Improved bootstrap and adaptive kde-based transformer vibration probability modeling evaluation method and system

Abstract

The application discloses a transformer vibration probability modeling and evaluation method and system based on improved Bootstrap and adaptive KDE, and solves the problems of limited transformer vibration characteristic parameter samples, complex distribution, inaccurate probability modeling, and lack of statistical confidence of state evaluation threshold in the prior art.The method comprises the following steps: collecting transformer vibration signals, extracting characteristic parameters to construct an original sample set; using the improved Bootstrap method to resample the original sample set with replacement and add noise to realize sample expansion; and performing probability modeling on the expanded sample set based on adaptive kernel density estimation KDE.The application realizes effective expansion of transformer vibration characteristic parameter samples under limited sample conditions, accurate fitting of the expanded vibration characteristic parameter samples, and improves the accuracy and reliability of transformer operation state uncertainty evaluation.

Description

Technical Field

[0001] This invention belongs to the field of power equipment condition monitoring and fault diagnosis technology, specifically involving a method and system for extracting characteristic parameters of transformer vibration signals, expanding samples, modeling probability density, and evaluating operating status based on improved Bootstrap and adaptive kernel density estimation. Background Technology

[0002] As a critical hub in the power system, the operational reliability of transformers directly affects the safety and stability of the entire power grid. Vibration signal analysis methods, due to their ability to effectively reflect the internal mechanical state of transformers, have become an important technical means for transformer condition assessment. Current technologies typically involve collecting vibration signals from normally operating transformers, extracting their time-domain or frequency-domain characteristic parameters, and then judging the transformer's condition based on empirical thresholds or simple statistical laws.

[0003] However, existing technologies still have the following shortcomings: First, traditional methods often rely on fixed thresholds or thresholds set based on histograms of characteristic parameter distributions. These methods fail to fully utilize the global continuous information of characteristic parameter distributions, resulting in inaccurate estimations and susceptibility to instantaneous changes in operating conditions. They are also difficult to accurately assess transformers near threshold boundaries or experiencing abnormal fluctuations. Second, due to limitations in on-site monitoring conditions, the number of vibration samples of normally operating transformers is limited. Directly performing statistical regularity analysis on these limited samples can lead to insufficient reliability. Third, traditional kernel density estimation uses a fixed bandwidth calculated based on empirical rules. For complex distribution patterns such as skewed and multi-peaked transformer vibration characteristics, the fitted curves are often too smooth, especially in the peak and tail regions where the fitting accuracy is insufficient. Furthermore, most studies do not fully consider the differences in the distribution characteristics of vibration characteristic parameters at different voltage levels, often combining vibration characteristics from multiple voltage levels for analysis, further affecting the accuracy of the assessment.

[0004] Therefore, this invention proposes an improved method and system for modeling and evaluating transformer vibration probabilistics using Bootstrap and adaptive KDE. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method for probabilistic modeling of transformer vibration characteristic parameters based on improved Bootstrap and adaptive KDE, and then for state evaluation of the transformer, in order to solve the problems of low fitting accuracy of transformer vibration characteristic distribution and inaccurate threshold setting under limited samples.

[0006] To achieve the above objectives, the present invention adopts the following technical solution;

[0007] An improved method and system for probabilistic modeling and evaluation of transformer vibration using Bootstrap and adaptive KDE, comprising the following steps:

[0008] S100. Collect transformer vibration signals, use Fast Fourier Transform to convert the collected signals from the time domain to the frequency domain, extract feature parameters, and construct the original sample set;

[0009] S200. The original sample set of transformer vibration characteristic parameters is expanded using the improved Bootstrap method to obtain the expanded sample set of vibration characteristic parameters;

[0010] S300. Based on adaptive kernel density estimation, probabilistic modeling is performed on the expanded vibration characteristic parameter sample set to obtain the probability density function;

[0011] S400. Based on the probability density function of each feature parameter, derive its cumulative distribution function, and calculate its 95% and 99% quantiles as the thresholds for state-level early warning.

[0012] As a further aspect of the present invention, the extracted feature parameters include fundamental frequency weight, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio.

[0013] As a further aspect of the present invention, the improved Bootstrap method includes: resampling the original samples with replacement to obtain a resampled subset, and introducing random noise into each sample in the resampled subset to generate a noisy sample subset.

[0014] As a further aspect of the present invention, the random noise is Gaussian noise.

