Probabilistic Prediction Method for Inflow Discharge of Reservoir Based on Mean Shift Clustering and WOA-QRLSTM

Abstract

The present invention discloses a probabilistic prediction method for reservoir inflow based on mean shift clustering and WOA-QRLSTM, including: 1) preprocessing the collected reservoir inflow and its influencing factors; 2) clustering the preprocessed data set using the mean shift clustering algorithm and dividing the data into a training set and a test set; 3) putting the training set data into a quantile regression long short-term neural network prediction model optimized by the whale optimization algorithm, namely WOA-QRLSTM, for training, and putting the test set data into the trained WOA-QRLSTM prediction model to obtain the predicted values of reservoir inflow at different quantiles; 4) calculating the probability density of future reservoir inflow from the predicted values of reservoir inflow at different quantiles through kernel density estimation. The present invention can improve the accuracy of reservoir inflow prediction, thereby providing effective reservoir inflow prediction information for reservoir operation and scheduling.

Description

Technical Field

[0001] The present invention belongs to the field of reservoir inflow prediction, and specifically relates to a probabilistic prediction method for reservoir inflow based on mean shift clustering and WOA-QRLSTM. Background Art

[0002] The prediction of reservoir inflow affects the operation and scheduling arrangement of the reservoir and the rational utilization of water resources, and is an important decision-making basis for reservoir operation and scheduling; various uncertain factors such as upstream inflow, rainfall, and climate change will affect the prediction result of reservoir inflow. How to improve the prediction accuracy and stability is an important research direction. Compared with the traditional point prediction method for reservoir inflow, the probabilistic prediction method for reservoir inflow can better reflect the uncertainty of reservoir inflow, thus providing a more scientific and reasonable basis for reservoir inflow prediction and optimal scheduling.

[0003] Traditional prediction models based on historical data, such as multiple linear regression models, artificial neural network models, support vector machine algorithms, etc., use a single prediction model to describe the relationship between reservoir inflows and between reservoir inflows and factors. Generally, the prediction effect is not ideal, the prediction accuracy is not high, and it is difficult to obtain a more accurate prediction result of reservoir inflow. Summary of the Invention

[0004] The present invention is to solve the above-mentioned deficiencies existing in the prior art, and proposes a probabilistic prediction method for reservoir inflow based on mean shift clustering and WOA-QRLSTM, in order to fully consider the influence of reservoir inflow influencing factors on the prediction accuracy of reservoir inflow, so as to more accurately and effectively predict the future reservoir inflow and provide effective reservoir inflow prediction information for reservoir operation and scheduling.

[0005] The present invention adopts the following technical solutions to achieve the above invention purpose:

[0006] The probabilistic prediction method for reservoir inflow based on mean shift clustering and WOA-QRLSTM prediction model of the present invention is characterized in that it is carried out according to the following steps:

[0007] Step 1: Collect reservoir inflow data and factor data affecting reservoir inflow and perform preprocessing to obtain the processed dataset Dataset = {[W(t), G m (t)]|t = 1, 2,..., T; m = 1, 2,..., M}, where W(t) represents the reservoir inflow on the t-th day; M represents the number of types of factors affecting reservoir inflow, and G m (t) represents the value of the m-th influencing factor on the t-th day; T represents the total number of days of collection;

[0008] Step 2: Divide the preprocessed dataset Dataset at time intervals of a certain time period D to obtain I groups of sample data {Datagruop i |i = 1, 2, ..., I}, and I satisfies [T / D], where Datagroup i represents the i-th group of sample data, and Datagroup i = [W′(i), G′ m (i)], G′ m (i) = (G m (d×(i - 1)+1), G m (d×(i - 1)+2), ..., G m (d×i)) T is the m-th influencing factor of the i-th group of sample data, G m (d×i) represents the m-th influencing factor on the d×i-th day, W′(i) = (W(d×(i - 1)+1), W(d×(i - 1)+2), ..., W(d×i)) T is the reservoir inflow of the i-th group of sample data, and W(d×i) represents the reservoir inflow on the d×i-th day, i = 1, 2, ..., I;

