Insulation resistance estimation device and control device
By generating a learning model and utilizing the insulation resistance and status time series data of the servo motor, the problem of insufficient diagnostic accuracy for servo motor insulation degradation is resolved, achieving high-precision insulation resistance estimation.
Patent Information
- Application Number
- CN202010946714.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2019-09-10
- Filing Date
- 2020-09-10
- Publication Date
- 2025-09-30
- Estimated Expiration
- 2040-09-10
AI Technical Summary
The conventional technology has insufficient accuracy in diagnosing insulation degradation in servo motors, making it difficult to estimate insulation resistance with high precision.
By generating a learning model and using multiple training data including the insulation resistance and state time series data of the servo motor, supervised learning is performed to generate a learning model that can estimate the insulation resistance with high accuracy.
This achieves high-precision estimation of the servo motor's insulation resistance, improving the estimation accuracy of the insulation resistance.
Smart Images

Figure CN112561072B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a machine learning device, a method for generating a learning model, an insulation resistance estimating device, and a control device. Background Art
[0002] Conventionally, there is a device that performs insulation degradation diagnosis of a motor (for example, Japanese Patent Application Laid-Open No. 2009-060767). Summary of the Invention
[0003] However, there is still room for improvement in the accuracy of conventional motor insulation degradation diagnosis.
[0004] The present invention is completed to solve the above-mentioned problems, and its purpose is to provide a machine learning device that generates a learning model that can improve the estimation accuracy of the insulation resistance of a servo motor, a method for generating a learning model, and an insulation resistance estimation device and control device that can improve the estimation accuracy of the insulation resistance of a servo motor.
[0005] A first embodiment of the present invention is a method for generating a learning model for estimating the insulation resistance of a servo motor to ground. The method comprises obtaining a plurality of training data, the training data including the insulation resistance of the servo motor at the beginning of a specified period, timing data indicating the state of the servo motor during the specified period, and the insulation resistance of the servo motor at the end of the specified period. Supervised learning is performed using the training data to generate a learning model that outputs the insulation resistance of the servo motor at the end of another specified period based on the insulation resistance of the servo motor at the beginning of another specified period different from the specified period and the timing data indicating the state of the servo motor during the another specified period.
[0006] A second aspect of the present invention is a machine learning device that generates a learning model for estimating the insulation resistance between a servo motor and ground, and includes a processing device that executes the learning model generation method of the first aspect.
[0007] A third aspect of the present invention is an insulation resistance estimating device for estimating the insulation resistance of a servo motor to ground, comprising: a storage unit storing a learning model generated by acquiring a plurality of training data and performing supervised learning using the training data, the training data including the insulation resistance of the servo motor at the beginning of a predetermined period, time-series data indicating a state of the servo motor during the predetermined period, and the insulation resistance of the servo motor at the end of the predetermined period; an acquisition unit acquiring the insulation resistance of the servo motor at the beginning of another predetermined period different from the predetermined period; an estimating unit estimating the time-series data indicating the state of the servo motor during the another predetermined period; and a processing unit using the learning model stored in the storage unit to output the insulation resistance of the servo motor at the end of the another predetermined period, corresponding to the acquired insulation resistance of the servo motor at the beginning of the another predetermined period and the acquired time-series data indicating the state of the servo motor during the another predetermined period.
[0008] A fourth aspect of the present invention is a control device for controlling industrial machinery, including the above-mentioned insulation resistance estimating device.
[0009] According to the present invention, it is possible to improve the estimation accuracy of the insulation resistance of a servo motor.
[0010] The above-mentioned objects, features and advantages will be easily understood from the following description of the embodiments with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Figure 1 This is a block diagram showing a machine tool, a machine learning device, and an insulation resistance estimation device.
[0012] Figure 2 This is a block diagram showing the configuration of a machine learning device.
[0013] Figure 3 This is a flowchart showing the flow of processing performed in the machine learning device.
[0014] Figures 4A to 4E This is a graph showing data related to the state of the servo motor acquired as training data by the training data acquisition unit.
[0015] Figure 5 This is a block diagram showing the configuration of an insulation resistance estimating device.
[0016] Figure 6 This is a flowchart showing the flow of processing performed in the insulation resistance estimating device.
