Frequency modulation continuous wave-based cable local insulation defect detection method

Abstract

The invention discloses a frequency modulated continuous wave cable local insulation defect detection method, which comprises the following steps: S1, realizing an FMCW method by using an FMCW cable fault positioning system, performing spectrogram function extraction and analysis on an incident signal and a reflected signal at a certain moment in the FMCW method to obtain a frequency difference between the incident signal and the reflected signal at the certain moment, and determining the frequency difference between the incident signal and the reflected signal at the certain moment; therefore, the position information from the cable defect to the head end of the cable is obtained, and effective fault diagnosis is realized. S2, time domain, frequency domain and power spectrum characteristic index extraction is carried out on the spectrogram function analysis signals, and index data of the analyzed signals are known more comprehensively; the method solves the problems that in the prior art, a reflection method is limited by frequency domain reflection signal amplitude attenuation, the detection distance is short, the requirement for long-distance cable detection cannot be met, FFT positioning spectrum covering information is single, interference of environmental factors is likely to happen, and cable state evaluation is not comprehensive enough.

Description

Technical Field

[0001] This invention belongs to the field of power equipment, and specifically relates to a method for detecting local insulation defects in frequency-modulated continuous wave cables. Background Technology

[0002] Cross-linked polyethylene (XLPE) cables have become the mainstream in urban power transmission and distribution networks due to their excellent insulation performance, ease of manufacturing, simple installation, reliable power supply, and low maintenance workload. However, the harsh operating environment of cables makes them susceptible to localized insulation defects caused by external forces, localized heat sources, and moisture ingress. Over time, these defects can lead to sudden power outages, causing significant economic losses and adverse social impacts. Effective cable inspection is crucial for improving power grid reliability. Traditional methods for detecting localized insulation defects in cables include Time Domain Reflectometry (TDR) and Frequency Domain Reflectometry (FDR). FDR is rapidly developing due to its higher sensitivity in detecting minor defects in cables (e.g., moisture in joints, localized aging, insulation damage). It has made significant progress in cable defect location in recent years. However, traditional FDR is limited by the attenuation of the frequency reflection signal amplitude, resulting in a short detection distance that cannot meet the needs of long-distance cable inspection. Furthermore, the FFT location spectrum provides limited information and is easily affected by environmental factors, leading to an incomplete assessment of cable condition. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a method for detecting local insulation defects in frequency-modulated continuous wave (FM-CW) cables. This method overcomes the limitations of existing reflection methods, which are subject to the attenuation of the frequency domain reflected signal amplitude, resulting in a short detection distance that fails to meet the requirements for long-distance cable detection. Furthermore, the FFT positioning spectrum covers only a limited range of information, is easily affected by environmental factors, and does not provide a comprehensive assessment of the cable's condition.

[0004] The technical solution of the present invention is as follows:

[0005] A method for detecting local insulation defects in frequency-modulated continuous wave cables includes the following steps:

[0006] Step S1: Implement the FMCW method using the FMCW cable fault location system. In the FMCW method, the incident signal and reflected signal at a certain moment are extracted and analyzed using the spectrogram function to obtain the frequency difference between the incident signal and the reflected signal at a certain moment, thereby obtaining the location information of the cable defect from the cable head end, and realizing effective fault diagnosis.

[0007] Step S2: Extract time-domain, frequency-domain, and power spectrum characteristic indicators from the spectrogram function analysis signal to gain a more comprehensive understanding of the indicator data of the analyzed signal.

[0008] Preferably, the FMCW method in step S1 includes the following steps:

[0009] Step S11: The frequency of the FMCW signal changes with time, and the reflected signal and the incident signal have a transmission time difference t. d This will result in a frequency difference f b ;

[0010] Step S12: Time difference signal t d Positively correlated with the target distance D, and with the frequency difference signal f b It is directly proportional, and its target distance D is expressed as:

[0011]

[0012] In the formula, ∆f is half the bandwidth of the frequency modulation; Ts is the frequency modulation period.

