A fractional domain noise reduction method for electrical energy signals

Abstract

The application provides a fractional domain noise reduction method of an electric energy signal, comprising the following steps: S1, estimating an optimal fractional Fourier transform angle of an original signal x(t); S2, calculating a fractional Fourier transform of the original signal under the optimal fractional Fourier transform angle; S3, performing band-pass filtering in the optimal fractional Fourier transform domain; S4, calculating a fractional Fourier transform under the angle; S5, judging whether the angle is equal to π / 2 or not, if yes, ending the noise reduction, and if not, eliminating a recovered signal component and then repeating steps S1-S5 until the estimated optimal FRFT rotation angle is equal to π / 2. The application is not only suitable for transient stationary disturbance signals, such as voltage transient rise, transient drop and interruption signals, but also suitable for transient non-stationary disturbance signals, such as linear frequency modulation interference. Experimental results show that the improved noise reduction algorithm based on the fractional Fourier transform can effectively realize noise filtering and retention of transient disturbance positioning information.

Description

Technical Field

[0001] This application relates to the field of power electronics technology, and in particular to a fractional-domain noise reduction method for electrical signals. Background Technology

[0002] The large-scale grid connection of new energy sources, the rapid development of ultra-high voltage AC / DC transmission and smart grids have led to the increasing electronic characteristics of the power grid at all stages, including power generation, grid, and load. The application of numerous power electronic devices and nonlinear loads, such as frequency converters, variable frequency speed control systems, and electric vehicle charging devices, has resulted in severe signal pollution, leading to power quality (PQ) problems. High-quality power system monitoring is becoming increasingly challenging.

[0003] Transient power quality disturbances are an important research topic related to power quality in power systems, significantly impacting both the grid and user sides. These disturbances typically include voltage sags, voltage swells, voltage interruptions, transient pulses, and transient oscillations. Effective power quality monitoring is essential to determine the causes of these disturbances and prevent equipment damage. Power quality monitoring generally includes noise reduction, feature extraction, and classification. In practical applications, power quality signals are often contaminated by noise during transmission, measurement, and reception, causing useful signal features to be overwhelmed and affecting the accurate processing and analysis of subsequent signals. Therefore, effective denoising algorithms are crucial for power quality monitoring and analysis. In recent years, numerous research results have emerged on power quality denoising, such as denoising methods based on Fourier transform, wavelet transform, S-transform, and empirical mode decomposition algorithms. While these methods have good denoising effects, most of them analyze and process signals in the time and frequency domains. However, with the integrated application of numerous nonlinear fast loads, transient power quality disturbances and noise may exhibit non-stationary characteristics. Unlike common transient power quality disturbances, the frequency of non-stationary transient disturbances often changes over time, and the energy distribution in the frequency domain is no longer concentrated, which makes it impossible to effectively separate them from noise along with the power frequency signal.

[0004] As an extension of the traditional Fourier transform, the fractional Fourier transform (FRFT) can characterize signals in the time-fractional frequency domain, thereby achieving a high degree of energy aggregation for different signal components. Furthermore, since the FRFT kernel is based on an orthogonal chirp basis, it is highly suitable for processing non-stationary signals, especially linear frequency modulated (LFM) signals. In addition, the computational speed of the discrete FRFT algorithm is comparable to that of the fast Fourier transform (FFT) algorithm. Based on these advantages, FRFT can be applied to the denoising of non-stationary power quality disturbances. Existing techniques have been studied for denoising and identification methods of common power quality disturbance signals based on the FRFT algorithm. Preliminary discussions have been made regarding non-stationary LFM interference, but the disturbance signal model is not a transient disturbance. Summary of the Invention

[0005] In view of this, this application proposes the characteristics of non-stationary transient disturbance signals in power electronic power systems, and then proposes a new efficient denoising algorithm for power quality disturbances based on fractional Fourier transform.

[0006] To achieve the above objectives, this application proposes a fractional-domain noise reduction method for electrical energy signals, comprising:

[0007] S1. Estimate the optimal fractional Fourier transform angle of the original signal x(t).

[0008] S2. Calculate the fractional Fourier transform of the original signal at the optimal fractional Fourier transform angle, and obtain...

[0009] S3. Perform bandpass filtering in the optimal fractional Fourier transform domain to obtain...

