V-KGRU-based heating system set temperature prediction method

Abstract

The invention relates to the technical field of heating system temperature prediction, and particularly discloses a V-KGRU-based heating system set temperature prediction method. The method comprises the following steps: firstly, carrying out missing value filling and normalization preprocessing on original temperature data; secondly, decomposing the preprocessed data into K intrinsic mode functions through variational mode decomposition, and comprehensively determining the optimal decomposition number K through five indexes including sample entropy, energy entropy, information entropy, correlation coefficients and reconstruction errors; then, a gating circulation unit model based on a Kolmogorov-Arnold Network activation function is constructed, and then a gating circulation unit model is constructed based on the Kolmogorov-Arnold Network activation function; respectively predicting each intrinsic mode function component; and finally, weighting and stacking the prediction result according to the energy contribution proportion to obtain a temperature prediction value. According to the method, multi-scale feature extraction and self-adaptive nonlinear modeling are combined, the prediction precision is remarkably improved, experiments show that the mean absolute error is as low as 0.0850, the root-mean-square error is 0.0620, the method is superior to traditional gating circulation unit models, long-short-term memory network models and other models, and effective support is provided for heating intelligent regulation and control.

Description

Technical Field

[0001] This invention relates to the field of heating system temperature prediction technology, specifically a method for predicting the set temperature of a heating system based on V-KGRU. Background Technology

[0002] In the intelligent regulation of modern heating systems, accurate temperature prediction is a key technology for achieving efficient energy utilization and improving residents' comfort. With the development of deep learning and signal processing technologies, time series prediction models have been widely used in the field of heating temperature prediction. However, existing prediction methods still have many shortcomings when dealing with nonlinear and non-stationary data. For example, traditional recurrent neural networks (RNNs) are prone to gradient vanishing or gradient exploding problems when processing long-sequence data, making it difficult for them to capture long-term dependencies in time series. Although Long Short-Term Memory (LSTM) networks and gated recurrent units (GRUs) alleviate these problems to some extent by introducing gating mechanisms, they are still insufficient when dealing with complex nonlinear features, and the interpretability of the models is low. In addition, traditional time series prediction models usually model the raw data directly without fully considering the multi-scale features that may exist in the data, which limits the prediction accuracy and generalization ability of the models.

[0003] On the other hand, in the field of signal processing, Variational Mode Decomposition (VMD), as an advanced signal decomposition method, can decompose complex non-stationary signals into multiple relatively stationary intrinsic mode functions (IMFs), thereby effectively extracting multi-scale features from the signal. However, the decomposition effect of VMD is highly dependent on the choice of the number of decomposition modes. An inappropriate choice may lead to mode aliasing or the introduction of redundant information, thus affecting the accuracy of subsequent modeling. At the same time, existing methods, when combined with signal processing techniques and deep learning algorithms, often lack further optimization of the model's nonlinear expressive power, resulting in limited performance of the model when dealing with complex dynamic systems.

[0004] To address the aforementioned problems, there is an urgent need for a prediction model that combines advanced signal processing techniques and deep learning algorithms to improve the accuracy and intelligence of heating temperature prediction. Specifically, the following technical challenges need to be solved: first, how to effectively extract and utilize multi-scale features from time-series data; second, how to enhance the model's ability to capture complex nonlinear relationships while improving its interpretability and adaptability; and third, how to adaptively determine the optimal number of modes for signal decomposition to improve the efficiency and quality of feature extraction. To this end, this paper proposes a V-KGRU-based method for predicting the setpoint temperature of heating systems. This model significantly enhances the GRU model's ability to express complex nonlinear features by introducing the Kolmogorov-Arnold Network (KAN) activation function. Simultaneously, it utilizes VMD to extract multi-scale features from the original data and optimizes the number of decomposition modes through comprehensive indices, thereby achieving accurate prediction and intelligent control of heating temperature. This innovative combination not only improves the model's prediction accuracy but also provides deeper technical insights into time-series prediction problems, possessing significant practical application value. Summary of the Invention

[0005] This invention addresses the limitations of existing heating system temperature prediction methods by proposing a V-KGRU-based method for predicting setpoint temperatures in heating systems. The proposed model, by combining advanced signal processing techniques with deep learning algorithms, overcomes the shortcomings of traditional time series prediction models in handling nonlinear and non-stationary data.

