A method for diagnosing a planetary gearbox fault based on modulated carrier spectrum demodulation

Abstract

The application discloses a kind of modulation carrier spectrum demodulation-based planetary gearbox fault diagnosis method, belongs to the technical field of planetary gearbox fault diagnosis, comprising the following steps: obtaining the gear data of planetary gearbox under multiple health states, and constructing sample set;Time domain signal is mapped to frequency domain by Fourier transform;According to the characteristic frequency of the inherent parameters and motor rotation frequency of planetary gearbox, the amplitude of each characteristic frequency is obtained based on spectrum analysis;ECCK is used to convolve the amplitude-frequency signal, and modulation carrier spectrum (MCS) is obtained;Match the fault characteristic frequency of each component in MCS;According to the characteristic frequency demodulated from signal, diagnose the fault of planetary gearbox.

Description

Technical Field

[0001] This invention belongs to the field of planetary gearbox fault diagnosis technology, specifically relating to a planetary gearbox fault diagnosis method based on Modulation-Carrier Spectrum Demodulation (MCSD). In particular, it relates to a novel Elastic Comb-shape Convolutional Kernel (ECCK) to automatically extract modulation information from the spectrum into the Modulation-Carrier Spectrum (MCS). Background Technology

[0002] Rotating machinery is indispensable in most manufacturing and production industries. Due to harsh working environments and variable operating conditions, rotating machinery is inevitably subject to damage. Periodic shocks caused by faults can lead to internal equipment failure and even serious safety accidents. Therefore, revealing and interpreting the fault-related frequency components in monitored vibration signals is of great significance for fault diagnosis.

[0003] Modulation phenomena are widespread in the vibration response of rotating machine resonators (RMs), such as planetary gearboxes (PGs) and rolling bearings (RBs), due to periodic rotation, gear meshing, internal fault-induced shocks, and external excitations. Furthermore, from the sensor's perspective, the complex signal transmission path from the vibration source to the sensor also contributes to modulation. Therefore, the monitored vibration signals exhibit various modulation types, including amplitude modulation (AM), frequency modulation (FM), and stacked / nested AM-FM coupling effects. These modulations primarily represent the dynamic characteristics and motion behavior of internal components. During RM operation, if a fault occurs, the modulation caused by or associated with the periodic shocks of the damaged component will distinguish it from the modulation of healthy components, thus providing an appropriate diagnostic opportunity. To date, researchers have made considerable efforts to elucidate modulation phenomena in RM signals, primarily focusing on frequency sideband analysis and effective demodulation methods.

[0004] The vibration signals monitored by RM (Resonance Meridian) often suffer from complex modulation phenomena and background noise, making it difficult to extract valuable information about changes in health status from the complex spectrum. Therefore, frequency demodulation is another research topic for interpreting RM vibration signals. Initially, manually identifying the carrier frequencies and sidebands on both sides was both time-consuming and inconvenient. Researchers have made great efforts to develop efficient demodulation methods. McFadden proposed a demodulation method to calculate AM and phase modulation, which was applied to the early detection of local faults. Olhede and Walden introduced a time-frequency analysis method called generalized demodulation for extracting single-component signals from complex modulated signals. This method converts non-stationary signals with curved instantaneous frequencies into steady-state signals with linear instantaneous frequencies parallel to the time axis. However, some overlooked problems need to be addressed:

[0005] 1. Single-component demodulation methods, such as EMD, VMD, ITD, and their improved versions, introduce cumbersome parameters and complex processing steps. More importantly, due to the coarse selection of nearby instantaneous frequencies, it is difficult to determine the true carrier frequency.

[0006] 2. The CSD-based method is basically demodulated through cyclic steady-state analysis of statistical indicators, so the original modulation-carrier frequency pair cannot be obtained directly.

[0007] 3. The modulation-carrier frequency pair and modulation type are the cornerstones for revealing the operating status of an RM. However, existing methods cannot identify the modulation type and modulation-carrier frequency.