[0010] S4, Calculation At angle Fractional Fourier transform of the following order;

[0011] S5, Judgment If the signal is equal to π / 2, then noise reduction ends; otherwise, the recovered signal component is eliminated. Then repeat steps S1-S5 until the estimated optimal FRFT rotation angle is equal to π / 2.

[0012] Furthermore, the fractional Fourier transform is defined as follows:

[0013]

[0014]

[0015] Where p is the FRFT transform order, α is the angle between the FRFT axis and the time axis, and α = pπ / 2, K p (α;u;t) is the kernel function of the fractional Fourier transform, where n is an integer.

[0016] Furthermore, the original signal x(t) is represented as

[0017] x(t)=s(t)+d(t)+n(t) (5)

[0018] Where s(t) is the power frequency signal, d(t) is the transient disturbance signal, and n(t) is Gaussian white noise.

[0019] Furthermore, the fourth-order origin moment of the fractional-order spectrum of the original signal x(t) is defined as follows:

[0020]

[0021] Then the optimal transformation angle It can be estimated

[0022]

[0023] Furthermore,

[0024] in, and These are the FRFT results for signals x(t), s(t), d(t), and n(t) at the optimal transform angle, respectively.

[0025] Furthermore, d(t) represents a non-stationary transient disturbance signal.

[0026] d(t)=A·(u(t-t1)-u(t-t2))·exp(j2πf1t+jπkt 2 (8)

[0027] In the formula, A is the amplitude of the disturbance signal, u(t) is the unit step signal, t1 and t2 are the start and end times of the disturbance signal, f1 is the starting frequency of the linear frequency modulated disturbance signal, and k is its modulation frequency.

[0028] Furthermore, the window function used in the bandpass filter includes at least one of the following: rectangular window, Hanning window, Hamming window, and Blackman window.

[0029] Furthermore, the peak energy of the power frequency signal is less than the peak energy of the transient disturbance signal.

[0030] In summary, the advantages of this application and the user experience it brings are as follows:

[0031] This application proposes an improved denoising algorithm based on fractional Fourier transform to address the denoising problem of transient power quality signals. This method is applicable not only to transient stationary disturbance signals, such as voltage swells, drops, and interruptions, but also to transient non-stationary disturbance signals, such as linear frequency modulation (LFM) interference. During the denoising process, LFM interference, like noise, is filtered out from the original power frequency signal, but it can be recovered through inverse fractional Fourier transform, allowing for the extraction of interference signal features to analyze the cause of the disturbance. Furthermore, this application discusses a method for determining the optimal fractional transform angle, which can be efficiently determined through one-dimensional peak search based on the fourth-order origin moment of the fractional spectrum. Experimental results show that the improved denoising algorithm based on fractional Fourier transform can effectively achieve noise filtering and preservation of transient disturbance location information. Attached Figure Description

[0032] In the accompanying drawings, unless otherwise specified, the same reference numerals throughout the various drawings denote the same or similar parts or elements. These drawings are not necessarily drawn to scale. It should be understood that these drawings depict only some embodiments disclosed in this application and should not be construed as limiting the scope of this application.

[0033] Figure 1 This is a block diagram of a traditional signal denoising algorithm based on fractional Fourier transform.

[0034] Figure 2 This is a flowchart of the improved power signal noise reduction method based on fractional Fourier transform in this application.

[0035] Figure 3 This is the energy distribution diagram of the linear frequency modulated signal of this application on the two-dimensional plane (α, u).

[0036] Figure 4 This is a fourth-order origin moment distribution diagram of the fractional-order spectrum of the linear frequency modulated signal in this application.

[0037] Figure 5 The waveforms of the voltage sag signal before and after noise reduction and the residual noise are shown in this application.

[0038] Figure 6 The waveforms of the voltage interruption signal before and after noise reduction and the residual noise in this application are shown.

[0039] Figure 7 This is a waveform diagram of the chirp transient disturbance signal affected by noise in this application.

[0040] Figure 8 This is a schematic diagram of the noise reduction process for the linear frequency modulation disturbance power signal in this application.

[0041] Figure 9This is a schematic diagram showing the root mean square error of the estimated start and end times of transient disturbances under different signal-to-noise ratios in this application. Detailed Implementation

[0042] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0043] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] Based on the analysis of common transient disturbance signals, this application focuses on the characteristics of non-stationary chirp-type disturbance signals in power electronic power systems, and proposes a new efficient denoising algorithm for power quality disturbances based on fractional domain analysis.

