Planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model

Abstract

According to the planetary gear box fault diagnosis method based on order analysis and the time domain non-stationary model, a non-stationary vibration signal appearance model is established, and intelligent diagnosis of actual vibration signals of the gear box under the non-stationary working condition is achieved. The method comprises the following steps: firstly, proposing a manifestation model which considers modulation components and modulation intensity at the same time; for a variable speed signal, a signal model based on an angular domain order component is established. Secondly, accurately extracting a modulation order component by using a VMD method, providing a method for quantifying the contribution degree of the modulation component, and training and verifying the effectiveness of a modulation intensity coefficient; and finally, verifying the model through an actual gearbox signal, extracting an intensity coefficient, inputting the intensity coefficient into a support vector machine for classification, and completing fault diagnosis. The model is used for fault diagnosis of the gear box under the non-stable working condition, the modeling idea can be widely applied to modeling analysis of various rotating machines, and the fault diagnosis capability of the gear box in the actual complex environment is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of planetary gearbox fault diagnosis, and relates to a rotating equipment fault diagnosis method, and in particular to an analysis method for non-stationary signal modeling based on signal modulation, VMD method and order tracking technology, which can be used for modeling analysis and fault diagnosis of vibration signals of various rotating mechanical equipment. Background Art

[0002] Planetary gearboxes have the advantages of high transmission ratio, high load efficiency, and compact mechanical structure. They are often used as key transmission components in industrial equipment and play an irreplaceable role. However, due to the complex and harsh working environment of gearboxes, their key components will inevitably fail, such as tooth root cracks, missing teeth, tooth surface wear, etc., affecting the normal operation of the entire transmission system. Therefore, it is very necessary to monitor and analyze the operating status of the gearbox.

[0003] During the periodic operation of a planetary gearbox, the impact caused by gear damage will cause amplitude modulation and frequency modulation on the meshing vibration. The amplitude modulation frequency is called the characteristic frequency of the faulty gear. Observing the characteristic frequency has always been an effective method for monitoring the operating status of a planetary gearbox. Different faults will produce different modulation phenomena, that is, corresponding to different modulation relationships and characteristic frequencies. Fast Fourier transform is a common method for observing the spectrum of vibration signals, and researchers have conducted a lot of research in this area.

[0004] Kahraman and Inalapolat[1,2] established a dynamic model of the gearbox based on the gearbox process and structure, and summarized the characteristics of the vibration sidebands caused by characteristic frequency modulation.

[0005] There are many kinds of components in the gearbox, the vibration response is complex, and the vibration modulation of different components is coupled with each other, making it difficult to analyze the spectrum of the vibration signal. In order to better study the modulation of the gearbox vibration signal, researchers widely use empirical mode decomposition (EMD) and its derived time-frequency method [3,4].

[0006] Frei[5] proposed intrinsic time-scale decomposition (ITD), which decomposes the signal into the sum of multiple rotational components and retains accurate time scale information.

[0007] K.Dragomiretskiy[6] proposed variational mode decomposition (VMD) which can adaptively match the optimal center frequency and finite bandwidth of each mode. VMD can decompose a signal into multiple sub-signals. Its advantage is that it can determine the order of mode decomposition.

[0008] Feng[7,8,9] proposed the idea of ​​matching characteristic frequencies, and this demodulation method is suitable for gearboxes. Wang used the boundary condition processing method of support vector regression to partially solve the modal aliasing problem.

[0009] Zhang

[10] used the grasshopper optimization algorithm (GOA) to adaptively optimize the VMD parameters of the gearbox signal.

[0010] At present, it is still difficult to model the non-stationary state of the gearbox. There is still a lack of methods to select reasonable order spectrum modulation components. Existing models often stay at the interpretation of the modulation components without judging the intensity and mode of the modulation. To this end, a non-stationary signal modeling and solution method based on signal modulation, VMD method and order tracking technology is proposed. By establishing an angular domain stationary model, the order analysis of the vibration signal of the planetary gearbox under non-stationary conditions is performed to complete the classification and diagnosis of faults.

[0011] [1] M.Inalpolat, A.Kahraman, A theoretical and experimental investigation of modulation sidebands of planetary gear sets, Journal of sound and vibration 323 (2009) 677–696.

[0012] [2] M.Inalpolat, A.Kahraman, A dynamic model to predict modulationsidebands of a planetary gear set having manufacturing errors, Journal of Sound and Vibration 329 (2010) 371–393.

