A method for electrical spectrum analysis based on combined sparse transform

Abstract

The application discloses a kind of electric energy spectrum analysis methods based on combination sparse conversion.The method steps are: real-time monitoring electric power signal in power system and pre-processing, different scale frequency domain wavelet coefficients are obtained using fast Fourier transform, then frequency domain wavelet coefficients are optimized by time-frequency coupling method, then time-domain signal is reconstructed, and it is converted back to frequency domain using integer discrete Fourier transform, then frequency spectrum adaptive adjustment is carried out to frequency domain signal, and the frequency distribution of optimization is carried out, finally, frequency spectrum analysis is carried out based on adjusted frequency domain signal.The application improves the frequency spectrum resolution of electric energy signal by combining fast Fourier transform and integer discrete Fourier transform, and using multi-scale analysis and time-frequency coupling optimization technology, realizes high-precision frequency spectrum analysis and interference suppression, has the advantages of anti-dynamic current interference, adaptive enhancement key frequency band and the advantages such as improvement of signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of electrical energy spectrum analysis technology, specifically relating to an electrical energy spectrum analysis method based on combined sparse transformation. Background Technology

[0002] With the continuous expansion and increasing complexity of power systems, power quality issues are receiving increasing attention, particularly in the field of power signal analysis. During actual power system operation, current and voltage signals may be affected by various factors, including but not limited to rapid changes in dynamic loads, sudden equipment failures, and complex environmental noise. These disturbances typically manifest as instantaneous current and voltage fluctuations, significantly impacting the stable operation and security of the power system. Therefore, achieving accurate and stable power signal spectrum analysis has become a crucial research direction in the field of power system monitoring and fault detection.

[0003] Currently used spectral analysis methods, such as Fourier transform and wavelet transform, while providing effective spectral information in specific applications, often struggle to achieve sufficiently high spectral resolution and analysis stability when faced with complex dynamic current interference and non-stationary signals. Specifically, these methods suffer from the following drawbacks:

[0004] 1. While the traditional Fourier transform can provide basic spectral information, its ability to handle non-stationary signals and transient interference is significantly insufficient. This method cannot accurately capture subtle changes in electrical signals and is also difficult to effectively address the complex transient changes and non-stationary characteristics commonly found in power systems.

[0005] 2. While traditional wavelet transform offers advantages in multi-scale analysis, its resolution and stability in spectral analysis are suboptimal under operating environments with strong dynamic current interference. This method is also ineffective in noise suppression, easily leading to blurred spectral distributions and failing to provide the accuracy required for engineering applications.

[0006] 3. Existing technical solutions generally lack effective mechanisms for adaptively adjusting spectral resolution and dynamically optimizing frequency range. This deficiency makes it difficult to achieve efficient optimization of signal characteristics during time-frequency domain analysis, thereby affecting the system's ability to accurately identify abnormal operating conditions. Summary of the Invention

[0007] This invention proposes an energy spectrum analysis method based on combined sparse transform. Its purpose is to solve the problems of existing methods, such as insufficient ability to process non-stationary signals and transient interference, poor resolution and stability, lack of adaptive adjustment of spectral resolution and dynamic optimization of frequency range.

[0008] The technical solution of this invention is as follows:

[0009] An energy spectrum analysis method based on combined sparse transform, the method comprising:

[0010] Step 1: Monitor the electrical energy signals in the power system in real time and preprocess the collected electrical energy signals;

[0011] Step 2: Using the Fast Fourier Transform algorithm for processing real-valued data, perform multi-scale analysis on the preprocessed power signal data in time and frequency to obtain frequency domain wavelet coefficients at different scales.

[0012] Step 3: Optimize the frequency domain wavelet coefficients at different scales using time-frequency coupling to obtain the optimized frequency domain wavelet coefficients;

[0013] Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained through inverse wavelet transform;

[0014] Step 5: Use integer-order discrete Fourier transform to convert the reconstructed time-domain signal into a frequency-domain signal;

[0015] Step 6: Perform adaptive spectrum adjustment on the frequency domain signal to obtain the adjusted frequency domain signal;

[0016] Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

[0017] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the preprocessing in step 1 includes DC component removal and high-pass filtering.

[0018] As a further improvement to the energy spectrum analysis method based on combined sparse transformation, step 2 specifically includes:

[0019] Step 2-1: Perform wavelet transform on the signal to obtain coefficients at different scales;

[0020] Step 2-2: Perform frequency domain analysis on the coefficients at each scale to obtain the frequency domain wavelet coefficients at different scales.

