Fractional-order power system chaos prediction method and system based on optimal variational modal decomposition and mosta
Patent Information
- Application Number
- CN202610946676.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-29
- Publication Date
- 2026-10-09
AI Technical Summary
[0007]针对分数阶电力系统混沌时间序列预测精度和稳定性不佳的问题，本发明的目的是提供一种基于最优变分模态分解和MOSTA的分数阶电力系统混沌预测方法及系统，以有效提高预测精度和稳定性
（1）建立分数阶五维混沌电力系统数学模型，并分析其动力学行为，使系统描述更加准确和具有真实性。
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system chaos prediction technology, specifically relating to a fractional-order power system chaos prediction method and system based on optimal variational mode decomposition and multi-objective state transition algorithm (MOSTA). Background Technology
[0002] Extensive research has revealed that instability in power systems arises from chaotic oscillations under certain parameters and operating conditions. When a power system is in a chaotic state, generator output voltage, frequency, and speed exhibit irregular oscillations. As these oscillations intensify, the power system may collapse. Therefore, predicting the occurrence of chaotic phenomena in power systems and ensuring their stable operation is of significant research value.
[0003] Currently, chaotic prediction models mainly include time series analysis models, phase space reconstruction models, improved weighted first-order local prediction models, locally linearized models, neural network prediction models, and models combining genetic algorithms. Due to the extreme complexity and unpredictable nature of the data, these methods struggle to achieve high-precision predictions using complex models. While neural network prediction methods, which have been the most studied, offer strong robustness and fault tolerance, they are prone to getting trapped in local optima and overfitting. Therefore, researchers have begun to focus on combined prediction methods, combining two or more prediction models in specific ways to leverage their respective advantages and improve prediction accuracy.
[0004] There are several main combined models: the first model combines several different models into a completely new model for prediction; the second model weights the results of multiple prediction models; and the third model processes the data and uses swarm intelligence algorithms to optimize the hyperparameters or key parameters of the prediction model.
[0005] Jiang Qiang et al. (A Chaotic Prediction Model for Power Systems Based on Reconstructed Phase Space FLS-SVM, Information and Control, 2011, 40(02): 175-179) proposed a chaotic prediction model for power systems based on reconstructed phase space improved fuzzy least squares support vector machine to improve the prediction accuracy, addressing the problem of low prediction accuracy in power system chaos. Lu Yingdong et al. (DLSTM Chaotic Prediction for Power Systems Based on Genetic Attention Mechanism, Computational Physics, 2022, 39(03): 371-378) proposed a chaotic prediction model based on genetic algorithm optimized deep long short-term memory network and applied it to power systems, achieving higher prediction accuracy. Lu Yingdong et al. (Multivariate Chaotic Time Series Prediction for Power Systems Based on Optimized Time Spectral Graph Neural Network, Vibration and Shock, 2023, 42(11): 156-162) proposed a power system chaotic time series prediction model based on deep learning for chaotic prediction of fourth-order power systems with excitation constraints.
[0006] The combined prediction methods described above have improved the accuracy of chaotic prediction in power systems. However, due to system complexity and nonlinearity, as well as factors related to the type of prediction model, certain errors still exist. Therefore, finding a combined prediction model that effectively improves both prediction accuracy and stability is of significant research value. Summary of the Invention
[0007] To address the issues of poor accuracy and stability in predicting chaotic time series data of fractional-order power systems, the present invention aims to provide a method and system for predicting chaotic data of fractional-order power systems based on optimal variational mode decomposition and MOSTA, so as to effectively improve prediction accuracy and stability.
[0008] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting chaos in fractional-order power systems based on optimal variational mode decomposition and MOSTA includes the following steps: Step 1: Obtain chaotic time series data of the fractional-order power system, and decompose the data using the optimal variational mode decomposition method to obtain multiple sub-mode components; Step 2: Reconstruct the data of the multiple submodal components, and input the reconstructed data into multiple preset neural network models for prediction to obtain multiple initial prediction results; Step 3: Calculate the optimal weight coefficients for multiple neural network models using a multi-objective state transition algorithm; Step 4: Based on the optimal weight coefficient, the multiple initial prediction results are weighted and combined to obtain the final chaotic prediction result.
