A cable fault locating method based on double-ended pulse matching

Abstract

The application discloses a cable fault positioning method based on double-end pulse matching and relates to the technical field of discharge fault monitoring. The application effectively distinguishes reflection events from independent events by performing waveform cross-correlation analysis, amplitude and time stamp deviation determination on pulse events in the same HFCT, and the width of a shielding window is obtained by using reflection interval and candidate basic interval statistical fusion, so that false reflection pulses are marked as invalid events or are re-determined, thereby eliminating the interference of reflection pulses on independent event counting. Further, through time regularization alignment of double-end independent events, Hungarian algorithm minimum weight matching and Mahalanobis distance secondary matching, it is ensured that the same discharge event is correctly matched at both ends, and false positioning points caused by reflection are avoided. Finally, the method can output a discharge repetition rate based on true independent event statistics and accurately position a discharge point.

Description

Technical Field

[0001] This invention relates to the field of discharge fault monitoring technology, specifically to a cable fault location method based on dual-end pulse matching. Background Technology

[0002] During online monitoring of partial discharge in cables, the same discharge pulse, after being reflected at the end face of the cable's metallic sheath, may be captured again by the same high-frequency current sensor (HFCT). This phenomenon is not caused by a single physical factor, but is the result of the coupling effect of multiple parameters such as end face reflection, waveform similarity, and time interval periodicity, leading to the repeated recording of the same discharge event. When a discharge occurs, the original pulse and the reflected pulse are closely adjacent in the time domain and have highly similar waveforms. However, existing technologies lack effective means for reflection identification and rejection, resulting in the following drawbacks: First, existing methods usually distinguish pulses based solely on amplitude thresholds or simple time windows, making it difficult to accurately identify reflected pulses with similar waveforms but attenuated amplitudes. This leads to the reflected pulse being misjudged as a new independent discharge event, resulting in a significant overestimation of the discharge repetition rate. Secondly, existing technologies lack adaptive modeling and dynamic shielding mechanisms for the inherent time interval (reflection interval) between the reflected pulse and the original pulse. The reflection intervals generated by discharges at different locations vary greatly and drift with temperature and wave velocity. Fixed time windows cannot adapt to all situations, resulting in the reflection pulses not being effectively filtered. Consequently, multiple reflected waves from the same discharge event are mistakenly identified as multiple different discharge points, leading to a large number of false positioning results.

[0003] Therefore, a cable fault location method based on two-end pulse matching is needed. Through waveform cross-correlation analysis, reflection interval statistical weighted fusion, and adaptive shielding window, the reflection event and independent event can be accurately separated within the same HFCT. Combined with two-end matching and verification, the discharge repetition rate statistics and location results are not affected by the reflection pulse when the time of reflection cannot be predicted. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a cable fault location method based on dual-end pulse matching, which solves the problem in online monitoring of partial discharge in cables where the reflection from the metal sheath end face causes a single-end sensor to record the same discharge event as multiple pulses, resulting in an overestimation of the discharge repetition rate and the generation of multiple false location points.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: a cable fault location method based on dual-end pulse matching, comprising the following steps: sorting pulse events recorded by the same HFCT according to the arrival timestamp, and judging the pulse events based on waveform cross-correlation analysis, combined with amplitude and arrival timestamp deviation; if judged as a reflection event, recording the reflection interval; if judged as an independent event, using the timestamp difference between consecutively occurring independent events as the candidate basic interval.

[0006] Frequency statistics are performed on the candidate base intervals, and the final value of the reflection interval is obtained by weighted fusion with the median of the reflection interval. The width of the shielding window is then determined based on the final value of the reflection interval.

[0007] If the absolute value of the difference between the arrival timestamps corresponding to the reflection event is less than or equal to the width of the masking window, it is marked as an invalid event; otherwise, it is re-evaluated as an independent event.

[0008] The two-terminal HFCT exchanges information on independent events, aligns them through time warping, and performs minimum weight matching by combining the Hungarian algorithm, waveform correlation coefficient, and amplitude ratio to identify unpaired events. Then, it uses Mahalanobis distance for secondary matching. After verification, it determines that the two-terminal discharge event is the same.

[0009] The discharge point is located based on the same discharge event at both ends, and the true repetition rate is output.

[0010] Compared with existing technologies, this invention has the following advantages: By performing waveform cross-correlation analysis, amplitude and timestamp deviation determination on pulse events within the same HFCT, this invention effectively distinguishes between reflected events and independent events. Furthermore, by statistically fusing the reflection interval and candidate base interval to obtain the shielding window width, false reflected pulses are marked as invalid events or re-determined, thus eliminating the interference of reflected pulses on the counting of independent events. Further, through time warping and alignment of independent events at both ends, minimum weight matching using the Hungarian algorithm, and secondary matching using Mahalanobis distance, it ensures that both ends correctly match the same discharge event, avoiding false location points caused by reflection. Finally, this method can output the discharge repetition rate based on the statistics of real independent events and accurately locate the discharge point, solving the technical problems of overestimation of the discharge repetition rate and the generation of multiple false location points due to reflection from the metal sheath end face. Attached Figure Description

[0011] Figure 1 This is a flowchart of the cable fault location method based on dual-ended pulse matching of the present invention; Figure 2 This is a flowchart illustrating the determination of pulse events in the cable fault location method based on dual-ended pulse matching of the present invention. Figure 3 This is a flowchart illustrating the method for locating discharge points in the cable fault location method based on dual-ended pulse matching of the present invention. Detailed Implementation

[0012] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Please refer to the accompanying drawings. Figure 1 The present invention provides a technical solution: a cable fault location method based on dual-end pulse matching, comprising the following steps: S1, sorting pulse events recorded by the same HFCT according to the arrival timestamp, and judging the pulse events based on waveform cross-correlation analysis, combined with amplitude and arrival timestamp deviation. If it is judged as a reflection event, the reflection interval is recorded. If it is judged as an independent event, the timestamp difference between consecutive independent events is used as the candidate basic interval.

[0013] In online monitoring of partial discharge in cables, a single HFCT will receive a large number of pulse events. These include both the original pulses generated by actual discharges and reflected pulses that are reflected off the cable's metallic sheath end face and then captured again by the same sensor. Because the reflected pulses and the original pulses are highly similar in waveform, they are difficult to distinguish effectively based solely on amplitude or time thresholds. Misclassifying reflected pulses as independent discharge events will lead to a significant overestimation of the discharge repetition rate and introduce false arrival timestamps for subsequent dual-end positioning, resulting in multiple non-existent discharge points.

[0014] Therefore, considering the inherent physical relationship between the reflected pulse and the original pulse—the waveform shape of the reflected pulse is basically the same as that of the original pulse (only the amplitude attenuates), and the arrival time interval between them is determined by the cable length and propagation speed, exhibiting a certain periodicity—it is necessary to design a method that combines waveform similarity, amplitude attenuation relationship, and time interval stability to accurately identify the original pulse and its multiple reflected pulses generated by the same discharge event from the pulse sequence and record the reflection interval as a basis for subsequent shielding.

[0015] like Figure 2 As shown, the process of determining the pulse event is as follows: S101, the arranged pulse events are taken as a pulse sequence. For each pulse event in the pulse sequence, the amplitude of all sampling points in its time domain waveform is extracted, the maximum value is found, and the amplitude of each sampling point is divided by this maximum value, thereby scaling the waveform amplitude range to between -1 and 1, and obtaining the waveform vector of each pulse event.