[0006] This invention provides a method for predicting the set temperature of a heating system based on V-KGRU, comprising the following technical solutions: First, variational mode decomposition is used to extract multi-scale features from the original temperature data; second, a gated recurrent unit (KGRU) model based on the Kolmogorov-Arnold Network (KAN) activation function is constructed; finally, the prediction results of each decomposition mode are superimposed to obtain the final predicted value. The specific implementation of the technical solution is as follows:

[0007] Implementation of S1 variational mode decomposition

[0008] The variational mode decomposition (VMD) decomposes the original temperature data into multiple relatively stable intrinsic mode functions (IMFs). The decomposition effect is comprehensively evaluated using five metrics: sample entropy, energy entropy, information entropy, correlation coefficient, and reconstruction error, to determine the optimal number of decompositions, K. Specifically, for each IMF, the embedding dimension and time delay parameters are set to fixed values ​​to ensure computational consistency. When calculating sample entropy, the complexity of the time series is quantified by statistically counting the number of vector pairs satisfying the distance condition. Energy entropy, information entropy, and correlation coefficient are evaluated by calculating the energy distribution, probability distribution dispersion, and the strength of the linear relationship between the original and reconstructed signals, respectively. The reconstruction error is measured using Euclidean distance to measure the difference between the decomposed signal and the original signal. Combining these five metrics, a weighted summation is defined, and the number of decompositions that minimizes CM is selected as the optimal number of decompositions. After determining the optimal number of decompositions, an iterative solution is performed using the alternating direction multiplier method to update the IMFs, center frequencies, and Lagrange multipliers until the convergence condition is met.

[0009] Furthermore, S2 is constructed based on the gated recurrent unit of the Kolmogorov-Arnold Network.

[0010] The KGRU model replaces the activation function in the traditional GRU with a learnable KAN activation function. The KAN activation function approximates a multivariable function through a combination of univariate functions, and its core formula is as follows:

[0011] Update Gate:

[0012]

[0013] Reset Door:

[0014]

[0015] Candidate state:

[0016]

[0017] Current hidden state:

[0018]

[0019] in, and The KAN activation function's output range is adaptively adjusted using spline basis functions. Specifically, the mathematical expression for the spline basis function is:

[0020]

[0021] in, For B-spline basis functions, These are learnable coefficients. By optimizing these coefficients during training, the shape of the spline function is adjusted to adapt to the dynamic characteristics of the input data.

[0022] In particular, S3 predictions are overlaid with results.

[0023] Each IMF component is predicted using the KGRU model separately, yielding the corresponding prediction results. The prediction results of all IMF components are then superimposed to obtain the final prediction value. The superposition process employs a point-by-point weighted summation method, with weights determined based on the energy contribution ratio of each IMF component to ensure the accuracy of the prediction results.

[0024] The beneficial effects of this invention are as follows:

[0025] The V-KGRU model combines the deep learning-based GRU with VMD from the signal processing field, fully leveraging the advantages of both to significantly improve the model's ability to process complex nonlinear time series data. Furthermore, it introduces the KAN activation function to replace the activation function in the traditional GRU, enabling the model to adaptively adjust according to the dynamic characteristics of the data, better capturing complex nonlinear relationships in the sequence data, thereby improving the model's prediction accuracy. In addition, multiple metrics such as sample entropy and energy entropy are used to calculate a comprehensive index to optimize the number of decomposition modes in VMD, allowing the model to adaptively determine the optimal number of decompositions, thus extracting and utilizing key features from time series data more efficiently.

[0026] The technical effects of this invention have been demonstrated through experimental verification:

[0027] Experimental results show that the V-KGRU model performs excellently on the two key evaluation metrics: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), specifically: MAE = 0.0850 and RMSE = 0.0620. Compared with other methods (such as GRU, LSTM, RNN, etc.), the V-KGRU model significantly improves prediction performance, validating its advantages in capturing the nonlinear characteristics and complex relationships of heating temperature.