[0045] 1. Fractional Fourier Transform

[0046] The fractional Fourier transform is the general form of the Fourier transform, possessing linear and singular properties, and is defined as follows:

[0047]

[0048]

[0049] Where p is the FRFT transform order, α is the angle between the FRFT axis and the time axis, and α = pπ / 2, K p (α;u;t) is the kernel function of the fractional Fourier transform, where n is an integer.

[0050] Let the frequency of the signal x(t) be f(t), then its rate of change of frequency can be defined as follows:

[0051]

[0052] According to the definition of FRFT, it can be derived that the optimal transformation angle of x(t) in the fractional domain can be obtained from its rate of change of frequency, i.e.

[0053] α0=-arccot(μ) (4)

[0054] At the optimal transformation angle, signal x(t) can achieve optimal energy concentration in the fractional domain, i.e., |X α (u)| 2 To obtain the maximum value.

[0055] 2. Power Quality Noise Reduction Algorithm Based on Fractional Fourier Transform

[0056] 2.1 Traditional Algorithm

[0057] Depending on the transformation angle, power quality signals contaminated by noise will form varying degrees of energy accumulation in different fractional domains. To filter out noise to the greatest extent, the signal needs to be transformed to the optimal fractional domain to form the optimal energy accumulation.

[0058] Let the power quality signal affected by noise be represented as:

[0059] x(t)=s(t)+d(t)+n(t) (5)

[0060] Where s(t) is the power frequency signal, d(t) is the transient disturbance signal, and n(t) is Gaussian white noise.

[0061] Since voltage sags, swells, and interruptions only change the amplitude of the power frequency signal for a short period of time, without affecting its rate of frequency change, the fractional domain for optimal energy concentration of these disturbances is consistent with that of the power frequency signal. Performing an optimal fractional Fourier transform on the signal yields...

[0062]

[0063] Where, α 0s Xα is the optimal fractional-domain transformation angle for s(t). 0s (u), Sα 0s (u), Dα 0s (u) and Nα 0s (u) represent the FRFT results of signals x(t), s(t), d(t), and n(t) at the optimal transform angle, respectively. Since Gaussian white noise cannot form energy accumulation in the fractional domain, a bandpass filter H(u) can be used to separate the signal from the noise in the optimal fractional transform domain, thus obtaining...

[0064]

[0065] Subsequently, X′α 0s (u) performs -α 0s The fractional Fourier transform of the angle, i.e., the inverse fractional Fourier transform, yields the denoised signal. Figure 1 The diagram shown is a block diagram of a traditional signal denoising algorithm based on fractional Fourier transform.

[0066] 2.2 Improved Algorithm

[0067] As analyzed in Section 2.1, when the disturbance signal and the power frequency signal have the same modulation frequency, the optimal fractional Fourier transform angles for both types of signals are consistent, and traditional algorithms based on fractional Fourier transform can effectively achieve noise reduction. However, in power electronic power systems, with the widespread application of nonlinear and fast loads, power quality disturbances may exhibit non-stationary behavior, meaning that the frequency of the disturbance signal cannot remain constant within an observation period. For example, taking a transient linear frequency modulation disturbance signal, a transient non-stationary disturbance can be defined as...

[0068] d(t)=A·(u(t-t1)-u(t-t2))·exp(j2πf1t+jπkt 2 (8)

[0069] In the formula, A is the amplitude of the disturbance signal, u(t) is the unit step signal, t1 and t2 are the start and end times of the disturbance signal, f1 is the starting frequency of the linear frequency modulated disturbance signal, and k is its modulation frequency.

[0070] Since the modulation frequency of the linear frequency modulated (RF) disturbance signal is not zero, the angle of its optimal fractional Fourier transform will no longer coincide with that of the power frequency signal, resulting in multiple energy concentration peaks in the fractional domain. In this case, traditional FRFT-based noise reduction algorithms are no longer applicable. To address this issue, we can start by considering the relationship between the energy peak values ​​of the power frequency signal and the disturbance signal, and discuss two different scenarios.