[0015] As a further aspect of the present invention, the adaptive kernel density estimation includes: using a Gaussian kernel function, calculating the initial bandwidth using the Silverman rule, finding the globally optimal bandwidth by minimizing the mean square integral error, and calculating the probability density function under the optimal bandwidth.

[0016] As a further aspect of the present invention, the minimization of the mean square integral error is performed by replacing the true density function with an empirical histogram and using a discretized form for optimization calculation.

[0017] As a further aspect of the present invention, the feature parameter value corresponding to the 95% quantile is used as the boundary threshold between the normal operation state and the attention state, and the feature parameter value corresponding to the 99% quantile is used as the boundary threshold between the attention state and the abnormal state.

[0018] Another aspect of this application provides an improved transformer vibration probability modeling and evaluation system based on Bootstrap and adaptive KDE, including:

[0019] The data acquisition module is used to collect vibration acceleration signals from the surface of the transformer housing.

[0020] The feature extraction module is used to convert time-domain signals into frequency-domain signals and extract feature parameters such as fundamental frequency weight, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio to construct the original sample set.

[0021] The sample augmentation module is used to augment the original sample set using an improved Bootstrap method to obtain an augmented sample set.

[0022] The probability modeling module is used to perform probability modeling on the expanded sample set based on adaptive kernel density estimation to obtain the probability density function.

[0023] The condition assessment module is used to calculate the cumulative distribution function based on the probability density function and to classify and assess the transformer operating condition according to the 95% and 99% quantiles.

[0024] As a further aspect of the present invention, the evaluation rules of the state evaluation module are as follows:

[0025] If the characteristic parameter value is ≤95% quantile, it is determined to be in normal operating condition;

[0026] If the 95th percentile < the characteristic parameter value ≤ the 99th percentile, it is determined to be a state of attention;

[0027] If the characteristic parameter value is greater than 99 percentile, it is judged as an abnormal state.

[0028] A third aspect of this application provides a computer read storage medium storing at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement an improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method.

[0029] In summary, due to the adoption of the above technical solution, the beneficial technical effects of the invention are as follows:

[0030] First, this invention expands the original sample set by introducing an improved Bootstrap method. Specifically, it resamples the original samples with replacement and introduces random noise, effectively overcoming the problem of insufficient sample diversity generated by traditional Bootstrap methods. This method significantly expands the sample capacity while maintaining the original sample distribution characteristics, solving the technical shortcomings of limited sample size and sparse distribution in field monitoring, which lead to large variance and insufficient reliability in probability estimation. This lays a data foundation for subsequent accurate probability density modeling.

[0031] Second, this invention employs an adaptive kernel density estimation method based on the Minimum Mean Square Integral Error (MISE) criterion. It optimizes the calculation of the globally optimal bandwidth using a discretized empirical histogram, replacing the fixed bandwidth based on empirical rules in traditional methods. This approach can adaptively fit the complex skewed and multi-peak distributions of transformer vibration characteristic parameters, significantly improving the fitting accuracy of the probability density function in the peak and tail regions. It overcomes the problems of traditional kernel density estimation curves being too smooth and insensitive to complex distribution structures, thus achieving a high-precision characterization of the true distribution of characteristic parameters.

[0032] Third, this invention derives the cumulative distribution function based on a precisely constructed probability density function and scientifically sets the 95% and 99% quantiles as three-level early warning thresholds for normal operation, alert status, and abnormal status. This scheme fully utilizes the global continuous probability information of the characteristic parameter distribution, providing a quantitative evaluation standard with clear statistical confidence, and solving the problems of inaccurate and easily interfered-prone setting of traditional fixed thresholds or histogram thresholds. Verification through actual substations has proven that this invention can effectively provide early warning of transformer abnormalities, significantly improving the accuracy and reliability of transformer operating status uncertainty assessment. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the overall technical solution framework provided in the embodiments of the present invention;

[0034] Figure 2 This is a schematic diagram illustrating the steps of expanding transformer vibration characteristic parameter samples using the improved Bootstrap method according to an embodiment of the present invention.

