A distribution network fault type identification method based on big data

Abstract

The present invention discloses a method for identifying distribution network fault types based on big data, which relates to the technical field of distribution network fault type identification. The present invention aligns the time axis of multi-source data while retaining the original sampling accuracy through clock drift correction and adaptive interpolation algorithm, completely eliminating the problem of misjudgment or missed faults caused by time asynchrony of voltage / current signals; marks communication delay data with low confidence and restricts participation in calculation to avoid noise interference in feature extraction; based on the fault type association mechanism of misjudgment samples, accurately locates the network layer that needs to be adjusted, avoiding the resource overhead of retraining the entire model; combines adversarial sample generation technology to expand scarce fault data, and improves the recognition robustness of complex scenarios such as high-impedance grounding.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network fault type identification, and in particular to a distribution network fault type identification method based on big data. Background Art

[0002] Currently, the identification of distribution network fault types mainly relies on the collaborative analysis of multi-source data such as voltage, current, and communication status. However, different data acquisition devices have clock deviations and sampling accuracy differences, such as a current sampling rate of 1kHz and a voltage sampling rate of 100Hz. Direct fusion will lead to misalignment of key features.

[0003] Common solutions include the spatiotemporal graph convolutional network (ST-GCN) to construct a device relationship graph, but most methods force a unified sampling rate, resulting in the loss of high-frequency details. As the distribution network continues to connect to new elements such as distributed power sources and flexible loads, the distribution of fault characteristics drifts accordingly. For example, after the photovoltaic inverter is connected, the amplitude of the single-phase grounding fault current decreases by 40% to 60%. The original model mistakenly judges it as a normal state due to outdated training data. Some adaptive solutions, such as incremental learning, can perform local updates but rely on retraining on a central server, which takes several hours and cannot meet the minute-level fault handling requirements.

[0004] Some solutions use edge computing and ST-GCN to retain the spatiotemporal relationship of data locally, but the graph structure is static and fixed, and nodes cannot be added or removed dynamically, such as temporarily connecting to a mobile energy storage vehicle. The feedback mechanism mostly uses regular full updates, which has high computational overhead and high response delay. It can be seen that current technology has failed to form a closed loop of data alignment-feature extraction-model evolution, and there is an urgent need for lightweight and adaptive edge intelligence solutions. Summary of the Invention

[0005] In view of the above existing problems, the present invention is proposed.

[0006] The present invention provides a distribution network fault type identification method based on big data to solve the problems of feature misalignment caused by data asynchrony, model failure caused by environmental changes, and static solutions being difficult to adapt to dynamic power grids.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0008] The embodiment of the present invention provides a method for identifying distribution network fault types based on big data, which includes:

[0009] Step S1, constructing a dynamic spatiotemporal graph: collecting voltage, current, and communication status data of multiple monitoring points in real time, and constructing a spatiotemporal graph with monitoring point devices as nodes and physical connections or logical associations between devices as edges;

[0010] The original sampling timestamp and accuracy of each node data are retained, and the time series of different node data are aligned through the time offset compensation mechanism;

[0011] Step S2, spatiotemporal feature extraction: The spatiotemporal graph is input into the spatiotemporal graph convolutional network ST-GCN, the node state change features are extracted through the time dimension convolution layer, the device association features are extracted through the spatial dimension convolution layer, and the fused feature vector is output;

[0012] Step S3, fault classification and identification: classify the fault types into short circuit, grounding, and disconnection according to the feature vector, and output the confidence score;

[0013] Step S4, feedback trigger update: real-time comparison of recognition results and emergency repair work order records. When the number of consecutive misjudgments reaches a preset number or an undefined fault type occurs, an update instruction is triggered;

[0014] Step S5, lightweight retraining: According to the update instruction, only the local network layers that are strongly correlated with the misjudged samples are selected, and the incremental data is used to fine-tune the weights at the edge nodes.

[0015] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the time offset compensation mechanism of step S1 includes:

[0016] Based on the distribution network synchronization clock source, the timestamp of each node data is drift corrected;

[0017] For data with different sampling precisions, a continuous sequence under a unified time axis is generated through interpolation algorithm;

[0018] Node data whose communication delay exceeds the threshold is marked as low confidence, restricting its participation in graph convolution calculations.

