Multi-type fault arc edge recognition and positioning method

Abstract

The application discloses a multi-type fault arc edge recognition and positioning method, comprising: acquiring synchronous current signals of a multi-branch power distribution system and preprocessing; intercepting the first half cycle window of the signals, constructing a parameterized time-frequency atom library and performing sparse decomposition to acquire high-resolution frequency domain envelope features, and simultaneously extracting high-resolution time domain pulse features; establishing a time scale mapping relationship between the time domain pulse features and the frequency domain envelope features, performing alignment and cross-domain fusion based on the mapping relationship to generate a physically consistent fusion feature vector; inputting the vector into a pre-configured lightweight classification network to obtain an arc type label; and determining a fault branch based on high-frequency component propagation characteristics. The application effectively solves the time-frequency feature asynchronous aliasing problem under limited edge end computing power, and realizes rapid and accurate recognition and positioning of multi-type fault arcs.

Description

Technical Field

[0001] This invention relates to the field of power system fault detection technology, and in particular to a method for identifying and locating the edge of arcs in multiple types of faults. Background Technology

[0002] Arc faults are one of the main causes of electrical fires in low-voltage power distribution systems. Achieving rapid identification and accurate location of arcs at edge devices with limited computing resources is of significant technical importance for ensuring the safe and stable operation of power systems. In particular, how to overcome the resolution limitations of traditional time-frequency analysis within milliseconds and achieve high-precision real-time detection at the edge, especially when facing various fault types such as series, parallel, and high-resistance grounding faults, is a pressing technical challenge in the field of power electronics.

[0003] Existing technologies typically employ Short-Time Fourier Transform (STFT) or Wavelet Transform to extract the time-frequency features of electric arcs, and then use convolutional neural networks for classification and recognition. Regarding feature fusion, mainstream solutions often involve directly concatenating time-domain waveform features and frequency-domain spectra at the same timestamp, or performing simple weighted fusion using multi-stream networks. For fault location, fault point distance is often determined based on the attenuation ratio of the current amplitude or using Time-Domain Reflection (TDR). These methods are currently mainly applied in cloud server or industrial workstation environments with sufficient computing power to achieve offline or online monitoring of electric arc faults.

[0004] However, existing technologies face significant challenges when applied at the edge, primarily due to feature aliasing caused by the asynchronicity of the physical scales of time-frequency features, and the contradiction between high computational load and real-time performance. Specifically, the arc discharge process manifests as microsecond-level random high-frequency pulses in the time domain, while in the frequency domain it appears as a millisecond-level macroscopic energy envelope, exhibiting a difference in physical time scale. Existing methods, based on the synchronous alignment assumption, force the microscopic pulses and macroscopic envelopes to align simultaneously, ignoring the asynchronicity of the physical process. This leads to distorted feature representation and makes it difficult to effectively distinguish between similar faults such as series arcs and high-resistance grounding arcs in the feature space. Furthermore, the traditional sparse decomposition algorithms used to obtain high-resolution features have excessively high computational complexity, making it difficult to meet the real-time detection requirements within the first half-cycle on resource-constrained edge devices. Summary of the Invention

[0005] The purpose of this invention is to provide a method for identifying and locating the edges of multiple types of fault arcs, in order to solve at least one of the aforementioned problems in the prior art.

[0006] According to one aspect of this application, a method for identifying and locating the edges of multi-type fault arcs includes:

[0007] Acquire the synchronous current signal of the multi-branch power distribution system and preprocess it to obtain a synchronous current signal set;

[0008] The first half-cycle window of the synchronous current signal set is extracted, a parameterized time-frequency atom library is constructed and sparse decomposition is performed to obtain high-resolution frequency domain envelope features and extract high-resolution time domain pulse features.

[0009] Establish a time-scale mapping relationship between high-resolution temporal pulse features and high-resolution frequency-domain envelope features, and perform alignment and cross-domain fusion accordingly to generate a physically consistent fused feature vector.

[0010] The physical consistency fusion feature vector is input into a pre-configured lightweight classification network to obtain the arc type label;

[0011] In response to the presence of a fault indicated by the arc type label, the fault branch number is determined based on the propagation characteristics of the high-frequency components extracted from the synchronous current signal set.

[0012] Beneficial effects: This invention effectively solves the problem of asynchronous aliasing of time and frequency features under limited computing power at the edge, and realizes rapid and accurate identification and location of multiple types of fault arcs. Attached Figure Description

[0013] Figure 1 The flowchart shows the overall process of the multi-type fault arc edge identification and localization method provided in the embodiments of the present invention.

[0014] Figure 2 This is a schematic diagram illustrating the process of obtaining a synchronous current signal set according to an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of the process for extracting high-resolution time-domain pulse features according to an embodiment of the present invention.

[0016] Figure 4 This is a schematic diagram illustrating the process of constructing a bidirectional consistency alignment mechanism provided in an embodiment of the present invention. Detailed Implementation

[0017] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] Example 1 details the overall technical framework of the multi-type fault arc edge identification and localization method proposed in this invention. It addresses the contradiction between computational bottlenecks and identification accuracy in existing edge detection technologies. Through a combination of physical model-driven feature transformation and lightweight deep learning, it achieves rapid and accurate identification and localization of various fault arcs, including series, parallel, and high-resistance grounding faults. Figure 1 As shown.

[0019] The hardware environment of this embodiment mainly includes: a high-frequency current transformer (HFCT) deployed in a low-voltage distribution box, an edge computing unit based on an embedded graphics processing unit (GPU) / neural network processor (NPU), such as the commercial edge AI computer NVIDIA Jetson Nano or the commercial heterogeneous multi-core microprocessor STM32MP1 series, and a smart circuit breaker. The HFCT is responsible for collecting high-frequency current signals from each branch, the edge computing unit executes the algorithm flow of this embodiment, and sends a trip command to the smart circuit breaker when a fault is detected.

[0020] Step 101: Obtain the synchronization current signal of the multi-branch power distribution system and perform preprocessing to obtain the synchronization current signal set.

[0021] In this step, acquiring the synchronous current signal of the multi-branch power distribution system is mainly achieved through a multi-channel synchronous acquisition card, ensuring strict alignment of the signals of each branch on the time axis. The preprocessing process is used to eliminate environmental noise interference and standardize the data benchmark, providing high-quality input for subsequent feature extraction. Specifically, the system acquires the current data of each branch circuit within the distribution box in real time, and performs denoising, filtering, and normalization processing, ultimately outputting a standardized set of synchronous current signals. This process forms the basis for all subsequent time-frequency analysis and location algorithms, ensuring the comparability of data between different branches.

[0022] Step 102: Extract the first half-cycle window from the synchronous current signal set, construct a parameterized time-frequency atom library and perform sparse decomposition to obtain high-resolution frequency domain envelope features, and extract high-resolution time domain pulse features.

[0023] This step addresses the detection problem in the initial stage of arc ignition in a faulty electric arc. Extracting the first half-cycle window means analyzing only the data from the first half-cycle of the power frequency (e.g., 10ms) starting from the zero moment of the fault occurrence. Traditional Fourier transforms have low frequency resolution within such a short window, making it impossible to distinguish between the transient interference of the electric arc and normal load. This embodiment employs sparse decomposition technology, utilizing a pre-built parameterized time-frequency atom library to perform super-resolution reconstruction of the signal, obtaining high-resolution frequency domain envelope features that overcome the limitations of the Heisenberg uncertainty principle. Simultaneously, high-resolution time-domain pulse features reflecting the microscopic discharge process of the electric arc are extracted in parallel, providing multi-dimensional physical information for subsequent time-frequency fusion.

[0024] Step 103: Establish the time-scale mapping relationship between high-resolution time-domain pulse features and high-resolution frequency-domain envelope features, and perform alignment and cross-domain fusion based on the time-scale mapping relationship to generate a physically consistent fused feature vector.

[0025] This step addresses the asynchrony between time-domain pulses and frequency-domain envelopes on the physical time scale. Arc pulses often occur on the microsecond scale, while spectral features reflect average energy on the millisecond scale; direct splicing leads to feature misalignment. Establishing a time-scale mapping involves aligning discrete time-domain pulses and continuous frequency-domain envelopes on the same time reference through predetermined mathematical transformations. Based on this, cross-domain fusion is performed, organically combining the two types of features to generate a physically consistent fused feature vector that includes both transient details and statistical regularities. This fused feature effectively eliminates time-frequency aliasing, improving the model's ability to discriminate complex arc waveforms.

[0026] Step 104: Input the physical consistency fusion feature vector into the pre-configured lightweight classification network to obtain the arc type label.

[0027] In this step, the pre-configured lightweight classification network refers to a deep learning model designed for edge computing environments. Considering the storage and computing power limitations of edge devices, lightweight structures such as depthwise separable convolutions are adopted, significantly reducing the number of parameters while ensuring recognition accuracy. The network receives physically consistent fused feature vectors as input, undergoes multiple layers of nonlinear transformation and feature extraction, and finally outputs an arc type label. The label not only indicates whether a fault exists, but also specifically distinguishes the fault type, such as series arc, parallel arc, or high-resistance grounding fault.

[0028] Step 105: In response to the arc type label indicating a fault, the fault branch number is determined based on the propagation characteristics of the high-frequency components extracted from the synchronous current signal set.

[0029] This step primarily addresses fault location in multi-branch power distribution systems. After the system identifies a fault arc, it needs to further determine which specific branch the fault occurred in, in order to accurately cut off the fault source without affecting other normal branches. The high-frequency component propagation characteristics utilize the physical laws governing the propagation of high-frequency arc signals on transmission lines, such as phase delay and spectral distortion. Due to differences in distance and path impedance from the fault point to each detection point, the high-frequency signals received by each branch will exhibit certain differences. By analyzing these differences, the location of the fault source can be deduced in reverse, outputting an accurate fault branch number.

[0030] The scope of application and system parameter boundaries of this invention are described below. The method of this invention is applicable to low-voltage power distribution systems within the following conditions:

[0031] Voltage level: Single-phase 220V or three-phase 380V AC system, power frequency is 50Hz or 60Hz.

[0032] Rated current range: 10A to 400A. For high current applications exceeding 400A, a current transformer with the appropriate current range is required.

