A method for predicting load timing adjustment potential based on error correction
By combining random forest and singular spectral analysis with TCN neural network for load potential prediction, the problems of data noise and high complexity are solved, and high-precision and efficient load potential analysis is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2023-08-30
- Publication Date
- 2026-06-30
AI Technical Summary
Existing technologies suffer from data noise and inaccurate measurement effects in load potential analysis. Furthermore, traditional methods require a large amount of actual operational data and are difficult to obtain due to the high complexity and limited accuracy of the analysis.
The random forest algorithm is used to handle missing values, the singular spectrum analysis method is used to decompose the time series into low-frequency, mid-frequency and high-frequency modes, the TCN neural network is combined for potential prediction, and the dynamic mode decomposition algorithm is used for error correction to obtain the final adjustable potential prediction result.
It effectively handles the impact of data disturbances, improves the accuracy and smoothness of potential analysis, reduces prediction complexity and error, and enhances prediction accuracy and speed.
Smart Images
Figure CN117293791B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power load potential response assessment, and more particularly to a method for predicting load timing adjustment potential based on error correction. Background Technology
[0002] Currently, potential analysis methods mainly fall into two categories. The paper "Analysis Model of Adjustable Potential for Large Industrial Users Based on Fusion FCN-TCN-LSTM," by Li Bin, North China Electric Power University, proposes a combined neural network potential analysis method. This method selects industrial users with high adjustable potential load data, combines the impact of real-time electricity prices and user costs on potential, and uses LSTM to address the error in adjusting potential. However, this paper does not address the influence of noise and inaccurate measurement in the acquired raw data. Furthermore, some related technologies employ extensive mathematical statistics and on-site surveys to obtain relevant user potential. The paper "Analysis of Adjustable Load Potential on the Demand Side of Electricity in the Industrial Sector," by Cheng Yuan, NARI Group, assesses various load adjustment characteristics and load response potential through surveys and visits, combined with users' actual electricity consumption patterns and actual electricity demand. However, this method of obtaining potential requires a large amount of actual operational data and actual modeling of each production stage of the load, resulting in a huge workload. In addition, the electricity data involves highly confidential aspects related to users' actual operations and costs, making data acquisition difficult. Summary of the Invention
[0003] Purpose of the invention: The purpose of this invention is to provide a load timing adjustment potential prediction method based on error correction that can effectively handle the impact of data disturbances and improve the accuracy of potential analysis.
[0004] Technical solution: The load timing adjustment potential prediction method of the present invention includes the following steps:
[0005] S10, Obtain raw load response data;
[0006] S20, perform RF processing on the raw load response data to obtain complete time series data;
[0007] S30: Use SSA to decompose the complete time series data, extract the time series sub-modes, and perform potential prediction. The predictions of each sub-mode are superimposed and summed to obtain the preliminary time series regulation potential prediction results.
[0008] S40, the difference between the preliminary time series conditioning potential and the original time series conditioning potential is calculated to obtain the time series conditioning potential error. The dynamic mode decomposition algorithm is used to correct the time series conditioning potential error of the preliminary time series conditioning potential prediction result to obtain the final time series conditioning potential prediction result.
[0009] Furthermore, in step S10, the original load response data includes upper limit adjustment data and lower limit adjustment data.
[0010] Furthermore, in step S20, the steps to obtain the complete time series data are as follows:
[0011] S201, classify the collected raw load response data into data with missing information and data without missing information;
[0012] S202, Use the data without missing data to train the RF model and obtain the trained RF model;
[0013] S203 involves dividing the missing data into multiple decision tree models and substituting them into the trained RF model to fill in the missing values, thus obtaining complete time series data.