[0019] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, in step S1, after clock drift correction and communication delay marking, the original sampling data of each node is Perform the following interpolation processing to construct a uniform equally spaced time series, including:

[0020] Detection data: Collection node No. Sub-original moment With measured value ,

[0021] Calculate the uniform time step, the formula is:

[0022] ,

[0023] in, represents the uniform time step in seconds, Representation node No. Sampling time, in seconds;

[0024] Build Aligned Timeline ,

[0025] in, Indicates the first Time point, in seconds, Indicates the alignment start time, It represents the length of the sequence minus one and is dimensionless;

[0026] Calculate linear interpolation, the formula is:

[0027] ,

[0028] in, Representation node At the moment The interpolation result of represents the interpolation weight factor, ;

[0029] Where,

[0030] ,

[0031] Among them, the molecule is the interpolation time offset, in seconds, the denominator is the original two sampling intervals;

[0032] Compute the interpolation residual within a sliding window:

[0033] , Indicates the Node in The absolute residual between the difference moment and the reference difference result; if , then adjust Or switch to a higher-order interpolation method, where is the high-order interpolation reference result, is the residual threshold.

[0034] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the operation of the spatial dimension graph convolution layer in step S2 includes:

[0035] Dynamically calculate the adjacency matrix weight coefficient based on the electrical distance of the equipment;

[0036] For devices whose physical connection is disconnected but logically associated, the virtual connection edge is retained.

[0037] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the local network layer selection rule in step S5 includes:

[0038] For misjudgment of short-circuit faults, update the weights of the transient current feature extraction layer in ST-GCN;

[0039] For ground fault misjudgment, update the weight of the zero-sequence voltage feature extraction layer;

[0040] The network layer number that needs to be updated is determined through the correlation analysis function.

[0041] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, in step S5, the network layer to be updated is determined based on correlation analysis, and before local retraining, the network layer number with the greatest impact on fault type discrimination is accurately selected from the misjudged samples, the steps include:

[0042] Define the misclassified sample set ,in, For the network The prediction type of samples, is the actual fault type;

[0043] For each misclassified sample , record network The output feature map tensor of the layer ,in, is the number of channels, is the time series length;

[0044] The tensor Take the norm in the two dimensions of channel and time series to get the layer For samples The response amplitude of:

[0045] ,

[0046] in, represents the square root norm of the elements, Indicates the Layer Channel ,time For samples The activation value of

[0047] Defining false positive intensity ,

[0048] in, For the network to sample The confidence score of is obtained from the forward propagation Softmax output, for misjudgment of instructions;

[0049] Computational layer The correlation between the response amplitude and the misjudgment intensity is as follows:

[0050] ,

[0051] in, , sample response mean, , the mean misjudgment, , measurement layer the degree of linear correlation with misjudgment;

[0052] For adaptive layer selection, the statistics of global correlation distribution are introduced, which is expressed as:

[0053] ,

[0054] in, is the total number of candidate update layers,

[0055] And define the threshold ,in, is the threshold adjustment coefficient;

[0056] Finally, the layer number whose absolute value of correlation is not less than the threshold is selected:

[0057] ,

[0058] in, A set of network layer numbers that need to be fine-tuned;

[0059] like, Then press Recalculate in descending order , until , and finally only perform incremental fine-tuning on the inner layers.

[0060] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the incremental data fine-tuning in step S5 includes:

[0061] Only the data of monitoring points that trigger misjudgment are collected, and the time range covers before and after the fault occurs;

[0062] Adversarial sample generation technology is introduced to expand scarce fault scenario data such as high-impedance grounding.

[0063] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the dynamic maintenance of the spatiotemporal graph in step S1 further includes:

[0064] When adding a distributed power supply node, it automatically inherits the topological relationship of the associated feeder;

[0065] For offline device nodes, historical data is retained but real-time data stream input is blocked.

[0066] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, the fault classification identification in step S3 includes:

[0067] When the confidence score is lower than the threshold, the feature vectors of the three adjacent monitoring points are combined to make a collaborative decision;

[0068] For undefined fault types, their spatiotemporal feature vectors are extracted and stored in the template library and an alarm is issued.

[0069] As a preferred solution of the method for identifying distribution network fault types based on big data described in the present invention, after the update instruction is triggered in step S4:

[0070] Generate a model update container on the edge node to isolate the retraining process from the online recognition service;

[0071] After the update is completed, cross-verification is performed, and after the verification is passed, hot switching to the online recognition module is performed.

[0072] The beneficial effects of the present invention are as follows: the present invention, through clock drift correction and adaptive interpolation algorithm, aligns the time axis of multi-source data while retaining the original sampling accuracy, completely eliminating the problem of misjudgment or missed fault judgment caused by time asynchrony of voltage / current signals; marks communication delay data with low confidence and limits its participation in calculation, avoiding noise interference in feature extraction.

