An online monitoring method for fastener loosening based on transformer vibration characteristics

Abstract

The present application relates to the technical field of vibration monitoring, in particular to an online monitoring method for fastener loosening based on transformer vibration characteristics, comprising the following steps: arranging vibration sensors in the areas of the box body, the iron core nail and the coil pressing plate of the transformer, continuously picking up vibration signals, cutting off the vibration signals according to a preset length, forming multiple time window vibration data, filtering the vibration data of each time window, and obtaining filtered time window vibration data. Based on the real-time cutting and filtering operation of the vibration signal, the continuity of the signal data and the isolation of the noise interference are ensured, and the stability and reliability of the subsequent feature extraction are enhanced. By extracting the multi-fractal spectrum parameters of the vibration signal in each time window and combining the kurtosis analysis of the entropy value variation, a multi-scale and structure-sensitive impact feature sequence is constructed, and the recognition ability for local weak disturbance and loosening-induced abnormalities is strengthened.

Description

Technical Field

[0001] This invention relates to the field of vibration monitoring technology, and in particular to an online monitoring method for fastener loosening based on transformer vibration characteristics. Background Technology

[0002] Vibration monitoring technology is a key engineering testing technology that senses, collects, analyzes, and identifies the dynamic response behavior of equipment during operation. It is widely used in industrial systems such as power, machinery, aerospace, transportation, and manufacturing.

[0003] Current technologies focus on monitoring and analyzing the fluctuation trends of single physical quantities such as acceleration, frequency, or displacement in the time or frequency domains, lacking the ability to deeply quantify changes in the complex structure of signals. In actual operation, judging the operating status solely through macroscopic indicators such as frequency domain peak drift and amplitude abrupt changes is insufficient to capture subtle signal disturbances caused by minor loosening or local connection instability, leading to missed early anomalies or delayed status assessments. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose an online monitoring method for fastener loosening based on transformer vibration characteristics.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: an online monitoring method for fastener loosening based on transformer vibration characteristics, comprising the following steps:

[0006] Vibration sensors are arranged in the transformer housing, core clamping nails and coil clamping plate areas to continuously pick up vibration signals. The vibration signals are truncated according to a preset length to form multiple time window vibration data. The vibration data of each time window is filtered to obtain the filtered time window vibration data.

[0007] The filtered vibration data of the time window is retrieved, and the multifractal spectrum parameter set of each time window is calculated for each segment of the filtered vibration data. The impact feature kurtosis sequence is calculated based on the multifractal spectrum parameter set.

[0008] Using the filtered time window vibration data, a spectrum transformation is performed on each data segment to identify the energy of the transformer core's working fundamental frequency. Simultaneously, the energy values ​​of each harmonic and subharmonic frequency band are extracted to form harmonic energy data. The proportion of the energy of the second harmonic and subharmonic in the fundamental frequency energy is calculated to obtain the proportion of nonlinear harmonic energy.

[0009] By integrating the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio, a normal fluctuation threshold range for the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio is set to form a fastener state reference parameter. The deviation between the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio and the fastener state reference parameter is compared to track the evolution trajectory and output the transformer fastener loosening state judgment.

[0010] Preferably, the steps for acquiring the vibration data within the time window are as follows:

[0011] Vibration sensors are installed in the transformer housing, core nails, and coil pressure plate areas to continuously collect all real-time vibration signals generated by the transformer housing, core nails, and coil pressure plate areas, thus obtaining continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas.

[0012] Based on the continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas, the continuous vibration signals are divided into time segments according to a set fixed duration to generate a segmented fixed-length vibration signal sequence.

[0013] Based on the segmented fixed-length vibration signal sequence, each segment of vibration signal is renumbered and identified according to the time index to generate time window vibration data.

[0014] Preferably, the step of obtaining the filtered time window vibration data is as follows:

[0015] Read all vibration signal values ​​within each time window of the vibration data, retrieve the amplitude sequence of the vibration signal within each time window, identify interference components and noise distribution characteristics, and truncate the vibration signal data of the time window using a high-pass filter and a low-pass filter to obtain the vibration signal data of the time window after preliminary filtering.

[0016] Based on the pre-filtered vibration signal data within the time window, the continuity of the signal waveform within each time window is detected, and the instantaneous pulses and distortion peaks in the waveform are located and identified. Band-stop filters are then applied sequentially to attenuate the signal, generating filtered vibration data within the time window.

[0017] Preferably, the steps for obtaining the multifractal spectral parameter set are as follows:

[0018] Read each segment of vibration signal from the filtered time window vibration data, and divide each segment of vibration signal into multiple subsequences of equal length to obtain the set of initial measure values ​​corresponding to each subsequence.

[0019] Calculate the multifractal spectrum entropy value based on the initial set of measure values;

[0020] Based on the multifractal spectrum entropy value, the entropy parameter results corresponding to all time windows are summarized in the order of time windows and combined into an ordered vector to represent the multifractal spectrum features of each time window, thereby generating a multifractal spectrum parameter set for each time window.

[0021] Preferably, the steps for obtaining the impact feature kurtosis entropy sequence are as follows:

[0022] Based on the multifractal spectrum parameter set and the original sample data of vibration signals within the time window, the mean of the current time window is calculated point by point based on the original sample data, and the squared deviation between each sample point and the mean is statistically analyzed. At the same time, the multifractal spectrum entropy value corresponding to the window is recorded, and the original statistical term set is generated.

[0023] Based on the original set of statistical terms, calculate the impact feature kurtosis value for each time window;

[0024] Based on the impact feature kurtosis entropy value, the impact feature kurtosis entropy values ​​corresponding to all time windows are integrated into an impact feature kurtosis entropy sequence in chronological order.

[0025] Preferably, the steps for acquiring the harmonic energy data are as follows:

[0026] Read each vibration signal from the filtered time window vibration data, expand each vibration signal according to the complete time axis and perform full-segment frequency domain conversion, output the frequency response curve corresponding to each signal segment and establish the amplitude spectrum structure corresponding to each frequency point to obtain the spectrum data of each time window.

[0027] Based on the spectral data of each time window, the characteristic frequency band index range within the frequency identification range is set, and the frequency point and amplitude at the working fundamental frequency of the transformer core are extracted accordingly. The frequency axis is matched and compared with the fundamental frequency standard frequency point to locate the position. At the same time, the amplitude coordinates are recorded and converted into energy values ​​to generate the fundamental frequency energy value of each time window.

[0028] Based on the fundamental frequency energy value of each time window, the corresponding segments of integer multiples of the fundamental frequency and non-integer interval frequencies above the fundamental frequency in the spectrum data are scanned to identify the frequency point positions and amplitude responses of all subharmonic and subharmonic frequency bands. The amplitude information of the corresponding frequency segments is converted into energy quantization results and combined to form the harmonic energy data of that time window.

[0029] Preferably, the step of obtaining the proportion of nonlinear harmonic energy is as follows:

[0030] Read the energy values ​​of the frequency bands corresponding to each time window in the harmonic energy data, sequentially filter out the energy values ​​of all frequency points marked as subharmonic frequency bands in each time window, summarize the energy values ​​of all frequency points of subharmonic frequency bands, calculate the sum as the total subharmonic energy of that time window, and generate the total subharmonic energy of each time window.