[0016] S102. For each current pulse event in the pulse sequence starting from the second pulse event, construct a candidate association set. The candidate association set contains all pulse events in the pulse sequence that are preceding the current pulse event and have not yet been determined as reflection events. Note that pulse events that have already been determined as reflection events will not be included in the candidate association set because they are not the original discharge pulses themselves and cannot be the source of reflection.

[0017] S103. Calculate the cross-correlation coefficient between the waveform vector of the current pulse event and the waveform vectors of each pulse event in the candidate correlation set, as well as the ratio of the peak amplitude of the current pulse event to the peak amplitude of each pulse event in the candidate correlation set. The cross-correlation coefficient is calculated by dividing the covariance of the two vectors by the product of their respective standard deviations.

[0018] S104. Select pulse events from the candidate association set whose peak amplitude is greater than the peak amplitude of the current pulse event and whose cross-correlation coefficient is greater than the arithmetic mean of all cross-correlation coefficients in the candidate association set, and form the initial association subset.

[0019] S105. If the initial screening subset is empty, the current pulse event is determined to be an independent event. If the initial screening subset is not empty, the pulse event with the largest ratio is selected from the initial screening subset as a candidate associated pulse event.

[0020] S106. Based on the candidate associated pulse event, and combining the arithmetic mean and standard deviation of the arrival timestamp differences of adjacent pulse events before the candidate associated pulse event and the geometric mean of the peak amplitude ratio, the current pulse event is judged: taking the candidate associated pulse event as the benchmark, all continuous pulse events before the candidate associated pulse event are extracted from the pulse sequence, the arithmetic mean and standard deviation of the arrival timestamp differences between each two adjacent pulse events are calculated, and the geometric mean of the peak amplitude ratio between each two adjacent pulse events is calculated.

[0021] Calculate the difference in arrival timestamps between the current pulse event and the candidate associated pulse events, as well as the ratio of the peak amplitudes of the current pulse event and the candidate associated pulse events.

[0022] If the absolute value of the difference between the arrival timestamps and the arithmetic mean is less than the standard deviation, and the peak amplitude ratio is greater than the geometric mean, then the current pulse event is determined to be a reflection event generated by the candidate associated pulse event after reflection at the end face in the cable's metallic sheath. The difference in arrival timestamps between the reflected event and the candidate associated pulse event is recorded as the reflection interval, and the peak amplitude ratio between the reflected event and the candidate associated pulse event is also recorded. Otherwise, the current pulse event is determined to be an independent event.

[0023] When there are at least two consecutive independent events in the pulse sequence, calculate the arrival timestamp difference between any two adjacent independent events and use the arrival timestamp difference between any two adjacent independent events as a candidate base interval.

[0024] The waveform vector is a sequence of values ​​obtained by normalizing the amplitude of the time-domain waveform of each pulse event, used to describe the shape characteristics of the pulse. It is obtained by dividing the amplitude of the original time-domain waveform sampling points of the pulse event by the maximum amplitude value in that waveform to obtain the normalized vector. Each element is between -1 and 1, reflecting the relative amplitude change of the waveform at each time point, eliminating the influence of absolute amplitude and making the waveform shapes comparable.

[0025] The cross-correlation coefficient is a statistic that measures the similarity between two waveform vectors. Its value ranges from -1 to 1; a value closer to 1 indicates a more consistent shape between the two waveforms. A value greater than 0.7 is generally considered highly similar, while a value less than 0.3 indicates a significant difference. In reflection determination, the cross-correlation coefficient between the reflected pulse and the original pulse is typically greater than 0.8.

[0026] Peak amplitude is the maximum absolute value of voltage or current in the time-domain waveform of a pulse event. A larger amplitude indicates stronger discharge energy. The peak amplitude of a reflected pulse is always smaller than that of the original pulse that generated it, and the attenuation coefficient is typically between 0.3 and 0.8.

[0027] The ratio refers to the ratio of the peak amplitude of the current pulse event to the peak amplitude of all pulse events in the candidate associated set. A ratio less than 1 indicates that the amplitude of the reflected pulse is smaller than that of the original pulse. The closer the ratio is to 1, the smaller the attenuation and the smaller the reflection path loss.

[0028] The candidate correlation set is a collection of all pulse events preceding the current pulse that have not yet been identified as reflection events. The size of the set represents the number of candidate original pulses that may be correlated; a larger set indicates more historically unmatched pulses.

[0029] The initial correlation subset is a subset of pulses selected from the candidate correlation set that simultaneously satisfy the following conditions: the peak amplitude is greater than the current pulse's peak amplitude, and the cross-correlation coefficient is greater than the arithmetic mean of all cross-correlation coefficients in the candidate set. A non-empty subset indicates the existence of historical pulses with similar shapes and larger amplitudes; the current pulse may be a reflection of one of these. The number of elements in the subset reflects the richness of high-similarity candidates.

[0030] The arrival timestamp difference is the difference in the times when two pulse events are recorded by the HFCT. It is obtained by subtracting the timestamp of the preceding pulse from the timestamp of the following pulse. The value is equal to twice the time required for the pulse to propagate a certain distance in the cable (for a reflection path). A typical value is determined by the cable length and wave velocity; for example, approximately 1 microsecond corresponds to 100 meters of cable.

[0031] The arithmetic mean reflects the typical interval of the pulse cycle in the region and serves as a benchmark for judging whether the current interval deviates.

[0032] The standard deviation represents the dispersion of the timestamp differences mentioned above. A smaller standard deviation indicates a more stable pulse interval. In reflection determination, a current difference that deviates from the average by less than one standard deviation is considered reasonable.

[0033] The geometric mean is the geometric average of the ratios of the peak amplitudes of consecutive adjacent pulses preceding a candidate correlated pulse. It is obtained by multiplying each ratio and then taking the nth root. This reflects a typical factor of amplitude attenuation; the amplitude ratio of the reflected pulse should be greater than this geometric mean to ensure that the attenuation is not excessively drastic.

[0034] The reflection interval is the difference in arrival timestamps between a reflected event and the candidate associated pulse event that generated it. It is obtained by directly calculating and recording the difference in timestamps when the event is determined to be a reflection event. The value equals the round-trip time of the pulse from the sensor to the end face and back, determined by the distance from the partial discharge point to the end face, and forms the basis for the subsequent shielding window width.

[0035] The candidate baseline interval is the difference in arrival timestamps between two consecutive independent events. It is obtained by calculating the timestamp difference between every two adjacent independent events when at least two consecutive independent events exist in the pulse sequence. The magnitude of the value reflects the time interval between actual discharge events, and its statistical distribution is used to determine the discharge repetition rate.

[0036] This embodiment sorts pulse events recorded by the same HFCT by time, and then performs waveform cross-correlation analysis, amplitude comparison, and timestamp deviation analysis on each current pulse event and previous pulse events that were not identified as reflections. This effectively distinguishes reflection events from independent events.

[0037] The specific advantages are as follows: First, because the reflected pulse has undergone end-face reflection, its amplitude is inevitably smaller than the original pulse, and its waveform shape is highly similar. By selecting pulses with peak amplitudes greater than the current pulse and large cross-correlation coefficients as candidate correlations, possible reflection sources can be accurately located. Second, by using the arithmetic mean and standard deviation of the timestamp differences of consecutive pulses preceding the candidate correlation pulse as a statistical benchmark, and combining this with whether the deviation of the timestamp difference between the current pulse and the candidate pulse is less than the standard deviation, and whether the amplitude ratio is greater than the geometric mean, accidental similarities caused by random noise or different discharge events can be eliminated, thereby accurately determining the reflection event.

