Wind speed and direction prediction method and device based on data double-layer two-dimensional reconstruction

Abstract

The application discloses a wind speed and wind direction prediction method and device based on data double-layer two-dimensional reconstruction, which comprises the following steps: obtaining wind speed and wind direction data; preprocessing the wind speed and wind direction data; calculating the X-direction component of wind speed and the Y-direction component of wind speed by using the preprocessed wind speed and wind direction data; performing double-layer two-dimensional reconstruction on the X-direction component of wind speed and the Y-direction component of wind speed to obtain double-layer two-dimensional data, wherein the double-layer two-dimensional data is composed of a group of matrices, each matrix is divided into an upper layer and a lower layer, the time step of each layer is 1, and the time step between two adjacent matrices is 1; inputting the double-layer two-dimensional data into a trained CNN-LSTM model to obtain wind speed and wind direction prediction results. The method can accurately predict future wind speed and wind direction, thereby providing an effective reference for the advance scheduling of a wind turbine.

Description

Technical Field

[0001] This application relates to the field of wind speed and wind direction prediction technology, and in particular to a method and apparatus for predicting wind speed and wind direction based on two-dimensional reconstruction of data. Background Technology

[0002] With the rapid development of the global economy, the energy market is undergoing profound changes. Traditional fossil fuels have caused serious environmental pollution, while human demand for energy continues to grow. Against this backdrop, promoting the advancement of new energy technologies and achieving energy transition has become a global consensus. Wind energy, as a widely distributed and abundant green energy source, has become one of the important ways to solve the energy crisis. In recent years, the wind power industry has developed rapidly, with global wind turbine installed capacity continuing to grow. However, due to the intermittent, unstable, and abrupt characteristics of wind energy, accurate and timely prediction of wind speed and direction is crucial for the operation of wind power systems.

[0003] The pitch angle of a wind turbine is a crucial parameter for controlling its output power. Improper adjustment can lead to unnecessary losses and reduce the turbine's power generation efficiency. The yaw system is another important component of a wind turbine; adjusting the yaw angle appropriately can improve the turbine's output power. Accurate wind speed and direction forecasts provide a basis for wind farm operation and maintenance scheduling. For example, adjusting the pitch and yaw angles in advance based on forecasts can increase wind farm capacity.

[0004] Current wind speed and direction prediction methods can be mainly divided into three categories: physical methods, statistical methods, and data-driven modeling methods. Existing wind speed prediction methods based on two-dimensional data reconstruction can predict wind speed relatively effectively, but their accuracy is low when directly applied to wind direction prediction, and they only use wind speed data and not wind direction data during prediction. Summary of the Invention

[0005] The purpose of this application is to provide a method and apparatus for predicting wind speed and direction based on two-dimensional reconstruction of data, so as to solve the problems of significant prediction lag and the need to design different feature extraction methods when predicting wind speed and direction in related technologies.

[0006] According to a first aspect of the embodiments of this application, a method for predicting wind speed and direction based on two-layer two-dimensional reconstruction of data is provided, including:

[0007] Obtain wind speed and wind direction data;

[0008] The wind speed and direction data are preprocessed;

[0009] The X-direction component and Y-direction component of wind speed are calculated using the preprocessed wind speed and direction data.

[0010] The X-direction component and Y-direction component of the wind speed are reconstructed in two layers to obtain two-layer two-dimensional data. The two-layer two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1.

[0011] The two-dimensional data is input into the trained CNN-LSTM model to obtain wind speed and wind direction prediction results, wherein:

[0012] Before training the CNN-LSTM model, the wind direction data is scaled.

[0013] The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data to obtain high-dimensional features, which are then input into the LSTM network after dimensionality reduction.

[0014] When training the CNN-LSTM model, a loss function that takes into account the periodicity of wind direction is used for wind direction.

[0015] After obtaining the output of the CNN-LSTM model, the wind direction output value is inversely scaled to obtain the final prediction results of wind speed and wind direction.

[0016] Optionally, the X-direction component and Y-direction component of the wind speed can be calculated using the preprocessed wind speed and direction data, including:

[0017] The formulas for calculating the X-axis and Y-axis components of wind speed are as follows:

[0018]

[0019]

[0020] In the formula, This is the wind speed value. This is the wind direction value. Let X be the X-axis component of the wind speed. This represents the Y-axis component of the wind speed.

