CN111754034A - Time sequence prediction method based on chaos optimization neural network model - Google Patents
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Abstract
The invention discloses a time sequence prediction method based on a chaos optimization neural network model, which comprises the steps of firstly, obtaining urban historical daily water demand time sequence data from a database on line and carrying out data preprocessing, and simultaneously carrying out chaos feature recognition; then, determining the structure of the chaotic optimization BP neural network by using the embedding dimension of the model input data reconstruction phase space, and simultaneously carrying out model training; in the model training process, the global optimal value of the BP neural network weight is found through chaotic optimization search; after the model training is finished, carrying out chaotic parameter control on the output time sequence predicted value by a parameter control method; and finally, forecasting the daily water demand time sequence of the city. The urban daily water demand time sequence prediction method based on the chaos optimization neural network model requires few training data samples, has high convergence rate, is easy to reach the global minimum value, has good indexes of the overall error of the prediction result, and presents good comprehensive prediction performance.
Description
Technical Field
The invention belongs to the technical field of model prediction control, and particularly relates to a time series prediction method based on a chaos optimization neural network model.
Background
The rapid development of economy brings continuous development of urbanization and industrial production scale, so that the contradiction between supply and demand of an urban water supply system becomes prominent, and particularly, the phenomenon that the urban water supply is in short supply in summer is more and more common. The prediction of urban daily water demand time series is an important research field in the discipline of modern water supply dispatching systems. Because the time series growth of daily water demand of cities is influenced by a plurality of factors such as economic development, industrial structure, income level of residents, climate and the like, the model is established by a conventional mathematical method, so that the workload is large, and the precision is difficult to ensure.
At present, the urban daily water demand time sequence prediction model method adopted at home and abroad mainly comprises a time sequence prediction model, a gray prediction model, an artificial neural network model and the like. The time series prediction model is a quantitative analysis method, and is based on time series variable analysis, a prediction model is established by using a certain mathematical method, so that the time trend is extended outwards, the future development change trend is predicted, and the variable prediction value is determined. The method has the advantages of simple operation process, better effect on medium-short term prediction than long-term prediction and the like. However, the method has the defect of prediction error because the influence of external factors is not considered for the time sequence. When the external factors are changed greatly, the deviation is always large. The grey prediction model is used for mining the change rule of the system by processing the original data and establishing a corresponding differential equation, so that the future development condition of the object is predicted. The prediction effect of the complex system with uncertain factors is good, and the required sample data is small; however, the prediction based on the exponential rate does not consider the randomness of the system, and the accuracy of the medium-long term prediction is poor. The artificial neural network model is an algorithmic mathematical model simulating animal neural network behavior characteristics and performing distributed parallel information processing. The network achieves the aim of processing information by adjusting the mutual connection relationship among a large number of nodes in the network depending on the complexity of the system. The network has strong nonlinear approximation capability, good self-adaptability and self-organization, and strong learning, association, fault tolerance and anti-interference capabilities, so that the network can be widely applied to various fields, and can solve the numerical fitting prediction problem related to multivariable, strong coupling, nonlinearity and the like. The disadvantages are as follows: the network algorithm has low learning speed and high probability of network training failure, the number of hidden layer numbers and the number of neurons of an input layer are difficult to determine, the hidden layer numbers and the number of neurons of the input layer are generally selected according to an empirical formula and by combining practical problems, and the selection of the network structure has no unified and complete theoretical guidance and can be generally selected only by experience.
Disclosure of Invention
The invention aims to provide a time sequence prediction method based on a chaos optimization neural network model, and solves the problems that the existing urban daily water demand time sequence prediction model method needs more training samples, has large prediction error, is slow in algorithm learning convergence speed, is difficult to determine the network structure and the like.
