Industrial process one-dimensional time series signal self-supervised change point detection method and system
By using a self-supervised Siamese neural network and a one-dimensional convolutional layer model, and training a change point detection model with unlabeled data, the problem of change point detection in complex industrial scenarios is solved, achieving high-precision and widely applicable change point recognition results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2024-05-10
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies struggle to effectively detect changes in time-series signals in complex industrial scenarios, especially abrupt and continuous changes due to shifts in data distribution. Furthermore, the high cost of acquiring data labels and the unique nature of the labels prevent the methods from being universally applicable.
A change point detection model consisting of a self-supervised Siamese neural network and a one-dimensional convolutional layer is adopted. The model is trained using unlabeled historical time series data. Anchor points and negative samples are generated through sliding windows and data augmentation. The model is trained to identify change points by comparing the temporal representation encoding module of the Siamese neural network with the downstream classifier.
It achieves high-precision and highly generalizable change point detection under unlabeled data conditions, and can identify both abrupt and continuous change points. It is applicable to different industrial processes and improves the accuracy and applicability of change point detection.
Smart Images
Figure CN118965206B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of information technology, specifically to a method and system for detecting one-dimensional time-series signals in industrial processes using self-supervised change points. Background Technology
[0002] A change point refers to a point in a sequence or process where observed values exhibit different properties before and after a certain position or time. In industrial processes, anomalies typically manifest as switching of production states, leading to changes in the properties of related signals. Identifying the time points where production state switching occurs within time-series signals related to industrial processes is known as change point detection. Detecting change points helps in understanding behavioral changes in industrial systems and provides timely alerts for potential faults.
[0003] A review of existing literature reveals that current time series change point detection methods can be categorized into two main types: The first type is based on statistical analysis, which designs statistical indicators to measure the differences in properties between different intervals of a time series. When two adjacent intervals of a time series have different statistical properties, the time point between them is identified as a change point. The second type is data-driven supervised detection methods, which assign pattern labels to each data point or segment in the sequence and then learn the mapping relationship between sequence features and pattern labels through a classification model. When the sequence before and after a certain time point has different labels, that time point is identified as a change point.
[0004] In existing technologies, the first type of change point detection method based on statistical analysis requires accurate modeling of the time series distribution state and continuity before detection. However, time series signals collected in complex industrial scenarios have dynamic and coupled characteristics, making it difficult to model them using ordinary time series models. The second type of data-driven supervised change point detection method requires a large amount of high-quality labeled data for model training. However, collecting comprehensive data labels in complex industrial scenarios is costly, and the labels have task-specific characteristics, making them unsuitable for different industrial processes. Furthermore, in actual industrial time series signals, there are both abrupt change points due to changes in the data distribution state and more potential continuous change points that do not conform to sequence consistency. Most of these two types of methods only focus on the single-class properties of the sequence, neglecting the detection of continuous change points. Summary of the Invention
[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a self-supervised change point detection method and system for one-dimensional time-series signals in industrial processes.
[0006] According to one aspect of the present invention, a method for self-supervised change point detection of one-dimensional time-series signals in industrial processes is provided, comprising:
[0007] The training set is obtained based on unlabeled historical time series that do not contain change points;
[0008] A change point detection model is established, which includes a temporal representation encoding module based on a Siamese neural network and a downstream classifier composed of one-dimensional convolutional layers. The temporal representation encoding module maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments. The downstream classifier determines whether the two temporal representations are similar.
[0009] Based on the training set, the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier are calculated to train the change point detection model.
[0010] Two adjacent sliding windows are used to continuously extract two adjacent time segments from the test time series samples, which are then input into the trained change point detection model to perform online detection and determine the change point location.
[0011] Preferably, the training set includes: anchor samples obtained through a sliding window, negative samples established through data augmentation, negative sample pairs formed by negative samples and their corresponding anchor samples, and positive sample pairs formed by different anchor samples.
