Comprehensive transmission vibration signal fluctuation rotating speed accurate extraction and signal correction method

Abstract

The present application belongs to the technical field of fault diagnosis of complex transmission system, and particularly relates to a method for accurately extracting fluctuating speed from vibration signals of integrated transmission and correcting signals, the implementation of the method involves a speed fluctuation amplification unit, a speed fluctuation extraction unit and a speed fluctuation removal unit; the method can accurately estimate speed fluctuation from vibration signals without actually measuring speed signals, and remove speed fluctuation to obtain a stable signal. The present application improves the accuracy of speed fluctuation extraction and the accuracy of speed fluctuation removal by amplifying speed fluctuation for several times, and greatly reduces the time consumption of the algorithm through multiple frequency modulation. The method solves the problem of accurately extracting fluctuating speed from vibration signals of integrated transmission system and removing the influence of speed fluctuation, and provides a low-computing-cost and high-precision method for extracting and removing speed fluctuation.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology for complex transmission systems, and specifically relates to a method for accurate extraction and correction of rotational speed fluctuations in comprehensive transmission vibration signals. Background Technology

[0002] Fault diagnosis of complex transmission systems typically involves operating under stable conditions, collecting vibration signals, and then performing spectral analysis to determine the amplitude of characteristic frequency components and calculate relevant indicators. This allows for the assessment of the transmission system's health status or the analysis and localization of faults. However, in actual operating conditions, a stable operating condition with constant speed is impossible, whether on a test bench or in a real vehicle. Even if the target speed is set to a fixed value, the actual operating speed usually fluctuates around the target speed due to the influence of other systems and the control accuracy of the test bench. This causes the frequency components of the actual vibration signal to change with the speed fluctuations, greatly complicating vibration signal processing and related condition monitoring and diagnosis. Therefore, it is urgent to extract and remove speed fluctuations from the vibration signal. The traditional method is to add speed sensors to key components of the transmission system, such as the input shaft, to collect real-time fluctuating speed signals, and then use signal processing methods to remove the influence of speed fluctuations. However, due to the highly integrated and compact structure of the integrated transmission system of tracked armored vehicles, adding additional speed sensors to meet signal processing requirements is impractical for both test bench tests and real vehicles.

[0003] In fact, adding extra sensors to complex transmission systems of most important equipment, not just integrated transmission systems, can significantly impact equipment reliability. Therefore, dedicated signal processing methods are needed to directly remove the influence of speed fluctuations from vibration signals. One common method for estimating speed fluctuations is phase demodulation. This method selects a certain harmonic frequency component related to the speed in the vibration signal, filters out this component using a filter, and then performs phase demodulation to obtain its phase. The speed information is then obtained from the first derivative of the phase information. However, this method is severely limited by noise, and in noisy environments, it produces significant analysis errors. Another method for estimating speed fluctuations is time-frequency analysis. This method performs time-frequency analysis on a certain component of the vibration signal, such as using a short-time Fourier transform to obtain its time-frequency distribution, and then extracts ridges from the time-frequency distribution results to estimate speed fluctuations. However, due to limitations in time-frequency resolution, the accuracy of speed fluctuation extraction methods based on time-frequency analysis is limited, and they cannot accurately extract speed fluctuations. Furthermore, analyzing signals with high sampling frequencies requires significant computational costs.

[0004] A search of existing technologies revealed patent number CN202011427884.0, published on March 30, 2021, which discloses a method for extracting the envelope order spectrum fault features of rolling bearings under speed fluctuations. This method obtains the envelope signal through Hilbert transform, acquires the time spectrum of the envelope signal through short-time Fourier transform, and extracts the frequency sequence from the time spectrum using a peak search algorithm as an estimate of the speed fluctuation. This method belongs to the aforementioned speed fluctuation estimation methods based on time-frequency analysis, and due to limitations in time-frequency resolution, it cannot achieve accurate detection of speed fluctuations.

[0005] A search of existing technologies revealed that patent number CN201710781137.9, published on March 9, 2018, discloses a method for estimating the instantaneous rotational speed of rotating equipment. This method first uses parametric time-frequency analysis to roughly estimate the instantaneous frequency of the vibration signal, then uses envelope tracking filtering technology to estimate the signal envelope, and finally uses phase demodulation to extract the instantaneous frequency of the envelope signal. This method is essentially a combination of time-frequency analysis and phase demodulation. However, due to the influence of noise, the speed estimation has a significant error. Furthermore, both parametric time-frequency analysis and envelope signal calculation require high computational costs.

