A method for identifying characteristic quantities of a same-turn rotating arc sensing signal

By identifying the characteristic quantities α and β of the rotating arc sensor signal, the problem that the rotating arc sensor cannot identify arc stability is solved, realizing the quantitative evaluation and automatic control of arc stability, and improving the quality of robotic automatic welding.

CN115935159BActive Publication Date: 2025-11-18NANCHANG UNIV
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Patent Information

Application Number
CN202211413319.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-11
Publication Date
2025-11-18
Estimated Expiration
2042-11-11

AI Technical Summary

Technical Problem

Existing rotating arc sensors cannot identify arc stability, which affects the quality of weld formation.

Method used

By identifying the characteristic quantities of the magnitude and direction changes of adjacent sampled welding currents within the same rotating arc, the characteristic quantities of the rotating arc sensing signal, including characteristic quantities α and β, are calculated to reflect the stability state of the arc.

Benefits of technology

This enables quantitative evaluation of arc stability, laying the foundation for automatic control of arc stability and improving the quality of robotic automatic welding.

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Abstract

The application discloses a same-circle rotating electric arc sensing signal characteristic quantity identification method, which comprises a method for identifying the size change characteristic quantity of adjacent sampling welding currents in the same-circle rotating electric arc, a method for identifying the direction change times characteristic quantity of the sampling welding currents in the same-circle rotating electric arc, and a method for calculating the same-circle rotating electric arc sensing signal characteristic quantity capable of reflecting the stability state of the rotating electric arc. The size of the characteristic quantity can be used to further identify whether the electric arc is in an unstable state or an understable state, so that the same-circle rotating electric arc sensing signal characteristic quantity capable of reflecting the stability state of the rotating electric arc can be identified based on a mathematical model, the stability of the rotating electric arc can be quantitatively evaluated according to the characteristic quantities, a foundation is laid for automatic control of the stability of the electric arc, and the quality of automatic welding of a machine is improved.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of electronic information technology, in particular to a method for identifying a same-rotation-arc-sensor-signal feature quantity capable of reflecting a stability state of a rotating arc. BACKGROUND

[0002] At present, a rotating arc sensor is mainly used for weld pose recognition, but the arc stability is not recognized, and the arc stability in a welding process directly affects the weld forming quality. Therefore, a same-rotation-arc-sensor-signal feature quantity capable of reflecting a stability state of a rotating arc is needed to be proposed, and a method for identifying the feature quantity is needed to be invented. The method of the present application is helpful for realizing the arc stability recognition based on the rotating arc sensor, and can improve the quality of automatic welding of a rotating arc sensor robot. SUMMARY

[0003] In order to solve the problems in the prior art, the present application provides a method for identifying a same-rotation-arc-sensor-signal feature quantity capable of reflecting a stability state of a rotating arc. The smaller the identified feature quantity describing the size change of adjacent sampling welding currents in a same-rotation-arc is, the better the arc stability is. The greater the identified feature quantity of the direction change times of the sampling welding currents in the same-rotation-arc is, the greater the arc instability degree is, and the arc unstable or sub-stable state can be further identified by the size of the feature quantity. The identified feature quantity can be used for quantitatively evaluating the stability of the rotating arc, laying a foundation for the automatic control of the arc stability, and being beneficial to improving the quality of automatic welding of a robot.

[0004] To achieve the above purpose, the present application adopts the following technical solutions:

[0005] A method for identifying a same-rotation-arc-sensor-signal feature quantity capable of reflecting a stability state of a rotating arc, characterized in that: the method comprises a method for identifying a feature quantity describing the size change of adjacent sampling welding currents in a same-rotation-arc, a method for identifying a feature quantity of the direction change times of the sampling welding currents in the same-rotation-arc, and a method for calculating a same-rotation-arc-sensor-signal feature quantity capable of reflecting a stability state of a rotating arc.