[0013] Preferably, the spectrogram function analysis of the signal includes the following steps:

[0014] Step S21: Analyze the frequency content of the signal as it changes over time based on the Short Time Fourier Transform (STFT).

[0015] Step S22: Decompose the signal into time segments based on the STFT function, and perform Fourier transform on each time segment to obtain the spectrum diagram that varies with time.

[0016] Step S23: Analyze the signal using a fixed window function. Once the parameters of the window function are selected, the entire time spectrum will use the same time-frequency resolution. The window function and its parameters determine the results of the spectrum analysis. The results of the spectrum analysis include time resolution and frequency resolution.

[0017] Step S24: In actual vibration signal time-frequency analysis, the STFT function needs to select appropriate window functions and parameters to obtain high frequency resolution for the low-frequency part of the signal and high time resolution for the high-frequency part.

[0018] Preferably, the Short-Time Fourier Transform (STFT) is specifically:

[0019] The signal is segmented and analyzed by using a window function to divide the measured signal into several segments of equal length. A Fourier transform is then performed on each segment to determine the frequency of each segment.

[0020] Preferably, the Fourier transform is as follows:

[0021] Transforming the changes of a signal in the time domain into changes in the frequency domain, that is, representing the signal on the frequency axis, allows us to observe the characteristics of the signal in both the time and frequency domains.

[0022] Preferably, the FMCW cable fault location system in step S1 includes: a signal source, a power divider, a circulator, a mixer, an oscilloscope, a computer, and a cable;

[0023] The signal source is connected to a power divider, which is connected to a mixer and a circulator respectively; the circulator is connected by a cable, the mixer is connected to an oscilloscope, and the oscilloscope is connected to a computer.

[0024] Preferably, the signal source is used to generate a continuous linear frequency modulated signal;

[0025] The power divider is used to retain the original signal on one side, inject the signal on the other side into the cable through a circulator, and extract the reflected signal generated by the impedance mismatch point in the cable through the lower port of the circulator; the mixer is used to mix the saved set of original signals with the extracted reflected signals, and finally the output mixed signal is received by an oscilloscope.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. The method proposed in this invention effectively improves the current situation of insufficient detection and location of local insulation defects in cables, significantly increases the detection distance and anti-interference strength of local insulation defects in cables, and expands the location information from two-dimensional fast Fourier transform amplitude-frequency diagram to three-dimensional spectrogram time-frequency diagram, covering rich information components, and extracting frequency component information at any time more clearly and intuitively, thereby realizing cable fault location.

[0028] 2. This invention improves the defect detection capability by replacing the traditional frequency domain reflection method with a spectrogram-based method for local insulation defects in FMCW cables, effectively avoiding sudden power outages. This method provides a more comprehensive and clear assessment of the cable's condition through spectrogram time-frequency analysis and extraction of signal characteristic indicators.

[0029] 3. This invention transforms the experimental device into practical applications through technology licensing or transfer. Due to the large number of cables, harsh operating environment, high accident rate, and urgent need, this invention has broad prospects. Attached Figure Description

[0030] To more clearly illustrate the purpose, design concept, and innovation of the proposed method for detecting local insulation defects in frequency-modulated continuous wave cables, the invention will be described in detail below with reference to the accompanying drawings and tables.

[0031] Figure 1A diagram of the FMCW cable fault location system of the present invention is shown.

[0032] Figure 2 A diagram of the cable fault location module based on the spectrogram function of the present invention is shown.

[0033] Figure 3 A time-frequency diagram of an incident wave and a reflected wave according to the present invention is shown.

[0034] Figure 4(a) shows the time-domain plot of the time-frequency results in the spectrogram function of the present invention.

