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CN-121980180-A - Time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A

CN121980180ACN 121980180 ACN121980180 ACN 121980180ACN-121980180-A

Abstract

A time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A comprises the steps of collecting runoff data, optimizing parameters of VMD by IRFO, decomposing a runoff time sequence into K intrinsic mode functions IMFs by utilizing the optimized VMD, extracting dynamic characteristics of the runoff time sequence by adopting a phase space reconstruction PSR, dividing the runoff data into a training set, a verification set and a test set, training a ITCN-A model by the obtained training set and verification set containing the dynamic characteristics of the runoff time sequence, and predicting the test set by the trained model. And analyzing the prediction result of the model by adopting three evaluation indexes of Root Mean Square Error (RMSE), average absolute error (MAE) and average absolute percentage error (MAPE). The method has good prediction effect on the historical data of different hydrologic stations, and the stability of the prediction model and the accuracy of the prediction effect are obviously improved.

Inventors

  • FU WENLONG
  • CHEN JUNJIE
  • Chi Baotong
  • LIU YUAN
  • ZHANG XIN
  • LI NAN

Assignees

  • 三峡大学

Dates

Publication Date
20260505
Application Date
20260120

Claims (10)

  1. 1. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A is characterized by comprising the following steps of: step 1, collecting runoff data; Step 2, optimizing parameters of the VMD by utilizing IRFO, and decomposing the runoff time sequence into K eigen mode functions (IMFs) by utilizing the optimized VMD; Extracting dynamic characteristics of a runoff time sequence by adopting Phase Space Reconstruction (PSR), and dividing runoff data into a training set, a verification set and a test set; And 4, training the ITCN-A model by the training set and the verification set which are obtained in the step 3 and contain the dynamic characteristics of the runoff time sequence, and predicting the test set by the trained model.
  2. 2. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-a according to claim 1, wherein: and 5, analyzing the prediction result of the model by adopting three evaluation indexes of Root Mean Square Error (RMSE), mean Absolute Error (MAE) and Mean Absolute Percent Error (MAPE).
  3. 3. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-a according to claim 1, wherein: Step 2 includes providing IRFO, introducing a reverse learning mechanism and combining with a simulated annealing selection strategy, so that the global searching efficiency and the convergence rate are effectively improved; in the reverse learning mechanism, the reverse individual is constructed as follows: (1); in the formula (1), the components are as follows, Representing a reverse learning individual; Representing the lower bound of the individual; Representing an upper bound of the individual; Is the ith individual; if the fitness of the reverse solution is better than that of the original individual, the original individual is replaced by the reverse solution, otherwise, the original individual is kept unchanged, and the mathematical expression is as follows: (2); In the formula (2), the amino acid sequence of the compound, An fitness function value representing X op ; an fitness function value representing X i ; reverse learning probability introducing dynamic decay with iteration number Only if the random number r subject to the uniform distribution (0, 1) is smaller than the reverse learning probability When the reverse learning operation is executed, the reverse learning probability is defined as follows: (3); In the formula (3), a and b respectively represent the termination probability and the start probability, T is the current iteration number, and T is the maximum iteration number.
  4. 4. The method for time-by-time runoff joint prediction based on IRFO-VMD and ITCN-A according to claim 3, wherein the simulated annealing selection strategy avoids the algorithm from falling into local optimum by accepting inferior solutions with a certain probability, and converges by means of a temperature gradual decay guiding algorithm, and the i-th individual current solution is set as M i , the fitness is f (M i ), new candidate solutions are generated as X i1 after iteration, the fitness is f (X i1 ), and the fitness difference is defined as follows: (4); In the formula (4), the amino acid sequence of the compound, Representing the difference value of the fitness function between the candidate solution and the current solution; The simulated annealing updates the individual position formula as follows: (5); In the formula (5), r is a uniformly distributed random number in a obeying interval (0, 1), T e is the current temperature, the attenuation is carried out along with the iteration times, and the temperature after the attenuation is calculated as follows: (6); In the formula (6), the amino acid sequence of the compound, Representing updated temperature, alpha (0, 1) Is the temperature decay coefficient, and T f is the minimum temperature.