[0031] Based on the total subharmonic energy of each time window, the energy values ​​of all frequency points marked as subharmonic bands within the corresponding time window are extracted from the harmonic energy data. The energy points of this type of band are retrieved according to the frequency index position and accumulated one by one to form the total subharmonic energy of the time window. The total energy values ​​corresponding to the two bands are added together to obtain the nonlinear harmonic total energy of each time window.

[0032] Based on the total nonlinear harmonic energy of each time window, the fundamental frequency energy value under the same time window is called, the ratio of the total nonlinear harmonic energy to the fundamental frequency energy value is calculated, and the ratio value is arranged into a sequence structure corresponding to the time order to generate the nonlinear harmonic energy proportion.

[0033] Preferably, the step for determining the loose state of the transformer fasteners is as follows:

[0034] Read all time-series values ​​of the impact feature kurtosis entropy sequence and the nonlinear harmonic energy ratio, synchronize and align the two sequences window by window, and combine the impact feature kurtosis value and the nonlinear harmonic energy ratio under each time window into a feature vector according to the time index to generate a fused feature vector sequence.

[0035] Based on the fused feature vector sequence, according to the upper and lower boundary values ​​of the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy under normal operating conditions of transformer fasteners in historical samples, the maximum fluctuation range of each index in the typical state range is extracted, and this range is set as the standard condition range for stable operation to generate fastener state benchmark parameters.

[0036] Based on the fastener state reference parameters, deviation detection is performed on each set of time window data in the fused feature vector sequence, the relative change amplitude between the fastener state reference parameters is calculated, and the continuous change trend is sorted by time axis and fitted with trajectory curve to determine whether it is stably maintained within the normal threshold range, thus forming a transformer fastener loosening state determination.

[0037] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0038] This invention, based on real-time truncation and filtering of vibration signals, ensures the continuity of signal data and isolation from noise interference, enhancing the stability and reliability of subsequent feature extraction. By extracting multi-fractal spectrum parameters from the vibration signals within each time window and combining this with kurtosis analysis of entropy changes, a multi-scale, structure-sensitive impact feature sequence is constructed, strengthening the ability to identify anomalies caused by local weak disturbances and loosening. In the frequency domain, the distribution characteristics of the fundamental frequency and nonlinear harmonic components are clarified through spectral transformation, while quantitative analysis of the energy proportion of subharmonic and partial harmonic frequency bands is performed, achieving a joint assessment of signal complexity and harmonic disturbance degree. By combining the kurtosis entropy sequence and the nonlinear harmonic energy proportion to form a state feature vector and constructing a normal fluctuation threshold range, a quantifiable benchmark model of fastening state is established. Combined with trajectory evolution for deviation tracking, dynamic determination of fastener structural state changes is achieved. This improves the response accuracy and monitoring coverage for minor anomalies and early loosening of transformer structures. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] Please see Figure 1 This invention provides a technical solution: an online monitoring method for fastener loosening based on transformer vibration characteristics, comprising the following steps:

[0042] Vibration sensors are arranged in the transformer housing, core clamping nails and coil clamping plate areas to continuously pick up vibration signals. The vibration signals are truncated according to a preset length to form multiple time window vibration data. The vibration data of each time window is filtered to obtain the filtered time window vibration data.

[0043] Retrieve the vibration data of the filtered time window, calculate and obtain the multifractal spectrum parameter set for each time window for each segment of the filtered time window vibration data, and calculate the impact feature kurtosis entropy sequence based on the multifractal spectrum parameter set.

[0044] Using the filtered vibration data within the time window, a spectrum transformation is performed on each data segment to identify the energy of the transformer core's fundamental frequency. Simultaneously, the energy values ​​of each harmonic and subharmonic frequency band are extracted to form harmonic energy data. The proportion of the energy of the second and third harmonics in the fundamental frequency energy is calculated to obtain the proportion of nonlinear harmonic energy.

[0045] By integrating the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy, and setting the normal fluctuation threshold range of the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy, a fastener state benchmark parameter is formed. The deviation between the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy and the fastener state benchmark parameter is compared, the evolution trajectory is tracked, and the transformer fastener loosening state judgment is output.

[0046] The steps for obtaining vibration data within a time window are as follows:

[0047] Vibration sensors are installed in the transformer housing, core nails, and coil pressure plate areas to continuously collect all real-time vibration signals generated by the transformer housing, core nails, and coil pressure plate areas, thus obtaining continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas.

[0048] Based on the continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas, the continuous vibration signals are divided into time segments according to a set fixed duration to generate a segmented fixed-length vibration signal sequence.

[0049] Based on the segmented fixed-length vibration signal sequence, each segment of vibration signal is renumbered and identified according to the time index to generate time window vibration data.

[0050] Specifically, piezoelectric vibration sensors should be installed on key pressure plate locations that directly contact the coils and transmit the clamping force, such as the transformer tank surface, the core clamping nails (especially those bearing the main clamping force), and the coil clamping plates. The sampling frequency of these sensors should be set. For example, considering that the transformer's power frequency is 50Hz, and its main vibration harmonics and abnormal vibration frequencies that may be caused by loosening are typically in the range of several hertz to several kilohertz, according to the Nyquist theorem, the sampling frequency should be at least twice the highest frequency of interest, with a certain margin. Therefore, a sampling frequency of at least twice the highest frequency of interest can be set. The frequency is set to 10kHz or higher, such as 20kHz, to ensure that vibration information up to 10kHz is captured without distortion. The sensor is connected to the industrial control computer via a data acquisition card. The industrial control computer controls the data acquisition card to continuously and in real time pick up the raw voltage or acceleration values ​​of vibration signals generated by all installed sensors in the enclosure, core nail, and coil pressure plate areas. These signals are continuous in time and faithfully reflect the instantaneous vibration state of the corresponding monitoring point. By summarizing these raw vibration signal streams from different locations, a continuous vibration signal covering the transformer enclosure, core nail, and coil pressure plate areas is obtained.

[0051] Based on the continuous vibration signals from the transformer tank, core clamping nails, and coil clamping plate areas, each continuous vibration signal acquired from each sensor channel is independently divided into time segments. A pre-set fixed duration is used for each segmentation. This fixed duration must balance the frequency resolution requirements of the signal analysis with the real-time requirements. For example, if the transformer's operating frequency is 50Hz and its period is 0.02 seconds, a fixed duration can be set to ensure that the extracted time segments contain enough operating frequency periods for stable spectrum analysis and to capture the gradual changes in the fault evolution process. The duration is 1 second, meaning each time segment will contain 50 power frequency cycles. This duration selection also takes into account the data length requirements of subsequent multifractal spectrum analysis. If higher frequency transient impacts are the focus and computational resources allow, the duration can be appropriately shortened, such as by 0.5 seconds. Conversely, if lower frequency vibration characteristics need to be analyzed, the duration can be appropriately extended, such as by 2 seconds. In practice, once this fixed duration is set, it remains unchanged throughout the entire monitoring process to ensure consistency in the length of each time segment. Each continuous vibration signal is processed according to this determined fixed duration. (For example, 1 second) Starting from the starting point, the data is divided sequentially to form a series of time segments that do not overlap at the beginning and end or partially overlap as needed (for example, the overlap rate is 50%, that is, a 1-second data segment is taken every 0.5 seconds). The segments divided by all channels at the same time constitute a batch. This process is repeated continuously to generate a fixed-length vibration signal sequence after the segments are connected in time or moved according to a set step size.