[0035] Figure 4(b) shows the time-frequency representation of the spectrogram function in this invention. Figure 3 D-type. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0037] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0038] A method for detecting local insulation defects in frequency-modulated continuous wave cables includes the following steps:

[0039] Step S1: Implement the FMCW method using the FMCW cable fault location system. In the FMCW method, the incident signal and reflected signal at a certain moment are extracted and analyzed using the spectrogram function to obtain the frequency difference between the incident signal and the reflected signal at a certain moment, thereby obtaining the location information of the cable defect from the cable head end, and realizing effective fault diagnosis.

[0040] Step S2: Extract time-domain, frequency-domain, and power spectrum characteristic indicators from the spectrogram function analysis signal to gain a more comprehensive understanding of the indicator data of the analyzed signal.

[0041] The FMCW method in step S1 of this implementation scheme includes the following steps:

[0042] Step S11: The frequency of the FMCW signal changes with time, and the reflected signal and the incident signal have a transmission time difference t. d This will result in a frequency difference f b ;

[0043] Step S12: Time difference signal t d Positively correlated with the target distance D, and with the frequency difference signal f b It is directly proportional, and its target distance D is expressed as:

[0044]

[0045] In the formula, ∆f is half the bandwidth of the frequency modulation; Ts is the frequency modulation period.

[0046] The spectrogram function analysis of the signal in this implementation scheme includes the following steps:

[0047] Step S21: Analyze the frequency content of the signal as it changes over time based on the Short Time Fourier Transform (STFT).

[0048] Step S22: Decompose the signal into time segments based on the STFT function, and perform Fourier transform on each time segment to obtain the spectrum diagram that varies with time.

[0049] Step S23: Analyze the signal using a fixed window function. Once the parameters of the window function are selected, the entire time spectrum will use the same time-frequency resolution. The window function and its parameters determine the results of the spectrum analysis. The results of the spectrum analysis include time resolution and frequency resolution.

[0050] Step S24: In actual vibration signal time-frequency analysis, the STFT function needs to select appropriate window functions and parameters to obtain high frequency resolution for the low-frequency part of the signal and high time resolution for the high-frequency part.

[0051] The Short-Time Fourier Transform (STFT) of this implementation scheme is as follows:

[0052] The signal is segmented and analyzed by using a window function to divide the measured signal into several segments of equal length. A Fourier transform is then performed on each segment to determine the frequency of each segment.

[0053] The Fourier transform of this implementation scheme is as follows:

[0054] Transforming the changes of a signal in the time domain into changes in the frequency domain, that is, representing the signal on the frequency axis, allows us to observe the characteristics of the signal in both the time and frequency domains.

[0055] The FMCW cable fault location system in step S1 of this implementation scheme includes: a signal source, a power divider, a circulator, a mixer, an oscilloscope, a computer, and a cable;

[0056] The signal source is connected to the power divider, which in turn connects to the mixer and the circulator; the circulator is connected by a cable, the mixer is connected to the oscilloscope, and the oscilloscope is connected to the computer.

[0057] The signal source in this implementation scheme is used to generate a continuous linear frequency modulated signal;

[0058] The power divider is used to retain the original signal on one side, inject the signal on the other side into the cable through a circulator, and extract the reflected signal generated by the impedance mismatch point in the cable through the lower port of the circulator; the mixer is used to mix the saved set of original signals with the extracted reflected signals, and finally the output mixed signal is received by an oscilloscope.

[0059] The specific implementation plan is as follows:

[0060] This invention provides a method for detecting local insulation defects in frequency-modulated continuous wave (FMCW) cables. Its working principle is based on the fact that FMCW signal modulation methods are widely used in automotive collision avoidance systems, liquid level measurement, and other fields. An FMCW cable fault location system, such as... Figure 1 As shown, the system comprises a signal source, power divider, circulator, mixer, and oscilloscope. The signal source generates a continuous linear frequency modulation (LFM) signal, with its frequency varying linearly over time. The power divider retains the original signal from one side and injects the signal from the other side into the cable via the circulator. It also extracts the reflected signal from the cable caused by impedance mismatch points through the lower port of the circulator. The mixer mixes the stored original signal with the extracted reflected signal, and the final mixed signal is received by the oscilloscope.

