Gear fault diagnosis method based on sub-signal joint weighting envelope anti-noise correlation

Abstract

The application discloses a gear fault diagnosis method based on sub-signal joint weighting envelope anti-noise correlation. Firstly, the original vibration signal sequence is converted into an envelope signal through a signal sequence element-by-element squaring-low-pass filtering-square root calculation process, then the envelope signal is reconstructed according to different time intervals to obtain a series of sub-signals, and the fault information representation of each sub-signal is calculated based on the L-matrix theory index, then the Sigmoid function is combined to assign a weight to each sub-signal, and then the joint weighting envelope anti-noise correlation function of the envelope signal sequence and the reconstructed sub-signals is calculated based on the envelope signal, the reconstructed sub-signals and the corresponding weights, finally, the characteristic frequency is determined according to the reciprocal of the time interval value corresponding to the characteristic peak in the change graph of the joint weighting envelope anti-noise correlation function with the time interval, and finally the gear fault is identified. The application can reliably identify the gear fault based on time domain analysis only under the condition of limited signal length and complex noise interference.

Description

Technical Field

[0001] This invention relates to the field of condition monitoring and fault diagnosis of rotating machinery gearbox equipment, and in particular to a gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation. Background Technology

[0002] Gearboxes, primarily consisting of a housing, gears, rolling bearings, shafts, fixed components, seals, and other elements, are the most commonly used speed-transmission components in various large rotating machinery such as wind turbines, rotary compressors, and steam turbines. On the one hand, the quality, operational smoothness, and noise levels of gearboxes are often important indicators of mechanical manufacturing quality, and statistical data shows that the main causes of various mechanical transmission system failures are deficiencies in design, manufacturing, and maintenance. On the other hand, gearboxes, operating under harsh conditions of high speed and heavy load for extended periods, are prone to various malfunctions, ranging from minor performance degradation to potentially system-wide catastrophic accidents. Therefore, improving gearbox reliability requires both improvements in design, manufacturing, and assembly quality, as well as enhanced operation and maintenance. Real-time monitoring and fault diagnosis of gearbox operating conditions, timely detection of early gear failures, and prompt intervention can effectively improve equipment prognosis and health management, thereby ensuring industrial safety and stable production. This has significant practical engineering implications.

[0003] Due to its structural and operational characteristics, the vibration signals of gearboxes are highly complex, often requiring analysis in both the time and frequency domains for fault diagnosis. The characteristic frequencies of gearbox gear faults essentially consist of two parts: a carrier signal composed of the gear meshing frequency and its harmonics; and a modulated signal composed of the amplitude and phase variations of low-frequency components (mainly the rotational speed frequency of the shaft where the faulty gear is located), including amplitude modulation and frequency modulation. The following summarizes the spectral and waveform characteristics of gearbox gear faults:

[0004] (1) The axial frequency and its higher harmonics exist;

[0005] (2) There is a gear meshing frequency and its higher harmonics;

[0006] (3) The meshing frequency and its harmonics are used as the carrier frequency, and the rotation frequency of the shaft where the gear is located and its multiples are used as the modulation frequency of the meshing frequency sideband.

[0007] (4) The natural frequency of the gear and its harmonics are used as the carrier frequency, and the rotational frequency of the shaft where the gear is located and its multiples are used as the sideband of the modulation frequency.

[0008] (5) The natural frequency of the gearbox and its harmonics are used as the carrier frequency, and the rotational frequency of the shaft where the gear is located and its multiples are used as the modulation frequency sideband.

[0009] In general, the frequency-modulated carriers for gearbox gear faults are: gear meshing frequency, gearbox natural frequency, and gear natural frequency. In spectrum analysis, amplitude or power spectra with a Hanning window are typically used. Due to the complexity of gear fault symptoms and signals, fault diagnosis of gearbox gears requires extracting clear fault feature information while minimizing noise interference and improving the signal-to-noise ratio. Common vibration signal processing methods include refined spectrum analysis, cepstral analysis, time-domain synchronous averaging, adaptive noise reduction techniques, resonance demodulation, and signal deconvolution. However, due to the influence of complex noise interference during actual signal acquisition, these signal processing methods often fail to effectively extract gearbox gear fault features. Furthermore, in practical applications, most spectrum analysis-based signal processing methods are constrained by the availability of signals in limited systems. For example, when using wireless vibration sensors to monitor the condition of gearbox equipment in rotating machinery, the length of the acquired signal sequence is often too short due to limitations in power consumption, communication bandwidth, and storage, resulting in poor frequency resolution of the signal spectrum, which cannot meet the requirements of spectrum analysis and thus cannot accurately identify gearbox gear faults. Summary of the Invention