[0013] [3] Y. Lei, Z. Liu, J. Lin, F. Lu, Phenomenological models of vibration signals for condition monitoring and fault diagnosis of epicyclic gearboxes, Journal of Sound and Vibration 369 (2016) 266–281.

[0014] [4]M.D.Choudhury,K.Blincoe,J.S.Dhupia,An overview offault diagnosisofindustrial machines operatingundervariable speeds,AcousticsAustralia49(2021)229–238.

[0015] [5]M.G.Frei,I.Osorio,Intrinsic time-scaledecomposition:time–frequency–energy analysis andreal-time filtering ofnon-stationary signals,Proceedings ofthe Royal SocietyA:Mathematical,Physical andEngineeringSciences 463(2007)321–342.

[0016] [6]K.Dragomiretskiy,D.Zosso,Variational mode decomposition,IEEEtransactions on signal processing 62(2013)531–544.

[0017] [7]Z.Feng,D.Zhang,M.J.Zuo,Planetary gearbox fault diagnosis viajointamplitude and frequency demodulation analysis based on variational modedecomposition,Applied Sciences 7(2017)775.

[0018] [8]Z.Feng,M.J.Zuo,Vibration signal models for fault diagnosis ofplanetary gearboxes,Journal ofSoundandVibration 331(2012)4919–4939.

[0019] [9] Z.Feng,

[0020]

[10] Summary of the invention

[0021] The purpose of the present invention is to address the defects of non-stationary signal processing in the prior art and to propose a planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model.

[0022] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0023] The fault diagnosis method of planetary gearbox based on order analysis and time domain non-stationary model, the specific steps of its modeling and analysis method are as follows:

[0024] (1) Obtain the vibration signal of the planetary gearbox under non-steady working conditions at different health levels

[0025] The assembly of the planetary gearbox is set, the acceleration and deceleration states, sampling frequency, and sampling time of the drive motor are set, and the vibration signal is collected with the help of an accelerometer installed on the housing of the planetary gearbox. The vibration data of the sun gear under four different health conditions and two non-stationary working conditions are collected as the data set.

[0026] (2) Angular domain resampling to establish an angular domain stationary model

[0027] The time domain non-stationary vibration model is resampled in the angular domain, and the bias is decomposed by factor decomposition. The dimensionless constants obtained by decomposition are used to represent the overall amplitude of the vibration signal and the modulation intensity contribution of each modulation component pair. At the same time, considering the influence of noise, a more comprehensive angular domain modulation model is proposed.

[0028] (3) VMD method demodulation to obtain modulation components

[0029] VMD is a frequency domain decomposition method for non-periodic signals. The VMD method can decompose complex signals into intrinsic mode functions (IMFs). VMD decomposes the original signal into k modal components, which have limited bandwidth and center frequency. The optimal solution and the center frequency corresponding to the optimal solution are calculated through the Lagrangian function and the multiplier alternating direction method.

[0030] (4) Model building and model parameterization

[0031] The real vibration signal is linked to the modulation relationship of different order components in the model through gradient descent. Then, combined with the angular domain stationary model, a simulation model containing three modulation components is proposed.

[0032] For the model established by the formula, the corresponding planetary gear order value, amplitude parameter and phase parameter are set according to the mechanical structure characteristics, and experimental simulation is carried out.

[0033] (5) Model training and modulation parameters for fitting

[0034] The mean square error (MSE) function is used as the target loss function, the vibration signal is used as the real value, and the modulation parameters of the model are used as the output value for loss analysis. The learning rate and parameter update strategy are set, and the model parameters are updated through the gradient update process to fit different modulation parameters.

[0035] (6) Use machine learning methods to classify the results and complete fault diagnosis

[0036] The support vector machine method is adopted to set the kernel function, penalty factor, Gamma value and other parameters of the support vector machine for classification. The training parameters of the actual signal in step (5) are classified by the support vector machine to diagnose the corresponding fault type.

[0037] Furthermore, step (2) includes the following specific steps:

[0038] (2a) Under stable conditions, the mathematical model of the vibration signal of the solar wheel failure is:

[0039]

[0040] Where x sun(t) is the vibration signal of the sun gear, f mesh is the gear meshing frequency, f shaft and f sun is the characteristic frequency of the planetary gear. A and B represent f sun to f mesh The amplitude and frequency modulation intensity. They represent the fault amplitude modulation, frequency modulation and the initial phase of the entire signal respectively.

