Cable remaining life prediction method and system considering aging trend
Through predicting the operating temperature of the cable and the combination of aging trend to correct the service life, the problem of inaccurate life of the remaining life of the cable in the existing technology has been solved, and the accuracy and practicality of the prediction is improved.
Patent Information
- Application Number
- CN202411178048.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-27
- Publication Date
- 2025-01-24
- Estimated Expiration
- 2044-08-27
AI Technical Summary
The existing cable residual life prediction method fails to effectively consider the development trend and actual operating status of the cable, resulting in inaccurate prediction results and lack of practicality.
By obtaining the historical load data of the cable, the training model is predicted to predict the operating temperature of the training model, and the effective service life is determined in combination with the aging trend, and the operating time is considered to consider the effect of the load, and then calculate the surplus life of the forecast.
It improves the accuracy and practicality of the remaining life of the cable, and can more accurately reflect the impact of the future development and operating temperature of the cable on life.
Smart Images

Figure CN118709571B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of cable remaining life prediction, and in particular to a cable remaining life prediction method and system taking aging trends into consideration. Background Art
[0002] The statements in this section merely mention background art related to the present invention and do not necessarily constitute prior art.
[0003] Cables are an important part of the power system, and their reliability and lifespan directly affect the stable operation and power supply quality of the power system. Therefore, accurately predicting the remaining life of cables and repairing and replacing them is of great significance to ensuring the safe and stable operation of the power system.
[0004] With the development of machine learning technology, the existing remaining life prediction methods of cables are mostly to process historical operation data through machine learning algorithms to predict the remaining life of cables. Although the calculation efficiency is high, it still has the following shortcomings:
[0005] (1) Only the useful information reflected in the historical operation data is considered, and the impact of the cable operation development trend on the prediction of the remaining life of the cable is not considered, which affects the accuracy of the prediction and makes the prediction results less practical for maintenance scheduling in the future time period.
[0006] (2) Different cable operating loads will have different effects on the cable service life. It can be imagined that the service life of a cable that is overloaded for a long time will inevitably be shortened. However, the current remaining life prediction method ignores the impact of this factor and is divorced from the actual operating status of the cable. Summary of the invention
[0007] In order to address the deficiencies in the prior art, the present invention provides a method, system, electronic device, computer-readable storage medium and computer program product for predicting the remaining life of a cable taking into account the aging trend, which predicts the remaining life of the cable taking into account the actual operating conditions and future development trends of the cable to be predicted, thereby improving the accuracy and practicability of the prediction.
[0008] In a first aspect, the present invention provides a method for predicting the remaining life of a cable taking into account the aging trend;
[0009] A method for predicting the remaining life of a cable considering aging trends, comprising:
[0010] Obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted in the next time period;
[0011] According to the predicted operating temperature, combined with the aging trend of the cable to be predicted, determine the effective service life of the cable to be predicted at the predicted operating temperature; obtain the operating time of the cable to be predicted, and according to the historical load data and operating time of the cable to be predicted, consider the service life loss of the cable to be predicted, and determine the actual operating time of the cable to be predicted;
[0012] Combining the actual operating time and effective service life of the cable to be predicted, the predicted remaining service life of the cable to be predicted is obtained;
[0013] Among them, the effective service life of the cable to be predicted at the predicted operating temperature is determined based on the predicted operating temperature and the aging trend of the cable to be predicted. Specifically, the aging characteristic quantity at the predicted operating temperature is calculated using the Arrhenius equation, and the effective service life of the cable to be predicted at the predicted operating temperature is determined using the aging characteristic quantity.
[0014] In some implementations, before the historical load data is processed by the trained temperature prediction model, the method further includes:
[0015] A white noise sequence that satisfies the normal distribution is repeatedly added to the historical load data and multiple EEMD decompositions are performed.
[0016] In some embodiments, the effective service life is expressed as:
[0017] ;
[0018] in, For effective service life, , , are the empirical parameters, To predict the operating temperature, is the aging characteristic, expressed as follows:
[0019] ;
[0020] In the formula, is the frequency factor, is an empirical constant, For the running time.