In order to solve the problems, the technical scheme of the invention comprises the following steps:
a time sequence prediction method based on a chaos optimization neural network model is characterized in that city historical daily water demand time sequence data are obtained on line from a database and are subjected to data preprocessing, and chaos feature recognition is carried out at the same time; then, determining the structure of the chaotic optimization BP neural network by using the embedding dimension of the model input data reconstruction phase space, and simultaneously carrying out model training; in the model training process, the global optimal value of the BP neural network weight is found through chaotic optimization search; after the model training is finished, carrying out chaotic parameter control on the output time sequence predicted value by a parameter control method; and finally, forecasting the daily water demand time sequence of the city.
Further, the method specifically comprises the following steps:
step 1: acquiring time series data of the original historical daily water demand of a certain city from an ORACLE database; dividing the time series data sets of all input models into a training input time series data set and a testing input time series data set;
step 2: carrying out data preprocessing on the acquired water demand time data sequence of a certain city day, and inputting the processed data into the model;
and step 3: after the preprocessed data is input into the model, performing chaotic feature recognition in the model, performing data phase space reconstruction, and calculating delay time tau and saturation embedding dimension m to determine the number of layers of the network model and the number of neurons in an input layer; and determining an input vector and a desired output vector;
and 4, step 4: calculating each neuron output of a network hidden layer and an output layer, and calculating an error function E; if the error function E reaches the threshold range, predicting an output value through a parameter control method, and if the error function E does not reach the threshold range, optimizing a weight threshold of the network model through chaotic search;
and 5: and judging whether the iteration of the network model reaches the maximum training times, if so, predicting an output value by a parameter control method, if not, continuously calculating the unit error and the error gradient of the hidden layer of the network, learning the weight of the model, and returning to the fourth step to continuously execute.
Further, in step 1, the original time series data includes historical time series characteristic data of the daily water consumption of users in a region corresponding to a water plant in a certain city.
Further, in step 2, the data preprocessing refers to processing of data outliers, missing points, and duplicate points in the historical time-series data of a certain market.
Furthermore, the calculation delay time τ and the saturation embedding dimension m in step 3 are used for performing chaotic feature identification inside the model, providing parameter basis for data phase space reconstruction, and providing calculation data support for determining the number of layers of the network model and the number of neurons in the input layer.
Further, the step 4 is a model training part, and comprises a forward propagation process and a backward propagation process in the chaos optimization neural network model time series data training process, and a chaos search optimization process.
Further, in step 5, a model prediction part is adopted, namely a time series data set is input through a historical daily water demand test of a certain city to verify the effectiveness and the practicability of the time series prediction method based on the chaos optimization neural network model.
The invention has the beneficial effects that:
compared with the existing urban daily water demand time sequence prediction model method, the urban daily water demand time sequence prediction method based on the chaos optimization neural network model has the advantages that the number of required training data samples is smaller through the chaos feature recognition technology, the data phase space reconstruction technology and the like, the model convergence speed is higher through the chaos optimization search technology, the internal weight value can be kept away from the local minimum value in the model training process, the global minimum value is easier to achieve, finally, the prediction result precision is higher through the parameter control method technology, the overall error index is better, and good comprehensive prediction performance is presented.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a flow chart of a city daily water demand time series prediction method based on a chaos optimization BP neural network model;
FIG. 2 is a block diagram of a chaos optimized BP neural network model according to the present invention.
Fig. 3 and 4 are graphs showing the actual effect of the test data set prediction by training in combination with the data sequence of the actual daily water demand time of a certain city.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The time data sequence of the daily water demand of the city has various uncertainties and nonlinearities, and an accurate mathematical model is not easy to establish. The chaos optimization BP neural network model method combined with the BP neural network theory can overcome the defects that the traditional prediction model method needs more training samples, has large prediction error, is low in algorithm learning convergence speed, is difficult to determine the network structure and the like in urban daily water demand time data sequence prediction.