[0041] (2b) The time domain signal is converted into the angular domain by angular domain resampling, and the signal model of the gearbox sun gear fault in the angular domain is established, which is described as follows:

[0042]

[0043] Among them, x sun (Θ) represents the angular domain vibration signal model. shaft , O sun , O mesh Characteristic orders representing shaft vibration, sun gear fault rotation and gear meshing. r and B r It is an indicator of amplitude modulation and frequency modulation of vibration.

[0044] (2c) In actual vibration, considering the complexity of amplitude modulation and frequency modulation components, a general angular domain model is proposed to represent a more realistic vibration of the planetary gearbox.

[0045]

[0046] Among them, x gm (θ) is a refined vibration model including all modulation components. C is a dimensionless constant representing the contribution of the FM of the second banner. i Indicates the components involved in modulation. j Indicates the number of components involved in modulation. i and B i O i The induced amplitude and frequency modulation vibration indicators are related to the modulation order. The variable r represents the bias, which represents the accumulation of the modulation component to the amplitude.

[0047] (2d) The bias r is expressed as a constant peripheral coefficient by factorization:

[0048]

[0049] The dimensionless constants obtained from the decomposition represent the overall amplitude of the vibration signal and the modulation intensity contribution of each modulation component pair, while the effect of noise is taken into account to achieve a comprehensive angular domain modulation model.

[0050]

[0051] Among them, X is the vibration angular domain signal, u is a dimensionless constant related to the amplitude and amplitude modulation contribution, and Q is a white noise signal that obeys Gaussian distribution.

[0052] Furthermore, step (3) includes the following specific steps:

[0053] (3a) VMD decomposes the original signal into k modal components with finite bandwidth and center frequency. It is necessary to construct a constrained variational problem with the minimum estimated bandwidth and the constraint that all modal sums are equal to the original signal.

[0054]

[0055] Where k is the number of target intrinsic mode functions (IMFs) to be extracted, u k =u1,u2,...,u k is a per-mode function. w k =w1,w2,...,w k is the center frequency of each mode.

[0056] (3b) The augmented Lagrangian function is introduced to transform the constrained variational problem into an unconstrained variational problem:

[0057]

[0058] (3c) The minimum value of the above formula is calculated using the alternating direction method of multipliers (ADMM) to obtain the optimal solution and the center frequency corresponding to the optimal solution. The optimal solution and its corresponding center frequency are:

[0059]

[0060] Furthermore, step (4) includes the following specific steps:

[0061] (4a) Through the gradient descent method, the real vibration signal is linked to the modulation relationship of different order components in the model, a specific coefficient is used to represent the intensity of this modulation, and the frequency demodulation strategy is combined to deeply evaluate the applicability and accuracy of the model.

[0062] (4b) Combined with the angular domain stationary model, a simulation model containing three modulation components O1, O2 and O3 is proposed.

[0063]

[0064] Furthermore, step (5) includes the following specific steps:

[0065] (5a) The mean square error (MSE) function is used as the target loss function, the actual modulation intensity of the vibration signal is linked to the predicted modulation intensity of the model, and the vibration signal is used as the real value and the modulation parameter of the model is used as the output value for loss analysis. Substituting the model into the loss function, the loss function obtained is:

[0066]

[0067] Among them, y(Θ) represents the true characteristic order of the vibration signal, x sun (Θ) represents the feature order predicted by the model.

[0068] (5b) The gradient descent method is used to fit different modulation parameters. For the angular domain model, the partial differentials of the parameters are solved respectively, and after setting the learning rate, the parameters are updated according to the process in the following table.

[0069] The updating process of the function is expressed as:

[0070] x sun (Θ) i+1 =x sun (Θ)-x sun (Θ) i

[0071] Furthermore, step (6) includes the following specific steps:

[0072] (6a) Set the parameters of the support vector machine, including kernel function, penalty factor, Gamma value, error convergence, classification strategy, and training and test set splitting.

[0073] (6b) The training parameters of the actual signal of step (5) are classified by support vector machine to diagnose the corresponding fault type, which includes four types: normal state, tooth root crack, missing tooth, and tooth surface wear.

[0074] Compared with the prior art, the present invention has the following advantages:

[0075] First, a non-stationary modal model of the planetary gearbox based on the perfect angular domain is proposed.

[0076] Second, a modeling idea is proposed to find the modulation component qualitatively and describe the modulation intensity quantitatively. This modeling idea can be widely used in fault modeling of rotating machinery.

[0077] Third, considering the complexity of modulation components, the VMD method is used to find the comprehensive fault modulation sequence.

[0078] Fourth, in order to quantify the contribution of different modulation components to the carrier signal, a parameterized modulation component method is proposed.

