Load prediction multidimensional data preprocessing method
By combining kernel function and factor analysis, the problem of traditional linear dimensionality reduction methods failing to capture the nonlinear characteristics of load data is solved, thus improving the accuracy of load forecasting and the dimensionality reduction effect.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGDONG UNIV OF TECH
- Filing Date
- 2025-12-05
- Publication Date
- 2026-04-24
AI Technical Summary
Traditional linear dimensionality reduction methods struggle to capture the nonlinear characteristics of load data, leading to information loss or decreased model interpretability.
A method combining kernel functions and factor analysis is adopted. Trend components are extracted through STL decomposition, inflection points are detected, and linear and adaptive polynomial kernel functions are used for approximation. After constructing the kernel matrix, factor analysis is performed to reduce dimensionality.
It effectively captures the nonlinear relationships in load data, provides accurate multi-dimensional data predictions, reduces redundant analysis and calculations, simplifies observation data, and interprets complex problems.
Smart Images
Figure CN121920586A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of load forecasting, specifically relating to a method for preprocessing multidimensional load forecasting data. Background Technology
[0002] Load forecasting is crucial for optimizing power resource allocation, reducing power supply costs, ensuring the reliability of electricity supply for residential use, and for power grid planning and upgrading. However, power load data contains multidimensional variables such as user electricity consumption behavior, seasonal cycles, and weather characteristics. Directly modeling high-dimensional data can lead to the curse of dimensionality and increase the computational burden on algorithms.
[0003] Traditional linear dimensionality reduction methods, such as principal component analysis and factor analysis, are unable to capture the nonlinear characteristics of load data, leading to information loss or decreased model interpretability. Summary of the Invention
[0004] In order to overcome the problem that existing technologies are unable to capture the nonlinear characteristics of load data, this invention provides a multidimensional data preprocessing method for load forecasting.
[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention relates to a method for preprocessing multidimensional load forecasting data, comprising the following steps: Step 1: Obtain the time series of load data composed of multidimensional load data; Step 2: Decompose the load data time series to obtain trend components, where the trend components refer to the long-term trend series in the load data time series; Step 3: Based on the trend components, obtain the inflection point of the load data time series; Step 4: Approximate the load data at non-inflection points using a linear kernel function. For the load data at inflection points, approximate it using a preset adaptive polynomial kernel function. Obtain the first kernel function based on the linear kernel function and the adaptive polynomial kernel function. Step 5: Construct the kernel matrix based on the first kernel function; Step 6: Perform nonlinear analysis on the kernel matrix using factor analysis to obtain the dimensionality-reduced load data.
[0006] The multidimensional load data includes load dimension, temperature dimension, humidity dimension, precipitation dimension, and special day dimension.
[0007] Specifically, the time series of the load data is decomposed to obtain trend components, including: The load data time series is decomposed using STL to obtain trend components.
[0008] Further, based on the trend components, the inflection points of the load data time series are obtained, including: The trend components are smoothed. Then, the second derivative of the smoothed trend component is taken to obtain the inflection point of the load data time series.
[0009] The preset adaptive polynomial kernel function includes:
[0010] In the formula, It is the output of the kernel function. , These represent the load data input vectors in the i-th row and j-th column of the original feature space, respectively. It is a feature mapping function; It is the scaling factor; Indicates transpose. It is a learnable feature interaction matrix. This represents the bias term, and d is the degree of the polynomial.
[0011] Specifically, the eigenvectors of the feature interaction matrix W are:
[0012] In the formula: Weights for load data, Weighting of average temperature Weighting for the highest temperature Weighted by the lowest temperature For the weight of humidity, For the weight of precipitation, For the weekend weight, Weighting for holidays.
[0013] Furthermore, the feature interaction matrix W is optimized end-to-end using a gradient descent algorithm with the objective of minimizing the loss function of the load prediction task; the loss function is the mean squared error loss method, and the formula is:
[0014] In the formula, It is the mean squared error. This is the actual load value at time point a. The predicted load value is backpropagated to the feature interaction matrix W using the loss gradient. This represents the Nth time point.
[0015] In step 5, the kernel matrix is constructed. The kernel matrix is calculated by the first kernel function, and the formula for the first kernel function is as follows: Y ij =
[0016] In the formula: m represents the number of rows or columns of the feature interaction matrix W, T represents the transpose, and Y... ij、 These represent the kernel matrix elements in the i-th row and j-th column of the first kernel function, and the elements in the i-th row and j-th column of the feature interaction matrix, respectively.