Referring to fig. 1, a method for predicting a time series of daily water demand of an city based on a chaos optimization BP neural network model comprises the following steps:
s1: data source acquisition
The data acquisition and transmission process comprises the following steps: data are collected from an operation site through the sensor, the sensor transmits the collected data to the PLC, and the PLC program transmits the data to the upper computer and stores the data in an upper computer database. And the upper computer transmits the data to a remote ORACLE database in a remote transmission mode. And the user side realizes the online acquisition of the historical time data sequence of the daily water demand of the city through a web service interface of the ORACLE database.
S2: data pre-processing
In the process of data acquisition and transmission, data is transferred for multiple times, and the transfer mode comprises a wired network and a wireless network. Therefore, the abnormity is easy to occur in the data acquisition, data transmission and data storage processes. The resulting data needs to be compared with each other to eliminate possible abnormal data points. To ensure the accuracy of the model input data, it becomes important to perform data cleansing.
(1) Data anomaly point processing:
taking the daily water demand time-series data sample flow of a city as an example, the change between adjacent data flows should be relatively smooth, but the analysis of the data finds that the distribution of the flow sample data mainly has a burr phenomenon. At this point, two rules are employed to process the data at the exception point: 1. data flow value threshold constraints; 2. and (4) data traffic adjacent value change rate threshold constraint.
1. The data flow value threshold value constraint is that a reasonable upper limit value and a reasonable lower limit value are set for the original daily water demand value taking each day as a unit according to the actual operation condition of a branch of a water supply network in a certain city, so that the original data flow value is always in the lower limit flow value QminAnd an upper limit flow rate value QmaxIn the meantime. The specific calculation processing rule is shown as the following formula:
2. the threshold value of the change rate of the adjacent values of the data flow is restricted by the data flow value Q at a certain timetData flow rate value Q at a time adjacent to the timet-1，Qt+1And (5) performing analysis comparison. If the relative error absolute value of the data flow value at the current moment and the data flow values at two adjacent moments before and after the moment exceeds 10 percent, the data flow value Q at the moment is determinedtThe exception data is set. The specific calculation processing rule of the abnormal data traffic value at this time is shown as the following formula:
(2) data miss point handling
The invention adopts a piecewise linear interpolation function to estimate the data flow value of the breakpoint missing. If the data flow value at t moment at a certain breakpoint of the data set is missing, only the nearest t moment before and after the t moment away from the certain breakpoint is searchedAAnd tBTime (t)A＜t＜tB) Data flow value, if t is setAAnd tBThe data flow rate value at the time is QtAAnd QtBIf the data flow value Q is missing at the moment t of a certain breakpointtThe estimated value calculation formula is as follows:
s3 chaos analysis and discrimination of daily water demand time data sequence
The premise of researching the prediction problem of the short-term daily water demand time sequence of the city by applying the Chaos theory is to determine whether the preprocessed daily water demand time data sequence of the city is a chaotic time sequence, namely, the urban daily water demand time data sequence is chaotic, analyzed and judged. The invention adopts the association dimension D2The method carries out chaos analysis and discrimination. The specific determination method is as follows:
in an m-dimensional reconstruction phase space of the preprocessed urban daily water demand time data sequence { x (t) }, t ═ 0,1, 2..,., n }, an Euclidean distance between any two phase points is set as rij(m):
rij(m)＝||Xm(ti)-Xm(tj)|| (4)
And (3) randomly giving a scale r, counting the proportion of the number of the point pairs smaller than r in all the points, wherein the proportion is shown in the following formula:
wherein n is the number of phase points; θ is the Heaviside function.
Let the correlation dimension D (m) of the m-dimensional reconstruction phase space be noted as:
if the trend of the correlation dimension D (m) does not change with m as r approaches the zero limit, then the correlation dimension for obtaining the time data series of the daily water demand of the city is as follows:
when D is present2If the number is more than 2 or is a fraction, the urban daily water demand time data sequence has chaotic characteristics; otherwise, the system is judged to be a random system.
