A kurtosis-based dynamic threshold method for detecting the abnormality of the rolling bearing

Abstract

The application discloses a KDE-GRU load interval prediction method considering interval optimization, and comprises the following steps: 1. obtaining historical load data of a certain area; 2. calculating load power difference values of adjacent time points; 3. adopting a MEMD algorithm to simultaneously decompose the load variation ΔP t and the basic load P t into two groups of K load components; 4. establishing a ΔP1 interval prediction model based on a KDE method; 5. establishing a ΔP2 point prediction model of the reconstructed component based on a GRU network; 6. superimposing the interval prediction result [ΔP 1,min , ΔP 1,max ] of the high-frequency component ΔP1 and the point prediction result ΔP' 2t of the reconstructed component ΔP2 to obtain a prediction interval of the load variation; and 7. establishing a prediction interval optimization model based on an interval optimization coefficient. The prediction method of the application is based on the analysis of load time sequence correlation, calculates the difference component of the load sequence, divides the difference component into two parts of a basic load and a load variation, accurately defines an interval boundary optimization coefficient, establishes a prediction model of the interval boundary optimization coefficient based on a GRU network, and optimizes the initial prediction result.

Description

Technical Field

[0001] This invention relates to the field of power load forecasting technology, and in particular to a KDE-GRU load interval forecasting method that considers interval optimization. Background Technology

[0002] With the continuous integration of high-proportion distributed power sources and new loads such as electric vehicles and electric heating into the power grid, load characteristics and curve trends have undergone significant changes, leading to more diversified uncertainties in load forecasting. Traditional point forecasting models can only provide single-value load forecasts for future moments, which is insufficient to meet the requirements of economical and stable operation of modern power systems. Interval forecasting, on the other hand, can describe the possible range of load fluctuations in the future in the form of confidence intervals, quantifying the uncertainty information hidden in deterministic forecast results, thereby revealing the potential uncertainty risks of future loads.

[0003] Most existing load interval forecasting methods do not consider the temporal correlation between load data and are difficult to simultaneously achieve high coverage and narrow interval width. In response, this patent proposes a GRU-KDE load interval forecasting method that considers interval optimization. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a KDE-GRU load interval forecasting method that considers interval optimization. This forecasting method, based on the analysis of load time-series correlation, calculates the difference component of the load sequence, dividing it into two parts: base load and load variation. It then uses multivariate empirical mode decomposition to decompose the base load and load variation, establishes an interval forecasting model for high-frequency components using the KDE method, and establishes a point forecasting model for reconstructed components based on a GRU network. Furthermore, it precisely defines interval boundary optimization coefficients to establish a forecasting model with these coefficients, thereby optimizing the forecast interval.

[0005] A KDE-GRU load interval prediction model considering interval optimization, characterized in that the prediction method includes the following steps:

[0006] Step 1: Obtain historical load data for a certain region. This data consists of actual load data collected at fixed time intervals. It is a time series of load values ​​with time labels, and the duration of one historical load data point is one day.

[0007] Step 2: Calculate the load power difference between adjacent time periods, and break down the original load into the base load P. t and load change ΔP t The calculation formula is shown in equation (1): (Two parts)

[0008] ΔP t =P t+1 -P t(1)

[0009] In the formula, P t P represents the electrical load power at time t; t+1 ΔP represents the electrical load power at time t+1. t This represents the change in load at time t+1 relative to time t.

[0010] Step 3: Simultaneously use the MEMD algorithm to measure the load change ΔP t and base load P t Decomposed into two groups of K load components (Mode1, Mode2, ..., Mode...) K The first component is designated as a high-frequency component, denoted as ΔP1 and P1, and the remaining components are superimposed to form reconstructed components, denoted as ΔP2 and P2.