[0073] Based on the fault type association mechanism of misjudgment samples (such as updating the current layer for short circuit misjudgment), the network layer that needs to be adjusted is accurately located to avoid the resource overhead of retraining the entire model; combined with adversarial sample generation technology, scarce fault data is expanded to improve the recognition robustness of complex scenarios such as high-impedance grounding.

[0074] Lightweight retraining only requires edge node resources, and the model update process is isolated from the online identification service to ensure uninterrupted fault identification. The dynamic spatiotemporal graph structure automatically adapts to changes in distribution network topology (such as the addition of new photovoltaic equipment) without the need for manual model reconstruction.

[0075] Confidence scoring links multiple monitoring points for collaborative decision-making, reducing the frequency of manual review; undefined fault characteristics are automatically stored and alarmed, accelerating the closed-loop handling of new fault types.

[0076] The present invention forms a closed loop of data alignment, feature extraction, and model evolution, and uses edge intelligence to achieve adaptability, accuracy, and efficiency in distribution network fault identification and differentiation. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0078] Figure 1 This is a flow chart of the method for identifying distribution network fault types based on big data in Example 1. DETAILED DESCRIPTION

[0079] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0080] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0081] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0082] Example 1, with reference to Figure 1 , this embodiment provides a method for identifying distribution network fault types based on big data, comprising the following steps:

[0083] Step S1, constructing a dynamic spatiotemporal graph: collecting voltage, current, and communication status data of multiple monitoring points in real time, and constructing a spatiotemporal graph with monitoring point devices as nodes and physical connections or logical associations between devices as edges;

[0084] The original sampling timestamp and accuracy of each node data are retained, and the time series of different node data are aligned through the time offset compensation mechanism;

[0085] The time offset compensation mechanism of step S1 includes:

[0086] Based on the distribution network synchronization clock source, the timestamp of each node data is drift corrected;

[0087] For data with different sampling precisions, a continuous sequence under a unified time axis is generated through interpolation algorithm;

[0088] Node data whose communication delay exceeds the threshold is marked as low confidence, restricting its participation in graph convolution calculations;

[0089] In step S1, after clock drift correction and communication delay marking, the original sampling data of each node is Perform the following interpolation processing to construct a uniform equally spaced time series, including:

[0090] Detection data: Collection node No. Sub-original moment With measured value ,

[0091] Calculate the uniform time step, the formula is:

[0092] ,

[0093] in, represents the uniform time step in seconds, Representation node No. Sampling time, in seconds;

[0094] Build Aligned Timeline ,

[0095] in, Indicates the first Time point, in seconds, Indicates the alignment start time, It represents the length of the sequence minus one and is dimensionless;

[0096] Calculate linear interpolation, the formula is:

[0097] ,

[0098] in, Representation node At the moment The interpolation result of represents the interpolation weight factor, ;

[0099] Where,

[0100] ,

[0101] Among them, the molecule is the interpolation time offset, in seconds, the denominator is the original two sampling intervals;

[0102] Compute the interpolation residual within a sliding window:

[0103] , Indicates the Node in The absolute residual between the difference moment and the reference difference result; if , then adjust Or switch to a higher-order interpolation method, where is the high-order interpolation reference result, is the residual threshold;

[0104] Specifically, while maintaining the original sampling moment and data integrity, the interpolation process generates a globally unified time axis through the minimum step size method to avoid losing high-frequency information. The linear interpolation calculation is concise and easy to execute in real time on edge devices. The weight factor accurately reflects the time interval, which helps to smoothly transition to the downstream spatiotemporal graph convolutional network. The sliding window residual judgment and dynamic step size adjustment mechanism improve the compatibility with data of various sampling precisions and avoid oversampling or undersampling problems caused by fixed step sizes.

[0105] The dynamic maintenance of the spatiotemporal graph in step S1 also includes:

[0106] When adding a distributed power supply node, it automatically inherits the topological relationship of the associated feeder;

[0107] For offline device nodes, historical data is retained but real-time data stream input is blocked;

[0108] Step S2, spatiotemporal feature extraction: The spatiotemporal graph is input into the spatiotemporal graph convolutional network ST-GCN, the node state change features are extracted through the time dimension convolution layer, the device association features are extracted through the spatial dimension convolution layer, and the fused feature vector is output;

[0109] The operations of the spatial dimension graph convolution layer in step S2 include:

[0110] Dynamically calculate the adjacency matrix weight coefficient based on the electrical distance of the equipment;

[0111] For devices that are physically disconnected but logically associated (e.g., partitions on the same feeder), a virtual connection edge is retained;

[0112] Step S3, fault classification and identification: classify the fault types into short circuit, grounding, and disconnection according to the feature vector, and output the confidence score;