[0009] In step 1, the optimal variational mode decomposition method includes: determining the total number K of modes by using the center frequency observation method, and using the residual index exponent. Optimize update step size Among them, the residual index The calculation formula is as follows:
[0010] in, Indicates the first This is one model.
[0011] The determination of the total number of modes K includes: when K=5, the center frequencies of mode 3 and mode 4 are close, resulting in over-decomposition, so the total number of modes is set to 4; wherein, mode 3 and mode 4 are the 3rd and 4th mode components arranged in ascending order of center frequency.
[0012] In step 1, the fractional-order power system is a five-dimensional chaotic power system containing energy storage devices, and its mathematical model is constructed based on the Caputo definition of fractional-order differential.
[0013] In step 2, the multiple preset neural network models include a radial basis function neural network model, an evolutionary neural network model, and a gated recurrent unit neural network model.
[0014] In step 3, the parameters of the multi-objective state transition algorithm are set as follows: maximum number of iterations 40, population size 25.
[0015] The multi-objective state transition algorithm in step 3 is a multi-objective version of the single-objective state transition algorithm, and the state transition form is defined as follows:
[0016] in, This represents the current state vector, which maps to a solution to the optimization problem. , This is the state transition matrix; Functions that represent state and history; This represents the evaluation function.
[0017] The state transition operations include: vector rotation, linear translation, scaling transformation, and coordinate adjustment.
[0018] Following step 4, the method further includes evaluating the prediction results using root mean square error, absolute average error, and mean absolute percentage error.
[0019] A fractional-order power system chaos prediction system based on optimal variational mode decomposition and multi-objective state transition algorithm, comprising: The data acquisition and decomposition module is used to acquire chaotic time series data of fractional-order power systems and decompose the data using the optimal variational mode decomposition method to obtain multiple sub-mode components. The multi-model prediction module is used to reconstruct the data of the multiple sub-modal components and input the reconstructed data into multiple preset neural network models for prediction to obtain multiple initial prediction results. The weight optimization module is used to calculate the optimal weight coefficients of the multiple neural network models using a multi-objective state transition algorithm; The result combination module is used to weight and combine the multiple initial prediction results according to the optimal weight coefficient to obtain the final chaotic prediction result.
[0020] Beneficial effects
[0021] Compared with the prior art, the present invention has the following beneficial effects: (1) Establish a mathematical model of a fractional-order five-dimensional chaotic power system and analyze its dynamic behavior to make the system description more accurate and realistic.
[0022] (2) The original sequence is decomposed into a series of different sub-modes by using optimal variational mode decomposition. At the same time, optimal variational mode decomposition can smooth out the influence of the complex fluctuations of the data on the prediction results, effectively reduce the complexity of chaotic characteristics, and improve the accuracy of prediction.
[0023] (3) By utilizing the advantages of radial basis function neural networks, evolutionary neural networks, and gated recurrent unit neural networks, and combining them with multi-objective state transition algorithms, the accuracy and robustness of prediction are effectively improved. At the same time, the linear weights of each neural network model are optimized by using multi-objective state transition algorithms, thereby improving the prediction accuracy.
[0024] (4) It emphasizes both accuracy and stability, overcoming the shortcomings of single-objective optimization algorithms and the inability of a single prediction model to achieve good prediction accuracy.
[0025] (5) Simulation results show that, compared with traditional prediction models, the combined prediction model proposed in this invention has higher prediction accuracy and stability. Attached Figure Description
[0026] Figure 1 This is a point prediction block diagram of the combined prediction model proposed in this invention;
[0027] Figure 2 This is a schematic diagram of the three-node power system model used in this invention;
[0028] Figure 3 This is a two-dimensional phase diagram of the integer-order chaotic power system of the present invention;
[0029] Figure 4 This is a schematic diagram of a power system model containing an energy storage device according to the present invention;
[0030] Figure 5 This is the Lyapunov exponent spectrum of the system as parameter Q3 changes according to the present invention;
[0031] Figure 6 This is the Lyapunov exponent spectrum of the system as parameter Q7 changes according to the present invention;
[0032] Figure 7 This is a timing diagram of the fractional-order five-dimensional chaotic power system containing an energy storage device according to the present invention;
[0033] Figure 8 The diagram shows the results of the optimal variational mode decomposition of the data in this invention, where (a) is the decomposition result of variable x1 and (b) is the decomposition result of variable x2.