[0012] Preferably, the anchor point samples obtained through the sliding window include:
[0013] Using a sliding window of length w, the time series X = {x0, x1, x2, ..., xn} is continuously extracted. T The fragments of} constitute the anchor point sample set;
[0014] The starting point i of the sliding window increases continuously as the window moves. The segment from time t = i to time t = i + w - 1 is the i-th anchor point sample.
[0015] Preferably, the negative sample s corresponding to the anchor sample is constructed through data augmentation. neg The data augmentation methods include three forms: scaling, rotation, and translation; among them,
[0016] Scaling-based data augmentation amplifies time series values by a ratio k ~ N(0,1), altering the original distribution of the time series: x' i =kx i ;
[0017] Rotational data augmentation involves adding an upward or downward trend g ~ N(0,1) to a time series, altering the original continuity property of the time series: x' i =x i ±gi;
[0018] Translational data augmentation involves randomly selecting a subsequence of arbitrary length from a time series and adding ascending or descending abrupt values s ~ N(0,1) to its sequence values, thereby altering the original distribution of the time-domain sequence: x' i =x i ±s.
[0019] Preferably, the input of the temporal representation encoding module based on the Siamese neural network is two temporal segments, and the output is two temporal representations. Its structure includes:
[0020] The two network branches have identical structures and share network weights. Each network branch includes a one-dimensional convolutional block, and each one-dimensional convolutional block includes two convolutional layers and a max pooling layer.
[0021] The fully connected layer fuses the outputs of the two network branches to output a temporal representation.
[0022] Preferably, the contrast loss of the time-series characterization encoding module is:
[0023] in Let i be the temporal representation of the i-th anchor point sample. Let i be the temporal representation of the i-th negative sample. Let be the temporal representation of the j-th anchor point sample, D(·) be the similarity measurement function between each pair of temporal representations calculated using cosine distance, and T1 and T2 be the temperature coefficients for adjusting the similarity values of sample pairs.
[0024] Preferably, the downstream classifier is trained using a variable-point discriminant loss based on binary cross-entropy loss. The downstream classifier has two inputs, where the input is the anchor sample representation. and negative sample characterization When training the downstream classifier, the output is 1, representing a negative sample. Unlike anchor point samples; if the input consists of two anchor point samples... and The downstream classifier outputs 0 during training.
[0025] According to a second aspect of the present invention, a self-supervised change point detection system for one-dimensional time-series signals in an industrial process is provided, comprising:
[0026] Data acquisition module: Obtains training set based on unlabeled historical time series data that does not contain variable points;
[0027] The temporal representation encoding module based on Siamese neural network maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments.
[0028] A downstream classifier composed of one-dimensional convolutional layers determines whether two temporal representations are similar.
[0029] Training module: Based on the training set, calculate the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier, and train the change point detection model;
[0030] Application module: Using two adjacent sliding windows, two adjacent time segments are continuously extracted from the test time series samples, and then input into the trained change point detection model to perform online detection and determine the change point location.
[0031] According to a third aspect of the present invention, a terminal is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, can be used to perform the method described therein, or to run the system described therein.
[0032] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, can be used to perform the method described thereon, or to run the system described thereon.
[0033] Compared with the prior art, the embodiments of the present invention have at least one of the following beneficial effects:
[0034] This invention discloses a self-supervised change point detection method for one-dimensional time-series signals in industrial processes. It utilizes contrastive learning to achieve self-supervised, non-parametric detection. This method can train a model by learning effective and generalized data representations on unlabeled and unknown data, ensuring model accuracy and generalization for different tasks. It effectively solves problems such as the difficulty in obtaining data labels and the easy invalidation of labels in industrial processes.
