Bayesian neural network-based power system load probability prediction method and device

Abstract

The application discloses a power system load probability prediction method and device based on a Bayesian neural network. The method obtains original historical load data from a power distribution system or a user-side load collection device, and pre-processes the original historical load data to obtain a standardized model input sequence. A double-branch feature extraction module is constructed to extract load internal time sequence features and multiple fractal features from the standardized model input sequence. Cross-attention mechanism is used to fuse the two features, and SHAP mechanism is used for feature refining to obtain refined features. The refined features are input into a Bayesian attention layer, a fractal-guided Bayesian feedforward neural network and a Bayesian linear output layer. The fractal parameters guide the Bayesian neural network to adaptively adjust the inference parameters, complete the load probability prediction and output the probability prediction result. The application solves the problems of existing technologies, such as difficulty in self-adaptive adaptation to load complexity and uncertainty.

Description

Technical Field

[0001] This invention relates to the field of power system load forecasting technology, and specifically to a method and apparatus for probabilistic power system load forecasting based on Bayesian neural networks. Background Technology

[0002] Currently, load forecasting technology has been widely applied in distribution systems at all levels, electricity market transactions, and demand-side response mechanisms. With the high proportion of distributed generation connected to the grid and the advancement of new power system construction, load characteristics are exhibiting strong randomness, multi-timescale coupling, and complex nonlinear features. Traditional load forecasting methods are also gradually evolving from single-point forecasting to probabilistic forecasting. At present, the mainstream technical path in the industry is mostly based on deep learning models (such as CNN, LSTM, Transformer, etc.) to build a forecasting framework, achieving short-term / medium-to-long-term load forecasting by mining the temporal dependencies of load sequences. At the same time, Bayesian neural networks, due to their ability to quantify model forecasting uncertainty, are widely used in probabilistic forecasting scenarios, showing good application potential in areas such as grid dispatch risk assessment, reserve capacity configuration, and refined management of user-side load. Related technologies have been implemented in engineering projects in distribution network operation and maintenance platforms and power load management systems in many places.

[0003] However, existing load probability prediction technologies still face core bottlenecks that are difficult to overcome: First, most solutions only focus on the explicit temporal patterns of load sequences, ignoring the implicit structural complexity behind load fluctuations. This results in models failing to accurately characterize the long-range correlation and self-similarity of load sequences, leading to a significant decrease in prediction accuracy and robustness when facing complex load scenarios. Second, traditional Bayesian neural networks often use fixed-value settings for inference parameters, lacking a dynamic correlation mechanism with load fractal characteristics. This makes it difficult to adaptively adjust the model structure and inference strategy according to the complexity of the load sequence, resulting in insufficient characterization of prediction uncertainties in complex scenarios and redundant computational resources in simple scenarios. Furthermore, existing methods lack multi-dimensional and accurate quantification and evaluation mechanisms for prediction results, making it difficult to effectively support the actual needs of safe operation and decision optimization in power systems.

[0004] Therefore, there is an urgent need for a power system load probability prediction method based on Bayesian neural networks to solve the problems of difficulty in adaptively adapting to load complexity and uncertainty in existing technologies. Summary of the Invention

[0005] To address these issues, this invention provides a power system load probability prediction method and apparatus based on Bayesian neural networks, which solves the problems of existing load prediction technologies neglecting the multifractal characteristics of loads, having fixed Bayesian inference parameters, and being unable to adaptively adapt to load complexity and uncertainty.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a power system load probability prediction method based on Bayesian neural networks, characterized in that it includes: The original historical load data is obtained from the power distribution system or user-side load acquisition device, and the original historical load data is preprocessed to obtain a standardized model input sequence. Based on the explicit temporal regularity and implicit structural complexity of the load sequence, a dual-branch feature extraction module is constructed; the dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model; The internal temporal features of the load and the multifractal features are fused using a cross-attention mechanism to obtain fused features; the fused features are then refined using a SHAP mechanism to obtain refined features. The refined features are input into a Bayesian attention layer, a fractal-guided Bayesian feedforward neural network, and a Bayesian linear output layer; the fractal parameters in the multifractal features guide the Bayesian neural network to adaptively adjust the inference parameters, complete the load probability prediction, and output the probability prediction result.

[0007] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural network, the original historical load data is preprocessed by performing time alignment, sample window construction, sequence segmentation, and min-max normalization to obtain the standardized model input sequence.

[0008] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural network, in the process of extracting the load internal time series features and the multifractal features from the input sequence of the standardized model through the dual-branch feature extraction module, the dual-branch feature extraction module includes: a load internal feature extraction branch and a multifractal feature extraction branch; The load internal feature extraction branch includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from the frequency domain perspective and extract seasonal features. The exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series and obtains growth trend features. Based on the original load sequence, the seasonal features, and the growth trend features, the horizontal baseline features are calculated. The expression for the horizontal baseline feature is: ; ; ; In the formula,X level Features of the horizontal baseline; X This is the original load sequence; X season and X growth These represent seasonal characteristics and growth trend characteristics, respectively; Ω represents the dominant frequency set. R k This represents the amplitude of the corresponding frequency component; ϕ k For phase; k Frequency index; n For time step; L The length of the input sequence; G m For the first m The growth representation extracted from the smooth head; M This refers to the number of smoothing heads; The multifractal feature extraction branch extracts fractal detrending fluctuation analysis parameters, including the generalized Hurst exponent, multifractal spectral width, and spectral center, through a multifractal detrending fluctuation analysis strategy.

[0009] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural networks, the calculation formula for the fused features is as follows: ; In the formula, Features of fusion; H t This represents the temporal decomposition features. Z This is the result of cross-attention fusion; The expression for the refining feature is: = ⊙Repeat(g); In the formula, is for refining features; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product.

[0010] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural networks, in the process of guiding the Bayesian neural network to adaptively adjust the inference parameters through the fractal parameters in the multifractal features, the prior variance is adjusted based on the generalized Hurst exponent: ; In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; HThe generalized Hurst exponent; The number of Monte Carlo sampling times is adjusted based on the aforementioned multifractal spectral width. ; In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; The multifractal spectral width is represented by `clip(.)`, which is the clipping function. This is the adjustment coefficient; N min , N max These are the lower and upper limits for the number of samples, respectively. Adjusting the effective depth of the Bayesian neural network based on the aforementioned spectral center: ; In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; This is the current spectral center.