[0038] In this way, reflected pulses that would otherwise be misjudged as multiple independent discharges are correctly classified as reflected events and their reflection intervals are recorded. Meanwhile, the real independent events are extracted, and the timestamp difference when they occur consecutively is used as a candidate base interval. This provides a clean data foundation for the subsequent statistics of the actual discharge repetition rate and directly solves the problem of overestimation of the discharge repetition rate caused by single-ended sensors recording the same discharge event as multiple pulses.

[0039] S2. Perform frequency statistics on the candidate basic intervals, and weight and fuse them with the median of the reflection intervals to obtain the final value of the reflection interval. Then, determine the width of the shielding window based on the final value of the reflection interval.

[0040] In online monitoring of partial discharge in cables, multiple candidate base intervals and multiple reflection intervals have been obtained through step S1. However, due to the influence of random noise, independent event interval variations from different discharge points, and occasional lost pulses, the statistical distribution of the candidate base intervals may exhibit multiple peaks. Directly using a single value as the benchmark for the reflection interval will lead to inaccurate subsequent shielding window widths. Furthermore, although the reflection interval has a clear physical meaning, it can slowly drift due to factors such as changes in the discharge point location and temperature-induced wave velocity.

[0041] The following reasons are taken into consideration: Firstly, the most frequently occurring value among the candidate base intervals in the most recent power frequency cycle represents the most stable actual discharge cycle and has statistical reliability; secondly, the median of multiple recently generated reflection interval data can quickly respond to changes in the current cable condition, and the median itself is not sensitive to outliers. However, these two have different emphases: the main value of the base interval reflects long-term statistical regularities, while the median of the reflection interval reflects short-term actual conditions.

[0042] Therefore, the two need to be weighted and merged, and the weights should be adaptively adjusted according to the length of the reflection interval buffer queue. When the buffer queue is long, it indicates that enough reliable reflection data has been accumulated, and the median should be trusted more. When the queue is short, the statistical principal value is relied upon more to ensure that the final value of the reflection interval is both stable and adaptable to changes.

[0043] Specifically, the process of obtaining the final value of the reflection interval is as follows: S201. First, establish a basic interval circular queue, specifically for storing all candidate basic intervals generated in the recent period. Count the occurrence frequency of all candidate basic intervals in the most recent power frequency cycle in a basic interval circular queue, and take the candidate basic interval with the highest occurrence frequency as the main value of the reflection basic interval.

[0044] S202. Take the median of the most recently generated reflection interval data from a reflection interval buffer queue and perform a weighted fusion with the principal value of the reflection base interval. The weighting coefficient is adaptively determined according to the length of the reflection interval buffer queue. The longer the reflection interval buffer queue is, the higher the weight of the reflection interval median. The fusion result is used as the final value of the reflection interval.

[0045] The basic interval circular queue is a fixed-length first-in-first-out queue used to store all candidate basic intervals generated in the most recent period. The recommended length of the basic interval circular queue is 100-200 samples, corresponding to approximately 2-4 power frequency cycles (50Hz system).

[0046] The power frequency cycle is a complete cycle of alternating current in a power system, typically 0.02 seconds (50Hz system) or 0.0167 seconds (60Hz system).

[0047] The frequency of occurrence refers to the recurrence of a candidate basic interval with a specific value in the basic interval circular queue. The higher the frequency of occurrence, the more common the time interval is in the most recent power frequency cycle, and the more likely it is to be the true basic discharge interval.

[0048] The principal value of the reflection base interval is the candidate base interval value that appears most frequently in the most recent power frequency cycle after frequency statistics. It represents the time interval between the most stable actual discharge events, usually in microseconds or nanoseconds. The smaller the value, the higher the discharge repetition rate.

[0049] The reflection interval buffer queue is a fixed-length first-in-first-out queue specifically used to store the reflection interval (i.e., the difference in arrival timestamps between the reflection event and the candidate associated pulse event) recorded each time a reflection event is determined in step S1. The recommended length of the reflection interval buffer queue is 20-50 samples.

[0050] The median of the reflection interval data is the value in the middle after sorting all current reflection interval values ​​in the reflection interval buffer queue from smallest to largest (or the average of the two middle values ​​if the queue length is even). The median is more resistant to interference than the average value and reflects the typical value of the pulse round-trip propagation time in the current cable. Its value is determined by the distance from the discharge point to the end face and the wave velocity.

[0051] The weighting coefficient is a value used to adjust the weight of the median reflection interval in the fusion, ranging from 0 to 1. The weight of the principal value of the base reflection interval is 1 minus this coefficient. It is obtained adaptively based on the length of the reflection interval buffer queue. Specifically, the coefficient is equal to the queue length divided by (the queue length plus a constant, with the constant ranging from 5 to 20), or a piecewise function is used; the larger the queue length, the closer the coefficient is to 1. A larger coefficient indicates a higher proportion of the median reflection interval in the final result, and a longer queue length results in a larger coefficient, thus enhancing the reliability of short-term measured data.

[0052] Weighted fusion linearly combines the principal values ​​of the basic reflection interval with the median of the reflection interval data according to their respective weights to obtain a comprehensive estimate of the reflection interval. The fusion result lies between the principal values ​​and the median, taking into account both long-term statistical stability and short-term change response.

[0053] The final reflection interval value is the reflection interval value determined after weighted fusion and used for subsequent calculation of the shielding window width. It represents the current optimal estimated pulse round-trip time, and its accuracy directly affects the rationality of the shielding window width.

[0054] This embodiment effectively eliminates occasional abnormal intervals through frequency statistics, ensuring that the principal value of the reflection interval reflects the true discharge cycle and avoiding contamination of the reference by a single outlier. Using the median instead of the average value to process the reflection interval data further suppresses the influence of outliers, making the fusion result more robust. The weighting coefficients are adaptively adjusted according to the length of the reflection interval buffer queue; a longer queue indicates richer and more reliable reflection data, with a higher weight for the median, and vice versa, greater trust in the principal statistical value. This adaptive mechanism allows the final reflection interval value to fully utilize historical statistical patterns while also tracking changes in cable condition in a timely manner. This more reliably distinguishes between reflected pulses and independent pulses, further reducing the probability of misclassifying reflected events as independent discharges.

[0055] While the final reflection interval value has been obtained in S201 and S202, this final value is a fixed value based on historical statistics and fusion. However, in actual cable operation, the recurrence interval of partial discharge will fluctuate slowly due to factors such as changes in the discharge point location, insulation state evolution, and temperature changes leading to changes in wave velocity. If the fixed final reflection interval value is used directly as the shielding window width, when the actual reflection interval drifts slightly, the timestamp difference that originally belonged to the reflection event may exceed the fixed window, causing the reflection event to be misjudged as an independent event. Conversely, if the window is too wide, it may incorrectly shield independent events.

