Wave recording analysis method, device, equipment and medium

Abstract

Embodiments of the present application provide a recording wave analysis method, device, equipment and medium. The method comprises: first acquiring a recording wave fault data set, and constructing a recording wave feature matrix according to the recording wave fault data set; then classifying each recording wave feature vector in the recording wave feature matrix based on an unsupervised clustering algorithm, and determining a classification result of each recording wave feature vector; then performing regression processing on each recording wave feature vector by using a multivariate linear regression prediction model, and determining a predicted value of each recording wave feature vector; finally, determining a fault type of each recording wave feature vector according to the classification result and the predicted value. Through the above method, the efficiency and quality of power system fault recording wave analysis are improved.

Description

Technical Field

[0001] This application relates to the field of inverter fault location technology, and in particular to a waveform analysis method, apparatus, equipment and medium. Background Technology

[0002] With continuous economic development, my country's power grid construction scale is constantly expanding, and the number of protection devices is also increasing rapidly. Faced with the increasing number of protection devices and the frequency of faults, it is crucial to manage existing protection devices effectively, ensure the timely detection of potential problems in relay protection devices, and quickly obtain fault report waveform data for the entire power grid during power grid faults.

[0003] In existing technologies, commonly used waveform data analysis methods are generally performed manually by technicians. Specifically, the monitoring system first acquires waveform data at the time of the fault, and then technicians with professional power system knowledge manually interpret the waveform files. By identifying the changing characteristics of waveforms such as voltage and current, and combining this with system topology and relay protection action information, the fault type, fault location, and fault cause are determined.

[0004] However, existing waveform data analysis methods suffer from high labor costs and low analysis efficiency. Summary of the Invention

[0005] This application provides waveform analysis methods, apparatus, equipment, and media to address the problems of high labor costs and low analysis efficiency in the prior art.

[0006] In a first aspect, embodiments of this application provide a waveform analysis method, including:

[0007] Obtain the waveform fault dataset and construct the waveform feature matrix based on the waveform fault dataset;

[0008] Based on an unsupervised clustering algorithm, each waveform feature vector in the waveform feature matrix is ​​classified to determine the classification result of each waveform feature vector. The classification result is used to characterize the category belonging relationship of the waveform feature vector in the feature space.

[0009] A multiple linear regression prediction model is used to perform regression processing on each of the recorded waveform feature vectors to determine the predicted value of each recorded waveform feature vector. The predicted value is used to characterize the correlation between the recorded waveform feature vector and the classification result.

[0010] Based on the classification results and the predicted values, the fault type of each recorded waveform feature vector is determined.

[0011] In one possible implementation, acquiring the waveform fault dataset and constructing a waveform feature matrix based on the waveform fault dataset includes:

[0012] Obtain a waveform fault dataset, and construct a waveform feature vector corresponding to each fault sample based on the waveform fault dataset. The waveform fault dataset includes at least one of the following: time series feature vector, analog quantity feature vector, setpoint sensitivity feature vector, external circuit anomaly feature vector, and sampling circuit feature vector.

[0013] Each of the recorded waveform feature vectors is normalized to construct a recorded waveform feature matrix.

[0014] In one possible implementation, classifying each waveform feature vector in the waveform feature matrix based on an unsupervised clustering algorithm and determining the classification result for each waveform feature vector includes:

[0015] The number of clusters is determined empirically.

[0016] Randomly select wave recording feature vectors from the wave recording feature matrix as cluster centers;

[0017] For each recorded waveform feature vector, the spatial distance between the recorded waveform feature vector and the cluster center is calculated until several cluster centers are determined.

[0018] Based on the cluster centers, each waveform feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to determine the cluster center to which each waveform feature vector belongs;

[0019] The cluster center to which each of the recorded waveform feature vectors belongs is determined as the classification result of that recorded waveform feature vector.

[0020] In one possible implementation, the step of calculating the spatial distance between each recorded feature vector and the cluster center until several cluster centers are determined includes:

[0021] Step a: For each recorded waveform feature vector, calculate the spatial distance between the recorded waveform feature vector and the cluster center;

[0022] Step b: Sort the spatial distance values ​​from smallest to largest, and select the waveform feature vector corresponding to the largest spatial distance as the new cluster center;

[0023] Repeat steps a through b until the cluster centers are determined.

[0024] In one possible implementation, after determining the cluster centers, the method further includes: for each waveform feature vector, calculating the Euclidean distance between the waveform feature vector and its corresponding cluster center;

[0025] The sum of the squares of each Euclidean distance is accumulated to obtain the sum of squared errors of the waveform characteristic matrix;

[0026] If the sum of squared errors is less than a preset value, then the classification result is determined to be reliable.

[0027] If the sum of squared errors is less than a preset value, the classification result is determined to be unreliable and needs to be reclassified.

[0028] In one possible implementation, the multiple linear regression prediction model includes

[0029]

[0030] in, The predicted value of the i-th recorded waveform feature vector; It is the intercept; It is the skewness coefficient for each variable; It is the p-th feature value in the i-th recorded wave feature vector.

[0031] In one possible implementation, determining the fault type of each recorded waveform feature vector based on the classification result and the predicted value includes:

[0032] Obtain the classification result and the corresponding predicted value for each of the recorded waveform feature vectors;

[0033] If the predicted value is greater than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be the fault type corresponding to the classification result;

[0034] If the predicted value is less than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be a fault to be confirmed.