[0010] To address the aforementioned problems in the prior art, this invention provides a gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation. This method can detect and diagnose gear faults in rotating machinery gearboxes based on vibration acceleration signal analysis, even when limited system signals are available and complex noise interference exists.

[0011] The technical solution of the present invention is as follows:

[0012] A gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation includes:

[0013] Step 1: Acquire signal sequences from the rotating machinery gearbox using a vibration acceleration sensor;

[0014] Step 2: Squaring each element of the acquired discrete vibration acceleration signal sequence to obtain a discrete vibration acceleration signal square sequence;

[0015] Step 3: Perform low-pass filtering on the square sequence of the discrete vibration acceleration signal;

[0016] Step 4: Calculate the square root of the low-pass filtered signal to obtain the direct envelope signal of the original signal;

[0017] Step 5: Reconstruct the envelope signal according to different time intervals to obtain a series of sub-signals;

[0018] Step Six: Calculate the fault information representation metric for each sub-signal based on L-moment theory indices;

[0019] Step 7: Assign weights to each sub-signal based on fault information representation metrics and Sigmoid function transformation;

[0020] Step 8: Based on the weights of the direct envelope signal from Step 4, the reconstructed sub-signal from Step 5, and the sub-signal from Step 7, calculate the joint weighted envelope noise-resistant correlation function of the envelope signal sequence and the reconstructed sub-signal;

[0021] Step 9: Plot the change of the joint weighted envelope noise-resistant correlation function over time intervals;

[0022] Step 10: Determine the characteristic frequency based on the reciprocal of the time interval value corresponding to the characteristic peak in the graph drawn in Step 9, and further identify gear faults.

[0023] Further, in step one, the acquired signal sequence is denoted as s(t), t = 1, 2, 3, ..., N, where N is the total number of sampling points, and the sampling frequency is denoted as f. s The frequency response parameter of the vibration acceleration sensor used should be no less than 2kHz, and the sampling frequency f of the vibration signal sequence should be... s The frequency should be no less than 5.12kHz and no more than 64kHz, and the number of sampling points should satisfy max{f s / 10, min{f s / 8, 2f s / Fr}}≤N≤f s / 2, where Fr is the lowest speed among all shaft speeds of the gearbox equipment being tested.

[0024] Furthermore, in step three, a low-pass filter with a stopband attenuation of 60dB is used to perform zero-phase filtering on the vibration signal, and the cutoff frequency ω of the low-pass filter is... FL It is 500Hz.

[0025] Furthermore, the calculation formula for step five is as follows:

[0026]

[0027] in, This represents the floor operation, where the time interval T is a positive integer and... Represents the subsignal θ T The reconstruction coefficients of y(t); y(t) represents the envelope signal.

[0028] Furthermore, the fault information characterization metric LI in step six... T The calculation formula is as follows:

[0029]

[0030] in, and Representing the sub-signals θ T The L-skewness and L-kurtosis of (t) are calculated using L-moment theory, respectively:

[0031]

[0032]

[0033] Where, λ r (θ T (t) represents the signal sequence θ T The r-th order L-moment of (t).

[0034] Furthermore, regarding the signal sequence θ T The calculation process of the r-th order L-moment of (t) is as follows:

[0035] Suppose X = [X1, X2, ..., X...] n Let X be a sequence of n consecutive independent samples from the cumulative distribution F(x), and let X be a series of samples from the cumulative distribution F(x). 1：n ≤X 2：n ≤…≤X n：n Let λ be the order statistic of the random variable extracted from X. Then, what is the r-th order L-moment λ about the sequence X? r The calculation formula is as follows:

[0036]

[0037] Wherein, E(X) (r-k)：r X is the order statistic. (r-k)：r The expected value is calculated using the following formula:

[0038]

[0039] Furthermore, the calculation formula for step seven is as follows:

[0040]

[0041] Where γ and v are the scaling factor and bias factor, respectively.