[0011] Step 4: Establish an interval prediction model for ΔP1 based on the KDE method, which includes the following steps:

[0012] Step 4.1: Calculate the range of variation of P1 [P 1,min ,P 1,max Divide it into appropriate intervals and place the corresponding ΔP1 into the corresponding interval;

[0013] Step 4.2: Use the KDE method to fit the probability distribution curve of ΔP1 within each interval segment, and calculate the confidence interval [ΔP] of ΔP1 at different confidence levels for each interval segment. 1,min ,ΔP 1,max ];

[0014] Step 5: Establish a prediction model for the reconstructed component ΔP2 point based on the GRU network, which includes the following steps:

[0015] Step 5.1: Analyze the autocorrelation of ΔP2 using the autocorrelation function to determine the input feature dimension of the GRU model;

[0016] Step 5.2: Use the input features determined in Step 5.1 from the training dataset as the input to the GRU network after parameter initialization, use the predicted value of ΔP2 as the output of the GRU network, and select the mean squared error function as the network loss function, as shown in Equation (2):

[0017]

[0018] In the formula, ΔP 2,i Let ΔP2 be the actual value of ΔP2 at the i-th point, and ΔP′ be the actual value of 2,i Let ΔP2 be the predicted value of the i-th point, and n be the number of samples in the training set.

[0019] Adjust the parameters of the GRU network in reverse according to the value of the loss function. If the value of the loss function obtained by the current network parameters is less than the preset value or the number of iterations is reached, the training of the network parameters is completed;

[0020] Step 5.3: Input the characteristic data of the prediction time t that is the same as the training data set into the GRU network model with the completed parameter training in Step 5.2 to obtain the predicted value ΔP′ of ΔP2 at the prediction time t 2t ;

[0021] Sixth step: Based on Equation (3), superimpose the interval prediction results [ΔP 1,min , ΔP 1,max of the high-frequency component ΔP1 and the point prediction result ΔP′ of the reconstructed component ΔP2 2t to obtain the prediction interval of the load change amount, and further calculate the initial prediction interval [P L,t , P u,t of the training set and the test set according to Equation (1);

[0022]

[0023] In the formula, ΔP min,t and ΔP max,t are respectively the lower prediction bound and the upper prediction bound of the load change amount at time t.

[0024] Seventh step: Establish a prediction interval optimization model based on the interval optimization coefficient, which specifically includes the following steps:

[0025] Step 7.1: Calculate the interval boundary optimization coefficients w 1,t and w 2,t of the training set according to Equations (4)-(5);

[0026]

[0027]

[0028] In the formula, P s,t is the actual load value at time t, P u,t and P L,t respectively represent the initial prediction upper bound and the initial prediction lower bound of the load at time t, b 1,t and b<000003​​​​​​​Step 7.2: Based on the GRU network, establish prediction models for the interval boundary optimization coefficients respectively, and obtain the predicted values ​​of the interval boundary optimization coefficients for the test set;

[0030] Step 7.3: Combine the initial prediction interval [P] from step 5 L,t ,P u,t The optimized load forecast interval is calculated according to equation (6) based on the predicted interval boundary optimization coefficient values ​​from step 7.2 and the interval boundary optimization coefficient prediction values ​​from step 7.2.

[0031]

[0032] In the formula, w′ 1,t and w′ 2,t P′ represents the predicted values ​​of the upper and lower bound optimization coefficients of the interval at time t, respectively. u,t and P′ L,t These represent the upper and lower bounds of the optimized load forecast at time t, respectively.

[0033] Furthermore, in the above technical solution, the process of establishing the interval boundary optimization coefficient prediction model based on the GRU network in step 7.2 is the same as the process of establishing the reconstruction component ΔP2 point prediction model in step 5.

[0034] Compared with existing methods, the advantages of the present invention are as follows:

[0035] (1) This method uses multivariate empirical mode decomposition to decompose the load change and the base load. This not only reduces the non-stationary characteristics of the original data, but also decomposes the multi-channel data synchronously, while ensuring that the number of components in each pair of components is the same and the oscillation frequency is matched.

[0036] (2) This method uses the KDE method to fit the probability distribution curve of the high-frequency component of the load change. Compared with the parametric distribution, the KDE method directly estimates the probability density function based on the characteristics of the data itself, which better reflects the true distribution of the original data and has a better fitting effect.