[0021] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the calculation formula for the coefficients at different scales obtained by wavelet transform in step 2-1 is as follows:

[0022] ;

[0023] in, These are the coefficients of the time-domain signal under wavelet transform, representing the scaling factor. and displacement Signal characteristics below; It is a time-domain signal, that is Preprocessed electrical energy signal data corresponding to the given time; These are the normalization coefficients of the wavelet function, used to ensure that the wavelet function maintains the normality of its energy when scaled. As a scale factor, This is the translation factor, which controls the shift of the wavelet function along the time axis; It is the original wavelet mother function, determined by the chosen wavelet basis functions.

[0024] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the calculation formula for frequency domain analysis in step 2-2 is as follows:

[0025] ;

[0026] in, These are the coefficients of the time-domain signal under wavelet transform. It is a coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficients; It is the frequency variable in the Fourier transform.

[0027] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the formula for time-frequency coupling optimization in step 3 is as follows:

[0028] ;

[0029] in, It is a scale and displacement Frequency domain wavelet coefficients, These are the optimized frequency domain wavelet coefficients; These are adaptive coefficients used to control the scaling in the time-frequency coupling optimization process. The effect on frequency adjustment was obtained through experiments; It is a scale The corresponding frequency range indicates that in The range of signal frequency estimation at different scales is determined by the characteristics of the wavelet basis function, and is estimated by calculating the frequency distribution of the wavelet basis function.

[0030] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the reconstructed time-domain signal is obtained in step 4. The method is: first to Performing the inverse Fourier transform yields Then to Perform inverse wavelet transform to obtain .

[0031] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the formula for calculating the integer-order discrete Fourier transform in step 5 is as follows:

[0032] ;

[0033] in, This represents the frequency domain signal after performing an integer number of Discrete Fourier Transforms; it is the reconstructed time-domain signal's representation in the frequency domain, indicating the signal's frequency response. Spectrum information at the location; For reconstructed time-domain signal In the time domain, the first The value of each sampling point; Represents the frequency variable in the frequency domain; It is the total number of sampling points for the signal; It is the kernel function of the integer-order discrete Fourier transform, used to map a time-domain signal to the frequency domain, representing the contribution of each frequency variable to the time-domain signal. It is the imaginary unit.

[0034] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the formula for adaptive spectrum adjustment in step 6 is:

[0035] ;

[0036] in, It is the frequency domain signal obtained in step 5. The adjusted frequency domain signal is represented by the frequency domain signal. The frequency obtained after adaptive adjustment Spectrum information at the location; It is each scale The weighting coefficients, with a range of values. ; Represents the optimized wavelet coefficients The absolute value of.

[0037] As a further improvement to the energy spectrum analysis method based on combined sparse transform, the spectrum analysis in step 7 includes:

[0038] (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, i.e., the peak value of the spectrum;

[0039] (2) The total energy is obtained by summing the squares of the frequency domain signals at different adjusted frequencies.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. This invention effectively improves the spectral resolution of power signals under dynamic current interference by combining the Fast Fourier Transform (WFTA) algorithm and the Integer-order Discrete Fourier Transform (IDFT), and employing multi-scale analysis and time-frequency coupling optimization techniques. This combined sparse transform method can provide high-precision spectral analysis in complex power system environments, effectively reducing the impact of interference signals on the analysis results, thereby improving the stability and accuracy of power data in power systems.

[0042] 2. This invention uses an adaptive wavelet transform optimization method to dynamically adjust the amplitude of the spectrum according to the actual frequency characteristics of the power signal, thereby enhancing important frequency components while effectively suppressing noise and interference components. This not only improves the spectral accuracy of the signal but also maintains a high signal-to-noise ratio in complex power systems, significantly enhancing the recognition capability of power signals. Especially in environments with strong current interference, it can more accurately capture the effective information of the signal.

[0043] 3. This invention introduces a spectrum adaptive adjustment mechanism, which, based on optimized wavelet coefficients, enhances key frequency bands in the spectrum and suppresses interference signals, providing more reliable support for fault diagnosis and abnormal operating condition identification in power systems. Furthermore, by extracting key information such as spectral peak values ​​and total energy, this invention further quantifies the characteristics of the signal, helping to identify abnormal fluctuations in power signals, thereby improving the effectiveness of power system monitoring. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0045] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0046] like Figure 1 An energy spectrum analysis method based on combinatorial sparse transformation includes:

[0047] Step 1: Monitor the power signals in the power system in real time and preprocess the collected power signals.