[0079] Fifth, the quantization coefficients are used to classify different faults, which achieves good results and has better interpretability compared to deep learning methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is the overall flow chart of the system of the present invention.

[0081] Figure 2 This is the health-fault diagram of the sun gear of the present invention.

[0082] Figure 3 The speed and vibration waveform of the acceleration condition of the present invention, including (a) speed RPM, and (b) related time domain vibration.

[0083] Figure 4 The speed and vibration waveform of the deceleration condition of the present invention, including (a) speed RPM, and (b) related time domain vibration.

[0084] Figure 5 The instantaneous order spectrum is obtained by fast Fourier transform (FFT) in the present invention.

[0085] Figure 6 It is the instantaneous order of the acceleration condition of the present invention, where (a) normal, (b) tooth root crack, (c) missing tooth, and (d) tooth surface wear.

[0086] Figure 7 It is the instantaneous order of the deceleration condition of the present invention, where (a) normal, (b) tooth root crack, (c) missing tooth, and (d) tooth surface wear.

[0087] Figure 8 The amplitude modulation and frequency modulation parameters A and B under acceleration conditions are solved for the present invention.

[0088] Fig. 9 The amplitude modulation and frequency modulation parameters A and B under the deceleration condition are solved for the present invention.

[0089] Fig.10 Parameter C is solved for the present invention.

[0090] Fig.11 This is the simulation fitting process of the present invention.

[0091] Fig.12 It is a scatter diagram of the amplitude modulation and frequency modulation of a single component of the present invention. DETAILED DESCRIPTION

[0092] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0093] Example:

[0094] The present invention is based on the fault diagnosis research of the vibration signal under the non-stationary working state of the planetary gear. It relates to the technical field of planetary gearbox fault diagnosis, and in particular designs a planetary gearbox fault diagnosis method based on signal modulation, VMD method and order analysis technology. Figure 1 , the present invention comprises the following steps:

[0095] (1) Obtain the vibration signal of the planetary gearbox under non-steady working state with different health levels.

[0096] The present invention can be used for intelligent fault diagnosis of planetary gearbox faults, rolling bearings and other rotating machinery under non-stationary working conditions. This experiment takes a planetary gearbox as an example and uses the fault data of the gearbox under non-stationary conditions for experimental analysis.

[0097] The vibration signal was collected by using an accelerometer vertically mounted on the planetary gearbox housing. The vibration data of the sun gear under four different health conditions and two working conditions were collected as a data set, as follows:

[0098] The vibration time domain signal data used in this example are all from the dynamic transmission system simulator (DDS) test bench of the Equipment Reliability and Prediction and Health Management Laboratory (ERPHM) of the University of Electronic Science and Technology of China (UESTC). The experiment considered four different types of sun gear health conditions, namely normal state, gear crack, missing teeth, and tooth surface wear. The health-fault state conditions are as follows: Figure 2 shown.

[0099] In the experiment, the planetary gearbox was driven by a 2.24kW (3HP) three-phase servo motor and provided two working conditions: acceleration and deceleration. The speed range was 0-1800r / min under acceleration and 1800-450r / min under deceleration. The sampling frequency of the vibration signal was 7680Hz, and the sampling time was 10s under different health states and working conditions. The vibration signals of the planetary gearbox under four fault types and two non-stationary working conditions were obtained. The waveforms are shown in the figure below. Figure 3 and Figure 4 shown.

[0100] Table 1 Assembly parameters of planetary gearbox on DDS platform

[0101] Sun gear teeth number Ring gear teeth number Number of planetary gears Number of planetary gear teeth Gear Ratio 28 100 4 36 4.57

[0102] (2) Angular domain resampling to establish an angular domain stationary model

[0103] (2a) The vibration signal model of the planetary gearbox can clearly express the modulation effect of different components in the vibration process. Under stable conditions, taking the failure of the solar wheel as an example, its vibration signal mathematical model can be expressed as:

[0104]

[0105] Where x sun (t) is the vibration signal of the sun gear, f mesh is the gear meshing frequency, f shaft and f sun is the characteristic frequency of the planetary gear, as shown in Table 2. A and B represent f sun to f mesh The amplitude and frequency modulation intensity. They represent the fault amplitude modulation, frequency modulation and the initial phase of the entire signal respectively.