[0035] Secondly, embodiments of this application provide a waveform analysis device, comprising:

[0036] A construction module is used to acquire a waveform recording fault dataset and construct a waveform recording feature matrix based on the waveform recording fault dataset;

[0037] The first determining module is used to classify each waveform feature vector in the waveform feature matrix based on an unsupervised clustering algorithm, and determine the classification result of each waveform feature vector. The classification result is used to characterize the category belonging relationship of the waveform feature vector in the feature space.

[0038] The processing module is used to perform regression processing on each of the recorded waveform feature vectors using a multiple linear regression prediction model to determine the predicted value of each recorded waveform feature vector. The predicted value is used to characterize the correlation between the recorded waveform feature vector and the classification result.

[0039] The second determining module is used to determine the fault type of each of the recorded waveform feature vectors based on the classification results and the predicted values.

[0040] In one possible implementation, the building module is specifically used for:

[0041] Obtain a waveform fault dataset, and construct a waveform feature vector corresponding to each fault sample based on the waveform fault dataset. The waveform fault dataset includes at least one of the following: time series feature vector, analog quantity feature vector, setpoint sensitivity feature vector, external circuit anomaly feature vector, and sampling circuit feature vector.

[0042] Each of the recorded waveform feature vectors is normalized to construct a recorded waveform feature matrix.

[0043] In one possible implementation, the first determining module is specifically used for:

[0044] The number of clusters is determined empirically.

[0045] Randomly select wave recording feature vectors from the wave recording feature matrix as cluster centers;

[0046] For each recorded waveform feature vector, the spatial distance between the recorded waveform feature vector and the cluster center is calculated until several cluster centers are determined.

[0047] Based on the cluster centers

[0048] Each recorded feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to determine the cluster center to which each recorded feature vector belongs;

[0049] The cluster center to which each of the recorded waveform feature vectors belongs is determined as the classification result of the recorded waveform feature vector.

[0050] In one possible implementation, the first determining module is specifically used for:

[0051] Step a: For each recorded waveform feature vector, calculate the spatial distance between the recorded waveform feature vector and the cluster center;

[0052] Step b: Sort the spatial distance values ​​from smallest to largest, and select the waveform feature vector corresponding to the largest spatial distance as the new cluster center;

[0053] Repeat steps a through b until the cluster centers are determined.

[0054] In one possible implementation, after determining the cluster centers, the first determining module is further configured to:

[0055] Each recorded feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to it, thereby determining the cluster center to which each recorded feature vector belongs;

[0056] For each recorded waveform feature vector, calculate the Euclidean distance between the recorded waveform feature vector and its corresponding cluster center;

[0057] The sum of the squares of each Euclidean distance is accumulated to obtain the sum of squared errors of the waveform characteristic matrix;

[0058] If the sum of squared errors is less than a preset value, then the classification result is determined to be reliable.

[0059] If the sum of squared errors is less than a preset value, the classification result is determined to be unreliable and needs to be reclassified.

[0060] In one possible implementation, the multiple linear regression prediction model includes

[0061]

[0062] in, The predicted value of the i-th recorded waveform feature vector; It is the intercept; It is the skewness coefficient for each variable; It is the p-th feature value in the i-th recorded wave feature vector.

[0063] In one possible implementation, the second determining module is specifically used for:

[0064] Obtain the classification result and the corresponding predicted value for each of the recorded waveform feature vectors;

[0065] If the predicted value is greater than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be the fault type corresponding to the classification result;

[0066] If the predicted value is less than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be a fault to be confirmed.

[0067] Thirdly, embodiments of this application provide an electronic device, including: a memory and a processor;

[0068] The memory stores computer-executed instructions;

[0069] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0070] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0071] The waveform analysis method, apparatus, device, and medium provided in this application first acquire a waveform fault dataset, then perform feature extraction and normalization on the multi-source data in the waveform fault dataset to construct a waveform feature matrix characterizing the operating state of each waveform sample, making features of different dimensions and scales comparable. Based on this, an unsupervised clustering algorithm is used to perform similarity analysis on each waveform feature vector in the waveform feature matrix, classifying waveform feature vectors with similar feature distributions into the same category, thereby achieving automatic mining of the intrinsic structure and fault modes of historical waveform fault samples, and obtaining the classification result corresponding to each waveform feature vector. This classification result is used to characterize the category affiliation of the waveform feature vector in the feature space. Subsequently, using pre-defined... The established multiple linear regression prediction model performs regression processing on each waveform feature vector. Based on the linear mapping relationship between each waveform feature and the target variable, it outputs the corresponding predicted value, which is used to quantify the correlation strength or confidence level between the waveform feature vector and its corresponding fault type. Finally, the classification results and predicted values ​​are fused together for judgment. When the predicted value meets the preset judgment conditions, the fault type corresponding to the waveform feature vector is confirmed as the fault type indicated by the classification result. When the predicted value does not meet the preset judgment conditions, the confidence level of the classification result is reduced and further auxiliary analysis or manual review is triggered. This improves the accuracy and reliability of fault type determination while ensuring the objectivity of the classification results, and realizes intelligent analysis and auxiliary decision-making of waveform fault data. Attached Figure Description

[0072] 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.

[0073] Figure 1 A flowchart illustrating the waveform analysis method provided in the embodiments of this application. Figure 1 ;

[0074] Figure 2 A flowchart illustrating the waveform analysis method provided in the embodiments of this application. Figure 2 ;

[0075] Figure 3 This is a schematic diagram of the waveform analysis device provided in the embodiments of this application;

[0076] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0077] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0078] 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.

[0079] With continuous economic development, my country's power grid construction scale is constantly expanding, and the number of protection devices is also increasing rapidly. Faced with the increasing number of protection devices and the frequency of faults, it is crucial to manage existing protection devices effectively, ensure the timely detection of potential problems in relay protection devices, and quickly obtain fault report waveform data for the entire power grid during power grid faults.