[0061] Figure 3 The frequency of the FMCW signal changes with time, and the reflected signal and the incident signal differ due to the transmission time difference t. d This will result in a frequency difference f b Wherein, frequency difference f b Mainly composed of f b + Signal composition. Time difference signal t d Positively correlated with the target distance D, and with the frequency difference signal f b Proportional, the target distance D can be calculated using the formula:

[0062]

[0063] In the formula: ∆f is half the bandwidth of the frequency modulation; T sThe frequency modulation period is used. After the signal is measured from the mixer output, it undergoes a fast Fourier transform (FFT) to calculate the signal's spectrum, which serves as the location spectrum for cable defects.

[0064] The Fourier transform is a linear integral transform that converts the changes of a signal in the time domain into changes in the frequency domain, representing the signal on the frequency axis, thus allowing observation of the signal's characteristics in both the time and frequency domains. However, the Fourier transform primarily obtains the overall spectrum of the signal's change from the time domain to the frequency domain; it is a global transform and cannot represent the local characteristics of the signal or the changes in frequency over time. Therefore, the Windowed Time Fourier Transform (STFT) was proposed. The basic idea of ​​the STFT is to perform segmented analysis of the signal, using a window function to divide the measured signal into several segments of equal length, and then performing a Fourier transform within each segment to determine the frequency of each segment. The STFT is also known as the Windowed Time Fourier Transform.

[0065] The spectrogram function is based on the Short-Time Fourier Transform (STFT) and is used to analyze the frequency content of a signal as it changes over time. The STFT function decomposes the signal into time segments and performs a Fourier transform on each segment, resulting in a time-varying spectrogram as shown in Figure 4. The colored regions represent the decibel values ​​of the signal power spectral density at the corresponding frequencies, describing the energy distribution of the signal in the frequency domain. Figure 4 shows an example of the spectrogram time-frequency result according to the present invention. Figure 4(a) is the extracted time-frequency graph, where lighter colors represent higher frequencies in that time period. Figure 4(b) shows the time-frequency graph... Figure 3 D-type.

[0066] The spectrogram function relies on a fixed window function to analyze the signal. Once the window function parameters are selected, the entire time spectrum will use the same time-frequency resolution. This means that the window function and its parameters determine the results of the spectrum analysis, which include both time resolution and frequency resolution. In practical vibration signal time-frequency analysis, it is necessary to obtain high frequency resolution for the low-frequency part of the signal and high time resolution for the high-frequency part. Therefore, STFT requires the selection of appropriate window functions and parameters when performing time-frequency analysis. Common window functions include rectangular windows, triangular windows, Hanning windows, Hamming windows, and Gaussian windows.

[0067] If a highly distinguishable time-frequency analysis plot can be obtained, and the energy distribution of each category is relatively consistent, then the identification signal can be easily distinguished. In the FMCW method, by extracting and analyzing the incident and reflected signals at a certain moment using the spectrogram function, the frequency difference between the incident and reflected signals at that moment can be obtained, thereby determining the location information of the cable defect from the cable head, thus achieving effective fault diagnosis. Furthermore, the time-domain, frequency-domain, and power spectral characteristic indicators of the analyzed signal can be extracted using the spectrogram function, providing a more comprehensive understanding of the analyzed signal's indicator data.

[0068] Table 1 Signal Characteristic Indicators

[0069]

[0070] This implementation plan is further implemented as follows:

[0071] The signal used in FMCW is a linear frequency modulation (LFM) signal. The LFM waveform has the following expression in the time domain:

[0072]

[0073] In the formula: A is the signal amplitude; frect(t / τ) represents a rectangular pulse with width τ; f0 is the center frequency; t and μ control the signal duration and bandwidth, respectively. In the frequency domain, the continuous waveform of the s1 signal is transmitted in a sawtooth pattern, which can be written as follows:

[0074]

[0075] In the formula, ω0(t) is the angular frequency of the s1 cosine signal; φ0 is the initial phase of the s1 signal. The frequency f of the s1 signal can be calculated as follows:

[0076]

[0077] In the formula, ω0(t) is the angular frequency of the s1 cosine signal, f0 is the center frequency; t and μ control the duration and bandwidth of the signal, respectively.