[0014] Furthermore, in step S30, the complete time series data is decomposed into multiple time series-based low-frequency, mid-frequency, and high-frequency modes using SSA, as follows:
[0015] S301, transform the time column vector into a two-dimensional matrix form to obtain the trajectory matrix Y:
[0016]
[0017] In the formula, K is the embedding dimension; M = H - K + 1, where H is the total number of time column vectors;
[0018] S302, Solving for the trajectory matrix Y, and using mathematical operations to obtain the corresponding eigenvalues and eigenvectors, we have:
[0019] Y = Y1 + Y2 + ... + Y c +...+Y n
[0020] in, λ n Let S be the eigenvalue of Y. n and F n These are the left and right eigenvectors of Y, respectively;
[0021] S303, Given the mathematical relationship between K and M, respectively, matrix Y... n Convert to the corresponding one-dimensional sub-load time series [y n1 y n2 , ..., y nk ], y nk The expression is as follows:
[0022]
[0023] In the formula, k = 1, 2, ..., H; K * =min(K, M); M * =max(K, M); L * =min(L,K); y * a,k-a+1 For matrix Y n In the elements, a and k represent the elements in Y. n The position in the middle.
[0024] Furthermore, in step S30, the TCN algorithm is used to sum the predictions of each sub-mode superposition. The specific steps are as follows:
[0025] First, the residuals are stacked and combined with dilated convolutions to construct a complete TCN prediction model;
[0026] Secondly, each sub-modality is fed into the TCN prediction model for training;
[0027] Finally, the prediction results of each sub-mode are summed to obtain the preliminary prediction results of the time series conditioning potential.
[0028] Furthermore, in step S40, the implementation steps for correcting the timing adjustment potential error of the preliminary timing adjustment potential prediction results using the dynamic mode decomposition algorithm are as follows:
[0029] S401, Constructing the error Hankel matrix
[0030] The time-series adjustment potential error is normalized by converting the normalized error sequence into a multi-dimensional data matrix. The normalized error time series of length N is X = [x1, x2, x3, ..., x...]. i , ..., x N ], x i It is the error snapshot at time i, where the time interval between any two adjacent error snapshots is Δt;
[0031] Expand the error time series X into a multidimensional data matrix with a window length of L∈[2≤L≤(N / 2)] and an overlap of K=N-L+1 segments, and construct the Hankel matrix X. * :
[0032]
[0033] In the formula, the Hankel matrix X * The elements on each of these diagonals are equal;
[0034] S402, Error Mode Decomposition
[0035] Construct a snapshot matrix X1 using error snapshots from 1 to L. * =[x1* x2 * , ..., x L-1 * ] and X2 * =[x2 * x3 * , ..., x L * ];
[0036] Wherein, the lag vector x L * The average interval is Δt, therefore there is a mapping A between the continuous lag vectors, such that X2 * =AX1 * ;
[0037] For X1 * Perform singular value decomposition:
[0038]
[0039] In the formula, U and U H It is a singular vector with the left and right sides, V * Let Σ be the adjoint matrix of V, and let X1 be the adjoint matrix of V. * The singular diagonal matrix, where "H" denotes matrix transpose;
[0040] The expression for calculating B is:
[0041]
[0042] Combining the above formula, we get:
[0043] g i =Re{lg(μ i )} / Δt
[0044] f i =Im{lg(μ i )} / Δt
[0045] Where, μ i Let g be the i-th eigenvalue of B; i f is the growth rate of the i-th error pattern; i Let be the frequency of the i-th error pattern;
[0046] S403, Reconstruct the error sequence
[0047] Error snapshots are obtained through singular value decomposition. The eigenvalues of the subspace matrix B of the mapping are expressed as:
[0048] B = WDW -1
[0049] D = diag(μ1, μ2, ..., μr )
[0050] In the formula, W is the error eigenvector w i The matrix W -1 is the inverse matrix of W; D is the diagonal matrix of the singular values of B;
[0051] The error snapshot at any given time is estimated as follows:
[0052]
[0053]
[0054] An erroneous snapshot reconstructed at any given time is represented as:
[0055]
[0056] In the formula, α=[α1, α2,…,α r ] T α r It is the amplitude of the r-th mode, Ф j =Uw j For the error pattern; reconstruct an error time series matrix X with a window length of p. R * :
[0057]
[0058] Where Φ=[Φ1,…,Φ r [] indicates the error mode corresponding to the amplitude; p>r;
[0059] S404, Prediction Error Sequence
[0060] The reconstructed error values are denormalized to recover the true error values, and the denormalized error matrix is reconstructed into X. R ^,X R The matrix is represented as:
[0061]
[0062] According to the above formula, in X R Average operation on the diagonal of ^:
[0063]
[0064] In the formula, m and n represent the elements in matrix X. R The position within ^;
[0065] The final time series conditioning potential prediction result x is represented as:
[0066] x = [x1, x2, ..., xf ]
[0067] Among them, X R ^∈R g*f , g = p - f + 1, R represents the set of real numbers.