[0037] (3) This method uses GRU as the basic prediction model. Compared with other deep neural networks, GRU can not only mine the nonlinear temporal information of the input data, but also has fewer parameters and faster convergence speed.

[0038] (4) This method proposes a load forecast interval optimization model based on interval boundary optimization coefficient, which avoids the problem that most load interval forecasting methods cannot simultaneously take into account high coverage and narrow interval width. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the principle of the prediction method of the present invention;

[0040] Figure 2This is a schematic diagram of the MEMD decomposition results in this invention (schematic diagram of the MEMD decomposition results of the basic load);

[0041] Figure 3 This is a schematic diagram of the MEMD decomposition results in this invention (MEMD decomposition results of load change).

[0042] Figure 4 This is a schematic diagram of the autocorrelation of the reconstructed component ΔP2 of the load change in this invention;

[0043] Figure 5 This is a comparison chart of the predicted and actual load interval values ​​at different confidence levels (90% confidence level) obtained by using the method of this invention to predict the load interval on December 2, 2018 in the historical dataset.

[0044] Figure 6 This is a comparison chart of the predicted and actual load interval values ​​at different confidence levels (confidence level 80%) obtained by using the method of this invention to predict the load interval on December 2, 2018 in the historical dataset. Detailed Implementation

[0045] To further understand the content, features, and effects of this invention, the following embodiments are provided, and detailed descriptions are given below in conjunction with the accompanying drawings. It should be noted that these embodiments are descriptive, not limiting, and should not be construed as limiting the scope of protection of this invention.

[0046] See attached document Figure 1 This invention provides a flowchart of a KDE-GRU load interval forecasting method considering interval optimization, the method comprising the following steps:

[0047] Step 1: Obtain historical load data for a certain region from January 1, 2018 to December 31, 2018. This data consists of actual load data collected at 15-minute intervals, and is a time series of load values ​​with time labels. Each historical load data point lasts for one day and contains 96 data points.

[0048] Step 2: Calculate the load power difference between adjacent time periods to break down the original load into the basic load P. t and load change ΔP t The calculation formula is shown in equation (1): (Two parts)

[0049] ΔP t =P t+1 -P t (1)

[0050] In the formula, P t P represents the power load at time t; t+1 ΔP represents the power load at time t+1. tThis represents the change in load at time t+1 relative to time t.

[0051] Step 3: Simultaneously use the MEMD algorithm to measure the load change ΔP t and base load P t Decomposed into two groups of 14 load components (Mode1, Mode2, ..., Mode...). 14 (See attached) Figure 2 The first component is designated as a high-frequency component, denoted as ΔP1 and P1, and the remaining components are superimposed to form reconstructed components, denoted as ΔP2 and P2.

[0052] Step 4: Establish the ΔP1 interval prediction model using the KDE method, which includes the following steps:

[0053] Step 4.1: Calculate the range of P1 [-15.89, 12.21], divide it into appropriate intervals, and place the corresponding ΔP1 into the corresponding interval;

[0054] Step 4.2: Use the KDE method to fit ΔP within each interval segment. 1t Given the probability distribution curve, calculate the confidence interval [ΔP1] for ΔP1 at different confidence levels for each interval segment. 1,min ,ΔP 1,max See Appendix 1;

[0055] Table 1

[0056]

[0057] Step 5: Establish a prediction model for the reconstructed component ΔP2 point based on the GRU network, which includes the following steps:

[0058] Step 5.1: Use the autocorrelation function to analyze the autocorrelation of the reconstructed component ΔP2 to determine the input feature dimension of the GRU model, as shown in the appendix. Figure 3 ;

[0059] Step 5.2: According to Step 5.1, the first 96 reconstructed components ΔP2 in the training dataset are used as the input to the GRU network after parameter initialization, and the predicted value of ΔP2 is used as the output of the GRU network. The mean squared error function is selected as the network loss function, as shown in Equation (2):

[0060]

[0061] In the formula, ΔP 2,t Let ΔP2 be the actual value of ΔP2 at the i-th point, and ΔP′ be the actual value of 2,t Let ΔP2 be the predicted value of the i-th point, and n be the number of samples in the training set.