[0078] Assume the distance of signal s1 to the impedance mismatch point is D, and the received signal s r It can be calculated as:

[0079]

[0080] In the formula: α is the signal transmission attenuation factor; t d=2D / v is the bidirectional time delay to the target, where v is the signal transmission speed in the cable, which can be measured by the pulse reflection method to determine the average wave speed of the signal in the cable. The frequency f of the received signal... r The following can be calculated:

[0081]

[0082] In the formula, ω0(t) is the angular frequency of the s1 cosine signal, and f0 is the center frequency; t and μ control the duration and bandwidth of the signal, respectively. d The periodic delay between the transmitted and incident signals can be expressed as:

[0083]

[0084] Where v represents the signal transmission speed in the cable, and v is closely related to the characteristic impedance of the cable, and x is the distance from the fault location to the beginning of the cable.

[0085] Will receive signal s r After mixing with the reference signal s1 and extracting the lower sideband, the output signal can be expressed as:

[0086]

[0087] In the formula, f b (t) represents the frequency difference, and φ represents the signal s. out The phase.

[0088]

[0089] f b (t) waveform as shown Figure 2 As shown, where f b Mainly composed of f b + The signal composition can be obtained from the following formula:

[0090]

[0091] Extracting D, we get the following formula:

[0092]

[0093] In the formula: v represents the signal transmission speed in the cable, Ts is the frequency modulation period, and ∆f is half the bandwidth of the frequency modulation. From Figure 2 It can be seen that the time difference signal t d Positively correlated with the target distance D, and with the frequency difference signal f b It is directly proportional, and the target distance D can be calculated using the formula.

[0094] The spectrogram function is based on the Short-Time Fourier Transform (STFT) and is a commonly used time-frequency analysis method. This method is an improvement upon the classical Fourier Transform. The classical Fourier Transform is a very important method in signal analysis; the expression for the Fourier Transform of any signal x(t) is:

[0095]

[0096] Where t represents time, ω represents angular frequency, and X(ω) is the result of the Fourier transform of signal x(t). By extracting and analyzing the incident and reflected signals acquired at a certain moment using the spectrogram function, the signal is decomposed into time segments, and a Fourier transform is performed on each segment to obtain a time-varying spectrum, defined as:

[0097]

[0098] Where ω(t) is a window of width T, with center τ, τ is the time position parameter of the window function, f is the frequency of the signal, and ω*(t) is the conjugate of the complex function ω(t). The parameters for calling the spectrogram function are as follows:

[0099]

[0100] x represents the vector of the input signal; window represents the window function; nooverlap represents the number of overlapping samples in each segment; nfft represents the number of points for calculating the discrete Fourier transform; fs represents the sampling frequency; S represents the short-time Fourier transform of the input signal x; F represents the use of the F frequency vector in the input variables; T represents the time point for calculating the spectrum; P represents the power spectral density (PSD); the time axis represents the signal duration, and its length n is:

[0101]

[0102] In the formula, N x The input signal length is given by length(window), the window function length is given by length(window), and nooverlap is the number of overlapping samples in each segment.

[0103] The frequency axis is represented by analog frequencies, and its display range is half of the sampling frequency. Therefore, its length is nfft / 2+1 or (nfft+1) / 2. The resolution of the frequency axis is affected by nfft, which is 1 / nfft*fs. The larger nfft is, the higher the resolution of the frequency domain, but the further away from the instantaneous frequency. The choice of nfft is consistent with that in the Fast Fourier Transform, and is usually taken as the nearest power of 2 to the signal length.

[0104]

[0105] In the formula, nextpow2 calculates the smallest power of 2 greater than or equal to the input value and returns the corresponding exponent, and length(window) is the length of the window function.