[0017] Figure 7AThis is a graph showing data related to the state of the servo motor currently acquired by the data acquisition unit. Figures 7B to 7E This is a graph showing data related to the state of the servo motor estimated by the time series data estimation unit.
[0018] Figure 8 This is a block diagram showing a machine tool and a machine learning device.
[0019] Figure 9 This is a block diagram of a remaining life notification device.
[0020] Figure 10 This is a flowchart showing the flow of processing performed in the remaining life notification device.
[0021] Figure 11 It is a graph used to illustrate the remaining life. DETAILED DESCRIPTION
[0022] [First embodiment]
[0023] Figure 1 It is a block diagram showing the machine tool 10 , the machine learning device 12 , and the insulation resistance estimating device 14 .
[0024] The machine tool 10 includes a numerical control unit (hereinafter referred to as CNC) 16 and a processing machine body 20. The CNC 16 controls the processing machine body 20 according to a processing program. The processing machine body 20 includes a servo motor 22 as a feed axis motor, and the servo motor 22 is controlled by the CNC 16 according to the processing program.
[0025] The machine learning device 12 generates a learning model used by the insulation resistance estimating device 14 to estimate the insulation resistance of the servo motor 22. The machine learning device 12 inputs data related to the state of the servo motor 22 as training data, performs supervised learning based on the input training data, and generates a learning model.
[0026] The insulation resistance estimating device 14 estimates the future insulation resistance of the servo motor 22 to the ground using the learning model generated by machine learning in the machine learning device 12 and state data related to the state of the servo motor 22 .
[0027] In this embodiment, a machine learning device 12 is described that generates a learning model for estimating the insulation resistance of a servo motor 22 of a machine tool 10, and an insulation resistance estimation device 14 that uses the generated learning model to estimate the insulation resistance of the servo motor 22 of the machine tool 10. However, the servo motor 22 is not limited to being used in the machine tool 10 and may also be used in other industrial machines such as electrical discharge machines, injection molding machines, and robots.
[0028] [Machine Learning Device]
[0029] Figure 2 1 is a block diagram showing the configuration of the machine learning device 12. The machine learning device 12 includes a training data acquisition unit 24 and a learning model generation unit 26. The training data acquisition unit 24 includes an initial data acquisition unit 28, a time series data acquisition unit 30, and a label acquisition unit 32.
[0030] The machine learning device 12 is a computer equipped with a processing device (processor) such as a CPU or GPU, a main storage device, memory, and wired or wireless communication means. The initial data acquisition unit 28, time series data acquisition unit 30, label acquisition unit 32, and learning model generation unit 26 of the training data acquisition unit 24 are implemented by having the processing device execute a predetermined program.
[0031] Figure 3 1 is a flowchart showing the flow of processing performed by the machine learning device 12. The processing performed by the machine learning device 12 will be described below based on an example of generating a learning model using data related to the state of the servo motor 22 during the period ΔTa from time ta to time tb as training data.
[0032] Figures 4A to 4E Graph 24 is a graph showing data related to the state of the servo motor 22 acquired as training data by the training data acquisition unit 24 . Figure 4A Graphs showing the insulation resistance of the servo motor 22 at the beginning (time ta) and the end (time tb) of the period ΔTa. Figure 4B ΔTa is a graph showing time series data of the current supplied to the servo motor 22 during the period ΔTa. Figure 4C ΔTa is a graph showing time series data of the temperature of the servo motor 22 during the period ΔTa. Figure 4D 3 is a graph showing time series data of the humidity around the servo motor 22 during the period ΔTa. Figure 4E 3 is a graph showing time series data of the state (pH) of the cutting fluid used in the processing machine body 20 during the period ΔTa.
[0033] In step S1, the initial data acquisition unit 28 acquires the insulation resistance of the servo motor 22 at the beginning of the period ΔTa (time ta), and the process proceeds to step S2. The insulation resistance of the servo motor 22 refers to the absolute resistance to ground measured when the processing machine body 20 is in an emergency stop, that is, when power is not supplied to the servo amplifier (not shown).
[0034] In step S2 , the time series data acquisition unit 30 acquires time series data of the current supplied to the servo motor 22 during the period ΔTa, and the process proceeds to step S3 .