[0011] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural networks, two parallel Bayesian linear heads are provided at the output of the Bayesian neural network to predict the mean and variance of future loads, respectively; the expression for the probability prediction result is as follows: ; In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , This is a bias term.

[0012] As a preferred embodiment of the power system load probability prediction method based on Bayesian neural networks, the probability prediction results are evaluated by continuous ranking probability scores, average calibration errors, and normalized average interval widths; the formula for calculating the continuous ranking probability scores is as follows: ; In the formula, CRPS is the probability score of continuous ranking;N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y Values ​​are assigned to the load. The formula for calculating the average calibration error is as follows: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; and PINC is the nominal confidence level. The formula for calculating the normalized average interval width is: ; In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

[0013] This invention also provides a power system load probability prediction device based on a Bayesian neural network, employing the above-mentioned power system load probability prediction method based on a Bayesian neural network, including: The original historical load data acquisition and preprocessing unit is used to acquire original historical load data from the power distribution system or user-side load acquisition device, and preprocess the original historical load data to obtain a standardized model input sequence. A dual-branch feature extraction module and feature extraction unit are used to construct a dual-branch feature extraction module based on the explicit temporal regularity and implicit structural complexity of the load sequence; the dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model; The feature fusion and refinement unit is used to fuse the temporal features within the load and the multifractal features through a cross-attention mechanism to obtain fused features; and to refine the fused features through a SHAP mechanism to obtain refined features. The load probability prediction and output unit is used to input the refined features into the Bayesian attention layer, the fractal-guided Bayesian feedforward neural network, and the Bayesian linear output layer; and to guide the Bayesian neural network to adaptively adjust the inference parameters through the fractal parameters in the multifractal features, thereby completing the load probability prediction and outputting the probability prediction result.

[0014] As a preferred embodiment of the power system load probability prediction device based on Bayesian neural network, the original historical load data acquisition and preprocessing unit performs time alignment, sample window construction, sequence segmentation and min-max normalization on the original historical load data during the preprocessing process to obtain the standardized model input sequence.

[0015] As a preferred embodiment of a power system load probability prediction device based on Bayesian neural networks, in the construction and feature extraction unit of the dual-branch feature extraction module, during the process of extracting the load internal time-series features and the multifractal features from the input sequence of the standardized model through the dual-branch feature extraction module, the dual-branch feature extraction module includes: a load internal feature extraction branch and a multifractal feature extraction branch; The load internal feature extraction branch includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from the frequency domain perspective and extract seasonal features. The exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series and obtains growth trend features. Based on the original load sequence, the seasonal features, and the growth trend features, the horizontal baseline features are calculated. The expression for the horizontal baseline feature is: ; ; ; In the formula, X level Features of the horizontal baseline; X This is the original load sequence; X season and X growth These represent seasonal characteristics and growth trend characteristics, respectively; Ω represents the dominant frequency set. R k This represents the amplitude of the corresponding frequency component; ϕ k For phase; k Frequency index; n For time step; L The length of the input sequence; G m For the first m The growth representation extracted from the smooth head; M This refers to the number of smoothing heads; The multifractal feature extraction branch extracts fractal detrending fluctuation analysis parameters, including the generalized Hurst exponent, multifractal spectral width, and spectral center, through a multifractal detrending fluctuation analysis strategy.

[0016] As a preferred embodiment of a power system load probability prediction device based on Bayesian neural networks, the calculation formula for the fused features in the feature fusion and refinement unit is as follows: ; In the formula, Features of fusion; H t This represents the temporal decomposition features. Z This is the result of cross-attention fusion; The expression for the refining feature is: = ⊙Repeat(g); In the formula, is for refining features; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product.

[0017] As a preferred embodiment of a power system load probability prediction device based on a Bayesian neural network, in the load probability prediction and output unit, during the process of adaptively adjusting the inference parameters of the Bayesian neural network guided by the fractal parameters in the multifractal features, the prior variance is adjusted based on the generalized Hurst exponent. ; In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; H The generalized Hurst exponent; The number of Monte Carlo sampling times is adjusted based on the aforementioned multifractal spectral width. ; In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; The multifractal spectral width is represented by `clip(.)`, which is the clipping function. This is the adjustment coefficient; N min , N max These are the lower and upper limits for the number of samples, respectively. Adjusting the effective depth of the Bayesian neural network based on the aforementioned spectral center: ; In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; This is the current spectral center.

[0018] As a preferred embodiment of the power system load probability prediction device based on Bayesian neural network, the load probability prediction and output unit includes two parallel Bayesian linear heads at the output of the Bayesian neural network, which respectively predict the mean and variance of the future load; the expression for the probability prediction result is as follows: ; In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , This is a bias term.

[0019] As a preferred embodiment of a power system load probability prediction device based on a Bayesian neural network, the load probability prediction and output unit evaluates the probability prediction results using continuous sorting probability scores, average calibration errors, and normalized average interval widths; the formula for calculating the continuous sorting probability scores is as follows: ; In the formula, CRPS is the probability score of continuous ranking; N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y Values ​​are assigned to the load. The formula for calculating the average calibration error is as follows: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; and PINC is the nominal confidence level. The formula for calculating the normalized average interval width is: ; In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

[0020] The present invention has the following advantages: First, this invention extracts load time-series features and multifractal features in parallel through a dual-branch structure, which can fully explore the inherent structural characteristics of the load sequence, improve the model's adaptability to complex load scenarios, and enhance the stability of prediction results.

[0021] Second, this invention uses fractal parameters to guide the Bayesian neural network to adaptively adjust the inference parameters, which can dynamically optimize the model structure and inference strategy according to the complexity of the load sequence, thereby optimizing the allocation of computing resources while ensuring the prediction effect.

[0022] Third, this invention achieves complementary fusion of temporal features and fractal features through a cross-attention mechanism, and completes feature refinement by combining it with the SHAP mechanism, which can effectively suppress redundant feature interference and improve the feature utilization efficiency of the model.

[0023] Fourth, this invention generates prediction intervals with multiple confidence levels by outputting the prediction mean and variance in parallel through a Bayesian network, thereby effectively characterizing the uncertainty of load forecasting and providing support for power system operation decisions.

