Short-term load forecasting method and terminal

Abstract

The application provides a short-term load prediction method and a terminal, the application combines a transformer model and an AR model to improve the prediction effect of transformer bus load together, the transformer model is mainly responsible for the prediction of high-frequency nonlinear part in time series data, and the AR model is mainly responsible for the prediction of low-frequency linear part in time series data.In the encoder part, the features are distilled along the time dimension layer by layer first, so that the periodic characteristics of different frequencies in the load data are extracted while the total memory usage is reduced, then the periodic characteristics of multiple frequencies are superimposed and aggregated to obtain the fusion characteristics across the cycle.In the process of gathering information by using the attention mechanism, more attention is paid to the part where the data is similar and the data change trend is similar, so that the sequence level connection of time series information is realized, and more reliable time dependence is mined.

Description

Technical Field

[0001] This invention relates to the field of power grid bus load forecasting technology, and in particular to a short-term load forecasting method and terminal based on AR-Transformer. Background Technology

[0002] Existing load forecasting methods can be broadly categorized into two types: traditional load forecasting methods and machine learning-based load forecasting methods. Traditional load forecasting typically employs classic linear statistical models, such as exponential smoothing (MA), autoregressive integrated moving average (ARIMA), seasonally adjusted autoregressive integrated moving average (SARIMA), and the Prophet model based on sequence decomposition. Traditional models achieve a good balance between forecasting accuracy and simplicity. However, they exhibit significant limitations in modeling nonlinear relationships in the data and in terms of forecast length. Artificial intelligence-based load forecasting often uses neural network models to learn the dependencies between time series data. For example, Marino et al. first attempted to use Long Short-Term Memory (LSTM) networks for equal load forecasting, achieving relatively good results in shorter-term load forecasts. However, LSTM and other RNN models struggle to accurately capture long-term dependencies between inputs and outputs. Therefore, as the forecast sequence grows, the performance of these models on load forecasting tasks declines sharply. Furthermore, existing models often fail to accurately capture long-term dependencies between inputs and outputs. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention provides a short-term load forecasting method. This invention combines the Transformer model and the AR model to improve the forecasting effect of transformer bus load. The Transformer model is mainly responsible for the prediction of the high-frequency nonlinear part in the time series data, while the AR model is mainly responsible for the prediction of the low-frequency linear part in the time series data.

[0004] The method includes: Step 1: Input encoding is performed, processing load information, weather information, rate of change information, and time information to obtain initial load characteristics and auxiliary characteristics. These two parts are then input into the model to obtain the predicted value of the sequence to be predicted. The mean square error between the actual value and the predicted value of the sequence to be predicted is calculated, and backpropagation is performed from the model output to update the model parameters.

[0005] Assume the load input of the model at time t is: The rate of change is obtained by differentiating it along the time dimension and then normalizing it. To align dimensions with other features, first use a one-dimensional convolution with a kernel of 3 to convolve X... t and C t Transform from 1D to d hidenDimension, obtained and For weather features, a one-dimensional convolution with a kernel of 3 is also used to transform them from dimension d. weather Convert to dimension d hiden ,get The load characteristics with added time information and location coding are: Where PE represents location coding, TE represents global time coding, and p represents the type of time information to be coded. The weather feature with added time information and location coding is: The rate of change features for adding time information and location encoding are as follows: The weather features, rate of change features, and load features are concatenated along the feature dimension and then subjected to a one-dimensional convolution to obtain the auxiliary feature s. t,i =Conv(Concat(x) t,i ,k t,i ,c t,i The final input model has two parts: auxiliary features s t,i and load characteristics x t,i .

