METHOD FOR OPTIMALLY SELECTING FLOOD-CONTROL OPERATION SCHEME BASED ON TEMPORAL CONVOLUTIONAL NETWORK

Abstract

A method for optimally selecting a flood-control operation scheme based on a temporal convolutional network. The method includes evaluating the flood-control operation schemes in a group of reservoirs; a time-sequence evaluating indicator matrix combining the comprehensive evaluation indicators and the time sequence, which serves as an input of the temporal convolutional network, is constructed to calculate comprehensive scores for training samples of the flood-control operation schemes based on a fuzzy set theory and an improved entropy weight method; a structure of the temporal convolutional network is determined; the temporal convolutional network is trained by adopting a loss function combining a mean square error and a Nash efficiency coefficient; and the time-sequence evaluating indicator matrix for the flood-control operation schemes is input into the temporal convolutional network to obtain the comprehensive evaluation values for the schemes, and an optimal comprehensive evaluation value is taken as an optimal flood-control operation scheme.

Claims

1. A method for optimally selecting a flood-control operation scheme based on a temporal convolutional network, wherein the method comprises the following steps: Step 1, establishing an evaluating indicator system for flood-control operation schemes of a group of reservoirs; Step 2, constructing a time-sequence evaluating indicator matrix for the flood-control operation schemes, wherein the matrix serves as an input of the temporal convolutional network, calculating comprehensive scores for training samples of the flood-control operation schemes based on a fuzzy set theory and an improved entropy weight method: establishing a fuzzy decision matrix, determining relative membership degrees between quantitative evaluation indicators and qualitative evaluation indicators to obtain a matrix of the relative membership degrees, thereby constructing the time-sequence evaluating indicator matrix for the flood-control operation schemes; taking the matrix as the input of the temporal convolutional network, and improving a calculation formula of entropy weights with respect to different types of the evaluation indicators; calculating the comprehensive evaluation values for the flood-control operation schemes based on the fuzzy set theory and the improved entropy weight method, and taking the comprehensive evaluation values used to eventually determine pros and cons of the schemes as outputs, wherein the comprehensive evaluation values are obtained by a fuzzy comprehensive evaluation method; expanding the training samples of the temporal convolutional network by adopting a supervised interpolation-based multi-sample data enhancement method SMOTE to generate new samples for small sample types; Step 3, determining a structure of the temporal convolutional network, including an inputting layer, a causal dilated convolution, an activation function, a residual connection, a fully connected layer and an outputting layer; Step 4, training the temporal convolutional network by adopting a loss function that combines a mean square error and a Nash efficiency coefficient; and Step 5, inputting the time-sequence evaluating indicator matrix for the flood-control operation schemes into the temporal convolutional network to obtain the comprehensive evaluation values for the schemes, and taking an optimal comprehensive evaluation value as an optimal flood-control operation scheme for the group of reservoirs.