[0021] Optionally, the upper layer of the matrix is ​​the result of reconstructing the X-direction component of the wind speed, and the lower layer is the result of reconstructing the Y-direction component of the wind speed. The two-dimensional data is generated by... The size is The matrix is ​​constructed, and the values ​​of the elements in the matrix are:

[0022]

[0023]

[0024]

[0025] In the formula Indicates the first The matrix at level 1 Line number The values ​​of the elements in the column. express t+n+i+j- The X-component of the wind speed at time 2. Indicates the first The second layer of the matrix Line number The values ​​of the elements in the column. express t+n+i+j- The Y-axis component of the wind speed at time 2.

[0026] Optionally, before training the CNN-LSTM model, the wind direction data is scaled, including:

[0027] Divide the wind direction data by the scaling factor, as shown in the following formula:

[0028]

[0029] In the formula The wind direction before scaling. This is the scaled-down wind direction. This is the scaling factor.

[0030] Optionally, the CNN-LSTM model uses a 3DCNN to extract features from the two-layer two-dimensional data. The output of the 3DCNN is a high-dimensional feature, and its convolution kernel calculation formula is as follows:

[0031]

[0032] In the formula, , For the input and output matrices, the first... Line number The column values, where ReLU is the activation function. For the first Line number Column weights For bias.

[0033] Optionally, the formula for the loss function Loss is:

[0034]

[0035] In the formula This is the wind direction output value. This represents the true wind direction. c This is the scaling factor.

[0036] Optionally, the formula for the inverse scaling is:

[0037]

[0038] In the formula This is the wind direction output value. This is the final wind direction forecast. c This is the scaling factor.

[0039] According to a second aspect of the embodiments of this application, a wind speed and wind direction prediction device based on data two-layer two-dimensional reconstruction is provided, comprising:

[0040] The acquisition module is used to acquire wind speed and wind direction data;

[0041] The preprocessing module is used to preprocess the wind speed and wind direction data;

[0042] The calculation module is used to calculate the X-direction component and Y-direction component of wind speed using preprocessed wind speed and direction data.

[0043] The reconstruction module is used to perform two-layer two-dimensional reconstruction of the X-direction component and the Y-direction component of the wind speed to obtain two-layer two-dimensional data. The two-layer two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1.

[0044] The prediction module is used to input the two-layer two-dimensional data into the trained CNN-LSTM model to obtain wind speed and wind direction prediction results, wherein:

[0045] Before training the CNN-LSTM model, the wind direction data is scaled.

[0046] The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data to obtain high-dimensional features, which are then input into the LSTM network after dimensionality reduction.

[0047] When training the CNN-LSTM model, a loss function that takes into account the periodicity of wind direction is used for wind direction.

[0048] After obtaining the output of the CNN-LSTM model, the wind direction output value is inversely scaled to obtain the final prediction results of wind speed and wind direction.

[0049] According to a third aspect of the embodiments of this application, an electronic device is provided, comprising:

[0050] One or more processors;

[0051] Memory, used to store one or more programs;

[0052] When the one or more programs are executed by the one or more processors, the one or more processors perform the method as described in the first aspect.

[0053] According to a fourth aspect of the embodiments of this application, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the steps of the method as described in the first aspect.

[0054] The technical solutions provided by the embodiments of this application may include the following beneficial effects:

[0055] As can be seen from the above embodiments, this application adopts a two-dimensional reconstruction of data processing, and then uses 3DCNN to extract high-dimensional features between wind speed components at different times, which effectively overcomes the problems of insufficient feature extraction capability and obvious prediction lag in existing prediction methods, and uses the same feature extraction method to predict wind speed and wind direction.

[0056] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0057] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0058] Figure 1 This is a flowchart illustrating a wind speed and direction prediction method based on two-dimensional reconstruction of data, according to an exemplary embodiment.

[0059] Figure 2 This is an example diagram illustrating the result of a two-dimensional reconstruction of data according to an exemplary embodiment.

[0060] Figure 3 This is a block diagram illustrating a wind speed and direction prediction device based on two-dimensional reconstruction of data, according to an exemplary embodiment. Detailed Implementation

[0061] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0062] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0063] Figure 1 This is a flowchart illustrating a wind speed and direction prediction method based on two-layer two-dimensional data reconstruction, according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0064] S1: Obtain wind speed and wind direction data;

[0065] Specifically, wind speed and direction data are acquired using wind turbine anemometers to construct a dataset. This section uses wind speed and direction data from an offshore wind farm located in New Jersey, USA. This example selects 13,200 wind speed and direction data points each from March 1, 2007 to May 31, 2007, with a sampling interval of 10 minutes.