[0056] Considering the arrival timestamp difference between newly generated independent events, it should be very close to the final value of the reflection interval when the actual discharge is stable. Furthermore, since the amplitude attenuation of the reflected pulse is regular, the median of the amplitude ratio can reflect the typical degree of attenuation. Therefore, the arrival timestamp difference between two consecutive independent events can be used as a real-time observation sample, and the reliability of the sample can be judged by its relative deviation from the final value of the reflection interval. Simultaneously, since the fluctuation amplitude of the reflection interval varies under different operating conditions, the allowable fluctuation range should not be fixed but should be correlated with the median of the actual observed amplitude ratio (because amplitude attenuation is related to propagation distance, and thus to time interval). In addition, when updating the final value of the reflection interval, the most recent valid sample needs to be given a higher weight, and the weight should be dynamically adjusted according to the sample dispersion. When the sample variance is large, it indicates drastic fluctuations, and the confidence in the latest sample should be reduced; conversely, it should be increased, ensuring that the shielding window width can adaptively track the actual changes in the reflection interval, rather than being a rigid fixed value.

[0057] The process of obtaining the shielding window width is as follows: S203, establish a real-time monitoring mechanism to continuously receive newly generated independent events determined as independent events in step S1. Whenever two consecutive independent events occur, calculate the difference in arrival timestamps between the two consecutive independent events and compare the difference in arrival timestamps with the current final value of the reflection interval.

[0058] The permissible fluctuation range is equal to the median of the peak amplitude ratios of the most recent N (N≥5) reflection event records. For example, if the most recent 5 amplitude ratios are 0.52, 0.55, 0.53, 0.51, and 0.54, and the median is 0.53, then the permissible fluctuation range is 0.53. In other words, only differences with a relative deviation less than 0.53 are considered valid samples.

[0059] S204. If the relative deviation of the arrival timestamp difference from the final reflection interval value is less than the allowable fluctuation range corresponding to the median of the most recent multiple amplitude ratios obtained from the peak amplitude ratios of recorded reflection events, then the arrival timestamp difference is used as a valid sample to update the final reflection interval value. The update method is to perform an exponentially weighted moving average of multiple valid samples, where the weight of the latest sample is dynamically determined according to the variance of the valid samples. Otherwise, the arrival timestamp difference is discarded. After each update of the final reflection interval value, the shielding window width is recalculated according to the rules described in section S205, i.e., the smaller value between the latest final reflection interval value and half of the current candidate base interval median is taken.

[0060] It should be noted that the formula for calculating the weights is as follows: ,in The initial preset variance (with a value of 0.01 μs) 2 ), This is an adjustment factor (with a value of 10). When the variance... When approaching 0, the weight It approaches 1; as variance increases, weight decreases.

[0061] S205. The final value of the latest reflection interval is used as the lower limit of the shielding window width, and half of the median of all candidate base intervals in the current power frequency cycle is used as the upper limit of the shielding window width. The smaller of the lower limit and the upper limit is taken as the actual shielding window width. If the upper limit is less than the lower limit, the lower limit is directly used as the shielding window width.

[0062] The masking window width is a time length threshold used to determine whether a reflected event should be masked. When the absolute value of the difference between the arrival timestamps corresponding to the reflected event is less than this width, it is marked as an invalid event.

[0063] Two consecutive independent events refer to two independent events in a pulse sequence that occur adjacently in order of arrival timestamp, with no other independent events or reflection events in between. The difference in arrival timestamps between the two independent events reflects the actual time interval of the discharge.

[0064] Relative deviation refers to the degree to which the arrival timestamp difference deviates from the final reflection interval value, expressed in relative form. It is obtained by calculating the absolute value of the difference between the arrival timestamp difference and the final reflection interval value, and then dividing by the final reflection interval value. The value is usually a decimal between 0 and 1; the closer to 0, the more consistent the two values ​​are; a value greater than 0.1 indicates a significant deviation.

[0065] The allowable fluctuation range is a relative interval width centered on the final value of the reflection interval, used to determine whether the difference in arrival timestamps is acceptable as a valid sample.

[0066] A valid sample is the difference in arrival timestamps between two consecutive independent events that have passed the relative deviation test. It is considered to accurately reflect the current reflection interval and can be used to update the final value of the reflection interval.

[0067] The exponentially weighted moving average is a weighted averaging method in which the weight of each historical valid sample decays exponentially over time, with the most recent valid sample having the highest weight. It is obtained by following a recursive formula: the new final reflection interval equals (the latest valid sample multiplied by the weight of the latest sample) plus (the old final reflection interval multiplied by (1 minus the weight of the latest sample)).

[0068] The weight of the latest sample is a weighting coefficient assigned to the latest valid sample in the exponentially weighted moving average, ranging from 0 to 1. It is obtained dynamically based on the variance of the valid samples; specifically, the larger the variance, the smaller the weight, and vice versa. A weight closer to 1 indicates higher confidence in the latest sample and faster updates; a weight closer to 0 indicates smoother updates.

[0069] The variance of the effective sample is the degree of dispersion of the values ​​in the most recent batch of effective samples (or historical effective samples), reflecting the magnitude of fluctuations among the effective samples. It is obtained by calculating the average of the squared deviations of each value in a given number of effective samples from their arithmetic mean over a period of time. A larger variance indicates that the values ​​of the effective samples are more dispersed and the reflection intervals are unstable; a smaller variance indicates that the values ​​are more concentrated and the reflection intervals are stable.

[0070] This embodiment uses the relative deviation between the timestamp difference of consecutive independent events and the final value of the reflection interval to screen out valid samples that truly reflect the current reflection interval, eliminating invalid differences caused by abnormal discharges or interference. The median of the most recent multiple amplitude ratios is used to dynamically define the allowable fluctuation range, ensuring that the judgment criteria match the actually observed reflection attenuation characteristics and avoiding the inadequacy of fixed thresholds. An exponentially weighted moving average smoothly integrates historical valid samples with the latest samples, while the weights are dynamically adjusted according to the variance of the valid samples. When the variance is small, it indicates stable measurement, and the latest samples are given a higher weight for a rapid response; when the variance is large, it indicates large measurement fluctuations, and the weight of the latest samples is reduced to avoid over-adjustment, making the update of the final reflection interval both sensitive and robust.

[0071] S3. If the absolute value of the difference between the arrival timestamps corresponding to the reflection event is less than or equal to the width of the masking window, it is marked as an invalid event; otherwise, it is re-evaluated as an independent event.

[0072] By using an adaptive time threshold of the shielding window width, false reflection events that, although similar in waveform and time interval, do not actually originate from the same original pulse can be effectively filtered out, preventing them from being incorrectly marked as invalid and losing true discharge information. For cases that were originally misjudged as reflection events but are actually independent events, they are corrected by re-judging them as independent events, making the set of independent events used for subsequent discharge repetition rate statistics purer and reducing discharge underreporting caused by false shielding. This secondary judgment mechanism further ensures that only reflection pulses that truly meet the round-trip time condition are shielded, thus solving the problem of overestimating the discharge repetition rate due to mistakenly counting reflection pulses as independent events at the source, while avoiding the risk of mistakenly shielding true independent events.

[0073] It should be noted that the update of the masked window width depends only on the difference in arrival timestamps of consecutive independent events, and marking reflected events as invalid does not affect the statistics of independent events. Therefore, when reflected events are correctly masked, the sequence of independent events remains unchanged, and the window width will not be incorrectly updated due to the presence of reflected events; when reflected events are re-identified as independent events, it indicates that the original final value of the reflection interval is no longer accurate. At this time, newly generated consecutive independent events will trigger an adaptive adjustment of the window width, thereby achieving feedback correction.