[0006] Further, the method for identifying the feature quantity describing the size change of adjacent sampling welding currents in a same-rotation-arc is a rotating arc sensor signal feature quantity for characterizing the arc stability from the perspective of time correlation. The identification formula of the feature quantity a describing the size change of adjacent sampling welding currents in a same-rotation-arc is as follows,

[0007]

[0008] In the formula, α is a characteristic quantity describing the change in the magnitude of adjacent sampled welding currents within the same rotating arc, and λ1 is a normalization coefficient, adjusted according to experimental results; its value in the experiment was 0.5. ΔI i E[I(1),I(2),···,I(32)] represents the variation in the magnitude of adjacent sampled welding currents within the same rotating arc. E[I(1),I(2),···,I(32)] is the mathematical expectation of the range from the first filtered welding current I(1) to the 32nd filtered welding current I(32), which is the average value of the filtered welding currents corresponding to the first half-circle of the rotating arc. I(i+1) represents the (i+1)th filtered welding current, and I(i) represents the ith filtered welding current.

[0009] The identified characteristic quantity α describes the change in the magnitude of adjacent sampled welding currents within the same rotating arc, which is the relative value of the change in the magnitude of adjacent sampled welding currents within the same rotating arc. If the arc is stable, the change in the magnitude of adjacent sampled welding currents is small; if the arc is unstable, the change in the magnitude of adjacent sampled welding currents is large; if the arc is not stable, the change in the magnitude of adjacent sampled welding currents is between the two cases.

[0010] Furthermore, the method for identifying the characteristic quantity of the number of times the welding current direction changes within the same rotating arc is described. The identified characteristic quantity of the number of times the welding current direction changes is an important physical quantity for evaluating arc stability. By using three adjacent filtered welding currents, it is possible to identify whether the trend of the welding current change has changed, and this can be further analyzed using β. i The number of changes in the direction of the welding current is expressed by the following formula:

[0011]

[0012] In the formula, I(i+1) is the (i+1)th filtered welding current, I(i) is the ith filtered welding current, and I(i-1) is the (i-1)th filtered welding current. ΔI(i+1) is the change in welding current for the (i+1)th time, ΔI(i) is the change in welding current for the ith time, sgn(x) is the sign function, and β... i This indicates the number of times the welding current direction changes after three consecutive filters.

[0013] Furthermore, the number of times the sampling welding current direction changes within the same rotating arc can be determined. That is, the characteristic quantity β describing the number of times the sampling welding current direction changes within the same rotating arc satisfies the following formula.

[0014]

[0015] In the formula, β represents the number of times the direction of the sampling welding current changes within the same rotating arc. The meanings of other physical quantities have been introduced in formula (2).

[0016] Theoretically, when the arc is stable and the influence of the molten pool is ignored, the characteristic quantity β describing the number of times the welding current direction changes within the same rotating arc is 4 or 2. When the welding deviation is small, its value is 4; when the welding deviation is large, its value is 2. When the arc stability is poor, adjacent welding currents change significantly, and the number of current direction changes is high. Furthermore, the larger the characteristic quantity β, the greater the arc instability. The magnitude of this characteristic quantity can be used to further identify whether the arc is unstable or understable. Therefore, the characteristic quantity β describing the number of times the welding current direction changes within the same rotating arc is an important physical quantity for evaluating arc stability.

[0017] Furthermore, the method for calculating the characteristic quantities of the same-circle rotating arc sensing signal that reflect the stability state of the rotating arc can identify the characteristic quantities of the same-circle rotating arc sensing signal, and the stability of the rotating arc can be quantitatively evaluated based on these characteristic quantities. The method for calculating the characteristic quantities of the same-circle rotating arc sensing signal that reflect the stability state of the rotating arc is as follows:

[0018]

[0019] In the formula, P is the characteristic quantity of the sensing signal of the same rotating arc that reflects the stability state of the rotating arc, α is the characteristic quantity describing the change in the magnitude of the adjacent sampled welding current within the same rotating arc, β is the characteristic quantity describing the number of times the direction of the sampled welding current changes within the same rotating arc, and the meanings of other physical quantities and functions representing intermediate processes have been introduced in formula (1-3).