[0008] 4. When applying existing demodulation methods, multiple pseudo-modulation frequencies may appear, which can easily lead to misunderstandings or misjudgments of the modulation phenomena inside the RM. Summary of the Invention

[0009] The purpose of this invention is to provide a planetary gearbox fault diagnosis method based on frequency demodulation. The key features are a frequency demodulation method based on modulated carrier spectrum (MCSD), a novel elastic comb convolution kernel (ECCK), and an improved nonlinear activation function—R-ReLU.

[0010] Based on the frequency demodulation method of modulated carrier spectrum (MCSD), a novel elastic comb convolution kernel (ECCK) is proposed to automatically extract modulation information from the spectrum into the modulated carrier spectrum (MCS). This includes the following:

[0011] (1) Vibration signal acquisition: Vibration signals can be generated through the DDS (Drivetrain Dynamics Simulator) test bench. Vibration signals are acquired through sensors and data acquisition devices to obtain the time domain signal of the planetary gearbox.

[0012] (2) The fault characteristic frequencies of each component are calculated based on the structural parameters, assembly relationship and motor rotation speed of the planetary gearbox in the DDS test bench.

[0013] (3) Signal preprocessing: The time domain signal is preprocessed by normalization and then the mean is subtracted to reduce the influence of noise and highlight the main frequency, thus obtaining the amplitude-frequency signal.

[0014] (4) In order to search for the sidebands generated by the modulation-carrier frequency pairs in the complex spectrum, since the convolution kernel of the convolutional neural network can automatically extract task-related features during training, an elastic comb kernel (ECCK) was designed to interpretably extract information of all possible modulation carrier frequency pairs and their amplitudes.

[0015] (5) ECCK is essentially a one-dimensional weight matrix with an odd number of elements. The central element is fixed, while the elements on both sides can move synchronously to both ends, resembling a flexible "comb". Considering the characteristics of AM and FM, the weight matrix should contain at least three weight elements to match the carrier frequency and the sideband pairs on both sides. The central weight element W0 is expected to be related to the carrier frequency f. c The match is valid, and its position is fixed. Meanwhile, the weight elements W on both sides... ±1 It is mobile and searches for f generated by the modulation frequency by synchronously changing the weight distance. m Sidebands of f c ±f m In this case, the modulation carrier frequency pair {f} can be recorded. m ,f c The amplitude and position information of}.

[0016] (6) Fault diagnosis: Match the fault characteristic frequencies of each component in the MCS. Diagnose planetary gearbox faults based on the characteristic frequencies obtained from the demodulated signals.

[0017] The technical effects achieved by this invention are:

[0018] A planetary gearbox fault diagnosis method based on modulated carrier spectrum demodulation was invented. Leveraging the advantages of convolutional neural networks (CNNs), an elastic comb kernel (ECCK) and an activation function improved by limiting rectified linear units (R-ReLU) were proposed to automatically extract rich modulation information from the spectrum, including modulation frequency, modulated carrier frequency, and modulation intensity, to obtain the modulated carrier spectrum (MCS). Based on the MCS and the inherent fault characteristic frequencies of the planetary gearbox, the health status of the planetary gearbox can be analyzed, and its fault type can be identified. Attached Figure Description

[0019] Figure 1 This is a system block diagram of the invention.

[0020] Figure 2 This is a schematic diagram of the Drivetrain Dynamics Simulator (DDS) used in this invention.

[0021] Figure 3 The images show the sun gear in a healthy state (left side view) and a faulty state (right side view, where the circle indicates the faulty part).

[0022] Figure 4 It is the time-frequency spectrum of the vibration signal.

[0023] Figure 5 The graph shows the R-ReLU function.

[0024] Figure 6 This is a normal spectrum diagram of the solar wheel.

[0025] Figure 7 This is a spectrum diagram of sun gear failure. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments:

[0027] This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiment. (Appendix) Figure 1 The system block diagram of the present invention is shown in the appendix. Figure 1 :

[0028] 1. In the appendix Figure 2 A fault diagnosis dataset for rotating machinery is constructed on the experimental platform shown. Data is acquired through sensors, vibration signals are recorded, and the time-domain signals of the signals are obtained.

[0029] Simultaneously, the characteristic frequency of the vibration signal obtained from the rotating machinery test bench is derived. The AM and FM signal modulation carrier frequencies are obtained from theoretical derivation, and the peak combinations are identified.