S4 reconstruction of phase space of daily water demand time data sequence
The invention uses the delay coordinates of the original system variables to reconstruct the phase space, can construct the phase space equivalent to the original system by an 'embedding' method, and can recover the law of the original dynamic system in the space. The phase space reconstruction of the city daily water demand time data series can be expressed as follows:
setting a preprocessed city daily water demand time data sequence { x (t), where t is 0,1,2,.., n }, and embedding the sequence into an m-dimensional phase space to obtain a series of phase points of the m-dimensional phase space:
wherein: m is the embedding dimension, τ is the delay time, and N ═ N- (m-1) τ.
S5 method for selecting delay time
The delay time is an important phase-space reconstruction parameter of the time data sequence. The invention adopts the autocorrelation method to calculate the optimal delay time tau, and comprises the following steps:
(1) introducing a nonlinear correlation function to make the calculation delay time tau become a linear correlation and a nonlinear correlation:
linear correlation function:
calculating linear correlation between states;
nonlinear correlation function:
a non-linear correlation between the states is calculated.
(2) Let τxAnd
respectively correspond to phixx(τ) and
the value of the optimal delay time τ is shown as follows:
s6 selection method of saturated embedding dimension (input layer neuron number)
The invention adopts a depolarization autocorrelation method to determine the saturated embedding dimension. The specific steps of solving the saturated embedding dimension by adopting the depolarization autocorrelation method are as follows:
(1) setting a depolarization autocorrelation function of m-dimensional phase space reconstruction of the urban daily water demand time data sequence as follows:
in the formula (I), the compound is shown in the specification,
is an autocorrelation function; n is the number of test samples; m is the embedding dimension; siThe data sequence value of the ith daily water demand time is obtained;
and (4) averaging the data sequence of daily water demand time of the test sample. j tau is a data sequence { s } of daily water demand time of the test sampleiThe time span of } is; τ is a time delay; si+jτThe data sequence value of the (i + j) th day water demand time is the data sequence value of the (i + j) th day water demand time; if it is selected
The first zero of (a) is the time delay τ, and also determines the saturation embedding dimension of the reconstructed phase space, i.e., the number of input layer neurons.
(2) If the daily water demand time data sequence is a chaotic time data sequence, then
Will gradually tend to saturate as m increases. When visually inspecting the scalar quantity
When the trend of increasing embedding dimension is no longer changed with the increase of m, m at this time is determined as the optimal saturated embedding dimension. In the actual determination of the optimal saturated embedding dimension,
the value of this quantity tends to fluctuate, so that different calculation methods will give different results.
S7 model training
As shown in fig. 2, the chaos-optimized BP neural network model has three layers (an input layer, a hidden layer, and an output layer), the type of such a network model is an error back propagation type neural network with a hidden layer, that is, an intermediate layer (i.e., a hidden layer) is provided, and a node of the input layer transmits stimulation information (i.e., a city daily water demand time data sequence value) to a node of the hidden layer through a specific connection channel:
S_in＝W·S+θ0(13)
wherein, W is a (L, I) -dimensional weight value matrix; theta0Is a (L,1) -dimensional daily water demand time sequence value vector; s is a water demand value matrix of (I, J) dimension, and L is the input number of stimulation information of the chaos optimization BP neural network model.
Each node in the hidden layer converts an input water demand value into a corresponding reaction output through an activation function:
s＝f(S_in)＝f(W·S+θ0) (14)
where f is the activation function of the hidden layer.
Similarly, each neuron node of the network model output layer also converts the stimulation information transmitted by the hidden layer output into corresponding response output through an activation function:
＝g(Z·s+z0) (15)
wherein g is the activation function of the output layer; zAnd initializing a weight matrix for the (I, J) -dimensional random number; z is a radical of0Is an (I,1) -dimensional offset vector.
The chaos optimization BP neural network model training adopts an error back propagation learning algorithm, namely a gradient descent algorithm.