[0035] This invention discloses a self-supervised change point detection method for one-dimensional time-series signals in industrial processes. The method designs data augmentation techniques for time series data, providing reference objects for detecting both abrupt and continuous change points. This enables the model to comprehensively monitor multiple properties such as the distribution status of time-series data and temporal consistency / continuity, thereby improving the accuracy of change point identification. Attached Figure Description
[0036] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0037] Figure 1 This is a flowchart illustrating a method for detecting one-dimensional time-series signals in an industrial process according to an embodiment of the present invention.
[0038] Figure 2 This is a schematic diagram of the offline training process of the self-supervised change point detection method for one-dimensional time-series signals in industrial processes according to a preferred embodiment of the present invention.
[0039] Figure 3 This is a schematic diagram of the online change point detection process of the self-supervised change point detection method for one-dimensional time-series signals in industrial processes according to a preferred embodiment of the present invention;
[0040] Figure 4 This is a detection result diagram in a specific embodiment of the present invention, wherein (a) represents the change point detection from normal mode to periodic abnormal mode; (b) represents the change point detection from normal mode to upward trend abnormal mode; (c) represents the change point detection from normal mode to downward trend abnormal mode; (d) represents the change point detection from normal mode to upward step abnormal mode; and (e) represents the change point detection from normal mode to downward step abnormal mode.
[0041] Figure 5 This is a comparison result diagram of a specific embodiment of the present invention. Specific Implementation
[0042] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.
[0043] In one embodiment of the present invention, a self-supervised change point detection method for one-dimensional time-series signals in industrial processes is provided, such as... Figure 1 As shown, it includes:
[0044] S100: Obtain the training set based on unlabeled historical time series that do not contain change points;
[0045] S200, establish a change point detection model, which includes a temporal representation encoding module based on Siamese neural network and a downstream classifier composed of one-dimensional convolutional layers; the temporal representation encoding module maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments; the downstream classifier determines whether the two temporal representations are similar.
[0046] S300, based on the training set, calculates the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier to train the change point detection model;
[0047] S400 uses two adjacent sliding windows to continuously extract two adjacent time segments from the test time series samples, inputs them into the change point detection model trained by S300 to carry out online detection, and determines the change point location.
[0048] The above embodiments can effectively improve the accuracy of online change point identification in the case of unlabeled industrial process data and unquantified temporal properties. By introducing a contrastive learning approach for model training, the model is encouraged to extract valuable and generalizable information from the original data itself, enabling it to accurately identify the locations of abrupt and continuous change points. Furthermore, it exhibits excellent generalization ability, making it a universal change point detection method applicable to the monitoring of various industrial processes.
[0049] In a preferred embodiment, step S100 is performed to construct a model training set. Unlabeled historical time series data that do not contain change points are processed. Anchor point samples are obtained using a sliding window. Negative samples are created through data augmentation, forming negative sample pairs with their corresponding anchor point samples. Different anchor point samples form positive sample pairs with each other. Specifically, the steps are as follows:
[0050] S101, using a sliding window of length w, continuously extract historical time series data X = {x0, x1, x2, ..., x...} T The segments from time t = i to time t = i + w - 1 constitute the anchor point sample set. The starting point i of the sliding window will continuously increase as the window moves.
[0051] S102, Establish anchor point samples through data augmentation. The corresponding negative sample Data augmentation involves performing temporal transformations on data to expand the sample. To distinguish negative samples from anchor samples in terms of their distribution, continuity, and other temporal properties, data augmentation methods used to construct negative samples include scaling, rotation, and translation.
[0052] Scaling-based data augmentation amplifies the sequence values at random time steps by a certain ratio k ~ N(0,1), thereby altering the original distribution of the time-domain sequence.
[0053] x′ i =kx i
[0054] Rotational data augmentation adds an upward or downward trend g ~ N(0,1) to a time series, altering the continuity of the original time-domain series.
[0055] x′ i =x i ±gi
[0056] Translational data augmentation involves randomly selecting a subsequence of arbitrary length from a time series and adding rising or falling abrupt values s ~ N(0,1) to its sequence values, thereby altering the original distribution of the time-domain sequence.