[0052] Based on the segmented fixed-length vibration signal sequence, each segment of fixed-length vibration signal obtained from different sensor channels and different time points is systematically organized and labeled. A unique time index is assigned to each vibration signal segment. This time index can be based on the starting sampling time point of the signal segment. For example, if the first signal segment starts from time... Start, duration is Then its time index can be denoted as If the second signal immediately follows, the index is... Similarly, each vibration signal segment is renumbered. This number can be a globally unique serial number or a composite number combining sensor location information and time index, such as "Sensor A-Window 001", "Sensor B-Window 001", and then "Sensor A-Window 002", etc. The identification information further explains the source of the vibration signal segment, such as the specific physical location of the sensor (e.g., "upper left corner of the box", "core pressure nail No. 3", "middle of the coil pressure plate") and the sequence number of the time segment in the entire continuous monitoring process. The original vibration amplitude sequence (i.e., the continuous sampling point values ​​that constitute the signal segment) is integrated with these numbers, time indexes, and identification information to form a structured data unit. Each such data unit is a time window vibration data. All these units together constitute the time window vibration dataset required for subsequent analysis.

[0053] The steps for obtaining the filtered time window vibration data are as follows:

[0054] Read all vibration signal values ​​within each time window of the vibration data, retrieve the amplitude sequence of the vibration signal within each time window, identify interference components and noise distribution characteristics, and truncate the vibration signal data of the time window using a high-pass filter and a low-pass filter to obtain the vibration signal data of the time window after preliminary filtering.

[0055] Based on the vibration signal data of the time window after preliminary filtering, the continuity of the signal waveform in each time window is detected, the instantaneous pulses and distortion peaks in the waveform are located and identified, and the signal is attenuated by applying a band-stop filter in sequence to generate the vibration data of the time window after filtering.

[0056] Specifically, the vibration signal values ​​within each time window of the vibration data are read. This involves retrieving the complete vibration signal amplitude time series from all sampling points within each independent time window, and then performing preliminary identification of interference components and noise distribution characteristics. This identification process includes analyzing the power spectral density of the signal to observe whether there are known fixed-frequency interferences unrelated to the transformer's operating state, such as specific high-frequency noise introduced by the control system's switching actions, or mechanical vibrations transmitted from other nearby large rotating equipment. The overall energy level of background noise within the current time window and its approximate frequency domain distribution are also assessed to identify the frequency bands primarily affected by noise. Subsequently, a digital filter is used to truncate the vibration signal data within the time window at the boundary frequencies. First, a high-pass filter is applied with a cutoff frequency of... The setting principle is to effectively filter out potential DC bias, slow sensor drift caused by changes in ambient temperature, and extremely low-frequency background vibrations unrelated to the target frequency range for transformer structural loosening diagnosis. For example, if the monitoring system's sensors exhibit slow baseline drift, or if there are ground micro-vibrations with frequencies below 5Hz in the environment, then... The frequency can be set to 10Hz. This value is determined based on the spectral analysis of vibration signals collected from the transformer under normal operating conditions and no-load conditions. A frequency point is selected that can effectively suppress the aforementioned low-frequency interference without affecting the transformer's lowest effective operating characteristic frequency (such as the power frequency of 50Hz or its half-harmonic of 25Hz). Then, a low-pass filter is applied, with a cutoff frequency of... The filter is designed to retain all potential high-frequency vibration characteristics related to transformer fastener loosening, while filtering out high-frequency noise outside this range that is not helpful for fault diagnosis or may even cause confusion, such as high-frequency electronic noise from the sensor itself or high-frequency electromagnetic radiation interference. The cutoff frequency is typically determined based on existing research on the vibration characteristics of that transformer model or by performing spectral analysis on vibration sample data containing known loosening faults. If the analysis shows that the characteristic frequency components related to loosening are mainly concentrated below 2000Hz, the filter roll-off characteristics are taken into account, and a certain margin is retained. The frequency can be set to 2500Hz. Both the high-pass and low-pass filters can be Butterworth type filters, which have the flattest amplitude-frequency response characteristics in the passband. The appropriate filter order can be set according to the requirements for out-of-band suppression, such as using a 4th or 6th order design, to provide sufficient attenuation rate at their respective cutoff frequencies. After the combined action of the high-pass and low-pass filters, the vibration signal data of the time window after preliminary filtering is obtained.

[0057] Based on the vibration signal data within the pre-filtered time window, the signal waveform within each time window is first continuously monitored. This primarily checks for significant data point loss, numerical overflow, or illogical long periods of zero values ​​caused by momentary interruptions in data acquisition, transmission errors, or storage anomalies, ensuring the integrity and validity of the data for subsequent processing. The core step then involves locating and identifying transient pulses and distortion peaks in the waveform that may be caused by external impacts, accidental internal discharges, or non-periodic strong interference sources. This location and identification process is achieved through a dynamic amplitude threshold comparison method: specifically, the overall average value of the pre-filtered signal within the current processing time window is calculated. and standard deviation Based on this, a dynamic peak recognition threshold is set. Its calculation formula is ,in A preset sensitivity coefficient is used to adjust the sensitivity of the recognition, for example, The value can be set to 4. The value was selected based on statistical analysis of a large amount of historical normal operation data and sample data containing known non-persistent interference surges. A balance was chosen that effectively captures abnormal spikes while avoiding misjudging large fluctuations within the normal operating range as interference. For example, if the average signal value within a time window is 0.005g and the standard deviation is 0.01g, then... At that time, Any signal amplitude whose absolute value exceeds this The data points will be initially labeled as components of instantaneous pulses or distortion peaks. These labeled points and their neighboring points will be analyzed to determine the start and end times of the pulses and the peak magnitude. If these identified instantaneous pulses or distortion peaks show, after analysis using Short Time Fourier Transform (STFT) or wavelet packet analysis, that their energy is mainly concentrated at a specific narrowband frequency, then... In and around (for example, if the main energy of an impact is around 315Hz), then targeting that specific interference frequency. Design and apply band-stop filters sequentially for targeted attenuation, with the center frequency of the band-stop filters strictly set to the identified interference frequency. Its stopband bandwidth The setting needs to strike a balance between effectively attenuating interference and preserving the nearest useful signal to the maximum extent. For example, it can be empirically set based on the spectral width of the interfering signal. The bandwidth can be set to 3% to 8%, or a fixed small bandwidth value, such as 10Hz to 30Hz. If an interference with a center frequency of 315Hz is identified, and its spectral energy is mainly distributed within ±10Hz, then the bandwidth of the band-stop filter can be set to 20Hz, covering the range of 305Hz to 325Hz. For all instantaneous pulses and distortion peaks with clear narrowband frequency characteristics identified in this way within the current time window, the corresponding band-stop filtering is applied, and finally the filtered time window vibration data is generated.

[0058] The steps for obtaining the multifractal spectrum parameter set are as follows:

[0059] Read each segment of vibration signal in the filtered time window vibration data, and divide each segment of vibration signal into multiple subsequences of equal length to obtain the set of initial measure values ​​corresponding to each subsequence.