  5. 5. The method for time-wise radial flow joint prediction based on IRFO-VMD and ITCN-A of claim 4, wherein the VMD decomposes the complex nonstationary signal into a plurality of eigenmode functions IMFs, each eigenmode function having a finite bandwidth and a specific center frequency, and the mathematical expression is expressed as: (7); In the formula (7), u k represents a kth mode function, ω k represents a center frequency of the kth mode function; Representing a set of modal functions; K represents the number of decomposition modes; Representing partial derivatives over time; Is a dirac function; representing imaginary units, t representing time; Representing a kth modality function; Representing a multiplication operator; Represents an L2 norm; Representing the original vibration signal sequence; The Lagrangian multiplier lambda and the quadratic penalty factor alpha are introduced to obtain an expanded Lagrangian function L, and the specific formula is defined as follows: (8); in the formula (8), the amino acid sequence of the compound, Representing a lagrangian function; A Lagrangian multiplier representing time variation; Representing the inner product; Solving the saddle points of the augmented lagrangian function by an alternate direction multiplier method so as to optimize each modal function u k (t) and the center frequency omega k , and updating the detailed description of the formula is as follows: (9); (10); (11); In the above-mentioned method, the step of, 、 、 And Respectively represents f (t), u i (t), lambda (t), Fourier transform expressions of (a); A frequency domain representation representing a kth modal function; A Lagrangian multiplier at iteration n+1th; a Lagrangian multiplier at the nth iteration; Representing the center frequency of the kth modal function in the n+1th iteration; Representing the frequency; And (3) obtaining K modal functions u k (t) and corresponding center frequencies omega k through iterative updating until the stopping condition is met.
  6. 6. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A, which is characterized in that, in order to realize the adaptive optimization of VMD key parameters, IRFO obtained by the method is selected to optimize the modal number K of VMD and penalty factor alpha, and minimum envelope entropy is taken as a fitness function, so that a runoff sequence is decomposed into K eigen mode functions (IMFs) with different frequencies, and the minimum envelope entropy formula is as follows: (12); (13); (14); In the above-mentioned method, the step of, The method is characterized in that the method is a parameter component to be optimized, wherein min is the minimum envelope entropy, and K is the modal number of VMD decomposition; Representing the number of samples, p i n being the normalized envelope probability, n being the index of the discrete time point, e i n being the envelope magnitude of the ith modality, H { } being the Hilbert transform.
  7. 7. The method for time-by-time radial flow joint prediction based on IRFO-VMD and ITCN-A of claim 6, wherein in the step 3, phase Space Reconstruction (PSR) is used for each eigenmode function IMF, and a training set, a validation set and a test set are divided, specifically as follows: 3.1 Phase Space Reconstruction (PSR) by appropriate choice of embedding dimension d and time delay tau, the original one-dimensional time sequence is mapped to Gao Weixiang spaces, (15); In the above formula, X i represents a sequence sample; i is an index, where i=1, 2,3,.. R is the length of the sequence after the embedding time delay, and d is the embedding dimension; L is the original sequence length; Representing the reconstructed phase space vector; R represents the sampling point number; A first sample point is indicated and is shown, Represents the 1+τ sample point; Represents the 1 < th+ > (d-1) tau sample point, The representation represents the i-th sample point; Representing the i+τ sample points; Representing the i+ (d-1) th τ sample point; Representing the R- (d-1) th sampling point; Representing the R- (d-2) th sampling point; Representing the R-th sampling point; Extracting dynamic characteristics of the runoff time sequence by adopting Phase Space Reconstruction (PSR), specifically, carrying out phase space reconstruction on the original runoff data by a formula (15), thereby obtaining reconstructed runoff data; and 3.2, dividing the reconstructed data containing the dynamic characteristics of the runoff time sequence into a training set, a verification set and a test set according to a proper proportion, and finally obtaining a divided data set.
  8. 8. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-a according to claim 7, wherein: In the step 4, training ITCN-A model by the training set and the verification set which are obtained in the step 3 and contain dynamic characteristics of the runoff time sequence, and predicting a test set by the trained model to obtain a prediction result, wherein the specific steps are as follows: 4.1, constructing a multi-scale TCN module, extracting multi-layer runoff time sequence dependent features through parallel expansion convolution of different convolution kernels, and thus enhancing the expression capability of the multi-scale features; The TCN is used for extracting local time sequence characteristics of the sequence along the time dimension by taking one-dimensional convolution as a basic operation unit, and the mathematical expression is as follows: (16); Wherein T t represents one-dimensional convolution output, W i is convolution kernel parameter, s t-i is input sequence of T-i time steps, k-1 is convolution kernel size, i represents index, b is bias parameter, T is time index, s is input sequence; To maintain time causality, TCN introduces a causal convolution mechanism in one-dimensional convolution, so that the output at the current moment is only dependent on the current and previous inputs, and the mathematical expression is as follows: (17); the TCN adopts a residual connection structure, each residual block consists of two layers of convolution and nonlinear activation functions, input features are directly added with convolution output through identity mapping, cross-layer information transfer is realized, and the mathematical expression is as follows: (18); (19); Wherein Conv 1 and Conv 2 are two layers of