[0042] Furthermore, the joint weighted envelope noise-resistant correlation function in step eight... The calculation formula is as follows:

[0043]

[0044] Furthermore, in step ten, the time interval T corresponding to the characteristic peak in the graph drawn in step nine is an integer multiple of the fundamental frequency and the reciprocal of its higher harmonic frequencies of the gear fault characteristic frequency.

[0045] Furthermore, the scaling factor y is set to 100, and the bias factor v is set to 0.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] This invention addresses the shortcomings and deficiencies of existing gear fault diagnosis technologies for rotating machinery gearboxes, particularly in situations where limited system signals are available and complex noise interference exists. It proposes a vibration acceleration signal analysis technique. First, the original vibration signal sequence is converted into an envelope signal through an element-by-element squaring, low-pass filtering, and square root calculation process. Then, the envelope signal is reconstructed according to different time intervals to obtain a series of sub-signals. Based on L-moment theory, the fault information representation metric for each sub-signal is calculated. Next, a sigmoid function transformation is used to assign weights to each sub-signal. Then, based on the envelope signal, the reconstructed sub-signals, and their corresponding weights, a joint weighted envelope noise-resistant correlation function is calculated for the envelope signal sequence and the reconstructed sub-signals. Finally, the characteristic frequency is determined by the reciprocal of the time interval value corresponding to the characteristic peak in the plotted graph of the joint weighted envelope noise-resistant correlation function versus time interval, ultimately identifying the gear fault. This invention is applicable to gear fault diagnosis and analysis of gearbox equipment in rotating machinery systems. It can reliably identify gear faults based solely on time-domain analysis of vibration acceleration signals without prior information. It is a non-parametric method, and the diagnosis process does not rely on spectrum analysis technology. It is suitable for scenarios with limited signal acquisition length in actual industrial field equipment condition monitoring, i.e., the signal availability constraint of finite systems. It also has excellent robustness to the unavoidable complex noise interference during signal acquisition and signal conversion processing in industrial environments, which is of great significance for practical engineering applications. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating a gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to the present invention.

[0049] Figure 2 This is a schematic diagram illustrating the acquisition of vibration signal sequences from a parallel shaft gearbox device of a rotating machinery system using a vibration acceleration sensor, as described in an embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram of a faulty large gear with worn teeth in a parallel shaft gearbox according to an embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of the original vibration signal collected in an embodiment of the present invention.

[0052] Figure 5 This is a schematic diagram of the envelope signal converted from the original vibration signal sequence through the process of element-by-element squaring, low-pass filtering, and square root calculation in an embodiment of the present invention.

[0053] Figure 6 This is a schematic diagram illustrating the variation of the joint weighted envelope noise-resistant correlation function calculated based on the envelope signal, the reconstructed sub-signal, and their corresponding weights as a function of time interval in an embodiment of the present invention. Detailed Implementation

[0054] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0055] This invention discloses a gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation. Based on vibration acceleration signal analysis, the method first converts the original vibration signal sequence into an envelope signal through an element-by-element squaring-low-pass filtering-square root calculation process. Then, the envelope signal is reconstructed according to different time intervals to obtain a series of sub-signals. The fault information representation metric of each sub-signal is calculated based on L-moment theory. Next, a weight is assigned to each sub-signal using a Sigmoid function transformation. Then, based on the envelope signal, the reconstructed sub-signals, and their corresponding weights, a joint weighted envelope noise immunity correlation function is calculated between the envelope signal sequence and the reconstructed sub-signals. Finally, the characteristic frequency is determined by the reciprocal of the time interval value corresponding to the characteristic peak in the plotted graph of the joint weighted envelope noise immunity correlation function versus time interval. This method ultimately identifies gear faults, enabling the detection and diagnosis of gearbox gear faults even with available signals in a limited system and under conditions of complex noise interference. This provides crucial technical support for timely monitoring and control, and safe and efficient operation and maintenance of gearbox equipment in rotating machinery systems.

[0056] like Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0057] Step 1: Acquire signal sequences from the rotating machinery gearbox equipment using a vibration acceleration sensor.