Initializing a weight matrix W, Z and a daily water demand time sequence value vector theta by selecting random numbers0Offset vector z0Time-series data s of historical daily water demand of n-1 cities1、s2、s3、··、si、··、sn-1And inputting the chaotic optimization BP neural network model for training. Taking an S (I, J) -dimensional daily water demand time sequence value input matrix to calculate the sum of input signals of each hidden layer node, and enabling the acquired signals to be transmitted through an activation function. Similarly, if signal transmission is also performed at the output layer node, the corresponding output vector is:
k＝g[Z(f(W·S+θ0))+z0](16)
in the formula (I), the compound is shown in the specification,koutputting a daily water demand time sequence value vector for the output node; f is the activation function of the hidden layer; g is the activation function of the output layer.
The output daily water demand time sequence value vector of the chaos optimization BP neural networkkAnd the measured output daily water demand time series vector value increment delta sk＝sn-1-sn-2And comparing, and calculating the output error of the chaotic optimization BP neural network:
ek＝Δsk-k(17)
the error is reversely propagated in the chaos optimization BP neural network: the error signal is reversely propagated back along the original connecting path through the network, and the weight matrix and the value of the offset vector of each stage are modified according to the minimum mean square error algorithm, so that the aim of training the chaos optimization BP neural network is fulfilled.
The minimum function magnitude value during each training is the variance of the output error of the chaotic optimization BP neural network:
Ekgradient with respect to Z matrix:
setting the two activation functions of the hidden layer and the output layer to be the same:
k＝f[Z(f(W·S+θ0))+z0]＝f(Z·yk+z0) (20)
then EkThe gradient with respect to the Z matrix can be calculated as follows:
from EkThe expression, the 1 st partial derivative, is derived as follows:
the 2 nd partial derivative derivation depends on the type of activation function chosen, the range of which increases non-linearly. The method for predicting the time sequence of the daily water demand of the city has good stability by adopting the unipolar s function.
The 2 nd partial derivative can be expressed by equation (23):
in the formula, I represents and outputs daily water demand time sequence value vectorkThe unit matrix of the same dimension, the "-" operation represents the product of term to term in the vector.
The 3 rd partial derivative is derived as follows:
updating the weight by a gradient descent algorithm, wherein the weight matrix Z in the step (k +1) is as follows:
wherein η is the network training gain;
the error is output for the network.
Offset vector Z0The update derivation method of (2) is as described above. The offset matrix for step (k + l) is:
the connection weight matrix W of the input layer node and the hidden layer node and the daily water demand time sequence value vector theta of each unit of the hidden layer node can be obtained in the same way0(k + l) step (b):
and alternately carrying out forward output calculation and reverse weight modification in the network model until the output error of the network model reaches a set wide range E, namely training and fitting of the chaotic optimization BP neural network model reach preset specified requirements.
S8: chaotic optimization search
The invention uses chaotic variable optimization training and BP neural network, and adopts Logistic mapping, namely
Xn+1＝μXn(1-Xn)(n＝0，1，...N，0＜X0＜1) (29)
In the formula: n is the chaos iteration number: mu is a chaotic control parameter, when mu is 4.0, the system completely enters a chaotic state, and a chaotic variable X is adopted0Traverse within the range of (0, 1).
Setting that the BP neural network has p connection weights, and adopting the following formula to carry out global optimization on the network connection weight vector:
Xn+1＝μXn(1-Xn)(n＝0，1，...，N，0＜X0＜1) (30)
Xn＝2Xn-1(n＝0,1，...，N) (31)
zl+1＝(1-λ)zl(0＜λ＜1) (33)
in the formula: xn+I、X’n、
W*Are all p-dimensional: w*Generating by the formula (31) and finding out an approximate optimal value of the weight vector of the BP neural network through chaotic coarse search; lambda, zt∈ R, λ is a time-varying parameter zlThe attenuation factor of (4) aims to find the global optimal value of the weight vector of the BP neural network by chaotic fine search in the neighborhood of the approximate optimal value.