[0035] In step S3, the time-series data acquisition unit 30 acquires time-series data on the temperature of the servo motor 22 during the period ΔTa, and the process then proceeds to step S4. The location where the temperature of the servo motor 22 is acquired is not particularly limited, as long as it is the temperature inside the housing of the servo motor 22. However, it is preferable to acquire the temperature at a location where the temperature changes depending on the load on the servo motor 22.
[0036] In step S4, the time-series data acquisition unit 30 acquires time-series data of the humidity around the servo motor 22 during the period ΔTa, and the process then proceeds to step S5. The humidity around the servo motor 22 is not particularly limited to the location where the humidity is acquired, as long as it is the humidity outside the housing of the servo motor 22. However, it is preferably acquired as close to the servo motor 22 as possible.
[0037] In step S5 , the time series data acquisition unit 30 acquires time series data on the state (pH) of the cutting fluid used in the processing machine body 20 during the period ΔTa, and the process proceeds to step S6 .
[0038] In step S6 , the tag acquisition unit 32 acquires the insulation resistance of the servo motor 22 at the end of the period ΔTa (time tb), and the process proceeds to step S7 .
[0039] In step S7, the learning model generation unit 26 uses an existing machine learning algorithm to generate a learning model based on the training data acquired by the training data acquisition unit 24. There is no particular limitation on the machine learning algorithm as long as it can adopt a regression method.
[0040] In step S8, the learning model generation unit 26 determines whether machine learning has ended. If machine learning has ended, processing in the machine learning device 12 ends. If machine learning has not ended, the process returns to step S1. Machine learning is determined to have ended when conditions such as machine learning having been repeated a predetermined number of times are met.
[0041] The training data acquisition unit 24 acquires a large amount of training data from the machine tool 10. The training data acquisition unit 24 can acquire the training data immediately from the machine tool 10 or acquire pre-prepared training data. Furthermore, the training data acquisition unit 24 can acquire the training data from a single machine tool 10 or from multiple machine tools 10 via a network.
[0042] The training data acquisition unit 24 acquires time-series data related to the state of the servo motor 22 during a certain period as training data. However, this time-series data is not limited to the data described above. Alternatively, the training data may include the current supplied to the servo motor 22, the temperature of the servo motor 22, the humidity around the servo motor 22, and the pH of the cutting fluid used in the processing machine body 20. Alternatively, the water content of the cutting fluid may be used as the state of the cutting fluid used in the processing machine body 20, in place of or in addition to the pH of the cutting fluid.
[0043] The learning model generation unit 26 may generate a learning model for each machining program executed by the CNC 16. Alternatively, the learning model generation unit 26 may generate a universal learning model regardless of the machining program. Furthermore, the learning model generation unit 26 may generate a learning model using the period from the start of machining a single product to its completion as a unit period, or the period from the start of machining a predetermined number of products to their completion as a unit period. Furthermore, the learning model generation unit 26 may generate a learning model using a predetermined length of time (e.g., one month) as a unit period.
[0044] [Insulation resistance estimation device]
[0045] The insulation resistance estimating device 14 estimates the insulation resistance of the servo motor 22 in the future after a predetermined period has passed from the present time, using the current insulation resistance of the servo motor 22 and time series data on the past state of the servo motor 22 .
[0046] Figure 5 1 is a block diagram showing the configuration of the insulation resistance estimation device 14 . The insulation resistance estimation device 14 includes a current data acquisition unit 34 , a time series data estimation unit 36 , a storage unit 38 , and a processing unit 40 .
[0047] The insulation resistance estimation device 14 is a computer equipped with a processing unit (processor) such as a CPU or GPU, a main storage device, memory, and wired or wireless communication means. The current data acquisition unit 34, the time series data estimation unit 36, and the processing unit 40 are implemented by having the processing unit execute a predetermined program. The storage unit 38 can be either internal to the insulation resistance estimation device 14 or located in the cloud, as long as it is a non-transitory, tangible, computer-readable storage medium.
[0048] Figure 6 This is a flowchart showing the flow of processing performed by the insulation resistance estimating device 14. The processing performed by the insulation resistance estimating device 14 will be described below using an example in which the insulation resistance estimating device 14 estimates the insulation resistance of the servo motor 22 at time tf after a predetermined period ΔTc has elapsed from the current time (time te).