[0060] Based on the initial set of measure values, the multifractal spectral entropy value is calculated using the following formula:

[0061] ;

[0062] in, For order is The multifractal spectral entropy value, For the first The range of vibration signals in each subsequence For the first The time span length of each subsequence This represents the total number of subsequences within the current time window. For the preset order factor, For the first The range of vibration signals in each subsequence. For the first The length of the time span of each subsequence;

[0063] Based on the multifractal spectrum entropy value, the entropy value parameter results corresponding to all time windows are summarized in the order of time windows and combined into an ordered vector to represent the multifractal spectrum features of each time window, thus generating the multifractal spectrum parameter set for each time window.

[0064] Specifically, the process reads each segment of vibration signal from the filtered time window vibration data. Specifically, for the currently processed time window, it extracts all the filtered vibration signal amplitude points contained within it. Then, this entire segment of vibration signal data is divided into multiple shorter subsequences of identical length according to a predetermined strategy. The length of each subsequence is... This is a key parameter, and its setting is based on two principles: firstly, ensuring that each subsequence contains enough data points to stably calculate its statistical characteristics (such as range); and secondly, the number of subsequences... Sufficient subsequences are also needed to effectively reveal the scale-invariant characteristics of the signal in subsequent multifractal spectral analysis. Typically, the number of subsequences... The recommended value is between 32 and 256, for example, if the vibration signal in the current time window contains... Each sampling point (e.g., sampling rate 10kHz, time window duration 1 second) is planned to be divided into... If there are subsequences, then the length of each subsequence is... That is The sampling points are divided into consecutive, non-overlapping segments. That is, the first subsequence contains sampling points 1 to 100, the second subsequence contains sampling points 101 to 200, and so on, until all sampling points are divided. For each of the subsequences, (in From 1 to ), calculate its corresponding initial measure value, which mainly includes two parts: first, the range of the vibration signal within the subsequence. By finding all of the subsequence The maximum and minimum values ​​of the vibration signal amplitude are obtained, and then the difference between the two is calculated. For example, if the first The vibration amplitude of each subsequence is in arrive If it fluctuates between these values, then its range is... Secondly, the time span length of this subsequence. Since all subsequences have the same length (all are...), (Number of sampling points) and the sampling rate is constant (e.g., 10kHz, i.e., sampling period). (seconds), then the time span of each subsequence Seconds, this This pair of parameters will be the same for all subsequences, and will be calculated for each subsequence. , Organize them to form the initial measure set corresponding to all subsequences within the current time window.

[0065] formula: The advantage of the formula lies in that it calculates the entropy value of the multifractal spectrum. It can quantify the irregularity and complexity distribution of vibration signals at different scales. When transformer fasteners loosen, the energy distribution and local fluctuation characteristics of the vibration signal change, and this change can be captured by multifractal spectrum entropy values. As a local intensity measure, its distribution heterogeneity is determined by... Reflection, parameters The introduction of this entropy value allows it to highlight the contributions of different intensity components in the signal, thus making it more sensitive to early, subtle signs of loosening.

[0066] parameter The steps to obtain it are as follows: For the first A subsequence, which is the filtered vibration signal of the current time window from the previous step, arranged in a fixed length. (For example, 100 sampling points) The subsequence is divided into segments. All vibration signal amplitudes within this subsequence are read, and the maximum value among these amplitudes is found by comparison. and minimum value Then the vibration signal range value For example, if the first The vibration signal amplitude data (unit: g) of each subsequence are as follows: (Actually includes 100 points), its maximum value is 0.08g, and its minimum value is -0.01g, then .

[0067] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The time span length of each subsequence, in the previous step, the time window vibration signal was divided into multiple subsequences of equal length, each subsequence containing... Given sampling points, if the sampling period of the vibration signal is known to be... (For example, when the sampling frequency is 10kHz,) Then the time span of each subsequence Due to the length of all subsequences The same (e.g., 100 points), therefore The same applies to all subsequences within the current time window, for example, .

[0068] parameter The steps to obtain this parameter are as follows: This parameter represents the total number of subsequences obtained by dividing the current time window. If the vibration signal in the current time window contains a total of... There are sampling points, and the length of each subsequence is . Given ___ sampling points, and that the subsequences do not overlap, then the total number of subsequences is ___. ,make sure yes Multiples of integers, or rounded down, for example, if the time window contains... Number of sampling points, length of each subsequence If there are 1 sampling point, then the total number of subsequences is 1. .

[0069] parameter The acquisition steps are as follows: This parameter is a preset order factor, and its value selection has an important impact on the sensitivity of multifractal spectrum entropy. It is not equal to 1. First, a large number of vibration signal samples are collected, including those of the transformer in normal operation and those of different degrees (such as slight, moderate, and severe) of fastener loosening. These samples should come from the same measuring points as the actual monitoring locations (box, core clamping nail, coil clamping plate). Second, all sample data are preprocessed in accordance with the same procedure as in this application, and then, for a specific... The candidate range of values ​​(e.g., from -4.0 to +4.0, in steps of 0.2, avoiding...) Calculate the polyfractal spectral entropy value for each sample. Secondly, through statistical analysis (such as comparing different states) Methods such as mean difference, analysis of variance, or evaluation using classifiers can be used to evaluate differences. Value The ability and sensitivity to distinguish between different states of fastener loosening; finally, select the one that can most significantly distinguish between different states of loosening, or that shows the most stable and monotonic response trend to the evolution of the degree of loosening. The value is used as the final preset order factor; for example, if experiments show that when hour, The mean values ​​for the three states of normal, slightly loose, and severely loose are respectively , , And at this time, all kinds of If the distribution overlap is minimal, then set .

[0070] parameter and Definition and and They are the same, only the indices are different, and they represent the common symbols used when traversing all subsequences.

[0071] Calculation process:

[0072] The current time window is divided into Subsequences, with a preset order factor .

[0073] The initial set of measure values ​​obtained from the previous step is:

[0074] Subsequence 1: , ;

[0075] Subsequence 2: , ;

[0076] Subsequence 3: , ;

[0077] Subsequence 4: , ;

[0078] First, calculate the value of each subsequence. Value (unit: g / s):

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] Secondly, calculate all Sum of values:

[0084] g / s

[0085] Then, the normalized measure of each subsequence is calculated. :

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] Next, calculate of power (here) ):

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] Calculate these The sum of powers:

[0096] ;

[0097] Finally, the multifractal spectral entropy value is calculated. (here ,so ):

[0098] ;

[0099] ;

[0100] ;

[0101] This result indicates that, for the vibration signal within the current time window, its order... The multifractal spectral entropy value is 1.290, which reflects the vibration intensity in the signal (in terms of...). The non-uniformity or complexity of the distribution (measured) will be discussed in conjunction with other time windows later. The values ​​form a sequence used to monitor the evolution of the transformer fastener condition. A trend in the value, such as a continuous increase or decrease, exceeding the normal fluctuation range, may indicate a change in the condition of the fastener.

[0102] Based on the multifractal spectral entropy value, which is a single scalar value calculated for each processed time window. (for example, the result calculated in the previous step) ), and these correspond to different time windows The values ​​are collected and arranged strictly according to their respective time windows in chronological order along the entire monitoring timeline, forming a time series. For example, if continuous monitoring has been conducted... If a time window is defined, a result will be obtained containing indivual sequence of values ,in Representing the The multifractal spectral entropy value calculated for each time window. Its "multifractal spectral features" in the current context are its corresponding The value itself, for the sake of consistency in subsequent processing and the standardization of data structures, can be considered a scalar. The value is represented as a single-element vector, i.e. This single-element vector was subsequently identified as the specific time window. The multifractal spectrum parameter set is thus generated by performing this operation on all processed time windows, resulting in a series of multifractal spectrum parameter sets arranged in chronological order for each time window. These parameter sets will serve as the basis for subsequent calculation of the impact feature kurtosis entropy.