[0074] In this embodiment, since the width of the shielding window is set to be no less than the final value of the reflection interval, when the absolute value of the timestamp difference between the reflection events is less than the window width, it must also be less than the final value of the reflection interval plus a margin, and thus can be safely marked as an invalid event. Conversely, if the difference is greater than or equal to the window width, it indicates that it may not originate from the reflection of the same original pulse, and is therefore reclassified as an independent event.

[0075] S4. The two-terminal HFCTs exchange information on independent events, align them through time warping, and perform minimum weight matching by combining the Hungarian algorithm, waveform correlation coefficient, and amplitude ratio. Unpaired events are identified and secondary matching is performed using Mahalanobis distance. After verification, the same discharge event at both ends is determined.

[0076] In online monitoring of partial discharge in a double-ended cable, two high-frequency current sensors (HFCTs) are located at opposite ends of the cable, each independently acquiring pulse events and processing them through the aforementioned steps to obtain an independent event list. Due to the physical distance between the two HFCTs, the same discharge pulse reaches the two ends at different times. Furthermore, the clocks of the two acquisition systems may drift and deviate, resulting in the timestamps recorded at both ends being incomparable. Simply comparing the timestamps directly at both ends will lead to numerous mismatches or missed matches due to time base discrepancies.

[0077] Considering that although there is an overall time shift at both ends, the interval pattern of discharge events (i.e., the time difference sequence of adjacent events) is similar in shape at both ends, only shifted by an unknown constant, dynamic time warping can find the optimal nonlinear alignment between the two time series, thereby estimating the overall shift. Furthermore, since partial discharge events may be detected at one end while missing at the other due to attenuation or interference, the number of events at both ends is not necessarily equal. Therefore, a matching method that can handle unequal-length sequences and tolerate missing events is needed.

[0078] The process for identifying unpaired events is as follows: S401, each of the two HFCTs sends the arrival timestamps and corresponding normalized waveform vectors of the processed independent events to each other via the communication link. Within the same time window, the independent events of one HFCT are sorted in ascending order of arrival timestamp to form the local event list, and the independent events of the other HFCT are sorted in ascending order of arrival timestamp to form the peer event list.

[0079] S402. Extract the arrival timestamp differences of each adjacent independent event from the local event list and the remote event list, respectively, to form two interval sequences. Perform dynamic time warping on the two interval sequences, calculate the alignment method that minimizes the total cost of the warped path, and use the overall time offset obtained after warping as an estimate of the relative time base deviation between the local and remote ends caused by propagation delay and clock drift. Correct all arrival timestamps in the local event list based on the estimate to obtain the corrected local timestamp sequence.

[0080] S403. For each independent event in the corrected local event list, select the peer event in the peer event list with the smallest absolute value of the difference between the corrected local timestamp and the original arrival timestamp of the peer event, and form the initial candidate pairing set.

[0081] S404. Extract the independent events from the local event list in order of timestamp and construct a bipartite graph. The left node of the bipartite graph is the local event, the right node is the peer event, and the edge weight is the absolute value of the difference between the arrival timestamps of the two independent events.

[0082] S405. Use the Hungarian algorithm to find the minimum weight perfect matching of a bipartite graph. Only retain edges whose weight is less than the median of all intervals in the local interval sequence multiplied by an adaptive coefficient. The adaptive coefficient is equal to the ratio of the current local event list length to the remote event list length.

[0083] S406. For the matching pairs obtained after minimum weight matching, calculate the waveform cross-correlation coefficient between the waveform vector of the local event and the waveform vector of the remote event in each matching pair, and at the same time calculate the ratio of the peak amplitude of the local event to the peak amplitude of the remote event.

[0084] S407. Divide the cross-correlation coefficient of the waveform and the peak amplitude ratio by their respective maximum values ​​among all current matching pairs to obtain the normalized score. Use the product of the two normalized scores as the overall confidence of the matching pair.

[0085] S408. Remove matching pairs whose overall confidence level is lower than the median overall confidence level of all matching pairs. Then, identify the matching pair with the highest overall confidence level among the remaining pairs as a valid pair and remove two independent events from both the local and remote event lists.

[0086] S409. Recalculate the standard deviation within the moving window of the arrival timestamp difference between the local and remote ends in the remaining independent events. Use the standard deviation as the new time tolerance threshold. Repeat the minimum weight matching and comprehensive confidence screening process until no matching pair with a comprehensive confidence greater than zero can be found.

[0087] S410. The remaining local events and remaining peer events that have not been paired after iteration are called unpaired events.

[0088] Dynamic Time Warping (DTW) is an algorithm for calculating the optimal alignment path between two sequences, allowing multiple points in one sequence to correspond to a single point in another sequence in order to find the warping method with the minimum cumulative distance.

[0089] The total cost of the regularized path is the sum of local distances accumulated along the regularized path during dynamic time warping, calculated using the DTW algorithm. A smaller cost indicates that the two interval sequences are more similar.

[0090] The overall time offset is the relative time base deviation between the local and remote ends, estimated through dynamic time warping, caused by propagation delay and clock drift. It is extracted from the alignment results of DTW, for example, by taking the median or average of the time differences between corresponding points after warping. A positive number indicates that the local timestamp is larger than the remote timestamp (or vice versa); this value is used to correct the local timestamp.

[0091] The relative time base deviation has the same meaning as the overall time offset, and is the combined result of the fixed difference between the time bases of the two acquisition systems plus the propagation delay.

[0092] A bipartite graph is a graph structure in which the nodes are divided into two disjoint sets (left nodes represent events at their own endpoint, and right nodes represent events at their opposite endpoint), and edges connect the left and right nodes. The number of edges is equal to the number of left nodes multiplied by the number of right nodes.

[0093] Edge weight is the weight assigned to each edge in a bipartite graph; in this case, it is the absolute value of the difference between the arrival timestamps of two independent events. The smaller the edge weight, the closer the timestamps of the two events are.

[0094] The Hungarian algorithm is a combinatorial optimization algorithm for finding minimum-weight perfect matchings in a bipartite graph. It finds a matching that minimizes the total weight of the matched edges. A minimum-weight perfect matching is a perfect matching that minimizes the sum of the weights of all matched edges.

[0095] The adaptive coefficient is a dynamically adjusted coefficient based on the ratio of the current length of the local event list to the length of the remote event list. It is used to multiply the median of the local interval sequence to obtain the edge weight threshold. When the number of local events is greater than that of the remote event list, the coefficient is greater than 1; otherwise, it is less than 1, thus adjusting the looseness of the matching.

[0096] The normalized score is calculated by dividing the waveform cross-correlation coefficient or peak amplitude ratio by its maximum value among all matching pairs, resulting in a dimensionless score between 0 and 1. A score closer to 1 indicates that the indicator is relatively better among all matching pairs.

[0097] The overall confidence score is the product of the two normalized scores of a match pair, used to comprehensively evaluate the reliability of the match pair. It ranges from 0 to 1; a larger product indicates that the match pair performs well on both metrics, resulting in a higher confidence score.

[0098] The standard deviation within the moving window is the standard deviation of the most recent differences between the arrival timestamps of the local and remote ends among the remaining independent events, and the window moves iteratively. It reflects the dispersion of the timestamp differences and serves as a new time tolerance threshold.