[0021] In some implementations, determining the actual operation time of the cable to be predicted based on historical load data and operation time of the cable to be predicted and taking into account the service life loss of the cable to be predicted specifically includes:
[0022] Based on historical load data, calculate the average load and maximum allowable load and generate load impact factors;
[0023] Determine the service life loss of the cable to be predicted based on historical load data and combined with temperature variation characteristics;
[0024] Based on load influence factors, service life loss and operating time, the actual operating time is determined.
[0025] In some embodiments, the temperature prediction model is an LSTM network.
[0026] In some embodiments, a callback function is introduced when training the temperature prediction model.
[0027] In a second aspect, the present invention provides a cable remaining life prediction system taking into account aging trends;
[0028] A cable remaining life prediction system considering aging trend, comprising:
[0029] The operating temperature prediction module is configured to: obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted at the next moment;
[0030] The actual operation time acquisition module is configured to: determine the effective service life of the cable to be predicted at the predicted operation temperature according to the predicted operation temperature and the aging trend of the cable to be predicted; obtain the operation time of the cable to be predicted, and determine the actual operation time of the cable to be predicted according to the historical load data and operation time of the cable to be predicted and considering the service life loss of the cable to be predicted;
[0031] The remaining life prediction module is configured to: obtain the predicted remaining life of the cable to be predicted in combination with the actual operating time and effective service life of the cable to be predicted; wherein, according to the predicted operating temperature and in combination with the aging trend of the cable to be predicted, the equivalent aging time of the cable to be predicted at the predicted operating temperature is determined specifically as follows: the aging characteristic quantity at the predicted operating temperature is calculated using the Arrhenius equation, and the effective service life of the cable to be predicted at the predicted operating temperature is determined using the aging characteristic quantity.
[0032] In a third aspect, the present invention provides an electronic device;
[0033] An electronic device comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned method for predicting the remaining life of a cable taking into account the aging trend.
[0034] In a fourth aspect, the present invention provides a computer-readable storage medium;
[0035] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for predicting the remaining life of a cable taking into account the aging trend.
[0036] In a fifth aspect, the present invention provides a computer program product;
[0037] A computer program product comprises a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for predicting the remaining life of a cable taking into account the aging trend.
[0038] Compared with the prior art, the present invention has the following beneficial effects:
[0039] 1. The technical solution provided by the present invention predicts the operating temperature of the cable to be predicted in the next time period in combination with the operating conditions of the cable to be predicted. The predicted operating temperature can intuitively reflect the operating development trend of the cable to be predicted, so that the calculated effective service life takes into account the future development of the cable to be predicted and the influence of the operating temperature on the cable life, thereby realizing the advance prediction of the remaining service life of the cable and improving the accuracy of the prediction.
[0040] 2. The technical solution provided by the present invention comprehensively considers the actual load conditions of the cable to be predicted and the impact of the corresponding temperature changes on the service life of the cable, corrects the operating time, and improves the accuracy of the prediction of the remaining service life of the cable. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.
[0042] Figure 1 A schematic flow chart of a method for predicting the remaining life of a cable taking into account the aging trend provided by an embodiment of the present invention;
[0043] Figure 2 A schematic diagram of the system architecture of a cable remaining life prediction system taking into account aging trends provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0044] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.
[0045] It should be noted that the terms used herein are only for describing specific embodiments, and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "include" and "have" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.
[0046] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.
[0047] Embodiment 1
[0048] In the existing cable remaining life prediction, the impact of the cable operation development trend and the actual effective operation degree of the cable on the cable remaining life prediction is ignored, which affects the accuracy and timeliness of the cable remaining life prediction; therefore, this embodiment provides a cable remaining life prediction method taking into account the aging trend, which reflects the cable operation development trend by predicting the operating temperature, and at the same time corrects the cable's usage time in combination with historical load data and service life loss, thereby improving the prediction accuracy.
[0049] Next, combine Figure 1 , a cable remaining life prediction method considering the aging trend disclosed in this embodiment is described in detail, and the cable remaining life prediction method considering the aging trend includes the following steps:
[0050] S1. Obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted in the next time period.