[0057] x′ i =xi ±s
[0058] S103: Construct positive and negative sample pairs. The i-th anchor sample and its negative sample form a negative sample pair. Together with other samples in the anchor sample set, they form a positive sample pair.
[0059] The above embodiments design data augmentation methods for time series, providing reference objects for detecting both abrupt and continuous change points, enabling the model to comprehensively monitor multiple properties such as the distribution status of time series data and temporal consistency / continuity, thereby improving the accuracy of change point identification.
[0060] In a preferred embodiment, step S200 is performed to establish a change point detection model. This embodiment is divided into two steps, as follows:
[0061] S201, Establish a temporal representation encoding module based on a Siamese neural network. A weight-sharing dual-channel network maps the two input temporal segments of the temporal representation encoding module to the same feature space, outputting temporal representations of the two temporal segments.
[0062] In some specific examples, S201 is divided into two steps. S201.1: Two network branches are established. The two network branches have identical structures and share network weights. Each network branch consists of a one-dimensional convolutional block. Each one-dimensional convolutional block contains two convolutional layers with a kernel size of 3 and a max pooling layer with a pooling size of 2.
[0063] In step S201.2, a fully connected layer is established to fuse the outputs of the two network branches, forming a complete temporal representation coding module. The input to the temporal representation coding module is two temporal segments in the time domain, and the output is two temporal representations.
[0064] S202, establish a downstream classifier consisting of one-dimensional convolutional layers. The input to the downstream classifier is two temporal representations output by the temporal representation encoding module, and it determines whether the two temporal representations are similar.
[0065] In this embodiment, the temporal representation module based on the Siamese neural network performs nonlinear feature transformation on the original data of the input temporal segment to reduce redundant information unrelated to the change point detection task, and transforms the original data into a temporal representation.
[0066] In a preferred embodiment, step S300 is implemented to train the change point detection model offline by comparing and learning the training strategy. The training process is as follows: Figure 2 As shown. Using the training set obtained from S100, the contrastive loss of the temporal representation encoding module and the change-point discrimination loss of the downstream classifier are calculated to train the entire model. Specifically, as... Figure 2 As shown:
[0067] S301: Using the dataset obtained through S100, train the temporal representation encoding module. Anchor samples are processed by the temporal representation encoding module to obtain their corresponding temporal representation h. anc The negative samples are used to calculate the time series representation h through the time series representation encoding module. neg Anchor point samples at different times have similar temporal properties, while negative samples s neg The temporal properties of the samples differ from those of the anchor samples, and the comparative loss function is designed as follows:
[0068]
[0069] in Let i be the temporal representation of the i-th anchor point sample. Let i be the temporal representation of the i-th negative sample. Let be the temporal representation of the j-th anchor point sample. D(·) is the similarity measurement function between pairwise temporal representations, calculated using cosine distance. T1 and T2 are temperature coefficients that adjust the similarity values of sample pairs. By training the temporal representation encoding module using this loss function, the distance between the temporal representations of different anchor point samples with similar properties can be made as close as possible, while the negative sample representations are kept as far away from them as possible, thereby improving the discriminative power of the temporal representations.
[0070] S302: Using the obtained temporal representation, train a downstream classifier using a change-point discriminant loss based on binary cross-entropy loss. The downstream classifier has two inputs. When the input is the anchor sample representation... and negative sample characterization When training the downstream classifier, the output is 1, representing a negative sample. Unlike anchor point samples, if the input consists of two anchor point samples... and The downstream classifier is trained to output 0. Specifically, the calculation formula is as follows:
[0071]
[0072] Among them, y i These are the true labels that represent whether the input data of the downstream classifier are similar. The discrimination result given by the downstream classifier
[0073] In a preferred embodiment, step S400 is implemented by using a trained change point detection model. Two adjacent time segments from the test time series samples are continuously extracted using two adjacent sliding windows, and then input into the change point detection model for online detection to determine the change point location. Specifically, as follows... Figure 3 As shown:
[0074] S401: Using two sliding windows of width w, extract timing segments from the test timing stream to be tested, namely historical segments s. history ={x k-w x k+1-w , ..., x k-1} and future fragments future ={x k+1 x w x k+2-w , ..., x k The future segment contains the most recently arrived data point x in the time-series stream. k Historical data is not included. Online change point detection requires verifying the latest data point x. k Is it a turning point?