[0006] To address the issue of removing the influence of speed fluctuations in vibration signals of integrated transmission systems without speed tracking, existing phase demodulation-based methods produce significant errors under noisy conditions, while time-frequency distribution-based methods are limited by time-frequency resolution, making it difficult to accurately extract speed fluctuations under noisy conditions, and even difficult to achieve when speed fluctuations are very weak. Therefore, these methods cannot remove speed fluctuations from vibration signals, and they also have high computational costs. Summary of the Invention

[0007] (a) Technical problems to be solved

[0008] The technical problem to be solved by this invention is: how to provide a method for accurately extracting and correcting the rotational speed of integrated transmission vibration signals.

[0009] (II) Technical Solution

[0010] To solve the above-mentioned technical problems, the present invention provides a method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals. The implementation of the method involves a rotational speed fluctuation amplification unit, a rotational speed fluctuation extraction unit, and a rotational speed fluctuation removal unit.

[0011] The rotational speed fluctuation amplification unit is used to select a high signal-to-noise ratio harmonic component of a certain order in the vibration signal and amplify the fluctuation of the instantaneous frequency.

[0012] The rotational speed fluctuation extraction unit is used to extract amplified instantaneous frequency fluctuations, and accurately extracts rotational speed fluctuations based on their relationship with the original components and the relationship between the original components and rotational speed.

[0013] The speed fluctuation removal unit is used to resample the signal based on the extracted high-precision speed fluctuation, thereby obtaining a comprehensive transmission system vibration signal without the influence of speed fluctuation.

[0014] The method includes the following steps:

[0015] Step A: The rotational speed fluctuation amplification unit selects a high signal-to-noise ratio harmonic component in the vibration signal and amplifies the fluctuation of the instantaneous frequency;

[0016] Step B: The rotational speed fluctuation extraction unit extracts the amplified instantaneous frequency fluctuation, and accurately extracts the rotational speed fluctuation based on its relationship with the original component and the relationship between the original component and the rotational speed.

[0017] Step C: The speed fluctuation removal unit is used to resample the signal based on the extracted high-precision speed fluctuation, thereby obtaining a comprehensive transmission system vibration signal without the influence of speed fluctuation.

[0018] Specifically, step A includes the following sub-steps:

[0019] Step A1: Shift a high-order component with a clear physical meaning and the same trend as the rotational speed change to a low frequency;

[0020] Step A2: Amplify the instantaneous frequency of the signal and extract the instantaneous frequency using the ridge line;

[0021] Step A3: Calculate the instantaneous frequency before amplification using the ridge extraction results;

[0022] Step A4: Calculate the speed fluctuation based on the selected order;

[0023] Step A5: Resample the original signal into a stable signal based on the calculated speed fluctuation.

[0024] The process from step A1 to step A5 involves applying a two-up, two-down modulation method to the selected feature components, which can significantly reduce the computational cost of time-frequency distribution required for ridge extraction, thereby improving the computational efficiency of instantaneous rotational speed estimation.

[0025] Step A1 includes:

[0026] Step A1-1: During the first descent, select the higher-order component s(t) from the vibration signal s(t) that has a clear first-order physical meaning and the same trend as the rotational speed change. h (t), let its instantaneous frequency be f. h The order relative to the input axis is m. hThat is, f h =m h f r , where f r The input shaft rotation frequency; except for higher-order components, this component should have a high signal-to-noise ratio within its frequency band.

[0027] Step A1-2: Negatively modulate the component components, that is, shift the instantaneous frequency downwards, denoted as s l (t)=s(t)exp(-j2πf0t), f l =f h -f0; f o f represents the negative modulation distance. l This represents the instantaneous frequency after the first descent.

[0028] The reason for performing the downsampling in step A1 is that the time complexity of time-frequency analysis is relatively high. Shifting the signal to a lower frequency and downsampling can reduce the sampling frequency of the analyzed signal, reduce the number of data points required for time-frequency analysis, and improve computational efficiency. In addition, downsampling also smooths the instantaneous frequency to a certain extent, which helps to fit the parameterized instantaneous frequency.

[0029] Step A2 includes the following sub-steps:

[0030] Step A2-1: First rise, square the signal, then perform bandpass filtering. This represents a filter with a center frequency of 2f. l The bandwidth is f band This resulted in a signal whose instantaneous frequency fluctuation was doubled.