[0062] Adjust the parameters of the GRU network in reverse according to the value of the loss function. If the value of the loss function obtained by the current network parameters is less than the preset value or the number of iterations is reached, the training of the network parameters is completed;

[0063] Step 5.3: Input the feature data of the prediction time t that is the same as the training data set into the GRU network model with the trained parameters in Step 5.2 to obtain the predicted value ΔP′ of ΔP2 at the prediction time t 2t ;

[0064] Sixth step: Based on Equation (3), superimpose the interval prediction results [ΔP 1,min , ΔP 1,max of the high-frequency component ΔP1 and the point prediction result ΔP′ of the reconstructed component ΔP2 2t to obtain the prediction interval of the load change amount at time t, and further calculate the initial prediction interval [P L,t , P u,t of the training set and the test set according to Equation (1);

[0065]

[0065]

[0066] [[ID=??]]where ΔP min,t and ΔP max,t are the lower prediction bound and the upper prediction bound of the load change amount at time t, respectively.

[0067] Seventh step: Establish a prediction interval optimization model based on the interval optimization coefficient, specifically including the following steps:

[0068] Step 7.1: Calculate the interval boundary optimization coefficients w 1,t and w 2,t of the training set according to Equations (4)-(5);

[0069]

[0070]

[0071] where P s,t is the actual load value at time t, P u,t and P L,t represent the initial prediction upper bound and the initial prediction lower bound of the load at time t, respectively, b 1,t and b 2,t represent the upper bound ratio and the lower bound ratio at time t, respectively, w 1,t and w 2,t represent the interval upper bound optimization coefficient and the interval lower bound optimization coefficient at time t, respectively, and k1 and k2 represent the interval upper bound constraint factor and the interval lower bound constraint factor, and their values satisfy 0 < k1 ≤ 1, k2 ≥ 1, and can be set artificially according to experience.

[0072] It should be noted that there seems to be an error in the original text where "式中,ΔP min,t [[ID=2??]]和ΔP " has an incorrect "??" in the middle. This has been translated as best as possible while maintaining the integrity of the original structure.Step 7.2: Based on the GRU network, establish prediction models for the upper / lower bound optimization coefficients of the intervals respectively, and obtain the predicted values ​​of the interval boundary optimization coefficients of the test set;

[0073] Step 7.3: Combine the initial prediction interval [P] from step 5 L,t ,P u,t The optimized load forecast intervals under different confidence levels are calculated according to Equation (6) based on the predicted interval boundary optimization coefficients from step 7.2 and the interval boundary optimization coefficients from step 7.2.

[0074]

[0075] In the formula, w′ 1,t and w′ 2,t P′ represents the predicted values ​​of the upper and lower bound optimization coefficients of the interval at time t, respectively. u,t and P′ L,t These represent the upper and lower bounds of the optimized load forecast at time t, respectively.

[0076] Furthermore, in the above technical solution, the process of establishing the interval boundary optimization coefficient prediction model based on the GRU network in step 7.2 is the same as the process of establishing the ΔP2 point prediction model in step 5.

[0077] Finally, any aspects not fully described in this invention utilize existing mature products and technologies.