[0080] In existing technologies, commonly used waveform data analysis methods are generally performed manually by technicians. Specifically, the monitoring system first acquires waveform data at the time of the fault, and then technicians with professional power system knowledge manually interpret the waveform files. By identifying the changing characteristics of waveforms such as voltage and current, and combining this with system topology and relay protection action information, the fault type, fault location, and fault cause are determined.

[0081] However, existing waveform data analysis methods rely on the experience and expertise of technicians, resulting in high labor costs and low efficiency; moreover, the analysis results are easily affected by subjective factors, posing a risk of misjudgment or omission.

[0082] To address the shortcomings of existing technologies in waveform fault analysis, which primarily rely on the manual experience of relay protection personnel, resulting in low analysis efficiency and insufficient consistency and objectivity, the inventors propose a waveform analysis method based on the multidimensional characteristics of waveform fault data, the similar distribution of similar faults in the feature space, and the principle that there are modelable correlations between fault types and various waveform features. The method first acquires a waveform fault dataset, performs unified feature extraction and normalization on multi-source data, and constructs a waveform feature matrix. Then, an unsupervised clustering algorithm is used to perform similarity clustering on the waveform feature vectors in the feature matrix, automatically classifying waveform data with similar feature distributions to uncover and characterize typical feature patterns of different fault types. Furthermore, a multiple linear regression prediction model is used to regress each waveform feature vector, obtaining corresponding predicted values ​​to quantify the correlation strength or confidence level between the waveform feature vector and its corresponding fault type. Finally, the final fault type of each waveform feature vector is determined by fusing the clustering classification results with the regression prediction values. The above technical solution enables automatic classification and intelligent identification of waveform fault data without manual annotation. This not only significantly improves the efficiency and consistency of waveform analysis, but also enhances the accuracy and reliability of fault type determination, providing relay protection personnel with effective auxiliary decision-making basis.

[0083] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0084] Figure 1 A flowchart illustrating the waveform analysis method provided in the embodiments of this application. Figure 1 ;like Figure 1 As shown, the method includes:

[0085] S101. Obtain the waveform fault dataset and construct the waveform feature matrix based on the waveform fault dataset.

[0086] In one possible approach, the waveform fault dataset is first obtained, and a waveform feature vector corresponding to each fault sample is constructed based on the waveform fault dataset. Then, each waveform feature vector is normalized to construct a waveform feature matrix.

[0087] The waveform fault dataset includes at least one of the following: timing feature vector, analog quantity feature vector, setpoint sensitivity feature vector, external circuit anomaly feature vector, and sampling circuit feature vector.

[0088] It should be understood that, in specific implementation, the first step is to obtain a fault dataset corresponding to a fault event from the substation's waveform recording device. This dataset contains raw information from multiple sources and of multiple types. Based on this, a waveform feature vector corresponding to each fault sample is constructed. Its multidimensional features may include: a time-series feature vector obtained by parsing the protection event and waveform data; an analog quantity feature vector formed by calculating the amplitude and phase of electrical quantities (such as voltage and current) vectors within a specific time window before and after the fault (such as 20ms before the fault and 30ms after the fault); a setpoint sensitivity feature vector generated by comparing the measured values ​​of protection components (such as differential current, measured impedance, and zero-sequence current) calculated from the waveform data with the device's preset values; a loop feature vector formed by detecting abnormalities such as switch quantity changes and pressure plate status; and a sampling loop feature vector that determines whether the sampling loop is correct by analyzing the sequence components of the three-phase electrical quantities before the fault, i.e., by using the positive sequence components, zero sequence components, and negative sequence components of the three-phase current and three-phase voltage before the fault to determine whether the phase sequence of the sampling loop is correct and whether there is a break in the circuit.

[0089] The calculation process for the analog signal eigenvector is as follows:

[0090]

[0091] in, The vector size is the value of the vector 20ms prior to the fault. This represents the vector size 30ms after the fault.

[0092] The calculation process for the constant sensitivity eigenvector is as follows:

[0093]

[0094] in, These are the measured values ​​at the time of the fault; Set the value for the device itself.

[0095] Furthermore, to eliminate the influence of differences in the dimensions of different features, each feature vector needs to be normalized, converting the original variable data x into a normalized value within the interval [0,1]. All normalized fault sample feature vectors are arranged in rows to construct a structured waveform recording feature matrix.

[0096] The specific formula for normalization is:

[0097]

[0098] Where y represents the normalized data. and These are the minimum and maximum values ​​of the feature in the dataset, respectively.

[0099] Understandably, by transforming heterogeneous and multi-source field fault data into a standardized and structured numerical matrix, a unified and comparable data foundation is provided for subsequent machine intelligent analysis. This achieves the quantification and standardization of raw waveform data, solves the problems of scattered data sources and inconsistent formats, and lays a solid data foundation for automated analysis.

[0100] S102. Based on the unsupervised clustering algorithm, classify each waveform feature vector in the waveform feature matrix and determine the classification result of each waveform feature vector.

[0101] The classification results are used to characterize the class assignment relationship of the recorded wave feature vector in the feature space.

[0102] It should be noted that the specific implementation process of the embodiments of this application is as follows: Figure 2 The details are explained in the previous section, and will not be repeated in this embodiment.