S9: chaotic parameter control
The invention adopts a parameter control method in the Chaos theory to control the predicted value of the 'cusp' of the daily water demand time data sequence (the data mutation point caused by factors such as outside climate, precipitation, holidays and the like) output by the Chaos optimization BP neural network model, and the prediction error is further reduced on the premise of meeting the prediction performance of the model.
Let SnTo sn+1The mapping of (a) is:
Sn+1＝sn+Δ (34)
when β is a main prescribed value, control is started:
when beta is less than or equal to a specified value, the control is started again:
di＝si-si-1i＝1，2，...，n (36)
when β is far from the predetermined value, the control is turned off, and the predicted value is input to the mountain according to equation (37).
In the formula, Sn+IN + l predicted values of the city daily water demand time data sequence; snFor the nth measured time data sequence value of the daily water demand of the city: Δ is a control parameter: Δ ═ sn-Sn-I+k|＝|β+k|；kFor outputting the time sequence value vector of the water demand of the urban opening: sn-1And obtaining the n-l historical time data sequence value of the daily water demand of the city.
S10: model prediction
Once the network training is finished, the time sequence value S of the daily water demand of the nth city is obtainednInputting the data into a chaos optimization BP neural network model, and outputting the data at the moment:
sn+1＝sn+k(37)
sn+lthe predicted value is obtained according to a certain function fitting mapping relation based on the rule summarized from the model input historical data, and is more accurate when the next actual daily water demand time sequence value accords with the rule possessed by the previous n-l model input historical data.
Fig. 3 and 4 are graphs showing the actual effect of the method of the present invention on the prediction of the training test data set in combination with the data sequence of the actual daily water demand time in a certain city.
The present invention has been described in terms of specific examples, which are provided to aid understanding of the invention and are not intended to be limiting. Any partial modification or replacement within the technical scope of the present disclosure by a person skilled in the art should be included in the scope of the present disclosure.
Claims (4)
1. A time sequence prediction method based on a chaos optimization neural network model is characterized in that city historical daily water demand time sequence data are obtained on line from a database and are subjected to data preprocessing, and chaos feature recognition is carried out at the same time; then, determining the structure of the chaotic optimization BP neural network by using the embedding dimension of the model input data reconstruction phase space, and simultaneously carrying out model training; in the model training process, the global optimal value of the BP neural network weight is found through chaotic optimization search; after the model training is finished, carrying out chaotic parameter control on the output time sequence predicted value by a parameter control method; and finally, forecasting the daily water demand time sequence of the city.
2. The chaos optimization neural network model-based time series prediction method according to claim 1, specifically comprising the steps of:
step 1: acquiring time series data of the original historical daily water demand of a certain city from an ORACLE database; dividing the time series data sets of all input models into a training input time series data set and a testing input time series data set;
step 2: carrying out data preprocessing on the acquired water demand time data sequence of a certain city day, and inputting the processed data into the model;
and step 3: after the preprocessed data is input into the model, performing chaotic feature recognition in the model, performing data phase space reconstruction, and calculating delay time tau and saturation embedding dimension m to determine the number of layers of the network model and the number of neurons in an input layer; and determining an input vector and a desired output vector;
and 4, step 4: calculating each neuron output of a network hidden layer and an output layer, and calculating an error function E; if the error function E reaches the threshold range, predicting an output value through a parameter control method, and if the error function E does not reach the threshold range, optimizing a weight threshold of the network model through chaotic search;
and 5: and judging whether the iteration of the network model reaches the maximum training times, if so, predicting an output value by a parameter control method, if not, continuously calculating the unit error and the error gradient of the hidden layer of the network, learning the weight of the model, and returning to the fourth step to continuously execute.
3. The chaotic optimization neural network model-based time series prediction method according to claim 2, wherein in step 1, the original time series data comprise historical time series characteristic data of daily water consumption of users in a corresponding area of a water plant in a certain city.
4. The method for predicting time series based on the chaos optimization neural network model according to claim 2, wherein in the step 2, the data preprocessing refers to processing of abnormal points, missing points and repeated points of data in the historical time series data of a certain market.
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