[0066] S2: Preprocess the wind speed and wind direction data;

[0067] Specifically, the preprocessing involves filling in missing values ​​in the wind speed and wind direction data. In this embodiment, the mean linear interpolation method is used to fill in the missing values ​​in the wind speed and wind direction data. The calculation formula is as follows:

[0068]

[0069] In the formula, The time at which the missing value occurs. and They are respectively The nearest non-missing value before and after the given time.

[0070] S3: Calculate the X-direction component and Y-direction component of the wind speed using the preprocessed wind speed and direction data.

[0071] Specifically, the formulas for calculating the X-direction component and the Y-direction component of wind speed are as follows:

[0072]

[0073]

[0074] In the formula, This is the wind speed value. This is the wind direction value. Let X be the X-axis component of the wind speed. This represents the Y-axis component of the wind speed.

[0075] S4: Perform a two-dimensional reconstruction of the X-direction component and the Y-direction component of the wind speed. The two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1.

[0076] Specifically, the upper layer of the matrix represents the reconstructed result of the X-direction component of the wind speed, and the lower layer represents the reconstructed result of the Y-direction component of the wind speed. This dual-layer two-dimensional data is generated by... The size is The matrix is ​​constructed, and the values ​​of the elements in the matrix are:

[0077]

[0078]

[0079]

[0080] In the formula Indicates the first The matrix at level 1 Line number The values ​​of the elements in the column. express t+n+i+j- The X-component of the wind speed at time 2. Indicates the first The second layer of the matrix Line number The values ​​of the elements in the column. express t+n+i+j- The Y-axis component of the wind speed at time 2.

[0081] This two-dimensional reconstruction method utilizes information from both wind speed and wind direction. After the data is reconstructed in two dimensions, it can be input into a 3DCNN to extract high-dimensional features between wind speed components at different times, thereby enabling the model to better learn the high-dimensional relationships between wind speed components.

[0082] by Figure 2 Taking an example, a two-layer two-dimensional reconstruction of the X-axis and Y-axis components of wind speed is performed, resulting in a 6×3×2 matrix. For the X-axis and Y-axis components of wind speed, the time step between adjacent rows and columns is 1. For example, the first row and first column represent... t The data for each moment, represented in the first row and second column. t The data at time +1, represented in the first row and third column. t The data at time +2 is used for further calculations.

[0083] In this embodiment of the invention, the size of the matrix is ​​selected as 6×3, and the reconstructed data is divided into a training set, a validation set, and a test set, with 8000, 2500, and 2700 data entries in the training set, validation set, and test set, respectively.

[0084] S5: Input the two-dimensional data into the trained CNN-LSTM model to obtain the predicted values ​​of wind speed and wind direction;

[0085] Specifically, before training the CNN-LSTM model, the wind direction data is scaled using the following formula:

[0086] In the formula The wind direction before scaling. This is the scaled-down wind direction. This is the scaling factor. This scaling method is easy to calculate and makes the wind speed distribution range during model training close to the scaled wind direction distribution range.

[0087] Specifically, the CNN in the CNN-LSTM model is a 3D CNN. In time series prediction, CNN is a common network structure used for feature extraction, employing convolution operations in the spatial dimension to extract features from the data. In this model, the 3D CNN extracts high-dimensional features between wind speed components at different times through multi-level feature extraction. The formula for calculating its convolution kernel is:

[0088]

[0089] in, , For the input and output matrices, the first... Line number The column values, where ReLU is the activation function. For the first Line number Column weights For bias.

[0090] In this embodiment of the invention, the number of 3DCNN convolutional kernels is 128, and the kernel size is 3*3*2.

[0091] Since the output of 3DCNN is high-dimensional features, the data needs to be reconstructed into a format suitable for LSTM networks. That is, the high-dimensional features need to be reconstructed into two-dimensional feature vectors, including:

[0092] Using Keras' Reshape function, the three-dimensional features output by 3DCNN are reconstructed into two-dimensional feature vectors based on the matrix size and the size and number of 3DCNN convolution kernels.