[0020] The beneficial effects of this invention are as follows:

[0021] The advantage of this invention lies in the invention of a method for identifying the characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc. By using the calculation method of the characteristic quantities of the same rotating arc sensing signal, the characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc can be identified, and the stability of the rotating arc can be quantitatively evaluated based on these characteristic quantities, laying the foundation for the automatic control of arc stability and helping to improve the quality of robotic automatic welding. Attached Figure Description

[0022] Figure 1 This is a schematic diagram showing the relationship between the stability state of the rotating electric arc and the sensing signal of the same rotating electric arc in this invention;

[0023] Figure 2 This is a distribution diagram of the same rotating arc sensing signal of the present invention;

[0024] Figure 3 This is a graph showing the characteristic changes in the magnitude of adjacent sampled welding currents within the same rotating arc identified by this invention.

[0025] Figure 4 This is a curve of the characteristic quantity of the number of times the welding current direction changes within the same rotating arc, as identified by this invention;

[0026] In the diagram: 1. Welding torch; 2. Arc length; 3. Horizontal steel plate; 4. Weld seam; 5. Vertical steel plate. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0028] Figure 1 This diagram illustrates the relationship between the stability state of a rotating arc and the sensing signal of the same rotating arc. The stability state of the rotating arc is determined by the welding current value. For each rotation of the arc, 256 welding currents are continuously collected by the data acquisition system and arranged into a vector I0 according to the acquisition sequence. Further, the data processing system filters these raw currents, transforming the 256 raw welding currents into 64 filtered welding currents. The filtered welding current waveforms are smoother, and the noise-removed welding currents represent the sensing signal of the same rotating arc. Furthermore, based on the needs of arc stability identification, some characteristic quantities of the rotating arc sensing signal are proposed. Through theoretical analysis and experimental verification, a relationship model can be established between the characteristic quantity P of the same rotating arc sensing signal and the detected welding current value I0. This transforms the collected raw welding currents into characteristic quantities of the same rotating arc sensing signal related to arc stability, allowing for the quantitative evaluation of arc stability.

[0029] To process the welding current, this invention proposes two physical quantities to characterize the features of the rotating arc sensing signal: a feature quantity α describing the magnitude change of adjacent sampled welding currents within the same rotating arc, and a feature quantity β describing the number of changes in the direction of sampled welding currents within the same rotating arc. To explain the identification process of these features in detail, it is necessary to combine... Figure 2 The distribution diagram of the same rotating electric arc sensing signal is shown below.

[0030] like Figure 2As shown, the intersection of the horizontal steel plate (3) and the vertical steel plate (5) is the weld (4) being welded. At this time, the radius of rotation of the rotating arc is r, and the angular velocity of rotation is w. When welding reaches the HF segment of the weld (4), the position corresponding to the rotating arc is E′F′G′H′, and the rotation center is point I′. For each revolution of the arc, a set of welding currents is continuously collected at equal time intervals, for a total of 256 currents. After filtering, the 256 welding currents are transformed into 64 filtered welding currents. When the contact tip at the end of the welding torch (1) is at point E″, the first welding current is collected when the arc rotates to point E′, corresponding to the first filtered welding current; when the arc rotates to point F′, the 65th welding current is collected, corresponding to the 17th filtered welding current; when the arc rotates to point G′, the 129th welding current is collected, corresponding to the 33rd filtered welding current; when the arc rotates to point H′, the 193rd welding current is collected, corresponding to the 49th filtered welding current.

[0031] The following will combine Figure 2 This paper details two methods for identifying characteristic quantities of rotating arc sensing signals that characterize the stability of rotating arcs.

[0032] (1) A method for identifying the characteristic quantity α of the magnitude change of adjacent sampled welding currents within the same rotating arc.

[0033] like Figure 2 As shown, when the rotating arc welding reaches the weld seam (4) in the HF segment, point E′ corresponds to the first filtered welding current, point F′ corresponds to the 17th filtered welding current, and point G′ corresponds to the 33rd filtered welding current. Furthermore, along the welding direction, curves E′F′G′ correspond to the first half of the rotating arc's rotation. The sampled welding current corresponding to this half-circle is less affected by the molten pool. Therefore, using these current values ​​to identify the arc's stability can improve the accuracy and reliability of the identification. When the arc is stable, the magnitude of adjacent sampled welding currents within the same rotating arc changes little; when the arc is unstable, the arc cannot burn stably, and the welding current changes significantly, resulting in large variations in the magnitude of adjacent sampled welding currents within the same rotating arc. Based on this principle, the identification formula for the characteristic quantity α describing the magnitude variation of adjacent sampled welding currents within the same rotating arc is as follows:

[0034]

[0035] In the formula, α is a characteristic quantity describing the change in the magnitude of adjacent sampled welding currents within the same rotating arc, and λ1 is a normalization coefficient, adjusted according to experimental results; its value in the experiment was 0.5. ΔI iE[I(1),I(2),···,I(32)] represents the variation in the magnitude of adjacent sampled welding currents within the same rotating arc. E[I(1),I(2),···,I(32)] is the mathematical expectation of the range from the first filtered welding current I(1) to the 32nd filtered welding current I(32), which is the average value of the filtered welding currents corresponding to the first half-circle of the rotating arc. I(i+1) represents the (i+1)th filtered welding current, and I(i) represents the ith filtered welding current.

[0036] The identified feature quantity α, describing the change in welding current magnitude between adjacent samples within the same rotating arc, is a rotating arc sensing signal feature quantity characterizing arc stability from the perspective of time correlation. In other words, it is the relative value of the change in welding current magnitude between adjacent samples within the same rotating arc. If the arc is stable, the change in welding current magnitude between adjacent samples is small; if the arc is unstable, the change is large; if the arc is unstable, the change is between the two cases.

[0037] (2) Identification method for the characteristic quantity β describing the number of times the welding current direction changes within the same rotating arc.

[0038] like Figure 2 As shown, welding is currently underway on weld seam HF (4). As the arc gradually rotates from point E to point F on weld seam (4), the arc length (2) changes from line segment |EE"| to line segment |FF"|, the arc length (2) becomes longer, and the welding current gradually decreases. When the arc gradually rotates from point F on weld seam (4) to point G, the arc length (2) changes from line segment |FF"| to line segment |GG"|, the arc length (2) becomes shorter, and the welding current gradually increases. Since point E corresponds to the first sampling point after filtering, and point G corresponds to the 33rd sampling point after filtering, the welding current first decreases and then increases during the process of the arc rotating from point E to point G. At point F, the direction of the welding current changes once. Similarly, when the arc passes through points G, H, and E, the direction of the welding current changes once each. Figure 2 This indicates a scenario where the welding deviation is small and the tracking accuracy is good. In this case, the weld (4)HF passes through the inside of the arc, and the welding current changes direction 4 times. If the welding deviation is large, the weld (4)HF does not pass through the inside of the curve EFGH, and the welding current changes direction 2 times.

[0039] By using three adjacent filtered welding currents, it is possible to identify whether the trend of welding current change has changed, and β is used. i The number of changes in the direction of the welding current is expressed by the following formula:

[0040]

[0041] In the formula, I(i+1) is the (i+1)th filtered welding current, I(i) is the ith filtered welding current, and I(i-1) is the (i-1)th filtered welding current. ΔI(i+1) is the change in welding current for the (i+1)th time, ΔI(i) is the change in welding current for the ith time, sgn(x) is the sign function, and β... i This indicates the number of times the welding current direction changes after three consecutive filters.

[0042] Furthermore, the number of times the welding current direction changes during one revolution of the arc can be calculated. That is, the characteristic quantity β describing the number of times the sampling welding current direction changes within the same revolution of the arc satisfies the following formula.

[0043]

[0044] In the formula, β is Figure 2 The number of times the welding current direction changes within the curve EFGH is used to characterize the number of times the sampling welding current direction changes within the same rotating arc. The meanings of other physical quantities have been introduced in equation (2).

[0045] Theoretically, when the arc is stable and the influence of the molten pool is ignored, the characteristic quantity β describing the number of times the welding current direction changes within the same rotating arc is 4 or 2. When the welding deviation is small, its value is 4; when the welding deviation is large, its value is 2. When the arc stability is poor, adjacent welding currents change significantly, and the number of current direction changes is high. Furthermore, the larger the characteristic quantity β, the greater the arc instability. The magnitude of this characteristic quantity can be used to further identify whether the arc is unstable or understable. Therefore, the characteristic quantity β describing the number of times the welding current direction changes within the same rotating arc is an important physical quantity for evaluating arc stability.