[0006] Let the input of the attention layer be X t ∈R L*d and S t ∈R L*d And the output of the Att(.) function is O. t ∈R L*d The output obtained after passing through the attention layer is:

[0007] O t =Att(S t X t )

[0008] Here, Att(.) represents the attention function, and its time and space complexity are both O(Ld). 2 );

[0009] The attention function Att(.) is calculated as follows:

[0010] O = S(Q, K)V = (Q cos K cos +Q sin K sin V = Q cos (K cos V)+Q sin (K sin V)

[0011] Where Q = W Q S t K = W K S t V = Wv X t W Q W K With W v Represents weight;

[0012] Step 2: Configure the encoder. The encoder consists of multiple encoding layers. In the encoding layers of the encoder, attention layers and convolutional layers are used for selective temporal feature updates. Then, the sequence segmentation module and convolutional layers are used to reduce the dimensionality of the input sequence along the time dimension, while extracting periodic features from the temporal sequence. The specific operations in the j-th encoding layer are as follows:

[0013] X′ t，j =ELU(Conv(Att(X) t，j S t，j )))

[0014] X t，j+1 =ELU(Conv(SeriesPartion(X′ t，j )))

[0015] Time-series data first passes through a self-attention layer (Att), then a convolutional layer, followed by processing along the time dimension using the sequence segmentation module (SeriesPartion), and finally another convolutional layer. Except for the first encoding layer, the remaining encoding layers... t，j =X t，j .

[0016] Step 3: Configure the decoder: The decoder consists of multiple decoding layers, each consisting of two multi-head attention layers and two one-dimensional convolutional layers stacked together; the initial payload feature input of the decoder is:

[0017]

[0018] in, Represents the start character; The placeholders representing the predicted values ​​are all composed of 0.

[0019] The dimension of the decoder's payload feature input is The rate of change feature input for the decoder is: This represents a placeholder, consisting entirely of 0s. Corresponding weather characteristics This can be directly obtained from the data. The decoder's input also undergoes input encoding, adding local and global temporal features to obtain load features and auxiliary features. The output after multiple decoding layers is linearly encoded into feature dimensions identical to the true values. The encoder's final output is represented as...

[0020] Step 4: Configure AR components:

[0021] The AR component is used to predict the low-frequency linear portion of a time series. The AR component is implemented using linear regression.

[0022] The specific method is as follows: in,

[0023] The final output of the model is

[0024]

[0025] It should be further noted that in step one, Query and Key use convolution kernels with a size greater than 1 for convolution operations.

[0026] It should be further noted that in step two, the encoder in the nonlinear component consists of m coding layers, and the coding layers include attention layers, sequence segmentation modules, and convolutional layers.

[0027] It should be further noted that the step size is configured to 2, and the dimensions after partitioning the time series data are from L. input *d hiden become Then, they are fused along the time dimension by a one-dimensional convolution with a kernel of 3. The fused dimension is from... Convert to Finally, it is activated by the ELU function.

[0028] It should be further explained that the encoder consists of m coding layers connected in series. The outputs of multiple coding layers are first downsampled to the same dimension, and then the multi-layer outputs are compressed by splicing and aggregation.

[0029] The specific steps are as follows:

[0030]

[0031] in, The output represents the fused result, Maxpooling represents downsampling, Concat represents the concatenation function, and W represents the concatenation function. fuse ∈R m*1 These are the learned aggregation parameters; the fused features pass through an attention layer and two convolutional layers to obtain the encoder output.

[0032]

[0033] The present invention also provides a terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the steps of a short-term load forecasting method.

[0034] As can be seen from the above technical solutions, the present invention has the following advantages:

[0035] This invention uses the Transformer model to solve the long-distance dependency between input and output in long-term time series forecasting, thereby improving the effectiveness of load forecasting.

[0036] Due to the nonlinear characteristics of the activation layer, existing technologies such as Transformer are prone to introducing additional errors when modeling linear relationships, making them less sensitive to linear scaling in time-series data. This invention introduces an AR model, combining the Transformer and AR models to improve prediction performance.

[0037] This invention improves the encoder part in the classic Transformer model. The improved encoder adopts a hierarchical design and uses a "layer-by-layer distillation-multi-layer fusion" approach to solve the problem of high memory usage while extracting cross-periodic features from time-series data in a more targeted manner.