[0035] Figure 3 This is a schematic diagram illustrating the steps of using the adaptive KDE method to probabilistically model the vibration characteristic parameter samples of the expanded transformer, as provided in an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0038] The core objective of this invention is to address the problems of limited sample size, complex distribution patterns, and inaccurate threshold settings in existing methods for probabilistic modeling and state assessment of transformer vibration characteristics. This invention provides an improved Bootstrap and adaptive KDE-based method for probabilistic modeling and assessment of transformer vibration. This method amplifies the limited sample size by introducing noise-enhanced resampling technology, accurately fits the true distribution of feature parameters using bandwidth-adaptive kernel density estimation, and finally sets graded early warning thresholds based on probability quantiles, thereby achieving accurate and reliable assessment of the transformer's operating state.

[0039] The core technical logic of this method is:

[0040] First, vibration acceleration signals on the surface of the transformer tank are collected and converted to the frequency domain using fast Fourier transform. Four types of characteristic parameters that can characterize the mechanical state of the transformer are extracted, including fundamental frequency ratio, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio, to construct the original sample set.

[0041] Secondly, to address the issues of small sample size and sparse distribution of the original samples, an improved Bootstrap method is used to resample the original samples with replacement and add random noise to generate a diverse expanded sample set. Then, based on the expanded sample set, an adaptive kernel density estimation method is adopted with the criterion of minimizing the mean square integral error to construct the probability density function of each feature parameter, overcoming the problem of insufficient fitting accuracy of traditional fixed bandwidth kernel density estimation in the peak and tail regions.

[0042] Finally, based on the probability density function, the cumulative distribution function is derived, and the 95% and 99% quantiles are extracted as the graded early warning thresholds for normal operation, alert status and abnormal status, so as to realize the quantitative assessment and graded early warning of transformer operation status.

[0043] like Figure 1 As shown, this application illustrates an exemplary improved Bootstrap and adaptive KDE method for transformer vibration probability modeling and evaluation, specifically including the following steps:

[0044] S100. Feature parameter extraction;

[0045] S200. Sample expansion using an improved Bootstrap;

[0046] S300. Probabilistic modeling is performed using adaptive KDE vibration characteristic parameter samples;

[0047] S400. Probability threshold determination.

[0048] In an improved Bootstrap and adaptive KDE method for probabilistic modeling and evaluation of transformer vibration, the goal of S100 is to extract key feature parameters from the original vibration signal and construct an original sample set for subsequent modeling.

[0049] The specific steps include:

[0050] S110. The vibration acceleration signal of the transformer tank surface is synchronously collected using the Saturn TX3200 transformer online detection system and the W100 wireless vibration sensor. Three measuring points are set up for each transformer. The collected time-domain signal is converted into a frequency-domain signal using Fast Fourier Transform. The specific formula for Fast Fourier Transform is as follows:

[0051] ;

[0052] In the formula, The total length of the time and frequency domains; For the index of discrete points in the time domain; For the index of discrete points in the frequency domain; This represents the input time-domain signal; For the first Each frequency domain value represents the amplitude and phase of the corresponding frequency domain component. is the rotation factor.

[0053] S120. Four characteristic parameters—fundamental frequency proportion, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio—are selected as key indicators to characterize the transformer's operating status. The average value of the vibration characteristic parameters calculated at three measuring points for each transformer is taken as the characteristic parameter value of that transformer. The calculation formulas for each characteristic parameter are as follows:

[0054] Fundamental frequency weight:

[0055] ;

[0056] In the formula, The order of the harmonics; This is the fundamental frequency amplitude; For 50Hz Subharmonic vibration amplitude.

[0057] Odd-even harmonic ratio: ;

[0058] High-low frequency ratio: ;

[0059] In the formula, It is the dividing point between high and low frequencies.

[0060] Spectral complexity:

[0061] In the formula, The proportion of the 50Hz harmonic vibration amplitude.

[0062] Please refer to Figure 2 The flowchart of an exemplary improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method and system S200 of this application is shown.

[0063] In an improved method and system for modeling and evaluating transformer vibration probabilistics using Bootstrap and adaptive KDE, the purpose of S200 is to address the problems of small original sample size and sparse distribution, thereby improving the diversity and reliability of the sample set.