[0049] Figure 7A Graph 34 is a graph showing data related to the state of the servo motor 22 acquired by the current data acquisition unit 34 . Figures 7B to 7E This is a graph showing data related to the state of the servo motor 22 estimated by the time series data estimation unit 36 . Figure 7A : is a graph showing the insulation resistance of the servo motor 22 at the current time te. Figure 7B Graph 1 is a graph showing time series data of the current supplied to the servo motor 22 during the past period ΔTb (time tc to time td) and time series data of the period ΔTc estimated from the time series data of the period ΔTb. Figure 7C 1 is a graph showing time series data of the temperature of the servo motor 22 in the past period ΔTb and time series data of the period ΔTc estimated from the time series data of the period ΔTb. Figure 7D 1 is a graph showing time series data of the ambient humidity of the servo motor 22 in the past period ΔTb and time series data of the period ΔTc estimated from the time series data of the period ΔTb. Figure 7E It is a graph showing time series data of the state (pH) of the cutting fluid used in the processing machine body 20 during the past period ΔTb and time series data of the period ΔTc estimated from the time series data of the period ΔTb.
[0050] In step S11 , the current data acquisition unit 34 acquires the current insulation resistance of the servo motor 22 , and the process proceeds to step S12 .
[0051] In step S12 , the time series data estimation unit 36 estimates the time series data of the current supplied to the servo motor 22 in the period ΔTc based on the time series data of the current supplied to the servo motor 22 in the past period ΔTb, and the process proceeds to step S13 .
[0052] In step S13 , the time series data estimating unit 36 estimates the time series data of the temperature of the servo motor 22 in the period ΔTc based on the time series data of the temperature of the servo motor 22 in the past period ΔTb, and the process proceeds to step S14 .
[0053] In step S14 , the time series data estimating unit 36 estimates the time series data of the humidity around the servo motor 22 in the period ΔTc based on the time series data of the humidity around the servo motor 22 in the past period ΔTb, and the process proceeds to step S15 .
[0054] In step S15, the timing data estimation unit 36 estimates the timing data of the state (pH) of the cutting fluid used in the processing machine body 20 during the period ΔTc based on the timing data of the state (pH) of the cutting fluid used in the processing machine body 20 during the past period ΔTb, and transfers to step S16.
[0055] In step S16 , the processing unit 40 estimates the insulation resistance of the servo motor 22 at time tf after a predetermined period ΔTc has elapsed from the current time (time te) using the acquired data and the stored learning model, and terminates the processing in the insulation resistance estimating device 14 .
[0056] For each piece of timing data estimated by the timing data estimation unit 36, each piece of timing data obtained when the CNC 16 executed the machining program to control the processing machine body 20 during the past period ΔTb may be used as each piece of timing data obtained when the CNC 16 executes the same machining program to control the processing machine body 20 during the future period ΔTc. Furthermore, when a machining program that was not executed by the CNC 16 in the past is executed by the CNC 16 during the future period ΔTc, each piece of timing data may be newly acquired by executing the machining program that was not executed by the CNC 16 in the past.
[0057] [Effects]
[0058] The machine learning device 12 of this embodiment generates a learning model using the insulation resistance of the servo motor 22 at the beginning and end of a predetermined period, as well as time-series data related to the state of the servo motor 22 during the predetermined period, as training data. This allows the machine learning device 12 to generate a learning model that can accurately estimate the insulation resistance of the servo motor 22.
[0059] Furthermore, the insulation resistance estimating device 14 of this embodiment estimates the insulation resistance of the servo motor 22 using a learning model generated using the insulation resistance of the servo motor 22 at the beginning and end of a predetermined period, as well as time-series data related to the state of the servo motor 22 during the predetermined period, as training data. This allows the insulation resistance estimating device 14 to estimate the insulation resistance of the servo motor 22 with high accuracy.
[0060] [Second embodiment]
[0061] Figure 8 1 is a block diagram showing a machine tool 10 and a machine learning device 12. The second embodiment differs from the first embodiment in that a CNC 16 of the machine tool 10 includes an insulation resistance estimating device 14. The remaining configuration is the same as that of the first embodiment.
[0062] [Effects]
[0063] The CNC 16 of this embodiment includes the insulation resistance estimating device 14. This allows the CNC 16 to estimate the insulation resistance of the servo motor 22 with high accuracy.