[0033] Number of branches: 2 to 16. When there are more than 16 branches, it is recommended to use a group detection strategy to control the amount of data processed in a single operation.

[0034] Arc frequency characteristic range: This method optimizes the high-frequency characteristics of arcs with center frequencies ranging from 5 kHz to 500 kHz. For arc types with frequency characteristics exceeding this range, the frequency coverage range of the parameterized time-frequency atom library needs to be adjusted.

[0035] Minimum configuration requirements for edge computing devices: ARM Cortex-A53 or higher processor with a clock speed of at least 1.2GHz and at least 512MB of RAM. Recommended configurations include ARM Cortex-A72 or edge computing platforms with Neural Processing Unit (NPU) acceleration capabilities.

[0036] Example 2 details the process of obtaining the synchronization current signal set and extracting time-domain features, focusing on how to obtain a high-quality synchronization current signal set and high-resolution time-domain pulse features through strict hardware synchronization and sophisticated signal processing algorithms, such as... Figure 2 , Figure 3 As shown.

[0037] Step 201: Synchronously collect data from each branch of the multi-branch power distribution system using a shared clock source to construct the original multi-branch current matrix.

[0038] In this step, to ensure strict temporal consistency of the multi-branch signals, the system employs a parallel acquisition architecture based on a Field-Programmable Gate Array (FPGA). All analog-to-digital converter (ADC) channels are clocked by the same high-precision crystal oscillator, guaranteeing a sampling time deviation of less than 10 nanoseconds. The acquired data is organized into a matrix, where each row represents the current data of one branch, and each column represents a sampling time. The original multi-branch current matrix is ​​the direct output of this acquisition process, fully preserving the original amplitude and phase information of each branch's current waveform.

[0039] Step 202: Detect the zero-crossing time of the power frequency current of each branch in the original multi-branch current matrix, calculate the timestamp deviation between each branch, perform clock alignment compensation on the original multi-branch current matrix based on the timestamp deviation of the power frequency current zero-crossing time, and perform anti-aliasing filtering to obtain the clock-aligned current matrix.

[0040] Despite using a shared clock source, response delays from different sensors and cable transmission delays can still introduce minor phase errors. Compensation is based on the timestamp deviation of the power frequency current zero-crossing point. Specifically, this involves detecting the zero-crossing time of the power frequency current in each branch, using a reference branch as a benchmark, calculating the time offset of other branches, and then fine-tuning the waveform using an interpolation algorithm to eliminate phase errors. To prevent aliasing caused by high-frequency noise, the system performs anti-aliasing filtering on the signal. In this embodiment, a fourth-order Butterworth low-pass filter with a cutoff frequency of 800kHz is preferably used. This filter has a flat amplitude-frequency characteristic within the passband and can effectively filter out noise components higher than half the sampling rate, resulting in a clean clock-aligned current matrix.

[0041] Step 203: Acquire the power frequency voltage signal synchronously collected with the multi-branch power distribution system. Specifically, a voltage transformer is deployed at the incoming end of the distribution box, sharing the same clock source with the current acquisition channel for synchronous sampling. Based on the zero-crossing point of the power frequency voltage signal synchronously collected with the multi-branch power distribution system, the clock-aligned current matrix is ​​divided into half-cycle segments, and the half-cycle segments are normalized with the fundamental current amplitude as a reference to obtain the synchronous current signal set.

[0042] This step completes the data standardization process. Segmentation based on the zero-crossing point of the power frequency voltage means using the voltage signal as a phase reference to cut the continuous current waveform into independent power frequency half-cycle (i.e., 10ms) data segments. This segmentation method conforms to the physical characteristics of zero arc crossover. Furthermore, to eliminate the influence of load size on the characteristic amplitude, normalization is required. Specifically, for the current value I(t) at any time t, its normalized value It is... norm The formula for calculating (t) is:

[0043] I norm (t)=I(t) / I base ,

[0044] Where I base This represents the amplitude of the fundamental current during this half-cycle.

[0045] After normalization, the arc characteristics under different power loads are mapped to the same scale, forming the final set of synchronous current signals.

[0046] Step 204: Use a morphological filter to perform opening and closing operations on the current sequence in the synchronous current signal set to obtain the fundamental envelope estimate.

[0047] This step separates the fundamental frequency component from a current signal superimposed with complex elements. Morphological filters are set-theoretic nonlinear signal processing tools suitable for extracting the geometric features of a signal. In this embodiment, a flat structuring element g with a length of 20 microseconds (corresponding to approximately 40 sampling points, assuming a sampling rate of 2MHz) is designed. First, an opening operation is performed on the current sequence I, denoted as:

[0048] ;

[0049] in Indicates corrosion. It indicates expansion.

[0050] This operation can erase positive narrow pulses; then a closing operation is performed, denoted as:

[0051] .

[0052] This operation can fill in narrow negative depressions. The fundamental envelope estimate Env is ultimately obtained by averaging the two values, i.e.:

[0053] .

[0054] This method can smoothly fit the profile of the power frequency current without being affected by high-frequency glitches.

[0055] Step 205: Calculate the difference between the current sequence and the fundamental envelope estimate to obtain the transient residual signal.

[0056] After obtaining the fundamental envelope, the high-frequency components containing arc characteristics can be separated through simple differential operations. Specifically, the fundamental envelope estimate obtained in step 204 is subtracted from the original normalized current sequence, i.e., the residual Residual = I - Env. The resulting transient residual signal removes the power frequency background and highlights the random high-frequency pulses and noise generated during arc combustion.

[0057] Step 206: Determine an adaptive threshold based on the statistical characteristics of the transient residual signal, identify local maxima points in the transient residual signal that exceed the adaptive threshold, mark the local maxima points as pulse events, and record the timestamp and peak amplitude of the pulse events to form high-resolution time-domain pulse features, wherein the adaptive threshold is determined based on the statistical characteristics of the transient residual signal.

[0058] This step transforms the continuous residual signal into a discrete sequence of pulse events to achieve a sparse representation of the features. To adapt to different noise environments, this embodiment employs an adaptive threshold strategy. Specifically, the standard deviation σ of the transient residual signal is calculated, and the threshold is set to 3σ, i.e., three times the standard deviation. All local maxima points whose amplitude exceeds this threshold are considered valid pulse events. For each detected pulse event i, its precise occurrence time t is recorded. i and peak amplitude a i The set of all detected pulse events constitutes a high-resolution time-domain pulse feature, whose data format can be represented as containing multiple tuples (t... i ,a i The sequence of ) . This sparse representation compresses the amount of data while preserving the most critical temporal physical information of the electric arc.

[0059] In practical applications, abnormal situations such as sensor failure, signal saturation, or communication interruption may occur. This embodiment adopts the following handling strategy:

[0060] In response to signal loss or communication interruption, the system is equipped with a timeout monitoring mechanism. If a branch fails to receive valid data within two consecutive power frequency cycles, the branch is marked as having an unknown status, excluded from subsequent fault diagnosis, and an alarm message is sent to the upper-level system.

[0061] To address signal saturation, i.e., when the ADC output reaches full scale, the system checks during the preprocessing stage whether the normalized amplitude exceeds a preset saturation threshold, such as 0.98. If saturation is detected, the half-cycle data is marked as potentially distorted and its weight is reduced during classification confidence calculation.

[0062] In cases where the confidence level of the classification result is too low, such as when the maximum posterior probability is less than 0.7, the system adopts a delayed decision-making strategy, accumulating the judgment results of three consecutive half-cycles for multi-frame joint judgment, and triggering the protection action only when multiple frames consistently point to the same fault type.

[0063] Example 3 describes the high-resolution frequency domain feature extraction process based on sparse decomposition, detailing how to use a parameterized time-frequency atom library to perform sparse decomposition on the first half-cycle current signal to obtain high-resolution frequency domain envelope features. Addressing the computational constraints in edge computing scenarios, it provides a basic standard orthogonal matching pursuit scheme and a preferred two-stage hierarchical scheme, the latter significantly reducing computational complexity.

[0064] Step 301: The parameterized time-frequency atom library is composed of Gaussian-modulated complex exponential atoms. The Gaussian-modulated complex exponential atoms are uniquely determined by the following parameters: center frequency, bandwidth parameter, time center, and attenuation coefficient. Among them, the center frequency is discretely distributed at logarithmic intervals, and the time center covers the first half-cycle window.

[0065] In this step, the parameterized time-frequency atom library is the cornerstone of sparse decomposition. Unlike Fourier transforms with fixed basis functions, the atomic structure used in this embodiment can more flexibly match the physical waveform of the electric arc. Specifically, the mathematical expression of any atom g(t) is as follows:

[0066] ;

[0067] Where g(t) represents the amplitude of the parameterized time-frequency atom at time t, and f c Let f represent the center frequency, σ represent the bandwidth parameter, t0 represent the time center, α represent the attenuation coefficient, and j' represent the imaginary unit. To cover the frequency band where the electric arc might occur, the center frequency f... c The frequency range is divided into 64 discrete values ​​at logarithmic intervals within the range of 5kHz to 500kHz; the time center t0 covers the entire first half-cycle window of 10ms; the attenuation coefficient α is set to three levels: fast, medium and slow, to match the damping characteristics at different times.

[0068] Step 302, in a basic implementation, involves performing sparse decomposition to obtain high-resolution frequency domain envelope features, including: initializing the residual signal as a current sequence from a set of synchronous current signals; iteratively executing the following steps: calculating the inner product of the residual signal and each atom in the parameterized time-frequency atom library; selecting the atom with the largest absolute value of the inner product and adding it to the selected atom set; updating the combination coefficients of the selected atom set using the least squares method and updating the residual signal; stopping the iteration when a preset termination condition is met; and constructing a super-resolution spectrum based on the selected atom set and its combination coefficients as the high-resolution frequency domain envelope features. The preset termination condition includes: the energy of the residual signal being lower than a preset proportion of the energy of the original signal or the number of atoms in the selected atom set reaching a preset upper limit.