[0048] The electrical energy signals in the power system are monitored in real time by current and voltage transformers, and then the current signals and / or voltage signals are converted into digital signals by a high-speed analog-to-digital converter (ADC).

[0049] During the data acquisition process, to reduce interference from external environmental noise, the acquired signals must be preprocessed, including DC component removal and high-pass filtering. DC component removal involves calculating the signal mean as the DC component and then removing it from the signal to eliminate any low-frequency interference that may be introduced. High-pass filtering filters out low-frequency noise components, retaining the parts of the signal useful for spectral analysis.

[0050] Step 2: Using the Fast Fourier Transform algorithm for processing real-valued data, perform multi-scale analysis on the preprocessed power signal data in time and frequency to obtain frequency domain wavelet coefficients at different scales.

[0051] This embodiment designs a combined sparse transform model based on an improved WFTA algorithm and an improved integer-order discrete Fourier transform algorithm to improve the resolution and stability of spectrum analysis.

[0052] Step 2-1: Perform wavelet transform on the signal to obtain coefficients at different scales.

[0053] The goal of wavelet transform is to decompose a time-domain signal (i.e., pre-processed electrical signal data) into detailed and approximate components in different frequency ranges, thereby enabling multi-scale analysis of the signal in both time and frequency. Wavelet functions localize the frequency components of a signal by adjusting the scale and position of the wavelet mother function.

[0054] The formula for calculating the coefficients at different scales obtained through wavelet transform is as follows:

[0055] ;

[0056] in, These are the coefficients of the time-domain signal under wavelet transform, representing the scaling factor. and displacement Signal characteristics below; It is a time-domain signal, that is Preprocessed electrical energy signal data corresponding to the given time; These are the normalization coefficients of the wavelet function, ensuring that the wavelet function maintains the normality of its energy when scaled. As a scale factor, This is the translation factor, which controls the shift of the wavelet function along the time axis; It is the original wavelet mother function, determined by the chosen wavelet basis functions.

[0057] By scaling the wavelet mother function and time translation This allows us to obtain local features at different scales and time locations, and then extract multi-scale information from the signal.

[0058] Step 2-2: Perform frequency domain analysis on the coefficients at each scale to obtain the frequency domain wavelet coefficients at different scales, so as to obtain accurate information on the frequency components.

[0059] For a certain scale Its wavelet coefficients It is represented in the time domain, but can be transformed to the frequency domain through Fourier transform to reveal the characteristics of its frequency components. Therefore, the formula is:

[0060] ;

[0061] in, It is a coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficients; It is the frequency variable in the Fourier transform.

[0062] This calculation can extract the frequency components of a signal in the frequency domain, thereby enhancing the ability of spectrum analysis.

[0063] Step 3: Optimize the frequency domain wavelet coefficients at different scales using time-frequency coupling to obtain the optimized frequency domain wavelet coefficients.

[0064] By combining the wavelet transform and Fourier transform results, a joint spectral information is generated, obtaining signal characteristics in both the time and frequency domains. For each scale... In the frequency domain, optimization is performed by weighting the wavelet coefficients after Fourier transform to obtain the optimized spectrum for each scale.

[0065] The formula for time-frequency coupling optimization is as follows:

[0066] ;

[0067] in, These are the optimized frequency domain wavelet coefficients; These are adaptive coefficients used to control the scaling in the time-frequency coupling optimization process. The effect on frequency adjustment was obtained through experiments; It is a scale The corresponding frequency range indicates that in The range of signal frequency estimation at different scales is determined by the characteristics of the wavelet basis function, and is estimated by calculating the frequency distribution of the wavelet basis function.

[0068] Time-frequency coupling optimization enables wavelet transform to effectively decompose signals under dynamic current interference and optimize information extraction in each frequency band.

[0069] Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained through inverse wavelet transform.

[0070] The wavelet coefficients after time-frequency coupling optimization represent the characteristics of the signal in the frequency domain. This step uses inverse wavelet transform to restore it to the time domain signal, thus providing a basis for subsequent spectrum analysis.

[0071] The inverse wavelet transform process involves multiplying the optimized wavelet coefficients at each scale with the corresponding wavelet basis functions and summing the results to obtain the reconstructed time-domain signal. First to Performing the inverse Fourier transform yields Then to Perform inverse wavelet transform to obtain .

[0072] Step 5: Use integer-order discrete Fourier transform to convert the reconstructed time-domain signal into a frequency-domain signal.

