A power load variable interval prediction method based on hammerstein-slfn under data missing

Abstract

The application belongs to the technical field of power load prediction, and relates to a power load variable interval prediction method based on Hammerstein-SLFN under data loss. A Hammerstein-SLFN nonlinear dynamic model is constructed, a variable interval parameter estimation framework is established, and parameters are updated only at measurable time points. Missing time points are recursively filled in by using the nearest measurable parameters, and a complete load sequence is constructed by fusing measured data and filling results. A variable interval multi-innovation mechanism is introduced, and a multi-innovation stochastic gradient recursion algorithm is used to complete parameter optimization and online prediction. The application directly realizes high-precision and high-stability power load prediction on original data containing loss without pre-interpolation or data elimination, and is suitable for smart grid, integrated energy management and other scenes.

Description

Technical Field

[0001] This invention belongs to the field of power load forecasting technology, specifically relating to a variable-interval power load forecasting method based on Hammerstein-SLFN under conditions of missing data. Background Technology

[0002] In new power systems, smart grids, integrated energy management, industrial park energy optimization, and user-side load analysis, power load forecasting is a core support for grid dispatching, demand response, energy storage synergy, and supply-demand balance. The accuracy of forecasting directly determines the rationality of power generation plans, the safety of grid operation, and energy utilization efficiency. Actual power load is influenced by multiple factors, including electricity consumption behavior, time-of-day patterns, meteorological disturbances, and equipment status, exhibiting strong nonlinearity, dynamic time-varying characteristics, and non-stationary characteristics.

[0003] Traditional linear models struggle to characterize complex temporal relationships in load forecasting, limiting their accuracy. The Hammerstein model, employing a static nonlinearity coupled with a dynamic linear series structure, enhances expressive power while reducing identification complexity, making it widely used for dynamic system modeling. The Hammerstein-SLFN model, which uses a single hidden layer feedforward neural network (SLFN) as the nonlinear element, accurately characterizes the nonlinear and temporal dynamics between load input and output, making it suitable for power load forecasting.

[0004] Existing Hammerstein-like model parameter identification methods (least squares, stochastic gradient, multi-innovation identification, etc.) all assume that the data is fully measurable and rely on continuous sampling to achieve recursive updates. However, in actual data acquisition, factors such as meter failures, sensor anomalies, communication interruptions, data packet loss, synchronization failures, and storage errors can lead to random, intermittent, or locally continuous missing load data. This prevents traditional algorithms from constructing effective innovations, reduces the number of available samples, and ultimately causes parameter estimation drift and a sharp deterioration in prediction performance.

[0005] To address data gaps, existing technologies generally employ a two-step process: interpolation followed by modeling. Independent interpolation introduces additional errors and disrupts the original temporal correlations. Interpolation and modeling are decoupled, making them unsuitable for online real-time prediction. Traditional multi-innovation methods rely on continuous and complete historical outputs, which cannot adapt to scenarios with varying intervals and irregular updates. The parameter update interval is fixed and cannot be adaptively adjusted according to the missing data pattern, making it difficult to balance real-time performance, data utilization, and prediction accuracy.

[0006] Currently, there is no power load forecasting method that can run directly on original load sequences containing missing values, while integrating variable interval parameter updates, online recursive filling of missing data, and multi-information optimization of variable intervals. This method cannot meet the high-precision and high-robustness online forecasting requirements of complex data environments in engineering sites. Summary of the Invention

[0007] To address the shortcomings of existing technologies, such as low prediction accuracy, poor robustness, inability to operate online, and reliance on pre-interpolation when data is missing, this invention provides a Hammerstein-SLFN-based method for predicting power load with varying intervals when data is missing, achieving end-to-end high-precision online prediction without interpolation or sample removal.

[0008] To achieve the objectives of this invention, the following technical solutions are adopted.

[0009] A method for predicting power load with varying intervals based on Hammerstein-SLFN under conditions of missing data includes the following steps:

[0010] S1. Construct a Hammerstein-SLFN power load prediction model with a single hidden layer feedforward neural network (SLFN) as the static nonlinear module and connected in series with a dynamic linear module, and form the parameter vector to be estimated and the corresponding information matrix.

[0011] S2. Divide the measurable time into the missing time and establish a variable interval parameter estimation framework. Perform parameter recursive updates only at the measurable time, and keep the parameters of the most recent measurable time unchanged at the missing time.