[0069] This basic implementation employs the standard Orthogonal Matching Pursuit (OMP) algorithm. The system first uses the original current signal as the initial residual, then iterates through all atoms in the atom library to find the optimal atom with the highest correlation to the current residual. Once found, it is added to the support set, and the component of that atom in the residual is removed through orthogonal projection. This process is iterated repeatedly until the residual energy is below 5% of the original energy, or the number of atoms reaches a preset upper limit, such as 32. The resulting sparse coefficient vector represents the energy distribution of the signal in the super-resolution frequency domain, effectively overcoming the frequency resolution limitations of short time windows.

[0070] Step 303, in a preferred embodiment, involves performing sparse decomposition to obtain high-resolution frequency domain envelope features. A two-stage hierarchical strategy is employed, specifically including: constructing a sparse detector atom library based on a parameterized time-frequency atom library; calculating the projected inner product of the synchrotron current signal set and each detector atom in the sparse detector atom library to obtain the activity index of each frequency band; selecting a predetermined number of frequency bands with the highest activity index ranking to form an active frequency band set; and extracting atoms belonging to the active frequency band set from the parameterized time-frequency atom library to form a local atom sub-library; using the local atom sub-library as a basis, performing orthogonal matching pursuit decomposition on the synchrotron current signal set to obtain high-resolution frequency domain envelope features.

[0071] This preferred embodiment solves the problem of excessive computational cost in searching the entire atom library. First, coarse-grained bandgap detection is performed, calculating the current sequence x and the detection atom g. f The absolute value of the inner product yields the activity index γ. f The calculation formula is as follows:

[0072] γ f =| <x,g f >|;

[0073] Among them, g f This represents the probe atom vector with frequency f, |...| represents the modulo operation (absolute value), and <...> represents the vector dot product operation.

[0074] This metric allows for the rapid identification of frequency bands with concentrated signal energy, enabling fine-grained OMP decomposition only within the local atomic sub-libraries corresponding to these active frequency bands. This strategy avoids ineffective searches in signal-free frequency bands, thereby improving computational efficiency by an order of magnitude.

[0075] Step 304: The sparse probe atom library is constructed in the following way: the center frequency parameter of the parameterized time-frequency atom library is sparsely downsampled, and discrete frequency points with logarithmic equal intervals are retained; the time center parameter is fixed to the midpoint of the first half-cycle window, and the bandwidth parameter and attenuation coefficient are fixed to preset values, thereby generating a sparse probe atom library with fewer atoms than the parameterized time-frequency atom library.

[0076] This step details the tools used in the first stage of detection. To achieve extremely rapid scanning, the sparse detector atom library underwent significant parameter reduction. Specifically, only eight key frequency points were retained for the center frequency parameter, distributed logarithmically at equal intervals within the range of 5kHz to 500kHz; the time center parameter was fixed at 5ms; and the bandwidth and attenuation coefficient were set to the middle range. The detector library constructed in this way contains only a very small number of atoms, such as eight, allowing the calculation of activity indices to be completed in microseconds, meeting the real-time requirements of the edge.

[0077] To illustrate the effect of two-stage sparse decomposition more intuitively, a simplified numerical example is given here. Assume that the length of the first half-cycle current sequence is 20,000 sampling points, 10 ms, and the sampling rate is 2 MHz.

[0078] In the first stage, the projected inner product is calculated using eight detector atoms at eight frequency points ranging from 5 kHz to 500 kHz. The activity indices corresponding to the eight detector frequencies are assumed to be 0.12, 0.18, 0.35, 0.82, 0.71, 0.15, 0.08, and 0.05, respectively. The frequency bands with the three highest values ​​are selected as the active frequency band set. This stage requires only eight inner product calculations and takes approximately 0.2 ms.

[0079] In the second stage, an atomic sub-library belonging to the aforementioned three active frequency bands was extracted from approximately 120,000 atoms. This sub-library, about 3 / 8 the size of the original atomic library (approximately 45,000 atoms), was then subjected to OMP decomposition, yielding a super-resolution spectrum after 32 iterations. Compared to performing OMP on the entire atomic library, the computational cost was significantly reduced.

[0080] Example 4 describes the time-frequency asynchronous alignment and cross-domain fusion process based on point process kernel embedding. It elaborates on how to solve the mismatch between time-domain micro-pulses and frequency-domain macro-envelopes on the physical time scale. By introducing point process kernel embedding and a bidirectional consistency mechanism, it achieves feature fusion with precise physical alignment.

[0081] Step 401, in a basic implementation, establishes a time-scale mapping relationship between high-resolution time-domain pulse features and high-resolution frequency-domain envelope features, including: dividing the first half-cycle window into multiple consecutive macroscopic time periods; traversing each pulse event in the high-resolution time-domain pulse features, determining the macroscopic time period index to which the pulse event belongs based on the timestamp of the pulse event; establishing a correspondence between the pulse event and the high-resolution frequency-domain envelope features within the corresponding indexed macroscopic time period, as the time-scale mapping relationship.

[0082] This basic approach employs a rule-based hard mapping strategy. For example, a 10ms window is evenly divided into four macroscopic time periods of 2.5ms each. If a pulse event occurring at t=3.1ms is detected, the system directly classifies it into the second time period, from 2.5ms to 5.0ms, and establishes a correlation with the frequency domain characteristics of that time period. This method is computationally simple and suitable for scenarios where high positioning accuracy is not required.

[0083] Step 402, in a preferred embodiment, establishes a time-scale mapping relationship between high-resolution time-domain pulse features and high-resolution frequency-domain envelope features, including: modeling discrete pulse events in the high-resolution time-domain pulse features as time-domain point processes; using a kernel function containing learnable bandwidth parameters, embedding the discrete pulse events into continuous-time pulse intensity functions, and converting the discrete time-domain features into a continuous representation isomorphic to the high-resolution frequency-domain envelope features in the physical time dimension.

[0084] This preferred approach incorporates point process theory from statistical signal processing. An electric arc pulse manifests as randomly occurring discrete points in the time domain, while its frequency domain envelope is a continuously changing curve; these different dimensions prevent direct fusion. Through kernel function embedding, the discrete Dirac delta function sequence can be smoothed into a continuous intensity function curve, making it mathematically isomorphic to the frequency domain energy distribution curve, thus providing a mathematical basis for alignment.

[0085] Step 403 involves embedding discrete pulse events into a continuous-time pulse intensity function using a kernel function containing a learnable bandwidth parameter. Specifically, this includes: constructing a Gaussian kernel function group centered on multiple discrete moments covering the first half-cycle window; calculating the weighted sum of the Gaussian kernel responses of all discrete pulse events at each discrete moment as the pulse intensity value at that moment, where the Gaussian kernel response is proportional to the peak amplitude of the discrete pulse event and decreases Gaussianly with increasing time distance; and constructing a continuous-time pulse intensity function from the pulse intensity values ​​of all discrete moments.

[0086] In this step, the specific mathematical implementation is as follows: Assume that K kernel function positions are preset within the first half-cycle window, and the center time of the k-th position is μ. k The bandwidth parameter is σ k For the detected i-th pulse event (timestamp t) i , amplitude a i The Gaussian kernel response Φ generated at the k-th position ik The calculation formula is:

[0087] ;

[0088] Where, Φ ik t represents the response contribution of the i-th pulse at the k-th nucleus position. i For pulse timestamps, μ k For the center time of the k-th nucleus, σ k Let a be the bandwidth parameter of the k-th core. i This represents the pulse amplitude.

[0089] The total pulse intensity value λ at this location k The result is obtained by summing the responses of all M pulses:

[0090] ;

[0091] By calculating the intensity values ​​at all K locations, the continuous-time pulse intensity function vector λ=[λ1,λ2,...,λ] can be obtained. K ].

[0092] Step 404, establishing a time-scale mapping relationship, also includes constructing a bidirectional consistency alignment mechanism: resampling the high-resolution frequency domain envelope features to the same time sampling position as the continuous-time pulse intensity function to obtain the frequency domain energy distribution vector; calculating the forward alignment weight with reference to the frequency domain energy distribution vector and the reverse alignment weight with reference to the continuous-time pulse intensity function; generating bidirectional consistency alignment weights based on the combination of the forward and reverse alignment weights, and using the bidirectional consistency alignment weights to construct the mapping relationship, such as... Figure 4 As shown.

[0093] This step proposes a physical consistency check: if the frequency domain energy is high during a certain time period, then there should be dense pulses in the time domain; and vice versa.

[0094] The frequency domain envelope time resolution resampling process is as follows:

[0095] Obtain high-resolution frequency domain envelope features and adjust their resolution to match the K time positions of the pulse intensity function vector.

[0096] Since the frequency domain envelope originates from a sparse spectral coefficient matrix, it inherently lacks fine temporal resolution. A time-center weighting method based on selected atoms is used to reconstruct the temporal resolution. Let L be the selected atoms in the orthogonal matching tracing, and let τ be the time center of the j-th atom. j The coefficient amplitude is c j .

[0097] For the k-th nucleus position μ k Calculate the equivalent energy contribution of the frequency domain envelope at that moment:

[0098] ;

[0099] Among them, E k c represents the frequency domain energy response at the k-th time position. j Let τ be the coefficient of the j-th selected atom. j μ is the time center parameter of this atom. k For the center time of the k-th nucleus, σ k This represents the bandwidth parameter for the k-th core.

[0100] By traversing all K kernel positions, we obtain the K-dimensional frequency domain energy distribution vector E = (E1, E2, ..., E...).K This vector has the same time sampling position as the pulse intensity function vector λ, which facilitates subsequent alignment calculations. The reliability of this correspondence can be verified from two directions.

[0101] Step 405: Calculate the forward alignment weight and the reverse alignment weight respectively. Specifically, this includes: calculating the normalized product of the frequency domain energy distribution vector and the continuous-time pulse intensity function at each time step; defining the weight that is positively correlated with the distribution trend of the frequency domain energy distribution vector as the forward alignment weight, which characterizes the degree of verification of the existence of the time domain pulse by the frequency domain energy; and defining the weight that is positively correlated with the distribution trend of the continuous-time pulse intensity function as the reverse alignment weight, which characterizes the degree of verification of the existence of the frequency domain energy by the time domain pulse.