[0017] Furthermore, in the nonlinear analysis of the kernel matrix using factor analysis, the dimensionality-reduced loading data obtained includes: Factor analysis was used to calculate the constructed kernel matrix, and the factor loading matrix of the loading data was obtained. Then, the factor loading matrix is analyzed to separate out the common factors; Then, based on the common factors, the dimensionality-reduced load data is obtained.
[0018] The factor analysis method described above has the following expression:
[0019] In the formula, This refers to standardized multidimensional load data; These are common components, representing the shared information of common factors in the load data; Let Y be the factor loading matrix, and Y be the kernel matrix calculated by the first kernel function. This is a special factor vector that represents the portion of the load data that cannot be explained by common factors.
[0020] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: Traditional linear dimensionality reduction methods, such as principal component analysis and factor analysis, struggle to capture the nonlinear characteristics of load data, leading to information loss or decreased model interpretability. This method combines the dual characteristics of kernel functions and factor analysis, enabling it to capture nonlinear relationships in load data and provide a low-dimensional representation for subsequent tasks such as load forecasting and anomaly detection. Furthermore, this method continuously adapts to changes in load forecasting, providing accurate predictions for multi-dimensional data and reducing redundant analysis and calculations. This simplifies observational data and allows for the explanation of complex problems using a few variables. Attached Figure Description
[0021] Figure 1 The flowchart illustrates a multidimensional data preprocessing method for load forecasting provided by this invention.
[0022] Figure 2 This is a diagram of the kernel factor feature interaction matrix after performing the novel kernel matrix factor analysis method in the third embodiment of the present invention. Detailed Implementation
[0023] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.
[0024] The terms "first," "second," "third," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.
[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0026] In the first embodiment of the present invention, a method for preprocessing multidimensional load forecasting data is provided. The specific technical method is as follows, and based on... Figure 1 The content will be explained and clarified: This invention relates to a method for preprocessing multidimensional load forecasting data, comprising the following steps: Step 1: Obtain the time series of load data composed of multidimensional load data; The multidimensional load data includes load dimension, temperature dimension, humidity dimension, and precipitation dimension.
[0027] Step 2: Decompose the load data time series to obtain trend components, where the trend components refer to the long-term trend series in the load data time series; Specifically, the time series of the load data is decomposed to obtain trend components, including: The load data time series is decomposed using STL to obtain trend components.
[0028] Step 3: Based on the trend components, obtain the inflection point of the load data time series; The inflection point of the load data time series is obtained based on the trend component, including: The trend components are smoothed. Then, the second derivative of the smoothed trend component is taken to obtain the inflection point of the load data time series.
[0029] Step 4: Approximate the load data at non-inflection points using a linear kernel function. For the load data at inflection points, approximate it using a preset adaptive polynomial kernel function. Obtain the first kernel function based on the linear kernel function and the adaptive polynomial kernel function. The preset adaptive polynomial kernel function includes:
[0030] In the formula, It is the output of the kernel function. , These represent the load data input vectors in the i-th row and j-th column of the original feature space, respectively. It is a feature mapping function; It is the scaling factor; Indicates transpose. It is a learnable feature interaction matrix. This represents the bias term, and d is the degree of the polynomial.
[0031] Specifically, the eigenvectors of the feature interaction matrix W are:
[0032] In the formula: Weights for load data, Weighting of average temperature Weighting for the highest temperature Weighted by the lowest temperature For the weight of humidity, The weighting of precipitation.
[0033] Furthermore, the feature interaction matrix W is optimized end-to-end using a gradient descent algorithm with the objective of minimizing the loss function of the load prediction task; the loss function is the mean squared error loss method, and the formula is:
[0034] In the formula, It is the mean squared error. This is the actual load value at time point a. The predicted load value is backpropagated to the feature interaction matrix W using the loss gradient. This represents the Nth time point.
[0035] Step 5: Construct the kernel matrix based on the first kernel function; The kernel matrix is constructed by calculating a first kernel function, the formula of which is as follows: Y ij =
[0036] In the formula: m represents the number of rows or columns of the feature interaction matrix W, T represents the transpose, and Y... ij、 These represent the kernel matrix elements in the i-th row and j-th column of the first kernel function, and the elements in the i-th row and j-th column of the feature interaction matrix, respectively.
[0037] Step 6: Perform nonlinear analysis on the kernel matrix using factor analysis to obtain the dimensionality-reduced load data.