[0103] The steps for obtaining the impact feature kurtosis entropy sequence are as follows:

[0104] Based on the multifractal spectrum parameter set and the original sample data of vibration signals within the time window, the mean of the current time window is calculated point by point based on the original sample data, and the squared deviation between each sample point and the mean is statistically analyzed. At the same time, the multifractal spectrum entropy value corresponding to the window is recorded, generating the original statistical term set.

[0105] Based on the original set of statistical terms, the kurtosis entropy value of the impact feature for each time window is calculated using the following formula:

[0106] ;

[0107] in, For the first The kurtosis entropy value of the impact feature within each time window. For the first The first time window One vibration signal sample point, For the first The average value of the signal within a time window. For the first Multifractal spectral entropy values ​​for a time window For the first The total number of sample points within a time window For the first The variance of the signal within a time window, To prevent extremely small positive numbers with a denominator of zero, To prevent extremely small positive numbers with zero denominators when the variance is close to zero;

[0108] Based on the kurtosis entropy value of the impact feature, the kurtosis entropy values ​​of the impact feature corresponding to all time windows are integrated into an impact feature kurtosis entropy sequence in chronological order.

[0109] Specifically, based on the multifractal spectrum parameter set and the original sample data of vibration signals within the time window, for the currently processed... Within a time window, the most original vibration signal amplitude sequence, without any filtering, is extracted from the original sample data of the vibration signal within that time window, denoted as... ,in This is the total number of sample points within the given time window. Then, based on this original sample data sequence, the average value for the current time window is calculated point by point. Next, for each sample point in the sequence (in From 1 to ), calculate the sample point and the mean. The square of the deviation between them, i.e. All these squared deviation values ​​are collected to form a sequence of squared deviation values. Simultaneously, the corresponding current value generated in the previous step is... Extract the multifractal spectral entropy value of a given time window from the multifractal spectral parameter set. The calculated mean The sequence of squared deviations of all sample points and the corresponding multifractal spectral entropy value Together with the total number of sample points in that time window Together, they form a structured data record, which is the record for the current data point. The raw statistics for each time window are generated by performing this operation on all time windows, resulting in a set of raw statistics arranged in chronological order.

[0110] formula: The advantage of the formula is that it constructs a new feature parameter—the impact feature kurtosis entropy. This parameter integrates the statistical characteristics of the original vibration signal (mean, variance, sample point bias) and the signal complexity information (multifractal spectral entropy) obtained through multifractal analysis. ), molecular part Essentially, the multifractal spectral entropy value is used to weight or normalize the squared deviation of each sample point. When there are impulsive components in the signal, the squared deviation value will increase significantly. If the multifractal spectral entropy value is then... If the value is relatively small (indicating a relatively simple signal structure or concentrated impulses), this term will become very large, and vice versa. The denominator... This represents the variance of the signal, indicating the overall energy fluctuation level of the signal. Therefore, the entire fractional part can be seen as a measure of the signal's impulsiveness or dispersion, adjusted by multifractal spectral entropy. It is similar to kurtosis but incorporates considerations of signal complexity. By taking the logarithm and adding 1, it becomes... It is more sensitive to changes in the ratio of the numerator to the denominator, especially when the ratio is small, and ensures... The non-negativity of indicates that when loose fasteners cause characteristic impacts or irregular fluctuations in the vibration signal, Compared to kurtosis or entropy values ​​alone, it can capture these changes more effectively;

[0111] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The first time window The amplitude of the nth vibration signal sample point is directly derived from the "time window vibration data" generated in the previous step, specifically for the nth vibration signal sample point being processed. The value of a specific sampling point in the original, unfiltered vibration signal sequence extracted within a time window; for example, if the first... Each time window contains 10,000 sampling points, when hour, It refers to the vibration amplitude at the 500th sampling point within this time window, for example... .

[0112] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The average value of all vibration signal sample points within a time window has been calculated in the "Generate Original Statistical Item Set" step, and its calculation formula is as follows: ,in It is the first The first time window One vibration signal sample point, It is the total number of sample points within that time window. For example, if the first... There are several time windows. The sum of each sample point ,but .

[0113] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The multifractal spectral entropy value for the nth time window is obtained in the aforementioned step of "generating the multifractal spectral parameter set for each time window" for the nth time window. Calculated in time windows The value has been recorded in the "original statistical item set," for example, in the aforementioned example, it was calculated for a certain time window. So for that time window, That is, 1.290.

[0114] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The total number of vibration signal sample points within a time window. This value is determined when dividing the time window and is recorded in the "Generate Original Statistical Item Set" step. It is equal to the duration of the time window. Multiply by sampling frequency For example, if the time window duration seconds, sampling frequency Hz, then .

[0115] parameter The steps to obtain this parameter are as follows: This parameter represents the first... The variance of the vibration signal within a time window is calculated using the following formula: ,in These are sample points. It is the mean. This is the total number of sample points. This value can be obtained by directly averaging the squared deviations of each sample point from the mean, or by using standard statistical library functions. For example, for the nth... If the variance of the sample data is calculated within a time window, then... ,but .

[0116] parameter The steps to obtain this parameter are as follows: This parameter is used to prevent the denominator from being divided. The smallest positive number introduced to be zero is set as follows: .

[0117] parameter ,set up .

[0118] Calculation process:

[0119] Let the current one be the first... There are several time windows with the following parameter values ​​(some parameter values ​​are reused or referenced from the calculation examples in previous steps):

[0120] (Total number of sample points);

[0121] (Signal mean);

[0122] (Multifractal spectral entropy value);

[0123] (Signal variance);

[0124] ;

[0125] ;

[0126] For example, it has already been calculated. .

[0127] To calculate the summation term in the numerator What is actually needed is .

[0128] Therefore, the summation term in the numerator can be rewritten as:

[0129] ;

[0130] Substitute the values:

[0131] ;

[0132] Denominator term:

[0133] ;

[0134] Calculate the fractional part:

[0135] ;

[0136] Final calculation :

[0137] ;

[0138] ;

[0139] The result indicates that, for the current time window, the impact feature kurtosis entropy value is 0.5739.

[0140] Based on the impact characteristic kurtosis entropy value, a corresponding value is calculated for each analyzed time window. Value (e.g., obtained in the previous step) These data were obtained from different time windows during the continuous monitoring process. The values ​​are collected and arranged strictly according to their respective time windows on the original timeline to construct a time series. Specifically, if the values ​​have been processed... A time window will then be used to... Each impact feature kurtosis entropy value (in Representing the The kurtosis entropy values ​​of the impact features of each time window are organized into an ordered vector or list, the order of which is exactly the same as the order in which the time windows were generated. This final ordered list... The value list is the shock feature kurtosis entropy sequence.

[0141] The steps for obtaining harmonic energy data are as follows:

[0142] Read each vibration signal from the filtered time window vibration data, expand each vibration signal along the complete time axis and perform full-segment frequency domain conversion, output the frequency response curve corresponding to each signal segment and establish the amplitude spectrum structure corresponding to each frequency point to obtain the spectrum data of each time window.