[0102] Specifically, the positive alignment weight w at position k k fwd The calculation formula is as follows: reverse alignment weight w k bwd Formal symmetry:

[0103] ;

[0104] Where, λ k Let l be the continuous time pulse intensity at the k-th time position, l be the summation index, and ε be a small constant to prevent division by zero, which can be chosen to be 10. -8 .

[0105] For the reverse alignment weights, the consistency of the frequency domain energy distribution is verified using the pulse intensity distribution as a reference. The physical meaning is that dense pulse regions should correspond to higher frequency domain energy, and dense pulses represent continuous arc discharge.

[0106] Calculate the reverse consistency weight vector:

[0107] .

[0108] Due to symmetry, the positive and negative consistency weights are numerically equal, but their physical meanings are different. The positive weights emphasize the guidance of the frequency domain on the time domain, while the negative weights emphasize the verification of the frequency domain by the time domain.

[0109] Bidirectional consistency score ρ k It is generated by the combination of the two, for example, ρ k =(w k fwd *w k bwd ) (1 / 2) The higher the score, the higher the consistency of the time-frequency characteristics at that moment, and the greater the fusion value.

[0110] In other embodiments, calculating the forward alignment weight and the reverse alignment weight separately further includes the following steps:

[0111] Using the frequency domain energy distribution vector as the normalization benchmark, the proportion of the continuous time pulse intensity function value to the frequency domain energy distribution vector value at each time moment is calculated and used as a positive alignment weight to characterize the degree of verification of the existence of the time domain pulse by the frequency domain energy.

[0112] Using the continuous-time pulse intensity function as the normalization benchmark, the proportion of the frequency domain energy distribution vector value to the continuous-time pulse intensity function value at each time step is calculated and used as the reverse alignment weight to characterize the degree of verification of the existence of frequency domain energy by the time domain pulse.

[0113] Specifically, the positive alignment weight w at position k k fwd A normalization strategy based on the total amount of time-domain pulses is adopted, and its calculation formula is as follows:

[0114] ;

[0115] The first term represents the distribution weight of the pulse intensity, and the second term is the ratio factor of the frequency domain energy at that location to the peak energy. The physical meaning of the positive weight is that locations with both higher pulse density and higher frequency domain energy receive a greater weight.

[0116] Reverse alignment weight w k bwd A normalization strategy based on the total energy in the frequency domain is adopted, and its calculation formula is as follows:

[0117] ;

[0118] Because of the different normalization benchmarks—forward normalization using total pulse amount and reverse normalization using total energy amount—the weights for forward and reverse are generally unequal, reflecting the differences in verifying time-frequency consistency from different physical perspectives. Bidirectional consistency score ρ k It is obtained from the geometric mean of the two, i.e., ρ k =(w k fwd *w k bwd ) (1 / 2) .

[0119] Step 406 involves constructing a mapping relationship using bidirectional consistency alignment weights. Specifically, this includes: constructing a pulse event alignment mapping matrix, where the rows of the matrix correspond to each discrete pulse event in the high-resolution time-domain pulse features, and the columns correspond to each time position on the continuous time axis; calculating the element values ​​in the matrix, where the element weight of the i-th discrete pulse event at the k-th time position is determined by the product of the Gaussian kernel response of the i-th discrete pulse event at the k-th time position and the bidirectional consistency alignment weight at the k-th time position.

[0120] This step ultimately generates a mapping matrix A for cross-domain fusion. The element A in the i-th row and k-th column of the matrix... ik This determines the proportion of information from the i-th pulse that flows into the k-th fusion feature node. The calculation formula is:

[0121] ;

[0122] Where, Φ ik Let ρ be the Gaussian kernel response of the i-th pulse at the k-th position. k The bidirectional consistency score for the k-th position is typically obtained by combining positive and negative weights, Φ. il Let be the Gaussian kernel response of the i-th pulse at position l, where l is the summation index and ε represents a small constant to prevent the denominator from being zero. This weighting matrix comprehensively considers the temporal proximity of the pulses (via Φ). ik ) and time-frequency consistency confidence (via ρ k ).

[0123] To illustrate this more clearly, a simplified numerical calculation example is provided here.

[0124] Suppose the system detects a pulse event occurring at t1 = 1.2 ms with amplitude a1 = 1.0. The first kernel function is centered at μ1 = 1.0 ms with bandwidth σ1 = 0.2 ms. Then, the original response Φ of this pulse at the first kernel position is... 11 The value is approximately exp(-0.5)≈0.606. If the bidirectional consistency check finds that the frequency domain energy at this location is also high, and the consistency score ρ1=0.9 is calculated, then the contribution weight of this pulse to the first feature node will be enhanced; if the frequency domain energy is extremely low, resulting in ρ1=0.1, then this weight will be suppressed to avoid mistaking noise pulses for valid arc features. Through the above mechanism, the system achieves accurate alignment and denoising in a physically meaningful sense.

[0125] The process of performing alignment and cross-domain fusion based on time-scale mapping to generate a physically consistent fusion feature vector specifically includes: using bidirectional consistency alignment weights to project high-resolution time-domain pulse features onto the same time scale as high-resolution frequency-domain envelope features to obtain time-domain aligned features; concatenating the time-domain aligned features with the high-resolution frequency-domain envelope features and inputting them into a gated fusion unit, which adaptively determines the contribution ratio of time-domain features and frequency-domain features in each dimension; and performing layer normalization on the output of the gated fusion unit to obtain a physically consistent fusion feature vector.

[0126] Specifically, cross-domain fusion includes the following steps: projecting the time-domain pulse features onto the pulse event alignment mapping matrix A to obtain time-domain aggregated features aligned with the frequency domain envelope time. Specifically, the amplitude information of each pulse event is weighted and aggregated to K time positions through the row vectors of matrix A, forming a K-dimensional time-domain aggregated vector.

[0127] A gated fusion unit is constructed, which concatenates the time-domain aggregation vector and the frequency-domain energy distribution vector E along the feature dimension, maps them to a K-dimensional gated vector G through a single-layer fully connected network, and constrains it to the interval of 0 to 1 by the Sigmoid activation function.

[0128] Before the input gated fusion unit, the time-domain aggregation vector and the frequency-domain energy distribution vector are standardized with zero mean and unit variance to bring the two types of features to the same scale. The k-th element F of the fused feature vector F... k Calculate using the following formula:

[0129] F k =G k ·v agg_k +(1-G k )·E k ;

[0130] Among them, G k v is the k-th element of the gated vector. agg_k This represents the temporal aggregation intensity at the k-th time position. The gating mechanism adaptively selects either more discriminative temporal or frequency domain information at each time position. After layer normalization of F, a physically consistent fusion feature vector is obtained.

[0131] Example 5 details the specific architecture and decision-making mechanism of the lightweight classification network, addressing how to accurately distinguish fine-grained categories such as series arcs, parallel arcs, and high-resistance grounding faults when computing resources are limited at the edge.

[0132] Step 501: The lightweight classification network is composed of cascaded depthwise separable convolutional blocks, each containing sequentially connected channel-wise convolutional layers and pointwise convolutional layers. The physically consistent fused feature vector is input into the pre-configured lightweight classification network, including: using the depthwise separable convolutional blocks to encode the physically consistent fused feature vector, and compressing it through a global average pooling layer to obtain a deep encoded feature vector.

[0133] In this step, depthwise separable convolutional blocks are a crucial component for achieving network lightweighting. Unlike standard convolution, which simultaneously handles spatial and channel correlations, this structure decouples the convolution process into two steps: first, channel-wise convolution, using a K×1 kernel to independently convolve each input channel, extracting local patterns of time-frequency features; second, pointwise convolution, using a 1×1 kernel to linearly combine the output channels of the previous layer, enabling information exchange between channels. Through this decoupling, the computational cost can be reduced to one-eighth to one-tenth of that of standard convolution.

[0134] As a concrete example of network configuration, a lightweight classification network can contain four cascaded depthwise separable convolutional blocks. Assume the physical consistency fusion feature vector of the input has dimensions (1, L'), where L' is the feature length. The first convolutional block has 32 output channels, the second has 64, the third has 128, and the fourth has 256. As the network depth increases, the number of feature channels doubles layer by layer to extract higher-order abstract semantic features. Each convolutional layer is followed by a batch normalization layer and a modified linear unit activation function (ReLU6). A global average pooling layer compresses the variable-length feature map into a fixed-length (e.g., 256-dimensional) deep encoded feature vector z, which condenses the class discrimination information of the input signal.

[0135] Step 502, obtaining the arc type label, specifically includes: obtaining a preset arc type prototype anchor matrix, which contains central feature vectors corresponding to different arc types and normal states; calculating the distance metric between the deep encoding feature vector and each central feature vector in the arc type prototype anchor matrix, and calculating the posterior probability of belonging to each category based on the distance metric; selecting the category with the highest posterior probability as the arc type label.

[0136] In this step, the arc-type prototype anchor matrix C is a matrix with dimension N. class A matrix of size D, where N class Let c be the number of categories, for example, 4 categories: normal, series, parallel, high impedance; D is the feature dimension, for example, 256. Each row of the matrix contains c. jThis represents the ideal center point of the j-th type of arc in the feature space, i.e., the prototype anchor point. Unlike traditional fully connected classification layers, this embodiment uses a distance-based metric learning method. Specifically, it calculates the relationship between the feature vector z of the input sample and each prototype anchor point c. j The Euclidean distance between them is denoted as d(z,c). j )=||zc j ||2.

[0137] To convert distance into probability, the posterior probability P(y=j|z) of belonging to class j is calculated using the negative exponential form of the Softmax function (normalized exponential function):

[0138] ;

[0139] Where P(y=j|z) represents the posterior probability that the input feature z belongs to the j-th type of arc, and d(z,c j ) represents the input feature vector z and the prototype anchor point c of the j-th class. j The distance between them (e.g., Euclidean distance), c k This represents the prototype anchor vector of the k-th class.

[0140] The system ultimately selects the class index with the highest probability value as the output. This prototype-based decision-making mechanism has clear geometric interpretation, that is, it determines which class center a sample is closest to in the feature space. In some optional implementations, a confidence threshold can be set, for example, 0.7. If the maximum posterior probability is lower than this threshold, an uncertain label is output to avoid false positives. The classification confidence threshold of 0.7 comprehensively considers the balance between false positive and false negative rates. In experimental verification, a threshold of 0.7 can control the false positive rate to within 5% while keeping the false negative rate below 3%.