[0071] (1) The peak energy of the power frequency signal is greater than that of the disturbance signal. Since the modulation frequency of the power frequency signal is 0, its optimal FRFT angle α... 0s =π / 2. Therefore, if the estimated optimal fractional Fourier transform angle is equal to π / 2, then traditional denoising algorithms can be directly applied to filter out non-stationary disturbances with non-zero modulation frequencies and Gaussian white noise. If further analysis of the characteristics of transient non-stationary disturbance signals is required, the denoised electrical signal can be removed from the original signal, and a FRFT-based denoising algorithm can be applied to the remaining signal to reconstruct the transient disturbance.

[0072] (2) The peak energy of the power frequency signal is less than the peak energy of the disturbance signal. In this case, the optimal FRFT rotation angle of the non-stationary disturbance signal d(t) will be estimated first. The estimated value d′(t) of the non-stationary disturbance signal can be obtained using a bandpass filter and fractional Fourier inverse transform. Then, d′(t) is eliminated from the original signal x(t), and the FRFT noise reduction algorithm is applied again to x′(t) = x(t) - d′(t) until the estimated optimal FRFT rotation angle equals π / 2. The relevant characteristics of the transient disturbance can be obtained by analyzing d′(t).

[0073] Figure 2A flowchart of the improved power signal denoising algorithm based on fractional Fourier transform is given, including the following steps:

[0074] S1. Estimate the optimal fractional Fourier transform angle of the original signal x(t).

[0075] S2. Calculate the fractional Fourier transform of the original signal at the optimal fractional Fourier transform angle, and obtain...

[0076]

[0077] in, and These are the FRFT results for signals x(t), s(t), d(t), and n(t) at the optimal transform angle, respectively.

[0078] S3. Perform bandpass filtering in the optimal fractional Fourier transform domain to obtain...

[0079] S4, Calculation At angle Fractional Fourier transform of the following order;

[0080] S5, Judgment If the signal is equal to π / 2, then noise reduction ends; otherwise, the recovered signal component is eliminated. Repeat steps S1-S5 until the estimated optimal FRFT rotation angle equals π / 2.

[0081] 2.3. Estimation Method for Optimal Fractional Fourier Transform Angle

[0082] As analyzed in Section 2.2, denoising algorithms based on fractional Fourier transform (FRFT) require processing the signal in its optimal fractional transform domain. Therefore, estimating the optimal fractional transform angle of the signal is crucial to the performance of the denoising algorithm. Typically, the optimal transform angle of FRFT is obtained by searching for peaks in a two-dimensional plane comprised of the fractional transform domain (u) and the transform angle domain (α). This process can be described as follows:

[0083]

[0084] in It is an estimate of the optimal transformation angle. These are the coordinates corresponding to the energy peak in the optimal transform domain.

[0085] Clearly, two-dimensional peak search leads to considerable computational complexity. To address this issue, the second-order FRFT central moments, based on the ambiguity function, have been shown to be useful for quickly obtaining the optimal transform angle. However, the second-order FRFT central moments are highly sensitive to noise, and their performance is inferior to that of the fourth-order FRFT central moments. Further considering computational complexity, the fractional-order spectral fourth-order origin moments perform better.

[0086] The fractional-order spectrum of a signal x(t) with fourth-order raw moments is defined as follows:

[0087]

[0088] The optimal transformation angle can then be estimated as follows:

[0089]

[0090] Figure 3 , Figure 4 The energy distribution |X| of the linear frequency modulated signal on the two-dimensional plane (α, u) is shown. α (u)| 2 The distribution of its fractional-order spectrum and fourth-order origin moment η(α) on a one-dimensional plane (α).

[0091] Compared to two-dimensional peak search, the optimal fractional Fourier transform angle can be determined through a one-dimensional search based on the fourth-order origin moment of the signal's fractional-order spectrum, thus significantly improving computational efficiency. Furthermore, from... Figure 4 It can also be observed that the fractional-order fourth-order raw moment of the spectrum under different transformation angles increases as the noise increases. Therefore, the fractional-order fourth-order raw moment of the spectrum has good noise resistance performance, and this application adopts it as the estimation algorithm for the optimal transformation angle.