[0093] In this embodiment of the invention, the shape of the output tensor of the 3DCNN is (4,1,1,128). After reshaping its shape to (4,128) using the Reshape function in Keras, it is input into the LSTM network.

[0094] For wind speed, the loss function chosen is MAE. For wind direction, since the wind direction sensor measures a range of... When the wind direction is When the wind direction changes from left to right, even small changes can cause significant fluctuations in the data, generating many "spurious singularities" and leading to decreased prediction accuracy. To address this issue, the loss function for wind direction prediction is defined as:

[0095]

[0096] In the formula This is the wind direction output value. This represents the true wind direction. c The scaling factor is used. The loss function takes into account the periodicity of wind direction, effectively solving the problem of "pseudo-singularities" and making the wind direction prediction results more accurate.

[0097] After obtaining the model's output, the wind direction output value is inversely scaled. The inverse scaling formula is:

[0098]

[0099] In the formula This is the wind direction output value. This is the final wind direction forecast. c This is the scaling factor.

[0100] Once the CNN-LSTM model is trained, it can be used for wind speed and direction prediction.

[0101] When predicting wind speed, this embodiment uses two statistical indicators, Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), to evaluate the estimation performance of the model. Their calculation formulas are as follows:

[0102]

[0103]

[0104] in, and These represent the actual value and the estimated value of the data, respectively.

[0105] When predicting wind direction, this embodiment uses two statistical indicators, the modified root mean square error (RMSE) and the modified mean absolute error (MAE), to evaluate the estimation performance of the model. Their calculation formulas are as follows:

[0106]

[0107]

[0108] An LSTM network predicts wind speed and direction using a sliding time window method. The prediction performance is compared with that of the wind speed and direction prediction method based on two-layer two-dimensional data reconstruction in this embodiment of the invention. Wind speed and direction values ​​are predicted for the next 10, 20, 30, 40, and 50 minutes. The wind speed prediction results are shown in the table below:

[0109]

[0110] The wind direction forecast results are shown in the table below:

[0111]

[0112] It can be seen that the wind speed and wind direction prediction method based on two-layer two-dimensional reconstruction of data in this embodiment of the invention is superior to the LSTM network in terms of accuracy, and the same feature extraction method is used to predict wind speed and wind direction.

[0113] As can be seen from the above embodiments, this application adopts a two-dimensional reconstruction of data processing, and then uses 3DCNN to extract high-dimensional features between wind speed components at different times, which effectively overcomes the problems of insufficient feature extraction capability and obvious prediction lag in existing prediction methods, and uses the same feature extraction method to predict wind speed and wind direction.

[0114] Corresponding to the aforementioned embodiments of the wind speed and direction prediction method based on two-dimensional reconstruction of data, this application also provides embodiments of a wind speed and direction prediction device based on two-dimensional reconstruction of data.

[0115] Figure 3 This is a block diagram illustrating a wind speed and direction prediction device based on two-layer two-dimensional data reconstruction, according to an exemplary embodiment. (Refer to...) Figure 3 The device includes:

[0116] Module 1 is used to acquire wind speed and wind direction data;

[0117] Preprocessing module 2 is used to preprocess the wind speed and wind direction data;

[0118] Calculation module 3 is used to calculate the X-direction component and Y-direction component of wind speed using preprocessed wind speed and direction data.

[0119] Reconstruction module 4 is used to perform two-dimensional reconstruction of the X-direction component and the Y-direction component of the wind speed to obtain two-dimensional data. The two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1.

[0120] Prediction module 5 is used to input the two-layer two-dimensional data into the trained CNN-LSTM model to obtain wind speed and wind direction prediction results, wherein:

[0121] Before training the CNN-LSTM model, the wind direction data is scaled.

[0122] The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data to obtain high-dimensional features, which are then input into the LSTM network after dimensionality reduction.

[0123] When training the CNN-LSTM model, a loss function that takes into account the periodicity of wind direction is used for wind direction.

[0124] After obtaining the output of the CNN-LSTM model, the wind direction output value is inversely scaled to obtain the final prediction results of wind speed and wind direction.

[0125] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0126] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0127] Accordingly, this application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the wind speed and wind direction prediction method based on data two-layer two-dimensional reconstruction as described above.

[0128] Accordingly, this application also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, implement the wind speed and wind direction prediction method based on two-dimensional reconstruction of data as described above.