[0141] Example 6: This example details the specific implementation of fault location using the propagation characteristics of high-frequency components. It utilizes the physical attenuation and delay characteristics of high-frequency arc signals during transmission in low-voltage power distribution lines to solve the problem of fault source location in multi-branch systems.

[0142] Step 601, based on the propagation characteristics of the high-frequency components extracted from the synchronous current signal set, determines the fault branch number, including: extracting the high-frequency components within the arc characteristic frequency band from the current of each branch in the synchronous current signal set; calculating the relative phase delay between the high-frequency components of each branch and constructing a phase delay difference matrix; taking the branch with the largest high-frequency component amplitude as a reference, calculating the amplitude spectrum ratio of the high-frequency components of other branches relative to the reference branch to obtain the spectral distortion characteristics; combining the phase delay difference matrix and the spectral distortion characteristics, identifying the branch where the fault source is located, and obtaining the fault branch number.

[0143] In this step, a bandpass filter with a center frequency of 150kHz and a bandwidth of 100kHz is first designed to filter the currents of each branch and extract the high-frequency components. The high-frequency signal x of any two branches i and j is then calculated. i (t) and x j The cross-correlation function R of (t) ij (τ), the lag time corresponding to its peak value is the relative phase delay τ. ij To improve accuracy, parabolic interpolation is preferred for subsampling point estimation of the cross-correlation peak. This is derived from all τ... ij The resulting matrix is ​​the phase delay difference matrix. Simultaneously, the amplitude spectrum ratio of each branch relative to the reference branch (the one with the largest amplitude) is calculated. This ratio reflects the frequency-selective attenuation characteristics of the signal when coupled to adjacent branches via the bus, i.e., the spectral distortion characteristics.

[0144] Step 602: Combining the phase delay difference matrix and spectral distortion features, identify the branch where the fault source is located. Specifically, this includes: constructing a fault branch hypothesis testing logic; for each branch, assuming it to be a fault branch, and calculating the phase violation degree and distortion matching degree; the phase violation degree characterizes the degree of conflict between the phase delay direction derived based on the hypothesis and the observed phase delay difference matrix; the distortion matching degree characterizes the similarity between the spectral shape of the branch and the spectrum of the ideal fault arc; weighted fusion of the phase violation degree and distortion matching degree of each branch, and selecting the branch with the highest fusion score as the fault branch.

[0145] This step employs hypothesis testing logic for decision-making. Specifically, for the k-th branch, if it is assumed to be the fault source, according to physical laws, the signal should flow from this branch to the busbar and then to other branches, and its phase relative to all other branches should be leading. The proportion of elements violating this law in the system's statistical phase delay difference matrix is ​​defined as the phase violation degree V. k V k The smaller the value, the more likely the hypothesis is to hold true.

[0146] Simultaneously, the correlation coefficient between the spectrum of the high-frequency component of this branch and the preset source-end arc spectrum template is calculated, which serves as the distortion matching degree M. k The source signal has not undergone long-distance transmission attenuation, and its spectral characteristics should be closest to the template. The final fusion score S k It can be calculated using a weighted formula, for example:

[0147] S k =w1*(1-V k )+w2*M k ;

[0148] w1 and w2 are weighting coefficients, for example, 0.6 and 0.4 respectively. The weight of phase delay evidence is higher than that of spectral distortion evidence because in low-voltage short-distance power distribution systems, the signal-to-noise ratio of phase delay information is usually better than that of spectral distortion information.

[0149] Traverse all branches and score S. k The one with the highest score is determined to be the actual faulty branch.

[0150] Example 7 details the offline training process of the important model in this invention—the learnable kernel function and the lightweight classification network—and discloses a specific training method, namely the manufacturing process, that enables the model to have physical consistency and high discriminative power.

[0151] During the pre-training phase, a sufficient quantity and variety of fault arc sample data must be prepared. The training data can consist of the following three sources:

[0152] Laboratory simulation data: On an arc fault simulator conforming to UL1699 or GB / T31143 standards, series arcs, parallel arcs, and high-resistance grounding faults were simulated respectively. Current waveforms were collected under different load types (resistive, inductive, capacitive, and mixed loads) and different fault impedances (0.1Ω to 100Ω). No less than 5000 half-cycle samples were collected for each fault type.

[0153] On-site data acquisition: Deploy HFCTs in the actual power distribution system for long-term monitoring, collecting current waveforms under normal operating conditions and historical fault events. The number of samples under normal conditions should be balanced with the number of samples for each type of fault to avoid model bias caused by class imbalance.

[0154] Data augmentation samples: Gaussian noise is added to the original samples, and slight time axis shifts and amplitude scaling are applied to increase sample diversity and improve the model's generalization ability.

[0155] Data annotation was completed by engineers with a background in power systems. The annotation categories included four types: normal operation, series arc fault, parallel arc fault, and high-resistance grounding fault. The annotation results underwent cross-validation to ensure at least 95% consistency.

[0156] Step 701: The learnable bandwidth parameter is obtained in the pre-training stage by minimizing the physical constraint alignment loss function. The physical constraint alignment loss function includes: an energy consistency loss term, which is used to constrain the maximization of the correlation between the continuous-time pulse intensity function and the frequency domain energy distribution vector; a kernel bandwidth smoothness loss term, which is used to constrain the smoothness of the change of the kernel function bandwidth parameter at adjacent time points; and a kernel coverage sufficiency loss term, which is used to penalize the response blind zone of the continuous-time pulse intensity function in the first half-cycle window.

[0157] In this step, in order to ensure the learnable kernel parameter θ kernel Converging to a solution that conforms to the physical properties of an electric arc, define the physical constraint alignment loss function L. align L align L is the energy consistency loss term. consist Kernel bandwidth smoothness loss term L smooth and the nuclear coverage adequacy loss item L cover Weighted sum of the three:

[0158] L align =α1*L consist +α2*L smooth +α3*L cover .

[0159] Where α1, α2, and α3 are the weight coefficients for each item, and the possible values ​​are α1=1.0, α2=0.1, and α3=0.5. Each loss item has been converted to a dimensionless form through data normalization before weighting. This loss function is jointly optimized with the classification task loss.

[0160] Energy consistency loss term L consist The Pearson correlation coefficient, used to maximize the time-domain intensity (pulse intensity function vector) λ and the frequency-domain energy distribution vector E, is calculated using the following formula:

[0161] ;

[0162] λ k This represents the pulse intensity value at the k-th position. This represents the mean of the pulse intensity vector λ. Let E represent the mean of the frequency domain energy vector E, and ε represent a small constant to prevent the denominator from being zero.

[0163] L consist The value ranges from 0 to 2, with 0 for two vectors that are perfectly positively correlated and 2 for two vectors that are perfectly negatively correlated.

[0164] Kernel bandwidth smoothness loss term L smooth To prevent drastic changes in bandwidth parameters that could disrupt time continuity, the calculation formula is as follows:

[0165] ;

[0166] σ k+1 σ represents the learnable kernel bandwidth parameter at position k+1. k This represents the learnable kernel bandwidth parameter at the k-th position.

[0167] Nuclear coverage adequacy loss term L coverTo ensure that the superimposed response of all kernel functions covers the entire observation window and avoids detection blind spots, the minimum response value after superimposing the kernel functions is used as the coverage index, and its calculation formula is as follows:

[0168] ;

[0169] Where, θ cover The coverage threshold can be set to 0.5; T is the observation window duration (10ms).

[0170] Step 702: The lightweight classification network and the arc class prototype anchor matrix are jointly optimized during the pre-training stage in the following ways: a training triplet containing positive and negative sample pairs is constructed, the contrast loss that makes the distance between positive sample pairs less than the distance between negative sample pairs is calculated, and the parameters of the lightweight classification network are updated based on the contrast loss; the feature mean of each class in the training batch is statistically analyzed, and the central feature vector in the arc class prototype anchor matrix is ​​dynamically updated using an exponential moving average strategy.

[0171] In this step, triplet loss from metric learning is used to enhance the discriminative power of the features. For an anchor sample x a Select similar samples x p As positive samples, different class samples x n As a negative sample, the contrast loss L triplet The requirement is that the distance between negative sample pairs is at least one margin greater than the distance between positive sample pairs. By backpropagating this loss, the network parameters are optimized so that similar features cluster in the space and dissimilar features are separated.

[0172] Meanwhile, to stabilize the position of the prototype anchor point, an exponential moving average (EMA) strategy is used for updating. In the t-th iteration, the prototype vector c of the j-th class... j The updated formula is:

[0173] ;

[0174] Among them, c j (t) Let c represent the prototype anchor vector of class j after the t-th iteration update. j (t-1) This represents the prototype anchor vector from the previous iteration (t-1), where β is the momentum coefficient, for example, 0.9. Let be the mean value of the features of the j-th type of samples in the current batch. The momentum coefficient β is preferably set to 0.9 to strike a balance between prototype stability and sample adaptability. Too small a β will cause drastic fluctuations in the prototype, while too large a β will make the prototype react slowly to new samples. The joint optimization strategy ensures that the features extracted by the network and the prototype anchor points always maintain the best matching relationship.

[0175] The weighted sum of the contrast loss and cross-entropy classification loss described above, together with the physical constraint alignment loss described in step 701, constitutes the overall optimization objective of the training, and performs end-to-end joint optimization of the parameters of the lightweight classification network and the bandwidth parameters of the learnable kernel function.

[0176] Example 8 illustrates the complete process of the method of the present invention from fault occurrence to fault location, using a four-branch low-voltage power distribution system as an example.

[0177] Scenario setting: The rated current of the main incoming line of the distribution box is 100A, with four branch circuits numbered 1 to 4. Branch circuit 2 is connected to a 15kW motor load. A series arc fault caused by poor contact occurs at a terminal of the motor power line.

[0178] Step 801: Signal acquisition and preprocessing are performed. Four HFCTs synchronously acquire current signals at a sampling rate of 2MHz. During the first half-cycle after the fault occurs, within a 10ms window, the original current matrix is ​​acquired. After clock alignment compensation, significant high-frequency glitches are detected superimposed on the current waveform of branch 2. After normalization, a synchronous current signal set is obtained.