[0106] The characteristic modulation frequency of the planetary gearbox is shown in the following table:

[0107] Table 2 Characteristic modulation frequency of planetary gearbox

[0108]

[0109] (2b) The time domain signal is converted into the angular domain by angular domain resampling, and a preliminary signal model of the gearbox sun gear fault in the angular domain is established, which is described as follows:

[0110]

[0111] Among them, x sun (Θ) represents the angular domain vibration signal model. shaft , O sun , O mesh Characteristic orders representing shaft vibration, sun gear fault rotation and gear meshing. r and B r It is an indicator of amplitude modulation and frequency modulation of vibration.

[0112] (2c) Although the above formula establishes the vibration model of the planetary gearbox in the angular domain, it cannot include the more complex modulation situation in actual vibration. In actual vibration, considering the complexity of amplitude modulation and frequency modulation components, the above angular domain model is developed into a general angular domain model to represent the more realistic situation of the vibration of the planetary gearbox.

[0113]

[0114] Among them, x gm (θ) is a refined vibration model including all modulation components. C is a dimensionless constant representing the contribution of the FM of the second banner. i Indicates the components involved in modulation. j Indicates the number of components involved in modulation. i and B i O iThe induced amplitude and frequency modulation vibration indicators are related to the modulation order. The variable r represents the bias, which represents the accumulation of the modulation component to the amplitude.

[0115] (2d) The bias r is expressed as a constant peripheral coefficient by factorization:

[0116]

[0117] The dimensionless constant obtained by the decomposition not only represents the overall amplitude of the vibration signal, but also represents the modulation intensity contribution of each modulation component to the modulation intensity. Therefore, it becomes a corrected offset 1 to offset the variable A. i The positive and negative values ​​of θ are taken into account while taking into account the effect of noise to achieve a comprehensive angular domain modulation model.

[0118]

[0119] Among them, X is the vibration angular domain signal, u is a dimensionless constant related to the amplitude and amplitude modulation contribution, and Q is a white noise signal that obeys Gaussian distribution.

[0120] (3) VMD method demodulation to obtain modulation components

[0121] (3a) VMD is a frequency domain decomposition method for non-periodic signals, which can decompose complex signals into some intrinsic mode functions (IMFs).

[0122] u k (t) = A k (t)cos(φ k (t))

[0123] where u k (t) is the amplitude modulation part, φ k (t) is the frequency modulation part.

[0124] VMD decomposes the original signal into k modal components, which have finite bandwidths and center frequencies. It is necessary to construct a constrained variational problem with the minimum estimated bandwidth and the constraint that all modal sums are equal to the original signal. The constrained variational model of VMD can be expressed as:

[0125]

[0126] Where k is the number of target intrinsic mode functions (IMFs) to be extracted, u k =u1,u2,...,u k is a per-mode function. w k =w1,w2,...,w k is the center frequency of each mode.

[0127] (3b) The augmented Lagrangian function is introduced to transform the constrained variational problem into an unconstrained variational problem:

[0128]

[0129] (3c) Use the alternating direction method of multipliers (ADMM) to calculate the minimum value of the above formula and obtain the optimal solution and the center frequency corresponding to the optimal solution. The optimal solution is:

[0130]

[0131] The center frequency corresponding to the optimal solution is:

[0132]

[0133] (3d) The resampled angle signal is decomposed into multiple intrinsic mode functions (IMFs), and the IMF5 component is selected and Fourier transformed to obtain the instantaneous order spectrum, as shown in Figure 5 As shown. Figure 6 and Figure 7 It can be seen that the signal mainly contains several characteristic order components.

[0134] (4) Model building and model parameterization

[0135] (4a) Through the gradient descent method, the real vibration signal is linked to the modulation relationship of different order components in the model, a specific coefficient is used to represent the intensity of this modulation, and the frequency demodulation strategy is combined to deeply evaluate the applicability and accuracy of the model.

[0136] (4b) Combined with the angular domain stationary model, a simulation model containing three modulation components O1, O2 and O3 is proposed.

[0137]

[0138] (4c) For the model established by the formula, reasonable parameters are set according to the characteristics of the mechanical structure to conduct simulation experiments. The experimental parameters are set as follows:

[0139] Table 3 Planetary gear order values

[0140] Order <![CDATA[O mesh ]]> <![CDATA[O sun ]]> <![CDATA[O shaft ]]> <![CDATA[O crraier ]]> Numeric 21.8750 3.1250 1.0000 0.1288

[0141] Table 4 Amplitude parameter settings for simulation

[0142] parameter C <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[B1]]> <![CDATA[B2]]> <![CDATA[B3]]> Numeric 0.8 0.1 0.2 0.3 0.15 0.25 0.35

[0143] Table 5 Simulated phase parameters

[0144] (5) Model training and verification, modulation parameters for fitting

[0145] (5a) Setting the loss function

[0146] In order to link the actual modulation intensity of the vibration signal with the predicted debugging intensity of the model, the mean square error (MSE) function is used as the target loss function, the vibration signal is taken as the real value, and the modulation parameters of the model are taken as the output value for loss analysis.