[0028] Furthermore, this invention clarifies the process of determining the optimal number of decompositions by analyzing evaluation indices for different decomposition numbers K. Experimental results show that when K=6, the comprehensive index CM reaches its minimum value, indicating that the decomposed intrinsic mode function components at this point have high regularity and can better reconstruct the original signal. This result supports the interpretability and analyzability of the model, making it easier to understand and apply.

[0029] In summary, the V-KGRU model proposed in this invention not only improves the accuracy of heating setpoint prediction but also provides deeper insights into time series forecasting problems through its modular design. Future research can further explore the model's generalization ability, computational efficiency, and integration with other input features to achieve more precise heating regulation, improve residents' quality of life, and reduce energy consumption and costs. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the variational mode decomposition process in an embodiment of the present invention;

[0031] Figure 2 This is a comprehensive evaluation index curve of the number of decomposition modes K in an embodiment of the present invention;

[0032] Figure 3 This is a time-frequency characteristic diagram of each IMF component after VMD decomposition in an embodiment of the present invention;

[0033] Figure 4 This is a comparison chart of the prediction results of each model and the actual values ​​in the embodiments of the present invention. Detailed Implementation

[0034] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] This invention provides a method for predicting the set temperature of a heating system based on V-KGRU, combined with the appendix. Figure 1 To be continued Figure 4 The specific implementation method is described in detail below. The specific implementation process of this invention combines signal processing technology with deep learning algorithms to achieve accurate prediction of the set temperature of a heating system, overcoming the shortcomings of traditional methods in handling nonlinear and non-stationary data.

[0036] The core of this invention lies in combining Variational Mode Decomposition (VMD) with a Gated Recurrent Unit (KGRU) based on the Kolmogorov-Arnold Network (KAN) activation function. By performing multi-scale feature extraction and modeling prediction on the raw temperature data, high-precision prediction of the set temperature of the heating system is ultimately achieved. The specific embodiments of this invention are described in detail below with reference to the accompanying drawings.

[0037] First, the raw temperature data undergoes preprocessing, including missing value imputation and normalization. Missing values ​​are imputed using the mean value method; for each feature, the mean of that feature is used to fill in the missing values, with the following formula: ,in Indicates missing values. This represents the sum of all valid values ​​for this feature. This indicates the number of valid values. Normalization is performed using the formula... This allows the data range to be limited to between 0 and 1, facilitating subsequent calculations and model training.

[0038] After preprocessing, the process proceeds to the Variational Mode Decomposition (VMD) stage. (See attached diagram.) Figure 1 As shown, VMD is used to decompose raw temperature data into multiple relatively stationary intrinsic mode functions (IMFs). In practice, the optimal number of decompositions, K, needs to be determined first. To achieve this, five evaluation metrics are introduced: sample entropy (SE), energy entropy (EE), information entropy (SHANNON), correlation coefficient (CORR), and reconstruction error (RE). These metrics measure the decomposition effect from different perspectives, and the K value that minimizes the comprehensive metric CM is selected as the optimal number of decompositions. Specifically, sample entropy quantifies the time series complexity through embedding dimension and time delay parameters, and its calculation formula is as follows: ,in This represents the number of vector pairs that satisfy the distance condition; the energy entropy is calculated by considering the energy distribution of each mode function, and the formula is... ,in Indicates the first The energy proportion of each modal function; information entropy assesses signal uncertainty through the degree of dispersion of the probability distribution, as shown in the formula: The correlation coefficient is calculated by examining the strength of the linear relationship between the original signal and the reconstructed signal, using the following formula: ,in Describing covariance, and Let represent the standard deviations respectively; the reconstruction error is measured by the Euclidean distance between the decomposed signal and the original signal, and the formula is: Based on the above five indicators, the comprehensive indicator CM is defined as a weighted summation, i.e. ,in The weighting coefficient is set according to actual needs. By calculating the CM value under different K values, the K value that minimizes CM is selected as the optimal number of decompositions. Specific test data is shown in the table below:

[0039]

[0040] The minimum sample entropy (0.1218) occurs at K=4, reflecting the lowest modal complexity; the minimum reconstruction error (74.1118) and the minimum comprehensive index (30.1039) both occur at K=6; although the correlation coefficient is highest at K=2 (0.6869), its reconstruction error (92.8554) is significantly higher than that at K=6. Based on the global optimality of the comprehensive index CM (CM is minimum at K=6) and the core weight of the reconstruction error, K=6 is selected as the optimal decomposition parameter, as follows. Figure 2 As shown in the graph.

[0041] After determining the optimal number of decompositions, the Alternating Directional Multiplier Method (ADMM) is used for iterative solution. Specifically, the formulas for updating the mode function, center frequency, and Lagrange multipliers are as follows: The mode function update formula is... The center frequency update formula is: The Lagrange multiplier update formula is: until the convergence condition is met. , where ϵ is a small positive number. (See attached diagram) Figure 3 As shown, the decomposed modal components (IMFs) exhibit different frequency characteristics in the same time domain, verifying the goodness of the decomposition effect.

[0042] After VMD decomposition, the model proceeds to the KGRU (Kind-Gated Recurrent Unit) construction phase based on the KAN activation function. The KGRU model replaces the activation function in the traditional GRU with a learnable KAN activation function to enhance the model's ability to capture complex nonlinear features. The KAN activation function approximates a multivariable function through a combination of univariate functions; its core formula is as follows: Update Gate Reset the door Candidate state The hidden state at the current moment ,in and The KAN activation function's output range is adaptively adjusted using spline basis functions. Specifically, the mathematical expression for the spline basis function is: ,in For B-spline basis functions, These are learnable coefficients. By optimizing these coefficients during training, the shape of the spline function is adjusted to adapt to the dynamic characteristics of the input data.

[0043] After constructing the KGRU model, predictions are made for each IMF component using the KGRU model. Specifically, the input data is mapped to a high-dimensional feature space through an embedding layer to obtain a feature representation, which is then fed into the KGRU layer along with the previous time step's hidden state. In the KGRU layer, the update gate and reset gate are calculated using the KAN activation function. The update gate controls the degree to which the previous time step's hidden state is preserved, while the reset gate determines the influence of the previous time step's hidden state on the candidate state. The candidate state is calculated using the activation function and combined with the result of the reset gate to generate the candidate state for the current time step. Finally, the hidden state for the current time step is obtained by weighted summation of the previous time step's hidden state and the candidate state through the update gate. The output of the KGRU layer is mapped to the target space through a fully connected layer to generate the final prediction result.

[0044] After forecasting each IMF component, the prediction results are superimposed to obtain the final predicted value. The superposition process employs a point-by-point weighted summation method, with weights determined based on the energy contribution ratio of each IMF component to ensure the accuracy of the prediction results. Specifically, the superposition formula is as follows: ,in Indicates the first Prediction results for each IMF component, This indicates the corresponding weight.

[0045] To comprehensively evaluate the predictive power of the proposed method (VMD-Kolmogorov Arnold Network Based on Gated Recurrent Unit, V-KGRU), this section compares it with several popular prediction models, including: Linear Regression (LR), Random Forest (RF), Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and the proposed method (V-KGRU). All methods were tested on the same benchmark dataset. The prediction results for different methods are shown in the table below:

[0046]

[0047] The above charts show that V-KGRU performs best among all methods, with the lowest MAE and RMSE values. This leads to the conclusion that the proposed V-KGRU model, based on a Gated Recurrent Unit (GRU), introduces the Kolmogorov-Arnold Network (KAN) activation function and incorporates decomposition and optimization steps, resulting in superior prediction performance compared to other methods. This demonstrates its advantage in capturing the nonlinear characteristics and complex relationships of heating temperatures. Comparing MAE and RMSE, GRU's prediction performance is slightly better than LSTM, indicating that GRU, as an excellent variant of LSTM, can improve prediction performance to some extent by introducing a gating mechanism. Furthermore, by simplifying the LSTM structure and reducing the number of parameters, it maintains high prediction capability. LSTM and GRU, as advanced models in deep learning, significantly outperform RNNs in prediction performance, demonstrating their ability to effectively address problems such as vanishing or exploding gradients encountered by RNNs. By introducing gating mechanisms, LSTM and GRU can better capture long-term dependencies in time series, thereby improving prediction accuracy.