[0064] In the existing technology, the original sample size for the fundamental frequency proportion of 110kV transformers is 148, and the original sample size for the spectral complexity of 220kV transformers is 54. These sample sizes are relatively small and sparsely distributed in some intervals. Directly using these samples for probability modeling can easily lead to problems such as large variance in probability estimation and insufficient reliability. Therefore, a sample expansion method is needed to expand the original sample set of transformer vibration characteristic parameters to obtain an expanded sample set. This invention utilizes an improved Bootstrap method to expand the original sample set. The traditional Bootstrap method is a non-parametric resampling method. Its core idea is to generate multiple sample sets of the same size as the original samples by repeatedly sampling the original samples with replacement, thereby achieving data expansion. However, the sample values ​​generated by the traditional Bootstrap method are limited by the original observation points, resulting in insufficient diversity. The improved Bootstrap method performs random sampling with replacement, introducing random perturbation to enhance the diversity and authenticity of the generated samples. The original samples and expanded samples are then merged to verify the sample expansion effect.

[0065] The specific steps include:

[0066] S210. Let the original sample set be denoted as Randomly generate integer sequences , The number of samples for each resampled subset, with samples drawn with replacement to form the resampled subset. .

[0067] S220. For the current resampled subset Noise injection is performed to generate an enhanced sample set. The mathematical model for noise injection is shown below.

[0068] ;

[0069] In the formula, For independently generated noise matrices, , This is a noise intensity parameter.

[0070] For the j-th resampled subset, the noise injection process can be represented in detail as follows:

[0071] ;

[0072] In the formula, The number of samples in each resampled subset. For feature dimensions. This represents the data after noise injection. This indicates resampled data. This represents independently generated noise.

[0073] Processed sample subset By merging, we obtain the final expanded sample set. The total number of samples after expansion is .

[0074] In this embodiment, the original samples of each characteristic parameter of the 110kV transformer are expanded from 148 to 700, and the original samples of each characteristic parameter of the 220 transformer are expanded from 54 to 300.

[0075] To evaluate the effect of the improved Bootstrap on sample expansion, this embodiment uses five statistical test indicators to compare and analyze the central tendency, dispersion, and distribution pattern of the sample distribution before and after expansion. Among them, the relative errors of the mean and standard deviation represent the central tendency and dispersion of the data, respectively; JS divergence and Wasserstein distance measure the overall similarity between the two distributions; and the KS test statistic reflects the maximum deviation between the two empirical distribution functions.

[0076] The expressions for JS divergence and Wasserstein distance are as follows:

[0077] JS divergence is a variation of KL divergence, assuming two probability distributions: the probability distribution of the original samples. Probability distribution of augmented samples Then the probability distribution of the original sample Probability distribution of augmented samples KL divergence for:

[0078] ;

[0079] Probability distribution of the original sample Probability distribution of augmented samples JS divergence The definition of is:

[0080] ;

[0081] The Wasserstein distance is defined as follows:

[0082] ;

[0083] In the formula, Marginal probability distribution of the original sample and Wasserstein distance between them; ,, , , It is a marginal distribution and The joint distribution express and All possible coupled distributions that can be combined; The infimum represents the boundary condition for all possible joint distributions. In the mean, the minimum expected value;

[0084] Please refer to Figure 3 The diagram illustrates an exemplary flowchart of an improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method and system S300 of this application;

[0085] In an improved method and system for probabilistic modeling and evaluation of transformer vibration using Bootstrap and adaptive KDE, the purpose of S300 is to construct the probability density function of the characteristic parameters and accurately fit their complex distribution.

[0086] Kernel density estimation, as a non-parametric estimation method, does not require a pre-defined distribution form and can directly learn distribution characteristics from the data itself. Its core idea is to apply a kernel function at each data point and then superimpose these local functions to construct the overall probability density distribution.

[0087] The specific steps include:

[0088] S310. Sample data Set as real PDF Then the estimated PDF value for:

[0089] ;

[0090] In the formula, For kernel function, The sample number. For the first Each sample observation value For the sample size, The bandwidth parameter serves as a smoothing scaling factor, regulating the influence range of the kernel function. The bandwidth-scaled function is defined as follows: , divided by The purpose is to ensure that the area under the kernel function always integrates to 1.

[0091] This invention uses the Gaussian function, whose expression is:

[0092] ;

[0093] In the formula, The value of the random variable. Indicates the point to be estimated With sample points Standardized distance between them; This is the exponential part of the Gaussian kernel;

[0094] The accuracy of kernel density estimation depends critically on the choice of bandwidth. Bandwidth parameter It controls the smoothness of the estimate. Bandwidth If the kernel size is too large, the influence range of the kernel function becomes too wide, leading to over-smoothing of the estimation; bandwidth Too small: If the influence range of the kernel function is too small, the estimation result will be too sensitive to noise, leading to an increase in the estimation variance.