2. The method for optimally selecting the flood-control operation scheme based on the temporal convolutional network according to claim 1, wherein S2 specifically comprises the following steps: Step 2.1, setting weights of the evaluation indicators of reservoirs, flood storage and detention areas, and hydrology stations; Step 2.1.1, normalizing the evaluating indicator matrix X=(x.sub.ij).sub.l×q to obtain a relative superiority-membership-degree matrix R=(r.sub.ij).sub.l×q, r.sub.ij∈[0,1]; where l represents evaluation indicators, q represents evaluation targets, i=1,2, . . . , q; j=1,2, . . . , l; and x.sub.ij is an eigenvalue of an indicator j of a target i; Step 2.1.2, calculating entropy weights ω.sub.hj of the evaluation indicators;
ω.sub.hj=H.sub.sω.sub.hsj+(1−H.sub.s)ω.sub.hkj where both ω.sub.hsj and ω.sub.hkj are weight coefficients of entropy value separation magnitudes, H.sub.s is a same part, starting from a first digit after a decimal point, of entropy values in an entropy value vector, r.sub.ij is a relative superiority-membership-degree value of the indicator j of the target i, H.sub.j is an entropy value corresponding to r.sub.ij, and e.sub.ij is a relative importance degree of r.sub.ij, ${\omega }_{\mathrm{hsj}}=\frac{\left(1-H_s\right)}{{.Math.}_{k=1,H_k\ne 1}^m\left(1-H_s\right)},{\omega }_{\mathrm{hkj}}=\frac{\left(1-H_j\right)}{{.Math.}_{k=1,H_k\ne 1}^m\left(1-H_j\right)},H_j=\frac{1}{\ln n}{.Math.}_{i=1}^n{e}_{\mathrm{ij}}\ln e_{\mathrm{ij}},e_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{{.Math.}_{i=1}^n{r}_{\mathrm{ij}}},j=1,2,.Math.,m;$ Step 2.2, setting weights of risk-and-effectiveness evaluation indicators; Step 2.2.1, constructing a risk-effectiveness negotiation decision model for the flood-control operation; assuming that the comprehensive risk-and-effectiveness evaluation indicators have a number of w+p, which comprises w risk evaluation indicators, and p effectiveness evaluation indicators, forming a risk set DM1 and an effectiveness set DM2 through systematic evaluation indicators, and defining u1(x) and u2(x) as utility gain functions of the risk and the effectiveness, the utility gain functions are as follows: $u_{1j}\left(x\right)=\underset{i=1}{\overset{w}{.Math.}}{\omega }_i\times r_{\mathrm{ji}},u_{2j}\left(x\right)=\underset{i=1}{\overset{p}{.Math.}}{\omega }_i\times r_{\mathrm{ji}}$ where ω.sub.i is a weight of a risk or effectiveness evaluation indicator, and r.sub.ji is a relative superiority-membership-degree value of a target i of an evaluation indicator j; wherein a problem of multi-attribute decision optimization is thus transformed into a problem of nonlinear programming; for the utility gain functions, they are capable of forming a two-dimensional curved surface in a space; for risk-and-effectiveness constraint conditions, they are capable of forming a plane in the space; it is known according to the utility gain function and the risk-and-effectiveness constraint conditions that the target is to acquire a maximum value for the utility gain functions among the plane and curved surface nodes, which is expressed as:
max{F(x)=[u.sub.1(x), u.sub.2(x)]} Step 2.2.2, calculating the risk-and-effectiveness weights; where a weight of a risk indicator is ${\omega }_e=\frac{{.Math.}_{k=1}^l{H}_k+1}{{.Math.}_{m=1}^l\left({.Math.}_{k=1}^{l}1-2H_k\right)},$ and a weight of an effectiveness indicator is ${\omega }_e^{\prime }=\frac{{.Math.}_{k=1}^{l}1-2H_k}{{.Math.}_{n=1}^l\left({.Math.}_{k=1}^l{H}_k+1\right)}$ where i=1,2, . . . , l, Σ.sub.i=1.sup.lω=1, and H.sub.k is an entropy value for an evaluation indicator j; Step 2.3, performing a calculation of fuzzy comprehensive evaluation; wherein a model for the fuzzy comprehensive evaluation is b.sub.j=Σ.sub.i=1.sup.mω(i) r.sub.ij, the schemes are sorted according to a principle of maximum membership degree, an optimal scheme is selected from the flood-control operation scheme, that is, B.sub.opt=max{b.sub.j}; and the training samples for the temporal convolutional network are expressed as {Y, b.sub.j|Y=(x.sub.ab).sub.t×12}; wherein Y is the time-sequence evaluating indicator matrix for the flood-control operation schemes, and a, b are sequence numbers of time and evaluation indicators respectively; and Step 2.4, defining an eigenspace, mapping each sample to a certain point in the eigenspace, and determining a sampling ratio N according to a sample imbalance ratio; finding, for each sample (x, y) in a small sample type, K nearest neighbor samples according to an Euclidean distance, and randomly selecting a sample point from the K nearest neighbor samples, randomly selecting, assuming that the selected neighbor point is (x.sub.n, y.sub.n), a point from a line segment between the sample point and the nearest neighbor sample point in the eigenspace as a new sample point, which satisfies a following formula:
(x.sub.new, y.sub.new)=(x, y)+rand(0−1)*((x.sub.n−x), (y.sub.n−y)), and repeating the above steps until numbers of large and small samples are balanced.

3. The method for optimally selecting the flood-control operation scheme based on the temporal convolutional network according to claim 1, wherein Step 3 comprises the following steps: setting a convolution kernel size of the causal convolution to be 3; setting a convolution kernel size of the dilated convolution to be 3 as well, where dilation factors are 1, 2, and 4 sequentially; and adopting a parameterized ReLU=max{ax, x} as an activation function, where 0<a<1; wherein two dilated causal convolution layers and two activation functions are present on a residual line respectively, 6 residual blocks are set to be stacked on the residual line, the dilation factors of the residual blocks from left to right are from 20 to 25; and an output of a last residual block is connected to a fully connected layer with a sigmoid activation function.