[0099] It should be noted that while the Hungarian algorithm can find the minimum-weight perfect match in a bipartite graph, directly using all edges may lead to incorrect matches, necessitating the introduction of constraints (edge ​​weight thresholds). Furthermore, waveform similarity and amplitude ratio are two independent but crucial matching criteria. These need to be combined into a comprehensive confidence score, and an iterative strategy should be employed to progressively confirm the most reliable matching pairs. Matched events are removed, and the time tolerance threshold is adjusted to rematch the remaining events. This avoids a single matching error affecting subsequent events. Ultimately, those events that cannot be matched in all iterations are the truly unmatched events, potentially corresponding to single-ended discharges or interference.

[0100] This embodiment's dynamic time warping accurately estimates the relative time base deviation caused by propagation delay and clock drift at both ends, and corrects the local timestamp, thereby eliminating systematic time offset and providing a correct time reference for subsequent matching. By setting edge weight thresholds, the matching range of the Hungarian algorithm is limited, avoiding forced pairing of irrelevant events with excessively different timestamps, thus improving matching accuracy. The comprehensive confidence level considers both waveform shape similarity and amplitude attenuation, making it more robust than single timestamp matching, and the use of normalized score products makes the confidence levels between different matching pairs comparable. The iterative matching strategy only confirms the valid pair with the highest comprehensive confidence level each time and removes the matched events. At the same time, it dynamically updates the time tolerance threshold based on the standard deviation within the moving window of the timestamp difference of the remaining events, which can gradually approach the optimal matching result and finally correctly identify the single-end events that cannot be paired, providing a clear candidate set for subsequent secondary matching.

[0101] After the minimum weighted matching and comprehensive confidence screening in steps S401 to S410, there are still unmatched local and remote events. These events fail to match because the waveforms of the same discharge pulse recorded at both ends are significantly distorted, making it difficult to establish a reliable matching relationship based solely on timestamp alignment, basic waveform cross-correlation coefficients, and peak amplitude ratios.

[0102] Considering that the waveform characteristics of a discharge pulse propagating in a cable contain information related to the propagation distance, although these characteristics may differ at both ends due to different propagation paths, for the same discharge event, the first-order difference sequence of the waveform reflects the local rate of change of the waveform, the offset of the waveform peak position relative to the pulse start point reflects the pulse rise time, the full width at half maximum (FWHM) of the waveform reflects the pulse duration, and the waveform tail attenuation exponent reflects the pulse attenuation characteristics in the medium. These characteristics are physically related to the discharge itself and the propagation path, and are distinguishable for different discharge events.

[0103] Therefore, these waveform features need to be extracted and normalized, and then Mahalanobis distance is used to assess the probability that two pulse events belong to the same discharge event, so that secondary matching can be achieved through waveform detail features when timestamp matching fails.

[0104] Specifically, the process of using Mahalanobis distance for secondary matching is as follows: S411, for the remaining local events and remaining peer events that have not been paired after minimum weight matching and comprehensive confidence screening, extract the first-order difference sequence of the normalized waveform, the offset of the waveform peak position relative to the pulse start point, the full width at half maximum (FWHM) of the waveform, and the waveform tail attenuation index of each remaining local event and each remaining peer event. Then, perform zero-mean normalization on the extracted first-order difference sequence, offset, FWHM, and attenuation index. Finally, concatenate the normalized first-order difference sequence with the normalized offset, FWHM, and attenuation index to form a normalized feature vector.

[0105] S412. Calculate the Mahalanobis distance between the normalized eigenvector of each remaining local event and the normalized eigenvector of each remaining peer event, and construct a distance matrix. The rows of the distance matrix correspond to the remaining local events, the columns correspond to the remaining peer events, and the matrix elements are the Mahalanobis distance between the corresponding two impulse events.

[0106] S413. Use the Hungarian algorithm to solve the distance matrix and obtain a matching pair that minimizes the total Mahalanobis distance.

[0107] It should be noted that before calculating the Mahalanobis distance, the covariance matrix is ​​first constructed. Specifically, the normalized eigenvectors of all remaining local events and remaining remote events are merged into a single sample set, with the number of samples being (number of remaining local events + number of remaining remote events), and each sample having a dimension of D (length of the first-order difference sequence + 3). The covariance matrix of this sample set is then calculated. ,like If the matrix is ​​singular, then invert it by adding a small perturbation to the diagonal elements. Calculate the Mahalanobis distance between two eigenvectors x. The formula is: .

[0108] The offset of the waveform peak position relative to the pulse start point is the time difference between the time position of the point with the largest amplitude (peak point) in the pulse waveform and the pulse start point (the point where the waveform begins to rise from the baseline). The method is as follows: find the index position corresponding to the maximum value in the normalized waveform vector as the peak position, find the index position where the waveform begins to deviate significantly from the baseline as the pulse start point, and calculate the number of sampling points between the two multiplied by the sampling interval time. This reflects the rise time of the pulse; the smaller the value, the steeper the pulse rise.

[0109] The full width at half maximum (FWHM) of a pulse waveform is the time width between two corresponding points on the waveform when the amplitude drops to half of its peak value. It reflects the duration of the pulse; a larger value indicates a wider pulse.

[0110] The waveform tail decay exponent is a parameter describing the rate of decay at the tail of a pulse waveform (the portion that drops to the baseline after the peak). It is typically obtained by exponentially fitting a sampled segment of the tail waveform to the baseline. The method is as follows: Take a segment of the tail waveform after the peak, take the natural logarithm of the amplitude, and then perform a linear fit. The absolute value of the slope of the fitted line is the decay exponent. A larger value indicates faster decay and a shorter pulse duration.

[0111] Zero-mean normalization is a data preprocessing method that subtracts the mean of each feature from the value of all samples and then divides it by the standard deviation of the feature, so that the mean of the processed feature is 0 and the standard deviation is 1.

[0112] Mahalanobis distance is a metric that measures the distance between two sample vectors. It considers the covariance relationship between features and can eliminate the influence of dimensions and correlation. The method for obtaining it involves calculating the difference vector between two normalized feature vectors, multiplying it by the inverse of the covariance matrix, and finally multiplying it by the transpose of the difference vector, then taking the square root. Specifically, the Mahalanobis distance equals the square root of the transpose of the difference vector multiplied by the inverse of the covariance matrix multiplied by the difference vector. A smaller Mahalanobis distance indicates that the two pulse events are more similar after considering feature correlation, and are more likely to originate from the same discharge event.

[0113] The distance matrix is ​​a two-dimensional matrix with the number of rows equal to the number of remaining local events and the number of columns equal to the number of remaining peer events. The element in the i-th row and j-th column of the matrix is ​​the Mahalanobis distance between the i-th remaining local event and the j-th remaining peer event.

[0114] This embodiment introduces four waveform features that characterize the detailed morphology of the pulse waveform from different dimensions. The first-order difference sequence reflects the slope change of the waveform and is sensitive to the waveform shape; the waveform peak position offset reflects the arrival pattern of the pulse; the full width at half maximum (FWHM) reflects the pulse's duration; and the waveform tail attenuation exponent reflects the pulse energy decay rate. These features are relatively stable to distortions caused by the propagation path, compensating for the shortcomings of relying solely on timestamps and basic cross-correlation coefficients. Zero-mean normalization eliminates differences in dimensions and numerical ranges between different features, making each feature comparable in distance calculations. Mahalanobis distance automatically considers the covariance structure between features and, compared to Euclidean distance, better reflects the intrinsic distribution of data and has better adaptability to the correlation between waveform features. The Hungarian algorithm ensures globally optimal matching, minimizing the total Mahalanobis distance, thereby finding the pair most likely belonging to the same discharge event among the remaining events, significantly improving the matching success rate in cases of severe waveform distortion or large timestamp deviations.