[0031] Step A2-2: Analyze the signal Continue with the squared bandpass filter operation to obtain This operation can be continued iteratively.

[0032]

[0033] Step A2-3: Perform a short-time Fourier transform on the obtained signal to obtain the time-frequency distribution. At this point, the amplified instantaneous frequency f can be obtained using the ridge extraction method. u .

[0034] In step A2-2, the instantaneous frequency fluctuation was obtained as 2 n The amplification completed the first increase in instantaneous frequency.

[0035] In step A3, the second descent occurs for the instantaneous frequency f. u Calculate the instantaneous frequency before the first rise as

[0036] In step A4, the second rise refers to the instantaneous frequency. Compensate for negative modulation and calculate the instantaneous frequency before the first descent. As can be seen, the subsequent descent and ascent processes are no longer directed at the signal itself, but rather at recovering the estimated instantaneous frequency; therefore, the estimated instantaneous rotational speed can be expressed as...

[0037] In step A5, theoretically, it is desirable for the instantaneous rotational speed to be constant, i.e. in The target instantaneous rotational speed is defined by `const`, which is a fixed value. This represents the desired instantaneous rotational speed under the test environment. It is known that instantaneous rotational speed can be obtained using resampling techniques. Resampling

[0038] (III) Beneficial Effects

[0039] Compared with existing technologies, this invention provides a method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals. This method involves rotational speed fluctuation amplification, extraction, and removal, with the rotational speed fluctuation amplification method being the most novel feature. This method amplifies the original rotational speed fluctuations, and extracting the amplified fluctuations improves the extraction accuracy, thereby ensuring the stability of the signal after extraction and enhancing the effectiveness of spectrum-based fault diagnosis methods. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method for accurately extracting and correcting the rotational speed of vibration signals in a comprehensive transmission system.

[0041] Figure 2 This is a time-frequency distribution diagram of the negative modulation of the higher-order components of the original signal to a low frequency in an embodiment of the present invention.

[0042] Figure 3 This is a time-frequency distribution diagram of the signal after its first rise in an embodiment of the present invention.

[0043] Figure 4 This is a schematic diagram of the estimated high-precision rotational speed signal in an embodiment of the present invention.

[0044] Figure 5 This is a schematic diagram of the spectrum of the original signal in an embodiment of the present invention.

[0045] Figure 6 This is a schematic diagram of the spectrum of the speed signal in an embodiment of the present invention.

[0046] Figure 7This is a partially enlarged schematic diagram of the original signal spectrum in an embodiment of the present invention.

[0047] Figure 8 This is a partially enlarged schematic diagram of the speed signal spectrum in an embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0049] To solve the above-mentioned technical problems, the present invention provides a method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals. The implementation of the method involves a rotational speed fluctuation amplification unit, a rotational speed fluctuation extraction unit, and a rotational speed fluctuation removal unit.

[0050] The rotational speed fluctuation amplification unit is used to select a high signal-to-noise ratio harmonic component of a certain order in the vibration signal and amplify the fluctuation of the instantaneous frequency.

[0051] The rotational speed fluctuation extraction unit is used to extract amplified instantaneous frequency fluctuations, and accurately extracts rotational speed fluctuations based on their relationship with the original components and the relationship between the original components and rotational speed.

[0052] The speed fluctuation removal unit is used to resample the signal based on the extracted high-precision speed fluctuation, thereby obtaining a comprehensive transmission system vibration signal without the influence of speed fluctuation.

[0053] The method includes the following steps:

[0054] Step A: The rotational speed fluctuation amplification unit selects a high signal-to-noise ratio harmonic component in the vibration signal and amplifies the fluctuation of the instantaneous frequency;

[0055] Step B: The rotational speed fluctuation extraction unit extracts the amplified instantaneous frequency fluctuation, and accurately extracts the rotational speed fluctuation based on its relationship with the original component and the relationship between the original component and the rotational speed.

[0056] Step C: The speed fluctuation removal unit is used to resample the signal based on the extracted high-precision speed fluctuation, thereby obtaining a comprehensive transmission system vibration signal without the influence of speed fluctuation.

[0057] Among the above implementation schemes, the rotational speed fluctuation amplification process is unique to this invention, has never been disclosed before, and its working method differs from any existing literature. This method can amplify the original rotational speed fluctuations, and extracting the amplified rotational speed fluctuations can improve the extraction accuracy, thereby ensuring the stability of the signal after the rotational speed fluctuations are extracted and improving the effectiveness of the spectrum-based fault diagnosis method.