4. The method for optimally selecting the flood-control operation scheme based on the temporal convolutional network according to claim 1, wherein Step 4 further comprises the following steps: constructing a loss function MSE′ that combines the mean square error and the Nash efficiency coefficient, and training, by adopting MSE′, the temporal convolutional network, which is expressed as: ${\mathrm{MSE}}^{\prime }\left(y,y^{\prime }\right)=\frac{{.Math.}_{i=1}^n{\alpha \left(y_i-y_i^{\prime }\right)}^2}{n},\alpha =1-\frac{{.Math.}_{t=1}^T{\left(y_i-y_i^{\prime }\right)}^2}{{.Math.}_{t=1}^T{\left(y_i-\stackrel{\_}{y_i}\right)}^2}$ where y.sub.i is an output value for a sample i, y.sub.i′ is a target value for the sample i, y.sub.l is an average value of output values for the sample i, α is a Nash correction parameter, and T is a time; and updating values of the weights and the parameters by a gradient descent method according to an obtained error to minimize an output error, and ending, when a number of training iterations satisfies requirements and the error is less than or equal to an expected value, the training.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0038] FIG. 1 illustrates a flow chart of a method according to an embodiment of the present disclosure.

[0039] FIG. 2 illustrates a preferred model diagram of a flood-control operation scheme according to an embodiment of the present disclosure.

[0040] FIG. 3 illustrates a structural diagram of a temporal convolutional network according to an embodiment of the present disclosure.

[0041] FIG. 4 illustrates a diagram of a process for training the temporal convolutional network according to an embodiment of the present disclosure.

DETAILED DESCRIP ON OF THE EMBODIMENTS

[0042] The evaluation indicators of the flood-control operation scheme in the reservoir is a set of a series of measurement dimensions that measure the pros and cons of the operation schemes from various target levels and various evaluation aspects, such as reservoirs, flood storages and detention areas, and hydrology stations. The scheme evaluation is essentially to use a certain mathematical model to integrate the indicator values into a comprehensive evaluation value, and to sort the schemes and select the optimal scheme according to the comprehensive evaluation value.

[0043] The facts found in the researches are that the existing researches on the evaluation of the flood-control operation schemes of reservoirs mainly focus on traditional evaluation methods and the improvements thereof, in which there is also great subjective arbitrariness in the selection of indicators, the impact of indicator correlations on the results of the comprehensive evaluation of the scheme is not considered, and experts are required to assign the weights to different indicators, which will not change with the flood control situation. Moreover, the existing researches are mostly directed to a single reservoir without considering the scenario of the flood-control operation for a group of reservoirs.

[0044] In order to optimally select the flood-control operation scheme more accurately, the problem of comprehensively evaluating the schemes seems to be more complicated, since it is necessary to select a second-level evaluation indicator for each first-level evaluation indicator for the reservoir group system, and the like. The eventually constructed indicator system is usually extremely huge, which increases the complexity of the modelling for selecting the optimal scheme. Therefore, for the optimal selection problem of the flood-control operation scheme for a large-scale group of reservoirs, the temporal convolutional network is used for optimally selecting the scheme in the present disclosure, which can greatly reduce the number of parameters in the complex model and better dig out the relationships between the evaluation indicators.

[0045] The present disclosure will be further described in detail below with reference to the accompanying drawings.

[0046] As illustrated in FIG. 1 and FIG. 2, provided is a method for optimally selecting a. flood-control operation scheme based on a temporal convolutional network according to the present disclosure. The method includes the following steps.

[0047] In Step 1, an evaluating indicator system for the flood-control operation schemes in a group of reservoirs is established.

[0048] The following principles should be complied to when establishing the evaluating indicator system for the flood-control operation: (1) objectivity, (2) independence, (3) systematicness, (4) operability, and (5) hierarchy. The number of evaluation indicators is less in the traditional method, and the correlation between the evaluation indicators is not considered. According to the above five principles and the disadvantages of the traditional methods, reservoirs, flood storage and detention areas, and hydrology stations are selected to serve as evaluation targets to establish the evaluating indicator system for the flood-control operation schemes, in comprehensive consideration of the risk and effectiveness of the flood-control operation schemes.