[0068] Compared with the prior art, the significant advantages of this invention are as follows:
[0069] This invention processes outlier and missing values in load response data to obtain a complete dataset, resulting in smoother and more stable curves. The processed data is then decomposed into low-frequency, mid-frequency, and high-frequency sub-modes based on time series, eliminating noise components that interfere with load prediction results. Potential prediction is then performed on each of these sub-modes. The prediction results are superimposed to obtain a preliminary prediction result, which is then corrected based on error correction principles to obtain a final, adjustable potential intelligent prediction result. This invention solves the problems of excessive complexity and limited generalization ability in traditional time-series potential prediction, effectively handles the influence of data disturbances, and improves the accuracy of potential analysis. Attached Figure Description
[0070] Figure 1 This is a schematic diagram of the process of the present invention;
[0071] Figure 2 This is a schematic diagram of the RF algorithm;
[0072] Figure 3 Diagram of TCN analysis model architecture
[0073] Figure 4 This is a schematic diagram of the overall modeling based on SSA-TCN-DMD;
[0074] Figure 5 This is a schematic diagram of the overall process based on SSA-TCN-DMD;
[0075] Figure 6 In the diagram, (a) shows the low-frequency component results of SSA, and (b) shows the mid-frequency component results of SSA.
[0076] (c) is the result diagram of the high-frequency components of SSA, and (d) is the result diagram of the frequency of each component.
[0077] Figure 7 The figure shows the results of the SSA-TCN-DMD potential analysis. Detailed Implementation
[0078] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0079] This invention utilizes random forests to fill missing values in the original data, and then decomposes the processed data into multiple low-frequency, mid-frequency, and high-frequency sub-modes based on time series using Singular Spectrum Analysis (SSA). A Temporal Convolutional Network (TCN) model is then established to overlay and predict each time series-based sub-mode. Using the preliminary prediction and the original potential error results, and based on the error correction principle, the prediction results are corrected to obtain the final intelligent prediction result of adjustable potential.
[0080] like Figure 1 As shown, the load timing adjustment potential prediction method of the present invention includes the following steps:
[0081] Step 1: Obtain raw load response data, including upper and lower limit adjustment data.
[0082] Step 2: Perform RF (Random Forest) processing on the raw load response data to obtain complete time series data;
[0083] like Figure 2 As shown, the raw load response data obtained in step 1 is processed by using random forest regression to supplement the data and obtain complete time series data, making the original potential curve smoother and laying the foundation for subsequent data decomposition.
[0084] The steps to supplement the data and obtain complete time series data using random forest regression are as follows:
[0085] First, the collected raw load response data was classified into data with missing information and data without missing information; second,
[0086] The Random Forest (RF) model is trained using data without missing data to obtain a trained RF model;
[0087] Finally, the missing data is divided into multiple decision tree models and fed into the trained RF model to fill in the missing values, thus obtaining complete time series data.
[0088] Step 3: Use SSA to decompose the complete time series data, extract the time series sub-modes, and perform potential prediction. Superimpose the predictions of each sub-mode to obtain the preliminary load time series adjustment potential prediction results. Each sub-mode includes multiple time series-based low-frequency modes, medium-frequency modes, and high-frequency modes to avoid interference between different frequency sub-modes.
[0089] The complete time series data obtained in step 2 is decomposed into several sub-modalities with distinct characteristics, including the following steps:
[0090] Step 31: Transform the time column vector into a two-dimensional matrix form to obtain the trajectory matrix Y:
[0091]
[0092] In the formula, K is the embedding dimension; M = H - K + 1, where H is the total number of time column vectors.
[0093] Step 32: Solve for the trajectory matrix Y, and use mathematical operations to obtain the corresponding eigenvalues and eigenvectors. Therefore:
[0094] Y = Y1 + Y2 + ... + Y c +…+Y n (2)
[0095] in, λ n Let S be the eigenvalue of Y. n and F n These are the left and right eigenvectors of Y, respectively.