[0034] Figure 9 This is a line graph showing the actual value and the predicted value of the present invention, where (a) is the predicted result of variable x1 and (b) is the predicted result of variable x2.
[0035] Figure 10 The distribution of prediction error results for the model proposed in this invention is shown in the figure, where (a) is the prediction error distribution of variable x1 and (b) is the prediction error distribution of variable x2. Detailed Implementation
[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. These embodiments are only for explaining the invention and are not intended to limit the scope of protection of the invention.
[0037] 1. Mathematical Model and Chaotic Dynamics Analysis of a Fractional-Order Five-Dimensional Electric System
[0038] 1.1 Three-node power system model
[0039] The three-node power system model used in this embodiment is as follows: Figure 2 As shown, it mainly consists of three parts: generator, load, and transmission and distribution lines.
[0040] 1.2 Generator Mathematical Model
[0041] Choosing a higher-order generator model leads to increased computational complexity and a more intricate solution. Therefore, for simplicity, we ignore secondary factors and adopt a simplified second-order synchronous generator model, as shown in the following formula:
[0042]
[0043] in, Represents the generator power angle. Represents rotational speed. , Represents the generator's moment of inertia and mechanical input power. This represents the generator's equivalent damping coefficient. The load voltage phase angle, For voltage, Indicates the first One generator.
[0044] 1.3 Load Model
[0045] As part of the power system, the stability of the electrical load is closely related to the dynamic characteristics of the load.
[0046] (1) Static load model, the specific expression is as follows:
[0047]
[0048] in, Represents bus voltage; and Represents the active and reactive power of the load; and These represent the active power and reactive power of the generator rotor, respectively. , Representative characteristic parameters.
[0049] (2) Dynamic load model, the specific expression is as follows:
[0050]
[0051] in, Indicates the phase angle of the load bus voltage. This indicates the voltage amplitude of the load bus. , represent , The load. The value is a constant and represents active power. The value is a constant and represents reactive power. , , , , , These represent the coefficients of the load model. For the capacitor C in the diagram, an equivalent transformation based on Thevenin's theorem yields:
[0052]
[0053] In the formula, , , These represent the Thevenin equivalent supply voltage magnitude, equivalent admittance magnitude, and equivalent admittance phase angle before the capacitor is connected, respectively. , , These are the network parameters of the Thevenin equivalent transformation, and Constants. Simultaneous equations , , The active and reactive power of the load bus are:
[0054]
[0055] 1.4 Power Network Model
[0056] The power network model is shown in the following equation:
[0057]
[0058] in, , For node voltage, , For conductivity and susceptance. This is the phase angle difference. Represents a node The amount of active power injected. Represents a node The amount of reactive power injected. This represents the total number of nodes in the power system.
[0059] 1.5 Mathematical Model of Power System
[0060] By combining the three mathematical models, a power system model is derived:
[0061]
[0062]
[0063] Table 1 System Parameter Table
[0064] Table 1 shows the system parameter table. After rearranging and transforming the above formulas, and substituting the parameter values from Table 1, we obtain the following equation:
[0065]
[0066] in, For maximum power angle, For rotational speed, The load voltage phase angle, The voltage is [voltage value], and the reactive power consumed by the load is [power value]. . When the value of changes, the system's state of motion will differ. The power system, as ... Changes in parameters can lead to periodic oscillations, bifurcation, and chaotic phenomena. When the parameters change to a certain value, voltage collapse occurs. Different parameter values correspond to different motion states. At that time, the time sequence diagram of the power system is shown in [reference needed]. Figure 3 , Figure 3 A two-dimensional phase diagram representing an integer-order chaotic power system.
[0067] Considering the actual operating conditions of the power system, energy storage devices are introduced to establish a model that is closer to the actual system, making traditional methods more practical. Figure 4 A representative power system model containing energy storage devices is established using the following formula:
[0068]
[0069] The Caputo fractional differential is defined as:
[0070]
[0071] in Not less than integers, It indicates the order of the fractional derivative. The state variable whose fractional derivative is being calculated. Describes a fractional integral operator. Represents the function to be integrated. This represents the Gamma function. To represent the integral variable, then .
[0072] The integer-order power system, through generalization using the Caputo fractional derivative definition, yields the following model:
[0073] when At that time, the system state changes with the parameters. Changes, such as Figure 5 As shown. Fractional order of the system equations. Same, select parameters .in , , , , With control parameters With changes in parameters, the power system will experience periodic oscillations, bifurcation, and chaos. If the parameters change to a certain extent, voltage and speed will collapse.