[0058] In this step, the acquired signal sequence is denoted as s(t), t = 1, 2, 3, ..., N, where N is the total number of sampling points, and the sampling frequency is denoted as f. s Furthermore, during signal acquisition, the frequency response parameter of the vibration acceleration sensor used should be no less than 2kHz, and the sampling frequency f of the vibration signal sequence should be... s The frequency should be no less than 5.12kHz and no more than 64kHz, and the number of sampling points should satisfy max{fs / 10, min{f s / 8, 2f s / Fr}}≤N≤f s / 2, where Fr is the lowest speed among all shaft speeds of the gearbox equipment being tested.

[0059] Step two: Squaring each element of the acquired discrete vibration acceleration signal sequence s(t) yields S(t) = s 2 (t), t=1, 2, 3,...,N.

[0060] Step 3: Perform low-pass filtering on the squared sequence S(t) of the discrete vibration acceleration signal, as follows:

[0061]

[0062] Among them, Filter L (·) represents the low-pass filtering operator for discrete signals, ω FL This indicates the cutoff frequency of the low-pass filter. This is the signal sequence obtained after low-pass filtering. In step three, a low-pass filter with a stopband attenuation of 60dB is used to perform zero-phase filtering on the vibration signal. The low-pass filter attenuation is lower than the specified passband frequency, which can compensate for the delay introduced by the digital filter. Considering the practical application effect, the cutoff frequency ω of the low-pass filter is set... FL Set to 500Hz.

[0063] Step four: Calculate the square root of the low-pass filtered signal to obtain the direct envelope signal y(t) of the original signal, t = 1, 2, 3, ..., N, as follows:

[0064]

[0065] The theoretical feasibility analysis process for converting the discrete vibration acceleration signal sequence s(t) into an envelope signal y(t) through calculation in steps two to four is as follows:

[0066] (1) Considering the standard modulation signal x0(t), its most basic form can be modeled as a single-component low-frequency signal x L (t) and a single-component high-frequency signal x H The product of (t) is as follows:

[0067] x0(t)=x L (t)×x H (t)=(U L cos(ω L t)+V)×U H cos(ω H t)

[0068] Where V represents the DC component, to ensure U L cos(ω L t)+V>0,U L and ω L These represent single-component low-frequency signals x and x respectively. L The amplitude and frequency of (t), U H and ω H These represent single-component high-frequency signals x, respectively. H The amplitude and frequency of (t).

[0069] (2) Squaring the modulation signal x0(t) yields:

[0070]

[0071] Wherein, ω H Much greater than ω L Therefore, low-pass filtering can be used to remove 2ω from the signal. H , (2ω H +2ω L ), (2ω H -2ω L ), (2ω H +ω L ) and (2ω H -ω L Frequency component removal, where the low-pass filter is required to have a cutoff frequency ω. FL Less than (2ω) H -2ω L ),as follows:

[0072]

[0073] (3) Calculate the signal after low-pass filtering The square root of the modulated signal can be used to obtain the envelope signal x(t):

[0074]

[0075] It can be seen that the original modulation signal x0(t) and the obtained envelope signal x(t) differ by only a constant multiple in amplitude at low frequencies. If the envelope signal x(t) is considered as a bounded signal sequence guided by the fault cycle, then the overall scaling of the amplitude has no effect on the diagnostic results of the gearbox gears.

[0076] The actual acquired signal s(t) will inevitably be affected by noise, and therefore can be modeled as follows:

[0077] s(t) = x0(t) + w0(t)

[0078] After the above process of square-low-pass filtering-square root calculation, the resulting direct envelope signal y(t) can be similarly expressed as:

[0079] y(t) = x(t) + w(t)

[0080] Where w0(t) and w(t) represent random noise signals, respectively.

[0081] Therefore, it is reasonable to convert the signal sequence s(t) containing random noise into the envelope signal y(t) containing random noise through the operations in steps two to four.

[0082] Step 5: Reconstruct the envelope signal y(t) according to different time intervals T to obtain a series of sub-signals θ. T (t), as follows:

[0083]

[0084] in, This represents the floor operation, where the time interval T is a positive integer and... Represents the subsignal θ T The reconstruction coefficients of (t).