[0009] Step 3: Divide the I groups of sample data {Datagruop i |i = 1, 2, ..., I} into a training set Train = {Datagroup i |i = 1, 2, ..., p} and a test set Test = {Datagroup i |i = p + 1, p + 2, ..., I}, then the training set Train contains p groups of sample data, and the test set Test contains I - p groups of sample data;

[0010] Use mean shift clustering to cluster the training set Train and the test set Test respectively to obtain K classes of sample data, including: K classes of training set samples {Train k |k = 1, 2, ..., K} and K classes of test set samples {Test k |k = 1, 2, ..., K}; where, represents the k-th class of training set, A k is the set of serial numbers of the sample data belonging to the k-th class of training set Train k among the p groups of sample data in the training set Train, is the m-th influencing factor of the i-th group of sample data in the k-th class of training set, represents the m-th influencing factor on the d×i-th day, W k (i) = (W k(d×(i - 1)+1),W k (d×(i - 1)+2),...,W k (d×i)) T is the reservoir inflow of the i - th group of sample data in the k - th training set, W k (d×i) represents the reservoir inflow on the d×i - th day; is the k - th test set; B k is the set of serial numbers of the sample data belonging to the k - th test set Test in the I - p group of sample data of the test set Test k ;

[0011] Step 4: Use the k - class sample data to train and optimize the whale algorithm - optimized quantile regression long - short - term neural network WOA - QRLSTM prediction model;

[0012] Step 4.1: The sample data Dataset′ on the t - th day of the i - th group of sample data in the k - th training set Train k ={[W i ′(t),G′ i (t)]|t = 1,2,...,D; m = 1,2,...,M}, where W′ i,m (t) represents the reservoir inflow on the t - th day of the i - th group of sample data in the k - th training set Train, and G′ i (t) represents the value of the m - th influencing factor of the i - th group of sample data in the k - th training set Train on the t - th day; k Take the reservoir inflow W′ i,m (D) on the D - th day as the response variable of the i - th group of sample data; Take the values of the M reservoir inflow influencing factors on the D - th day {G′ k (D)|m = 1,2,...,M} and the remaining D - 1 sample data Dataset″ of the i - th group of sample data in the k - th training set Train

[0013] ={[W′ i (t),G′ i,m (t)]t = 1,2,...,D - 1; m = 1,2,...,M} as the explanatory variables of the i - th group of sample data together, so as to construct a data set containing M + D - 1 explanatory variables and one response variable, denoted as k represents the explanatory variables of the i - th group of sample data in the k - th training set Train; and i is the k - th training set Train i (t),G′ i,m (t)]t = 1,2,...,D - 1; m = 1,2,...,M} together as the explanatory variables of the i - th group of sample data, thus constructing a data set containing M + D - 1 explanatory variables and one response variable, denoted as represents the explanatory variables of the i - th group of sample data in the k - th training set Train k ; and is the k - th training set Traink The β-th explanatory variable of the i-th group of sample data in is the response variable of the i-th group of sample data constructed in the k-th training set Train k ;

[0014] Step 4.2: According to the process of Step 4.1, for the k-th test set Test k a data set including M + D - 1 explanatory variables and one response variable is also constructed, denoted as where, is the explanatory variable of the i-th group of sample data constructed in the k-th test set Test k ; is the response variable of the i-th group of sample data constructed in the k-th test set Test k ;

[0015] Step 4.3: Use Equation (1) to construct the WOA-QRLSTM prediction model, and based on the data set constructed in the k-th training set Train k train the WOA-QRLSTM prediction model, and continuously adjust the weights and biases of the WOA-QRLSTM prediction model until the maximum number of iterations is reached, so as to obtain the trained WOA-QRLSTM prediction model; In Equation (1),

[0016]

[0017] represents the z-th quantile, and z = 1, 2,..., Z, where Z is the number of quantiles; N represents the number of groups of sample data in the k-th training set Train ; U(τ k ) represents the set of weight parameter matrices at the z-th quantile; V(τ z ) represents the set of connection bias vectors at the z-th quantile; z ;

[0018] Step 4.4: Use the explanatory variable of the i-th group of sample data in the data set constructed in the k-th test set Test k input it into the optimal WOA-QRLSTM prediction model, so as to obtain the conditional quantiles of the data sets in the K-class test set samples {Test |k = 1, 2,..., K} at Z quantiles respectively where, k represents the conditional quantile of the i-th group of data in the k-th test set Test at the z-th quantile; ; k