[0113] The fault classification identification in step S3 includes:

[0114] When the confidence score is lower than the threshold, the feature vectors of the three adjacent monitoring points are combined to make a collaborative decision;

[0115] For undefined fault types, extract their spatiotemporal feature vectors, store them in the template library and generate an alarm;

[0116] Step S4, feedback trigger update: real-time comparison of recognition results and emergency repair work order records. When the number of consecutive misjudgments reaches a preset number or an undefined fault type occurs, an update instruction is triggered;

[0117] After the update instruction is triggered in step S4:

[0118] Generate a model update container on the edge node to isolate the retraining process from the online recognition service;

[0119] After the update is completed, cross-verification is performed, and after passing the verification, hot switching to the online recognition module;

[0120] Step S5, lightweight retraining: According to the update instruction, only the local network layer that is strongly related to the misjudged samples is selected, and the weights are fine-tuned at the edge nodes using incremental data;

[0121] The local network layer selection rules of step S5 include:

[0122] For misjudgment of short-circuit faults, update the weights of the transient current feature extraction layer in ST-GCN;

[0123] For ground fault misjudgment, update the weight of the zero-sequence voltage feature extraction layer;

[0124] Determine the network layer number that needs to be updated through the correlation analysis function;

[0125] In step S5, the network layer to be updated is determined based on the correlation analysis. Before local retraining, the network layer number with the greatest impact on fault type discrimination is accurately selected from the misjudged samples. The steps include:

[0126] Define the misclassified sample set ,in, For the network The prediction type of samples, is the actual fault type;

[0127] For each misclassified sample , record network The output feature map tensor of the layer ,in, is the number of channels, is the time series length;

[0128] The tensor Take the norm in the two dimensions of channel and time series to get the layer For samples The response amplitude of:

[0129] ,

[0130] in, represents the square root norm of the elements, Indicates the Layer Channel ,time For samples The activation value of

[0131] Defining false positive intensity ,

[0132] in, For the network to sample The confidence score of is obtained from the forward propagation Softmax output, for misjudgment of instructions;

[0133] Computational layer The correlation between the response amplitude and the misjudgment intensity is as follows:

[0134] ,

[0135] in, , sample response mean, , the mean misjudgment, , measurement layer the degree of linear correlation with misjudgment;

[0136] For adaptive layer selection, the statistics of global correlation distribution are introduced, which is expressed as:

[0137] ,

[0138] in, is the total number of candidate update layers,

[0139] And define the threshold ,in, is the threshold adjustment coefficient;

[0140] Finally, the layer number whose absolute value of correlation is not less than the threshold is selected:

[0141] ,

[0142] in, A set of network layer numbers that need to be fine-tuned;

[0143] like, Then press Recalculate in descending order , until ,Finally, only incremental fine-tuning is performed on the inner layers, reducing the edge computing burden;

[0144] Specifically, this method leverages the statistical correlation between the network response and misjudgment intensity of misjudgment samples to accurately identify the network layers most sensitive to fault type discrimination. Through norm dimensionality reduction and Pearson correlation coefficient calculation, it preserves the overall energy information of the feature map while revealing the direct impact of the layer on the error. A dynamic correlation threshold, combined with global distribution statistics, overcomes the non-robustness of a single fixed threshold, ensuring that valid layers can be selected in different misjudgment scenarios. A decreasing threshold mechanism ensures that critical layers are not missed in the presence of insufficient or dispersed samples. The overall algorithm involves only one-dimensional vector operations and simple statistics, resulting in extremely high computational efficiency and suitable for real-time deployment on resource-constrained edge nodes.

[0145] The incremental data fine-tuning in step S5 includes:

[0146] Only the data of monitoring points that trigger misjudgment are collected, and the time range covers before and after the fault occurs;

[0147] Adversarial sample generation technology is introduced to expand scarce fault scenario data such as high-impedance grounding.