[0085] Step 6: Calculate θ for each sub-signal based on L-moment theory indices. T Fault information representation metric LI (t) T ,as follows:

[0086]

[0087] in, and Representing the sub-signals θ T The L-skewness and L-kurtosis of (t) are calculated using L-moment theory, respectively:

[0088]

[0089]

[0090] Where, λ r (θ T (t) represents the signal sequence θ T The r-th order L-moment of (t).

[0091] In step six, the r-th order L-moment λ of the signal sequence r The calculation process is as follows:

[0092] Suppose X = [X1, X2, ..., X...] nLet X be a sequence of n consecutive independent samples from the cumulative distribution F(x), and let X be a series of samples from the cumulative distribution F(x). 1：n ≤X 2：n ≤…≤X n：n Let be the order statistic of the random variable extracted from X. Then, let λ be the r-th order L-moment of the sequence X. r It can be defined as:

[0093]

[0094] Where E(X) (r-k)：r X is the order statistic. (r-k)：r The expected value can be calculated using the following formula:

[0095]

[0096] Therefore, the 2nd to 4th order L moments used in this invention can be calculated as follows:

[0097]

[0098]

[0099]

[0100] Step 7, based on fault information characterization metric LI T The Sigmoid function transforms each sub-signal θ T (t) Distribution weight The calculation process is as follows:

[0101]

[0102] Where γ and v are the scaling factor and bias factor, respectively. In this invention, according to LI T The numerical range characteristics of the index and the actual application of this method in gearbox gear fault diagnosis are shown. The scale factor γ is set to 100 and the bias factor v is set to 0.

[0103] Step 8: Reconstruct the sub-signal θ based on the envelope signal y(t). T (t) and its corresponding weights Calculate the joint weighted envelope robust correlation function of the envelope signal sequence and the reconstructed sub-signal. as follows:

[0104]

[0105] Step 9: Plot the calculated joint weighted envelope noise-resistant correlation function. A graph showing the change over time interval T.

[0106] Step 10, based on The reciprocal of the time interval value corresponding to the characteristic peak in the figure determines the characteristic frequency, and further identifies gear faults; and, the focus is on The time interval T corresponding to the characteristic peak in the figure should be an integer multiple of the fundamental frequency and the reciprocal of its higher harmonics of the gear fault characteristic frequency.

[0107] The following is an example of using the method of the present invention to diagnose and analyze gear fault signals of a gearbox device. The specific process of this example is as follows:

[0108] S01, a vibration signal sequence is acquired from the parallel shaft gearbox equipment of the rotating machinery system through a vibration acceleration sensor, such as... Figure 2 As shown, the rotating machinery testing system mainly consists of a servo motor, a parallel shaft gearbox, and a magnetic powder brake. The pinion of the parallel shaft gearbox has 30 teeth, and the gear has 70 teeth. However, one tooth of the gear has a wear defect. Figure 3 As shown. The servo motor drives the pinion to rotate at a speed of 3500 rpm, and the loading value of the magnetic powder brake is set to 8 N·m. During the experiment, the sampling frequency of the vibration acceleration sensor is set to 50000 Hz, the sampling time is 0.1 s, and the number of sampling points is 5000. The vibration signal sequence collected by the vibration acceleration sensor is as follows. Figure 4 As shown. Furthermore, the fault characteristic frequency f corresponding to the wear of the large gear can be calculated from the above. G It is equal to the rotational frequency of the axis it is located on, which is 3500 / 60*30 / 70Hz=25Hz.

[0109] S02 performs a squaring operation on each element of the acquired original discrete vibration acceleration signal sequence.

[0110] S03 performs low-pass filtering on the square sequence of discrete vibration acceleration signals.

[0111] S04, calculate the square root of the low-pass filtered signal to obtain the direct envelope signal of the original signal sequence, such as... Figure 5 As shown.

[0112] S05, the envelope signal is reconstructed according to different time intervals T to obtain a series of sub-signals. In this embodiment, the number of reconstructed sub-signals is...

[0113] S06, calculates the fault information representation metric for each sub-signal based on L-moment theory indices.

[0114] S07 assigns weights to each sub-signal based on fault information representation metrics and Sigmoid function transformation.

[0115] S08. Based on the envelope signal, the reconstructed sub-signal, and their corresponding weights, calculate the joint weighted envelope noise-resistant correlation function of the envelope signal sequence and the reconstructed sub-signal.