[0103] Understandably, by classifying each waveform feature vector in the waveform feature matrix using the above method based on unsupervised clustering algorithms, waveform data with similar operational and fault behavior characteristics can be automatically grouped into the same category based on the similarity relationship between waveform feature vectors in the feature space, without the need for manual pre-labeling of fault types. This allows for the discovery of potential intrinsic structures and typical fault modes in the waveform fault data. The classification results provide an objective data foundation for subsequent fault type determination, effectively reducing reliance on manual experience, improving the consistency and stability of waveform fault analysis, and helping to quickly identify batch faults or abnormal events with the same characteristics, thereby improving the overall efficiency of waveform data analysis and the automation level of fault diagnosis.

[0104] S103. Use a multiple linear regression prediction model to perform regression processing on each waveform feature vector to determine the predicted value of each waveform feature vector.

[0105] The predicted value is used to characterize the correlation between the recorded feature vector and the classification result.

[0106] It should be understood that, based on the preliminary clustering classification, a multiple linear regression prediction model is constructed and applied to further quantify and assess the correlation strength and trend between fault characteristics and specific fault states. The dependent variable of this model is a comprehensive index that can characterize the severity of the fault, the risk of development, or the correlation with a specific fault type (its calibration can be based on historical experience data), while the independent variables are the various feature components in the multidimensional waveform feature vector.

[0107] It should be noted that the multiple linear regression prediction model is as follows:

[0108]

[0109] in, The predicted value of the i-th waveform feature vector; It is the intercept; It is the skewness coefficient for each variable; Let p be the p-th eigenvalue in the i-th recorded waveform eigenvector.

[0110] Understandably, by establishing a linear mapping relationship between multiple input features and an output target based on statistical methods, and using statistical patterns in historical data to make quantitative predictions for the current sample, quantitative and continuous value assessment of fault risk or type is achieved. This makes up for the shortcomings of simple clustering classification, which can only provide discrete category labels, and provides probabilistic information or risk scores about the possibility of faults, making the analysis results more refined and have early warning significance.

[0111] S104. Based on the classification results and predicted values, determine the fault type of each recorded waveform feature vector.

[0112] In one possible approach, the classification result and the corresponding predicted value of each waveform feature vector are first obtained; if the predicted value is greater than a preset threshold, the fault type of the waveform feature vector is determined to be the fault type corresponding to the classification result; if the predicted value is less than the preset threshold, the fault type of the waveform feature vector is determined to be a fault to be confirmed.

[0113] It should be understood that, combining the discrete classification results (S102) and continuous predicted values ​​(S103) obtained from the aforementioned steps, a decision rule is used to finally determine the fault type. First, the clustering classification label and its corresponding multiple linear regression predicted value for each waveform feature vector are obtained, and an optimized preset threshold is set. If the regression predicted value of a sample is greater than or equal to the preset threshold, the sample is considered to have a strong enough correlation with its cluster category, and the prediction result is considered highly reliable. Therefore, its fault type is determined as the typical fault type corresponding to the classification result (such as "protection maloperation caused by local magnetic storm" or "permanent grounding fault of the line"). Conversely, if its regression predicted value is less than the preset threshold, it indicates that although the sample is close to a certain cluster in the feature space, its feature combination does not match the typical pattern well, and there may be atypical situations, compound faults, or novel faults. The system will determine its fault type as "fault to be confirmed" and suggest or automatically push it to relay protection experts for key review and analysis.

[0114] Understandably, by integrating the pattern discovery capabilities of unsupervised learning with the quantitative evaluation capabilities of regression models, a two-tiered decision-making mechanism is constructed, combining clustering for coarse screening with regression for fine-grained judgment. By setting thresholds, the accuracy and reliability of automated judgment are balanced. This significantly improves the accuracy and robustness of the intelligent diagnostic system. It can quickly and accurately identify typical faults automatically, while remaining cautious about unclear or abnormal cases, marking them for in-depth human analysis. This improves overall analysis efficiency while ensuring the quality and reliability of critical and complex fault analysis, ultimately providing operators with clear and highly reliable auxiliary decision support.

[0115] It should also be noted that this application uses an unsupervised clustering algorithm to classify multidimensional waveform data by geometric attributes, solving the problem of insufficient integration of multidimensional features in existing technologies. The clustering algorithm calculates the similarity between waveform data samples based on Euclidean distance, grouping data with the same or similar fault characteristics into the same category, avoiding the fragmentation problem of difficult integration of multidimensional data in traditional manual analysis. For example, when waveform data simultaneously contains multidimensional features such as time-series behavior, analog quantity changes, and setpoint sensitivity, this clustering method can automatically identify the similarity between data without relying on human experience. Furthermore, the multiple linear regression algorithm models and analyzes the relationship between various variables (such as voltage, current, and setpoints) in the clustering results and fault risk, enabling the prediction of potential risk points. For example, in power grid transient fault scenarios, K-means clustering can accurately classify fault types (such as sampling circuit anomalies, setpoint mismatches, etc.), while multiple linear regression can quantify the influence weight of each factor on fault risk, thus providing relay protection personnel with a more comprehensive fault feature analysis and risk warning. This method, through the combination of multidimensional data integration and intelligent analysis, significantly improves the efficiency and accuracy of waveform data processing, providing reliable technical support for the intelligent operation and maintenance of power systems.