[0019] ​​Step 5: Take the conditional quantiles at Z quantile points as the input of the Gaussian kernel function, and use Equation (2) to calculate the dataset k in the k-th test set Test the predicted result of the probability density of the reservoir inflow for any day e

[0020]

[0021] In Equation (2), h is the window width, and K(·) is the Gaussian kernel function.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] 1. The mean shift clustering algorithm adopted by the present invention is a parameter-free pattern matching algorithm, which finds several points with the maximum density of sample data, and then iteratively finds the maximum point value of the local density of sample data, and then clusters the sample data with the same density into the same class. The mean shift clustering algorithm is used to cluster the reservoir inflow and its influencing factors, and then a suitable method is selected for prediction according to each type of sample point, thereby improving the accuracy and stability of the prediction.

[0024] 2. The quantile regression long short-term neural network WOA-QRLSTM prediction method optimized by the whale algorithm of the present invention combines the standard quantile regression and the long short-term neural network, and combines kernel density estimation to achieve non-parametric probabilistic prediction of the reservoir inflow, which can better reflect the uncertainty of the reservoir inflow, more effectively quantify the uncertainty of the reservoir inflow, and make the prediction result more accurate. The whale algorithm is used to optimize the quantile regression long short-term neural network prediction model, and the parameters in the training model are optimized, so that the optimal combination can be found in the parameter space quickly, avoiding falling into the local optimum value during the training process, and improving the accuracy of the prediction model. Description of the Drawings

[0025] Figure 1 is the overall flow chart of the present invention. Detailed Embodiments

[0026] In this embodiment, a method for predicting the probability of reservoir inflow based on mean shift clustering and WOA-QRLSTM prediction model, as Figure 1 shown, is carried out according to the following steps:

[0027] Step 1: Collect the reservoir inflow data and the factor data affecting the reservoir inflow and perform preprocessing to obtain the processed dataset Dataset = {[W(t), G m(t)]|t = 1, 2, ..., T; m = 1, 2, ..., M}, where W(t) represents the reservoir inflow on the t-th day; M represents the number of factor types of the reservoir inflow, G m (t) represents the value of the m-th influencing factor on the t-th day; T represents the total number of days of collection;

[0028] Step 2: Divide the preprocessed dataset Dataset at a time interval of a certain time period D to obtain I groups of sample data {Datagruop i |i = 1, 2, ..., I}, and I satisfies [T / D], where Datagroup i represents the i-th group of sample data, and Datagroup i = [W′(i), G′ m (i)], G′ m (i) = (G m (d×(i - 1)+1), G m (d×(i - 1)+2), ..., G m (d×i)) T is the m-th influencing factor of the i-th group of sample data, G m (d×i) represents the m-th influencing factor on the d×i-th day, W′(i) = (W(d×(i - 1)+1), W(d×(i - 1)+2), ..., W(d×i)) T is the reservoir inflow of the i-th group of sample data, W(d×i) represents the reservoir inflow on the d×i-th day, i = 1, 2, ..., I;

[0029] Step 3: Divide the I groups of sample data {Datagruop i |i = 1, 2, ..., I} into a training set Train = {Datagroup i |i = 1, 2, ..., p} and a test set Test = {Datagroup i |i = p + 1, p + 2, ..., I}, then the training set Train contains p groups of sample data, and the test set Test contains I - p groups of sample data;

[0030] Use the mean shift clustering method to cluster the training set Train and the test set Test respectively. The steps are as follows:

[0031] (1) Taking the training set Train as an example, assume that the training set Train is divided into K classes, denoted as {Train k |k = 1, 2, ..., K}; Set a threshold η, and select an initial search region circle o in the sample point space of the training set Train, with its center as x o, with a radius of h; calculate the distance d from each sample point to the center of the circle. io , and mark all the sample points whose distance from the center of the circle x o is no greater than h as the set F = {x i |d io ≤ h}, and classify all the points in the set F into the same cluster L. At the same time, increase the access frequency of the sample points belonging to this class by 1;