[0064] [Third embodiment]
[0065] Figure 9 This is a block diagram of the remaining life notification device 42. The remaining life notification device 42 includes the insulation resistance estimation device 14, calculates the remaining life of the servo motor 22 based on the insulation resistance of the servo motor 22 estimated by the insulation resistance estimation device 14, and notifies the calculated remaining life.
[0066] In addition to the insulation resistance estimating device 14, the remaining lifetime notification device 42 includes a remaining lifetime calculator 44 and a notification unit 46. The remaining lifetime calculator 44 calculates the remaining lifetime of the servo motor 22 based on the insulation resistance of the servo motor 22 estimated by the insulation resistance estimating device 14. The notification unit 46, such as a display device or audio output device, notifies the operator of the remaining lifetime using text, images, or audio. The configuration of the insulation resistance estimating device 14 is the same as that of the insulation resistance estimating device 14 of the first embodiment.
[0067] The remaining lifetime notification device 42 is a computer equipped with a processing unit (processor) such as a CPU or GPU, a main storage device, memory, and wired or wireless communication means. The current data acquisition unit 34, time series data estimation unit 36, processing unit 40, and remaining lifetime calculation unit 44 of the insulation resistance estimation device 14 are implemented by having the processing unit execute a prescribed program. The storage unit 38 can be either a memory within the insulation resistance estimation device 14 or located in the cloud; any non-transitory, tangible, computer-readable storage medium is sufficient.
[0068] Figure 10 1 is a flowchart showing the flow of processing performed in the remaining life notification device 42 .
[0069] In step S21 , the remaining life calculation unit 44 acquires the insulation resistance of the servo motor 22 estimated by the insulation resistance estimation device 14 , and the process proceeds to step S22 .
[0070] In step S22, the remaining life calculation unit 44 determines whether the obtained insulation resistance of the servo motor 22 is less than a predetermined value. If the insulation resistance of the servo motor 22 is less than the predetermined value, the process proceeds to step S23. If the insulation resistance of the servo motor 22 is greater than the predetermined value, the process proceeds to step S24.
[0071] If the insulation resistance of the servo motor 22 obtained is less than the specified value, in step S23, the remaining life calculation unit 44 transmits the insulation resistance of the servo motor 22 obtained in step S21 to the insulation resistance estimation device 14, and the process returns to step S21. The insulation resistance estimation device 14 uses the insulation resistance of the servo motor 22 transmitted from the remaining life calculation unit 44 to estimate the insulation resistance of the servo motor 22 in the future.
[0072] When the insulation resistance of the servo motor 22 is equal to or greater than the predetermined value, the remaining life calculation unit 44 calculates the remaining life in step S24 , and the process proceeds to step S25 .
[0073] In step S25 , the remaining life calculation unit 44 controls the notification unit 46 to notify the remaining life, and the processing performed by the remaining life notification device 42 ends.
[0074] Figure 11 This is a graph used to illustrate the remaining lifetime. The insulation resistance estimating device 14 estimates the insulation resistance (insulation resistance Rh) of the servo motor 22 in the future (at time th) based on the insulation resistance (insulation resistance Rg) of the servo motor 22 at the present time (at time tg). Next, the insulation resistance estimating device 14 estimates the insulation resistance (insulation resistance Ri) of the servo motor 22 at a further future time (at time ti) based on the estimated insulation resistance (insulation resistance Rh) of the servo motor 22 at time th. By repeatedly estimating the insulation resistance of the servo motor 22 at further future times based on the estimated insulation resistance of the servo motor 22, the insulation resistance estimating device 14 can estimate the insulation resistance of the servo motor 22 at a desired future time.
[0075] The remaining life calculation unit 44 calculates the time from the current time tg to the future time tj when the estimated insulation resistance Rj becomes smaller than a predetermined value as the remaining life.
[0076] [Effects]
[0077] The remaining life notification device 42 of this embodiment calculates the remaining life of the servo motor 22 based on the insulation resistance estimated by the insulation resistance estimation device 14. Thus, the remaining life notification device 42 can calculate the remaining life of the servo motor 22 with high accuracy.