[0024] Fifth, this invention uses multi-dimensional indicators such as CRPS to evaluate the prediction results, which can comprehensively quantify the model performance, provide a basis for model parameter optimization and iteration, and improve the engineering practicality of the method. Attached Figure Description

[0025] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0026] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0027] Figure 1 This is a flowchart illustrating the power system load probability prediction method based on Bayesian neural network provided in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of load internal feature extraction in the power system load probability prediction method based on Bayesian neural network provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the fractal-guided Bayesian neural network in the power system load probability prediction method based on Bayesian neural network provided in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of multi-level probability interval prediction in one possible embodiment of Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of prediction uncertainty decomposition in one possible embodiment provided in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram illustrating the relationship between the generalized Hurst exponent H and the prior variance in one possible embodiment provided in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram illustrating the relationship between the multifractal spectral width Δα and the number of Monte Carlo samplings in one possible embodiment of Embodiment 1 of the present invention; Figure 8 This is a schematic diagram illustrating the relationship between the spectral center α0 and the activation depth of the Bayesian transform path in one possible embodiment of Embodiment 1 of the present invention. Figure 9 This is a schematic diagram of the architecture of the power system load probability prediction device based on Bayesian neural network provided in Embodiment 2 of the present invention. Detailed Implementation

[0028] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0029] Example 1

[0030] See Figure 1 Embodiment 1 of the present invention provides a power system load probability prediction method based on Bayesian neural network, comprising the following steps: S1. Obtain raw historical load data from the power distribution system or user-side load acquisition device, and preprocess the raw historical load data to obtain a standardized model input sequence; S2. Based on the explicit temporal regularity and implicit structural complexity of the load sequence, a dual-branch feature extraction module is constructed; the dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model; S3. The internal temporal features of the load and the multifractal features are fused using a cross-attention mechanism to obtain fused features; the fused features are then refined using a SHAP mechanism to obtain refined features. S4. Input the refined features into the Bayesian attention layer, the fractal-guided Bayesian feedforward neural network, and the Bayesian linear output layer; guide the Bayesian neural network to adaptively adjust the inference parameters through the fractal parameters in the multifractal features, complete the load probability prediction, and output the probability prediction result.

[0031] In this embodiment, in step S1, raw historical load data is obtained from the power distribution system or the user-side load acquisition device, and the raw historical load data is preprocessed to obtain a standardized model input sequence.

[0032] Specifically, historical load data obtained from power distribution systems or user-side data acquisition devices is acquired, organized, and uniformly represented to form the model's original input sequence. The original data originates from historical observation data acquired by load acquisition devices. After data extraction, a complete historical load sequence is formed and organized chronologically as model input. X t .

[0033] In the process of preprocessing the original historical load data, time alignment, sample window construction, sequence segmentation and min-max normalization are performed on the original historical load data to obtain the standardized model input sequence.

[0034] In this embodiment, in step S2, a dual-branch feature extraction module is constructed based on the explicit temporal regularity and implicit structural complexity of the load sequence; the dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model.

[0035] Specifically, in order to simultaneously characterize the explicit temporal regularity and implicit structural complexity of the load sequence, a dual-branch feature extraction module was constructed, namely, the load internal feature extraction branch and the multifractal feature extraction branch, which process the same input sequence in parallel.

[0036] In this embodiment, the historical load sequence is assumed to be... ,in L Given the length of the input sequence, the original sequence is first mapped to a high-dimensional hidden space using a one-dimensional convolutional embedding layer, and then positional encoding is superimposed to preserve temporal order information, resulting in the embedded temporal representation: ; In the formula, Conv1d(.) is a one-dimensional convolution mapping; PE For position encoding; H 0 represents the hidden representation of the input load sequence.

[0037] To fully extract interpretable time-series information from historical load sequences, a load internal feature extraction module is first constructed to embed the input load sequence into a representation and further decompose it into three categories of internal features: seasonal, growth, and level. Figure 2 As shown.

[0038] Specifically, the first branch is mainly used to extract the temporal component features within the load sequence. This branch successively includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from a frequency domain perspective and extract seasonal features; the exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series, thereby obtaining growth trend features. Building upon this, the internal characteristics of the load are represented by key features such as level, growth, and seasonality, thus achieving a decompositional expression of the load's temporal structure. Compared to directly modeling the original sequence as a whole, this approach can reveal the different driving factors in load changes in greater detail, improving the clarity and interpretability of the temporal feature representation.

[0039] The specific feature extraction process is as follows: For embedded representation H A certain characteristic channel of 0, denoted as its first characteristic channel. n The scalar value at each moment is a n Then, by using the discrete Fourier transform, we can map it to the frequency domain to obtain the complex coefficients of the corresponding frequency components: ; ; In the formula, k Frequency index; Ak These are the complex coefficients of the corresponding frequency components; R k This represents the amplitude of the corresponding frequency component; ϕ k For phase.

[0040] To preserve key periodic information, the largest amplitude is selected. K The dominant frequency components constitute the frequency set Ω, and the seasonal components are reconstructed through inverse transformation: ; In the formula, X season The seasonal characteristics obtained from the reconstruction; k Frequency index; L The input sequence length is given. This method can highlight the periodic patterns in the load sequence from a frequency domain perspective, thereby improving the model's ability to characterize seasonal fluctuations.

[0041] Growth features are used to characterize the trend changes in load sequences, i.e., the rise, fall, or slow evolution of load over a longer time span. To enhance the model's ability to perceive trend changes, an exponential smoothing attention module was designed, assigning decreasing weights to historical sequences over time, thus giving more influence to recent observations in trend extraction.

[0042] Its basic smoothing form is: ; In the formula, s t For a moment t A smooth state; x t As input features, α The smoothing coefficient is a learnable factor. From a matrix perspective, exponential smoothing can be represented as the product of the input sequence and the lower triangular decaying weight matrix: ; In the formula, G As a growth characteristic; W exp It is a lower triangular weight matrix with exponential decay characteristics.

[0043] Furthermore, to extract trend information from different smoothing scales, multiple exponential smoothing heads are constructed in parallel using a multi-head approach. Each smoothing head learns trend patterns at different time scales, and their outputs are concatenated and then subjected to a linear transformation to obtain the final growth component representation. ; In the formula, X growth Characterized by a growth trend;G m For the first m The growth representation extracted from the smooth head; M The number of smooth heads is used; through this structure, the model can simultaneously take into account both short-term and long-term trends, improving its ability to describe the dynamics of load evolution.