[0075] S402: Transfer historical fragment S history and future fragments future Input the trained time series representation encoding module to obtain the historical time series representation h. history and future time series representation h future .
[0076] S403: Input the two time-series representations obtained from S402 into the trained downstream classifier. If the downstream classifier outputs 1, it indicates that the nature of the future segment is different from that of the historical segment, that is, the latest time point sequence value x in the future segment is... k The addition of [something] changes the properties of the data; at this point, the latest data point x... k If the downstream classifier outputs 0, it means that the latest data point is not a change point. At this time, the sliding window of S401 is moved forward to extract the new data continuously generated in the test time stream. Steps S401-S403 are repeated for verification until a change point is detected.
[0077] Based on the same inventive concept, other embodiments of the present invention provide a self-supervised change point detection system for one-dimensional time-series signals in industrial processes, comprising:
[0078] Data acquisition module: Obtains training set based on unlabeled historical time series data that does not contain variable points;
[0079] The temporal representation encoding module based on Siamese neural network maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments.
[0080] A downstream classifier composed of one-dimensional convolutional layers determines whether two temporal representations are similar.
[0081] Training module: Based on the training set, calculate the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier, and train the change point detection model;
[0082] Application module: Using two adjacent sliding windows, two adjacent time segments are continuously extracted from the test time series samples, and then input into the trained change point detection model to perform online detection and determine the change point location.
[0083] The specific implementation techniques of each module / unit in the above examples of the present invention can be referred to the steps of the self-supervised change point detection method for one-dimensional time-series signals in industrial processes in the above embodiments, and will not be repeated here.
[0084] Based on the same inventive concept, in other embodiments of the present invention, a terminal is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it can be used to execute the method described therein, or to run the system described therein.
[0085] Based on the same inventive concept, in other embodiments of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, can be used to perform the method described thereon, or to run the system described thereon.
[0086] To verify the feasibility and technical effectiveness of the above embodiments, in a specific implementation of the present invention, online detection signals of body-in-white processing deviations are collected to form a body-in-white dataset. The processing deviations detected from multiple bodies-in-white continuously produced on the production line constitute a sequence, reflecting the production status of the processing. A total of 113 deviation sequences from detection points were collected. Each detection point corresponds to a one-dimensional sequence of processing deviations. The time point when the sequence switches from normal mode to abnormal mode is the change point that needs to be identified. Figure 4 Figures (a), (b), (c), (d), and (e) show the results of the change point detection method according to the embodiments of the present invention, which can effectively identify the change point location.
[0087] Figure 5 The results of the change point detection method and the comparison object method in this embodiment of the invention are used, and the effectiveness of the method is measured by three indicators: precision, recall, and mean absolute error. The method of this embodiment of the invention has significant advantages in all three indicators.
[0088] The method in this embodiment of the invention, through comparative learning, weakens the dependence of the method on training labels. Therefore, in the case of unlabeled industrial process data and unquantified data properties, it can improve the accuracy of change point detection and the generalization ability of the method through self-supervision and non-parametric methods, and can cope with different application scenarios. The method in this embodiment of the invention constructs reference objects for detecting both abrupt and continuous changes through data augmentation, enabling the change point detection model to comprehensively monitor multiple properties such as the distribution status of time series data and temporal consistency / continuity, thereby improving the accuracy of the detection results.
[0089] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention. The above preferred features can be used in any combination without conflict.