[0012] S3. For missing time points, online recursion is performed using the nonlinear and linear parameters of the most recently measurable time point to fill in the missing time point and obtain the predicted value of the missing time point.

[0013] S4. Integrate measured values ​​at measurable times with predicted values ​​at missing times to construct a complete available load sequence;

[0014] S5. Based on the measurable time sequence, construct a variable-interval stacked information vector containing current and historical measurable time information;

[0015] S6. Using the variable interval multi-innovation criterion function as the optimization objective, a negative gradient search is adopted to obtain the variable interval multi-innovation stochastic gradient recursion algorithm, which completes the recursive estimation of model parameters and online prediction of power load.

[0016] Furthermore, the Hammerstein-SLFN model characterizes the nonlinear dynamic time-series characteristics of power load through a static nonlinear and dynamic linear series structure; the model output is represented as a linear combination of parameter vectors and information matrices.

[0017] Furthermore, the variable interval parameter estimation framework adaptively adjusts the parameter update interval according to the data missing pattern. The set of update times consists only of measurable times, and the adjacent update intervals are not fixed but change dynamically with the missing data.

[0018] Furthermore, the predicted value of the missing time is calculated from the parameter of the most recently measurable time; when constructing the information matrix and information vector, historical missing data is replaced by the corresponding recursive predicted value.

[0019] Furthermore, the available load sequence takes the measured value at measurable times and the recursive predicted value at missing times, which is directly used for the construction of information matrix and information vector.

[0020] Furthermore, the stacked innovation vector is formed by stacking the innovations of the current time and the previous L−1 measurable times, where L is a preset innovation length, so as to make full use of the effective observation information of the variable interval.

[0021] Furthermore, the variable-interval multi-innovation criterion function adopts the vector 2 norm, which expands the single-time error into a multi-time cumulative error, thereby improving the accuracy of parameter estimation.

[0022] Furthermore, the variable-interval multi-innovation stochastic gradient recursion algorithm includes an adaptive step size, an overall extended information matrix, and a first-order partial derivative of the model output with respect to the parameters, thereby achieving stable recursive updates.

[0023] Furthermore, this method directly processes raw power load data containing random, intermittent, or continuous missing data, without the need for pre-interpolation or sample removal, and supports end-to-end online forecasting.

[0024] Beneficial effects:

[0025] 1. Directly handle missing data: No need for pre-imputation or sample removal, resulting in high data utilization;

[0026] 2. Variable interval adaptive update: The update time is automatically adjusted according to the missing pattern, resulting in strong stability;

[0027] 3. Online recursive imputation: Missing values ​​are predicted in real time without interrupting the prediction process;

[0028] 4. Enhanced accuracy through multiple new information: By accumulating historical effective new information, the parameters and prediction accuracy are significantly improved;

[0029] 5. Suitable for online engineering applications: low computational load, recursive execution, and strong real-time performance. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method described in this invention;

[0031] Figure 2 A graph showing the change of parameter estimation error with the number of iterations for different information lengths;

[0032] Figure 3 A graph showing the change in parameter estimation error with the number of iterations under a fixed information length;

[0033] Figure 4 This is a comparison chart of the actual load curve and the predicted curve under different news lengths. Detailed Implementation

[0034] The present invention will be further described in conjunction with the embodiments and accompanying drawings.

[0035] As an embodiment of the present invention, such as Figure 1 As shown, a method for predicting power load with varying intervals based on Hammerstein-SLFN under conditions of missing data is proposed:

[0036] Step 1, Problem Description:

[0037] Considering the significant nonlinear dynamic characteristics of power load sequences during their temporal evolution, the current load value is not only related to historical load conditions but also has a complex nonlinear mapping relationship with input features. To achieve recursive modeling and online prediction of power load sequences under conditions of missing data, a Hammerstein-SLFN network model is constructed, the mathematical model of which is described as follows:

[0038] ;

[0039] Among them, the model output This is the predicted value of electricity load; This is the parameter matrix for the linear dynamic part of the model; For connecting the first in SLFN The weight vectors of each hidden node and the output node; Connect the input node and the first node in SLFN The weight vector of each hidden node; For the first The bias of each hidden node; This represents the number of hidden layer nodes.