[0147] The MSE function is constructed as:

[0148]

[0149] Among them, Loss represents the overall error of the function, y(t) is the true value, x(t) is the predicted result of the training output, and N is the number of feature types.

[0150] (5b) Substitute the model into the loss function and obtain the new loss function:

[0151]

[0152] Among them, y(Θ) represents the true characteristic order of the vibration signal, x sun (Θ) represents the feature order predicted by the model.

[0153] (5c) Gradient descent to fit modulation parameters

[0154] The gradient descent method is used to fit different modulation parameters. For the angular domain model, the partial differentials of the parameters are solved respectively, with i representing the i-th dominant component in the gradient descent process. After setting the learning rate, the parameters are updated according to the process in the following table.

[0155] Table 6 Function analysis of relevant undetermined parameters

[0156]

[0157] The updating process of the function is expressed as:

[0158] x sun (Θ) i+1 =x sun (Θ)-x sun (Θ) i

[0159] (5d) The proposed model is fitted to the actual signal to obtain the new signal intensity modulation coefficient, and the modulation components shown in the table below are analyzed. The initial values ​​of all model parameters are set to 0. The subsequent analysis takes the fourth decimal place of the amplitude, and the results are shown in the figure Figure 8 , Fig. 9 and Fig.10 shown.

[0160] Table 7 Characteristic modulation order

[0161] Project and Description Numeric <![CDATA[Rotational Order (O shaft )]]> 1.0000 <![CDATA[Engagement order (O mesh )]]> 21.8750 <![CDATA[Sun gear fault order (O sun )]]> 3.1250 <![CDATA[Planetary gear carrier rotational order (O carrier )]]> 0.2188

[0162] The simulation signal time length is 10s, and the sampling frequency is 7680Hz. The learning rate of the parameter update process is set to 0.01, and the number of parameter iterations is 20000. The simulation fitting process is as follows Fig.11 The simulation results are shown in the following table:

[0163] Table 8 Function analysis of relevant undetermined parameters

[0164] C <![CDATA[A1]]> <![CDATA[A2]]> <![CDATA[A3]]> <![CDATA[B1]]> <![CDATA[B2]]> <![CDATA[B3]]> Setting Value 0.8 0.1 0.2 0.3 0.15 0.25 0.35 Fitted values 0.8 0.1 0.2 0.3 0.15 0.25 0.35

[0165] Table 9 Function analysis of relevant undetermined parameters

[0166]

[0167] Through partial differential processing, the influence of noise and other components is eliminated, and the modulation of each instantaneous order on the fault characteristic order is obtained. The results show that the proposed analytical method can accurately obtain the target parameter values ​​of the main modulation frequency components in the model from the target signal. Therefore, a non-stationary order model based on actual data can be established.

[0168] (6) Use machine learning methods to classify the results and complete fault diagnosis

[0169] (6a) Substitute the parameters of the trained output model into the support vector machine for classification

[0170] Set the parameters of the support vector machine as shown in the following table:

[0171] Table 10 SVM parameters

[0172] project set up Kernel function Radial Basis Kernel Function (RBF) Penalty term 1 Gamma Value Auto Error convergence 0.01 Classification strategy OVO Training test set split (traintestsplitsize) 14:14

[0173] (6b) Support vector machine classification results

[0174] Under acceleration and deceleration conditions, support vector machine is used to calculate the sun , O shaft and O carrier Different fault conditions are classified according to the feature order. The classification results of support vector machine are as follows: Fig.12 The accuracy of the classification results is shown in the following table:

[0175] Table 11 Classification accuracy of demodulation parameters

[0176] Training accuracy (%) Test accuracy (%) accelerate 94.38 91.30 slow down 93.25 93.61

[0177] (6c) From the classification results, it can be seen that the model can well reflect the vibration of the planetary gearbox under the conditions of lifting speed and constant speed, and complete the fault diagnosis of the planetary gearbox under non-stationary working conditions.

[0178] Based on the above implementation methods, the present invention uses quantization coefficients to classify different faults and achieves good results. Compared with deep learning methods, it has better interpretability.