[0048] To more intuitively demonstrate the prediction performance of each comparative experimental model, this method provides a comparison chart between the predicted and actual values ​​of each model, such as... Figure 4 As shown. The black dashed line represents the actual value of the heating setpoint temperature data, while the other colored solid or dashed lines represent the predicted values ​​of each model. From Figure 4 As can be seen, the V-KGRU model performs best in predicting heating setpoint temperatures, with its predicted curves highly overlapping with the actual values, significantly outperforming other models. In terms of the two key evaluation metrics, mean absolute error (MAE) and root mean square error (RMSE), the V-KGRU model achieves scores of 0.0850 and 0.0620, respectively, validating its advantage in capturing the nonlinear characteristics and complex relationships of heating temperatures.

[0049] In summary, the V-KGRU model proposed in this invention, by combining VMD and KGRU, fully leverages the advantages of both, significantly improving the model's ability to process complex nonlinear time series data. Furthermore, by introducing the KAN activation function and optimizing the number of VMD decomposition modes, the model's prediction accuracy and interpretability are further enhanced. Future research can further explore the model's generalization ability, computational efficiency, and integration with other input features to achieve more precise heating regulation, improve residents' quality of life, and simultaneously reduce energy consumption and costs.

[0050] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the set temperature of a heating system based on V-KGRU, characterized in that, Includes the following steps: S1. Preprocess the raw temperature data, including missing value imputation and normalization; S2. The preprocessed temperature data is decomposed into K IMFs using VMD, and the optimal number of decompositions K is determined by comprehensively considering five indicators: sample entropy, energy entropy, information entropy, correlation coefficient, and reconstruction error. S3. Construct a KGRU model based on the KAN activation function; S4. Predict each IMF component using the KGRU model; S5. The final temperature prediction value is obtained by weighting and superimposing the prediction results based on the energy contribution ratio of each IMF component.

2. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The method for determining the optimal number of decompositions K in step S2 is as follows: Calculate the index values ​​of sample entropy, energy entropy, information entropy, correlation coefficient, and reconstruction error under different K values; Define the comprehensive index CM as the weighted sum of five indicators, and select K, which minimizes the CM value, as the optimal number of decompositions.

3. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The method for constructing the KGRU model in step S3 is as follows: Replace the activation function in the traditional GRU with a learnable KAN activation function; The KAN activation function achieves adaptive adjustment of the output range through spline basis functions.

4. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 3, characterized in that, The KAN activation function is applied to the update gate, reset gate, candidate state and hidden state calculation of KGRU, and captures nonlinear features by dynamically adjusting spline coefficients.

5. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The weighted superposition method in step S5 is as follows: The weight of each IMF component is positively correlated with its energy contribution ratio; The final predicted value is the point-by-point weighted sum of the prediction results of each component.

6. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The preprocessing operation in step S1 includes: Missing values ​​were filled using the feature mean; Normalization scales the data to the 0,1 range.

7. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The VMD decomposition process in step S2 includes: The modal function, center frequency, and Lagrange multipliers are updated iteratively using the alternating direction multiplier method. The iteration termination condition is that the modal function converges to a preset threshold.

8. The method for predicting the set temperature of a heating system based on V-KGRU according to claim 1, characterized in that, The training process of the KGRU model includes: The input data is mapped to a high-dimensional feature space through the embedding layer; The KGRU layer controls the degree of retention of historical states by updating the gate and regulates the generation of candidate states by resetting the gate. The output layer maps the hidden state to the target temperature space.

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