[0092] 2.4. Selection of Fractional Domain Bandpass Filter

[0093] After determining the optimal fractional transform angle, bandpass filtering of the signal components in the optimal fractional transform domain is a crucial step in eliminating the influence of noise and non-stationary disturbances. Clearly, the performance of the bandpass filter directly affects the noise reduction effect. Therefore, it is necessary to design suitable bandpass filters based on the performance of different window functions. Common window functions mainly include rectangular windows, Hanning windows, Hamming windows, and Blackman windows, and their performance is shown in Table 1.

[0094] Table 1. Spectral characteristics of typical window functions

[0095]

[0096] To minimize signal energy loss and effectively filter out noise interference, the design of filters should ideally feature a narrow main lobe width and rapid attenuation of sidelobe amplitudes. However, typical window functions often fail to meet both performance requirements simultaneously, necessitating a comprehensive consideration based on specific engineering applications. Comparative analysis reveals that while the Hanning window's main lobe width is twice that of the rectangular window, its maximum peak value of both the main and side lobes and its attenuation performance are significantly superior. Its overall performance is relatively optimal among common window functions. Therefore, this application employs the Hanning window to design a fractional-domain bandpass filter to verify the performance of the noise reduction algorithm.

[0097] 3. Simulation Experiment

[0098] To verify the algorithm's performance, simulation experiments were conducted in MATLAB environment for three power quality problems: voltage swell, voltage interruption, and non-stationary transient disturbances (taking transient linear frequency modulation interference signal as an example). The signal sampling frequency was 15kHz, the fundamental frequency was 50Hz, and the Hanning window was selected as the bandpass filter. The signal-to-noise ratio (SNR) was defined to evaluate the noise reduction effect, as shown in Equation (12).

[0099]

[0100] Where s(t) and s′(t) are the signal before noise pollution and the recovered signal after noise reduction, respectively.

[0101] 3.1 Noise Reduction Process and Signal-to-Noise Ratio Analysis

[0102] 3.1.1 Voltage Sag Signal Noise Reduction Experiment

[0103] A voltage spur signal with an input signal-to-noise ratio of 10dB is subjected to a noise reduction algorithm based on an improved fractional Fourier transform. The waveforms before and after noise reduction, as well as the residual noise, are shown below. Figure 5 As shown. From Figure 5 As can be seen from (a) and (b), the signal waveform after noise reduction is smoother and the original signal characteristics are better preserved, with the output signal-to-noise ratio improved to 21.35 dB. Further narrowing the range of the vertical axis to observe residual noise, such as... Figure 5 As shown in (c), it can be observed that the waveform fluctuates significantly around the time points of voltage spurs at 0.045s and 0.085s. Further discussion is needed on the impact of the noise reduction algorithm on the positioning results.

[0104] 3.1.2 Voltage Interruption Signal Noise Reduction Experiment

[0105] Figure 6The results presented are the noise reduction results for the voltage interruption signal when the input signal-to-noise ratio is 10dB. Similarly, noise is effectively filtered out while the characteristics of the power quality signal are preserved, resulting in an output signal-to-noise ratio of 19.21dB. The residual noise is generally flat, but the waveform still fluctuates significantly around the voltage interruption times of 0.045s and 0.085s.

[0106] from Figure 5 , Figure 6 The simulation results show that the improved algorithm can effectively reduce the noise of electrical signals.

[0107] 3.1.3 Noise Reduction Experiment for Non-stationary Transient Disturbances

[0108] The simulation results for non-stationary transient disturbances are as follows: Figure 7 and Figure 8 As shown. First, Figure 7 (a) is the original power frequency signal. Figure 7 (b) is an electrical signal containing transient linear frequency modulation interference. Figure 7 (c) is the electrical signal after being polluted by noise, with a signal-to-noise ratio of 10dB.

[0109] To estimate the optimal fractional transform angle, the normalized fractional spectrum of the signal is calculated using the fourth-order origin moment, as shown in the following results. Figure 8 As shown in (a). Clearly, the peak energy of the power frequency signal is less than the peak energy of the disturbance signal at this time. Using a one-dimensional peak search, the optimal FRFT transform angle for the linear frequency modulated disturbance signal d(t) at this time is found to be 1.099 rad. Performing a fractional Fourier transform at this angle yields the energy distribution in the fractional domain, as shown in (a). Figure 8 As shown in (b). The estimated value d′(t) of the linear frequency modulated disturbance signal can be obtained using a bandpass filter and a fractional Fourier inverse transform, as follows: Figure 8 As shown in (c). Then, d′(t) is removed from the original signal x(t), and the FRFT denoising algorithm is applied again to the remaining signal x′(t) = x(t) - d′(t). Figure 8 (d) is the normalized fractional spectrum of x′(t) and its fourth-order origin moment. Figure 8 (e) is the fractional Fourier transform result of the optimal transformation angle. Figure 8 (f) is the power frequency signal restored after noise reduction processing. Figure 8 (g) represents residual noise.