[0073] The reconstructed time-domain signal obtained using inverse wavelet transform The signal needs to be transformed into the frequency domain using an integer-order Discrete Fourier Transform (IDFT) for spectral analysis. The purpose of the integer-order Discrete Fourier Transform is to extract the frequency components of the signal and provide a basis for subsequent spectral analysis. The integer-order Discrete Fourier Transform converts the reconstructed time-domain signal into a frequency-domain representation.

[0074] The formula for calculating the integer-order Discrete Fourier Transform is as follows:

[0075] ;

[0076] in, This represents the frequency domain signal after performing an integer number of Discrete Fourier Transforms; it is the reconstructed time-domain signal's representation in the frequency domain, indicating the signal's frequency response. Spectrum information at the location; For reconstructed time-domain signal In the time domain, the first The values ​​of each sampling point; Represents the frequency variable in the frequency domain; It is the total number of sampling points for the signal; It is the kernel function of the integer-order discrete Fourier transform, used to map a time-domain signal to the frequency domain, representing the contribution of each frequency variable to the time-domain signal. It is the imaginary unit.

[0077] Integer-order discrete Fourier transform converts the optimized time-domain signal into a frequency-domain representation, enabling analysis of the signal's frequency components in the frequency domain. This allows for in-depth research into the characteristics of electrical signals and further enhances the accuracy of the spectrum.

[0078] Step 6: Perform adaptive spectrum adjustment on the frequency domain signal to obtain the adjusted frequency domain signal.

[0079] The spectrum is adaptively adjusted to enhance key signal components and suppress interference. The adjusted frequency domain signal not only represents the spectral information optimized by time-frequency coupling, but also further enhances key signal components and suppresses interference through the adaptive spectrum adjustment process. The amplitude of the spectrum is adjusted according to the optimized wavelet coefficients at each scale, so that important frequency components are enhanced under dynamic current interference, while noise and interference components are effectively suppressed.

[0080] The formula for adaptive spectrum adjustment is:

[0081] ;

[0082] in, The adjusted frequency domain signal is represented by the frequency domain signal. The frequency obtained after adaptive adjustment Spectrum information at the location; It is each scale The weighting coefficients, with a range of values. This was determined through experiments; Represents the optimized wavelet coefficients The absolute value of.

[0083] Adaptive spectrum adjustment can enhance the low signal-to-noise ratio (SNR) portion of the spectrum while suppressing interfering frequency bands, thereby improving the SNR of the analysis. This method can reduce the influence of interference signals while preserving signal characteristics, thus improving the accuracy and stability of the spectrum, especially enhancing the reliability of power spectrum analysis under conditions of strong dynamic current interference.

[0084] Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

[0085] Peak values ​​and total energy of the spectrum are extracted to identify the main frequency components of the signal and their abnormal changes, providing a basis for power system diagnosis. Therefore, spectrum analysis includes:

[0086] (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, i.e. the peak frequency. This frequency represents the main component or frequency peak in the signal, accurately reflects the most significant frequency component in the power signal, and can effectively avoid noise influence and capture the true frequency characteristics, especially in environments with complex dynamic current interference.

[0087] (2) The total energy is obtained by summing the squares of the frequency domain signals at different adjusted frequencies.

[0088] By further quantifying the total energy of a signal, we can assess its overall strength and the concentration of its frequency distribution. Total energy is an important indicator of a signal's energy distribution in the spectral domain, helping to identify abnormal fluctuations or changes in the signal. When the energy in certain frequency bands of the spectrum is abnormal, it indicates that there are prominent features or abnormal operating conditions in the signal.

[0089] Spectrum analysis includes, but is not limited to, obtaining spectral peaks and total energy.

[0090] This method improves the spectral resolution and recognition accuracy of power spectrum analysis, especially in environments with dynamic current interference, enabling it to better capture detailed signal features and optimize its spectral representation. The adaptively adjusted spectral information can provide more accurate and stable support for power system monitoring and fault diagnosis, effectively improving the reliability and fault detection capabilities of power systems.

[0091] It should be noted that, as will be apparent to those skilled in the art, the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics thereof. The scope of the present invention is defined by the claims rather than the foregoing description.