[0116] S09, Plot the calculated joint weighted envelope noise-resistant correlation function. The graph showing the change over time interval T is as follows: Figure 6 As shown.

[0117] S10, from such Figure 6 shown As can be observed in the figure, there are two relatively obvious peaks, and the time intervals corresponding to them, 0.04s and 0.02s, are exactly the wear failure frequencies f of the large gear, respectively. G =25Hz and its second harmonic 2×f G = 50Hz is the reciprocal of Hz, so it can be determined that the large gear of the gearbox is faulty.

[0118] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation, characterized in that, include: Step 1: Acquire signal sequences from the rotating machinery gearbox using a vibration acceleration sensor; Step 2: Squaring each element of the acquired discrete vibration acceleration signal sequence to obtain a discrete vibration acceleration signal square sequence; Step 3: Perform low-pass filtering on the square sequence of the discrete vibration acceleration signal; Step 4: Calculate the square root of the low-pass filtered signal to obtain the direct envelope signal of the original signal; Step 5: Reconstruct the envelope signal according to different time intervals to obtain a series of sub-signals; Step Six: Calculate the fault information representation metric for each sub-signal based on L-moment theory indices; Step 7: Assign weights to each sub-signal based on fault information representation metrics and Sigmoid function transformation; Step 8: Based on the weights of the direct envelope signal from Step 4, the reconstructed sub-signal from Step 5, and the sub-signal from Step 7, calculate the joint weighted envelope noise-resistant correlation function of the envelope signal sequence and the reconstructed sub-signal. The calculation formula is as follows: ； Where T is the time interval, and is a positive integer. ; Represents sub-signal The reconstruction coefficients; N is the total number of sampling points. This represents the floor operation; y(t) represents the envelope signal. Sub-signal The corresponding weights; Step 9: Plot the change of the joint weighted envelope noise-resistant correlation function over time intervals; Step 10: Determine the characteristic frequency based on the reciprocal of the time interval value corresponding to the characteristic peak in the graph drawn in Step 9, and further identify gear faults.

2. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 1, characterized in that, In step one, the acquired signal sequence is denoted as follows: , The total number of sampling points is denoted as , and the sampling frequency is denoted as . The frequency response parameter of the vibration acceleration sensor used should be no less than 2 kHz, and the sampling frequency of the vibration signal sequence should be... The frequency should be no less than 5.12 kHz and no more than 64 kHz, and the number of sampling points should meet the following requirements. ,in The lowest speed among all shaft speeds of the gearbox equipment being tested.

3. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 1, characterized in that, In step three, a low-pass filter with a stopband attenuation of 60dB is used to perform zero-phase filtering on the vibration signal. The cutoff frequency of the low-pass filter is... It is 500 Hz.

4. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 1, characterized in that, The calculation formula for step five is as follows: ； in, This indicates the floor operation, with a time interval. are positive integers and , Represents sub-signal Reconstruction coefficients; This represents the envelope signal.

5. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 4, characterized in that, The fault information characterization metric LI in step six T The calculation formula is as follows: ； in, and They represent sub-signals respectively. The L-skewness and L-kurtosis are calculated using L-moment theory, respectively: ； ； in, Represents the signal sequence The r-th order L-moment.

6. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 5, characterized in that, Regarding signal sequences The calculation process for the r-th order L-moment is as follows: Assumption Let be a series of continuous independent sample sequences of length n derived from the cumulative distribution F(x), and let Let X be the order statistic of the random variable extracted from X. Then, what is the r-th order L-moment of the sequence X? The calculation formula is as follows: ； in, It is an order statistic The expected value is calculated using the following formula: 。 7. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity according to claim 6, characterized in that, The calculation formula for step seven is as follows: ； in and These are the scale factor and the bias factor, respectively.

8. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation according to claim 1, characterized in that, In step ten, the time interval corresponding to the characteristic peak in the graph drawn in step nine. It is an integer multiple of the reciprocal of the fundamental frequency and its higher harmonics of the characteristic frequency of gear faults.

9. The gear fault diagnosis method based on sub-signal joint weighted envelope noise immunity correlation according to claim 1, characterized in that, Scale factor Set to 100, bias factor Set it to 0.

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