[0179] First, a non-stationary modal model of a planetary gearbox based on a perfect angular domain is proposed. First, the vibration signals of the planetary gearbox under non-stationary working conditions with different health levels are obtained. By setting the assembly of the planetary gearbox, setting the acceleration and deceleration states, sampling frequency, and sampling time of the drive motor, and using the accelerometer installed on the planetary gearbox housing to collect vibration signals, the vibration data of the sun gear under two non-stationary working conditions with four different health levels are collected and used as the data set.

[0180] Second, a modeling idea is proposed to qualitatively find the modulation components and quantitatively describe the modulation intensity. Through angular domain resampling, an angular domain stationary model is established, and the time domain non-stationary vibration model is resampled in the angular domain. The bias is decomposed by factor decomposition, and the dimensionless constants obtained by decomposition are used to represent the overall amplitude of the vibration signal and the modulation intensity contribution of each modulation component pair. At the same time, considering the influence of noise, a more comprehensive angular domain modulation model is proposed. This modeling idea can be widely used in fault modeling of rotating machinery.

[0181] Third, considering the complexity of the modulation components, the VMD method is used to find the modulation order of the comprehensive fault. The modulation components are obtained by demodulation through the VMD method. VMD is a frequency domain decomposition method for non-periodic signals. The VMD method can decompose complex signals into intrinsic mode functions (IMFs). VMD decomposes the original signal into k modal components, which have limited bandwidth and center frequency. The optimal solution and the center frequency corresponding to the optimal solution are calculated through the Lagrangian function and the multiplier alternating direction method.

[0182] Fourth, in order to quantify the contribution of different modulation components to the carrier signal, a parameterized modulation component method is proposed, a model is established, and the model is parameterized. This method links the real vibration signal with the modulation relationship of different order components in the model by gradient descent, and then combines the angular domain stationary model to propose a simulation model containing three modulation components; for the model established by the formula, the corresponding planetary gear order value, amplitude parameter and phase parameter are set according to the characteristics of the mechanical structure, and experimental simulation is carried out.

[0183] Fifth, train the model and fit the modulation parameters. Use the mean square error (MSE) function as the target loss function, take the vibration signal as the real value, and use the modulation parameters of the model as the output value for loss analysis. Set the learning rate and parameter update strategy, and update the model parameters through the gradient update process to fit different modulation parameters. Use machine learning methods to classify the results and complete fault diagnosis. Use the support vector machine method to set the kernel function, penalty factor, Gamma value and other parameters of the support vector machine for classification. Use the support vector machine to classify the training parameters of the actual signal and diagnose the corresponding fault type.

[0184] It should be further explained that the above implementation modes are only used for understanding the technical concept of the present invention, and are not used to limit the protection scope of the present invention. Any obvious adjustments and changes made to the technical solutions belonging to the technical concept of the present invention should fall within the protection scope of the present invention.

Claims

1. A planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model, characterized by The method comprises the following steps: (1) Obtain the vibration signal of the planetary gearbox under non-steady working conditions at different health levels Set up the assembly of the planetary gearbox, set the acceleration and deceleration states, sampling frequency, and sampling time of the drive motor, collect vibration signals with the help of an accelerometer installed on the planetary gearbox housing, and collect the vibration data of the sun gear under four different health conditions and two non-stationary working conditions as the data set; (2) Angular domain resampling to establish an angular domain stationary model The time-domain non-stationary vibration model is resampled in the angular domain, and the bias is decomposed by factor decomposition. The dimensionless constants obtained by decomposition represent the overall amplitude of the vibration signal and the modulation intensity contribution of each modulation component pair. At the same time, considering the influence of noise, a more comprehensive angular domain modulation model is proposed. (3) VMD method demodulation to obtain modulation components VMD decomposes the original signal into k modal components, which have limited bandwidth and center frequency. The optimal solution and the center frequency corresponding to the optimal solution are calculated by Lagrangian function and multiplier alternating direction method. (4) Model building and model parameterization By gradient descent, the real vibration signal is linked to the modulation relationship of different order components in the model. Then, combined with the angular domain stationary model, a simulation model with three modulation components is proposed. For the model established by the formula, the corresponding planetary gear order value, amplitude parameter and phase parameter are set according to the mechanical structure characteristics, and experimental simulation is carried out; (5) Model training and modulation parameters for fitting The mean square error (MSE) function is used as the target loss function, the vibration signal is used as the real value, and the modulation parameters of the model are used as the output value for loss analysis. The learning rate and parameter update strategy are set, and the model parameters are updated through the gradient update process to fit different modulation parameters. (6) Use machine learning methods to classify the results and complete fault diagnosis The support vector machine method is adopted to set the parameters such as the kernel function, penalty factor, and Gamma value of the support vector machine for classification. The training parameters of the actual signal in step (5) are classified by the support vector machine to diagnose the corresponding fault type.