[0143] Based on the spectral data of each time window, the characteristic frequency band index range within the frequency identification range is set, and the frequency point and amplitude at the working fundamental frequency of the transformer core are extracted accordingly. The frequency axis is matched and compared with the fundamental frequency standard frequency point to locate the position. At the same time, the amplitude coordinates are recorded and converted into energy values ​​to generate the fundamental frequency energy value of each time window.

[0144] Based on the fundamental frequency energy value of each time window, the corresponding segments of integer multiples of the fundamental frequency and non-integer interval frequencies above the fundamental frequency in the spectrum data are scanned to identify the frequency point positions and amplitude responses of all subharmonic and subharmonic frequency bands. The amplitude information of the corresponding frequency segments is converted into energy quantization results and combined to form the harmonic energy data of that time window.

[0145] Specifically, each segment of vibration signal in the filtered time window vibration data is read. The specific operation involves treating each time window as a complete analysis unit, for example, a sequence of filtered vibration signal amplitudes within it. Sequence of sampling points (in The entire frequency domain is transformed using the Fast Fourier Transform (FFT) algorithm. The length of the FFT is usually chosen to be greater than or equal to [a certain value]. To improve computational efficiency, for example, if the least power of 2 is used. Then the FFT length can be taken as The missing parts can be padded with zeros. The output of FFT is a series of complex frequency coefficients. (in , (This is the FFT length). These complex coefficients represent the amplitude and phase information of the signal at different frequency points. The calculation of each frequency point is based on these complex frequency coefficients. (in The amplitude spectrum corresponding to the sampling frequency To facilitate observation and comparison, the power spectrum is usually obtained by squaring the frequency points or by directly using the amplitude. These frequency points are then organized with their corresponding amplitudes to form a discrete representation of the frequency response curve for that time window, i.e., the amplitude spectrum structure. The horizontal axis represents frequency and the vertical axis represents amplitude. This data set containing all frequency points and their corresponding amplitudes is the spectrum data for that time window.

[0146] Based on the spectral data for each time window, the first step is to determine a frequency identification range for identifying the transformer core's operating fundamental frequency. This range is set according to the transformer's rated operating frequency. For example, for a transformer in a 50Hz power system, its core operating fundamental frequency is theoretically twice 50Hz, i.e., 100Hz (because the magnetostrictive effect causes the core to undergo two dimensional changes within each power frequency cycle). However, considering the actual fluctuations in the power grid frequency (e.g., the Chinese power grid frequency is allowed to fluctuate between 49.8Hz and 50.2Hz), and the potential frequency resolution and peak broadening issues during spectral analysis, the set frequency identification range should revolve around the theoretical fundamental frequency value. For example, if the theoretical fundamental frequency is 100Hz, the identification range can be set to 98Hz to 102Hz to ensure that the actual fundamental frequency peak can be captured. Within this set frequency identification range, the actual frequency point at the transformer core's operating fundamental frequency is accurately located by using a peak search algorithm (e.g., finding the frequency point with the largest amplitude within this range) or by performing the closest matching with a preset fundamental frequency standard point (e.g., 100Hz). and its corresponding amplitude Record this amplitude. And convert it into an energy value. The energy calculation is proportional to the square of the amplitude; if the amplitude... If the voltage signal amplitude is the voltage signal amplitude, then the energy can be approximated as: ,in It is a constant related to the signal type and system impedance, or in a relative comparison scenario, the square of the amplitude can be directly used as a measure of energy, i.e. For example, if the maximum amplitude is found in the range of 98Hz-102Hz If it appears at 99.9 Hz and its value is 0.05g (unit of acceleration), then the fundamental frequency energy value is... This operation is performed for each time window to generate the fundamental frequency energy value for each time window.

[0147] Based on the fundamental frequency energy value for each time window, and the complete spectral data for that time window, the spectrum is further scanned and the energies of subharmonics and partial harmonics are identified. Subharmonics refer to frequencies equal to the fundamental frequency. Frequency components that are integer multiples of each other, i.e. ,in For example, if the fundamental frequency is 100Hz, then the second harmonic is 200Hz, the third harmonic is 300Hz, and so on. Subharmonics refer to frequency components whose frequencies are fractions of the fundamental frequency. We usually focus on... or (in It is an integer, and For example, if the fundamental frequency is 100Hz, then the 1 / 2 harmonic is 50Hz, the 1 / 3 harmonic is approximately 33.3Hz, the 2 / 3 harmonic is approximately 66.7Hz, etc. During scanning, for each theoretical subharmonic frequency point (such as...) ) and the subharmonic frequencies of interest (such as Set a small search bandwidth around the peak (e.g., ±2% or ±2Hz of the theoretical frequency; the specific bandwidth is determined based on the spectral resolution and expected peak width; for example, for the second harmonic of 200Hz, the search range could be 196Hz-204Hz). Within this bandwidth, find the amplitude peak and record its frequency position and amplitude response. Then, this amplitude information is also converted into energy quantization results. The energy values ​​of all identified subharmonic frequency bands and subharmonic frequency bands (each frequency band corresponds to one energy value) are collected and stored together with their respective frequency points or frequency band identifiers (such as "2nd harmonic" or "1 / 2 subharmonic"). The collection of these energy values ​​constitutes the harmonic energy data for that time window.

[0148] The steps for obtaining the proportion of nonlinear harmonic energy are as follows:

[0149] Read the energy values ​​of the frequency bands corresponding to each time window in the harmonic energy data, sequentially filter out the energy values ​​of all frequency points marked as subharmonic frequency bands in each time window, summarize the energy values ​​of all frequency points of subharmonic frequency bands, calculate the sum as the total subharmonic energy of that time window, and generate the total subharmonic energy of each time window.

[0150] Based on the total subharmonic energy of each time window, the energy values ​​of all frequency points marked as subharmonic bands within the corresponding time window are extracted from the harmonic energy data. The energy points of this type of band are retrieved according to the frequency index position and accumulated one by one to form the total subharmonic energy of the time window. The total energy values ​​corresponding to the two bands are added together to obtain the nonlinear harmonic total energy of each time window.

[0151] Based on the total nonlinear harmonic energy of each time window, the fundamental frequency energy value under the same time window is called, the ratio of the total nonlinear harmonic energy to the fundamental frequency energy value is calculated, and the ratio value is arranged into a sequence structure corresponding to the time order to generate the nonlinear harmonic energy proportion.

[0152] Specifically, the energy value of the frequency segment corresponding to each time window in the harmonic energy data is read. The specific operation is as follows: for the currently processed [number]th [time window]... Within a given time window, the system filters harmonic energy data (which includes the frequency positions and energy values ​​of all subharmonics and tertiary harmonics identified within that time window). The filtering is based on the frequency band identifier associated with each energy entry. First, it iterates through all entries in the harmonic energy data, selecting those explicitly marked as "subharmonic bands," such as energy values ​​marked as "2nd harmonic," "3rd harmonic," "4th harmonic," etc. Then, it sums the energy values ​​of all frequency points belonging to these selected subharmonic bands. For example, if the current time window identifies subharmonics such as the 2nd harmonic with an energy value of... The energy of the third harmonic is The energy of the 4th harmonic is The total energy of the subharmonics within that time window Perform this operation for all time windows to generate the total subharmonic energy for each time window.