[0032] (2) Calculate the vectors from the center of the circle o to each sample point in the set F = {x i |d io ≤ h}, and add up the above vectors to obtain the offset vector shift;

[0033] (3) Move the center of the circle xo along the direction of the offset vector shift, and the moving distance is the offset ||shift||;

[0034] (4) Repeat steps (2) and (3) until the offset is less than the set threshold η;

[0035] (5) Repeat steps (1) to (4) until all points are classified;

[0036] (6) Set the class with the highest access frequency of each point as the class to which the point belongs;

[0037] Use mean shift clustering to cluster the training set Train and the test set Test respectively, and obtain K types of sample data, including: K types of training set samples {Train k |k = 1, 2,..., K} and K types of test set samples {Test k |k = 1, 2,..., K}; where, represents the k-th type of training set, and A k is the set of serial numbers of the sample data belonging to the k-th type of training set Train k in the p groups of sample data of the training set Train, is the m-th influencing factor of the i-th group of sample data of the k-th type of training set, represents the m-th influencing factor on the d×i-th day, and W k (i) = (W k (d×(i - 1)+1), W k (d×(i - 1)+2),..., W k (d×i)) T is the reservoir inflow of the i-th group of sample data of the k-th type of training set, and W k (d×i) represents the reservoir inflow on the d×i-th day; is the k-th type of test set; B kThe set of serial numbers of the sample data belonging to the k-th test set Test in the I-p group sample data of the test set Test k ;

[0038] Step 4: Use the sample data of K classes to train the WOA-QRLSTM prediction model of the quantile regression long short-term neural network optimized by the whale algorithm;

[0039] Step 4.1: The i-th group of sample data on the t-th day in the k-th training set Train k The sample data Dataset′ i ={[W′ i (t),G′ i,m (t)]|t = 1,2,...,D; m = 1,2,...,M}, where W′ i (t) represents the reservoir inflow of the i-th group of sample data on the t-th day in the k-th training set Train k , and G′ i,m (t) represents the value of the m-th influencing factor of the i-th group of sample data on the t-th day in the k-th training set Train k ;

[0040] Taking the reservoir inflow W′ i (D) on the D-th day as the response variable of the i-th group of sample data; taking the values of M reservoir inflow influencing factors on the D-th day {G′ i ′ ,m (D)|m = 1,2,...,M} and the remaining D - 1 sample data Dataset″ k ={[W′ i (t),G′ i (t)]|t = 1,2,...,D - 1; m = 1,2,...,M} of the i-th group of sample data in the k-th training set Train as the explanatory variables of the i-th group of sample data together, thereby constructing a data set containing M + D - 1 explanatory variables and one response variable, denoted as i,m represents the explanatory variable of the i-th group of sample data in the k-th training set Train ; and k is the β-th explanatory variable of the i-th group of sample data in the k-th training set Train is the k-th training set Train k ; is the k-th training set Train k ;

[0041] Step 4.2: According to the process of Step 4.1, for the k-th test set Test kA dataset including M + D - 1 explanatory variables and one response variable is also constructed, denoted as wherein, is the explanatory variable of the i-th group of sample data constructed in the k-th test set Test k , and is the response variable of the i-th group of sample data constructed in the k-th test set Test k ;

[0042] Step 4.3: Construct a WOA-QRLSTM prediction model using Equation (1), and based on the dataset k constructed in the k-th training set Train , train the WOA-QRLSTM prediction model, and continuously adjust the weights and biases of the WOA-QRLSTM prediction model until the maximum number of iterations is reached, obtaining a trained WOA-QRLSTM prediction model;

[0043]

[0044] In Equation (1), represents the z-th quantile, where z = 1, 2,..., Z, and Z is the number of quantiles; N represents the number of groups of sample data in the k-th training set Train k ; U(τ z ) represents the set of weight parameter matrices at the z-th quantile, and where are the sets of weight parameter matrices of the forget gate f, input gate z , new memory state c, and output gate o of WOA-QRLSTM at the quantile τ respectively, and U S (τ z ) is the connection weight matrix between the hidden layer and the output layer; V(τ z ) represents the set of connection bias vectors at the z-th quantile, and where are the sets of bias vectors of the forget gate f, input gate z , new memory state c, and output gate o of WOA-QRLSTM at the quantile τ respectively, and V S (τ z ) is the connection bias vector between the hidden layer and the output layer;