[0044] After obtaining the seasonal and growth characteristics, the remaining stable baseline portion of the load series can be considered as the horizontal component. The horizontal component reflects the base load level of the load series after removing cyclical fluctuations and trend changes. The expression for the horizontal baseline characteristics is: ; In the formula, X level Features of the horizontal baseline; X This is the original load sequence.

[0045] In this embodiment, the second branch is used to extract the fractal features of the load sequence. This branch employs a multifractal detrended fluctuation analysis method to perform multi-scale analysis on the input sequence, sequentially obtaining... q Intermediate results such as wave functions, scaling exponents, and singular spectra are obtained, and compact fractal descriptive parameters, such as the Hurst exponent, singular spectral width, and spectral center position, are further extracted. This process effectively characterizes the long-term correlation, self-similarity, multi-scale volatility, and local irregularities present in the load sequence. Compared to traditional time-series features that only focus on the temporal dimension of change, fractal features further reveal the structural complexity of the load sequence, providing important prior information reflecting the complexity of the sequence for subsequent probabilistic modeling.

[0046] In this embodiment, in step S3, the internal temporal features of the load and the multifractal features are fused using a cross-attention mechanism to obtain fused features; the fused features are then refined using a SHAP mechanism to obtain refined features.

[0047] Specifically, to further characterize the correlation structure and complexity of the load series under multi-scale conditions, the model introduces the multifractal detrended fluctuation analysis method to extract fractal features from the original load series. Unlike conventional time series decomposition, the multifractal detrended fluctuation analysis method MF-DFA is mainly used to describe the long-term correlation, self-similarity, and multi-scale fluctuation characteristics in the load series.

[0048] Let the mean of the original sequence be... First, construct the cumulative and contour sequences: ; Then scale the sequence r Divide the data into multiple segments of equal length, and fit a local trend term within each segment.P v ( i ), calculate the local variance after detrending: ; Furthermore, calculate all sub-segments. q First-order wave function: ; When the power-law relationship is satisfied at different scales, we have: ; In the formula, h ( q ) is the generalized Hurst exponent. If h ( q ) q If the changes are significant, it indicates that the sequence has significant multifractal properties.

[0049] The mass index and singular spectrum are obtained through Legendre transform, and three compact fractal descriptors are extracted as inputs for subsequent modeling, namely the generalized Hurst index. H Multifractal spectral width Δα and spectral center α 0. These three parameters reflect the persistence of the sequence, multi-scale heterogeneity, and the complexity of the dominant structure, respectively.

[0050] In this embodiment, a cross-attention fusion module is constructed to effectively integrate temporal decomposition features and fractal features. This module uses temporal decomposition features as query terms and the expanded fractal description vector as keys and values, thereby realizing interactive modeling between local temporal dynamics and global fractal structure.

[0051] The basic calculation form is: ; ; In the formula, H t This represents the temporal decomposition features. F f Represented by fractal characteristics; W Q , W K , W V For learnable projection matrix; Z This is the result of cross-attention fusion.

[0052] The final fused features are obtained through residual connection and normalization operations: ; In the formula, This is a feature of fusion.

[0053] This fusion mechanism enables each time step feature to perceive the fractal structure information of the entire sequence, thereby simultaneously encoding local temporal patterns and global multi-scale complexity in a unified representation.

[0054] In this embodiment, after obtaining the fused features, to enhance model interpretability and highlight the contributions of key features, this invention constructs a SHAP-guided feature refinement module. This module uses SHAP values ​​to quantify the importance of each decomposed feature to the prediction task and converts them into gating weights for adaptive selection of the fused features.

[0055] To avoid a circular dependency between SHAP estimation and model training, a two-stage strategy is adopted. In the first stage, a basic prediction model without a gating module is trained, and the SHAP values ​​for each feature channel are calculated offline. In the second stage, a lightweight mapper is trained to map the fractal description vector to the predicted SHAP vector, and then weighted and fused with the offline SHAP values ​​to generate the final gating vector. g .

[0056] The refined characteristics after gating are represented as follows: = ⊙Repeat(g); In the formula, This refines the features; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product. This operation can preserve high-contribution features, suppress low-correlation features, and pass the importance information of fractal correlation to the final predicted representation.

[0057] In this embodiment, in step S4, the refined features are input into the Bayesian attention layer, the fractal-guided Bayesian feedforward neural network, and the Bayesian linear output layer; the fractal parameters in the multifractal features guide the Bayesian neural network to adaptively adjust the inference parameters, complete the load probability prediction, and output the probability prediction result.

[0058] Specifically, such as Figure 3 As shown, to achieve parameter uncertainty modeling, the model replaces the traditional deterministic network weights with Bayesian weight distributions and further embeds fractal descriptors into the Bayesian inference process, adaptively adjusting the prior variance, sampling budget, and model depth.

[0059] Under the guidance of the fractal mechanism, the refined feature representations are sequentially input into the Bayesian attention layer and the Bayesian feedforward neural network. For the first... s After the second sampling, the attention output can be expressed as: ; Then, it is further transformed by a Bayesian feedforward network: ; In the formula, For the first s Attention output features of subsamples; These are the query matrix, key matrix, and value matrix, respectively. For the first s The final refined features of the sub-Monte Carlo sampling; , The first s The first and second layer Bayesian weight matrices of the subsampled layer; , For bias terms; ϕ (.) is a non-linear activation function.

[0060] In this embodiment, fractal features are no longer used as ordinary inputs, but as guiding variables to directly regulate the Bayesian prediction process.

[0061] use H To characterize the long-range dependence and persistence of the load series, the prior variance of the Bayesian weights is adjusted. ; In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; H It is the generalized Hurst exponent; this mechanism enables the model to adaptively adjust the regularization strength based on sequence persistence.

[0062] Δα is used to measure the multi-scale heterogeneity of the sequence, and the number of Monte Carlo samplings is adjusted accordingly: ; In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; The multifractal spectral width is represented by `clip(.)`, which is the clipping function. This is the adjustment coefficient; N min , N max These represent the lower and upper limits of the number of samples, respectively; the larger the spectral width, the more complex the sequence structure, and the more samples the model needs to improve the accuracy of the posterior estimation.

[0063] use α 0 reflects the dominant local regularity and further adjusts the effective depth of the Bayesian neural network: ; In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; This is the current spectral center.

[0064] In this embodiment, to achieve probabilistic load forecasting, the model sets two parallel Bayesian linear heads at the output to predict the mean and variance of future loads, respectively. For the first... s The output format of the second sampling is as follows: ; In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , This is a bias term.