[0110] The experiments above show that the modulation frequency of the transient linear frequency modulation disturbance differs from that of the power frequency signal. When its energy is high, a denoising algorithm can be used to reconstruct and eliminate it first, and then the power frequency signal can be denoised without interference. After denoising, the residual noise is relatively flat overall, but there are still slight fluctuations at the start and end times of the interference signal. In addition, the non-stationary transient disturbance signal is reconstructed, which is beneficial for further extraction of its feature parameters.

[0111] When the input signal-to-noise ratio (SNR) varies from 10 dB to 20 dB, the improved algorithm proposed in this application and the Discrete Wavelet Transform (DWT) method are used to denoise voltage spurs, voltage interruptions, and linear frequency modulation (LFM) interference, respectively. The db6 wavelet is selected as the mother wavelet, and two-level decomposition and soft thresholding are performed. Table 2 shows a comparison of the output SNR.

[0112] Table 2. Comparison of output signal-to-noise ratio results after processing with two noise reduction algorithms when the input signal-to-noise ratio changes.

[0113]

[0114]

[0115] As can be seen, the two methods produce similar results for voltage spurs, while the improved algorithm proposed in this application outperforms the traditional wavelet transform algorithm for voltage interruption and linear frequency modulation interference.

[0116] 3.2 Positioning performance analysis at the start and end times of transient disturbances

[0117] In power quality signal processing, locating the start and end times of transient disturbances is an important research topic. However, after denoising, the location information of the power signal is often filtered out or weakened. Therefore, the ability to effectively preserve location information is an indicator of the performance of denoising algorithms. An improved FRFT-based algorithm was used to denoise power signals containing voltage swells, voltage interruptions, and non-stationary transient disturbances. Then, discrete wavelet transform was applied to the denoised power signals containing voltage swells and interruptions, as well as the reconstructed non-stationary transient signals. The start and end times of the transient disturbances were obtained based on the detail coefficients, and the results are shown in Table 3. The input signal-to-noise ratio of the power signal was 10 dB. The theoretical start time for each type of transient disturbance was t1 = 0.045 s, and the theoretical end time was t2 = 0.085 s. t'1 and t'2 are the detection estimates, and Δt1 and Δt2 are the estimation errors.

[0118] Table 3. Detection results of the start and end times of transient disturbance signals

[0119]

[0120] When the signal-to-noise ratio (SNR) varies, the localization effect of the signal start and end times after noise reduction algorithm processing is further discussed. The SNR range is set to 0 dB to 10 dB, and 100 Monte Carlo simulations are performed at each SNR. Figure 9 (a) represents the root mean square error of the measurements taken at the start of the disturbance under different signal-to-noise ratios. Figure 9 (b) is the root mean square error of the measurement at the termination time of the disturbance under different signal-to-noise ratios.

[0121] Experimental results show that after processing by the noise reduction algorithm of this application, the start and end time information of the transient disturbance signal is well preserved, and accurate positioning can be achieved.

[0122] 4. Summary

[0123] This application proposes an improved denoising algorithm based on fractional Fourier transform to address the denoising problem of transient power quality signals. This method is applicable not only to transient stationary disturbance signals, such as voltage swells, drops, and interruptions, but also to non-stationary transient disturbance signals, such as transient linear frequency modulation (LFM) interference. During denoising, non-stationary transient disturbances can be effectively reconstructed, which facilitates the extraction of disturbance signal features and analysis of the causes of the disturbances. Furthermore, this application discusses a method for determining the optimal fractional Fourier transform angle; based on the fourth-order origin moment of the fractional-order spectrum, the optimal transform angle can be efficiently determined through one-dimensional peak search. Experimental results show that the improved denoising algorithm based on fractional Fourier transform can effectively achieve noise filtering and preservation of transient disturbance location information.