[0049] Step 1 specifically includes the following sub-steps.

[0050] In Step 1.1, the evaluating indicator system is E.sub.i={e.sub.i1, e.sub.i2, e.sub.i3, . . . , e.sub.ij}, e.sub.ij (i=1,2, . . . , n; j=1,2, . . . , m) is the value for the j-th evaluation indicator of the i-th scheme.

[0051] In Step 1.2, the evaluating indicator system for the flood-control operation for the group of the reservoirs is as follows.

TABLE-US-00001 Evaluation Indicator targets Evaluation indicators significances Evaluation The maximum flood Effectiveness-oriented indicators in storage capacity the reservoirs of each reservoir Power generation Effectiveness-oriented effectiveness The maximum discharging Cost-oriented flow of the reservoirs Risk of exceeding Cost-oriented the water level limit Evaluation Guaranteed water level Cost-oriented indicators in the Peak flow Cost-oriented hydrology stations Time of exceeding the Cost-oriented flow threshold Risk of exceeding Cost-oriented the flow limit Evaluation Submerged duration Cost-oriented indicators in the Submerged range Cost-oriented flood storages and Economic loss Cost-oriented detention areas Disaster-affected Cost-oriented population

[0052] In Step 2, a time-sequence evaluating indicator matrix for the flood-control operation schemes is constructed, which serves as an input of the temporal convolutional network to calculate comprehensive scores for training samples of the flood-control operation schemes based on a fuzzy set theory and an improved entropy weight method.

[0053] The temporal convolutional network uses the convolutional network to solve the problem of time sequence data. For the optimal selection of the flood-control operation scheme for the reservoir, its main task is to enable the trained temporal convolutional network to make self-decision under time variation. Training samples of the network are generated based on the fuzzy set theory. The calculation formula of entropy weights is improved with respect to different evaluation indicators. The improved entropy weight method is used to set the weights of the evaluation indicators, so as to construct a time-sequence evaluating indicator matrix for the flood-control operation schemes, which serves as an input of the temporal convolutional network. The comprehensive evaluation values finally used to evaluate the pros and cons of the schemes serve as outputs. The comprehensive evaluation values are obtained by the fuzzy comprehensive evaluation method; Considering that the number of schemes generated in actual flood-control operation is generally finite, a supervised interpolation-based multi-sample data enhancement method (SMOTE) is used to expand the training samples of the temporal convolutional network to satisfy the requirements for the training precision of the neural network.

[0054] Step 2 specifically includes the following sub-steps.

[0055] In Step 2.1, a fuzzy decision matrix O=(o.sub.ij).sub.m×n is established, where O represents a matrix of target eigenvalues for rn targets and n decision schemes, where i =1,2, . . . , n; j=1,2, . . . , m; o.sub.ij is an eigenvalue for the target j in the scheme i. For the fuzzy comprehensive evaluation method, the objective is to determine the membership degree of each scheme to the fuzzy concept of “superiority”, and the scheme with the largest membership degree is the optimal scheme. Then, the relative membership degrees of the quantitative and qualitative evaluation indicators are determined. In order to eliminate the incommensurability caused by different dimensions and dimensional units, the absolute dimension of the evaluation indicators should be converted into the relative dimension, which is the relative membership degree. Generally, the relative membership of each indicator is a decimal within the interval of [0,1].

[0056] In Step 2.1.1, quantitative targets are standardized. The evaluation indicators involve two types of indicators, that is, the effectiveness-oriented (the greater the better) and the cost-oriented (the less the better). Different linear scale transformation methods are used corresponding to different types of evaluation indicators. The data indicators are normalized and standardized as follows:

[0057] for the effectiveness-oriented indicators:

[00005]$\begin{array}{cc}{r}_{\mathrm{ij}}=\frac{o_{\mathrm{ij}}-o_{\mathrm{jmin}}}{o_{\mathrm{jmax}}-o_{\mathrm{jmin}}}& \begin{array}{cc}i\in \left[1,n\right]& j\in \left[1,m\right],\end{array}\end{array}$

and

[0058] for the cost-oriented indicators:

[00006]$\begin{array}{ccc}{r}_{\mathrm{ij}}=\frac{o_{\mathrm{jmin}}-o_{\mathrm{ij}}}{o_{\mathrm{jmax}}-o_{\mathrm{jmin}}}& i\in \left[1,n\right]& j\in \left[1,m\right],\end{array}$

where o.sub.ij is a value for the j-th evaluation indicator in the i-th scheme, and o.sub.jmax and o.sub.jmin are the maximum value and the minimum value in the values for the j-th evaluation indicators in each scheme, respectively.