[0065] In this embodiment, the probability prediction results are evaluated by continuous sorting probability scores, average calibration error, and normalized average interval width. The Continuous Rank Probability Score (CRPS) is used to evaluate the overall difference between the predicted distribution and the actual observed values, and is one of the most commonly used comprehensive indicators in probabilistic forecasting. It considers not only the accuracy of the predicted mean but also the reasonableness of the predicted distribution itself, thus comprehensively reflecting the quality of the model's output distribution. The formula for calculating the Continuous Rank Probability Score is as follows: ; In the formula, CRPS is the probability score of continuous ranking; N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y The value is taken for the load.

[0066] This metric measures the distance between the predicted distribution and the actual result. The smaller the CRPS, the closer the predicted distribution is to the actual distribution, and the better the probability prediction performance.

[0067] The average calibration error (ACE) measures the calibrability of a probability prediction interval, that is, whether the coverage of the prediction interval given by the model is consistent with the theoretical confidence level. If the model claims that a certain prediction interval has a 90% confidence level, then ideally, the proportion of actual values ​​falling into that interval should also be close to 90%. The formula for calculating the average calibration error is: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; PINC is the nominal confidence level; ACE reflects the deviation between the actual coverage and the theoretical coverage. The closer ACE is to 0, the better the model calibration and the more reliable the predicted interval. If ACE is positive, it indicates that the interval is too wide and the coverage is too high; if ACE is negative, it indicates that the interval is too narrow and the coverage is insufficient.

[0068] Normalized average interval width (PINAW) is used to evaluate the sharpness of probabilistic prediction intervals, i.e., whether the prediction interval is sufficiently compact. For probabilistic prediction, provided that the coverage is reasonable, the narrower the interval, the more concentrated the information provided by the model and the more valuable it is for decision-making. The formula for calculating the normalized average interval width is: ; In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

[0069] This metric reflects the magnitude of the average width of the prediction interval relative to the actual data fluctuation range. The smaller the PINAW, the narrower the prediction interval and the sharper the prediction result.

[0070] In one possible implementation, a verification example is provided as follows: I. Experimental Design and Data Description To verify the effectiveness of the proposed fractal-guided Bayesian neural network in probabilistic load forecasting, this invention selected several load datasets with different regional attributes, spatial scales, and temporal resolutions for example analysis. As shown in Table 1, the datasets used include: utility regional load data provided by the Global Energy Forecasting Competition, residential load data from Austria and Belgium, regional load data from the UK and Germany, distribution network-level load data from Zetland and DalleySt., and building-level load data from Nanyang Technological University. Each dataset covers different load scenarios from the user level, building level, distribution network level to the regional level, enabling a relatively comprehensive test of the model's applicability under different complexities and time scales.

[0071] Table 1 Basic Information of Load Dataset

[0072] To ensure fairness in the comparative experiments, all datasets were partitioned using a uniform time-order method, dividing the samples into training, validation, and test sets in an 8:1:1 ratio. The prediction step size, data partitioning scheme, and evaluation metrics were maintained consistently across all comparative models. This invention emphasizes that each comparative model was reimplemented or adapted based on the original literature and further optimized on the validation set to reduce bias caused by implementation and parameter settings differences, ensuring that performance differences primarily reflect the model's inherent modeling capabilities.

[0073] In terms of data preprocessing, all input load data are processed using a min-max normalization method, the expression of which is: ; In the formula, The data is after normalization; This is the original load data; X This is the original historical workload dataset; , These are the minimum and maximum values ​​of the load dataset, respectively.

[0074] II. Analysis of Prediction Intervals and Uncertainty Decomposition Results at Multiple Confidence Levels To verify the probabilistic prediction capability of this invention, a multi-confidence level prediction interval experiment was first conducted on the Zetland distribution network load dataset, and the probabilistic prediction results for the next 250 time steps are presented. The confidence level of the prediction interval changes progressively from 50% to 98%, as shown below. Figure 4As shown in the figure. The results show that the prediction interval generated by the present invention can follow the changing trend of the actual load curve well. Most of the actual observations fall within the generated prediction interval, while the interval width remains relatively compact, indicating that the present invention achieves a good balance between interval reliability and interval sharpness.

[0075] This invention further decomposes prediction uncertainty, dividing the total uncertainty into two parts: accidental uncertainty and cognitive uncertainty, as follows: Figure 5 As shown, the results indicate that the total prediction uncertainty of this invention is mainly dominated by random uncertainty, which means that the load prediction error mainly originates from the random fluctuations of the load sequence itself and external disturbances, rather than from insufficient understanding of the invention itself. Meanwhile, the cognitive uncertainty remains at a low level overall, indicating that the invention's learning of load time-series patterns and structural characteristics is relatively stable.

[0076] III. Probability Prediction Results for Different Datasets On five representative datasets—NTU Building, Dalley St, Austria, Belgium, and Germany—the invention was compared with HMM, ProbSparse Transformer, DeepAR, and conventional BNN. The results are shown in Table 2. Table 2 Evaluation Indicators for Probabilistic Load Prediction of Different Models

[0077] As can be seen from the table, the CRPS of this invention achieved optimal or near-optimal results on all five datasets, demonstrating its significant advantage in overall distribution prediction quality. For example, on the NTU Building dataset, the CRPS of this invention was reduced from 0.0396 for DeepAR to 0.0316; on the Dalley St dataset, it was further reduced from 0.0076 for ProbSparse Transformer to 0.0045, reflecting higher distribution prediction accuracy.

[0078] In terms of the PINAW metric, this invention also performs better, demonstrating that it can generate narrower and more compact prediction intervals while ensuring reasonable coverage. For example, on the Germany dataset, the PINAW of this invention is 0.0868, significantly lower than the 0.1159 of DeepAR and conventional BNN. Meanwhile, the ACE of this invention is closer to 0 on most datasets, indicating that the actual coverage of the prediction interval is more consistent with the theoretical confidence level, and the interval calibration is better.

[0079] Overall, this invention demonstrates good comprehensive advantages in terms of distribution accuracy, interval sharpness, and interval calibration.