[0179] Step 802 involves sparse decomposition and feature extraction, performing a two-stage sparse decomposition on the first half-cycle signal of branch 2. The first-stage detection results show that the activity indices are highest in the 47kHz and 100kHz frequency bands, at 0.82 and 0.71 respectively, indicating that the arc energy is mainly concentrated in the mid-to-high frequency range. The second stage involves fine decomposition within the active frequency bands, obtaining a super-resolution spectrum that exhibits typical arc broadband energy distribution characteristics. Simultaneously, morphological filtering extracts five significant pulse events with timestamps of 1.2ms, 2.8ms, 5.1ms, 7.3ms, and 9.4ms, with peak amplitudes ranging from 0.15 to 0.28.

[0180] Step 803 involves time-frequency fusion. After kernel embedding, a continuous pulse intensity function is obtained. Bidirectional consistency verification shows that the position of each pulse is highly consistent with the frequency domain energy distribution, with an average consistency score of 0.87, indicating that these pulses are indeed generated by arc discharge rather than noise. The fused feature vector has a length of 256 dimensions.

[0181] Step 804: Classification and identification are performed. The fused feature vector is input into the lightweight network, and the posterior probabilities of each category are calculated: Normal = 0.02, Series Arc = 0.91, Parallel Arc = 0.04, High-resistance Grounding = 0.03. The system determines it to be a series arc fault.

[0182] Step 805: Fault location is performed. Using branch 2, which has the strongest amplitude, as a reference, the phase delay difference matrix is ​​calculated. The results show that the high-frequency components of branch 2 are in phase lead relative to the other three branches, τ...21 =-12μs,τ 23 =-15μs,τ 24 =-18μs, and its spectral distortion characteristics have the highest correlation coefficient with the source-end arc template (0.94). Hypothesis test fusion scores: branch 1, S1=0.21; branch 2, S2=0.98; branch 3, S3=0.18; branch 4, S4=0.15. The system output fault branch number is 2.

[0183] Compared to the traditional Fast Fourier Transform (FFT) + Convolutional Neural Network (CNN) approach, this scheme completes the entire identification and localization process within 10ms of the first half-cycle, while traditional schemes typically require accumulating 3 to 5 complete cycles (60-100ms) of data to provide a reliable conclusion. Furthermore, this scheme correctly identified the circuit as a series arc, whereas the FFT-based scheme, due to frequency resolution limitations, misidentified it as a normal operating state in this scenario.

[0184] The experimental results of the above embodiments show that, compared with the traditional FFT+CNN method, the method of the present invention has a higher fault detection rate and a lower false positive rate under the short time window condition of the first half-cycle. Those skilled in the art will understand that the specific recognition accuracy and positioning accuracy may vary depending on the power distribution system topology, load type, noise environment, and edge device configuration.

[0185] As a comparison, in the same four-branch system, if a parallel arc fault occurs in branch 3, its characteristics differ significantly from those of a series arc. The parallel arc has a larger pulse amplitude, with a peak value of 0.5 to 0.8, a wider frequency distribution (significant energy across the entire frequency range from 5kHz to 500kHz), and denser pulse intervals (8 to 12 pulses per half-cycle). The posterior probabilities output by the classification network are: normal = 0.01, series arc = 0.05, parallel arc = 0.89, high-resistance grounding = 0.05, correctly identifying it as a parallel arc.

[0186] According to one aspect of this application, the acquisition and synchronous preprocessing of multi-branch arc current signals specifically includes:

[0187] High-frequency current sensors deployed in each branch circuit of the distribution box are used to collect current data in parallel at a sampling rate of no less than 2MHz. All acquisition channels share the same hardware clock source to ensure strict synchronization of sampling times across branches. The current waveform data acquired from all N branches under the distribution box within the sampling period are organized into an original multi-branch current matrix, where rows correspond to branch numbers and columns correspond to sampling times.

[0188] For the original multi-branch current matrix, firstly, the sub-microsecond clock drift caused by sensor response delay is compensated by detecting the timestamp deviation of the zero-crossing point of the power frequency current in each branch, thus achieving fine clock alignment. Then, a fourth-order Butterworth low-pass filter with a cutoff frequency of 800kHz is used to perform anti-aliasing filtering on the signals of each branch, suppressing out-of-band noise interference above the Nyquist frequency, resulting in a clock-aligned current matrix.

[0189] The clock-aligned current matrix is ​​obtained, and the continuous current waveform is divided into independent power frequency half-cycle segments based on the zero-crossing point of the power frequency voltage. For each half-cycle segment, its fundamental current amplitude is used as a normalization reference, and the instantaneous current value is divided by this reference amplitude to eliminate the influence of differences in load size between different branches on subsequent feature extraction. After the above processing, a set of synchronous current signals is obtained, where each element is a normalized current sequence of a branch within one half-cycle.

[0190] According to one aspect of this application, the high-resolution time-frequency joint characterization of the first half-cycle is specifically as follows:

[0191] To address the problem of insufficient time-frequency resolution caused by the short observation window of the first half-cycle of an electric arc (less than or equal to 10 ms), a sparse parameterized time-frequency atom library conforming to the physical characteristics of electric arc discharge is constructed. An orthogonal matching pursuit algorithm is used to achieve super-resolution spectrum estimation. At the same time, sparse position representations of transient pulses in the time domain are extracted, ultimately forming high-resolution time-domain pulse features and high-resolution frequency-domain envelope features.

[0192] From the synchrotron current signal set, for the normalized current sequence of each branch, a first half-cycle observation window of 10ms is extracted, starting from the zero-crossing point of the power frequency voltage. For a 50Hz system, the first half-cycle window is 10ms; for a 60Hz system, the first half-cycle window is approximately 8.33ms. This window contains the earliest possible moment when the arc may ignite, and is a key data segment for achieving rapid detection. The first half-cycle data extracted from each branch is organized into a first half-cycle current window set.

[0193] To address the sparse distribution of arc current signals in the time-frequency domain, a parameterized time-frequency atom library is constructed for super-resolution characterization. The high-frequency components generated during arc discharge are mainly concentrated in several discrete frequency bands and exhibit exponentially decaying time-domain envelope characteristics. Based on this, Gaussian-modulated complex exponential atoms are designed as the basic characterization units.

[0194] Each atom is uniquely determined by four parameters: center frequency, bandwidth parameter, time center, and attenuation coefficient. The center frequency is divided into 64 discrete values ​​in a logarithmic interval within the range of 5kHz to 500kHz; the bandwidth parameter ranges from 10% to 50% of the center frequency in 5 increments; the time center covers the entire first half-cycle window with 128 positions; and the attenuation coefficient is set to three levels: fast attenuation, medium attenuation, and slow attenuation. The combination of these parameters constitutes a parameterized time-frequency atom library containing approximately 120,000 atoms. The redundancy of this atom library provides ample degrees of freedom for subsequent sparse decomposition.

[0195] The current sequences of each branch in the first half-cycle current window are obtained, and sparse decomposition is performed using an improved orthogonal matching pursuit algorithm with parameterized time-frequency atom library as the characterization basis.

[0196] The specific implementation process is as follows: Initialize the residual signal as the original current sequence, and iteratively perform the following operations: Calculate the inner product of the current residual and all atoms in the atom library; select the atom with the largest absolute value of the inner product and add it to the selected atom set; re-estimate the combination coefficients of the selected atoms using the least squares method; and update the residual to the original signal minus the weighted reconstruction of the selected atoms. The iteration terminates when the residual energy is less than 5% of the original signal energy or the number of selected atoms reaches a preset upper limit (32).

[0197] After iteration, the selected atoms are arranged according to their center frequencies, and the corresponding combination coefficient amplitudes are extracted to form the super-resolution spectral representation of that branch. The frequency resolution of this spectral representation is determined by the frequency partitioning accuracy of the atom library, which is approximately eight times the resolution of traditional FFT, breaking through the Heisenberg uncertainty principle limitation of short-window observation. The super-resolution spectral representations of each branch are then summarized into a sparse spectral coefficient matrix.

[0198] The arc combustion process is accompanied by the random occurrence of high-frequency spike pulses, and the time-domain location of these pulses carries key information about the arc combustion moment. Current sequences from each branch are collected from the first half-cycle current window, and transient pulse components are extracted using a morphological filter.

[0199] First, a flat structural element with a length of 20 microseconds is designed. Morphological opening and closing operations are sequentially performed on the current sequence to obtain a smooth fundamental envelope estimate. This envelope estimate is then subtracted from the original current sequence to obtain the transient residual signal. The absolute value of the transient residual signal is taken and compared with an adaptive threshold, which is three times the standard deviation of the residual signal. Local maxima exceeding the threshold are marked as impulse events, and their occurrence time and peak amplitude are recorded.

[0200] The detected pulse events are sorted by time, and the pulse occurrence time is used as the x-axis and the pulse peak amplitude is used as the y-axis to form the time-domain pulse sparse representation vector of that branch. The pulse sparse representations of each branch are summarized into a time-domain pulse event matrix, where each row of the matrix corresponds to a branch and each column corresponds to a pulse event slot.

[0201] By combining the sparse spectral coefficient matrix and the time-domain impulse event matrix, a complete time-frequency joint representation is constructed. For each branch, its super-resolution spectral coefficient vector is used as the frequency domain feature component, and its sparse impulse event vector is used as the time domain feature component. Both are standardized with zero mean and unit variance, and then concatenated along the channel dimension. The concatenated feature vector simultaneously retains the frequency domain energy distribution information and the time domain impulse position information, constituting the high-resolution time-domain impulse feature and high-resolution frequency-domain envelope feature of that branch.

[0202] According to one aspect of this application, the physical asynchronous alignment and cross-domain fusion of time-frequency features are specifically as follows:

[0203] Arc discharge has two fundamentally different time scale characteristics: on a microscale, the establishment and extinction of the arc channel occur on the order of tens of microseconds, corresponding to random high-frequency pulses in the time domain; on a macroscale, the average burning intensity of the arc changes periodically with the amplitude of the power frequency current, and its characteristic spectrum requires an observation window of a full cycle or half cycle to be stably estimated.

