, calculating an ARIMA residual error by using an initial ARIMA prediction model determined by the difference times parameter, the autoregressive item parameter and the moving average item parameter, and carrying out ARIMA residual error detection;
s15, if the ARIMA residual error obeys normal distribution with zero mean value and invariable variance, the test sample is used for carrying out significance test on the initial ARIMA prediction model by adopting ARIMA residual error judgment;
s16, if the result of the significance test meets a set standard, outputting the initial ARIMA prediction model as the ARIMA prediction model, otherwise, turning to the step S13;
the step of optimizing and constructing the wavelet neural network model by a genetic algorithm according to the historical time series data samples and the ARIMA prediction model in step S2 further comprises:
s21, based on the training sample, preliminarily predicting intermediate prediction data by using the ARIMA prediction model, and calculating intermediate residual data;
s22, initializing network parameters of the wavelet neural network model by adopting genetic algorithm optimization, and initializing the wavelet neural network model by initializing the learning rate and momentum factor of the wavelet neural network;
s23, based on the training sample, the intermediate prediction data and the intermediate residual data, performing forward prediction calculation by using an initialized wavelet neural network model, and performing reverse parameter correction through error judgment and iteration frequency judgment to obtain an initial wavelet neural network model;
and S24, testing the prediction accuracy of the initial wavelet neural network model by using the test sample through error judgment, if the accuracy reaches a set standard, outputting the initial wavelet neural network model as the wavelet neural network model, and otherwise, turning to the step S22.
2. The method according to claim 1, wherein the step of initializing network parameters of the wavelet neural network model using genetic algorithm optimization in step S22 further comprises:
s221, randomly obtaining a plurality of wavelet neural network parameter sets to perform population initialization, performing chromosome coding on each wavelet neural network parameter set to obtain a first generation population, wherein each wavelet neural network parameter set corresponds to a chromosome, each chromosome comprises a plurality of genes, and each gene corresponds to a wavelet neural network parameter;
s222, calculating the fitness of each chromosome in the first generation population based on the intermediate prediction data and the training samples;
s223, selecting the first generation population chromosomes with fitness meeting set requirements, and sequentially performing crossover operation and mutation operation with set probability on the selected chromosomes to respectively obtain a second generation population and a third generation population;
s224, selecting chromosomes with fitness meeting set conditions in the third generation population, decoding, and obtaining initial wavelet neural network parameters.
3. The method according to claim 2, further comprising, after the step of S224:
and adjusting the initial wavelet neural network parameters by using a mean square error method, minimizing an error function, obtaining an error function gradient, and performing back propagation of errors by using the error function gradient to correct the network weight.
4. The method of claim 1, further comprising, before the step of S11:
and judging the stationarity of the historical time series data sample by using an ADF (automatic force analysis) unit root test method.
5. The method of claim 1, further comprising, between the steps of S12 and S13:
respectively calculating the AIC values of the AR model, the MA model and the ARMA model based on the difference times parameter, and selecting the model type corresponding to the minimum AIC value as a target ARIMA prediction model;
accordingly, the initial ARIMA prediction model is determined from the target ARIMA prediction model, the autoregressive term parameter, and the moving average term parameter.
6. The method according to claim 1, wherein after the step of initializing network parameters of the wavelet neural network model by using genetic algorithm optimization in step S22, the method further comprises:
and further optimizing the network parameters of the wavelet neural network model optimized by the genetic algorithm by adopting a mean square error method.
7. The method according to claim 1, wherein before the step of outputting the initial wavelet neural network model as the wavelet neural network model in step S24, further comprising:
and evaluating the prediction performance of a combined network model based on the combination of the ARIMA prediction model and the initial wavelet neural network model by using the test sample and adopting one or more of an average absolute error method, a root-mean-square error method and a mean-square error method, and selecting the initial wavelet neural network model corresponding to the combined network model of which the prediction performance meets a given standard.
8. The method according to claim 2, wherein the step of randomly acquiring a plurality of sets of wavelet neural network parameters for population initialization in step S221 further comprises:
randomly selecting a plurality of arrays as the wavelet neural network parameter set according to the wavelet neural network parameter types, wherein the wavelet neural network parameter types comprise network weights, wavelet expansion and translation factors;
and carrying out initialization coding on the plurality of wavelet neural network parameter sets, initializing the cross scale, the selection probability, the cross probability, the mutation probability and the initial population number, and setting the maximum allowable genetic algebra.
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