[0106] The signal length here refers to the window function length, as it is a Fast Fourier Transform of each windowed signal. The introduction of the noverlap parameter increases the time axis resolution, meaning the frequency axis is updated every (Nw - noverlap) lengths. As the noverlap parameter approaches the window length, the time axis appears more "refined" in the image, but this inevitably increases the number of calculations. This method can extract the incident and reflected FMCW signals at the same time, derive the frequency difference between the two sets of signals, and thus determine the target fault distance, enabling effective fault diagnosis. The analyzed signal can undergo time-domain, frequency-domain, and power spectrum feature analysis, extracting relevant indicators for in-depth study and significantly improving the detection capability of local insulation defects in cables.

Claims

1. A method for detecting local insulation defects in frequency-modulated continuous wave cables, characterized in that, Includes the following steps: Step S1: Implement the FMCW method using the FMCW cable fault location system. In the FMCW method, the incident signal and reflected signal at a certain moment are extracted and analyzed using the spectrogram function to obtain the frequency difference between the incident signal and the reflected signal at a certain moment, thereby obtaining the location information of the cable defect from the cable head end, and realizing effective fault diagnosis. Step S2: Extract time-domain, frequency-domain, and power spectrum characteristic indicators from the spectrogram function analysis signal to gain a more comprehensive understanding of the indicator data of the analyzed signal.

2. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 1, characterized in that, The FMCW method in step S1 includes the following steps: Step S11: The frequency of the FMCW signal changes with time, and the reflected signal and the incident signal have a transmission time difference t. d This will result in a frequency difference f b ; Step S12: Time difference signal t d Positively correlated with the target distance D, and with the frequency difference signal f b It is directly proportional, and its target distance D is expressed as: ； In the formula, ∆f is half the bandwidth of the frequency modulation; Ts is the frequency modulation period.

3. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 1, characterized in that, The spectrogram function analyzes the signal by including the following steps: Step S21: Analyze the frequency content of the signal as it changes over time based on the Short Time Fourier Transform (STFT). Step S22: Decompose the signal into time segments based on the STFT function, and perform Fourier transform on each time segment to obtain the spectrum diagram that varies with time. Step S23: Analyze the signal using a fixed window function. Once the parameters of the window function are selected, the entire time spectrum will use the same time-frequency resolution. The window function and its parameters determine the results of the spectrum analysis. The results of the spectrum analysis include time resolution and frequency resolution. Step S24: In actual vibration signal time-frequency analysis, the STFT function needs to select appropriate window functions and parameters to obtain high frequency resolution for the low-frequency part of the signal and high time resolution for the high-frequency part.

4. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 3, characterized in that, The Short-Time Fourier Transform (STFT) specifically refers to: The signal is segmented and analyzed by using a window function to divide the measured signal into several segments of equal length. A Fourier transform is then performed on each segment to determine the frequency of each segment.

5. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 4, characterized in that, The Fourier transform is specifically as follows: Transforming the changes of a signal in the time domain into changes in the frequency domain, that is, representing the signal on the frequency axis, allows us to observe the characteristics of the signal in both the time and frequency domains.

6. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 1, characterized in that, The FMCW cable fault location system in step S1 includes: a signal source, a power divider, a circulator, a mixer, an oscilloscope, a computer, and a cable. The signal source is connected to a power divider, which is connected to a mixer and a circulator respectively; the circulator is connected by a cable, the mixer is connected to an oscilloscope, and the oscilloscope is connected to a computer.

7. The method for detecting local insulation defects in frequency-modulated continuous wave cables according to claim 6, characterized in that, The signal source is used to generate a continuous linear frequency modulated signal; The power divider is used to retain the original signal on one side, inject the signal on the other side into the cable through a circulator, and extract the reflected signal generated in the cable due to impedance mismatch through the lower port of the circulator. The mixer is used to mix the stored set of original signals with the extracted reflected signals, and finally the output mixed signal is received by an oscilloscope.

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