[0096] Step 33, given the mathematical relationship between K and M, respectively convert matrix Y... n Convert to the corresponding one-dimensional sub-load time series [y n1 y n2 , ..., y nk , y nk The expression is as follows:
[0097]
[0098] In the formula, k = 1, 2, ..., H; K * =min(K, M); M * =max(K, M); L * =min(L,K); y * a,k-a+1 For matrix Y n In the elements, a and k represent the elements in Y. n The position in the middle.
[0099] like Figure 3 As shown, the TCN algorithm is used to predict and sum the superposition of each sub-mode. The specific steps are as follows:
[0100] First, the residuals are stacked and combined with dilated convolutions to construct a complete TCN prediction model;
[0101] Secondly, each sub-modality is fed into the TCN prediction model for training;
[0102] Finally, the prediction results of each sub-mode are summed to obtain the preliminary prediction results of the time series conditioning potential.
[0103] Step 4: Correct the errors in the preliminary time series regulation potential prediction results in order to achieve better final time series regulation potential prediction results;
[0104] The simulation comparison uses a random forest-based data processing method, and adds a secondary prediction based on the error principle on the basis of the combined neural network (SSA-TCN). The prediction results of the time series conditioning potential with error correction using DMD (Dynamic Model Decomposition) are compared with the prediction results of the time series conditioning potential without correction.
[0105] The dynamic mode decomposition algorithm is used to correct the error in the preliminary time series conditioning potential prediction results, including the following steps:
[0106] Step 41, construct the error Hankel matrix
[0107] Before performing DMD decomposition, the error data needs to be normalized to improve the convergence speed of the prediction model.
[0108] To further capture the complete mode of the error sequence, the normalized error sequence is converted into a multi-dimensional data matrix. If the normalized error time series of length N is X = [x1, x2, x3, ..., x...], then... i , ..., x N ], x i It is the error snapshot at time i, where the time interval between any two adjacent error snapshots is Δt (the interval is 1 hour or 15 minutes).
[0109] The error time series X is expanded into a multidimensional data matrix with a window length of L ∈ [2 ≤ L ≤ (N / 2)] and an overlap of K = N - L + 1 segments. This allows the construction of the Hankel matrix X. * :
[0110]
[0111] In the formula, the Hankel matrix X * The elements on each of these diagonals are equal, and generating an error matrix with this special structure helps to better capture the dynamic change patterns of errors.
[0112] Step 42, Error Mode Decomposition
[0113] Using error snapshots from 1 to L, a snapshot matrix X1 can be constructed. * =[x1 * x2 * , ..., xL-1 * ] and X2 * =[x2 * x3 * , ..., x L * ].
[0114] Wherein, the lag vector x L * The average interval is Δt, therefore there is a mapping A between the continuous lag vectors, such that X2 * =AX1 * A is a high-dimensional error system matrix that reflects the dynamic characteristics of the error system.
[0115] Because the reconstructed system has better numerical stability, for X1 * Perform singular value decomposition:
[0116] X1 * =UΣV * (5)
[0117] A = UBU Z (6)
[0118] In the formula, U and U Z It is a singular vector with the left and right sides, V * Let Σ be the adjoint matrix of V, and let X1 be the adjoint matrix of V. * A singular diagonal matrix.
[0119] The calculation of B can be expressed as:
[0120]
[0121] Combining equations (5) and (7), we can obtain:
[0122] g i =Re{lg(μ i )} / Δt (8)
[0123] f i =Im{lg(μ i )} / Δt (9)
[0124] In the formula, μ i Let g be the i-th eigenvalue of B; i f is the growth rate of the i-th error pattern; i Let be the frequency of the i-th error pattern.
[0125] The error variation process is further estimated based on matrix B.
[0126] Step 43, Reconstruct the error sequence
[0127] Error snapshots are obtained through singular value decomposition. The eigenvalues of the subspace matrix B of the mapping are expressed as:
[0128] B = WDW -1 (10)
[0129] D = diag(μ1, μ2, ..., μ r )
[0130] In the formula, W is the error eigenvector w i The matrix W -1 D is the inverse matrix of W; D is the diagonal matrix of the singular values of B.