[0030] 2. Preprocess the time-domain signal by converting it into a frequency-domain signal using Fourier transform, such as... Figure 4 As shown, the Min-MaxNormalization function is used to normalize the spectrum to improve computational efficiency.

[0031]

[0032] Subtracting the average amplitude of the normalized spectrum from the spectral values ​​reduces the impact of noise and highlights the dominant frequency. This yields the input data X(f).

[0033] X(f) = O(f) - mean{O(f)}

[0034] 3. Convolution and Activation: In order to search for sidebands generated by modulation-carrier frequency pairs in complex spectra, since the convolution kernel of the convolutional neural network can automatically extract task-related features during training, an elastic comb kernel (ECCK) was designed to interpretably extract information of all possible modulation carrier frequency pairs and their amplitudes.

[0035] ①ECCK is essentially a one-dimensional weighted matrix with an odd number of elements. The central element is fixed in position, while the elements on both sides can move synchronously to both ends, resembling a flexible "comb". Considering the characteristics of AM and FM, the weighted matrix should contain at least three weight elements to match the carrier frequency and the sideband pairs on both sides. To better understand, consider an ECCK with three weight elements. The central weight element W0 is expected to be related to the carrier frequency f. c The match is valid, and its position is fixed. Meanwhile, the weight elements W on both sides... ±1 It is mobile and searches for f generated by the modulation frequency by synchronously changing the weight distance. m Sidebands of f c ±f m In this case, the modulation carrier frequency pair {f} can be recorded. m ,f c The amplitude and position information of}.

[0036] ② Construct a kernel group to cover carrier frequency f c It contains all possible modulation frequencies, including all length states of ECCK. ±1 W is tightly aligned with W0 in kernel1, with an initial weighted distance of 1. W moves synchronously at a speed of 1. ±1 Leave W0 and obtain kernel2. Then, continue moving W to either side. ±1 Each step yields a new core, until the length of ECCK is greater than or equal to the length L of the entire spectrum. It can be concluded that the last core is... Weighted distance

[0037] ③ Each kernel in the kernel group corresponds to a possible modulation frequency and produces a convolution output with respect to the current carrier frequency. Numerically, the convolution result is equal to multiplying the weight matrix by the three frequency amplitudes corresponding to a kernel and then summing them. For the same carrier frequency, the larger the modulation coefficient, the larger the sideband amplitude near the carrier frequency. Therefore, the weight matrix can be set to [W -1 The convolution result of [W0,W1] = [1,1,1] is actually the sum of the amplitudes of the carrier frequency and its sideband pairs. In this way, the convolution result of the kernel group and the spectrum can reflect the modulation intensity of each modulation carrier frequency pair.

[0038] Not all modulated carrier pairs with large amplitude values ​​conform to true modulation. Modulation is only possible when the amplitudes of all three frequencies corresponding to a core are greater than the noise. To address this, an improved activation function, called R-ReLU, is introduced to determine whether modulation is real and further restricts the convolution result of unmodulated modulation-carrier pairs.

[0039] Each frequency in the spectrum is a carrier frequency and is modulated. Therefore, the kernel set generated by ECCK can be applied to the entire spectrum. Whenever the center of the kernel set is aligned with a hypothetical carrier frequency, the modulation intensity of all modulation frequencies acting on that carrier frequency can be automatically calculated. The kernel set slides from the first frequency of the spectrum to the last frequency with a step size of 1, performing a convolution and activation at each step. This yields a feature map containing modulation information for all modulation-carrier frequency pairs, i.e., the modulation-carrier spectrum (MCS).

[0040] The calculation steps are as follows:

[0041] Based on the sampling frequency and sampling time, the length L of the spectrum can be calculated. Therefore, the elastic range of ECCK can be determined to be 1 to... Then, a kernel group can be constructed, which contains Each kernel has a weighted distance that increases sequentially from 1 to...