[0116] The waveform analysis method provided in this application first acquires a waveform fault dataset, then performs feature extraction and normalization on the multi-source data in the dataset to construct a waveform feature matrix representing the operating state of each waveform sample, making features of different dimensions and scales comparable. Based on this, an unsupervised clustering algorithm is used to perform similarity analysis on each waveform feature vector in the waveform feature matrix, classifying waveform feature vectors with similar feature distributions into the same category. This achieves automatic mining of the intrinsic structure and fault modes of historical waveform fault samples, thereby obtaining the classification result corresponding to each waveform feature vector. This classification result is used to characterize the category affiliation of the waveform feature vector in the feature space. Subsequently, a pre-established multivariate... The linear regression prediction model performs regression processing on each waveform feature vector. Based on the linear mapping relationship between each waveform feature and the target variable, it outputs the corresponding predicted value, which is used to quantify the correlation strength or confidence level between the waveform feature vector and its corresponding fault type. Finally, the classification result and the predicted value are fused for judgment. When the predicted value meets the preset judgment conditions, the fault type corresponding to the waveform feature vector is confirmed as the fault type indicated by the classification result. When the predicted value does not meet the preset judgment conditions, the confidence level of the classification result is reduced and further auxiliary analysis or manual review is triggered. This improves the accuracy and reliability of fault type determination while ensuring the objectivity of the classification result, and realizes intelligent analysis and auxiliary decision-making of waveform fault data.

[0117] Figure 2 A flowchart illustrating the waveform analysis method provided in the embodiments of this application. Figure 2 ;like Figure 2 As shown, in this embodiment... Figure 1 Based on the embodiments, the process of determining the classification results of each waveform feature vector is described in detail. The method includes:

[0118] S201. Determine the number of clusters using empirical methods.

[0119] It should be understood that determining the number of clusters, k, in the K-means algorithm is the primary step in its implementation. One approach is based on domain experience, where the value of k is preset based on the number of common fault mode categories with clear physical meaning observed in historical fault data analysis. For example, in a substation protection system, common typical fault modes might include single-phase ground faults, two-phase short circuits, three-phase short circuits, open circuits, and protection maloperation; k could be initially set to 5 or 6 accordingly. Another implementation method is the elbow rule, which calculates the sum of squared errors of the clustering results under different k values, plots a curve showing the relationship between k and the sum of squared errors, and selects the k value corresponding to the inflection point of the curve (i.e., the point where the rate of decrease in the sum of squared errors slows significantly) as the optimal solution.

[0120] Understandably, setting a reasonable expected number of groups for unsupervised clustering allows the algorithm to divide data into meaningful categories that align with business understanding, avoiding pattern fragmentation due to too many clusters or pattern confusion due to too few. This provides a reasonable structural framework for subsequent clustering analysis, ensuring that the clustering results have a certain correspondence and interpretability with the actual distribution of fault types. For example, relay protection experts, based on long-term experience, believe that the protection waveforms of a certain type of line mainly reflect four typical action characteristics; therefore, the initial value of k can be set to 4 as the starting point for algorithm exploration.

[0121] S202. Randomly select wave recording feature vectors from the wave recording feature matrix as cluster centers.

[0122] It should be understood that after determining the number of clusters k, the cluster centers are initialized. Typically, k different waveform feature vectors are randomly selected from the normalized waveform feature matrix constructed in step S101 as the initial cluster centers (centroids). Each selected feature vector represents an initial, hypothetical fault mode prototype.

[0123] Understandably, random sampling provides the starting point for iterative optimization of the algorithm. Since subsequent steps continuously adjust the centroid position, the algorithm can usually converge to a local optimum even if the initial selection is random. However, it should be noted that while this method is simple and fast to start the clustering process, different random seeds may lead to different final clustering results. Therefore, some implementations use multiple random initializations and select the optimal result to enhance stability.

[0124] S203. For each recorded wave feature vector, calculate the spatial distance between the recorded wave feature vector and the cluster center, until several cluster centers are determined.

[0125] In one possible approach, firstly, for each waveform feature vector, the spatial distance between the waveform feature vector and the cluster center is calculated; then, the spatial distance values ​​are sorted from smallest to largest, and the waveform feature vector corresponding to the largest spatial distance is selected as the new cluster center; finally, the above steps are repeated until several cluster centers are determined.

[0126] It should also be noted that after determining several cluster centers, for each waveform feature vector, the Euclidean distance between the waveform feature vector and its corresponding cluster center needs to be calculated; and the sum of squares of the Euclidean distances is calculated to obtain the sum of squares of the error of the waveform feature matrix; if the sum of squares of the error is less than a preset value, the classification result is determined to be reliable; if the sum of squares of the error is less than the preset value, the classification result is determined to be unreliable and reclassification is required.

[0127] It should be understood that the K-means clustering algorithm, by calculating the Euclidean distance between waveform data samples, groups data with similar fault characteristics into the same category, solving the problem of integrating multidimensional data in traditional manual analysis. For example, when waveform data simultaneously contains multidimensional features such as time-series behavior, analog quantity changes, and setpoint sensitivity, K-means clustering can automatically identify the similarity between data based on geometric attributes (such as Euclidean distance), avoiding reliance on human experience. Furthermore, the multiple linear regression algorithm, by modeling and analyzing the relationship between various variables (such as voltage, current, and setpoints) in the clustering results and fault risk, enables the prediction of potential risk points. This multidimensional data integration and intelligent analysis framework can comprehensively uncover fault patterns in waveform data, improving the completeness of the analysis results. For example, in power grid transient fault scenarios, K-means clustering can accurately classify fault types (such as sampling circuit anomalies, setpoint mismatches, etc.), while multiple linear regression can quantify the influence weight of each factor on fault risk, thereby providing relay protection personnel with more comprehensive fault characteristic analysis and risk warning, significantly improving the intelligence level of waveform data processing.

[0128] Specifically, the formula for calculating Euclidean distance is as follows:

[0129]

[0130] Where m is the dimension of the data object; Let i be the i-th cluster center.

[0131] The sum of squared errors is calculated as follows:

[0132]

[0133] Where S represents the quality of the clustering result.