[0078] [Technical Concepts that Can Be Obtained from the Implementation Methods]
[0079] The technical ideas that can be grasped from the above-mentioned embodiments are described below.
[0080] A method for generating a learning model for estimating the insulation resistance of a servo motor (22) to ground, comprising acquiring a plurality of training data, the training data including the insulation resistance of the servo motor at the beginning of a predetermined period, time series data indicating the state of the servo motor during the predetermined period, and the insulation resistance of the servo motor at the end of the predetermined period, performing supervised learning using the training data, and generating a learning model that outputs the insulation resistance of the servo motor at the end of another predetermined period based on the insulation resistance of the servo motor at the beginning of another predetermined period different from the predetermined period and the time series data indicating the state of the servo motor during the another predetermined period. Thus, a learning model capable of estimating the insulation resistance of the servo motor with high accuracy can be generated.
[0081] In the above-described method for generating a learning model, the time series data includes the current supplied to the servo motor. This allows generation of a learning model capable of estimating the insulation resistance of the servo motor with high accuracy.
[0082] In the above-described method for generating a learning model, the time series data includes the current supplied to the servo motor and the temperature of the servo motor. This allows generation of a learning model capable of estimating the insulation resistance of the servo motor with high accuracy.
[0083] In the above-described method for generating a learning model, the time series data includes the current supplied to the servo motor, the temperature of the servo motor, and the humidity around the servo motor. This allows generation of a learning model capable of accurately estimating the insulation resistance of the servo motor.
[0084] In the above learning model generation method, the time series data includes the current supplied to the servo motor, the temperature of the servo motor, the humidity around the servo motor, and a value indicating the state of the cutting fluid. This allows generation of a learning model capable of accurately estimating the insulation resistance of the servo motor.
[0085] A machine learning device (12) for generating a learning model for estimating the insulation resistance between a servo motor and ground includes a processing device that executes the above-described method for generating a learning model. The machine learning device can thereby generate a learning model capable of estimating the insulation resistance of a servo motor 22 with high accuracy.
[0086] An insulation resistance estimating device (14) for estimating the insulation resistance of a servo motor to ground comprises: a storage unit (38) storing a learning model generated by acquiring a plurality of training data and performing supervised learning using the training data, the training data including the insulation resistance of the servo motor at the beginning of a prescribed period, time series data indicating the state of the servo motor during the prescribed period, and the insulation resistance of the servo motor at the end of the prescribed period; an acquisition unit (34) acquiring the insulation resistance of the servo motor at the beginning of another prescribed period different from the prescribed period; an estimating unit (36) estimating the time series data indicating the state of the servo motor during the another prescribed period; and a processing unit (40) using the learning model stored in the storage unit to output the insulation resistance of the servo motor at the end of the another prescribed period corresponding to the acquired insulation resistance of the servo motor at the beginning of the another prescribed period and the acquired time series data indicating the state of the servo motor during the another prescribed period. Thus, the insulation resistance estimating device can estimate the insulation resistance of the servo motor with high accuracy.
[0087] A control device (16) for controlling industrial machinery includes the above-mentioned insulation resistance estimating device, whereby the control device can estimate the insulation resistance of a servo motor with high accuracy.
Claims
1. An insulation resistance estimating device for estimating the insulation resistance between a servo motor and ground, the insulation resistance estimating device comprising: a storage unit storing a learning model generated by acquiring a plurality of training data and performing supervised learning using the training data, the training data including the insulation resistance of the servo motor at the beginning of a predetermined period, time series data indicating a state of the servo motor during the predetermined period, and the insulation resistance of the servo motor at the end of the predetermined period; an acquisition unit that acquires the insulation resistance of the servo motor at the beginning of another predetermined period different from the predetermined period; an estimating unit configured to estimate time series data indicating a state of the servo motor in the other predetermined period based on the time series data indicating a state of the servo motor in the predetermined period; as well as a processing unit that uses the learning model stored in the storage unit to output the insulation resistance of the servo motor at the end of the other prescribed period, which corresponds to the insulation resistance of the servo motor at the beginning of the other prescribed period acquired by the acquisition unit and the time series data indicating the state of the servo motor in the other prescribed period estimated by the estimating unit.
2. A control device for controlling an industrial machine, wherein: A device for estimating insulation resistance according to claim 1 is provided.
Citation Information
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