[0051] The operating temperature reflects the thermal equilibrium state inside the cable when the cable is transmitting current. It is an intuitive reflection of the cable's operating state. It can also intuitively reflect the cable's aging rate, which has a great impact on the prediction of the cable's remaining life. At different operating temperatures, the effective service life of the cable is different. Therefore, in this embodiment, the operating temperature of the cable to be predicted in the next time period is predicted based on the historical load data of the cable to be predicted, and then the predicted operating temperature reflecting the operating development trend of the cable to be predicted is obtained, which provides a basis for the subsequent calculation of the effective service life.
[0052] In this embodiment, the temperature prediction model is an LSTM network, the input is historical load data, and the output is the predicted operating temperature of the cable to be predicted in the next time period. By inputting the historical load data into the trained LSTM network, the predicted operating temperature of the cable to be predicted in the next time period can be obtained.
[0053] When training the LSTM network, the historical load data of multiple cables and the corresponding operating temperatures are used to construct a training set for training the LSTM network. During the training process, a callback function is introduced to adjust the parameters of the LSTM network to prevent overfitting and save the optimal network parameters.
[0054] In this embodiment, the Adam optimizer and the MSE loss function are used to train the LSTM network. During the training process, callback functions are used including but not limited to EarlyStopping and ModelCheckpoint.
[0055] The historical load data described in this embodiment includes load value, resistance value, voltage value, operating temperature and ambient temperature, etc. The historical load data is collected by an on-site data collection system. Noise is inevitably generated during the collection process. Therefore, before the historical load data is input into the trained temperature prediction model, as an implementation method, it also includes: repeatedly adding a white noise sequence that satisfies the normal distribution to the historical load data and performing multiple EEMD decompositions; expressing the historical load data as a historical load time series. The specific process is as follows:
[0056] (1) In the historical load time series Repeatedly add a white noise sequence that satisfies the normal distribution , expressed as:
[0057] ;
[0058] In the formula, To join The historical load time series after the white noise sequence, To join The historical load time series after the white noise sequence, For the The white noise sequence is added.
[0059] (2) Adding white noise to the historical load time series Perform EMD decomposition to obtain IMF components and remainders. The decomposition process is as follows:
[0060] ;
[0061] In the formula, To join The first white noise sequence is obtained by EMD decomposition of the historical load time series. IMF components, is the remainder, J is the total number of IMF components.
[0062] (3) Considering the characteristic that the mean of uncorrelated random sequences is zero, the average value of each IMF component corresponding to each addition of white noise sequence is used to offset the influence of repeated white noise on the IMF component, that is, EEMD decomposition is performed. The average value of each IMF component is expressed as:
[0063] ;
[0064] In the formula, is obtained after EEMD decomposition IMF components, is the number of white noise sequences.
[0065] (4) After multiple EEMD decompositions, the final transformation result of the historical load time series is obtained, thereby offsetting the influence of noise. The final transformation result of the historical load time series is expressed as follows:
[0066] ;
[0067] In the formula, is the total remainder after multiple decompositions.
[0068] S2. According to the predicted operating temperature and the aging trend of the cable to be predicted, determine the effective service life of the cable to be predicted at the predicted operating temperature. Specifically, it includes:
[0069] S201. Calculate the aging characteristic quantity at the predicted operating temperature using the Arrhenius equation. The aging characteristic quantity is expressed as follows:
[0070] ;
[0071] In the formula, is the frequency factor, is an empirical constant, To predict the operating temperature, For the running time.
[0072] In this embodiment, the aging characteristic quantity is the elongation at break of the cable, which can reflect the aging rate of the cable. The frequency factor and the empirical constant are set according to the experience of the operation and maintenance personnel in actual applications.
[0073] S202, using the aging characteristic quantity to determine the effective service life of the cable to be predicted at the predicted operating temperature, the effective service life is expressed as follows:
[0074] ;
[0075] In the formula, For effective service life, , , They are empirical parameters, which are set according to the experience of operation and maintenance personnel in actual applications.
[0076] S3. Obtain the operation time of the cable to be predicted, and determine the actual operation time of the cable to be predicted based on the historical load data and operation time of the cable to be predicted and taking into account the service life loss of the cable to be predicted.
[0077] It is understandable that if the cable is in an overload state for most of the time, it will cause damage to the cable and shorten its service life. If the cable is not overused, its service life will be extended. Therefore, the operating time (operating time) of the cable to be predicted cannot effectively reflect its usage status. Therefore, in this embodiment, the usage time of the cable to be predicted is corrected in combination with the historical load data of the cable to be predicted.