[0134] It should be understood that the specific implementation of this embodiment includes two stages: iterative optimization and result evaluation. In the iterative optimization stage, firstly, for each waveform feature vector in the feature matrix, its Euclidean distance to all k current cluster centers is calculated. Next, each feature vector is assigned to the category of the nearest cluster center. After all sample assignments are completed, for each newly formed category, the average value of each feature dimension of all sample points in that category is recalculated to update the cluster center of that category. This process is repeated until the positions of the cluster centers no longer change significantly or the preset maximum number of iterations is reached, at which point the final k cluster centers are determined.

[0135] It should be understood that this strategy analyzes the distribution characteristics of waveform data using density sensing, prioritizing samples from high-density areas as initial centers to avoid overly concentrated or dispersed center points due to random selection. For example, when multiple fault modes exist in the waveform data (such as sampling loop faults, setting mismatches, etc.), density sensing's initial center selection ensures that each cluster center covers different fault feature regions, thus more accurately classifying fault mode categories. This technique significantly improves the convergence speed and result stability of K-means clustering, reducing cluster overlap problems caused by improper initial center selection. For instance, in power grid transient fault scenarios, the density sensing strategy can quickly identify key fault regions in the waveform data, improving the efficiency and accuracy of cluster analysis.

[0136] In the results evaluation phase, cluster quality needs to be calculated to assess its reliability. The specific method is as follows: For the final classification results, calculate the Euclidean distance from each waveform feature vector to its final cluster center, and sum the squared Euclidean distances of all samples to obtain the sum of squared errors (SSE) of the entire waveform feature matrix. This value measures the tightness of the samples within each category. The calculated SSE is compared with a preset threshold based on historical data or experience: if the SSE is less than the preset threshold, it indicates that the samples within each category are tightly clustered, the classification results have high cohesion, and the classification results can be judged as reliable; conversely, if the SSE is greater than or equal to the preset threshold, it indicates that the clustering effect is loose, the classification results are unreliable, and in this case, the number of clusters k needs to be adjusted or the cluster analysis needs to be repeated.

[0137] Understandably, iterative optimization continuously refines the location of cluster centers, minimizing the distance between samples within each category (i.e., minimizing the sum of squared errors). The sum of squared errors is then used as an objective quantitative indicator to evaluate whether the clustering effect meets business-acceptable standards. This approach automates the cluster center optimization process and provides a quality check to ensure that the output classification results are not only algorithmically convergent but also meet the tightness requirements, thus providing a reliable foundation for subsequent analysis. For example, if the centroids stabilize after 5 iterations and the calculated SSE is 12.5, below the empirical threshold of 15, the system determines that the clustering result is reliable and can proceed to the next step of analysis.

[0138] S204. Based on the cluster centers, each waveform feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to determine the cluster center to which each waveform feature vector belongs.

[0139] It should be understood that after the cluster centers are determined and the classification confidence meets the requirements, the final classification result of each waveform feature vector is determined based on the spatial distance relationship between each waveform feature vector and the cluster centers.

[0140] Specifically, after selecting several waveform feature vectors from the waveform feature matrix as cluster centers, each cluster center represents a typical waveform fault mode in the feature space. Further, for each waveform feature vector in the waveform feature matrix, its spatial distance to each cluster center is calculated, and the cluster center with the smallest distance is selected as the belonging center of that waveform feature vector, thus classifying it into the corresponding category. In this way, the originally discretely distributed waveform feature vectors are classified according to similarity, giving each waveform feature vector a corresponding classification label, which is the classification result.

[0141] For example, in a substation's recorded fault dataset, multiple recorded fault feature vectors are formed after feature extraction. Some of these feature vectors generally exhibit characteristics such as large current surge amplitudes, differential protection operation delays, and abnormal increases in zero-sequence current. Therefore, they are selected during the clustering process to form corresponding cluster centers, which are used to characterize abnormal fault modes of differential protection. Subsequently, for each new recorded fault feature vector, the spatial distance between it and each cluster center is calculated. When the distance between the recorded fault feature vector and the differential protection abnormal cluster center is minimized, the recorded fault feature vector is assigned to the corresponding category, and the category label corresponding to the cluster center is determined as the classification result of the recorded fault feature vector. This achieves automatic classification and fault mode recognition of recorded fault data.

[0142] Understandably, this method enables the automatic classification of a large number of recorded fault samples, significantly reducing the workload of manual analysis and providing a stable and reusable data foundation for subsequent fault type determination and risk assessment. For example, this step can classify recorded samples with similar current abrupt change characteristics and action timing characteristics into the same protection anomaly type, facilitating centralized analysis and processing.

[0143] S205. The cluster center to which each waveform feature vector belongs is determined as the classification result of that waveform feature vector.

[0144] It should be understood that after determining the cluster centers and calculating the spatial distance between the recorded feature vectors and each cluster center, each recorded feature vector will be assigned to the category corresponding to the cluster center with the smallest spatial distance. Therefore, this cluster center can characterize the category affiliation of the current recorded feature vector in the feature space and the corresponding fault mode characteristics. Based on this, the cluster center to which each recorded feature vector belongs is determined as the classification result of that recorded feature vector, thereby realizing the automatic classification of recorded fault data and grouping recorded data with similar operating state characteristics and protection behavior characteristics into the same category.

[0145] Figure 3This is a schematic diagram of the waveform analysis device provided in the embodiments of this application; as shown. Figure 3 As shown, the device includes:

[0146] Module 301 is used to acquire the waveform fault dataset and construct the waveform feature matrix based on the waveform fault dataset.