[0115] Although a pair of matched events obtained after the second matching using Mahalanobis distance may have similar waveform details, mismatches are still possible. For example, two different discharge events may be matched together due to accidental waveform similarity. Considering the pulses generated at both ends of the cable by the same discharge event, their arrival time difference (i.e., the difference in arrival timestamps between the two pulse events in the matched pair) is physically equal to the time difference of the pulse propagating from the discharge point to both ends. This time difference is related to the cable length, the location of the discharge point, and the wave velocity, and should be an integer multiple of the final reflection interval value. This is because the final reflection interval value reflects the round-trip time of the pulse from one end to the other, and the time difference from the discharge point to both ends can usually be expressed as a multiple or fraction of the final reflection interval value. Furthermore, real discharge events often exhibit periodicity, meaning that reflected pulses appear after the original pulse at integer multiples of the final reflection interval value.

[0116] Therefore, historical reflection interval data in the reflection interval buffer queue and candidate basic intervals in the basic interval circular queue can be used to verify whether the timestamp difference of the matched pair conforms to physical expectations. Simultaneously, it is checked whether there is a subsequent event with a time interval equal to the final value of the reflection interval after both the local and remote events in the matched pair, and whether the cross-correlation coefficients of the waveforms of these two subsequent events are higher than the average level of confirmed valid pairs. This can further confirm that the discharge event did indeed generate a subsequent pulse sequence conforming to the reflection law, thus ruling out accidental matching.

[0117] Specifically, the process of determining the same discharge event at both ends after verification is as follows: S414. For each matching pair in a set of matching pairs, the verification is performed using the most recent multiple reflection interval data taken from a reflection interval buffer queue and the most recent multiple candidate basic intervals taken from a basic interval circular queue: calculate the arrival timestamp difference between the two pulse events in the matching pair, and calculate the ratio of the arrival timestamp difference to the current reflection interval final value.

[0118] S415. If the absolute value of the difference between the ratio and a certain integer is less than the standard deviation of multiple reflection intervals obtained from the reflection interval buffer queue, then the matching pair is marked as a matching pair to be confirmed.

[0119] S416. For a pair to be confirmed, check whether there is a subsequent local event after the local event in the pair with a time interval equal to the final value of the reflection interval. At the same time, check whether there is a subsequent peer event after the peer event with a time interval equal to the final value of the reflection interval. If both exist and the cross-correlation coefficient between the waveform vectors of the subsequent local event and the subsequent peer event is greater than the average cross-correlation coefficient of all currently confirmed valid pairs, then the pair to be confirmed is confirmed as a valid pair; otherwise, it is discarded.

[0120] S417. All matching pairs retained after being matched and verified by Mahalanobis distance, together with previously confirmed valid pairs, are considered as the same discharge event at both ends.

[0121] This embodiment calculates the ratio of the arrival timestamp difference to the final reflection interval and uses the standard deviation of the reflection interval as the tolerance range for deviation. It effectively identifies matching pairs that conform to the propagation law by utilizing physical integer multiple relationships, eliminating erroneous matches due to random time differences. It further utilizes the characteristic of periodic reflection of discharge pulses by checking for the existence of subsequent events and ensuring that the waveform cross-correlation coefficient is above average. Only discharge events that truly produce a stable reflection sequence can pass verification. Through this verification mechanism, erroneous matches in Mahalanobis distance matching are eliminated, while correct matches are retained, improving the accuracy of identifying the same discharge event at both ends and avoiding positioning errors caused by misclassifying different discharge events as the same event.

[0122] S5. Locate the discharge point based on the same discharge event at both ends and output the true repetition rate.

[0123] Considering that the traveling wave pulse generated by partial discharge propagates from the discharge point to both ends of the cable, due to the different distances from the discharge point to the two ends, there is a time difference in the time it takes for the pulse to reach the HFCT at both ends. The absolute value of this time difference is proportional to the distance difference between the discharge point and the two ends. Given the total length of the cable and the propagation speed of the pulse in the cable, the actual position of the discharge point from one end can be accurately calculated using the double-ended traveling wave positioning formula. Simultaneously, after the identification and shielding of reflected events by S1 to S3, reflected pulses have been eliminated from independent events, and each independent event corresponds to one real partial discharge. Therefore, the number of occurrences of independent events within each power frequency cycle is the true discharge repetition rate, no longer affected by reflected pulses.

[0124] like Figure 3 As shown, the process of locating the discharge point based on the same discharge event at both ends is as follows: S501, for each confirmed same discharge event at both ends, the arrival timestamp of the same discharge event at both ends is obtained on the two high-frequency current sensors, and the side where one HFCT is located is recorded as the first end, and the side where the other HFCT is located is recorded as the second end.

[0125] S502. Calculate the absolute value of the time difference between the arrival timestamp of the first end and the arrival timestamp of the second end.

[0126] S503. Based on the total length of the cable and the propagation speed of the pulse in the cable, calculate the actual position of the discharge point from the first end using the double-ended traveling wave positioning formula.

[0127] S504. The calculated actual location is taken as the discharge point.

[0128] S505. In each power frequency cycle, after the reflection event is eliminated and re-judged, and the independent events corresponding to the same discharge event at both ends are confirmed, the number of occurrences of the independent events at the first end (such as the first end) shall be taken as the true repetition rate of partial discharge.

[0129] The dual-end traveling wave positioning formula is a mathematical expression used to calculate the actual distance between the discharge point and the first end. The formula is: the distance between the discharge point and the first end is equal to (total cable length plus pulse propagation speed multiplied by the absolute value of the time difference) divided by two, or it depends on the positive or negative direction of the time difference. According to the dual-end positioning principle, if the timestamp at the first end is less than that at the second end (i.e., the pulse arrives at the first end first), then the distance between the discharge point and the first end is (total cable length minus propagation speed multiplied by the absolute value of the time difference) divided by two; if the timestamp at the first end is greater than that at the second end, then it is (total cable length plus propagation speed multiplied by the absolute value of the time difference) divided by two.

[0130] This embodiment utilizes the time difference between two sensors to eliminate the problem of difficult-to-identify reflected waves in single-end positioning, resulting in higher positioning accuracy. Since reflected events and false events have been effectively eliminated through steps such as reflection identification, shielding windows, and matching verification, the arrival timestamps used for positioning are derived from real discharges and the two ends are correctly matched, thus ensuring the accuracy of the positioning results and avoiding multiple false positioning points caused by reflected pulses. The true repetition rate is directly based on the statistics of independent events, solving the problem of overestimating the repetition rate due to misjudging reflected events as independent discharges, making the assessment of discharge severity more reliable.

[0131] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0132] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0133] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0134] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0135] Finally, the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A cable fault location method based on dual-ended pulse matching, characterized in that, Includes the following steps: The pulse events recorded by the same HFCT are sorted according to the arrival timestamp. Based on waveform cross-correlation analysis, the pulse events are judged in combination with amplitude and arrival timestamp deviation. If the event is judged to be a reflection event, the reflection interval is recorded. If the event is judged to be an independent event, the timestamp difference between consecutive independent events is used as the candidate basic interval. Frequency statistics are performed on the candidate base intervals, and the final value of the reflection interval is obtained by weighted fusion with the median of the reflection interval. The width of the shielding window is then determined based on the final value of the reflection interval. If the absolute value of the arrival timestamp difference corresponding to the reflection event is less than or equal to the width of the masking window, it is marked as an invalid event; otherwise, it is re-evaluated as an independent event. The two-terminal HFCT exchanges information on independent events, aligns them through time warping, and performs minimum weight matching by combining the Hungarian algorithm, waveform correlation coefficient, and amplitude ratio to determine unpaired events. Then, it uses Mahalanobis distance for secondary matching. After verification, it determines that the two-terminal same discharge event is determined. The discharge point is located based on the same discharge event at both ends, and the true repetition rate is output.