[0038] The nonlinear analysis of the kernel matrix using factor analysis to obtain the dimensionality-reduced loading data includes: Factor analysis was used to calculate the constructed kernel matrix, and the factor loading matrix of the loading data was obtained. Then, the factor loading matrix is analyzed to separate out the common factors; Then, based on the common factors, the dimensionality-reduced load data is obtained.
[0039] The factor analysis method described above has the following expression:
[0040] In the formula, This refers to standardized multidimensional load data; These are common components, representing the shared information of common factors in the load data; Let Y be the factor loading matrix, and Y be the kernel matrix calculated by the first kernel function. This is a special factor vector that represents the portion of the load data that cannot be explained by common factors.
[0041] In a second embodiment of the present invention, a method for preprocessing multidimensional load forecasting data is provided, the specific technical method of which is as follows: This invention relates to a method for preprocessing multidimensional load forecasting data, comprising the following steps: Step 1: Obtain the time series of load data composed of multidimensional load data; The multidimensional load data includes load dimension, temperature dimension, humidity dimension, and special day dimension. The special day dimension includes the weekend dimension and the holiday dimension.
[0042] Step 2: Decompose the load data time series to obtain trend components, where the trend components refer to the long-term trend series in the load data time series; Specifically, the time series of the load data is decomposed to obtain trend components, including: The load data time series is decomposed using STL to obtain trend components.
[0043] Step 3: Based on the trend components, obtain the inflection point of the load data time series; The inflection point of the load data time series is obtained based on the trend component, including: The trend components are smoothed. Then, the second derivative of the smoothed trend component is taken to obtain the inflection point of the load data time series.
[0044] Step 4: Approximate the load data at non-inflection points using a linear kernel function. For the load data at inflection points, approximate it using a preset adaptive polynomial kernel function. Obtain the first kernel function based on the linear kernel function and the adaptive polynomial kernel function. The preset adaptive polynomial kernel function includes:
[0045] In the formula, It is the output of the kernel function. , These represent the load data input vectors in the i-th row and j-th column of the original feature space, respectively. It is a feature mapping function; It is the scaling factor; Indicates transpose. It is a learnable feature interaction matrix. This represents the bias term, and d is the degree of the polynomial.
[0046] Specifically, the eigenvectors of the feature interaction matrix W are:
[0047] In the formula: Weights for load data, Weighting of average temperature Weighting for the highest temperature Weighted by the lowest temperature For the weight of humidity, Weighting for holidays.
[0048] Furthermore, the feature interaction matrix W is optimized end-to-end using a gradient descent algorithm with the objective of minimizing the loss function of the load prediction task; the loss function is the mean squared error loss method, and the formula is:
[0049] In the formula, It is the mean squared error. This is the actual load value at time point a. The predicted load value is backpropagated to the feature interaction matrix W using the loss gradient. This represents the Nth time point.
[0050] Step 5: Construct the kernel matrix based on the first kernel function; The kernel matrix is constructed by calculating a first kernel function, the formula of which is as follows: Y ij =
[0051] In the formula: m represents the number of rows or columns of the feature interaction matrix W, T represents the transpose, and Y... ij、 These represent the kernel matrix elements in the i-th row and j-th column of the first kernel function, and the elements in the i-th row and j-th column of the feature interaction matrix, respectively.
[0052] Step 6: Perform nonlinear analysis on the kernel matrix using factor analysis to obtain the dimensionality-reduced load data.
[0053] The nonlinear analysis of the kernel matrix using factor analysis to obtain the dimensionality-reduced loading data includes: Factor analysis was used to calculate the constructed kernel matrix, and the factor loading matrix of the loading data was obtained. Then, the factor loading matrix is analyzed to separate out the common factors; Then, based on the common factors, the dimensionality-reduced load data is obtained.
[0054] The factor analysis method described above has the following expression:
[0055] In the formula, This refers to standardized multidimensional load data; These are common components, representing the shared information of common factors in the load data; Let Y be the factor loading matrix, and Y be the kernel matrix calculated by the first kernel function. This is a special factor vector that represents the portion of the load data that cannot be explained by common factors.
[0056] In a third embodiment of the present invention, a method for preprocessing multidimensional load forecasting data is provided. The specific technical method is as follows, combined with... Figure 2 Explanation: Electricity load data from a coastal city in Guangdong Province from January to December 2018 was selected. This data includes data collected over a 15-minute period, including the highest, lowest, and average temperatures, humidity, rainfall, and load within that timeframe.