Claims

1. A method for energy spectrum analysis based on combinatorial sparse transformation, characterized in that, The method includes: Step 1: Monitor the electrical energy signals in the power system in real time and preprocess the collected electrical energy signals; Step 2: Using the Fast Fourier Transform algorithm for processing real-valued data, perform multi-scale analysis on the preprocessed power signal data in time and frequency to obtain frequency domain wavelet coefficients at different scales. Step 3: Optimize the frequency domain wavelet coefficients at different scales using time-frequency coupling to obtain the optimized frequency domain wavelet coefficients; The formula for time-frequency coupling optimization in step 3 is as follows: ； in, It is a scale and displacement Frequency domain wavelet coefficients, These are the optimized frequency domain wavelet coefficients; These are adaptive coefficients used to control the scaling in the time-frequency coupling optimization process. The effect on frequency adjustment was obtained through experiments; It is a scale The corresponding frequency range indicates that in The range of signal frequency estimation at different scales is determined by the characteristics of the wavelet basis function, and is estimated by calculating the frequency distribution of the wavelet basis function. Step 4: Based on the optimized frequency domain wavelet coefficients, the reconstructed time domain signal is obtained through inverse wavelet transform; Step 5: Use integer-order discrete Fourier transform to convert the reconstructed time-domain signal into a frequency-domain signal; Step 6: Perform adaptive spectrum adjustment on the frequency domain signal to obtain the adjusted frequency domain signal; Step 7: Perform spectrum analysis based on the adjusted frequency domain signal.

2. The energy spectrum analysis method based on combined sparse transformation as described in claim 1, characterized in that: The preprocessing in step 1 includes DC component removal and high-pass filtering.

3. The energy spectrum analysis method based on combined sparse transformation as described in claim 1, characterized in that, Step 2 specifically includes: Step 2-1: Perform wavelet transform on the signal to obtain coefficients at different scales; Step 2-2: Perform frequency domain analysis on the coefficients at each scale to obtain the frequency domain wavelet coefficients at different scales.

4. The energy spectrum analysis method based on combined sparse transformation as described in claim 3, characterized in that, The formula for calculating the coefficients at different scales obtained through wavelet transform in step 2-1 is as follows: ； in, These are the coefficients of the time-domain signal under wavelet transform, representing the scaling factor. and displacement Signal characteristics below; It is a time-domain signal, that is Preprocessed electrical energy signal data corresponding to the given time; These are the normalization coefficients of the wavelet function, used to ensure that the wavelet function maintains the normality of its energy when scaled. As a scale factor, This is the translation factor, which controls the shift of the wavelet function along the time axis; It is the original wavelet mother function, determined by the chosen wavelet basis functions.

5. The energy spectrum analysis method based on combined sparse transformation as described in claim 3, characterized in that, The calculation formula for frequency domain analysis in step 2-2 is as follows: ； in, These are the coefficients of the time-domain signal under wavelet transform. It is a coefficient The representation in the frequency domain is the corresponding frequency domain wavelet coefficients; It is the frequency variable in the Fourier transform.

6. The energy spectrum analysis method based on combined sparse transformation as described in claim 1, characterized in that, The reconstructed time-domain signal is obtained in step 4. The method is: first to Performing the inverse Fourier transform yields Then to Perform inverse wavelet transform to obtain .

7. The energy spectrum analysis method based on combined sparse transformation as described in claim 1, characterized in that, The formula for calculating the integer-order discrete Fourier transform in step 5 is as follows: ； in, This represents the frequency domain signal after performing an integer number of Discrete Fourier Transforms; it is the reconstructed time-domain signal's representation in the frequency domain, indicating the signal's frequency response. Spectrum information at the location; For reconstructed time-domain signal In the time domain, the first The values ​​of each sampling point; Represents the frequency variable in the frequency domain; It is the total number of sampling points for the signal; It is the kernel function of the integer-order discrete Fourier transform, used to map a time-domain signal to the frequency domain, representing the contribution of each frequency variable to the time-domain signal. It is the imaginary unit.

8. The energy spectrum analysis method based on combined sparse transformation as described in claim 1, characterized in that, The formula for adaptive spectrum adjustment in step 6 is: ； in, It is the frequency domain signal obtained in step 5. The adjusted frequency domain signal is represented by the frequency domain signal. The frequency obtained after adaptive adjustment Spectrum information at the location; It is each scale The weighting coefficients, with a range of values. ; Represents the optimized wavelet coefficients The absolute value of.

9. The energy spectrum analysis method based on combined sparse transformation as described in any one of claims 1 to 8, characterized in that, The spectral analysis in step 7 includes: (1) Extract the frequency corresponding to the maximum amplitude from the adjusted frequency domain signal, i.e., the peak value of the spectrum; (2) The total energy is obtained by summing the squares of the frequency domain signals at different adjusted frequencies.

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