[0074] when The motion state differs depending on the value of . When The range of values is At this time, the power system exhibits chaotic behavior. (Parameter selection...) When, the fractional order of the power system equations When the system becomes chaotic, it exhibits irregular oscillations, and the system completely becomes disordered. Figure 6 Representative parameters The Lyapunov exponent spectrum of the system as it changes. The time system has five Lyapunov exponents. , , , , A positive maximum value for the Lyapunov exponent indicates that the entire system is in a state of chaotic oscillation.
[0075] when , Time Figure 7 It can be seen that, with Figure 3 The time series diagrams for integer-order power systems are similar, with each state variable existing in an irregular, chaotic state. The time series diagrams for fractional-order power system models provide a more accurate and realistic description of the system.
[0076] 2. Optimal Variational Mode Decomposition (OVMD) Method
[0077] Variational mode decomposition is a complex algorithm for decomposing non-stationary signals. Its purpose is to transform non-stationary signals... Decomposed in the frequency domain into Modal components , During the decomposition process, each component is matched with a center frequency. The method is as follows:
[0078] Step 1: Use Hilbert calculation to obtain... The corresponding one-sided spectrum;
[0079] Step 2: Continuously correct the center frequency of each mode using an exponential method;
[0080] Step 3: Estimate each mode function using the Gaussian smoothing method. Given the fundamental frequency bandwidth, a constraint-based variational model is constructed as follows:
[0081]
[0082]
[0083] in, Indicates the first Types of patterns; The representative is the first Center frequency, Represented by partial derivative operators, This represents the original signal. The constraint problem is solved by adding a penalty factor and a Lagrange operator.
[0084]
[0085] in, and It represents the set of modal components and the center frequencies of each component. , , , These represent the penalty term, Lagrange multiplier, partial derivative operator, and convolution operator, respectively. No. During iteration, the first Modal components frequency The update result is obtained. By introducing the alternating direction multiplier method for alternating updates, the above variational problem can be solved to obtain... and The update formula is as follows:
[0086]
[0087]
[0088] In the formula , , , They are respectively , , , Fourier transform.
[0089] Indicates the first The modal component in the th ... Frequency domain results at the next iteration.
[0090] The size of the value affects the bandwidth of the IMF component. A larger value of K results in a smaller bandwidth, leading to center frequency overlap. Studies have found that when K is too large, the center frequencies of each mode tend to cluster together, potentially causing overlap. Conversely, when K is too small, some modes will be distributed to neighboring modes, potentially resulting in mode dropout. To investigate the optimal decomposition method, the center frequency observation method is used to determine the total number of modes K and to select appropriate Lagrange update parameters. Using residual index Optimize update step size The formula is as follows:
[0091]
[0092] This represents the total number of data points in the original signal. Indicates the first One sampling point, Indicates the first Each IMF component in time The value at the location. In this embodiment, the K value is determined based on a comparative study of the overall correlation coefficient. Variable and variables All correlation coefficients are shown in Tables 2 and 3. When k=5, the center frequencies of mode 3 and mode 4 are close, indicating over-decomposition; therefore, the total number of modes is set to 4. Furthermore, the penalty factor... The value is 2000. TAU is 0, TOL is 1e-6, DC is 0, and INIT is 1. After setting the parameters, the variables in the model... and variables The first 10,000 data points were decomposed using OVMD, and the results are as follows: Figure 8 As shown.
[0093] Table 2 Center frequencies (variables) for different values of K )
[0094]
[0095] Table 3 Center frequencies (variables) for different values of K )
[0096]
[0097] 3. State Transition Algorithm (STA) and Multi-Objective State Transition Algorithm (MOSTA)
[0098] The State Transition Algorithm (STA) is an intelligent optimization method whose theoretical foundation stems from the concepts of state transition and state space in modern control theory. This algorithm represents the solution to a problem as states and transitions between these states during the search process, thereby gradually approaching the optimal solution. This characteristic gives the State Transition Algorithm a unique advantage compared to other evolutionary algorithms.
[0099] Define the state transition form as follows:
[0100]
[0101] in, This represents the current state vector, which maps to a solution to the optimization problem. , This is the state transition matrix; Functions that represent state and history; This represents the evaluation function.