[0078] As an implementation method, S3 includes:
[0079] S301. According to the load data, the average load and the maximum allowable load of the cable to be predicted are calculated and a load influence factor is generated. The load influence factor is expressed as:
[0080] ;
[0081] In the formula, is the load influence factor, is the average load, is the maximum allowable load.
[0082] S302. Calculate the difference between the maximum operating temperature and the minimum operating temperature based on the operating temperature data, and determine the service life loss of the cable to be predicted in combination with the actual operating time; the service life loss is expressed as:
[0083] ;
[0084] In the formula, For the loss of service life, is the maximum operating temperature, is the maximum operating temperature.
[0085] In this embodiment, the service life loss of the cable caused by the temperature rise characteristics of the cable is taken into account, so as to further improve the reliability of the prediction of the remaining service life of the cable.
[0086] S303. Determine the actual operating time based on the load impact factor, service life loss and operating time; the actual operating time is expressed as:
[0087] ;
[0088] In the formula, is the actual running time, For the running time.
[0089] S4. Combining the actual operation time and effective service life of the cable to be predicted, the predicted remaining service life of the cable to be predicted is obtained; the predicted remaining service life is expressed as:
[0090] ;
[0091] In the formula, To predict the remaining life, For corner mark.
[0092] Embodiment 2
[0093] This embodiment discloses a cable remaining life prediction system considering aging trend, including:
[0094] The operating temperature prediction module is configured to: obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted at the next moment;
[0095] The actual operation time acquisition module is configured to: determine the effective service life of the cable to be predicted at the predicted operation temperature according to the predicted operation temperature and the aging trend of the cable to be predicted; obtain the operation time of the cable to be predicted, and determine the actual operation time of the cable to be predicted according to the historical load data and operation time of the cable to be predicted and considering the service life loss of the cable to be predicted;
[0096] The remaining life prediction module is configured to: obtain the predicted remaining life of the cable to be predicted in combination with the actual operating time and effective service life of the cable to be predicted; wherein, according to the predicted operating temperature and in combination with the aging trend of the cable to be predicted, the equivalent aging time of the cable to be predicted at the predicted operating temperature is determined specifically as follows: the aging characteristic quantity at the predicted operating temperature is calculated using the Arrhenius equation, and the effective service life of the cable to be predicted at the predicted operating temperature is determined using the aging characteristic quantity.
[0097] It should be noted that the operating temperature prediction module, the actual operating time acquisition module and the remaining life prediction module correspond to the steps in Embodiment 1, and the examples and application scenarios implemented by the modules and the corresponding steps are the same, but are not limited to the contents disclosed in Embodiment 1. It should be noted that the modules as part of the system can be executed in a computer system such as a set of computer executable instructions.
[0098] Embodiment 3
[0099] Embodiment 3 of the present invention provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of the above-mentioned method for predicting the remaining life of a cable taking into account the aging trend are completed.
[0100] Embodiment 4
[0101] Embodiment 4 of the present invention provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned cable remaining life prediction method considering the aging trend are completed.
[0102] Embodiment 5
[0103] Embodiment 5 of the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for predicting the remaining life of a cable considering the aging trend.
[0104] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0105] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.
[0106] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.
[0107] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.