[0057] The STL method is used to extract the trend term from the load curve, and then the inflection point of the trend term is detected. The STL decomposition method expression is:
[0058] in Time series, It is a trend term, representing smooth, low-frequency changes in the time series; It is a seasonal item, representing fluctuations within a fixed period; The residual term represents noise or anomalies.
[0059] The trend components are further smoothed, and the inflection points of the time series are obtained by detecting the second derivative.
[0060] A polynomial kernel function is used for the selected inflection points, and a linear kernel function is used for the other data points.
[0061] The kernel function expression is:
[0062] This function is a linear kernel function. c is a bias term, which is usually 0 or 1.
[0063] A novel adaptive polynomial kernel function expression is as follows:
[0064] W is an m×m learnable feature interaction matrix. The feature vectors are:
[0065] The feature interaction matrix is as follows:
[0066] in, express The weighting of the load's driving effect on temperature, and other factors, are similar. If Much larger This means that the model considers temperature to have a far greater impact on the load than humidity.
[0067] A kernel matrix is constructed using kernel functions, implicitly mapping data to a high-dimensional space H. A novel polynomial kernel is used to handle nonlinear, high-dimensional, and highly localized data, preserving key inflection points of the load curve. This kernel captures the interaction effects between features such as load, temperature, and special days through multivariate coupling. Other non-inflection points are approximated using linear kernel functions, and the large-scale data in the traditional dense kernel matrix is zeroed out to reduce data complexity and storage overhead.
[0068] Specifically, a polynomial kernel function is used for inflection points, and a linear kernel function is used for other data points. The two functions are combined into the first kernel function, and then the kernel matrix is constructed. The kernel matrix is calculated from the first kernel function, and the formula for the first kernel function is as follows: Y ij =
[0069] Wherein: , Let m represent the load data input vector in the i-th row and j-th column of the original feature space, m represent the number of rows or columns of the interactive matrix W, and T represent the transpose.
[0070] Then, factor analysis was used to analyze the kernel matrix. The expression for factor analysis is as follows:
[0071] In the formula, This refers to standardized multidimensional load data; These are common components, representing the shared information of common factors in the load data; Let Y be the factor loading matrix, and Y be the kernel matrix calculated by the first kernel function. This is a special factor vector that represents the portion of the load data that cannot be explained by common factors.
[0072] Factor analysis models are based on the following assumptions: (1) That is, the mean of each factor is 0; (2) That is, the common factors are all uncorrelated; (3) That is, the common factors and the specific factors are uncorrelated; (4) The mean of each specific factor is zero; That is, each special factor is independent of the others.
[0073] The covariance structure is as follows:
[0074] Log-likelihood function:
[0075] in, It is the sample covariance. It is the sample mean:
[0076]
[0077] Objective function:
[0078] The method for solving the objective function is as follows: Solve using the EM algorithm. E represents the expectation step, and the conditional expectation of the latent factors is calculated:
[0079]
[0080]
[0081] M represents the maximization step, updating parameters. :
[0082]
[0083] To ensure convergence, check for parameter changes:
[0084] The final loading matrices of the first three common factors are shown in Table 1: Table 1 Loading matrices of the first three common factors
[0085] As shown above, the kernel matrix successfully separated three factors, of which factor 1 is mainly driven by load trends; factor 2 is mainly driven by temperature, capturing the impact of weather on load; and factor 3 is mainly driven by special days, capturing the holiday effect.
[0086] Depend on Figure 2 The feature interaction matrix reveals that the similarity between special days is significantly higher than other combinations, indicating that special days at different time points have a similar trend and a significant driving force on load, thus forming clear highlighted blocks in the kernel matrix. The driving weight of temperature on load is significantly positive, consistent with the physical law that high temperatures lead to a surge in air conditioning load. The suppressive weight of special days on load is negative, reflecting the characteristic of decreased industrial electricity consumption during holidays. The inverse weight of load on temperature is close to zero, indicating that the model correctly ignores the physically infeasible impact of electricity load on air temperature. Temperature-to-temperature represents the contribution weight of temperature features to their own similarity; that is, if the temperature values at two time points are similar, their similarity should be high.
[0087] The variance contribution rate, efficiency, and sparsity of the novel kernel function are compared with those of polynomial and linear kernel functions. The results are shown in Table 2. Table 2 Comparison of the novel kernel function with polynomial and linear kernel functions
[0088] The above comparison shows that this novel kernel function can explain 89.36% of the variance using only 3 common factors, significantly higher than other methods, proving its higher information compression efficiency. It also boasts higher effective rank, meaning the kernel matrix contains more effective information dimensions; and moderate sparsity, meaning it reduces computation while retaining key information.