[0147] The first determining module 302 is used to classify each waveform feature vector in the waveform feature matrix based on an unsupervised clustering algorithm, and determine the classification result of each waveform feature vector. The classification result is used to characterize the category belonging relationship of the waveform feature vector in the feature space.

[0148] The processing module 303 is used to perform regression processing on each waveform feature vector using a multiple linear regression prediction model to determine the predicted value of each waveform feature vector. The predicted value is used to characterize the correlation between the waveform feature vector and the classification result.

[0149] The second determining module 304 is used to determine the fault type of each recorded waveform feature vector based on the classification results and the predicted values.

[0150] In one possible implementation, the construction module 301 is specifically used for:

[0151] Obtain the waveform fault dataset, and construct the waveform feature vector corresponding to each fault sample based on the waveform fault dataset. The waveform fault dataset includes at least one of the following: time series feature vector, analog quantity feature vector, setpoint sensitivity feature vector, external circuit anomaly feature vector, and sampling circuit feature vector.

[0152] Normalize each waveform feature vector to construct a waveform feature matrix.

[0153] In one possible implementation, the first determining module 302 is specifically used for:

[0154] The number of clusters is determined empirically.

[0155] Randomly select wave recording feature vectors from the wave recording feature matrix as cluster centers;

[0156] For each recorded feature vector, calculate the spatial distance between the recorded feature vector and the cluster center, until several cluster centers are determined;

[0157] Based on cluster centers,

[0158] Each waveform feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to determine the cluster center to which each waveform feature vector belongs;

[0159] The cluster center to which each waveform feature vector belongs is determined as the classification result of that waveform feature vector.

[0160] In one possible implementation, the first determining module 302 is specifically used for:

[0161] Step a: For each waveform feature vector, calculate the spatial distance between the waveform feature vector and the cluster center;

[0162] Step b: Sort the spatial distance values ​​from smallest to largest, and select the waveform feature vector corresponding to the largest spatial distance as the new cluster center;

[0163] Repeat steps a through b until several cluster centers are determined.

[0164] In one possible implementation, after determining several cluster centers, the first determining module 302 is further configured to:

[0165] For each waveform feature vector, calculate the Euclidean distance between the waveform feature vector and its corresponding cluster center;

[0166] The sum of the squares of each Euclidean distance is accumulated to obtain the sum of squared errors of the waveform characteristic matrix;

[0167] If the sum of squared errors is less than the preset value, the classification result is considered reliable.

[0168] If the sum of squared errors is less than the preset value, the classification result is determined to be unreliable and needs to be reclassified.

[0169] In one possible implementation, the multiple linear regression prediction model includes...

[0170]

[0171] in, The predicted value of the i-th waveform feature vector; It is the intercept; It is the skewness coefficient for each variable; Let p be the p-th eigenvalue in the i-th recorded waveform eigenvector.

[0172] In one possible implementation, the second determining module 304 is specifically used for:

[0173] Obtain the classification result and corresponding predicted value for each waveform feature vector;

[0174] If the predicted value is greater than the preset threshold, the fault type of the recorded waveform feature vector is determined to be the fault type corresponding to the classification result;

[0175] If the predicted value is less than the preset threshold, the fault type of the recorded waveform feature vector is determined to be a fault to be confirmed.

[0176] The waveform analysis device provided in this application embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0177] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 4 As shown, the electronic device 40 provided in this embodiment includes at least one processor 401 and a memory 402. Optionally, the device 40 further includes a communication component 403. The processor 401, memory 402, and communication component 403 are connected via a bus 404.

[0178] In a specific implementation, at least one processor 401 executes computer execution instructions stored in memory 402, causing at least one processor 401 to perform the above-described method.

[0179] The specific implementation process of processor 401 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0180] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0181] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0182] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0183] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0184] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0185] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0186] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0187] The units described as separate components may or may not be physically separate. 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 units can be selected to achieve the purpose of this embodiment according to actual needs.

[0188] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0189] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0190] Based on the above disclosure, those skilled in the art will understand that the computer-readable storage medium and its related implementation methods provided in the embodiments of the present invention are not limited to the specific hardware or logical partitioning forms described above. In actual product or system deployments, the computer execution instructions can be encapsulated in different software distribution packages or firmware modules and distributed via networks, optical discs, or mobile storage devices. When the computer execution instructions are loaded and executed by one or more processors, in addition to implementing the aforementioned method steps, hardware resource configurations can be automatically identified according to specific application scenarios, and thread priorities or memory allocation strategies can be dynamically adjusted to optimize execution efficiency without manual intervention. Furthermore, the computer-readable storage medium can also be integrated into IoT terminals, edge computing nodes, or cloud servers to form a distributed instruction storage and collaborative execution system to meet differentiated needs such as high concurrency, low latency, or data privacy protection.

[0191] Furthermore, it should be emphasized that the logical functions corresponding to the methods, units, modules, and storage media in this application, without departing from the core idea of ​​this invention, allow developers to make equivalent refactoring, renaming, or re-division based on specific programming languages ​​(such as C++, Java, Python, etc.) or framework characteristics. For example, the functions of multiple "units" can be merged into a single service process, or message queues or pipe communication can be used instead of direct function calls. Even if these implementation details are not completely the same as the foregoing embodiments, as long as they ultimately achieve the same technical effect and no creative effort is required, they should all be considered to fall within the protection scope of this invention. Similarly, any intermediate data processing forms, exception handling mechanisms, or logging methods embodied in the instructions in the computer-readable storage medium when executed are also derivative technologies of this invention and should not be construed as substantial limitations on the original solution.