[0038] This invention enables the model to not only focus on parts of the data similar to the predicted values ​​when gathering useful information using the attention mechanism, but also to favor information with similar trends of change to the predicted data based on the gradient changes in the data. This solves the problem that the attention mechanism in existing Transformer models typically only focuses on parts of the data that are similar to the predicted values, while ignoring parts with similar trends of change, making it unsuitable for time series prediction models. Attached Figure Description

[0039] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a diagram illustrating the architecture of a short-term load forecasting method.

[0041] Figure 2 This is a schematic diagram of the rate of change image and the original data image;

[0042] Figure 3 This is a schematic diagram of sequence-level connections. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0044] like Figures 1 to 3 As shown, the illustrations provided in the short-term load forecasting method of the present invention are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components. In actual implementation, the type, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0045] The short-term load forecasting method provided by this invention consists of nonlinear and linear components. This invention optimizes the traditional Transformer model as the nonlinear component to predict the nonlinear high-frequency portion of the time series, and uses the AR model as the linear component to predict the linear low-frequency portion. The loss function involved in this invention is the MSE loss, which first calculates the mean squared error between the actual and predicted values ​​of the sequence to be predicted, then backpropagates from the model's output to update the model parameters.

[0046] The embodiments of the present invention can acquire and process related data based on artificial intelligence technology. Artificial intelligence (AI) refers to the theories, methods, technologies, and application devices that use digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use that knowledge to obtain optimal results.

[0047] like Figures 1 to 3 A flowchart illustrating a preferred embodiment of the short-term load forecasting method based on AR-Transformer of the present invention is shown. The short-term load forecasting method based on AR-Transformer is applied to one or more terminals, which are devices capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions. Their hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0048] A terminal can be any electronic product that allows human-computer interaction, such as a personal computer, tablet computer, smartphone, personal digital assistant (PDA), interactive network television (IPTV), smart wearable device, etc.

[0049] The terminal may also include network devices and / or user equipment. The network devices include, but are not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of hosts or network servers.

[0050] The network in which the terminal is located includes, but is not limited to, the Internet, wide area network, metropolitan area network, local area network, and virtual private network (VPN).

[0051] The following detailed description, in conjunction with the accompanying drawings, of the AR-Transformer-based short-term load forecasting method of this invention. This forecasting method can accurately and timely predict the load on the power grid bus, providing a reference for power grid operation and control, and contributing to the goals of energy conservation, emission reduction, and refined power grid dispatch management. Furthermore, load forecasting can assist power companies in making decisions regarding power generation and purchase, load switching, voltage control, network reconfiguration, and infrastructure construction. Transformer bus load forecasting primarily refers to predicting the bus load for the next day, week, or even several weeks. By predicting the distribution of future power load, the level of precision in dispatch management can be improved, promoting the safe and stable operation of the power grid, achieving orderly electricity consumption, and realizing energy conservation and emission reduction.

[0052] In the short-term load forecasting method based on AR-Transformer provided in this invention, the long-term load forecasting task for the transformer bus mainly involves predicting the future long-term load changes of the transformer based on its historical bus load. The model input at time t is: Among them, L input The length of the input sequence. Leveraging the sequence-level prediction capabilities of the Transformer model, this invention can solve for the entire sequence to be predicted in one step: Among them, L output This represents the length of the output sequence.

[0053] In the Transformer model, if only load data is input, the attention mechanism tends to focus more on numerically similar portions. However, in time-series data, some numerically similar data may not actually have a meaningful correlation, and these similar data often distract the model, causing it to overlook more important information. Therefore, this invention uses the rate of change of load data as a feature input into the model, such as... Figure 2 As shown, line A1 represents the original load data, and line A2 represents the load change rate data. Compared to the original data, the change rate more clearly demonstrates the periodic characteristics of the data. Introducing the change rate can assist the attention mechanism in focusing more attention on parts of the data that are similar and have similar trends, thus enabling more selective information aggregation and achieving sequence-level connections, such as... Figure 3 As shown.