[0153] Based on the total subharmonic energy of each time window, the harmonic energy data of that time window is further utilized to extract the energy values ​​of all frequency points marked as "subharmonic bands." These subharmonic band markings typically indicate the frequency relative to the fundamental frequency. Non-integer multiples, such as "1 / 2 harmonic", "3 / 2 harmonic", "5 / 2 harmonic", etc., or some known specific non-integer multiples of frequency bands related to nonlinear behavior, are used to retrieve the energy points marked as subharmonics from the harmonic energy data according to their frequency index positions (i.e., the frequency values ​​when they are identified in the original spectrum data). These energy values ​​are then accumulated one by one to form the total subharmonic energy for that time window. For example, if the subharmonics identified in the current time window include: 1 / 2 subharmonic energy is The energy of the 3 / 2 harmonic is Then the total energy of the subharmonics in that time window Then, the total subharmonic energy of this time window calculated earlier is... (e.g., 0.0012) ) and the total energy of the subharmonics just calculated (e.g., 0.0007) The total nonlinear harmonic energy of the time window is obtained by adding the two groups together. ,Right now Perform this operation for all time windows to obtain the total nonlinear harmonic energy for each time window.

[0154] Based on the total nonlinear harmonic energy of each time window, i.e. (For example, the 0.0019 obtained in the aforementioned example) Simultaneously, retrieve the fundamental frequency energy value for each time window from the "Generate fundamental frequency energy value for each time window" step for the same... The fundamental frequency energy value is calculated and stored within a time window. (For example, the results obtained in the aforementioned example) The ratio of these two is calculated using the following formula: Nonlinear harmonic energy proportion. For example, the proportion of nonlinear harmonic energy in the current time window. This ratio is a dimensionless number that reflects the intensity of nonlinear harmonic components in the signal relative to the fundamental frequency energy. This ratio calculation is performed on all processed time windows, yielding a series of nonlinear harmonic energy proportions. These proportions are then strictly correlated with the temporal order of their respective time windows, forming a time series structure. ,in It is the total number of time windows. This final ordered list of proportion values ​​is the nonlinear harmonic energy proportion sequence.

[0155] The steps for determining the looseness of transformer fasteners are as follows:

[0156] Read all time-series values ​​of the impact feature kurtosis entropy sequence and the nonlinear harmonic energy ratio, synchronize and align the two sequences window by window, and combine the impact feature kurtosis value and the nonlinear harmonic energy ratio under each time window into a feature vector according to the time index, and generate a fused feature vector sequence.

[0157] Based on the fused feature vector sequence, according to the upper and lower boundary values ​​of the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy of transformer fasteners under normal operating conditions in historical samples, the maximum fluctuation range of each index in the typical state range is extracted, and this range is set as the standard condition range for stable operation to generate fastener state benchmark parameters.

[0158] Based on the fastener condition reference parameters, deviation detection is performed on each set of time window data in the fused feature vector sequence, the relative change amplitude between the fastener condition reference parameters and the data is calculated, and the continuous change trend is sorted on the time axis and fitted with the trajectory curve to determine whether it is stably maintained within the normal threshold range, thus forming the transformer fastener loosening state determination.

[0159] Specifically, the entire time series values ​​of the impact feature kurtosis entropy sequence and the proportion of nonlinear harmonic energy are read. The specific operation involves retrieving the complete impact feature kurtosis time series generated in the previous steps. and nonlinear harmonic energy proportion time series Ensure that the total number of time windows covered by these two sequences The time correspondence is consistent, and then each time window is processed. For the first... time windows (of which) From 1 to Extract the kurtosis entropy value of the impact feature corresponding to the time window. and the proportion of nonlinear harmonic energy These two values ​​were already labeled with their respective time indices (e.g., the start sampling time of the time window or the sequence number) when they were generated, so they can be aligned to the same point in time, making these two scalar values... and Combined into a two-dimensional feature vector For all Perform this operation in each time window to obtain a result from A sequence of two-dimensional feature vectors This sequence is the fused feature vector sequence.

[0160] The process of establishing fastener condition baseline parameters based on the fused feature vector sequence is as follows: First, a large amount of historical sample data needs to be collected. This data should come from long-term monitoring records of the target transformer or transformer of the same model under confirmed fastener conditions of good and normal operation. For these historical normal sample data, the corresponding impact characteristic kurtosis entropy sequence and nonlinear harmonic energy ratio sequence are calculated using the same steps as the current online monitoring. Then, for the impact characteristic kurtosis entropy index, its distribution characteristics are statistically analyzed from its historical normal operation data sequence to determine the upper limit of its normal fluctuation range. and lower limit value For example, the boundary can be taken as the mean of the indicator in historical normal data plus or minus three standard deviations. and Alternatively, a percentile method can be used, for example, taking the 5th percentile and 95th percentile as the lower and upper limits to cover the fluctuations under most normal conditions. Similarly, for the indicator of the proportion of nonlinear harmonic energy, the upper limit of its normal fluctuation range is also determined by statistical analysis of its historical normal operation data series. and lower limit value For example, if the mean of the historical shock characteristic kurtosis entropy is 0.4 and the standard deviation is 0.05, then its normal fluctuation range can be set as follows: If the mean of the historical nonlinear harmonic energy proportion is 0.3 and the standard deviation is 0.08, then its normal fluctuation range can be set as follows: These two parameters respectively address the normal fluctuation range of impact characteristic kurtosis entropy and the proportion of nonlinear harmonic energy. and Together, they constitute the standard condition range for stable operation, which is the fastener condition reference parameter.

[0161] Based on fastener condition baseline parameters, each time window data in the fused feature vector sequence obtained from the current online monitoring is analyzed. Deviation detection is performed by taking the impact feature kurtosis entropy value of the current time window. The normal fluctuation range in the corresponding fastener condition reference parameters Compare them and calculate their relative magnitude of change. For example, if... If the value exceeds the upper limit, calculate the relative magnitude of the excess portion. If it is below the lower limit, then calculate the relative magnitude of the lower portion. Similarly, regarding the proportion of nonlinear harmonic energy... Similar comparisons and relative change calculations are performed to record the deviations and changes of the two indicators. After performing such deviation detection over multiple consecutive time windows, these deviation information are arranged in chronological order to form the evolution trajectories of the two indicators. This can be visualized by plotting time series graphs, or time series analysis methods, such as moving averages, exponential smoothing, or more complex trend fitting algorithms (e.g., multinomial fitting or state-space model-based fitting), can be applied to these trajectory data points to smooth noise and reveal potential long-term trends. Then, based on preset judgment rules, it is determined whether the evolution trajectories of the two indicators are stably maintained within their respective normal threshold ranges. The judgment rules may include: a single indicator exceeding the normal threshold for several consecutive time windows (e.g., 3 to 5 consecutive windows), or two... If an indicator exceeds a threshold simultaneously, or if the relative change of a certain indicator exceeds a preset warning level (e.g., a relative change exceeding 20% ​​is considered a significant deviation), or if the evolution trajectories of two indicators in the two-dimensional feature space (with the impact characteristic kurtosis entropy as one axis and the nonlinear harmonic energy ratio as the other axis) significantly deviate from the center of the region corresponding to the normal state and show a trend of continuous movement in a specific direction (indicating the characteristic direction of loosening faults, which can be obtained by analyzing historical fault sample data), the loosening status of transformer fasteners is determined by combining these judgment results. For example, if the impact characteristic kurtosis entropy value is greater than 0.55 (its normal upper limit) for 5 consecutive time windows, and the nonlinear harmonic energy ratio also shows a synchronous upward trend and exceeds 0.54 (its normal upper limit), then it is determined that the fasteners may be loose.