[0192] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0193] Furthermore, based on the implementation scheme described in this application, the computer-executable instructions in the computer-readable storage medium can also be maintained through remote updates or differential upgrades. Specifically, when the method flow involves changes in business logic, parameter optimization, or security patches, only incremental patch packages or configuration files need to be issued. During execution, the instructions automatically detect the local version and complete merging and verification, thereby avoiding the complete replacement of the entire storage medium content. This design is particularly suitable for devices with limited storage space or sensitive network bandwidth, such as sensor nodes, wearable devices, or in-vehicle systems. Further, the computer-readable storage medium can be logically divided into a boot sector, a core instruction sector, and a user data sector. The core instruction sector stores the main execution logic of the method, the user data sector stores the rule base or model weights that can be dynamically loaded at runtime, and the boot sector is responsible for quickly verifying and starting the execution environment after the device is powered on. The access permissions and encryption methods between the three sectors can be configured independently to improve system security and maintainability. Based on this, even if the storage medium is physically separated from the processor (e.g., connected via SDIO, SPI, PCIe, etc.), the atomicity and integrity of instruction execution can still be guaranteed. It should be noted that the above-mentioned regional division and upgrade methods are merely exemplary preferred implementations. Any variations that adopt the core steps of the method in this application and are distributed or executed on a computer-readable storage medium shall not depart from the protection scope of this application.

[0194] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A waveform analysis method, characterized in that, include: Obtain the waveform fault dataset and construct the waveform feature matrix based on the waveform fault dataset; Based on an unsupervised clustering algorithm, each waveform feature vector in the waveform feature matrix is ​​classified to determine the classification result of each waveform feature vector. The classification result is used to characterize the category belonging relationship of the waveform feature vector in the feature space. A multiple linear regression prediction model is used to perform regression processing on each of the recorded waveform feature vectors to determine the predicted value of each recorded waveform feature vector. The predicted value is used to characterize the correlation between the recorded waveform feature vector and the classification result. Based on the classification results and the predicted values, the fault type of each recorded waveform feature vector is determined.

2. The method according to claim 1, characterized in that, The step of acquiring the waveform fault dataset and constructing a waveform feature matrix based on the waveform fault dataset includes: Obtain a waveform fault dataset, and construct a waveform feature vector corresponding to each fault sample based on the waveform fault dataset. The waveform fault dataset includes at least one of the following: time series feature vector, analog quantity feature vector, setpoint sensitivity feature vector, external circuit anomaly feature vector, and sampling circuit feature vector. Each of the recorded waveform feature vectors is normalized to construct a recorded waveform feature matrix.

3. The method according to claim 1 or 2, characterized in that, The unsupervised clustering algorithm is used to classify each waveform feature vector in the waveform feature matrix and determine the classification result for each waveform feature vector, including: The number of clusters is determined empirically. Randomly select wave recording feature vectors from the wave recording feature matrix as cluster centers; For each recorded waveform feature vector, the spatial distance between the recorded waveform feature vector and the cluster center is calculated until several cluster centers are determined. Based on the cluster centers, each waveform feature vector is assigned to the category corresponding to the cluster center with the smallest spatial distance to determine the cluster center to which each waveform feature vector belongs; The cluster center to which each of the recorded waveform feature vectors belongs is determined as the classification result of the recorded waveform feature vector.

4. The method according to claim 3, characterized in that, For each recorded waveform feature vector, the spatial distance between the recorded waveform feature vector and the cluster center is calculated until several cluster centers are determined, including: Step a: For each recorded waveform feature vector, calculate the spatial distance between the recorded waveform feature vector and the cluster center; Step b: Sort the spatial distance values ​​from smallest to largest, and select the waveform feature vector corresponding to the largest spatial distance as the new cluster center; Repeat steps a through b until the cluster centers are determined.

5. The method according to claim 1 or 4, characterized in that, After determining the cluster centers, the method further includes: For each recorded waveform feature vector, calculate the Euclidean distance between the recorded waveform feature vector and its corresponding cluster center; The sum of the squares of each Euclidean distance is accumulated to obtain the sum of squared errors of the waveform characteristic matrix; If the sum of squared errors is less than a preset value, then the classification result is determined to be reliable. If the sum of squared errors is less than a preset value, the classification result is determined to be unreliable and needs to be reclassified.

6. The method according to claim 1, characterized in that, The multiple linear regression prediction model includes in, The predicted value of the i-th recorded waveform feature vector; It is the intercept; It is the skewness coefficient for each variable; It is the p-th feature value in the i-th recorded wave feature vector.

7. The method according to claim 1, characterized in that, Determining the fault type of each recorded waveform feature vector based on the classification result and the predicted value includes: Obtain the classification result and the corresponding predicted value for each of the recorded waveform feature vectors; If the predicted value is greater than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be the fault type corresponding to the classification result; If the predicted value is less than a preset threshold, then the fault type of the recorded waveform feature vector is determined to be a fault to be confirmed.

8. A waveform analysis device, characterized in that, include: The module is used to acquire the waveform fault dataset and construct the waveform feature matrix; The first determining module is used to classify each waveform feature vector in the waveform feature matrix based on an unsupervised clustering algorithm, and determine the classification result of each waveform feature vector. The classification result is used to characterize the category belonging relationship of the waveform feature vector in the feature space. The processing module is used to perform regression processing on each of the recorded waveform feature vectors using a multiple linear regression prediction model to determine the predicted value of each recorded waveform feature vector. The predicted value is used to characterize the correlation between the recorded waveform feature vector and the fault type. The second determining module is used to determine the fault type of each of the recorded waveform feature vectors based on the classification results and the predicted values.

9. An electronic device, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-7.

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