[0054] The location encoding in Transformer can be viewed as a local temporal feature of time-series data. Therefore, this invention uses learnable parameters to learn the model's location encoding, that is, directly and randomly initializing a location encoding for different locations and using it as a parameter for training. When predicting long-term load data, the impact of global time information such as hours, weeks, months, and holidays on load data cannot be ignored. In addition to using the location encoding in Transformer as a local time feature, this invention also uniformly encodes hours, weeks, months, and holidays as global time features. Changes in transformer bus load are affected by additional factors such as weather. Therefore, this invention encodes weather information such as maximum and minimum temperatures as weather features and also inputs them into the model.

[0055] Assume the load input of the model at time t is: The rate of change is obtained by differentiating it along the time dimension and then normalizing it. To align dimensions with other features, first use a one-dimensional convolution with a kernel of 3 to convolve X... t and C t Transform from 1D to d hiden Dimension, obtained and For weather features, a one-dimensional convolution with a kernel of 3 is also used to transform them from dimension d. weather Convert to dimension d hiden ,get The load characteristics with added time information and location coding are: Where PE represents location coding, TE represents global time coding, and p represents the type of time information to be coded. The weather feature with added time information and location coding is: The rate of change features for adding time information and location encoding are as follows: The weather features, rate of change features, and load features are concatenated along the feature dimension and then subjected to a one-dimensional convolution to obtain the auxiliary feature s. t，i =Conv(Concat(x) t，i k t，i c t，i The final input model has two parts: auxiliary features s t，i and load characteristics x t，i .

[0056] Furthermore, as a refinement and extension of the specific implementation of the embodiments of the present invention, in order to fully illustrate the specific implementation process in this embodiment, the short-term load forecasting method based on AR-Transformer provided by the present invention includes:

[0057] Attention mechanism:

[0058] To reduce the time complexity of attention computation in Transformer while preserving more important attention information, this invention uses the cos-based re-weighting mechanism from its variant, Cosformer, to calculate the attention score in the time dimension. Assume the input to the attention layer is X. t ∈R L*d and S t ∈R L*d And the output of the Att(.) function is O. t ∈R L*d The output obtained after passing through the attention layer is:

[0059] O t =Att(S t X t )

[0060] Here, Att(.) represents the attention function, and its time and space complexity are both O(Ld). 2 The attention function Att(.) is calculated as follows:

[0061] O = Sim(Q, K) V = (Q cos K cos +Q sin K sin V = Q cos (K cos V)+Q sin (K sin V)

[0062] Where Q = W Q S t K = W K S t V = W v X tW Q W K With W v Represents weights; when calculating Query and Key, a convolution kernel with a size greater than 1 is used for convolution operations.

[0063] The present invention also includes an encoder, which consists of m encoding layers, each including an attention layer, a sequence segmentation module, and a convolutional layer. In the encoding layers, the present invention first uses the attention layer and convolutional layer to selectively update temporal features, and then uses the sequence segmentation module and convolutional layer to reduce the dimensionality of the input sequence along the time dimension, while simultaneously extracting periodic features from the temporal sequence. The specific operations in the j-th encoding layer are as follows.

[0064] X′ t，j =ELU(Conv(Att(X) t，j S t，j )))

[0065] X t，j+1 =ELU(Conv(SeriesPartion(X′ t，j )))

[0066] Time series data is first passed through a self-attention layer Att, and then processed along the time dimension using the sequence segmentation module SeriesPartion. Taking a step size of 2 as an example, the dimensions of the time series data after segmentation range from L... input *d hiden become Then, they are fused along the time dimension by a one-dimensional convolution with a kernel of 3. The fused dimension is from... Convert to Finally, activation is performed by the ELU function. It's important to note that, except for the first coding layer, S in the remaining coding layers... t，j =X t，j .