[0040] Define intermediate variables:

[0041] ;

[0042] ;

[0043] ;

[0044] Therefore, the Hammerstein-SLFN power load forecasting mathematical model described can be simplified as follows:

[0045] ;

[0046] Define the intermediate parameter vector and matrix:

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] And the information matrix:

[0052] ;

[0053] Furthermore, define the overall parameter vector:

[0054] ;

[0055] The Hammerstein-SLFN power load forecasting model can then be equivalently represented as the following identification model:

[0056] ;

[0057] Step Two: Prediction Method

[0058] Let the model output The predicted power load value is [value], while the actual measured load value is [value]. ,satisfy Define the set of all times as Load measurement value The set of missing moments is , for exist The complement in; when hour, Measurable data. Based on a set of measurable time points. With missing time set Define an integer sequence The sequence satisfies:

[0059] ;

[0060] And for all All have That is, the sequence consists only of measurable moments, and the update interval of adjacent parameters adapts to the power load data missing pattern.

[0061] For any missing time point satisfy The recursive prediction value used to fill in the missing power load data is:

[0062] ;

[0063] Among them, any missing time satisfy , , The most recent measurable time Nonlinear and linear parameter estimates; information vectors The construction relies on historical load data. If the load measurement value at a historical moment is missing, the corresponding recursive prediction value is used as a substitute.

[0064] Parameter updates are performed only at measurable times, and the parameter estimates remain unchanged between adjacent measurable times, i.e.:

[0065] ;

[0066] Based on this, usable output sequences are introduced. :

[0067]

[0068] in, For the missing time step, the recursive predicted value is; for the measurable time step... Available output Take the actual load measurement value ; at the missing moment (satisfy The output can be used to obtain the predicted value. This allows for the construction of a complete available load output sequence that integrates measured load data with missing data imputation results.

[0069] To enable the stacking and utilization of information from historically measurable moments, the following definition of information is made:

[0070] ;

[0071] in, The innovation length is used to characterize the number of historical measurable moments contained in the stacked innovation vector; To include only the currently measurable time. The expression for a single new interest is:

[0072] ;

[0073] Define the heap output vector corresponding to the heaped innovation vector:

[0074] ;

[0075] Define the stacked information matrix corresponding to the stacked information vector:

[0076] ;

[0077] Among them, information matrix The calculation depends on historical load output data, and its expression is:

[0078] ;

[0079] In the formula,

[0080] ;

[0081] At this point, the innovation vector can be equivalently represented as:

[0082] ;

[0083] Furthermore, to achieve dimension compatibility in matrix multiplication, the overall extended information matrix is ​​defined as follows:

[0084] ;

[0085] In the formula, Based on the most recently measurable time The single-time extended information vector constructed from the parameter estimates:

[0086] ;

[0087] In the formula, Output linear parameter estimates for the model The first-order partial derivative term, Output the model with respect to the nonlinear parameter estimates First-order partial derivatives:

[0088]

[0089] in:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] Minimize the following variable-interval multiple innovation criterion function using the negative gradient search:

[0097] ;

[0098] The variable-interval multi-innovation stochastic gradient recursion algorithm for estimating the parameters of the Hammerstein-SLFN power load forecasting model can be obtained as follows:

[0099] ;

[0100] in, The step size is used to control the magnitude of parameter updates and can be determined using a one-dimensional search method.

[0101] ,

[0102] Due to the information matrix Including nonlinear parameters to be estimated, the aforementioned one-dimensional search optimization problem exhibits nonlinear characteristics. To simplify the solution, this information matrix is... We perform a first-order Taylor expansion and discard higher-order terms; simultaneously, to ensure that the parameter estimates gradually converge to the true values, we constrain the step size to asymptotically approach zero, thus obtaining an approximately optimal step size:

[0103] ,

[0104] In the formula, For the step-size iteration term, satisfying the recurrence relation:

[0105]

[0106] Based on this, the variable-interval multi-innovation stochastic gradient recursion algorithm for estimating the parameters of the Hammerstein-SLFN power load forecasting model can be further expressed as:

[0107] .

[0108] As an embodiment 2 of the present invention, such as Figure 2 , Figure 3 and Figure 4 As shown, a simulation application example of a variable-interval modeling method based on Hammerstein SLFN under data missing conditions is presented.

[0109] First, numerical simulation is performed, assuming the true values ​​of the parameters are... , , , Zero-mean Gaussian white noise was used as the system disturbance, and the noise variance was set as follows: It covers low, medium, and high noise operating conditions. The system's initial state is set to... A total of 3000 sets of input and output data were collected. To simulate random data loss in actual engineering, the output was randomly marked as missing at a loss rate of 10%, with the missing locations randomly distributed and no large, continuous segments of missing data. The set of missing time points is defined as follows: Measurable time set is recorded as Measurable time series It consists of data from measurable time points. The initial values ​​for parameter estimation are set to... .