[0058] This process can be summarized as two decreases and two increases. It can remove minute fluctuations in rotational speed with relatively low computational cost. Assume the rotational speed is f. r .

[0059] Among them, such as Figure 1 As shown, step A specifically includes the following sub-steps:

[0060] Step A1: Shift a high-order component with a clear physical meaning and the same trend as the rotational speed change to a low frequency;

[0061] Step A2: Amplify the instantaneous frequency of the signal and extract the instantaneous frequency using the ridge line;

[0062] Step A3: Calculate the instantaneous frequency before amplification using the ridge extraction results;

[0063] Step A4: Calculate the speed fluctuation based on the selected order;

[0064] Step A5: Resample the original signal into a stable signal based on the calculated speed fluctuation.

[0065] The process from step A1 to step A5 involves applying a two-up, two-down modulation method to the selected feature components, which can significantly reduce the computational cost of time-frequency distribution required for ridge extraction, thereby improving the computational efficiency of instantaneous rotational speed estimation.

[0066] Step A1 includes:

[0067] Step A1-1: During the first descent, select the higher-order component s(t) from the vibration signal s(t) that has a clear first-order physical meaning and the same trend as the rotational speed change. h (t), let its instantaneous frequency be f. h The order relative to the input axis is m. h That is, f h =m h f r , where f r The input shaft rotation frequency; except for higher-order components, this component should have a high signal-to-noise ratio within its frequency band.

[0068] Step A1-2: Negatively modulate the component components, that is, shift the instantaneous frequency downwards, denoted as s l (t)=s(t)exp(-j2πf0t), f l =f h -f0; f o f represents the negative modulation distance. l This represents the instantaneous frequency after the first descent.

[0069] The reason for performing the downsampling in step A1 is that the time complexity of time-frequency analysis is relatively high. Shifting the signal to a lower frequency and downsampling can reduce the sampling frequency of the analyzed signal, reduce the number of data points required for time-frequency analysis, and improve computational efficiency. In addition, downsampling also smooths the instantaneous frequency to a certain extent, which helps to fit the parameterized instantaneous frequency.

[0070] Step A2 includes the following sub-steps:

[0071] Step A2-1: First rise, square the signal, then perform bandpass filtering. This represents a filter with a center frequency of 2f. l The bandwidth is f band This resulted in a signal whose instantaneous frequency fluctuation was doubled.

[0072] Step A2-2: Analyze the signal Continue with the squared bandpass filter operation to obtain This operation can be continued iteratively.

[0073]

[0074] In step A2-2, the instantaneous frequency fluctuation was obtained as 2 n The amplification completed the first increase in instantaneous frequency.

[0075] Step A2-3: Perform a short-time Fourier transform on the obtained signal to obtain the time-frequency distribution. At this point, the amplified instantaneous frequency f can be obtained using the ridge extraction method. u .

[0076] The squaring operation in this step is mainly based on a simple trigonometric function transformation formula: This can be understood as squaring a single-component signal, resulting in a signal containing a low-frequency component and a component whose phase is doubled. Bandpass filtering removes the low-frequency component, leaving only the component with doubled phase. Since the phase is doubled, the instantaneous frequency is also doubled, meaning the instantaneous frequency fluctuation is magnified by a factor of two. Because the signal remains a single-component signal after bandpass filtering, the "squaring + bandpass filtering" method can be used to geometrically amplify the instantaneous frequency fluctuation, allowing for extraction using parametric time-frequency analysis.

[0077] In step A3, the second descent occurs for the instantaneous frequency f. u Calculate the instantaneous frequency before the first rise as

[0078] In step A4, the second rise refers to the instantaneous frequency. Compensate for negative modulation and calculate the instantaneous frequency before the first descent. As can be seen, the subsequent descent and ascent processes are no longer directed at the signal itself, but rather at recovering the estimated instantaneous frequency; therefore, the estimated instantaneous rotational speed can be expressed as...