convolution layers respectively, f 1 and f 2 are nonlinear activation functions respectively, CC(s) is a residual block output, s represents an input sequence, J represents a residual connection final output; 4.2, designing a self-adaptive nonlinear projection layer, and realizing expansion and recompression of a runoff characteristic space through nonlinear mapping of an upper projection module and a lower projection module so as to capture a high-order nonlinear relation, wherein the mathematical expression is as follows: (20); (21); Wherein: The two values are respectively nonlinear activation functions, W up and W down are respectively the leachable weights of the upper projection layer and the lower projection layer, b up and b down are respectively the bias parameters of the upper projection layer and the lower projection layer, h up and h down are respectively the outputs of the upper projection layer and the lower projection layer, and s is an input sequence; and the fusion proportion of the nonlinear projection can be adaptively adjusted through the learnable gating parameters, and the mathematical expression is as follows: (22); Wherein g is a gating function, h down is the output of lower projection, s is an input sequence; the output is the gate control fusion; for element-by-element multiplication; Residual fusion is carried out on the regulated nonlinear projection and the multi-scale TCN module information, and the mathematical expression is as follows: (23); Wherein: Is the output after fusion; 4.3, introducing a light attention mechanism for enhancing the characterization capability of ITCN-A on the sequence key information, generating attention scores on the time dimension through linear mapping, and carrying out weight normalization processing by adopting a softmax function so as to carry out weight aggregation on runoff characteristics according to the importance of each time step, wherein the method comprises the following specific steps: Let the input feature sequence be , Representing three-dimensional feature vectors with dimensions B, T and C, wherein B, T and C respectively represent batch sizes, time steps and feature dimensions; through linear mapping, the attention score S of the time dimension can be obtained, and the calculation formula is as follows: (24); In the formula (24), the amino acid sequence of the compound, And (3) with Are all learnable parameters; The residual error is output after the residual error connection; S is an attention score; And carrying out normalization processing on the score vector in the time dimension by adopting a softmax function to obtain the attention weight a, wherein the specific expression is as follows: (25); where t is the time dimension, a t represents the attention weight at time t, S t represents the attention score at time t, S i represents the attention score at time i, i represents the index, Representing an exponential function; Then, the characteristics of each time step are weighted and summed according to the weight, so that characteristic aggregation of the time dimension is realized, and the calculation form is as follows: (26); In the formula (26), the amino acid sequence of the compound, And (3) with Respectively representing the attention weight and the characteristic sequence at the moment T, wherein T is a time step, T is a current time step, and O is a weighted aggregation result; 4.4 Obtaining a runoff prediction result of each IMF component by linear layer mapping of a result obtained by weighting aggregation, wherein the mathematical expression is as follows: (27); Wherein W z represents a learnable parameter, b z represents a paranoid vector, and Y z represents a runoff prediction result of each IMF component.
  9. 9. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-a according to claim 8, wherein: in the step 4, ITCN-A model adopts a multi-layer depth fusion integrated architecture design: Firstly, constructing a multi-scale TCN module according to a formula (16) to a formula (19); Secondly, the series self-adaptive nonlinear projection layers are connected in series, as shown in the formula (20) to the formula (21), the expansion and the recompression of the characteristic space are realized through the nonlinear mapping of the upper projection module and the lower projection module so as to capture the high-order nonlinear relation, Meanwhile, the fusion proportion of nonlinear projection is adaptively adjusted by introducing a learnable gating parameter as shown in a formula (22); Residual fusion is carried out on the regulated nonlinear projection and the multi-scale TCN module information, so that the flexibility and stability of the network are further improved; Subsequently, the attention layers are connected in series, as shown in the formulas (24) to (26), the characteristic weighting mechanism distributes differential weights for different scales and channels, Thereby highlighting the contribution of critical time steps and suppressing redundant information; Finally, as shown in equation (27), the series attention layer maps the fusion features to the output space by using the linear layer to obtain the prediction results of each IMF component, and adds up the prediction results of each component to generate a final runoff prediction result.
  10. 10. The time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-a according to claim 2, wherein: in the step 5, three specific calculation formulas of the evaluation indexes including the root mean square error RMSE, the average absolute error MAE and the average absolute percentage error MAPE are shown as follows: (28); (29); (30); in the above formula, n represents the number of samples, And Representing the actual and predicted values of the i-th sample, respectively.