[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A cable remaining life prediction method considering aging trend, characterized in that: include: Obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted in the next time period; According to the predicted operating temperature, combined with the aging trend of the cable to be predicted, determine the effective service life of the cable to be predicted at the predicted operating temperature; obtain the operating time of the cable to be predicted, and according to the historical load data and operating time of the cable to be predicted, consider the service life loss of the cable to be predicted, and determine the actual operating time of the cable to be predicted; Combining the actual operating time and effective service life of the cable to be predicted, the predicted remaining service life of the cable to be predicted is obtained; The method of determining the effective service life of the cable to be predicted at the predicted operating temperature according to the predicted operating temperature and the aging trend of the cable to be predicted is as follows: using the Arrhenius equation to calculate the aging characteristic quantity at the predicted operating temperature, and using the aging characteristic quantity to determine the effective service life of the cable to be predicted at the predicted operating temperature; The effective service life is expressed as: ; in, For effective service life, , , are the empirical parameters, To predict the operating temperature, is the aging characteristic, expressed as follows: ; In the formula, is the frequency factor, is an empirical constant, is the running time; The determining of the actual operation time of the cable to be predicted based on the historical load data and operation time of the cable to be predicted and taking into account the service life loss of the cable to be predicted specifically includes: Based on historical load data, calculate the average load and maximum allowable load and generate load impact factors; based on historical load data and combined with temperature variation characteristics, determine the service life loss of the cable to be predicted; Determine the actual operating time based on load impact factors, service life loss and operating time; The load influence factor is expressed as: ; In the formula, is the load influence factor, is the average load, is the maximum allowable load; According to the operating temperature data, the difference between the maximum operating temperature and the minimum operating temperature is calculated, and the service life loss of the cable to be predicted is determined in combination with the actual operating time; the service life loss is expressed as: ; In the formula, For the loss of service life, is the maximum operating temperature, is the maximum operating temperature; The actual running time is expressed as: ; In the formula, is the actual running time, For the running time.
2. The cable remaining life prediction method considering aging trend according to claim 1, characterized in that: Before the historical load data is processed by the trained temperature prediction model, it also includes: A white noise sequence that satisfies the normal distribution is repeatedly added to the historical load data and multiple EEMD decompositions are performed.
3. The cable remaining life prediction method considering aging trend according to claim 1, characterized in that: The temperature prediction model is an LSTM network.
4. The cable remaining life prediction method considering aging trend according to claim 1, characterized in that: When training the temperature prediction model, a callback function is introduced.
5. Cable remaining life prediction system considering aging trend, characterized by: include: The operating temperature prediction module is configured to: obtain historical load data of the cable to be predicted, process the historical load data through the trained temperature prediction model, and determine the predicted operating temperature of the cable to be predicted at the next moment; The actual operation time acquisition module is configured to: determine the effective service life of the cable to be predicted at the predicted operation temperature according to the predicted operation temperature and the aging trend of the cable to be predicted; obtain the operation time of the cable to be predicted, and determine the actual operation time of the cable to be predicted according to the historical load data and operation time of the cable to be predicted and considering the service life loss of the cable to be predicted; The remaining life prediction module is configured to: obtain the predicted remaining life of the cable to be predicted in combination with the actual operating time and the effective service life of the cable to be predicted; wherein, the equivalent aging time of the cable to be predicted at the predicted operating temperature is determined based on the predicted operating temperature and the aging trend of the cable to be predicted, specifically: calculate the aging characteristic quantity at the predicted operating temperature by using the Arrhenius equation, and determine the effective service life of the cable to be predicted at the predicted operating temperature by using the aging characteristic quantity; The effective service life is expressed as: ; in, For effective service life, , , are the empirical parameters, To predict the operating temperature, is the aging characteristic, expressed as follows: ; In the formula, is the frequency factor, is an empirical constant, is the running time; The determining of the actual operation time of the cable to be predicted based on the historical load data and operation time of the cable to be predicted and taking into account the service life loss of the cable to be predicted specifically includes: Based on historical load data, calculate the average load and maximum allowable load and generate load impact factors; based on historical load data and combined with temperature variation characteristics, determine the service life loss of the cable to be predicted; Determine the actual operating time based on load impact factors, service life loss and operating time; The load influence factor is expressed as: ; In the formula, is the load influence factor, is the average load, is the maximum allowable load; According to the operating temperature data, the difference between the maximum operating temperature and the minimum operating temperature is calculated, and the service life loss of the cable to be predicted is determined in combination with the actual operating time; the service life loss is expressed as: ; In the formula, For the loss of service life, is the maximum operating temperature, is the maximum operating temperature; The actual running time is expressed as: ; In the formula, is the actual running time, For the running time.
6. An electronic device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method for predicting the remaining service life of a cable considering the aging trend as described in any one of claims 1 to 4.
7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method for predicting the remaining life of a cable taking into account the aging trend as described in any one of claims 1 to 4 are implemented.
8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for predicting the remaining life of a cable taking into account the aging trend as described in any one of claims 1 to 4 are implemented.
Citation Information
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