[0067] The encoder consists of m cascaded coding layers. To integrate the periodic characteristics of different frequencies in the time sequence, this invention first downsamples the outputs of multiple coding layers to the same dimension, and then compresses the multi-layer outputs through a "concatenation + aggregation" method. The specific operation is as follows:

[0068]

[0069] in, This represents the merged load output, Maxpooling represents downsampling, Concat represents the concatenation function, and W... fuse ∈R m*1 These are learnable aggregation parameters. The fused features then pass through an attention layer and two convolutional layers to obtain the encoder's output.

[0070]

[0071] This invention also includes a decoder: the decoder consists of n decoding layers, each consisting of two multi-head attention layers and two one-dimensional convolutional layers stacked together. Inspired by the Informer, the initial payload features of the decoder input are:

[0072]

[0073] in, The starting character, derived from dynamic decoding techniques in natural language processing, is extracted from the encoder's input. Placeholders representing predicted values ​​are all zeros. By calculating multiple predicted values ​​uniformly, the goal is to output all predicted sequences in a single forward calculation. The rate of change feature requires similar processing. Future weather characteristics can be obtained through weather forecasts, thus enabling the acquisition of... Corresponding weather characteristics The decoder's input also undergoes input encoding, adding local and global temporal features. Similar to the encoder, in the decoder, except for the first decoding layer, the S... t,j =X t,j The final input load characteristics of the decoder are: and After multiple decoding layers and a final fully connected layer, the encoder's output is linearly encoded to the same feature dimension as the true value. The final output of the encoder can be represented as...

[0074] Configuring the AR component: Due to the non-linear nature of convolutional operations and attention mechanisms, a major drawback of neural network models such as Transformer in time series prediction is that the output is not very sensitive to non-periodic scaling changes in the input. Therefore, this invention uses an AR component to predict the low-frequency linear portion of the time series. The AR component is implemented using linear regression. It is important to note that after performing linear regression, the data needs to be restored along the time dimension. The specific method is as follows: The final output of the model is

[0075] Based on the above method, this invention combines the Transformer model and the AR model to jointly improve the prediction effect of transformer bus load. The Transformer model is mainly responsible for predicting the high-frequency nonlinear part of the time series data, while the AR model is mainly responsible for predicting the low-frequency linear part of the time series data.

[0076] In the encoder section, the model adopts a hierarchical design, first distilling the features layer by layer along the time dimension. This reduces the total memory usage while extracting periodic features of different frequencies from the workload data. Then, these periodic features of multiple frequencies are superimposed and aggregated to obtain cross-period fused features. The model involved in this invention, when using an attention mechanism to gather information, focuses more attention on parts of the data that are similar and have similar trends of change, thereby achieving sequence-level connections of time-series information and uncovering more reliable time dependencies.

[0077] Furthermore, due to the nonlinear characteristics of the activation layer, models such as Transformer are prone to introducing additional errors when modeling linear relationships, and are therefore not very sensitive to linear scaling in time series data. Therefore, this invention combines the Transformer model and the AR model to jointly improve the prediction performance of transformer bus load. The Transformer model is mainly responsible for predicting the high-frequency nonlinear components of the time series data, while the AR model is mainly responsible for predicting the low-frequency linear components.

[0078] Furthermore, in the encoder part of this invention, the model adopts a hierarchical design. First, the features are distilled layer by layer along the time dimension, thereby reducing the total memory usage while extracting periodic features of different frequencies in the load data. Then, these periodic features of multiple frequencies are superimposed and aggregated to obtain cross-period fused features.

[0079] This invention also incorporates the rate of change of load data as an additional feature into the calculation of Query and Key in the attention layer. This allows the model to focus more attention on parts with similar data and similar data change trends when using the attention mechanism to gather information, thereby achieving sequence-level connections of time-series information and thus uncovering more reliable time dependencies.