2. The cable fault location method based on dual-ended pulse matching according to claim 1, characterized in that, The process of determining pulse events is as follows: The arranged pulse events are taken as a pulse sequence. The amplitude of each pulse event in the pulse sequence is normalized to obtain a waveform vector. For each current pulse event starting from the second pulse event in the pulse sequence, construct a candidate association set. The candidate association set contains all pulse events in the pulse sequence that are preceding the current pulse event and have not yet been determined as reflection events. Calculate the cross-correlation coefficient between the waveform vector of the current pulse event and the waveform vectors of each pulse event in the candidate association set, and the ratio of the peak amplitude of the current pulse event to the peak amplitude of each pulse event in the candidate association set. The initial correlation subset is formed by selecting pulse events from the candidate correlation set whose peak amplitude is greater than the peak amplitude of the current pulse event and whose cross-correlation coefficient is greater than the arithmetic mean of all cross-correlation coefficients in the candidate correlation set. If the initial screening subset is empty, the current pulse event is determined to be an independent event; if the initial screening subset is not empty, the pulse event with the largest ratio is selected from the initial screening subset as a candidate associated pulse event. Based on candidate associated pulse events, the current pulse event is determined by combining the arithmetic mean and standard deviation of the arrival timestamp differences of the adjacent pulse events before the candidate associated pulse event and the geometric mean of the ratio of peak amplitude.

3. The cable fault location method based on dual-ended pulse matching according to claim 2, characterized in that, The process of determining the current pulse event is as follows: Based on the candidate associated pulse events, extract all pulse events that precede the candidate associated pulse events and are arranged in time stamp order from the pulse sequence. Calculate the arithmetic mean and standard deviation of the arrival time stamp differences between each pair of adjacent pulse events in the extracted pulse events, and calculate the geometric mean of the peak amplitude ratio between each pair of adjacent pulse events. Calculate the difference in arrival timestamps between the current pulse event and the candidate associated pulse events, as well as the ratio of the peak amplitudes of the current pulse event and the candidate associated pulse events; If the absolute value of the difference between the arrival timestamp and the arithmetic mean is less than the standard deviation, and the peak amplitude ratio is greater than the geometric mean, then the current pulse event is determined to be a reflection event generated by the candidate associated pulse event after reflection from the end face in the cable metal sheath. Otherwise, the current pulse event is determined as an independent event.

4. The cable fault location method based on dual-ended pulse matching according to claim 1, characterized in that, The process of obtaining the final value of the reflection interval is as follows: The occurrence frequency of all candidate base intervals within the most recent power frequency cycle is counted, and the candidate base interval with the highest occurrence frequency is taken as the main value of the reflection base interval. The median of the generated multiple reflection interval data is weighted and fused with the principal value of the reflection baseline interval, and the fusion result is used as the final reflection interval value.

5. The cable fault location method based on dual-ended pulse matching according to claim 4, characterized in that, The process of obtaining the width of the masking window is as follows: Whenever two consecutive independent events occur, calculate the difference in arrival timestamps between the two consecutive independent events; If the relative deviation of the arrival timestamp difference relative to the final value of the reflection interval is less than the allowable fluctuation range, then the arrival timestamp difference is used as a valid sample to update the final value of the reflection interval. Otherwise, discard the difference in arrival timestamps; The final value of the latest reflection interval is used as the lower limit of the shielding window width, and half of the median of all candidate base intervals in the current power frequency cycle is used as the upper limit of the shielding window width. The smaller of the lower limit and the upper limit is taken as the actual shielding window width. If the upper limit is less than the lower limit, the lower limit is directly used as the shielding window width.

6. The cable fault location method based on dual-ended pulse matching according to claim 1, characterized in that, The process for determining unpaired events is as follows: The independent events on both ends are sorted by timestamp, and the timestamps on the local end are corrected by dynamic time normalization. A bipartite graph is constructed using timestamp differences as edge weights. The Hungarian algorithm is used to solve for minimum weight matching. The comprehensive confidence is obtained by combining waveform cross-correlation coefficients and amplitude ratios. Valid pairs are iteratively filtered and removed until no matching is possible. The remaining events are the unpaired events.

7. The cable fault location method based on dual-ended pulse matching according to claim 6, characterized in that, The process of using Mahalanobis distance for quadratic matching is as follows: The first-order difference sequence, the offset of the waveform peak position relative to the pulse start point, the full width at half maximum (FWHM), and the attenuation exponent of the waveform tail are extracted from the normalized waveform of each remaining local event and each remaining remote event. The extracted first-order difference sequence, offset, FWHM, and attenuation exponent are then normalized to zero mean. The normalized first-order difference sequence is then concatenated with the normalized offset, FWHM, and attenuation exponent to form a normalized feature vector. Calculate the Mahalanobis distance between the normalized eigenvector of each remaining local event and the normalized eigenvector of each remaining peer event, and construct a distance matrix. The distance matrix is ​​solved using the Hungarian algorithm to obtain a set of matching pairs that minimizes the total Mahalanobis distance.

8. The cable fault location method based on dual-ended pulse matching according to claim 7, characterized in that, The process of determining the same discharge event at both ends after successful verification is as follows: For each of the matching pairs in a set of matching pairs, calculate the difference in arrival timestamps between the two pulse events in the matching pair, and then calculate the ratio of the difference in arrival timestamps to the final value of the current reflection interval. If the absolute value of the difference between the ratio and a certain integer is less than the standard deviation of multiple reflection intervals obtained from the reflection interval buffer queue, the matching pair is marked as a matching pair to be confirmed. For confirmed matching pairs, verify whether there are subsequent events after the local and remote events with an interval equal to the final value of the reflection interval, and whether the cross-correlation coefficient of the waveforms of the two subsequent events is greater than the average cross-correlation coefficient of all confirmed valid pairs. If so, they are confirmed as valid matching pairs; otherwise, they are discarded. All matched pairs retained after being matched and verified by Mahalanobis distance, together with previously confirmed valid pairs, are considered as the same discharge event at both ends.

9. A cable fault location method based on dual-ended pulse matching according to claim 1, characterized in that, The process of locating the discharge point based on the same discharge event at both ends is as follows: The arrival timestamps of the same discharge event at both ends are obtained on two high-frequency current sensors respectively. The side where one HFCT is located is marked as the first end, and the side where the other HFCT is located is marked as the second end. Calculate the absolute value of the time difference between the arrival timestamp of the first end and the arrival timestamp of the second end; Based on the total length of the cable and the propagation speed of the pulse in the cable, the actual position of the discharge point from the first end is calculated using the double-ended traveling wave positioning formula. The calculated actual location is taken as the discharge point.

10. A cable fault location method based on dual-ended pulse matching according to claim 9, characterized in that, The process of outputting the true repetition rate is as follows: Within each power frequency cycle, after the reflection events are eliminated and re-judged, the number of occurrences of the independent events corresponding to the same discharge event at both ends is taken as the true repetition rate of the partial discharge.

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