[0059] In Step 2.1.2, a bipolar ratio method is adopted to convert qualitative indicators into quantitative indicators. After the evaluation indicators are normalized and standardized, a relative membership-degree matrix R=(r.sub.ij).sub.m×n of n schemes to m evaluation indicators is therewith determined, where r.sub.ij(i=1,2, . . . , m; j=1,2, . . . , n) is the relative superiority membership degree for the j-th evaluation indicator in the i-th scheme.

[0060] In Step 2.2, for different evaluation indicators, the improved entropy weight method is respectively adopted to determine the weight set, and the weight vector of the evaluation indicators is W=(ω(1), 107 (2), . . . , ω(n)), Σ.sub.i=1.sup.nω(i)=1 (i=1˜n).

[0061] In Step 2.2.1, the weights of evaluation indicators in reservoirs, flood storage and detention areas, and hydrology stations are set.

[0062] The evaluating indicator matrix X=(x.sub.ij).sub.l×q is constructed, where l denotes the evaluation indicators, q denotes the evaluation targets, and i=1,2, . . . , q; j=1,2, . . . , l; x.sub.ij is an eigenvalue of the indicator j of the target i.

[0063] After normalization, the relative superiority-membership-degree matrix R=(r.sub.ij).sub.l×q∈[0,1] is obtained.

[0064] The entropy values for the evaluation indicators are calculated,

[00007]$H_j=\frac{1}{\ln n}{.Math.}_{i=1}^n{e}_{\mathrm{ij}}\ln e_{\mathrm{ij}},$

where

[00008]$e_{\mathrm{ij}}=\frac{r_{\mathrm{ij}}}{{.Math.}_{i=1}^n{r}_{\mathrm{ij}}},$

j=1,2, . . . , m.

[0065] The entropy weights for the evaluation indicators are calculated, ω.sub.hj=H.sub.sω.sub.hsj+(1−H.sub.s)ω.sub.hkj,

where

[00009]${\omega }_{\mathrm{hsj}}=\frac{\left(1-H_s\right)}{{.Math.}_{k=1,H_k\ne 1}^m\left(1-H_s\right)},{\omega }_{\mathrm{hkj}}=\frac{\left(1-H_j\right)}{{.Math.}_{k=1,H_k\ne 1}^m\left(1-H_j\right)}.$

[0066] It should be noted that H.sub.s is the same part, starting from a first digit after a decimal point, of the entropy values in an entropy value vector. Both of ω.sub.hsj, ω.sub.hkj are weight coefficients of entropy value separation magnitudes. r.sub.ij is a relative superiority-membership-degree value of the indicator j of the target i. e.sub.ij is a relative importance degree of r.sub.ij.

[0067] In Step 2.2.2, the weights of risk-and-effectiveness evaluation indicators are set.

[0068] A risk-effectiveness negotiation decision model for the flood-control operation is constructed. It is assumed that the comprehensive risk-and-effectiveness evaluation indicators have a number of w+p, which include w risk evaluation indicators and p effectiveness evaluation indicators. A risk set DM1 and an effectiveness set DM2 are formed through systematic evaluation indicators, and u1(x) and u2(x) are defined as utility gain functions of risk and effectiveness:

[00010]$u_{1j}\left(x\right)=\underset{i=1}{\overset{w}{.Math.}}{\omega }_i\times r_{\mathrm{ji}},u_{2j}\left(x\right)=\underset{i=1}{\overset{p}{.Math.}}{\omega }_i\times r_{\mathrm{ji}}$

where ω.sub.i is a weight of the risk or effectiveness evaluation indicator, and r.sub.ji is a relative superiority-membership-delzree value of an evaluation indicators j of a target i.