[0045] The specific steps are as follows:

[0046] (1) Set the maximum number of iterations of the WOA-QRLSTM algorithm, determine the topological structure of the WOA-QRLSTM neural network, and initialize the whale population, that is, initialize the weights and biases of the WOA-QRLSTM neural network;

[0047] (2) Use Equation (1) as the fitness function of the whale optimization algorithm, calculate the fitness value of each whale individual, sort the whale individuals according to the fitness value, and the whale with the smallest fitness is the best whale individual in each calculation, marked as X * , which has the best weights and biases;

[0048] (3) Update the positions of whale individuals using the shrinking encircling and spiral rising strategies; to simulate this behavior, a random number p is introduced and p ∈ [0, 1]. If p < 0.5, the shrinking encircling movement strategy is selected; if p ≥ 0.5, the spiral movement strategy is selected; when performing the encircling movement, the vector is used to determine the way to update the position of the best whale individual, and is a random number greater than 1 or less than -1. If , the best whale individual is selected to update the position of the whale individual, a random whale individual is selected to update the position of the whale individual;

[0049] (4) Repeat steps (2) and (3) until the WOA-QRLSTM reaches the maximum number of iterations, obtain the optimal weights and biases of the WOA-QRLSTM neural network, and output the trained optimal WOA-QRLSTM prediction model;

[0050] Step 4.4: Use the explanatory variables of the i-th group of sample data in the dataset constructed in the k-th type of test set Test k and input them into the optimal WOA-QRLSTM prediction model, so as to obtain the conditional quantiles of the datasets in the K-type test set samples {Test |k = 1, 2,..., K} at Z quantiles where, k represents the conditional quantile of the i-th group of data in the k-th type of test set Test at the z-th quantile; represents the conditional quantile of the i-th group of data in the k-th type of test set Test k at the z-th quantile;

[0051] Step 5: Use the conditional quantiles at Z quantiles as the input of the Gaussian kernel function, and use Equation (2) to calculate the reservoir inflow probability density prediction result for any day e in the dataset in the k-th type of test set Test k where, h is the window width, and K(·) is the Gaussian kernel function.

[0052]

[0053] In Equation (2), h is the window width, and K(·) is the Gaussian kernel function.