2. The planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model according to claim 1 is characterized in that Step (2) comprises: (2a) Under stable conditions, the mathematical model of the vibration signal of the solar wheel failure is: Where x sun (t) is the vibration signal of the sun gear, f mesh is the gear meshing frequency, f shaft and f sun is the characteristic frequency of the planetary gear, A and B represent f sun to f mesh The amplitude and frequency modulation intensity, φ, θ represents the fault amplitude modulation, frequency modulation and the initial phase of the entire signal respectively; (2b) The time domain signal is converted into the angular domain by angular domain resampling, and the signal model of the gearbox sun gear fault in the angular domain is established, which is described as follows: Among them, x sun (Θ) represents the angular domain vibration signal model, O shaft , O sun , O mesh Indicates the characteristic order of shaft vibration, sun gear fault rotation and gear meshing, A r and B r It is the amplitude modulation and frequency modulation index of vibration; (2c) In actual vibration, considering the complexity of amplitude modulation and frequency modulation components, a general angular domain model is proposed to represent a more realistic vibration of the planetary gearbox: Among them, x gm (Θ) is the refined vibration model including all modulation components, C is a dimensionless constant representing the contribution of the second-strip FM, O i Indicates the components involved in modulation, N j Indicates the number of components involved in modulation, A i and B i O i The amplitude and frequency modulation vibration indicators caused by them are the related modulation orders. The variable r represents the bias, which represents the accumulation of the modulation component to the amplitude. (2d) The bias r is expressed as a constant peripheral coefficient by factorization: The dimensionless constants obtained from the decomposition represent the overall amplitude of the vibration signal and the modulation intensity contribution of each modulation component, while taking into account the effect of noise to achieve a comprehensive angular domain modulation model: Among them, X is the vibration angular domain signal, u is a dimensionless constant related to the amplitude and amplitude modulation contribution, and Q is a white noise signal that obeys Gaussian distribution.

3. The planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model according to claim 1 is characterized in that Step (3) includes: (3a) VMD decomposes the original signal into k modal components, which have finite bandwidths and center frequencies. It is necessary to construct a constrained variational problem with the minimum estimated bandwidth and the constraint that the sum of all modes is equal to the original signal: Where k is the number of target intrinsic mode functions (IMFs) to be extracted, u k =u1,u2,...,u k is each mode function, w k =w1,w2,...,w k is the center frequency of each mode; (3b) The augmented Lagrangian function is introduced to transform the constrained variational problem into an unconstrained variational problem: (3c) The minimum value of the above formula is calculated using the alternating direction method of multipliers (ADMM) to obtain the optimal solution and the center frequency corresponding to the optimal solution. The optimal solution and its corresponding center frequency are:

4. The planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model according to claim 1 is characterized in that Step (4) comprises: (4a) By using the gradient descent method, the real vibration signal is linked to the modulation relationship of different order components in the model, a specific coefficient is used to represent the intensity of this modulation, and the frequency demodulation strategy is combined to deeply evaluate the applicability and accuracy of the model; (4b) Combined with the angular domain stationary model, a simulation model containing three modulation components O1, O2 and O3 is proposed.

5. The planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model according to claim 1 is characterized in that Step (5) comprises: (5a) The mean square error (MSE) function is used as the target loss function. The actual modulation intensity of the vibration signal is linked to the predicted modulation intensity of the model. The vibration signal is taken as the real value and the modulation parameter of the model is taken as the output value for loss analysis. The model is brought into the loss function, and the loss function obtained is: Among them, y(Θ) represents the true characteristic order of the vibration signal, x sun (Θ) represents the feature order predicted by the model; (5b) Use the gradient descent method to fit different modulation parameters. For the angular domain model, solve the partial differentials of the parameters respectively, set the learning rate, and update the parameters according to the process in the following table: The updating process of the function is expressed as: x sun (I) i+1 =x sun (Θ)-x sun (I) i 。 6. The planetary gearbox fault diagnosis method based on order analysis and time domain non-stationary model according to claim 1 is characterized in that Step (6) comprises: (6a) Set the parameters of the support vector machine, including kernel function, penalty factor, gamma value, error convergence, classification strategy, and SVM parameters for training and test set segmentation. (6b) The characteristic order of the actual signal in step (5) is classified by support vector machine to diagnose the corresponding fault type. The fault types include normal state, tooth root crack, missing tooth, and tooth surface wear.

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