[0042]

[0043] Where D is the MCS, and n corresponds to the nth core, i.e., the nth possible modulation frequency. L corresponds to the position of the kernel group center on the input data, i.e., the Lth hypothetical carrier frequency, which is a modulation carrier frequency pair. W is a weight element, W = {W -1 Let W0, W1}, and X(l+in) represent the input data (l+in). th The amplitude of the frequency, σ(·), represents the proposed nonlinear activation function: R-ReLU.

[0044] The specific calculation steps for the above formula are as follows:

[0045] ① First, the kernel group performs sliding and convolution on the entire input data: the center of the kernel group slides from the first frequency to the last, with a sliding stride of 1. Simultaneously, the kernel group performs convolution on the input data. The weights of each kernel are multiplied by the amplitudes of the three corresponding frequencies in the input data, and then summed. Furthermore, zero-padding is used when the convolution range exceeds the input data.

[0046] ② All convolution outputs are non-linearly activated by the R-ReLU function. R-ReLU is as follows: Figure 5 As shown, this diagram can be represented as:

[0047]

[0048] Here, b is a variable, also known as a constraint.

[0049] R-ReLU functionality is derived from the Corrected Linear Unit (ReLU): if the convolution result is negative, the output is 0 after activation. When the convolution result is positive, a constraint term b is introduced to limit its amplitude, which can be constructed as follows:

[0050] b = min{|W i X(l+in)|}

[0051] =min{|W -1 X(ln)|,|W0X(l)|,|W1X(l+n)|}

[0052] In the above equation, b equals the minimum absolute value of the product of the weight matrix and the corresponding three frequency amplitudes. Since the spectrum is normalized, the constraint b < 1 limits the amplitude of the convolution output. As assumed above, true modulation requires that the amplitudes of all three frequencies corresponding to the kernel be more significant than the noise. Therefore, the smaller the value of b, the less likely modulation will occur at the corresponding modulation-carrier frequency pair. Thus, the amplitude of the spurious modulation-carrier frequency can be limited.

[0053] 4. Match the peak values ​​between the characteristic frequency of the DDS test bench and the theoretically derived values ​​to generate the modulation spectrum and carrier spectrum. Project the modulation spectrum and carrier spectrum onto the modulation carrier spectrum to obtain the demodulation result.

[0054] The specific experimental data are shown below:

[0055] In practical applications, a dynamic transmission and simulation test bench is used to collect data on the sun gear failure of a planetary gearbox. The test bench mainly includes a servo drive motor; one input and one output torque encoder; a planetary gearbox; two acceleration sensors (100mv / g) in the horizontal and vertical directions to acquire data; a fixed-axis gearbox; and a programmable magnetic brake. The assembly gear parameters of the planetary gearbox are shown in Table 1.

[0056] Table 1. Gear Assembly Parameters for Planetary Gearbox

[0057] Gear parameters numerical values Number of teeth of the sun gear 28 Number of teeth on the gear ring 100 Planetary wheel number 4

[0058] In the case of sun gear failure, vibration data of various gear health were collected at a speed of 600 RPM for 5 seconds and a sampling frequency of 7680 Hz.

[0059] The characteristic frequencies studied in the sun gear experiment are shown in the table below:

[0060]

[0061] The MCS spectra of the normal state and the sun gear fault signal are as follows: Figure 6 , Figure 7 As shown, (a1) is the MCS spectrum, and (a2) and (a3) ​​are the projections of the MCS spectrum onto the xoz plane and yoz plane, respectively, representing the carrier spectrum and the modulation spectrum. Figure 6 , Figure 7 Note: A failure of the sun gear will cause a significant increase in the amplitude of the characteristic frequency of the sun gear failure, which can be used to diagnose a failure of the sun gear in the planetary gearbox.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described with reference to preferred embodiments, those skilled in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the present invention as defined in the appended claims, and all such changes should fall within the protection scope of the present invention.