[0148] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for identifying distribution network fault types based on big data, characterized in that: include, Step S1, constructing a dynamic spatiotemporal graph: collecting voltage, current, and communication status data of multiple monitoring points in real time, and constructing a spatiotemporal graph with monitoring point devices as nodes and physical connections or logical associations between devices as edges; The original sampling timestamp and accuracy of each node data are retained, and the time series of different node data are aligned through the time offset compensation mechanism; Step S2, spatiotemporal feature extraction: The spatiotemporal graph is input into the spatiotemporal graph convolutional network ST-GCN, the node state change features are extracted through the time dimension convolution layer, the device association features are extracted through the spatial dimension convolution layer, and the fused feature vector is output; Step S3, fault classification and identification: classify the fault types into short circuit, grounding, and disconnection according to the feature vector, and output the confidence score; Step S4, feedback trigger update: real-time comparison of recognition results and emergency repair work order records. When the number of consecutive misjudgments reaches a preset number or an undefined fault type occurs, an update instruction is triggered; Step S5, lightweight retraining: According to the update instruction, only the local network layer that is strongly related to the misjudged samples is selected, and the weights are fine-tuned at the edge nodes using incremental data; In step S1, after clock drift correction and communication delay marking, the original sampling data of each node is Perform the following interpolation processing to construct a uniform equally spaced time series, including: Detection data: Collection node No. Sub-original moment With measured value , Calculate the uniform time step, the formula is: ， in, represents the uniform time step in seconds, Representation node No. Sampling time, in seconds; Build Aligned Timeline , in, Indicates the first Time point, in seconds, Indicates the alignment start time, It represents the length of the sequence minus one and is dimensionless; Calculate linear interpolation, the formula is: ， in, Representation node At the moment The interpolation result of represents the interpolation weight factor, ; Where, ， Among them, the molecule is the interpolation time offset, in seconds, the denominator is the original two sampling intervals; Compute the interpolation residual within a sliding window: , Indicates the Node in The absolute residual between the difference moment and the reference difference result; like , then adjust Or switch to a higher-order interpolation method, where is the high-order interpolation reference result, is the residual threshold; In step S5, the network layer to be updated is determined based on the correlation analysis. Before local retraining, the network layer number with the greatest impact on fault type discrimination is accurately selected from the misjudged samples. The steps include: Define the misclassified sample set ,in, For the network The prediction type of samples, is the actual fault type; For each misclassified sample , record network The output feature map tensor of the layer ,in, is the number of channels, is the time series length; The tensor Take the norm in the two dimensions of channel and time series to get the layer For samples The response amplitude of: ， in, represents the square root norm of the elements, Indicates the Layer Channel ,time For samples The activation value of Defining false positive intensity , in, For the network to sample The confidence score of is obtained from the forward propagation Softmax output, for misjudgment of instructions; Computational layer The correlation between the response amplitude and the misjudgment intensity is as follows: ， in, , sample response mean, , the mean misjudgment, , measurement layer the degree of linear correlation with misjudgment; For adaptive layer selection, the statistics of global correlation distribution are introduced, which is expressed as: ， in, is the total number of candidate update layers, And define the threshold ,in, is the threshold adjustment coefficient; Finally, the layer number whose absolute value of correlation is not less than the threshold is selected: ， in, A set of network layer numbers that need to be fine-tuned; like, Then press Recalculate in descending order , until Finally, incremental fine-tuning is performed only on the inner layers.

2. A method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The time offset compensation mechanism of step S1 includes: Based on the distribution network synchronization clock source, the timestamp of each node data is drift corrected; For data with different sampling precisions, a continuous sequence under a unified time axis is generated through interpolation algorithm; Node data whose communication delay exceeds the threshold is marked as low confidence, restricting its participation in graph convolution calculations.

3. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The operations of the spatial dimension graph convolution layer in step S2 include: Dynamically calculate the adjacency matrix weight coefficient based on the electrical distance of the equipment; For devices whose physical connection is disconnected but logically associated, the virtual connection edge is retained.

4. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The local network layer selection rules of step S5 include: For misjudgment of short-circuit faults, update the weights of the transient current feature extraction layer in ST-GCN; For ground fault misjudgment, update the weight of the zero-sequence voltage feature extraction layer; The network layer number that needs to be updated is determined through the correlation analysis function.

5. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The incremental data fine-tuning in step S5 includes: Only the data of monitoring points that trigger misjudgment are collected, and the time range covers before and after the fault occurs; Adversarial sample generation technology is introduced to expand scarce fault scenario data such as high-impedance grounding.

6. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The dynamic maintenance of the spatiotemporal graph in step S1 also includes: When adding a distributed power supply node, it automatically inherits the topological relationship of the associated feeder; For offline device nodes, historical data is retained but real-time data stream input is blocked.

7. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: The fault classification identification in step S3 includes: When the confidence score is lower than the threshold, the feature vectors of the three adjacent monitoring points are combined to make a collaborative decision; For undefined fault types, their spatiotemporal feature vectors are extracted and stored in the template library and an alarm is issued.

8. The method for identifying distribution network fault types based on big data according to claim 1, characterized in that: After the update instruction is triggered in step S4: Generate a model update container on the edge node to isolate the retraining process from the online recognition service; After the update is completed, cross-verification is performed, and after the verification is passed, hot switching to the online recognition module is performed.

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