[0046] (3) Calculation method for characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc.

[0047] By processing the original sampled welding current and the filtered welding current using formula (1-3), characteristic quantities of two rotating arc sensing signals related to arc stability can be identified. Therefore, the calculation method for the characteristic quantities of the same rotating arc sensing signal that reflect the stability state of the rotating arc is as follows.

[0048]

[0049] In the formula, P is the characteristic quantity of the sensing signal of the same rotating arc that reflects the stability state of the rotating arc, α is the characteristic quantity describing the change in the magnitude of the adjacent sampled welding current within the same rotating arc, β is the characteristic quantity describing the number of times the direction of the sampled welding current changes within the same rotating arc, and the meanings of other physical quantities and functions representing intermediate processes have been introduced in formula (1-3).

[0050] To verify the feasibility of the invention's method for identifying the characteristic quantities of the same-circle rotating arc sensing signal that can reflect the stability state of the rotating arc, some robotic automatic tracking welding experiments were conducted, and the experimental data were analyzed using the method of this invention.

[0051] Figure 3 This is a graph showing the characteristic changes in the magnitude of adjacent sampled welding currents within the same rotating arc, as identified by this invention. The characteristic changes in the magnitude of adjacent sampled welding currents when the arc is stable are represented by a solid line. Figure 3 It can be observed that after arc ignition, the vast majority of the characteristic values ​​of the magnitude change of adjacent sampled welding current when the arc stabilizes are less than 0.5. The characteristic values ​​of the magnitude change of adjacent sampled welding current when the arc is unstable are represented by dashed lines. Figure 3 It can be observed that after arc ignition, the vast majority of the values ​​of the characteristic quantities of adjacent sampled welding current magnitude changes when the arc is unstable are greater than 1. Therefore, the values ​​of the characteristic quantities of adjacent sampled welding current magnitude changes when the arc is stable are less than the values ​​of the characteristic quantities of adjacent sampled welding current magnitude changes when the arc is unstable. The stability of the arc can be identified by the characteristic quantities of adjacent sampled welding current magnitude changes within the same rotating arc identified by this invention.

[0052] Figure 4 This is a graph showing the characteristic quantity of the number of times the sampling welding current direction changes within the same rotating arc, as identified by this invention. The characteristic quantity of the number of times the sampling welding current direction changes within the same rotating arc when the arc is stable is represented by a solid line. Figure 4 It can be observed that after arc ignition, the vast majority of the values ​​of the characteristic quantity of the number of times the welding current direction changes within the same rotating arc when the arc is stable are less than 6. The characteristic quantity of the number of times the welding current direction changes within the same rotating arc when the arc is unstable is represented by a dashed line. Figure 4 It can be observed that after arc ignition, the vast majority of the values ​​of the characteristic quantity of the number of times the welding current direction changes in adjacent samples when the arc is unstable are greater than 6. Therefore, the value of the characteristic quantity of the number of times the welding current direction changes in the same rotating arc when the arc is stable is less than the value of the characteristic quantity of the number of times the welding current direction changes in the same rotating arc when the arc is unstable. The characteristic quantity of the number of times the welding current direction changes in the same rotating arc identified by this invention can further assist in identifying the stability of the arc.

[0053] The present invention provides a method for identifying characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc. This method can identify characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc, and can quantitatively evaluate the stability of the rotating arc based on these characteristic quantities. This lays the foundation for automatic control of arc stability and is beneficial to improving the quality of automatic machine welding.

[0054] The above are embodiments of the present invention. The above embodiments and specific parameters are only for clearly illustrating the invention verification process and are not intended to limit the patent protection scope of the present invention. The patent protection scope of the present invention shall still be determined by its claims. Similarly, any equivalent structural changes made based on the description and drawings of the present invention shall also be included within the protection scope of the present invention.