[0204] Establish a dual-timescale physical model and define the microscopic time resolution δ. micro The time resolution is 10 microseconds, with a macroscopic time resolution of δ. macro The interval is 2.5 milliseconds, or one-quarter of a power frequency half-cycle. The microscale is used to describe the precise timing of each pulse event in the high-resolution time-domain pulse features, while the macroscale is used to describe the effective representation interval of the high-resolution frequency-domain envelope features. This dual-scale model provides the physical basis for subsequent asynchronous alignment, yielding a set of time-scale parameters.

[0205] The temporal pulse event matrix is ​​obtained from the high-resolution temporal pulse features, and each detected pulse event is precisely timestamped. A subsampling point time estimation method based on quadratic interpolation is adopted: a quadratic polynomial fitting is constructed using the amplitude of the pulse peak point and its two adjacent sampling points, and the precise time corresponding to the polynomial extremum point is calculated. The accuracy of this time can reach one-tenth of the sampling interval.

[0206] All pulse events detected by each branch are arranged according to their precise timestamps to form a pulse event timestamp sequence. At the same time, the peak amplitude, rise edge slope, and duration of each pulse event are recorded as auxiliary attributes to form a pulse event attribute table.

[0207] The sparse spectral coefficient matrix in the high-resolution frequency domain envelope feature is obtained, and the physical time interval it represents is analyzed. Since the spectral coefficients are obtained by orthogonal matched pursuit from the first half-cycle window of 10 ms, they represent the average intensity of arc combustion within this window and do not have sub-millisecond time positioning capability.

[0208] Based on the time scale parameter set, the first half-cycle window is divided into four segments of length δ. macro A macroscopic time period of 2.5 ms is used. By analyzing the distribution of the time center parameters of the selected atoms, the main contribution interval of the spectral energy is estimated. If more than 70% of the selected atoms' time centers are concentrated in a certain macroscopic time period, then this time period is marked as the effective characterization interval of the frequency domain envelope; otherwise, the entire first half-cycle window is taken as the effective interval. The effective frequency domain interval labels for each branch are obtained.

[0209] By combining the timestamp sequence of pulse events with the effective frequency domain interval labeling, an asynchronous correspondence between time domain features and frequency domain features is established.

[0210] The alignment mapping rule is defined as follows: For events occurring in the time domain at time t... pulse For a given pulse event, find its corresponding macroscopic time period number k, and associate the pulse event with the frequency domain envelope features of the kth macroscopic time period. If a macroscopic time period contains multiple pulse events, then perform weighted aggregation using the pulse peak amplitude as the weight; if a macroscopic time period contains no pulse events, then set the time domain features of that time period to a zero vector.

[0211] The above correspondence is expressed in matrix form, constructing an asynchronous alignment mapping matrix. This matrix has four rows equal to the number of pulse events and four columns equal to the number of macroscopic time periods. The matrix elements are normalized alignment weights. This matrix transforms the microscopic temporal information of time-domain pulses into a macroscopic temporal representation compatible with the frequency-domain envelope, eliminating the time-scale mismatch problem caused by direct splicing.

[0212] Based on the asynchronous alignment mapping matrix, cross-domain attention weighted fusion is performed on time-domain features and frequency-domain features.

[0213] First, the time-domain impulse event matrix is ​​projected onto a macroscopic time scale using an asynchronous alignment mapping matrix to obtain time-domain aggregated features aligned with the frequency-domain envelope time. A bidirectional cross-domain attention mechanism is then constructed: using the time-domain aggregated features as the query vector and the frequency-domain envelope features as the key vector, the attention weight from the time domain to the frequency domain is calculated; simultaneously, using the frequency-domain envelope features as the query vector and the time-domain aggregated features as the key vector, the attention weight from the frequency domain to the time domain is also calculated.

[0214] Attention weights are calculated using a scaled dot product, with the scaling factor being the square root of the feature dimension. The temporal aggregated features are added to their attention weights in the frequency domain to obtain the temporal enhanced features; similarly, the frequency domain envelope features are added to their attention weights in the temporal domain to obtain the frequency enhanced features. Both types of enhanced features retain cross-domain interaction information, resulting in cross-domain enhanced temporal features and cross-domain enhanced frequency features.

[0215] Cross-domain enhanced time-domain features and cross-domain enhanced frequency-domain features are deeply fused to generate the final physically consistent representation. A gated fusion unit is used to control the contribution ratio of the two types of features: the two types of features are concatenated and mapped to a gated vector of the same length as the original features through a single-layer fully connected network. The gated vector is activated by a Sigmoid function and takes values ​​ranging from 0 to 1.

[0216] The fusion calculation method is as follows: the gate vector is element-wise multiplied by the cross-domain enhanced time-domain feature, and then the gate vector complement (1 minus the gate vector) is element-wise multiplied by the cross-domain enhanced frequency-domain feature. This gating mechanism allows the network to adaptively select more discriminative time-domain or frequency-domain information on different feature dimensions.

[0217] The fused feature vectors are then subjected to layer normalization to obtain a physically consistent fused feature vector. This vector eliminates the time-scale aliasing problem in traditional synchronous fusion methods and accurately reflects the time-frequency joint characteristics of the arc combustion process.

[0218] According to one aspect of this application, a lightweight network provides fine-grained identification of multiple types of fault arcs, specifically:

[0219] To address the issue of boundary collapse in the discrimination of multiple types of electric arcs under the constraint of edge device parameter size (less than 500KB), a lightweight recognition network based on prototype dynamic anchoring and contrastive learning is designed. Within a limited parameter budget, the feature space distance between series arcs, parallel arcs, high-resistance grounding arcs and normal states is maximized to obtain arc type labels and type confidence vectors.

[0220] Physically consistent fusion feature vectors are obtained and deep feature encoding is performed through a lightweight classification network. The backbone network uses depthwise separable convolutions as the basic building blocks, decomposing standard convolutions into a cascade of channel-wise and pointwise convolutions, compressing the number of parameters to one-eighth to one-tenth of that of standard convolutions.

[0221] The network structure comprises four depthwise separable convolutional blocks, each consisting of a cascaded sequence of channel-wise convolution, batch normalization, ReLU6 activation, pointwise convolution, batch normalization, and ReLU6 activation. The number of channels obtained in each block is 32, 64, 128, and 256 respectively, doubling with each layer to extract multi-scale abstract features. The last convolutional block yields a fixed-length feature vector, denoted as the deep-encoded feature vector, which is compressed using global average pooling. The total number of parameters in the backbone network is kept below 120KB.

[0222] To address the issue of overlapping feature spaces among different arc types under lightweight constraints, a class prototype anchoring mechanism is introduced to enhance inter-class separability. A learnable prototype vector is maintained for each arc type and normal state, with the prototype vector dimension being the same as the deep encoding feature vector. The arc types include series arcs, parallel arcs, and high-resistance grounding arcs.

[0223] The prototype vector is dynamically updated during training: In each training batch, the mean of the deep encoding feature vectors of all samples belonging to the same category is calculated, and the prototype vector of the corresponding category is updated using an exponential moving average method, with a momentum coefficient set to 0.9. The prototype vector remains unchanged during the inference phase.

[0224] The prototype vectors of the four categories are organized into a class prototype anchor matrix, which marks the reference center position of each category in the embedding space, providing an anchoring benchmark for subsequent classification decisions and comparative learning.

[0225] To further widen the feature distance between highly confused category pairs such as series arcs and high-resistance grounding arcs, a contrastive learning auxiliary loss is introduced on top of the classification loss.

[0226] For each input sample's deep encoded feature vector, calculate its Euclidean distance to each prototype vector in the class prototype anchor matrix. A positive sample pair is defined as the pairing of the current sample's feature with its true class prototype, and a negative sample pair is the pairing of the current sample's feature with other class prototypes. The contrastive loss uses a triplet form: the distance between positive sample pairs must be less than the distance between negative sample pairs by at least one margin, with the margin set to 0.5.

[0227] Contrast loss encourages the network to learn feature representations that exhibit clear intra-class clustering and inter-class separation in the embedding space, effectively mitigating the collapse of the discrimination boundary caused by lightweight parameter constraints. The contrast loss and cross-entropy classification loss are weighted and summed in a 1:1 ratio to form the total training loss.

[0228] Obtain the deep encoding feature vector and class prototype anchor matrix, and calculate the similarity score between the sample feature vector and the prototype of each class. The similarity is expressed in the form of negative Euclidean distance, that is, the smaller the distance, the higher the similarity.

[0229] Softmax normalization is applied to the similarity scores of the four categories to obtain posterior probability estimates for each category, resulting in a type confidence vector. The category index corresponding to the maximum value in the confidence vector is taken as the final prediction result, yielding the arc type label.

[0230] At the same time, a confidence threshold is set, such as 0.7. If the maximum confidence is lower than this threshold, the sample is marked as uncertain and needs to be further judged in conjunction with subsequent cycle data to avoid false alarms under low confidence conditions.

[0231] According to one aspect of this application, reverse analysis and fault location of multi-branch propagation paths specifically includes:

[0232] Acquire a set of synchronous current signals. If the arc type label indicates the presence of a faulty arc, initiate a multi-branch location process. Extract high-frequency components from the preprocessed current of each branch for propagation path analysis.

[0233] A fourth-order Butterworth bandpass filter with a center frequency of 150kHz and a bandwidth of 100kHz was designed to filter the current sequences of each branch, extracting high-frequency components within the characteristic frequency band of the arc. The filtered high-frequency currents of each branch are organized into a multi-branch high-frequency component matrix, with rows corresponding to branch numbers and columns corresponding to sampling times. This matrix retains complete time information for phase analysis.

[0234] Obtain the high-frequency component matrix of multiple branches and calculate the relative phase delay of the high-frequency components between any two branches. The high-frequency components generated by the electric arc propagate from the fault point along the power distribution line to each detection point. The difference in propagation distance leads to different arrival times at each detection point, which manifests as a phase delay difference.