[0110] At every moment If the output If the information vector is obtained, the stacked information matrix and multiple information vectors are calculated using the index of the current measurable time step, and parameter updates are performed. If the output is missing, the parameter estimates are kept unchanged, and the predicted value is calculated using the parameter estimates from the previous measurable time step. And store it for subsequent information vector construction; the predicted value at the missing time point is... calculate.

[0111] To examine the impact of the innovation length on the algorithm performance, the innovation length was taken as follows: Compare them. When When the algorithm degenerates into a variable-interval single-inspiration stochastic gradient recursion algorithm, when... At that time, the algorithm utilizes the current and previous... Parameters are corrected based on historical information at measurable times. Fixed noise variance. With a data missing rate of 10%, the variable-interval multi-inspiration stochastic gradient recursion algorithm of this invention was run to estimate parameters under different inspiration lengths. The parameter estimation error increases with the number of recursions. The change curve, such as Figure 2 As shown, the error values ​​are summarized in Table 1. The results indicate that the parameter estimation error decreases significantly with increasing innovation length L. When After 3000 recursions, the parameter error decreased to 0.0468, while The error of the time interval (i.e., degenerating into a single-innovation algorithm) is 0.2070. The variable-interval multi-innovation algorithm reduces the error by about 77.39% compared with the variable-interval single-innovation algorithm, which verifies that by accumulating the innovations of historical measurable moments, the algorithm can make fuller use of the observation data and effectively improve the accuracy of parameter estimation.

[0112] Table 1. Parameter estimation errors under different innovation lengths ( (Data missing rate 10%)

[0113] Number of iterations k L=1 L=2 L=3 L=4 100 0.4680 0.3666 0.3277 0.3168 1000 0.2578 0.1201 0.0709 0.0534 2000 0.2227 0.0899 0.0534 0.0471 3000 0.2070 0.0817 0.0511 0.0468

[0114] Fixed news length The data missing rate is 10%, and the noise variance is calculated separately. The parameter estimation error varies with the number of iterations when running the variable-interval multi-innovation stochastic gradient recursion algorithm of this invention, as shown in the curve. Figure 3 As shown, the error values ​​are summarized in Table 2. The results indicate that the smaller the noise variance, the higher the parameter estimation accuracy; when... When, after 3000 recursions, the error is 0.0468; when At that time, the error was 0.3226, significantly higher than the former. This indicates that noise has a certain impact on the accuracy of the algorithm's parameter estimation, but the algorithm can still converge to a better estimation accuracy in high-noise environments by increasing the number of iterations.

[0115] Table 2 Parameter estimation errors under different noise variances ( (Data missing rate 10%)

[0116] Number of iterations k 100 0.3168 0.4896 0.6661 0.7799 1000 0.0534 0.1756 0.2672 0.3438 2000 0.0471 0.1728 0.2626 0.3303 3000 0.0468 0.1725 0.2598 0.3226

[0117] Furthermore, to verify the effectiveness of the proposed variable-interval multi-innovation stochastic gradient recursion algorithm on real data, a modeling and prediction experiment was conducted using 10 consecutive days of electricity load data from a certain region in August 2018. The load data sampling interval was 15 minutes, with 96 sampling points per day. The data from the first 9 days was used as the training set, and the data from the 10th day was used as the test set, constituting a single-step advance prediction task. The original load data was normalized, with the system state vector representing the load value at the previous moment, and the input vector containing the 7 historical load values ​​prior to the current moment and the intraday time trend term. To simulate the common random missing output situation in real systems, the 10% missing rate commonly used in engineering simulations was adopted. In the training set, some output samples were randomly marked as missing at a 10% missing rate, while ensuring that the first sample was not missing to guarantee algorithm startup.

[0118] To examine the length of the new information The impact on prediction performance was assessed by selecting multiple different groups. The algorithm of this invention is executed. When When the algorithm degenerates into the variable-interval single-inspiration stochastic gradient recursion algorithm (SG); when This refers to the Variable Interval Multiple Innovation Stochastic Gradient Recursive Algorithm (MISG) proposed in this invention. For each After training, a one-step advance prediction is performed on the test set, and the root mean square error between the predicted value and the true value is calculated.