[0131] According to equation (10), the error snapshot at any time can be estimated as follows:
[0132]
[0133]
[0134] An erroneous snapshot reconstructed at any given time can be represented as:
[0135]
[0136] In the formula, α=[α1, α2,…,α r ] T α r It is the amplitude of the r-th mode, Ф j =Uw j For the error pattern, reconstruct an error time series matrix X with a window length of p (p>r). R * , can be represented as:
[0137]
[0138] Where Φ=[Φ1,…,Φ r ] indicates the error mode corresponding to the amplitude.
[0139] By using the standard Vandermonde matrix V and (p) to form the time series of the DMD model, x R(p) * It can be increased to an appropriate error value.
[0140] Step 44, Predict the error sequence
[0141] Since the reconstructed error values range from [0, 1], inverse normalization is needed to recover the true error values. The inverse normalized error matrix is then reconstructed as X. R ^,X R ^∈R g*f, g = p - f + 1, R represents the set of real numbers. X R The matrix is represented as:
[0142]
[0143] To obtain the accurate error sequence with a window length of f, it is necessary to apply equation (15) to X. R Average operation on the diagonal of ^:
[0144]
[0145] In the formula, m and n represent the elements in matrix X. R The position within ^.
[0146] The final time series conditioning potential prediction result x can be expressed as:
[0147] x = [x1, x2, ..., x f (17)
[0148] like Figure 4 , Figure 5 As shown, the original potential data is decomposed using singular spectrum analysis, and then the time-series adjustable potential is initially obtained using TCN. The difference between the initial time-series adjustable potential and the original time-series adjustable potential is calculated to obtain the time-series adjustable potential error. The time-series adjustable potential error is predicted using DMD and superimposed with the initial time-series adjustable potential to obtain the final time-series adjustable potential prediction result.
[0149] like Figure 6 As shown in (a), (b), (c), and (d), the original time-series regulation potential data were decomposed using singular spectrum analysis and, combined with the results of multiple experiments, were divided into low-frequency, mid-frequency, and high-frequency modes.
[0150] like Figure 7 As shown, the preliminary results of the time series modulation potential, the time series modulation potential error, and the final results of the time series modulation potential analysis are presented. From Figure 7 The results show that the SSA-TCN-DMD model has higher accuracy in predicting load regulation potential. The MAPE (Mean Absolute Percentage Error) and RMSE (Root Mean Square Error) for the load user area are both less than 2, representing an average reduction of 34% in prediction error compared to the SSA-TCN combined prediction model. Prediction time is also reduced by 25% to 157 seconds.
[0151] This embodiment fills in missing values in the original data using a random forest; it uses the SSA-TCN algorithm to address the interference of data disturbances and measurement errors on load forecasting results, making the original potential curve smoother and laying the foundation for subsequent data decomposition, thus reducing errors caused by actual load development; and it uses the DMD algorithm to solve the problems of excessive complexity and poor accuracy in traditional time-series potential forecasting. Compared to traditional interpolation algorithms, the random forest algorithm used in this embodiment makes the curve smoother and fills in missing values; the SSA-TCN-DMD-based analysis model used in this embodiment can effectively handle the influence of data disturbances, taking into account the distance and morphological similarity between components to improve the accuracy of potential analysis.
Claims
1. A method for predicting load timing adjustment potential based on error correction, characterized in that, The steps include the following: S10, Obtain raw load response data; S20, perform RF processing on the raw load response data to obtain complete time series data; S30: Use SSA to decompose the complete time series data, extract the time series sub-modes, and perform potential prediction. The predictions of each sub-mode are superimposed and summed to obtain the preliminary time series regulation potential prediction results. S40, the difference between the preliminary time series conditioning potential and the original time series conditioning potential is calculated to obtain the time series conditioning potential error. The dynamic mode decomposition algorithm is used to correct the time series conditioning potential error of the preliminary time series conditioning potential prediction result to obtain the final time series conditioning potential prediction result. In step S10, the raw load response data includes upper limit adjustment data and lower limit adjustment data; In step S20, the steps to obtain complete time series data are as follows: S201, classify the collected raw load response data into data with missing information and data without missing information; S202, Use the data without missing data to train the RF model and obtain the trained RF model; S203 involves dividing the missing data into multiple decision tree models and feeding them into the trained RF model. Missing values are filled in to obtain complete time series data; In step S30, the complete time series data is decomposed into multiple time series-based low-frequency, mid-frequency, and high-frequency modes using SSA. The steps are as follows: S301, transform the time column vector into a two-dimensional matrix form to obtain the trajectory matrix Y: ， In the formula, K is the embedding dimension; M = H - K + 1, where H is the total number of time column vectors; S302, Solving for the trajectory matrix Y, and using mathematical operations to obtain the corresponding eigenvalues and eigenvectors, we have: ， in, , λ n Let S be the eigenvalue of Y. n and F n These are the left and right eigenvectors of Y, respectively; S303, knowing the mathematical relationship between K and M, respectively, the matrix Y n is converted to the corresponding one-dimensional sub-load time series [y n1 , y n2 ,..., y nk ] The expression of y nk is as follows: ， where k = 1, 2,..., H; K * = min(K, M); M * = max(K, M); L * = min(L, K); y * a,k-a+1 is an element in matrix Y n , where a and k denote the position of the element in Y n .