[0089] In this embodiment, the original six characteristic variables affecting the load were reduced in dimensionality and integrated into three factors that could well explain the original data through kernel matrix factor analysis. The factor loadings of each factor and the proportion of variance explained by the original data were calculated. Subsequent research was carried out between the three selected factors and the newly generated data, thus achieving dimensionality reduction of multidimensional data.
[0090] The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.
Claims
1. A method for preprocessing multidimensional load forecasting data, characterized in that, Includes the following steps: Step 1: Obtain the time series of load data composed of multidimensional load data; Step 2: Decompose the load data time series to obtain trend components, where the trend components refer to the long-term trend series in the load data time series; Step 3: Based on the trend components, obtain the inflection point of the load data time series; Step 4: Approximate the load data at non-inflection points using a linear kernel function. For the load data at inflection points, approximate it using a preset adaptive polynomial kernel function. Obtain the first kernel function based on the linear kernel function and the adaptive polynomial kernel function. Step 5: Construct the kernel matrix based on the first kernel function; Step 6: Perform nonlinear analysis on the kernel matrix using factor analysis to obtain the dimensionality-reduced load data.
2. The load forecasting multidimensional data preprocessing method according to claim 1, characterized in that, The multidimensional load data includes load dimension, temperature dimension, humidity dimension, precipitation dimension, and special day dimension.
3. The load forecasting multidimensional data preprocessing method according to claim 1, characterized in that, The time series of the load data is decomposed to obtain trend components, including: The load data time series is decomposed using STL to obtain trend components.
4. The load forecasting multidimensional data preprocessing method according to claim 3, characterized in that, Based on the trend components, the inflection points of the load data time series are obtained, including: 4.1 Smooth the trend components; 4.2 The second derivative of the smoothed trend component is taken to obtain the inflection point of the load data time series.
5. The load forecasting multidimensional data preprocessing method according to claim 1, characterized in that, The preset adaptive polynomial kernel function includes: In the formula, It is the output of the kernel function. , These represent the load data input vectors in the i-th row and j-th column of the original feature space, respectively. It is a feature mapping function; It is the scaling factor; Indicates transpose. It is a learnable feature interaction matrix. This represents the bias term, and d is the degree of the polynomial.
6. The load forecasting multidimensional data preprocessing method according to claim 5, characterized in that, The eigenvectors of the feature interaction matrix W are: In the formula: Weights for load data, Weighting of average temperature Weighting for the highest temperature Weighted by the lowest temperature For the weight of humidity, For the weight of precipitation, For the weekend weight, Weighting for holidays.
7. The load forecasting multidimensional data preprocessing method according to claim 6, characterized in that, The feature interaction matrix W is optimized end-to-end using a gradient descent algorithm with the objective of minimizing the loss function of the load prediction task; the loss function is the mean squared error loss method, and the formula is: In the formula, It is the mean squared error. This is the actual load value at time point a. The predicted load value is backpropagated to the feature interaction matrix W using the loss gradient. This represents the Nth time point.
8. The load forecasting multidimensional data preprocessing method according to claim 7, characterized in that: The kernel matrix is constructed in step 5. The kernel matrix is calculated by the first kernel function, and the formula for the first kernel function is as follows: Y ij = In the formula: m represents the number of rows or columns of the feature interaction matrix W, T represents the transpose, and Y... ij、 These represent the kernel matrix elements in the i-th row and j-th column of the first kernel function, and the elements in the i-th row and j-th column of the feature interaction matrix, respectively.
9. The load forecasting multidimensional data preprocessing method according to claim 8, characterized in that: In the nonlinear analysis of the kernel matrix using factor analysis, the dimensionality-reduced loading data is obtained, including: 9.1 The factor loading matrix of the loading data is obtained by calculating the constructed kernel matrix using factor analysis. 9.2 Analyze the factor loading matrix and isolate common factors; 9.3 Based on the aforementioned common factors, the dimensionality-reduced load data is obtained.
10. The load forecasting multidimensional data preprocessing method according to claim 9, characterized in that: The aforementioned factor analysis method has the following expression: In the formula, This refers to standardized multidimensional load data; These are common components, representing the shared information of common factors in the load data; Let Y be the factor loading matrix, and Y be the kernel matrix calculated by the first kernel function. This is a special factor vector that represents the portion of the load data that cannot be explained by common factors.