Description

Time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A Technical Field The invention relates to the technical field of runoff prediction, in particular to a time-by-time runoff combined prediction method based on IRFO-VMD and ITCN-A. Background With the continuous aggravation of global climate change, extreme weather events frequently occur, and the uncertainty of the prediction of the watershed hydrologic process also increases. Water resource shortage and flood disasters have become one of the key factors threatening human social security and sustainable development. The runoff prediction has important significance for drainage basin scheduling, flood control early warning, reservoir operation and ecological protection. Accurate runoff prediction provides an important basis for efficient scheduling of water resources. However, the radial flow process is affected by a number of complications, the inherent non-linear and non-stationary characteristics of which pose challenges to the accuracy of the predictions. Therefore, how to construct an accurate and stable runoff prediction model becomes a key problem to be solved in the hydrologic field. At present, the runoff prediction method mainly comprises three types, namely runoff prediction based on a traditional statistical method, runoff prediction based on machine learning and runoff prediction based on deep learning. In the traditional method, statistical models such as an autoregressive moving average model and an autoregressive integral moving average model can effectively capture the linear dynamic characteristics of a runoff sequence, so that simple and efficient prediction is realized. However, it is difficult to effectively characterize the nonlinear and non-stationarity features in the runoff sequence by the conventional statistical model, and the prediction accuracy is often limited in a complex watershed environment. The machine learning method can accurately capture complex nonlinear trends in the runoff sequence by means of excellent nonlinear fitting capacity of the machine learning model, so that good application prospects are shown in runoff prediction. Common machine learning models include extreme learning machines, nuclear extreme learning machines, random forests, extreme gradient lifted trees, and the like. Although the machine learning method achieves a certain effect in the runoff prediction, the dynamic characteristics and long-term dependence of the runoff process are difficult to comprehensively describe, so that the machine learning method brings challenges to the accuracy of the machine learning in the runoff prediction task. With the rapid development of artificial intelligence technology, deep learning is widely applied in runoff prediction tasks by utilizing the capability of a neural network for efficiently modeling time sequence dependency and dynamic change rules in a runoff sequence. Such as literature [1] Xu Junyang, luo Yuanlin, liu Yuexin, et al. Medium-long term runoff forecast based on CEEMDAN-IASO-TCN combined model [ J ]. Renshengjiang, 2025, 56 (04): 128-135. However, it is difficult to accurately capture non-stationarity in the runoff sequence due to a single neural network model. Researchers began introducing signal decomposition techniques into runoff predictions to reduce data complexity by decomposing complex runoff sequences into several subsequences with different time scales or feature patterns. In addition, the prediction model is sensitive to parameter setting in practical application, which may have an influence on the prediction accuracy thereof. With the rapid development of the group intelligent optimization algorithm and the meta heuristic algorithm, researchers start to perform self-adaptive optimization on model parameters by using the optimization algorithm, and the algorithms can quickly find out the optimal parameter combination in a high-dimensional search space, so that an effective solution is provided for parameter tuning in runoff prediction. Tu ppell's fox optimizer (RFO) is a heuristic optimization algorithm, the specific expression of which is shown in document [2]：Braik, M., Al-Hiary, H., 2025. Rüppell's fox optimizer: A novel meta-heuristic approach for solving global optimization problems. Cluster Comput. 28, 292., however, standard RFO is easy to fall into local optimum in complex optimization tasks. Disclosure of Invention In order to solve the technical problems, the invention provides a time-by-time runoff combined prediction method based on IRFO-VMD and ITCN-A, which has good prediction effects on historical data of different hydrologic stations, and obviously improves the stability of a prediction model and the accuracy of the prediction effects. The technical scheme adopted by the invention is as follows: the time-by-time runoff joint prediction method based on IRFO-VMD and ITCN-A comprises the following steps of: step 1, collecting runoff data; Step 2, optimiz