[0080] IV. Verification Results and Analysis of Fractal-Guided Bayesian Adaptive Mechanism To further verify the effectiveness of the proposed fractal-guided Bayesian adaptive mechanism, this invention conducted mechanistic verification experiments focusing on three key fractal descriptors, analyzing their influence on the model's internal behavior. These three fractal descriptors include: the generalized Hurst exponent H, the multifractal spectral width Δα, and the spectral center α0. They are used to characterize the persistence, multi-scale heterogeneity, and dominant structure center of the load sequence, respectively, and guide prior variance adjustment, posterior sampling intensity allocation, and network transformation depth selection in Bayesian modeling. Related results are as follows: Figure 6 , Figure 7 and Figure 8 As shown.

[0081] like Figure 6 As shown, the generalized Hurst exponent is given. H The relationship between the model and the prior variance of the Bayesian parameters is shown. The horizontal axis represents the persistence level of the load sequence, and the vertical axis represents the prior variance of the model assignment. As can be seen from the graph, both show an overall decreasing trend, i.e., when... H When the variance is small, the model tends to assign a larger prior variance; while when H When the variance is large, the prior variance of the allocation is relatively small.

[0082] This result indicates that load sequences with smaller generalized Hurst exponents typically exhibit weaker persistence and stronger irregularity. Therefore, the model is allowed to explore a larger parameter space in Bayesian inference, enhancing its adaptability to complex load patterns. Conversely, for sequences with stronger persistence and relatively stable changes, stronger regularization constraints are applied, thereby improving the stability of parameter estimation. This result validates… H It can effectively guide the adaptive adjustment of Bayesian prior strength.

[0083] like Figure 7 As shown, the relationship between the multifractal spectral width Δα and the number of Monte Carlo samplings is illustrated. The horizontal axis represents the spectral width, which characterizes the degree of multiscale heterogeneity of the loading sequence; the vertical axis represents the number of Monte Carlo samplings allocated in the posterior estimation process. Experimental results show that both generally exhibit an increasing trend, meaning that as the spectral width increases, the number of samplings used by the model also increases accordingly.

[0084] This indicates that when the load sequence has stronger multifractal properties and more complex multiscale structures, its posterior distribution is usually more complex, requiring the model to invest more sampling computation to obtain stable and reliable probability estimates. Conversely, for sequences with simpler fractal structures, fewer sampling times are sufficient to meet the posterior approximation requirements. This result demonstrates that the spectral width Δα can effectively guide the model to dynamically allocate posterior sampling resources, thereby achieving a match between computational resources and sequence complexity.

[0085] like Figure 8 As shown, the relationship between the spectral center α0 and the activation depth of the Bayesian transform path is presented. The horizontal axis represents the spectral center extracted by multifractal analysis, and the vertical axis represents the actual activation depth of the transform path in the Bayesian network. The results show that when the α0 value of the sample is close to the reference center, the model tends to activate shallower transform paths; while when α0 deviates significantly from the reference center, it is more likely to trigger deeper transform paths.

[0086] This phenomenon indicates that the spectral center can serve as an important indicator of the degree to which the dominant structure of a load sequence deviates. When the sequence structure is close to the normal state, shallow transformations are sufficient to represent the features; however, when the sequence structure deviates significantly from the normal distribution, the model requires deeper nonlinear transformations to enhance its expressive power. This result verifies that the spectral center α0 can effectively guide the adaptive selection of the depth of the Bayesian network.

[0087] V. Conclusion and Analysis Comparative analysis with models such as HMM, ProbSparse Transformer, DeepAR, and conventional BNN reveals that this invention exhibits superior probabilistic prediction performance on datasets with varying levels and time resolutions, demonstrating significant advantages in distribution accuracy, interval sharpness, and interval calibration. Furthermore, uncertainty decomposition results show that this invention can effectively distinguish between accidental and cognitive uncertainties. The fractal guidance mechanism verification experiment further demonstrates that this invention can adaptively adjust prior variance, sampling intensity, and network depth based on the fractal complexity of the load sequence. In summary, this indicates that this invention possesses high prediction accuracy, good reliability, strong interpretability, and significant engineering application value.

[0088] The application scenarios of this invention are as follows: In the scenario of distribution network operation and scheduling, this invention can be used for load probability prediction, providing data support for power grid reserve capacity configuration and power flow optimization, and improving the stability and economy of distribution network operation.

[0089] In the context of electricity market transactions, this invention can be used for user-side load probability prediction, assisting trading entities in formulating pricing strategies and reducing market transaction risks.

[0090] In demand-side response management scenarios, this invention can be used for load uncertainty analysis, supporting demand-side management tasks such as interruptible load regulation and virtual power plant optimized operation.

[0091] In distributed power grid integration scenarios, this invention can be used for load-wind-solar joint probability prediction to improve the grid's absorption capacity and operational reliability under high-proportion renewable energy grid integration.

[0092] In industrial user load management scenarios, this invention can be used for enterprise electricity load probability prediction, assisting users in formulating electricity plans, optimizing energy costs, and improving energy utilization efficiency.

[0093] In power grid planning and investment decision-making scenarios, this invention can be used for medium- and long-term load probability prediction, providing a reference for planning work such as distribution network expansion and substation site selection.

[0094] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0095] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0096] Example 2 See Figure 9 Embodiment 2 of the present invention also provides a power system load probability prediction device based on a Bayesian neural network, comprising: The original historical load data acquisition and preprocessing unit 001 is used to acquire original historical load data from the power distribution system or user-side load acquisition device, and preprocess the original historical load data to obtain a standardized model input sequence. The dual-branch feature extraction module construction and feature extraction unit 002 is used to construct a dual-branch feature extraction module based on the explicit temporal regularity and implicit structural complexity of the load sequence; the dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model; The feature fusion and refinement unit 003 is used to fuse the temporal features within the load and the multifractal features through a cross-attention mechanism to obtain fused features; and to refine the fused features through a SHAP mechanism to obtain refined features. The load probability prediction and output unit 004 is used to input the refined features into the Bayesian attention layer, the fractal-guided Bayesian feedforward neural network, and the Bayesian linear output layer; and to guide the Bayesian neural network to adaptively adjust the inference parameters through the fractal parameters in the multifractal features, thereby completing the load probability prediction and outputting the probability prediction result.

[0097] In this embodiment, the original historical load data acquisition and preprocessing unit 001 performs time alignment, sample window construction, sequence segmentation and min-max normalization on the original historical load data during the preprocessing process to obtain the standardized model input sequence.