[0080] Those skilled in the art will understand that various aspects of the short-term load forecasting method can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0081] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A short-term load forecasting method, characterized in that, The methods include: Step 1: Input encoding is performed, and load information, weather information, rate of change information, and time information are processed to obtain initial load characteristics and auxiliary characteristics. These two parts are then input into the model to obtain the predicted value of the sequence to be predicted. Calculate the mean squared error between the true value and the predicted value of the sequence to be predicted, backpropagate from the output of the model and update the model parameters; Assume the load input of the model at time t is: The rate of change is obtained by differentiating it along the time dimension and then normalizing it. ; First, use a one-dimensional convolution with a kernel of 3 to... and From 1D to Dimension, obtained and ; For weather features, a one-dimensional convolution with a kernel of 3 is used to transform them from dimensionality. Convert to dimensions ,get The load characteristics with added time information and location coding are: ,in Represents position code, Represents global time encoding. This represents the type of time information that needs to be encoded. Weather features with added time information and location codes are: The rate of change features for adding time information and location encoding are as follows: The auxiliary feature is obtained by concatenating weather features, rate of change features, and load features along the feature dimension and performing a one-dimensional convolution. ； The final input model has two parts: auxiliary features and load characteristics ; Let the input of the attention layer be and ,and The function output is The output obtained after passing through the attention layer is: in, ; The calculation method is as follows: in, , , , and Represents weight; Step 2: Configure the encoder. The encoder consists of multiple coding layers. Within these layers, attention layers and convolutional layers are used for selective temporal feature updates. Then, a sequence segmentation module and convolutional layers are used to reduce the dimensionality of the input sequence along the time dimension, while simultaneously extracting periodic features from the temporal sequence. The specific operations in the layer coding layer are as follows: = When the time series data first passes through the self-attention layer Then, it goes through another convolutional layer, and then uses a sequence segmentation module. It is processed along the time dimension, and finally passed through a convolutional layer; Step 3: Configure the decoder: The decoder consists of multiple decoding layers, each consisting of two multi-head attention layers and two one-dimensional convolutional layers stacked together; the initial payload feature input of the decoder is... : in, Represents the start character; The placeholders representing the predicted values ​​are all zeros; the rate of change feature input for the decoder is: , The placeholder is composed entirely of 0; and Corresponding weather characteristics The data is obtained from the input of the decoder; the input is also encoded to add local and global time features, resulting in load features and auxiliary features. The output after multiple decoding layers is linearly encoded into the same feature dimension as the true value. The final output of the encoder is represented as... ; Step 4: Configure AR components: The AR component is used to predict the low-frequency linear portion of a time series. The AR component is implemented using linear regression. The specific method is as follows: middle , ; The final output of the model is , .

2. The short-term load forecasting method according to claim 1, characterized in that, In step one, Query and Key are convolutional operations performed using convolution kernels with a size greater than 1.

3. The short-term load forecasting method according to claim 1, characterized in that, In step two, The encoder in the nonlinear component consists of m coding layers, which include attention layers, sequence segmentation modules, and convolutional layers.

4. The short-term load forecasting method according to claim 1, characterized in that, Sequence segmentation module The step size for processing time series data along the time dimension is 2, and the dimensions of the time series data after partitioning are from... become Then, it is fused along the time dimension by a one-dimensional convolution with a kernel of 3. The fused dimension is from Convert to Finally, it is activated by the ELU function.

5. The short-term load forecasting method according to claim 4, characterized in that, The encoder consists of m coding layers connected in series. The outputs of multiple coding layers are first downsampled to the same dimension, and then the multi-layer outputs are compressed by splicing and aggregation. The specific steps are as follows: in, Represents the output after fusion. This represents downsampling, and Concat represents the concatenation function. These are the learned aggregation parameters; the fused features pass through an attention layer and two convolutional layers to obtain the encoder output. : 。 6. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the short-term load forecasting method as described in any one of claims 1 to 5.

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