Claims

1. A probability prediction method for reservoir inflow based on mean shift clustering and WOA-QRLSTM prediction model, characterized by the following steps: Step 1: Collect the reservoir inflow data and the factor data affecting the reservoir inflow, and perform preprocessing to obtain the processed dataset Dataset = {[W(t), G m (t)]|t = 1, 2,..., T; m = 1, 2,..., M}, where W(t) represents the reservoir inflow on the t-th day; M represents the number of types of factors affecting the reservoir inflow, G m (t) represents the value of the m-th influencing factor on the t-th day; T represents the total number of days of collection; Step 2: Divide the preprocessed dataset Dataset at time intervals of a certain time period D to obtain I groups of sample data {Datagruop i |i = 1, 2,..., I}, and I satisfies [T / D], where Datagroup i represents the i-th group of sample data, and Datagroup i = [W′(i), G′ m (i)], G′ m (i) = (G m (d×(i - 1)+1), G m (d×(i - 1)+2),..., G m (d×i)) T is the m-th influencing factor of the i-th group of sample data, G m (d×i) represents the m-th influencing factor on the d×i-th day, W′(i) = (W(d×(i - 1)+1), W(d×(i - 1)+2),..., W(d×i)) T is the reservoir inflow of the i-th group of sample data, W(d×i) represents the reservoir inflow on the d×i-th day, i = 1, 2,..., I; Step 3: Divide the set of Group I sample data {Datagruop i | i = 1, 2, ..., I} into a training set Train = {Datagroup i | i = 1, 2, ..., p} and a test set Test = {Datagroup i | i = p + 1, p + 2, ..., I}. Then, the training set Train contains p sets of sample data, and the test set Test contains I - p sets of sample data; Use mean shift clustering to cluster the training set Train and the test set Test respectively to obtain K types of sample data, including: K types of training set samples {Train k | k = 1, 2, ..., K} and K types of test set samples {Test k | k = 1, 2, ..., K}; where, represents the k-th type of training set, A k is the set of serial numbers of the sample data belonging to the k-th type of training set Train k among the p groups of sample data of the training set Train, is the m-th influencing factor of the i-th group of sample data of the k-th type of training set, represents the m-th influencing factor on the d×i-th day, W k (i) = (W k (d×(i - 1)+1), W k (d×(i - 1)+2), ..., W k (d×i)) T is the reservoir inflow of the i-th group of sample data of the k-th type of training set, and W k (d×i) represents the reservoir inflow on the d×i-th day; is the k-th type of test set; B k is the set of serial numbers of the sample data belonging to the k-th type of test set Test k among the I - p groups of sample data of the test set Test; Step 4: Use K-class sample data to train and optimize the quantile regression long short-term neural network WOA-QRLSTM prediction model optimized by the whale optimization algorithm; Step 4.1, the sample data of the t-th day of the i-th group of sample data in the k-th training set Train k is Dataset′ i ={[W′ i (t), G′ i,m (t)]|t = 1, 2, ..., D; m = 1, 2, ..., M}, where W′ i (t) represents the reservoir inflow of the t-th day of the i-th group of sample data in the k-th training set Train k , and G′ i,m (t) represents the value of the m-th influencing factor of the i-th group of sample data in the k-th training set Train k on the t-th day; Use the reservoir inflow rate \(W'\) on the \(D\)th day i (D) as the response variable of the \(i\)th group of sample data; use the values of \(M\) reservoir inflow rate influencing factors on the \(D\)th day \(\{G' i,m (D)|m = 1, 2, ..., M\}\) and the remaining \(D - 1\) sample data Dataset″ k in the \(k\)th training set Train i =\(\{[W' i (t), G' i,m (t)]|t = 1, 2, ..., D - 1; m = 1, 2, ..., M\}\) together as the explanatory variables of the \(i\)th group of sample data, thereby constructing a dataset containing \(M + D - 1\) explanatory variables and one response variable, denoted as denotes the explanatory variables of the \(i\)th group of sample data in the \(k\)th training set Train k ; and is the \(\beta\)th explanatory variable of the \(i\)th group of sample data in the \(k\)th training set Train k , and is the response variable of the \(i\)th group of sample data constructed in the \(k\)th training set Train k ;​ Step 4.2: Follow the process of Step 4.1 to perform the same operations on the k-th type of test set Test k to also construct a data set including M + D - 1 explanatory variables and one response variable, denoted as where is the explanatory variable of the i-th group of sample data constructed in the k-th type of test set Test k , and is the response variable of the i-th group of sample data constructed in the k-th type of test set Test k . Step 4.3: Construct a WOA-QRLSTM prediction model using Equation (1), and based on the dataset constructed in the $k$-th training set Train k in the constructed dataset Train the WOA-QRLSTM prediction model, and continuously adjust the weights and biases of the WOA-QRLSTM prediction model until the maximum number of iterations is reached, so as to obtain a trained WOA-QRLSTM prediction model; In formula (1), represents the z-th quantile, where z = 1, 2, …, Z, and Z is the number of quantiles; N represents the number of groups of sample data in the k-th training set Train k ; U(τ z ) represents the set of weight parameter matrices at the z-th quantile; V(τ z ) represents the set of connection bias vectors at the z-th quantile; Step 4.4: Use the dataset constructed in the k-th test set Test k and the explanatory variables of the i-th group of sample data in to input into the optimal WOA-QRLSTM prediction model, so as to obtain the conditional quantiles of the datasets in the K-class test set samples {Test |k = 1, 2,..., K} at Z quantiles, where k represents the conditional quantile of the i-th group of data in the k-th test set Test at the z-th quantile; denotes the conditional quantile of the i-th group of data in the k-th test set Test k at the z-th quantile; Step 5: Take the conditional quantiles at Z quantile points as the input of the Gaussian kernel function, and use Equation (2) to calculate the dataset in the k-th test set Test k and the predicted result of the probability density of the reservoir inflow for any day e in ​ In formula (2), h is the window width, and K(·) is the Gaussian kernel function.

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