[0095] Traditional Gaussian kernel density estimation (GKDE) uses a fixed bandwidth based on empirical rules, which is difficult to flexibly adapt to the local distribution characteristics of different data regions. For example, its fitted curve is too smooth in peak and valley regions and is insensitive to complex distribution structures such as skewness and multimodality, resulting in a distribution that is often flatter than the actual distribution. To overcome these limitations, this embodiment proposes an adaptive bandwidth kernel density estimation method based on MISE optimization, the specific steps of which are as follows:

[0096] The specific steps for calculating the initial bandwidth using S320.Silverman are as follows:

[0097]

[0098] In the formula, This represents the sample standard deviation.

[0099] The expression for S330.MISE is:

[0100] ;

[0101] In practical applications, due to the true density This is usually unknown. Therefore, an empirical histogram is used instead of the true density to transform MISE into a discretized form:

[0102] ;

[0103] In the formula, For the first The center of each histogram bin is at The empirical probability density at that location, For bandwidth Below, kernel density estimation is in The value at that location, The width of the histogram bins. This represents the number of effective boxes.

[0104] Based on the improved Bootstrap and adaptive KDE-based probabilistic modeling and state assessment method for transformer vibration characteristic parameters, the final adaptive bandwidth in S300 is:

[0105] S340 selects the factor that minimizes MISE(h) as the optimal adjustment factor. The final adaptive bandwidth expression is:

[0106] ;

[0107] To quantitatively evaluate the fit of each model, this embodiment uses the KS test statistic. Root mean square error Mean absolute percentage error Coefficient of determination Four goodness-of-fit indices are used to evaluate the fitting results. The KS test statistic measures the maximum vertical distance between the empirical distribution and the estimated distribution; the smaller the value, the closer the estimated distribution is to the empirical distribution. The RMSE measures the average deviation between the estimated probability density and the empirical probability density; the smaller the RMSE value, the higher the fitting accuracy. The MAPE measures the percentage deviation of the estimated probability density from the empirical probability density; the smaller the value, the smaller the relative error of the fit. The closer the value is to 1, the better the model fit. The calculation formulas for each test index are shown below:

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] In the formula, In order to be in The estimated cumulative distribution function at a given location; the actual cumulative probability distribution function. In the estimation The true cumulative distribution function at that location.

[0113] In an improved method and system for probabilistic modeling and evaluation of transformer vibration using Bootstrap and adaptive KDE, the purpose of S400 is to set a state-level early warning threshold based on a probability density function to achieve a quantitative evaluation of the transformer's operating status.

[0114] The specific steps include:

[0115] Based on the probability density function of each feature parameter, its cumulative distribution function is derived, and its 95% and 99% quantiles are calculated as the thresholds for state-level early warning.

[0116] The cumulative distribution function of each feature parameter is calculated based on the probability density function obtained from the adaptive KDE. The values ​​corresponding to the 95th and 99th percentiles of each feature parameter are calculated. The value corresponding to the 95th percentile is used as the attention threshold for a normally operating transformer. If the detected feature parameter value is greater than this threshold, it indicates that the transformer has begun to deviate from its normal operating state. The 99th percentile is used as the anomaly threshold for a normally operating transformer. If the feature parameter value is greater than this threshold, it indicates that the transformer is in an abnormal state.

[0117] Example 2:

[0118] An improved system for probabilistic modeling and state assessment of transformer vibration characteristics using Bootstrap and adaptive KDE, the system comprising:

[0119] Data acquisition module:

[0120] It is used to connect with multiple wireless vibration sensors (such as the W100 type) and online detection systems (such as the Saturn TX3200 type) arranged on the surface of the transformer tank, to collect vibration acceleration signals on the surface of the transformer tank in real time and transmit the collected time domain signals to the feature extraction module.