[0119] Figure 4 The actual load curve is given. (SG) prediction curve and The following is a comparison of the MISG prediction curves. It can be seen that the MISG algorithm's predicted trajectory is closer to the actual load throughout the entire time axis, especially during periods of significant load fluctuation, where its tracking ability is significantly superior to the SG algorithm. The MISG algorithm demonstrates a significant performance improvement over the SG algorithm. Specifically, the root mean square error of MISG is reduced by approximately 32%, the mean absolute percentage error is reduced by approximately 36%, and the coefficient of determination... The accuracy improved from approximately 0.89 to approximately 0.95. These results fully demonstrate the superiority of the algorithm of this invention in scenarios where real load data is missing, significantly improving prediction accuracy and demonstrating good engineering application value.

[0120] In summary, the variable-interval multi-innovation stochastic gradient recursion algorithm proposed in this invention can effectively solve the parameter estimation problem of the Hammerstein-SLFN prediction model under conditions of missing power load data. By performing parameter updates at measurable times, keeping parameters unchanged at missing times, and using a recursive prediction mechanism to compensate for missing outputs, the algorithm can still achieve convergence of parameter estimation and high-precision prediction of power load even with a missing rate of 10%. The multi-innovation mechanism can significantly improve the accuracy of parameter estimation, thereby improving the accuracy of power load prediction. As the length of the innovation increases, the parameter estimation error gradually decreases, indicating that stacking historical innovations can make fuller use of limited effective data. This embodiment verifies the effectiveness of the proposed variable-interval multi-innovation stochastic gradient recursion algorithm in power load prediction scenarios, enabling high-precision prediction even when load data is not fully available.

Claims

1. A method for predicting power load with varying intervals based on Hammerstein-SLFN under conditions of missing data, characterized in that, Includes the following steps: S1. Construct a Hammerstein-SLFN power load prediction model with a single hidden layer feedforward neural network (SLFN) as the static nonlinear module and connected in series with a dynamic linear module, and form the parameter vector to be estimated and the corresponding information matrix. S2. Divide the measurable time into the missing time and establish a variable interval parameter estimation framework. Perform parameter recursive updates only at the measurable time, and keep the parameters of the most recent measurable time unchanged at the missing time. S3. For missing time points, online recursion is performed using the nonlinear and linear parameters of the most recently measurable time point to fill in the missing time point and obtain the predicted value of the missing time point. S4. Integrate measured values ​​at measurable times with predicted values ​​at missing times to construct a complete available load sequence; S5. Based on the measurable time sequence, construct a variable-interval stacked information vector containing current and historical measurable time information; S6. Using the variable interval multi-innovation criterion function as the optimization objective, a negative gradient search is adopted to obtain the variable interval multi-innovation stochastic gradient recursion algorithm, which completes the recursive estimation of model parameters and online prediction of power load.

2. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The Hammerstein-SLFN model characterizes the nonlinear dynamic time-series characteristics of power load through a static nonlinear and dynamic linear series structure; the model output is represented as a linear combination of parameter vectors and information matrices.

3. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The variable interval parameter estimation framework adaptively adjusts the parameter update interval according to the data missing pattern. The set of update times consists only of measurable times, and the adjacent update intervals are not fixed but change dynamically with the missing data.

4. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The predicted value of the missing time is calculated from the parameters of the most recently measurable time; when constructing the information matrix and information vector, historical missing data is replaced by the corresponding recursive predicted value.

5. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The available load sequence takes the measured value at measurable times and the recursive predicted value at missing times, and is directly used for the construction of information matrix and information vector.

6. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The stacked innovation vector is formed by stacking the innovations of the current time and the previous L−1 measurable times, where L is a preset innovation length, so as to make full use of the effective observation information of the variable interval.

7. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The variable-interval multi-innovation criterion function uses the vector 2 norm to expand the single-time error into a multi-time cumulative error, thereby improving the accuracy of parameter estimation.

8. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, The variable-interval multi-innovation stochastic gradient recursion algorithm includes an adaptive step size, an overall extended information matrix, and first-order partial derivatives of the model output with respect to the parameters, achieving stable recursive updates.

9. The method for predicting power load with varying intervals based on Hammerstein-SLFN under data missing conditions as described in claim 1, characterized in that, This method directly processes raw power load data containing random, intermittent, or continuous missing data, without the need for pre-interpolation or sample removal, and supports end-to-end online forecasting.

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