[0069] Thus, a problem of multi-attribute decision-making optimization is transformed into a problem of nonlinear programming. For the utility gain functions, they are capable of forming a two-dimensional curved surface in a space. For risk-and-effectiveness constraint conditions, they are capable of forming a plane in the space. It can be known according to the utility gain functions and the risk-and-effectiveness constraint conditions that the target is to acquire a maximum value for the utility gain functions among the plane and curved surface nodes, which can be expressed as:

max{F(x)=[u.sub.1(x), u.sub.2(x)]}.

[0070] A risk weight of

[00011]${\omega }_e=\frac{{.Math.}_{k=1}^l{H}_k+1}{{.Math.}_{m=1}^l\left({.Math.}_{k=1}^{l}1-2H_k\right)}$

and an effectiveness weight of

[00012]${\omega }_e^{\prime }=\frac{{.Math.}_{k=1}^{l}1-2H_k}{{.Math.}_{n=1}^l\left({.Math.}_{k=1}^l{H}_k+1\right)}$

are calculated, where i=1,2, . . . , l, Σ.sub.i=1.sup.lω=1, and H.sub.k is an entropy value for the evaluation indicator j.

[0071] In Step 2,3, a fuzzy comprehensive evaluation is calculated.

[0072] A model for fuzzy comprehensive evaluation is b.sub.j=Σ.sub.i=1.sup.mω(i) r.sub.ij. The schemes are sorted according to a principle of maximum membership degree, and an optimal scheme, that is, B.sub.opt=max{b.sub.j}, is selected from the flood-control operation schemes.

[0073] The training samples for temporal convolutional network are defined as {Y, b.sub.j|Y=(x.sub.ab).sub.t×12}, where Y is the time-sequence evaluating indicator matrix for the flood-control operation schemes, and a, h are sequence numbers of time and evaluation indicators respectively.

[0074] In Step 2.4, the training samples of the temporal convolutional network are expanded by adopting a supervised interpolation-based multi-sample data enhancement method MOTE) to generate new samples in the small sample type.

[0075] In Step 2.4.1, an eigenspace is defined. Each sample is mapped to a certain point in the eigenspace, and a sampling ratio N is determined according to a sample imbalance ratio,

[0076] In Step 2.4.2, K nearest neighbor samples are found according to an Euclidean distance for each sample (x, y) in the small sample type, and a sample point is randomly selected from the K nearest neighbor samples. It is assumed that the selected nearest neighbor point is (x.sub.n, y.sub.n), a point from a line segment between the sample point and the nearest neighbor sample point in the elgenspace is randomly selected as a new sample point, which satisfies the following formula:

(x.sub.new, y.sub.new)=(x, y)+rand(0−1)*((x.sub.n−x), (y.sub.n−y)).

[0077] In Step 2.4,3, the above steps are repeated until the numbers of large and small samples are balanced.

[0078] In Step 3, a structure of the temporal convolutional network is determined. The structure includes an inputting layer, a causal dilated convolution, an activation function, a residual connection, a fully connected layer and an outputting layer.

[0079] With reference to FIG. 3. Step 3 specifically includes the following steps.

[0080] In Step 3.1, the causal convolution.

[0081] The causal convolution is used in the temporal convolutional network to process the input data so as to calculate and extract the feature information of the underlying data. At any time t, a single convolution operation with a convolution kernel size of 3 is performed, where a filter is F=(f.sub.1, f.sub.2, . . . , f.sub.k), and a sequence is X=(x.sub.1, x.sub.2, . . . , x.sub.t). The causal convolution process at the position of x.sub.t can be expressed as (F*X) (x .sub.t)=Σ.sub.k−1.sup.Kf.sub.kx.sub.t−k+K.

[0082] In Step 3.2, dilated convolutions.

[0083] Dilated convolutions in different sizes are set. The dilation factor d represents the distance between the two elements of the convolution kernel. Firstly, the convolution kernel size is expanded, and then the elements of the expanded part of the convolution kernel are set to 0. The convolution kernel size is set to 3, and the expansion factors to 1, 2, and 4 sequentially. The filter is F=(f.sub.1, f.sub.2, . . . , f.sub.k), the sequence is X=(x.sub.1, x.sub.2, . . . , x.sub.t), the expansion factor is d, and the expansion convolution process at the position of x.sub.t can be expressed as (F*.sub.d X) (X.sub.t)=Σ.sub.k=1.sup.Kf.sub.kx.sub.t−(K−k)d.

[0084] In Step 3.3, the parameterized ReLU is used as the activation function.