Claims

1. A method for identifying characteristic quantities of a sensing signal from a rotating electric arc in the same circle, characterized in that: This includes methods for identifying characteristic quantities describing the magnitude variation of adjacent sampled welding currents within the same rotating arc, methods for identifying characteristic quantities describing the number of times the direction of sampled welding currents changes within the same rotating arc, and methods for calculating characteristic quantities of the sensing signal within the same rotating arc that reflect the stability state of the rotating arc. The method for identifying characteristic quantities describing the magnitude variation of adjacent sampled welding currents within the same rotating arc is a rotating arc sensing signal characteristic quantity that characterizes arc stability from the perspective of time correlation, describing the characteristic quantities describing the magnitude variation of adjacent sampled welding currents within the same rotating arc. The recognition formula is as follows: (1) In the formula, This is a characteristic quantity used to describe the variation in the magnitude of welding current between adjacent samples within the same rotating arc. This is the normalization coefficient, which was adjusted based on the experimental results; its value was 0.5 during the experiment. This represents the variation in welding current magnitude between adjacent samples within the same rotating arc. To obtain the first filtered welding current Up to the 32nd filtered welding current The mathematical expectation, which is the average value of the filtered welding current corresponding to the first half-turn of the rotating arc, is... Indicates the first i +1 filtered welding current, Indicates the first i The filtered welding current; Identified feature quantities describing the magnitude variation of adjacent sampled welding currents within the same rotating arc. This refers to the relative values ​​of the magnitude changes in adjacent sampled welding currents within the same rotating arc. If the arc is stable, the magnitude changes in adjacent sampled welding currents are small; if the arc is unstable, the magnitude changes in adjacent sampled welding currents are large; if the arc is not stable, the magnitude changes in adjacent sampled welding currents fall between the two cases. The method for identifying the characteristic quantity of the number of times the welding current direction changes within the same rotating arc is described. The identified characteristic quantity of the number of times the welding current direction changes is an important physical quantity for evaluating arc stability. It uses three adjacent filtered welding currents to identify whether the trend of welding current change has changed, and uses... The number of times the welding current direction changes is expressed by the following formula: (2) In the formula, For the first i +1 filtered welding current, For the first i The filtered welding current, For the first i -1 filtered welding current, For the first i+ The change in welding current in a single operation. For the first i The change in welding current, sgn( x ) is a symbolic function. This indicates the number of times the welding current direction changes after three consecutive filters; Furthermore, the number of times the sampling welding current direction changes within the same rotating arc is determined, which is the characteristic quantity describing the number of times the sampling welding current direction changes within the same rotating arc. Satisfy the following formula: (3) In the formula, To characterize the number of times the sampling welding current direction changes within the same rotating arc, the meanings of other physical quantities have been introduced in formula (2); When the arc is stable and the influence of the molten pool is ignored, the characteristic quantity describing the number of times the sampling welding current direction changes within the same rotating arc is described. The value is 4 or 2. When the welding deviation is small, the value is 4; when the welding deviation is large, the value is 2. When the arc stability is poor, the adjacent welding current changes significantly, the current direction changes frequently, and the characteristic quantity... The larger the value, the greater the instability of the arc. The magnitude of this characteristic quantity further identifies whether the arc is unstable or understable. Therefore, this characteristic quantity describes the number of times the welding current direction changes within the same rotation of the arc. It is an important physical quantity for evaluating arc stability; the method for calculating the characteristic quantity of the same rotating arc sensing signal that can reflect the stability state of the rotating arc identifies the characteristic quantity of the same rotating arc sensing signal and quantitatively evaluates the stability of the rotating arc based on these characteristic quantities. The calculation method for the characteristic quantity of the same rotating arc sensing signal that can reflect the stability state of the rotating arc is as follows: (4) In the formula, P is the characteristic quantity of the sensing signal of the same rotating arc that reflects the stability state of the rotating arc. This is a characteristic quantity used to describe the variation in the magnitude of welding current between adjacent samples within the same rotating arc. The characteristic quantity describing the number of times the direction of the sampling welding current changes within the same rotating arc is described in formula (1-3). Other physical quantities and functions representing intermediate processes have already been explained in formula (1-3). By using the calculation method of the characteristic quantities of the same rotating arc sensing signal, the characteristic quantities of the same rotating arc sensing signal that can reflect the stability state of the rotating arc are identified, and the stability of the rotating arc is quantitatively evaluated based on these characteristic quantities.

Citation Information

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