[0102] Four state change operations were designed to solve the optimization problem.
[0103] (1) Vector rotation operation:
[0104]
[0105] in, It is the vector rotation factor; It is obedience A random matrix drawn from a uniform distribution; Let L be the L2 norm of the vector; the vector rotation operator can be used to generate candidate solutions within the unit sphere.
[0106] (2) Linear translation operation:
[0107]
[0108] in, It is a linear translation factor; It is from Random variables drawn from a uniform distribution; the linear translation operator simulates a linear change, which is relative to the current point. Starting from the previous state, Search the largest possible area in the direction of the search.
[0109] (3) Scale expansion transformation operation:
[0110]
[0111] in, This is the proportional expansion transformation factor; It is a random matrix drawn from a Gaussian distribution. The scaling operator is mainly used to expand the search space.
[0112] (4) Coordinate adjustment operation:
[0113]
[0114] in, This is called the coordinate adjustment factor; It is a random diagonal sparse matrix drawn from a Gaussian distribution. The coordinate adjustment operator helps to enhance the search capability in a single dimension.
[0115] The Multi-Objective State Transition Algorithm (MOSTA) is a multi-objective version of the single-objective state transition algorithm, used to solve multi-objective optimization problems. This embodiment uses MOSTA to solve for the weight coefficients between the various models. Algorithm parameter settings: maximum number of iterations 40, population size 25. The remaining parameters of MOSTA are the same as in existing technologies.
[0116] 4. Specific implementation and experimental verification of the prediction model
[0117] 4.1 Overview of the Forecasting Process
[0118] The overall framework of the combined prediction model proposed in this invention is as follows: Figure 1 As shown. The entire prediction process is as follows:
[0119] Step 1: Use the model data and the OVMD algorithm to perform optimal mode decomposition;
[0120] Step 2: Reconstruct the data using the data from the optimal mode decomposition and use it as the basic input data for the combined model;
[0121] Step 3: Use the MOSTA algorithm to solve for the optimal weights of each model;
[0122] Step 4: Combine the prediction results of each model with the optimal weights to obtain the final prediction result.
[0123] Figure 1 It demonstrates the complete logical chain from raw data input to final predicted output.
[0124] 4.2 Data Acquisition and Preprocessing
[0125] Selecting the intermediate variables in a fractional-order five-dimensional power system model and variables We extracted 10,000 data points from the variables. We selected the first 8,000 time points as the training set and the 2,000 time points as the test set for the prediction model.
[0126] The above OVMD method is used to analyze variables. and variables The first 10,000 data points were decomposed, and the results are as follows: Figure 8 As shown, the multiple sub-modal components obtained from the decomposition are reconstructed and used as the basic input data for the combined model.
[0127] 4.3 Multi-model combined prediction
[0128] The reconstructed data is input into multiple preset neural network models for prediction, resulting in multiple initial prediction results. The neural network models used in this embodiment include: Radial Basis Function Neural Network (RBFNN), Evolutionary Neural Network (ENN), and Gated Recurrent Unit (GRU) neural network models. The learning rates for CNN-GRU, RBFNN, GRNN, ENN, and GRU are all set to 0.01.
[0129] 4.4 Weight Optimization
[0130] The Multi-Objective State Transition Algorithm (MOSTA) is used to calculate the optimal weight coefficients for each neural network model. Algorithm parameter settings: maximum number of iterations 40, population size 25. The remaining parameters of MOSTA are the same as in existing techniques.
[0131] 4.5 Combined Forecasting
[0132] Based on the optimal weight coefficients calculated by MOSTA, the initial prediction results of each model are weighted and combined to obtain the final chaotic prediction result.
[0133] 4.6 Evaluation Indicators and Experimental Results
[0134] The prediction results were evaluated using root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The system was run 30 times on a Windows 10 system with an AMD Ryzen 5 4600H CPU 3.00 GHz, and the best prediction results for each model were compared.
[0135] From a model perspective, the combined prediction model integrates the advantages of multiple model types, avoiding the shortcomings of a single model and thus improving prediction performance. As shown in Tables 4 and 5, the proposed combined prediction method outperforms other single models across all three evaluation metrics tested. For example, variables... Compared to other OVMD-CNN-GRU, OVMD-RBFNN, CNN-GRU, GRNN, and ENN models, the proposed model improves RMSE by 0.0008, 0.0006, 0.0011, 0.0502, and 0.0014, respectively. MAE is improved by 0.0008, 0.0008, 0.001, 0.0452, and 0.001, respectively. MAPE is improved by 0.0026, 0.0024, 0.0029, 0.1375, and 0.0029, respectively.