[0129] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0130] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for predicting wind speed and direction based on two-layer two-dimensional reconstruction of data, characterized in that, include: Obtain wind speed and wind direction data; The wind speed and direction data are preprocessed; The X-direction component and Y-direction component of wind speed are calculated using the preprocessed wind speed and direction data. The X-direction component and Y-direction component of the wind speed are reconstructed in two layers to obtain two-layer two-dimensional data. The two-layer two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1. The two-dimensional data is input into the trained CNN-LSTM model to obtain wind speed and wind direction prediction results, wherein: Before training the CNN-LSTM model, the wind direction data is scaled. The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data to obtain high-dimensional features, which are then input into the LSTM network after dimensionality reduction. When training the CNN-LSTM model, a loss function that takes into account the periodicity of wind direction is used for wind direction. After obtaining the output of the CNN-LSTM model, the wind direction output value is inversely scaled to obtain the final prediction results of wind speed and wind direction.

2. The method according to claim 1, characterized in that, The X-axis and Y-axis components of wind speed are calculated using the preprocessed wind speed and direction data, including: The formulas for calculating the X-axis and Y-axis components of wind speed are as follows: ； ； In the formula, This is the wind speed value. This is the wind direction value. Let X be the X-axis component of the wind speed. This represents the Y-axis component of the wind speed.

3. The method according to claim 1, characterized in that, The upper layer of the matrix represents the reconstructed result of the X-direction component of the wind speed, and the lower layer represents the reconstructed result of the Y-direction component of the wind speed. This dual-layer two-dimensional data is generated by... The size is The matrix is ​​constructed, and the values ​​of the elements in the matrix are: ； ； ； In the formula Indicates the first The matrix at level 1 Line number The values ​​of the elements in the column. express t+n+i +j- The X-component of the wind speed at time 2. Indicates the first The second layer of the matrix Line number The values ​​of the elements in the column. express t+n+i+j- The Y-axis component of the wind speed at time 2.

4. The method according to claim 1, characterized in that, Before training the CNN-LSTM model, the wind direction data is scaled, including: Divide the wind direction data by the scaling factor, as shown in the following formula: ； In the formula The wind direction before scaling. This is the scaled-down wind direction. This is the scaling factor.

5. The method according to claim 1, characterized in that, The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data. The output of the 3DCNN is a high-dimensional feature, and its convolution kernel calculation formula is as follows: ； In the formula, , For the input and output matrices, the first... Line number The column values, where ReLU is the activation function. For the first Line number Column weights For bias.

6. The method according to claim 1, characterized in that, The formula for the loss function Loss, which takes into account the periodicity of wind direction, is as follows: ； In the formula This is the wind direction output value. This represents the true wind direction. c This is the scaling factor.

7. The method according to claim 1, characterized in that, The formula for inverse scaling is: ； In the formula This is the wind direction output value. This is the final wind direction forecast. c This is the scaling factor.

8. A wind speed and direction prediction device based on two-layer two-dimensional data reconstruction, characterized in that, include: The acquisition module is used to acquire wind speed and wind direction data; The preprocessing module is used to preprocess the wind speed and wind direction data; The calculation module is used to calculate the X-direction component and Y-direction component of wind speed using preprocessed wind speed and direction data. The reconstruction module is used to perform two-layer two-dimensional reconstruction of the X-direction component and the Y-direction component of the wind speed to obtain two-layer two-dimensional data. The two-layer two-dimensional data consists of a set of matrices. Each matrix is ​​divided into an upper layer and a lower layer. The time step of adjacent rows and columns in each layer is 1, and the time step between two adjacent matrices is 1. The prediction module is used to input the two-layer two-dimensional data into the trained CNN-LSTM model to obtain wind speed and wind direction prediction results, wherein: Before training the CNN-LSTM model, the wind direction data is scaled. The CNN-LSTM model uses 3DCNN to extract features from the two-layer two-dimensional data to obtain high-dimensional features, which are then input into the LSTM network after dimensionality reduction. When training the CNN-LSTM model, a loss function that takes into account the periodicity of wind direction is used for wind direction. After obtaining the output of the CNN-LSTM model, the wind direction output value is inversely scaled to obtain the final prediction results of wind speed and wind direction.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-7.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the method as described in any one of claims 1-7.

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