[0124] It should be noted that:

[0125] The algorithms and displays provided herein are not inherently related to any particular computer, virtual system, or other device. Various general-purpose systems can also be used in conjunction with the teachings herein. The required structure for constructing such systems is apparent from the above description. Furthermore, this application is not directed to any particular programming language. It should be understood that the content of this application described herein can be implemented using various programming languages, and the above description of specific languages ​​is for the purpose of disclosing the best mode of implementation of this application.

[0126] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of this application may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0127] Similarly, it should be understood that, in order to simplify this application and aid in understanding one or more of the various inventive aspects, in the above description of exemplary embodiments of this application, various features of this application are sometimes grouped together into a single embodiment, figure, or description thereof. However, this method of disclosure should not be construed as reflecting an intention that the claimed application requires more features than are expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of this application.

[0128] Those skilled in the art will understand that modules in the device of the embodiments can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or components in the embodiments can be combined into a single module, unit, or component, and further, they can be divided into multiple sub-modules, sub-units, or sub-components. Except where at least some of such features and / or processes or units are mutually exclusive, any combination can be used to combine all features disclosed in this specification (including the accompanying claims, abstract, and drawings) and all processes or units of any method or device so disclosed. Unless expressly stated otherwise, each feature disclosed in this specification (including the accompanying claims, abstract, and drawings) may be replaced by an alternative feature that serves the same, equivalent, or similar purpose.

[0129] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are intended to be within the scope of this application and form different embodiments. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0130] The various component embodiments of this application can be implemented in hardware, or as software modules running on one or more processors, or a combination thereof. Those skilled in the art will understand that microprocessors or digital signal processors (DSPs) can be used in practice to implement some or all of the functions of some or all of the components in the virtual machine creation system according to the embodiments of this application. This application can also be implemented as a device or system program (e.g., a computer program and computer program product) for performing part or all of the methods described herein. Such an implementation of this application can be stored on a computer-readable medium, or can be in the form of one or more signals. Such signals can be downloaded from an Internet website, provided on a carrier signal, or provided in any other form.

[0131] It should be noted that the above embodiments are illustrative of this application and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. This application can be implemented by means of hardware comprising several different elements and by means of a suitably programmed computer. In the unit claims enumerating several systems, several of these systems may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.

[0132] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A fractional-domain noise reduction method for electrical signals, characterized in that, include: S1. Estimate the optimal fractional Fourier transform angle of the original signal x(t). ; S2. Calculate the fractional Fourier transform of the original signal at the optimal fractional Fourier transform angle, and obtain... ; S3. Perform bandpass filtering in the optimal fractional Fourier transform domain to obtain... ; S4, Calculation At the angle - Fractional Fourier transform of the following order; S5, Judgment If the signal is equal to π / 2, then noise reduction ends; otherwise, the recovered signal component is eliminated. Then repeat steps S1-S5 until the estimated optimal FRFT rotation angle is equal to π / 2. The fractional Fourier transform is defined as follows: (1) (2) Where p is the FRFT transform order, α is the angle between the FRFT axis and the time axis, and α = pπ / 2, K p (α;u;t) is the kernel function of the fractional Fourier transform, where n is an integer; The fractional-order spectrum and fourth-order origin moment of the original signal x(t) are defined as follows: (10) Then the optimal transformation angle It can be estimated (11)。 2. The method according to claim 1, characterized in that, The original signal x(t) is represented as (5) Where s(t) is the power frequency signal, d(t) is the transient disturbance signal, and n(t) is Gaussian white noise.

3. The method according to claim 1, characterized in that, ； in, , , and These are the FRFT results for signals x(t), s(t), d(t), and n(t) at the optimal transform angle, respectively.

4. The method according to claim 2, characterized in that, d(t) is a non-stationary transient disturbance signal. (8) In the formula, A is the amplitude of the disturbance signal, u(t) is the unit step signal, t1 and t2 are the start and end times of the disturbance signal, f1 is the starting frequency of the linear frequency modulated disturbance signal, and k is its modulation frequency.

5. The method according to claim 1, characterized in that, The window functions used in the bandpass filtering include at least one of the following: rectangular window, Hanning window, Hamming window, and Blackman window.

6. The method according to claim 2, characterized in that, The peak energy of the power frequency signal is less than the peak energy of the transient disturbance signal.

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