[0098] In this embodiment, in the dual-branch feature extraction module construction and feature extraction unit 002, during the process of extracting the load internal time series features and the multifractal features from the standardized model input sequence through the dual-branch feature extraction module, the dual-branch feature extraction module includes: a load internal feature extraction branch and a multifractal feature extraction branch; The load internal feature extraction branch includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from the frequency domain perspective and extract seasonal features. The exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series and obtains growth trend features. Based on the original load sequence, the seasonal features, and the growth trend features, the horizontal baseline features are calculated. The expression for the horizontal baseline feature is: ; ; ; In the formula, X level Features of the horizontal baseline; X This is the original load sequence; X season and X growth These represent seasonal characteristics and growth trend characteristics, respectively; Ω represents the dominant frequency set. R k This represents the amplitude of the corresponding frequency component; ϕ k For phase;k Frequency index; n For time step; L The length of the input sequence; G m For the first m The growth representation extracted from the smooth head; M This refers to the number of smoothing heads; The multifractal feature extraction branch extracts fractal detrending fluctuation analysis parameters, including the generalized Hurst exponent, multifractal spectral width, and spectral center, through a multifractal detrending fluctuation analysis strategy.

[0099] In this embodiment, the calculation formula for the fused features in the feature fusion and refinement unit 003 is as follows: ; In the formula, Features of fusion; H t This represents the temporal decomposition features. Z This is the result of cross-attention fusion; The expression for the refining feature is: = ⊙Repeat(g); In the formula, is for refining features; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product.

[0100] In this embodiment, in the load probability prediction and output unit 004, during the process of adaptively adjusting the inference parameters of the Bayesian neural network guided by the fractal parameters in the multifractal features, the prior variance is adjusted based on the generalized Hurst exponent: ; In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; H The generalized Hurst exponent; The number of Monte Carlo sampling times is adjusted based on the aforementioned multifractal spectral width. ; In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; The multifractal spectral width is represented by `clip(.)`, which is the clipping function. This is the adjustment coefficient;N min , N max These are the lower and upper limits for the number of samples, respectively. Adjusting the effective depth of the Bayesian neural network based on the aforementioned spectral center: ; In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; This is the current spectral center.

[0101] In this embodiment, the load probability prediction and output unit 004 has two parallel Bayesian linear heads at the output of the Bayesian neural network, which predict the mean and variance of the future load, respectively; the expression for the probability prediction result is: ; In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , This is a bias term.

[0102] In this embodiment, the load probability prediction and output unit 004 evaluates the probability prediction results using continuous sorting probability scores, average calibration errors, and normalized average interval widths; the formula for calculating the continuous sorting probability score is: ; In the formula, CRPS is the probability score of continuous ranking; N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y Values ​​are assigned to the load. The formula for calculating the average calibration error is as follows: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; and PINC is the nominal confidence level. The formula for calculating the normalized average interval width is: ; In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

[0103] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0104] Example 3 Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a power system load probability prediction method based on a Bayesian neural network. The program code includes instructions for executing the power system load probability prediction method based on a Bayesian neural network according to Embodiment 1 or any possible implementation thereof.

[0105] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0106] Example 4 Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor; The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute the power system load probability prediction method based on Bayesian neural network according to Embodiment 1 or any possible implementation thereof by calling the program instructions.

[0107] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0108] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0109] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0110] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A power system load probability prediction method based on Bayesian neural networks, characterized in that, include: The original historical load data is obtained from the power distribution system or user-side load acquisition device, and the original historical load data is preprocessed to obtain a standardized model input sequence. Based on the explicit temporal regularity and implicit structural complexity of the load sequence, a dual-branch feature extraction module is constructed. The dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model. The internal temporal features of the load and the multifractal features are fused using a cross-attention mechanism to obtain fused features. The fused features are refined using the SHAP mechanism to obtain refined features. The refined features are input into a Bayesian attention layer, a fractal-guided Bayesian feedforward neural network, and a Bayesian linear output layer; the fractal parameters in the multifractal features guide the Bayesian neural network to adaptively adjust the inference parameters, complete the load probability prediction, and output the probability prediction result.

2. The power system load probability prediction method based on Bayesian neural network according to claim 1, characterized in that, During the preprocessing of the original historical load data, time alignment, sample window construction, sequence segmentation, and min-max normalization are performed on the original historical load data to obtain the standardized model input sequence.

3. The power system load probability prediction method based on Bayesian neural network according to claim 2, characterized in that, In the process of extracting the load internal time-series features and the multifractal features from the input sequence of the standardized model through the dual-branch feature extraction module, the dual-branch feature extraction module includes: a load internal feature extraction branch and a multifractal feature extraction branch; The load internal feature extraction branch includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from the frequency domain perspective and extract seasonal features. The exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series and obtains growth trend features. Based on the original load sequence, the seasonal features, and the growth trend features, the horizontal baseline features are calculated. The expression for the horizontal baseline feature is: ； ； ； In the formula, X level Features of the horizontal baseline; X This is the original load sequence; X season and X growth These represent seasonal characteristics and growth trend characteristics, respectively; Ω represents the dominant frequency set. R k This represents the amplitude of the corresponding frequency component; ϕ k For phase; k Frequency index; n For time step; L The length of the input sequence; G m For the first m The growth representation extracted from the smooth head; M This refers to the number of smoothing heads; The multifractal feature extraction branch extracts fractal detrending fluctuation analysis parameters, including the generalized Hurst exponent, multifractal spectral width, and spectral center, through a multifractal detrending fluctuation analysis strategy.

4. The power system load probability prediction method based on Bayesian neural network according to claim 3, characterized in that, The formula for calculating the fusion feature is as follows: ； In the formula, Features of fusion; H t This represents the temporal decomposition features. Z This is the result of cross-attention fusion; The expression for the refining feature is: = ⊙Repeat(g); In the formula, Characterized by its refined nature; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product.

5. The power system load probability prediction method based on Bayesian neural network according to claim 4, characterized in that, In the process of guiding the Bayesian neural network to adaptively adjust inference parameters through the fractal parameters in the multifractal features, the prior variance is adjusted based on the generalized Hurst exponent: ； In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; H The generalized Hurst exponent; The number of Monte Carlo sampling times is adjusted based on the aforementioned multifractal spectral width. ； In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; For multifractal spectral width; clip(.) is the clipping function; This is the adjustment coefficient; N min , N max These are the lower and upper limits for the number of samples, respectively. Adjusting the effective depth of the Bayesian neural network based on the aforementioned spectral center: ； In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; This is the current spectral center.