[0078] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A KDE-GRU load interval forecasting method considering interval optimization, characterized in that, Includes the following steps: Step 1: Obtain historical load data for a certain region. This data consists of actual load data collected at fixed time intervals. It is a time series of load values ​​with time labels, and the duration of one historical load data point is one day. Step 2: Calculate the load power difference between adjacent time periods, and break down the original load into the base load P. t and load change ΔP t The calculation formula is shown in equation (1): (Two parts) ΔP t =P t+1 -P t (1) In the formula, P t P represents the electrical load power at time t; t+1 ΔP represents the electrical load power at time t+1. t This represents the change in load at time t+1 relative to time t; Step 3: Simultaneously use the MEMD algorithm to measure the load change ΔP t and base load P t Decomposed into two groups of K load components (Mode1, Mode2, ..., Mode...) K The first component is designated as a high-frequency component and denoted as ΔP1 and P1, respectively. The remaining components are superimposed to form reconstructed components and denoted as ΔP2 and P2, respectively. Step 4: Establish an interval prediction model for ΔP1 based on the KDE method; Step 5: Establish a prediction model for the reconstructed component ΔP2 point based on the GRU network; The fifth step also includes the following sub-steps: Step 5.1: Analyze the autocorrelation of ΔP2 using the autocorrelation function to determine the input feature dimension of the GRU model; Step 5.2: Use the input features determined in Step 5.1 from the training dataset as the input to the GRU network after parameter initialization, use the predicted value of ΔP2 as the output of the GRU network, and select the mean squared error function as the network loss function, as shown in Equation (2): In the formula, ΔP 2,i Let ΔP2 be the actual value of ΔP2 at the i-th point, and ΔP′ be the actual value of 2,i Let ΔP2 be the predicted value of the i-th point, and n be the number of samples in the training set. The parameters of the GRU network are adjusted in reverse based on the value of the loss function. If the value of the loss function obtained by the current network parameters is less than the preset value or the number of iterations is reached, the training of the network parameters is completed. Step 5.3: Input the feature data of the time to be predicted, t, which is the same as that in the training dataset, into the GRU network model that has completed parameter training in Step 5.2 to obtain the predicted value ΔP′ of ΔP2 at the time to be predicted, t. 2t ; Step 6: Based on Equation (3), superimpose the high-frequency component ΔP1 interval prediction results [ΔP 1,min ,ΔP 1,max ] and the predicted result of the reconstructed component ΔP2 point ΔP′ 2t Obtain the predicted range of load change, and further calculate the initial predicted range of load for the training set and the test set according to equation (1) [P]. L,t ,P u,t ]; In the formula, ΔP min,t and ΔP max,t These are the lower and upper bounds for predicting the load change at time t, respectively. Step 7: Establish a predictive interval optimization model based on the interval optimization coefficients, which includes the following steps: Step 7.1: Calculate the interval boundary optimization coefficient w of the training set according to equations (4)-(5). 1,t and w 2,t ; Where, P s,t is the actual load value at time t, P u,t and P L,t respectively represent the initial upper prediction bound and the initial lower prediction bound of the load at time t, b 1,t and b 2,t respectively represent the upper bound ratio and the lower bound ratio at time t, w 1,t and w 2,t respectively represent the upper bound optimization coefficient and the lower bound optimization coefficient of the interval at time t, k1 and k2 respectively represent the upper bound constraint factor and the lower bound constraint factor of the interval, and their values satisfy 0 < k1 ≤ 1, k2 ≥ 1, which can be artificially set according to experience; Step 7.2: Based on the GRU network, establish prediction models for the interval boundary optimization coefficients respectively, and obtain the predicted values ​​of the interval boundary optimization coefficients for the test set; Step 7.3: Combine the initial prediction interval [P] from step 5 L,t ,P u,t The optimized load forecast interval is calculated according to equation (6) based on the predicted interval boundary optimization coefficient values ​​from step 7.2 and the interval boundary optimization coefficient prediction values ​​from step 7.

2. In the formula, w′ 1,t and w′ 2,t P′ represents the predicted values ​​of the upper and lower bound optimization coefficients of the interval at time t, respectively. u,t and P′ L,t These represent the upper and lower bounds of the optimized load forecast at time t, respectively.

2. The KDE-GRU load interval prediction method considering interval optimization according to claim 1, characterized in that: The process of establishing the interval boundary optimization coefficient prediction model based on the GRU network in step 7.2 is the same as the process of establishing the reconstruction component ΔP2 point prediction model in step 5.

3. The KDE-GRU load interval prediction method considering interval optimization according to claim 1, characterized in that: The fourth step also includes the following sub-steps: Step 4.1: Calculate the range of variation of P1 [P 1,min ,P 1,max Divide it into appropriate intervals and place the corresponding ΔP1 into the corresponding interval; Step 4.2: Use the KDE method to fit the probability distribution curve of ΔP1 within each interval segment, and calculate the confidence interval [ΔP] of ΔP1 at different confidence levels for each interval segment. 1,min ,ΔP 1,max ].

Images