[0121] Feature extraction module:

[0122] This device receives the time-domain vibration signal output from the data acquisition module, converts the time-domain signal to a frequency-domain signal using a Fast Fourier Transform (FFT), and automatically calculates the following four characteristic parameters based on the frequency-domain signal:

[0123] Fundamental frequency weighting: The ratio of the fundamental frequency (50Hz) amplitude to the total harmonic frequency amplitude;

[0124] Spectral complexity: Information entropy based on harmonic amplitude distribution;

[0125] Even-odd harmonic ratio: The ratio of the sum of the amplitudes of odd harmonics to the sum of the amplitudes of even harmonics;

[0126] High-low frequency ratio: The ratio of the sum of the amplitudes of the high-frequency band (>700Hz) to the low-frequency band (≤700Hz);

[0127] The average value of the characteristic parameters of multiple measuring points of the same transformer is taken as the representative characteristic parameter of the transformer to construct the original sample set.

[0128] Sample expansion module:

[0129] This method is used to augment the original sample set using an improved Bootstrap approach, specifically including:

[0130] The original sample is resampled with replacement to generate multiple resampled subsets;

[0131] Add random noise that follows a Gaussian distribution to the samples in each resampled subset;

[0132] Multiple sets of noisy samples generated are merged with the original samples to form an expanded sample set, thereby improving sample diversity and model generalization ability.

[0133] Probabilistic modeling module:

[0134] This method is used to construct the probability density function of each feature parameter based on the expanded sample set using an adaptive kernel density estimation method, specifically including:

[0135] Use a Gaussian kernel function;

[0136] Calculate the initial bandwidth using Silverman rules;

[0137] The optimal bandwidth adjustment factor is searched based on the criterion of minimizing the mean square integral error (MISE).

[0138] Output the final probability density function under adaptive bandwidth.

[0139] Status assessment module:

[0140] The cumulative distribution function of each feature parameter is used to calculate the probability density function, and the 95% and 99% quantiles are extracted as state classification early warning thresholds. The specific evaluation rules are as follows:

[0141] If the characteristic parameter value is ≤ 95% quantile: it is determined to be in normal operating condition;

[0142] If the 95th percentile < the characteristic parameter value ≤ the 99th percentile: it is judged as a state of alert, indicating that the transformer may deviate from normal operation;

[0143] If the characteristic parameter value is greater than the 99th percentile, it is judged as an abnormal state, indicating that the transformer has a significant risk of mechanical failure.

[0144] The system can be deployed on a local server in a substation or on a cloud platform, supporting real-time or offline assessment.

[0145] Example 3:

[0146] An improved Bootstrap and adaptive KDE-based probabilistic modeling and state assessment system for transformer vibration characteristics was successfully applied and verified in a 110kV substation. The specific implementation method is as follows:

[0147] System configuration and testing plan:

[0148] Test equipment Saturn TX3200 Transformer Online Monitoring System, W100 Wireless Vibration Sensor Test object Three 110kV oil-immersed transformers, model numbers SFZ11-50000 / 110, SFZ11-63000 / 110, and SFZ11-80000 / 110 respectively. Measurement point layout Three vibration measuring points are arranged on the surface of each transformer tank (top of the tank, middle of the side, and near the cooler). sampling frequency 10 kHz Sampling duration Each transformer was continuously sampled for 120 minutes. Data preprocessing The acquired vibration signals are detrended and de-DC component processed.

[0149] Implementation steps:

[0150] Data acquisition and feature extraction:

[0151] Vibration acceleration signals from three transformers were simultaneously collected using wireless vibration sensors. After being converted into frequency domain signals by FFT, the fundamental frequency ratio, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio of each measuring point of each transformer were calculated. The average value of the three measuring points was taken as the characteristic parameter value of the transformer, and the original sample set was constructed (sample size = 3 × 120 minutes of sampling segments).

[0152] Sample expansion:

[0153] An improved Bootstrap method was used to resample the original sample set 500 times with replacement. After each resampling, Gaussian noise with a noise intensity of σ=0.02 was added to generate 500 enhanced samples, which were then merged with the original samples to form an expanded sample set.

[0154] Probability density modeling:

[0155] Based on the expanded sample set, an adaptive kernel density estimation method is used to construct the probability density function of each feature parameter. The bandwidth is optimized with the goal of minimizing MISE, and the final probability density function is obtained.

[0156] Threshold setting and status assessment:

[0157] The cumulative distribution function of each characteristic parameter is calculated based on the probability density function, and the 95% and 99% quantiles are extracted as the graded early warning thresholds to evaluate the real-time characteristic parameters of each transformer.