[0085] The activation function can perform nonlinear operations on the extracted features to increase the fitting ability of the network. The gradient of the ReLU function is 1 when x≥0 and 0 when x<0, in which it is difficult to train when encountering a convolution kernel smaller than 0. In order to solve the above detects, a parameterized ReLU function is used as the activation function:

ReLU(x)=max{ax, x}, 0<a<1.

[0086] For the parameter a as a learnable variable in the network model, an optimal value thereof can be automatically obtained in the overall training process of the network model.

[0087] In Step 3.4, a residual connection.

[0088] There are two dilated causal convolutional layers and activation functions respectively on the residual line. 6 residual blocks are set to be stacked, the dilation factors of which from left to right ranges from 20 to 25, and the baseline of each residual block is connected to the output of the last residual block through jump connections and tensors are added, which facilitates the identity learning for the network after any residual block, and mitigates the problem of network degradation to the greatest extent. The residual block contains two nonlinear transformation branches (F.sub.1, F.sub.2), and the output of the residual blocks can be regarded as a linear operation of the residual output F.sub.1 and the baseline output F.sub.2:

o=F.sub.1(x)+F.sub.2(x).

[0089] In Step 3.5, a fully connected layer.

[0090] The output of the last residual block is connected to the fully connected layer with a sigmoid activation function. The calculation formula from the fully connected layer to the output is:

SOC.sub.k.sup.*=σ(w.sub.outh.sub.k+b.sub.out).

where w.sub.out, b.sub.out represent the weight matrix and bias, respectively, h.sub.k is a hidden output tensor of the last residual block at the time step length k, and σ represents the sigmoid function.

[0091] In Step 4, the temporal convolutional network is trained by adopting a loss function that combines a mean square error and a Nash efficiency coefficient.

[0092] With reference to FIG. 4, Step 4 specifically includes the following steps.

[0093] In Step 4.1, the training data are selected by randomly sampling, and the network training samples are used for network training and network validating, respectively with a ratio of 80% and 20%. The learning and training of the temporal convolutional network includes a forward propagation phase and a backward propagation phase.

[0094] In Step 4.2, in the forward propagation phase, all filters and parameters/weights are initialized with random numbers. The time-sequence evaluating target matrix for the flood-control operation schemes that combines the comprehensive evaluation indicators and the time sequence is input, and then the output values are obtained by the forward propagation sequentially passing through the causal dilated convolution, the activation function, the residual connection, and the fully connected layer.

[0095] In Step 4.3, in the backward propagation phase, a loss function MSE′ that combines the mean square error and the Nash efficiency coefficient is constructed, which is used to train the temporal convolutional network to obtain the error between the output value and the target value of the network.

[0096] The loss function can be expressed as MSE′(y, y′),

[00013]${\mathrm{MSE}}^{\prime }\left(y,y^{\prime }\right)=\frac{{.Math.}_{i=1}^n{\alpha \left(y_i-y_{i^{\prime }}\right)}^2}{n},\alpha =1-\frac{{.Math.}_{t=1}^T{\left(y_i-y_{i^{\prime }}\right)}^2}{{.Math.}_{t=1}^T{\left(y_i-\stackrel{\_}{y_i}\right)}^2},$

where y.sub.i is an output value for the sample i, y.sub.i′ is a target value for the sample i, y.sub.i is an average value for the output value of the sample i, α is a Nash correction parameter, and T is a time.

[0097] According to the obtained error, the gradient descent method is adopted to update all of the values for filters; weights and parameters to minimize the output error. When the number of training iterations satisfies the requirements and the error is less than or equal to the expected values, the training is ended, and the temporal convolutional network reach the convergence.

[0098] In Step 5, the time-sequence evaluating indicator matrix for the flood-control operation schemes is input into the temporal convolutional network to obtain the comprehensive evaluation values for the schemes, and an optimal comprehensive evaluation value is taken as an optimal flood-control operation scheme for the group of reservoirs.

[0099] In summary, in the method for optimally selecting the flood-control operation scheme based on the temporal convolutional network according to the present disclosure, the number of parameters in the complex models can be greatly reduced, the relationships between the evaluation indicators can be better dug out, and the process of optimally selecting the optimal flood-control operation scheme, fully considered under time variation, can improve the evaluation performance of the optimal selection of the model by using fine-tuning techniques adequately based on the idea of transfer learning.