[0136] See prediction results Figure 9 The line graph showing the actual and predicted values demonstrates that the combined prediction model performs very well. Figure 10 This plot shows the distribution of the prediction error results of the proposed model.
[0137] Table 4 Summary of prediction results from different models (variables) )
[0138] Propose a model 0.0015 0.0010 0.0032 OVMD-CNN-GRU 0.0023 0.0018 0.0058 OVMD-RBFNN 0.0021 0.0018 0.0056 CNN-GRU 0.0026 0.0020 0.0061 GRNN 0.0517 0.0462 0.1407 ENN 0.0029 0.0020 0.0061
[0139] Table 5 Summary of prediction results from different models (variables) )
[0140] Propose a model 0.0060 0.0051 0.0764 OVMD-CNN-GRU 0.0085 0.0065 0.0613 GRNN 0.1572 0.1425 1.0049 ENN 0.0089 0.0062 0.0747
[0141] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for predicting chaos in fractional-order power systems based on optimal variational mode decomposition and MOSTA, characterized in that, Includes the following steps: Step 1: Obtain chaotic time series data of the fractional-order power system, and decompose the data using the optimal variational mode decomposition method to obtain multiple sub-mode components; Step 2: Reconstruct the data of the multiple submodal components, and input the reconstructed data into multiple preset neural network models for prediction to obtain multiple initial prediction results; Step 3: Calculate the optimal weight coefficients for multiple neural network models using a multi-objective state transition algorithm; Step 4: Based on the optimal weight coefficient, the multiple initial prediction results are weighted and combined to obtain the final chaotic prediction result.
2. The method according to claim 1, characterized in that, In step 1, the optimal variational mode decomposition method includes: determining the total number K of modes by using the center frequency observation method, and using the residual index exponent. Optimize update step size Among them, the residual index The calculation formula is as follows: in, Indicates the first This is one model.
3. The method according to claim 2, characterized in that, The determination of the total number of modes K includes: when K=5, the center frequencies of mode 3 and mode 4 are close, resulting in over-decomposition, so the total number of modes is set to 4; wherein, mode 3 and mode 4 are the 3rd and 4th mode components arranged in ascending order of center frequency.
4. The method according to claim 1, characterized in that, In step 1, the fractional-order power system is a five-dimensional chaotic power system containing energy storage devices, and its mathematical model is constructed based on the Caputo definition of fractional-order differential.
5. The method according to claim 1, characterized in that, In step 2, the multiple preset neural network models include a radial basis function neural network model, an evolutionary neural network model, and a gated recurrent unit neural network model.
6. The method according to claim 1, characterized in that, In step 3, the parameters of the multi-objective state transition algorithm are set as follows: maximum number of iterations 40, population size 25.
7. The method according to claim 1, characterized in that, The multi-objective state transition algorithm in step 3 is a multi-objective version of the single-objective state transition algorithm, and the state transition form is defined as follows: in, This represents the current state vector, which maps to a solution to the optimization problem. , This is the state transition matrix; Functions that represent state and history; This represents the evaluation function. The state transition operations include: vector rotation, linear translation, scaling transformation, and coordinate adjustment.
8. The method according to claim 1, characterized in that, Following step 4, the method further includes evaluating the prediction results using root mean square error, absolute average error, and mean absolute percentage error.
9. A fractional-order power system chaos prediction system based on optimal variational mode decomposition and multi-objective state transition algorithm, characterized in that, include: The data acquisition and decomposition module is used to acquire chaotic time series data of fractional-order power systems and decompose the data using the optimal variational mode decomposition method to obtain multiple sub-mode components. The multi-model prediction module is used to reconstruct the data of the multiple sub-modal components and input the reconstructed data into multiple preset neural network models for prediction to obtain multiple initial prediction results. The weight optimization module is used to calculate the optimal weight coefficients of the multiple neural network models using a multi-objective state transition algorithm; The result combination module is used to weight and combine the multiple initial prediction results according to the optimal weight coefficient to obtain the final chaotic prediction result.