Claims

1. A method for fault diagnosis of planetary gearboxes based on modulation carrier spectrum demodulation, characterized in that, The specific steps of the diagnostic method are as follows: (1) Vibration signal acquisition: The Drivetrain Dynamics Simulator test bench was used to acquire planetary gearbox gear data under various health conditions; (2) Signal preprocessing: The time domain signal is preprocessed into a frequency domain signal, normalized, and then the mean is subtracted to reduce the influence of noise, highlight the main frequency, and obtain the amplitude-frequency signal. (3) Convolution operation: Convolution processing is performed on the amplitude-frequency signal. During the training process, task-related features are automatically extracted. Information of all possible modulation carrier frequency pairs is extracted interpretably through the elastic comb convolution kernel ECCK to obtain the modulation carrier spectrum MCS. (4) Match the fault characteristic frequencies of each component in the MCS; (5) Diagnose planetary gearbox faults based on the characteristic frequencies obtained from demodulating the signal; The elastic comb convolution kernel ECCK in step (3) automatically extracts the modulation information from the spectrum into the modulation carrier spectrum MCS, specifically: ① This ECCK is essentially a one-dimensional weighted matrix with an odd number of elements. The central element is fixed in position, while the elements on both sides can move synchronously to both ends, resembling an elastic "comb". The central weight element... With carrier frequency The match is established, and its position is fixed. Meanwhile, the weight elements W on both sides... -1 W +1 It is mobile and searches for the modulation frequency-generated distance by synchronously changing the weight distance. Sideband pairs In this case, the modulation carrier frequency pair is recorded. Amplitude and position information; ② Construct a kernel group to cover the carrier frequency It contains all possible modulation frequencies, including all length states of ECCK, W -1 W +1 and exist Closely aligned in the middle, with an initial weight distance of 1, and moving synchronously at a speed of 1 W. -1 W +1 leave ,get Then, continue moving W to both sides. -1 W +1 Each step yields a new kernel until the length of ECCK is greater than or equal to the length L of the entire spectrum, at which point the last kernel is obtained. The weighted distance is ; ③ Each kernel in the kernel group corresponds to a possible modulation frequency and produces a convolution output for the current carrier frequency. Numerically, the convolution result is equal to multiplying the weight matrix by the three frequency amplitudes corresponding to a kernel, and then adding them together. The weight matrix is ​​set to... The convolution result is actually the sum of the amplitudes of the carrier frequency and its sideband pairs. The convolution result of the kernel group and the spectrum reflects the modulation intensity of each modulation carrier frequency pair.

2. The planetary gearbox fault diagnosis method according to claim 1, characterized in that, Step (2) preprocesses the time-domain signal by transforming it into a frequency-domain signal using Fourier transform and normalizing the spectrum using the Min-MaxNormalization function to improve computational efficiency. Subtracting the average amplitude of the normalized spectrum from the spectral values ​​reduces the impact of noise and highlights the dominant frequency, yielding the input data. , 。 3. The planetary gearbox fault diagnosis method according to claim 1, characterized in that, Step (3) uses the activation function R-ReLU to determine whether modulation is true, and further restricts the convolution result of the modulation-carrier pair without modulation, including: ① Calculate the length of the spectrum based on the sampling frequency and sampling time. The elastic range of ECCK is determined to be 1 to Then, construct a kernel group containing Each kernel has a weighted distance that increases sequentially from 1 to... Based on such a kernel group, the convolution and activation operations are represented as: ②Among them It is an MCS, where n corresponds to the nth core, and i = -1, 0, 1; that is, the nth possible modulation frequency. 'l' corresponds to the position of the kernel group center on the input data, i.e., the l-th assumed carrier frequency, which is the modulation carrier frequency pair. It is a weight element. , Indicates input data The amplitude of the frequency, The proposed nonlinear activation function is R-ReLU. ③ The kernel group performs sliding and convolution on the entire input data: the center of the kernel group slides from the first frequency to the last, with a sliding step of 1. At the same time, the kernel group performs convolution on the input data. The weight elements of each kernel are multiplied by the amplitudes of the three corresponding frequencies on the input data and then added together. In addition, zero padding is used when the convolution range exceeds the input data. ④ Next, all convolutional outputs are non-linearly activated by the R-ReLU function, as shown in the following formula: Here, b is a variable, also known as a constraint. In R-ReLU: if the convolution result is negative, the output after activation is 0; when the convolution result is positive, a constraint term is introduced. To limit its amplitude, its construction is as follows: 。

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