[0162] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An online monitoring method for fastener loosening based on transformer vibration characteristics, characterized in that, Includes the following steps: Vibration sensors are arranged in the transformer housing, core clamping nails and coil clamping plate areas to continuously pick up vibration signals. The vibration signals are truncated according to a preset length to form multiple time window vibration data. The vibration data of each time window is filtered to obtain the filtered time window vibration data. The filtered vibration data of the time window is retrieved, and the multifractal spectrum parameter set of each time window is calculated for each segment of the filtered vibration data. The impact feature kurtosis sequence is calculated based on the multifractal spectrum parameter set. Using the filtered time window vibration data, a spectrum transformation is performed on each data segment to identify the energy of the transformer core's working fundamental frequency. Simultaneously, the energy values ​​of each harmonic and subharmonic frequency band are extracted to form harmonic energy data. The proportion of the energy of the second harmonic and subharmonic in the fundamental frequency energy is calculated to obtain the proportion of nonlinear harmonic energy. By integrating the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio, a normal fluctuation threshold range for the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio is set to form a fastener state reference parameter. The deviation between the impact characteristic kurtosis entropy sequence and the nonlinear harmonic energy ratio and the fastener state reference parameter is compared to track the evolution trajectory and output the transformer fastener loosening state judgment.

2. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the vibration data within the time window are as follows: Vibration sensors are installed in the transformer housing, core nails, and coil pressure plate areas to continuously collect all real-time vibration signals generated by the transformer housing, core nails, and coil pressure plate areas, thus obtaining continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas. Based on the continuous vibration signals of the transformer housing, core nails, and coil pressure plate areas, the continuous vibration signals are divided into time segments according to a set fixed duration to generate a segmented fixed-length vibration signal sequence. Based on the segmented fixed-length vibration signal sequence, each segment of vibration signal is renumbered and identified according to the time index to generate time window vibration data.

3. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the filtered time window vibration data are as follows: Read all vibration signal values ​​within each time window of the vibration data, retrieve the amplitude sequence of the vibration signal within each time window, identify interference components and noise distribution characteristics, and truncate the vibration signal data of the time window using a high-pass filter and a low-pass filter to obtain the vibration signal data of the time window after preliminary filtering. Based on the pre-filtered vibration signal data within the time window, the continuity of the signal waveform within each time window is detected, and the instantaneous pulses and distortion peaks in the waveform are located and identified. Band-stop filters are then applied sequentially to attenuate the signal, generating filtered vibration data within the time window.

4. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the multifractal spectrum parameter set are as follows: Read each segment of vibration signal from the filtered time window vibration data, and divide each segment of vibration signal into multiple subsequences of equal length to obtain the set of initial measure values ​​corresponding to each subsequence. Calculate the multifractal spectrum entropy value based on the initial set of measure values; Based on the multifractal spectrum entropy value, the entropy parameter results corresponding to all time windows are summarized in the order of time windows and combined into an ordered vector to represent the multifractal spectrum features of each time window, thereby generating a multifractal spectrum parameter set for each time window.

5. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the impact feature kurtosis entropy sequence are as follows: Based on the multifractal spectrum parameter set and the original sample data of vibration signals within the time window, the mean of the current time window is calculated point by point based on the original sample data, and the squared deviation between each sample point and the mean is statistically analyzed. At the same time, the multifractal spectrum entropy value corresponding to the window is recorded, and the original statistical term set is generated. Based on the original set of statistical terms, calculate the impact feature kurtosis value for each time window; Based on the impact feature kurtosis entropy value, the impact feature kurtosis entropy values ​​corresponding to all time windows are integrated into an impact feature kurtosis entropy sequence in chronological order.

6. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the harmonic energy data are as follows: Read each vibration signal from the filtered time window vibration data, expand each vibration signal according to the complete time axis and perform full-segment frequency domain conversion, output the frequency response curve corresponding to each signal segment and establish the amplitude spectrum structure corresponding to each frequency point to obtain the spectrum data of each time window. Based on the spectral data of each time window, the characteristic frequency band index range within the frequency identification range is set, and the frequency point and amplitude at the working fundamental frequency of the transformer core are extracted accordingly. The frequency axis is matched and compared with the fundamental frequency standard frequency point to locate the position. At the same time, the amplitude coordinates are recorded and converted into energy values ​​to generate the fundamental frequency energy value of each time window. Based on the fundamental frequency energy value of each time window, the corresponding segments of integer multiples of the fundamental frequency and non-integer interval frequencies above the fundamental frequency in the spectrum data are scanned to identify the frequency point positions and amplitude responses of all subharmonic and subharmonic frequency bands. The amplitude information of the corresponding frequency segments is converted into energy quantization results and combined to form the harmonic energy data of that time window.

7. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for obtaining the proportion of nonlinear harmonic energy are as follows: Read the energy values ​​of the frequency bands corresponding to each time window in the harmonic energy data, sequentially filter out the energy values ​​of all frequency points marked as subharmonic frequency bands in each time window, summarize the energy values ​​of all frequency points of subharmonic frequency bands, calculate the sum as the total subharmonic energy of that time window, and generate the total subharmonic energy of each time window. Based on the total subharmonic energy of each time window, the energy values ​​of all frequency points marked as subharmonic bands within the corresponding time window are extracted from the harmonic energy data. The energy points of this type of band are retrieved according to the frequency index position and accumulated one by one to form the total subharmonic energy of the time window. The total energy values ​​corresponding to the two bands are added together to obtain the nonlinear harmonic total energy of each time window. Based on the total nonlinear harmonic energy of each time window, the fundamental frequency energy value under the same time window is called, the ratio of the total nonlinear harmonic energy to the fundamental frequency energy value is calculated, and the ratio calculation results are organized into a sequence structure corresponding to the time order to generate the nonlinear harmonic energy ratio.

8. The online monitoring method for fastener loosening based on transformer vibration characteristics according to claim 1, characterized in that, The steps for determining the loose state of the transformer fasteners are as follows: Read all time-series values ​​of the impact feature kurtosis entropy sequence and the nonlinear harmonic energy ratio, synchronize and align the two sequences window by window, and combine the impact feature kurtosis value and the nonlinear harmonic energy ratio under each time window into a feature vector according to the time index to generate a fused feature vector sequence. Based on the fused feature vector sequence, according to the upper and lower boundary values ​​of the impact characteristic kurtosis entropy sequence and the proportion of nonlinear harmonic energy under normal operating conditions of transformer fasteners in historical samples, the maximum fluctuation range of each index in the typical state range is extracted, and this range is set as the standard condition range for stable operation to generate fastener state benchmark parameters. Based on the fastener state reference parameters, deviation detection is performed on each set of time window data in the fused feature vector sequence, the relative change amplitude between the fastener state reference parameters is calculated, and the continuous change trend is sorted by time axis and fitted with trajectory curve to determine whether it is stably maintained within the normal threshold range, thus forming a transformer fastener loosening state determination.

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