[0079] In step A5, theoretically, it is desirable for the rotational speed to be constant, i.e. in The target instantaneous rotational speed is defined by `const`, which is a fixed value. This represents the desired instantaneous rotational speed under the test environment. It is known that instantaneous rotational speed can be obtained using resampling techniques. Resampling

[0080] Example 1

[0081] This embodiment uses measured signals from a transmission system as a case study to illustrate the specific implementation of the invention and verify its effectiveness. Assume the instantaneous rotational frequency is f. r ;

[0082] The method for accurate extraction and correction of the rotational speed fluctuation of the integrated transmission vibration signal specifically includes the following steps:

[0083] Step 1, First descent: Select the higher-order component s(t) from the vibration signal s(t) that has a clear first-order physical meaning and the same trend as the rotational speed change. h (t), let its instantaneous frequency be f. h The order is m h That is, f h =m h f r The test condition was set at a speed of 1500 RPM, which is equivalent to a rotational frequency of 25 Hz. A high-order component of order 180.4 was selected. Besides being high-order, this component should also have a high signal-to-noise ratio within its frequency band. Negative modulation of the component, i.e., shifting the instantaneous frequency downwards, can be expressed as s l (t)=s(t)exp(-j2πf0t), f l =f h -f0. f l This represents the instantaneous frequency after the first drop. After the higher-order components are bandpass filtered and negatively modulated at 4500Hz, down to the low-frequency range, the time-frequency diagram is as follows: Figure 1 As shown, the instantaneous frequency fluctuation is not amplified and is approximately a straight line. Due to the limited time-frequency resolution of the time-frequency transformation, the fluctuation of the instantaneous frequency is difficult to characterize. At this time, methods such as ridge extraction can only extract a straight line or a few local bends, which does not match the actual instantaneous frequency.

[0084] Step 2, the first rise: first square the signal, then perform bandpass filtering. This represents a filter with a center frequency of 2f. l The bandwidth is f band This yielded a signal with instantaneous frequency fluctuations doubled. Performing a squared bandpass filter on the signal yields... This operation can be continued iteratively.

[0085]

[0086] At this point, the instantaneous frequency fluctuation is 2. n The amplification completes the first rise in instantaneous frequency. A short-time Fourier transform is performed on the obtained signal to obtain the time-frequency distribution. At this point, the ridge extraction method can be used to obtain the amplified instantaneous frequency f. u For this signal, during the first rise, it is amplified four times, meaning the instantaneous frequency is amplified by a factor of 16. The time-frequency diagram of the amplified signal is shown below. Figure 2 As shown in the figure, the instantaneous frequency of the signal is increased by a factor of two after each squared bandpass filter operation, and the corresponding instantaneous frequency fluctuation is also amplified by a factor of two. This indicates that the squared bandpass filter can amplify the instantaneous frequency fluctuation of the signal. After amplification by 16 times, the instantaneous frequency fluctuation of the signal is quite considerable. The black line in the figure represents the fitted instantaneous frequency ridge.

[0087] Step 3, the second descent, for the instantaneous frequency f u Calculate the instantaneous frequency before the first rise as

[0088] Step 4, the second rise, for the instantaneous frequency Compensate for negative modulation and calculate the instantaneous frequency before the first descent. As can be seen, the subsequent descent and ascent processes are no longer based on the signal itself, but rather on the recovery of the estimated instantaneous frequency. Therefore, the estimated instantaneous rotational speed can be expressed as... The accuracy of estimating rotational speed fluctuations using this method is improved by m·2 compared to directly extracting rotational frequency components from time-frequency distribution. n =180.4·2 4 =2886.4. In this example, the precision has been improved by 2886.4 times, allowing the extremely weak instantaneous frequency fluctuations to be extracted accurately.

[0089] Step 5, theoretically, it is desirable for the rotational speed to be constant, that is... in The target instantaneous rotational speed is defined by `const`, which is a fixed value. This represents the desired instantaneous rotational speed under the test environment. It is known that instantaneous rotational speed can be obtained using resampling techniques. Resampling The measured speed fluctuations were eliminated by resampling. The spectra of the original signal and the spectra of the signal after speed fluctuation removal are as follows: Figure 5 and Figure 6 As shown in the figure. A partial magnified view of the spectrum of the original signal and the signal after speed fluctuation is shown in the figure. Figure 7 and Figure 8 As shown, compared to the signal before removing speed fluctuations, the spectral concentration of the signal after removing speed fluctuations is significantly improved, essentially eliminating the bandwidth broadening phenomenon and truly reflecting the energy status of the component. In the comparison of local methods, it can be seen that the signal spectrum after removing speed fluctuations has three distinct components. Before removing speed fluctuations, the amplitude was weakened due to bandwidth broadening, causing these components to be submerged by noise. Without removing speed fluctuations, it might be mistakenly assumed that these components are absent, thus affecting the mechanical fault diagnosis results based on the presence of these components. This example analysis based on measured data of the transmission system illustrates that the speed of the existing test bench is not truly constant under certain accuracy requirements (even if the speed is set to constant during testing), and its speed fluctuations can affect the amplitude of characteristic components and the judgment of their existence.