2. The load timing adjustment potential prediction method based on error correction according to claim 1, characterized in that, In step S30, the TCN algorithm is used to predict and sum the superposition of each sub-mode. The specific steps are as follows: First, the residuals are stacked and combined with dilated convolutions to construct a complete TCN prediction model; Secondly, each sub-modality is fed into the TCN prediction model for training; Finally, the prediction results of each sub-mode are summed to obtain the preliminary prediction results of the time series conditioning potential.
3. The load timing adjustment potential prediction method based on error correction according to claim 1, characterized in that, In step S40, the implementation steps for correcting the timing adjustment potential error of the preliminary timing adjustment potential prediction results using the dynamic mode decomposition algorithm are as follows: S401, Constructing the error Hankel matrix The time-series adjustment potential error is normalized by converting the normalized error sequence into a multi-dimensional data matrix. The normalized error time series of length N is X=[x1, x2, x3, ..., x...]. i , ..., x N ], x i It is the error snapshot at time i, where the time interval between any two adjacent error snapshots is ∆t; Expand the error time series X into a multidimensional data matrix with a window length of L∈[2≤L≤(N / 2)] and an overlap of K=N-L+1 segments, and construct the Hankel matrix X. * : ， In the formula, the Hankel matrix X * The elements on each of these diagonals are equal; S402, Error Mode Decomposition Construct a snapshot matrix X1 using error snapshots from 1 to L. * =[x1 * x2 * , ..., x L-1 * ] and X2 * =[ x2 * x3 * , ..., x L * ]; Wherein, the lag vector x L * The average interval is ∆t, therefore there is a mapping A between the continuous lag vectors such that X2 * =AX1 * ; For X1 * Perform singular value decomposition: ， ， In the formula, U and U H It is a singular vector with the left and right sides, V * Let Σ be the adjoint matrix of V, and let X1 be the adjoint matrix of V. * The singular diagonal matrix, where "H" denotes matrix transpose; The expression for calculating B is: ， Combining the above formula, we get: ， ， Where, μ i Let g be the i-th eigenvalue of B; i f is the growth rate of the i-th error pattern; i Let be the frequency of the i-th error pattern; S403, Reconstruct the error sequence Error snapshots are obtained through singular value decomposition. The eigenvalues of the subspace matrix B of the mapping are expressed as: ， ， In the formula, W is the error eigenvector w i The matrix W -1 is the inverse matrix of W; D is the diagonal matrix of the singular values of B; The error snapshot at any given time is estimated as follows: ， ， An erroneous snapshot reconstructed at any given time is represented as: ， In the formula, α=[α1, α2,…, α r ] T α r It is the amplitude of the r-th mode, Ф j =Uw j For the error pattern; reconstruct an error time series matrix X with a window length of p. R * : ， in, This indicates the error pattern corresponding to the amplitude; p>r; S404, Prediction Error Sequence The reconstructed error values are denormalized to recover the true error values, and the denormalized error matrix is reconstructed into X. R ^,X R ^ The matrix is represented as: ， According to the above formula, in X R ^ Average along the diagonal: ， In the formula, m and n represent the elements in matrix X. R ^ The position in the middle; The final time series conditioning potential prediction result x is represented as: ， Among them, X R ^ ∈R g*f , g = p - f + 1, R represents the set of real numbers.