Claims
1. A self-supervised method for detecting one-dimensional time-series signals in industrial processes, characterized in that, include: The training set is obtained based on unlabeled historical time series that do not contain change points; A change point detection model is established, which includes a temporal representation encoding module based on a Siamese neural network and a downstream classifier composed of one-dimensional convolutional layers. The temporal representation encoding module maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments. The downstream classifier determines whether the two temporal representations are similar. Based on the training set, the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier are calculated to train the change point detection model. Two adjacent sliding windows are used to continuously extract two adjacent time segments from the test time series samples, and input them into the trained change point detection model to carry out online detection and determine the change point location. The training set includes: anchor samples obtained through a sliding window, negative samples established through data augmentation, negative sample pairs formed by negative samples and their corresponding anchor samples, and positive sample pairs formed by different anchor samples. The input to the timing representation encoding module based on the Siamese neural network is two timing segments, and the output is two timing representations; the structure of the timing representation encoding module includes: There are two network branches with identical structures and shared network weights. Each network branch includes a one-dimensional convolutional block, and each one-dimensional convolutional block includes two convolutional layers and a max pooling layer. The fully connected layer fuses the outputs of the two network branches to output a temporal representation.
2. The method for detecting one-dimensional time-series signals in an industrial process according to claim 1, characterized in that, Anchor point samples obtained through a sliding window include: Use length is A sliding window continuously extracts time series data. The fragments constitute the anchor point sample set; Among them, the starting point of the sliding window It will continue to grow as the window moves, from time to time. At the time The segment is the first Anchor point sample .
3. The method for detecting one-dimensional time-series signals in an industrial process according to claim 2, characterized in that, Constructing negative samples corresponding to anchor samples through data augmentation The data augmentation methods include three forms: scaling, rotation, and translation; among them, Scaling data augmentation methods, by ratio Amplifying time series values alters the original distribution of the time series: ; Rotational data augmentation adds an upward or downward trend to a time series. This alters the continuity property of the original time series: ; Translational data augmentation involves randomly selecting a subsequence of arbitrary length from the time series and adding rising or falling abrupt values to the subsequence values. This changes the distribution state of the original time-domain sequence: .
4. The method for detecting one-dimensional time-series signals in an industrial process according to claim 1, characterized in that, The contrast loss of the temporal representation encoding module is ; in For the first Temporal representation of anchor point samples, For the first Temporal representation of negative samples, For the first Temporal representation of anchor point samples, D( () is a similarity measure function for pairwise time series representations, calculated using cosine distance. and To adjust the temperature coefficient of sample pair similarity values.
5. The method for detecting one-dimensional time-series signals in an industrial process according to claim 4, characterized in that, A downstream classifier is trained using a variable-point discriminant loss based on binary cross-entropy loss. The downstream classifier has two inputs: the input is the anchor sample representation. and negative sample characterization When training the downstream classifier, the output is 1, representing a negative sample. Unlike anchor point samples; if the input consists of two anchor point samples... and The downstream classifier is trained to output 0.
6. A self-supervised change point detection system for one-dimensional time-series signals in an industrial process, used to implement the method of claim 1, characterized in that, include: Data acquisition module: Obtains training set based on unlabeled historical time series data that does not contain variable points; The temporal representation encoding module based on Siamese neural network maps two temporal segments in the training set to the same feature space and outputs the temporal representations of the two temporal segments. A downstream classifier composed of one-dimensional convolutional layers determines whether two temporal representations are similar. Training module: Based on the training set, calculate the contrastive loss of the temporal representation encoding module and the change point discrimination loss of the downstream classifier, and train the change point detection model; Application module: Using two adjacent sliding windows, two adjacent time segments are continuously extracted from the test time series samples, and then input into the trained change point detection model to perform online detection and determine the change point location.
7. A terminal, 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 can be used to perform the method of any one of claims 1-5.
8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, this program can be used to perform the method described in any one of claims 1-5.