[0235] The relative time delay between branch pairs is estimated using a cross-correlation function: A normalized cross-correlation function is calculated for the high-frequency component sequences of branch i and branch j, and the time delay value corresponding to the peak cross-correlation value is taken as the relative phase delay τ of the branch pair. ij To improve the accuracy of time delay estimation, parabolic interpolation is used near the peak of cross-correlation to obtain accurate time delay at the subsampling point level.

[0236] Traverse all branch pairs and construct a phase delay difference matrix. This matrix is ​​an N-order antisymmetric matrix, where N is the number of branches, diagonal elements are zero, and off-diagonal elements are τ. ij This indicates the phase lead time of branch i relative to branch j.

[0237] The high-frequency component matrices of multiple branches were obtained, and the differences in the spectral morphology of the high-frequency components in each branch were analyzed. When the high-frequency components of the electric arc propagate in different branches, they undergo frequency-selective attenuation due to the influence of the distributed parameters of the line (resistance, inductance, capacitance), which manifests as spectral distortion.

[0238] Short-time Fourier transform is performed on the high-frequency components of each branch to obtain their amplitude spectrum. The branch with the strongest amplitude is taken as the reference branch and assumed to be a candidate for the faulty branch. The amplitude spectrum ratio of each other branch relative to the reference branch is calculated. This ratio approximately characterizes the amplitude-frequency characteristics of the transfer function from the reference branch to the target branch.

[0239] Analyze the frequency characteristics of the transfer function: if the low-frequency attenuation is greater than the high-frequency attenuation, it indicates that the propagation path contains more inductive elements; if the high-frequency attenuation is greater than the low-frequency attenuation, it indicates that the propagation path contains more capacitive elements. The transfer function characteristics of each branch are parameterized into three parameters: low-frequency attenuation coefficient, high-frequency attenuation coefficient, and corner frequency, forming a spectral distortion feature vector set.

[0240] By combining the phase delay difference matrix and the spectral distortion feature vector set, a multi-evidence fusion strategy is adopted to locate the fault branch.

[0241] A framework for testing the faulty branch hypothesis is constructed: For each branch k, it is assumed to be a faulty branch, and the consistency of this hypothesis with observational evidence is verified. Regarding phase delay evidence, if branch k is a faulty branch, then the phase delay of all other branches relative to branch k should be non-negative. High-frequency components propagate outward from the fault point, and the arrival times of other branches are delayed. The proportion of branches that do not satisfy this constraint is calculated as the phase violation degree. Regarding spectral distortion evidence, the high-frequency components of the faulty branch should have minimal distortion and not be attenuated by the propagation path. The correlation between the spectrum of branch k and the ideal arc spectrum template is calculated as the distortion matching degree.

[0242] For each branch hypothesis, the phase violation degree is inverted and converted into a consistency score, which is then weighted and fused with the distortion matching degree, with weights set to 0.6 and 0.4 respectively. The branch with the highest fusion score is identified as the faulty branch, and its number is used as the faulty branch number. At the same time, the normalized value of the fusion score of this branch is obtained as the location confidence, which is used by the upper-level decision system to evaluate the reliability of the location results.

[0243] This scheme employs a two-stage hierarchical sparse decomposition strategy and a depthwise separable convolutional lightweight network. By constructing a dimensionality-reduced sparse probe atom library, it first quickly identifies active frequency bands and then performs local fine decomposition, avoiding invalid searches in the full atom library. This significantly reduces the computational complexity of traditional super-resolution algorithms from the cubic level, enabling real-time feature extraction within the first half-cycle and solving the problem of insufficient computing power on edge devices. It also resolves the contradiction between high computational load and real-time performance at the edge.

[0244] This scheme proposes a kernel embedding and bidirectional consistency alignment mechanism based on the pulse point process. By introducing a learnable Gaussian kernel function, microsecond-level discrete time-domain pulses are transformed into continuous intensity functions, making them isomorphic to the millisecond-level frequency domain envelope in both mathematical form and physical time scale. Combined with bidirectional consistency verification, noise interference is eliminated, ensuring accurate alignment of time-frequency features in a physical sense. This effectively solves the problem of fine-grained faults caused by asynchronous feature aliasing, such as the difficulty in distinguishing between series connection and high-impedance grounding, thus improving recognition accuracy. It also addresses the aliasing and distortion problems caused by asynchronous physical scales of time-frequency features.

[0245] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for identifying and locating the edge of multi-type fault arcs, characterized in that, include: Acquire the synchronous current signal of the multi-branch power distribution system and preprocess it to obtain a synchronous current signal set; The first half-cycle window of the synchronous current signal set is extracted, a parameterized time-frequency atom library is constructed and sparse decomposition is performed to obtain high-resolution frequency domain envelope features and extract high-resolution time domain pulse features. Establish a time-scale mapping relationship between high-resolution temporal pulse features and high-resolution frequency-domain envelope features, and perform alignment and cross-domain fusion accordingly to generate a physically consistent fused feature vector. The physical consistency fusion feature vector is input into a pre-configured lightweight classification network to obtain the arc type label; In response to the presence of a fault indicated by the arc type label, the fault branch number is determined based on the propagation characteristics of the high-frequency components extracted from the synchronous current signal set. Establishing a time-scale mapping relationship between high-resolution time-domain pulse features and high-resolution frequency-domain envelope features includes: Model discrete pulse events in high-resolution time-domain pulse features as time-domain point processes; By using a kernel function containing a learnable bandwidth parameter, discrete pulse events are embedded into continuous-time pulse intensity functions, transforming discrete time-domain features into continuous representations that are isomorphic to high-resolution frequency-domain envelope features in the physical time dimension. Establishing a time-scale mapping relationship also includes building a two-way consistent alignment mechanism: The high-resolution frequency domain envelope features are resampled to the same time sampling position as the continuous-time pulse intensity function to obtain the frequency domain energy distribution vector; Calculate the forward alignment weight with reference to the frequency domain energy distribution vector and the reverse alignment weight with reference to the continuous-time pulse intensity function, respectively. Based on the combination of forward alignment weights and reverse alignment weights, a bidirectional consistent alignment weight is generated, and a mapping relationship is constructed accordingly.

2. The method according to claim 1, characterized in that, Acquire and preprocess the synchronization current signals of a multi-branch power distribution system to obtain a synchronization current signal set, including: By using a shared clock source, the current of each branch of the multi-branch power distribution system is synchronously collected to construct the original multi-branch current matrix; Clock alignment compensation is performed on the original multi-branch current matrix based on the timestamp deviation of the zero-crossing point of the power frequency current, and anti-aliasing filtering is performed to obtain the clock-aligned current matrix. The clock-aligned current matrix is ​​divided into half-cycle segments based on the zero-crossing point of the power frequency voltage. The half-cycle segments are normalized with the fundamental current amplitude as a reference to obtain the synchronous current signal set.

3. The method according to claim 1, characterized in that, The parameterized time-frequency atom library consists of Gaussian-modulated complex exponential atoms, which are determined by the following parameters: Center frequency, bandwidth parameters, time center, and attenuation coefficient; The center frequency is discretely distributed at logarithmic intervals, and the time center covers the first half-cycle window. Perform sparse decomposition to obtain high-resolution frequency domain envelope features, including: The initial residual signal is a current sequence from the synchronous current signal set; The following steps are executed iteratively: calculate the inner product of the residual signal and each atom in the parameterized time-frequency atom library, select the atom with the largest absolute value of the inner product and add it to the selected atom set, update the combination coefficients of the selected atom set using the least squares method, and update the residual signal; The iteration stops when the preset termination condition is met, and a super-resolution spectrum is constructed based on the selected set of atoms and their combination coefficients as a high-resolution frequency domain envelope feature.

4. The method according to claim 3, characterized in that, Sparse decomposition is performed to obtain high-resolution frequency domain envelope features. A two-stage hierarchical strategy is adopted, including: A sparse detector atom library is constructed based on a parameterized time-frequency atom library. The projected inner product of the synchronous current signal set and each detector atom in the sparse detector atom library is calculated to obtain the activity index of each frequency band. A set of active frequency bands is formed by selecting a predetermined number of frequency bands with the highest activity index, and atoms belonging to the active frequency band set are extracted from the parameterized time-frequency atom library to form a local atom sub-library. Using a local atomic sub-library as a basis, orthogonal matched pursuit decomposition is performed on the synchronous current signal set to obtain high-resolution frequency domain envelope features.

5. The method according to claim 4, characterized in that, The sparse probe atom library is constructed in the following way: The center frequency parameters of the parameterized time-frequency atom library are sparsely downsampled to retain discrete frequency points with logarithmic equal intervals. The time center parameter is fixed at the midpoint of the first half-cycle window, and the bandwidth parameter and attenuation coefficient are fixed at preset values ​​to generate a sparse probe atom library with fewer atoms than the parameterized time-frequency atom library.

6. The method according to claim 1, characterized in that, Extracting high-resolution temporal pulse features, including: The fundamental envelope estimate is obtained by performing opening and closing operations on the current sequence in the synchronous current signal set using morphological filters. The difference between the current sequence and the fundamental envelope estimate is calculated to obtain the transient residual signal; Local maxima exceeding an adaptive threshold in transient residual signals are identified, marked as pulse events, and their timestamps and peak amplitudes are recorded to form high-resolution temporal pulse features.

7. The method according to claim 1, characterized in that, Calculate the forward alignment weights and reverse alignment weights separately, including: Calculate the normalized product of the frequency domain energy distribution vector and the continuous-time pulse intensity function at each time step; The weights that are positively correlated with the distribution trend of the frequency domain energy distribution vector are defined as positive alignment weights, which characterize the degree of verification of the existence of the time domain pulse by the frequency domain energy. The weights that are positively correlated with the distribution trend of the continuous-time pulse intensity function are defined as reverse alignment weights, which characterize the degree of verification of the existence of frequency-domain energy by the time-domain pulse.

8. The method according to claim 1, characterized in that, The lightweight classification network consists of cascaded depthwise separable convolutional blocks, which contain sequentially connected channel-wise convolutional layers and pointwise convolutional layers. Inputting the physically consistent fused feature vector into a pre-configured lightweight classification network includes: We use depthwise separable convolutional blocks to encode the physically consistent fused feature vectors, and then compress them through a global average pooling layer to obtain deep encoded feature vectors.

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