[0090] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals, characterized in that, The implementation of the method involves a speed fluctuation amplification unit, a speed fluctuation extraction unit, and a speed fluctuation removal unit; The method includes the following steps: Step A: The rotational speed fluctuation amplification unit selects a high signal-to-noise ratio harmonic component in the vibration signal and amplifies the fluctuation of the instantaneous frequency; Step B: The rotational speed fluctuation extraction unit extracts the amplified instantaneous frequency fluctuation, and accurately extracts the rotational speed fluctuation based on the relationship between the instantaneous frequency fluctuation and the original component, as well as the relationship between the original component and the rotational speed. Step C: The speed fluctuation removal unit is used to resample the signal based on the extracted high-precision speed fluctuation, thereby obtaining a comprehensive transmission system vibration signal without the influence of speed fluctuation; Specifically, step A includes the following sub-steps: Step A1: Shift a high-order component with a clear physical meaning and the same trend as the rotational speed change to a low frequency; Step A2: Amplify the instantaneous frequency of the signal and extract the instantaneous frequency using the ridge line; Step A3: Calculate the instantaneous frequency before amplification using the ridge extraction results; Step A4: Calculate the speed fluctuation based on the selected order; Step A5: Resample the original signal into a stable signal based on the calculated speed fluctuation; The process from step A1 to step A5 involves applying a two-rise and two-fall modulation method to the selected feature components, which can significantly reduce the time-frequency distribution calculation cost required for ridge extraction, thereby improving the calculation efficiency of instantaneous rotational speed estimation. Step A1 includes: Step A1-1: First descent, select vibration signal The higher-order components with clear first-order physical meaning and the same trend as the rotational speed change Let its instantaneous frequency be... The order relative to the input axis is ,Right now ,in f r The input shaft rotation frequency; except for higher-order components, this component should have a high signal-to-noise ratio within its frequency band. Step A1-2: Negatively modulate the component components, that is, shift the instantaneous frequency downwards, expressed as... , ; f o Indicates the negative modulation distance. This represents the instantaneous frequency after the first descent.

2. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 1, characterized in that, The reason for performing the downsampling in step A1 is that the time complexity of time-frequency analysis is relatively high. Shifting the signal to a lower frequency and downsampling reduces the sampling frequency of the analyzed signal, reduces the number of data points required for time-frequency analysis, and improves computational efficiency. In addition, downsampling also smooths the instantaneous frequency to a certain extent, which helps to fit the parameterized instantaneous frequency.

3. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 1, characterized in that, Step A2 includes the following sub-steps: Step A2-1: First rise, square the signal, then perform bandpass filtering. , This represents a filter, where the center frequency of the filter is... bandwidth is This resulted in a signal whose instantaneous frequency fluctuation was doubled. ; Step A2-2: Analyze the signal Continue with the squared bandpass filter operation to obtain This operation continues iteratively. Step A2-3: Perform a short-time Fourier transform on the obtained signal to obtain the time-frequency distribution. Then, use the ridge extraction method to obtain the amplified instantaneous frequency. .

4. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 3, characterized in that, In step A2-2, the instantaneous frequency fluctuation was obtained. The amplification completed the first increase in instantaneous frequency.

5. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 3, characterized in that, In step A3, the second descent, for the instantaneous frequency... Calculate the instantaneous frequency before the first rise as .

6. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 5, characterized in that, In step A4, the second rise refers to the instantaneous frequency. Compensate for negative modulation and calculate the instantaneous frequency before the first descent. The subsequent decline and rise processes no longer target the signal itself, but rather recover the estimated instantaneous frequency; therefore, the estimated instantaneous rotational speed is expressed as... .

7. The method for accurate extraction and correction of rotational speed fluctuations in integrated transmission vibration signals as described in claim 6, characterized in that, In step A5, theoretically, it is desirable for the instantaneous rotational speed to be constant, i.e. ,in For the target instantaneous rotational speed, It is a fixed value; the desired result in the test environment. It is known that instantaneous rotational speed is obtained using resampling techniques. Resampling .

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