[0158] Application results:

[0159] This method successfully identified minor anomalies in two of the three transformers. Specifically:

[0160] The fundamental frequency proportion characteristic parameter of transformer A (SFZ11-50000 / 110) exceeds the 95th percentile, reaching 96.2%;

[0161] The fundamental frequency proportion characteristic parameter of transformer B (SFZ11-63000 / 110) exceeds the 95th percentile, reaching 97.5%;

[0162] All characteristic parameters of transformer C (SFZ11-80000 / 110) are below the 95th percentile, and it is judged to be normal.

[0163] Verification status:

[0164] By comparing with the substation maintenance records, transformers A and B were found to have problems with poor core grounding and slight loosening of windings, respectively, during subsequent maintenance. This was consistent with the actual assessment results and verified the effectiveness of the method in early anomaly identification.

[0165] Typical application cases:

[0166] In a 220kV substation, this system performs long-term monitoring of an operating 220kV transformer (model: SSZ11-180000 / 220). On the 45th day of continuous operation, the system identified that its spectral complexity characteristic parameter exceeded the 99th percentile, triggering an anomaly warning. Maintenance personnel shut down the transformer for inspection based on the warning information and discovered a loose core clamping fault. After tightening, the spectral complexity returned to normal levels. The system successfully issued a warning 7 days in advance, preventing the fault from escalating further.

[0167] Example 4:

[0168] According to Embodiment 1 of this application, a computer-readable storage medium is provided, which stores at least one instruction, at least one program, code set, or instruction set. The at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement an improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method.

[0169] The sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0170] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. An improved method for modeling and evaluating the probability of transformer vibration using Bootstrap and adaptive KDE, characterized in that, Includes the following steps: S100. Collect transformer vibration signals, use Fast Fourier Transform to convert the collected signals from the time domain to the frequency domain, extract feature parameters, and construct the original sample set; S200. The original sample set of transformer vibration characteristic parameters is expanded using the improved Bootstrap method to obtain the expanded sample set of vibration characteristic parameters; S300. Based on adaptive kernel density estimation, probabilistic modeling is performed on the expanded vibration characteristic parameter sample set to obtain the probability density function; S400. Based on the probability density function of each feature parameter, derive its cumulative distribution function, and calculate its 95% and 99% quantiles as the thresholds for state-level early warning.

2. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 1, characterized in that, The extracted feature parameters include fundamental frequency weight, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio.

3. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 1, characterized in that, The improved Bootstrap method includes: resampling the original samples with replacement to obtain a resampled subset, and introducing random noise into each sample in the resampled subset to generate a noisy sample subset.

4. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 3, characterized in that, The random noise is Gaussian noise.

5. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 1, characterized in that, The adaptive kernel density estimation includes: using a Gaussian kernel function, calculating the initial bandwidth using the Silverman rule, finding the globally optimal bandwidth by minimizing the mean square integral error, and calculating the probability density function under the optimal bandwidth.

6. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 5, characterized in that, The minimization of the mean square integral error is optimized by replacing the true density function with an empirical histogram and using a discretized form.

7. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation method according to claim 1, characterized in that, The feature parameter value corresponding to the 95% quantile is used as the boundary threshold between the normal operation state and the attention state, and the feature parameter value corresponding to the 99% quantile is used as the boundary threshold between the attention state and the abnormal state.

8. An improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation system, characterized in that, include: The data acquisition module is used to collect vibration acceleration signals from the surface of the transformer housing. The feature extraction module is used to convert time-domain signals into frequency-domain signals and extract feature parameters such as fundamental frequency weight, spectral complexity, odd-even harmonic ratio, and high-low frequency ratio to construct the original sample set. The sample augmentation module is used to augment the original sample set using an improved Bootstrap method to obtain an augmented sample set. The probability modeling module is used to perform probability modeling on the expanded sample set based on adaptive kernel density estimation to obtain the probability density function. The condition assessment module is used to calculate the cumulative distribution function based on the probability density function and to classify and assess the transformer operating condition according to the 95% and 99% quantiles.

9. The improved Bootstrap and adaptive KDE transformer vibration probability modeling and evaluation system according to claim 8, characterized in that, The evaluation rules of the status evaluation module are as follows: If the characteristic parameter value is ≤95% quantile, it is determined to be in normal operating condition; If the 95th percentile < the characteristic parameter value ≤ the 99th percentile, it is determined to be a state of attention; If the characteristic parameter value is greater than 99 percentile, it is judged as an abnormal state.

10. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the method as described in any one of claims 1 to 7.

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