6. The power system load probability prediction method based on Bayesian neural network according to claim 5, characterized in that, Two parallel Bayesian linear heads are set at the output of the Bayesian neural network to predict the mean and variance of the future load, respectively; the expression for the probability prediction result is: ； In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , This is a bias term.

7. The power system load probability prediction method based on Bayesian neural network according to claim 6, characterized in that, The probability prediction results are evaluated using the continuous ranking probability score, the average calibration error, and the normalized average interval width; the formula for calculating the continuous ranking probability score is as follows: ； In the formula, CRPS is the probability score of continuous ranking; N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y Values ​​are assigned to the load. The formula for calculating the average calibration error is as follows: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; and PINC is the nominal confidence level. The formula for calculating the normalized average interval width is: ； In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

8. A power system load probability prediction device based on a Bayesian neural network, employing the power system load probability prediction method based on a Bayesian neural network as described in any one of claims 1-7, characterized in that, include: The original historical load data acquisition and preprocessing unit is used to acquire original historical load data from the power distribution system or user-side load acquisition device, and preprocess the original historical load data to obtain a standardized model input sequence. The dual-branch feature extraction module construction and feature extraction unit are used to construct the dual-branch feature extraction module based on the explicit temporal regularity and implicit structural complexity of the load sequence. The dual-branch feature extraction module extracts the internal temporal features and multifractal features of the load from the input sequence of the standardized model. The feature fusion and refinement unit is used to fuse the internal temporal features of the load and the multifractal features through a cross-attention mechanism to obtain fused features. The fused features are refined using the SHAP mechanism to obtain refined features. The load probability prediction and output unit is used to input the refined features into the Bayesian attention layer, the fractal-guided Bayesian feedforward neural network, and the Bayesian linear output layer; and to guide the Bayesian neural network to adaptively adjust the inference parameters through the fractal parameters in the multifractal features, thereby completing the load probability prediction and outputting the probability prediction result.

9. The power system load probability prediction device based on Bayesian neural network according to claim 8, characterized in that, In the original historical load data acquisition and preprocessing unit, during the preprocessing of the original historical load data, time alignment, sample window construction, sequence segmentation, and min-max normalization are performed on the original historical load data to obtain the standardized model input sequence.

10. The power system load probability prediction device based on Bayesian neural network according to claim 9, characterized in that, In the construction and feature extraction unit of the dual-branch feature extraction module, during the process of extracting the load internal time series features and the multifractal features from the input sequence of the standardized model through the dual-branch feature extraction module, the dual-branch feature extraction module includes: a load internal feature extraction branch and a multifractal feature extraction branch; The load internal feature extraction branch includes a frequency attention submodule and an exponential smoothing attention submodule. The frequency attention submodule is used to identify the periodic fluctuation components in the original load sequence from the frequency domain perspective and extract seasonal features. The exponential smoothing attention submodule captures trend changes and slow evolution features by performing progressive smoothing modeling on the time series and obtains growth trend features. Based on the original load sequence, the seasonal features, and the growth trend features, the horizontal baseline features are calculated. The expression for the horizontal baseline feature is: ； ； ； In the formula, X level Features of the horizontal baseline; X This is the original load sequence; X season and X growth These represent seasonal characteristics and growth trend characteristics, respectively; Ω represents the dominant frequency set. R k This represents the amplitude of the corresponding frequency component; ϕ k For phase; k Frequency index; n For time step; L The length of the input sequence; G m For the first m The growth representation extracted from the smooth head; M This refers to the number of smoothing heads; The multifractal feature extraction branch extracts fractal detrending fluctuation analysis parameters, including the generalized Hurst exponent, multifractal spectral width, and spectral center, through a multifractal detrending fluctuation analysis strategy. In the feature fusion and refinement unit, the calculation formula for the fused features is as follows: ； In the formula, Features of fusion; H t This represents the temporal decomposition features. Z This is the result of cross-attention fusion; The expression for the refining feature is: = ⊙Repeat(g); In the formula, This is for refining features; Repeat(.) copies the gated vector along the time dimension; ⊙ is the Hadamard element-wise product; In the load probability prediction and output unit, during the process of adaptively adjusting the inference parameters of the Bayesian neural network guided by the fractal parameters in the multifractal features, the prior variance is adjusted based on the generalized Hurst exponent. ； In the formula, The prior variance after fractal guidance; The baseline prior variance; k H This is the adjustment coefficient; H The generalized Hurst exponent; The number of Monte Carlo sampling times is adjusted based on the aforementioned multifractal spectral width. ； In the formula, N MC Number of Monte Carlo samples; N b Used as a baseline sampling budget; The multifractal spectral width is represented by `clip(.)`, which is the clipping function. This is the adjustment coefficient; N min , N max These are the lower and upper limits for the number of samples, respectively. Adjusting the effective depth of the Bayesian neural network based on the aforementioned spectral center: ； In the formula, N layer The number of network layers; α ref The reference spectrum center is used; round(.) is the floor function; N b The baseline number of layers; This is the adjustment coefficient; As the current spectral center; In the load probability prediction and output unit, two parallel Bayesian linear heads are provided at the output end of the Bayesian neural network to predict the mean and variance of the future load, respectively; the expression for the probability prediction result is: ； In the formula, μ (s) To predict the mean; σ 2(s) To predict variance; h out This is the final hidden representation; , This is the Bayesian weight matrix; , For bias terms; In the load probability prediction and output unit, the probability prediction results are evaluated by continuous sorting probability scores, average calibration errors, and normalized average interval widths; the formula for calculating the continuous sorting probability scores is as follows: ； In the formula, CRPS is the probability score of continuous ranking; N The number of samples; F i ( y ) is the first i The predicted cumulative distribution function for each sample; y i The true observations are represented by 1(.); 1(.) represents the indicator function. y Values ​​are assigned to the load. The formula for calculating the average calibration error is as follows: ACE = PICP − PINC; In the formula, ACE is the average calibration error; PICP is the predicted interval coverage; and PINC is the nominal confidence level. The formula for calculating the normalized average interval width is: ； In the formula, PINAW is the normalized average interval width; U i and L i The first i The upper and lower bounds of the prediction interval for each sample; R The range of values ​​for the actual load sequence; N The total number of samples.

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