A method for extracting dynamic and static rub fault features based on full vector spectrum and complex empirical mode decomposition

Abstract

The application discloses a kind of based on full vector spectrum and complex EMD dynamic static rub-impact fault feature extraction method.The method first collects the double-channel vibration signal of the same section of rotor mutually perpendicular, and is constructed as complex signal;Then the complex signal is decomposed into several orders of complex intrinsic mode function arranged according to frequency by using complex empirical mode decomposition, to ensure that the scale of two-channel signal is unified under the same order;Then the main vibration vector of full vector spectrum is calculated for each order component after decomposition, the main vibration vector spectrum of each order is obtained, and the CIMF component sensitive to rub-impact response is selected according to the passband energy;Subsequently, the amplitude characteristics at fundamental frequency, multiple frequency and sub-frequency and the axis trajectory flatness characteristics are extracted from the sensitive components, and a multi-dimensional fault feature vector is constructed after normalization;Finally, the feature vector is input into the classifier to complete the automatic identification of rub-impact fault.The application overcomes the defects of traditional method that the decomposition order of double-channel does not correspond and the feature information is one-sided by complex domain overall decomposition and full vector spectrum fusion.

Description

Technical Field

[0001] This invention belongs to the field of coking equipment condition monitoring and fault diagnosis, specifically a method for extracting dynamic and static rubbing fault features based on full vector spectrum and complex EMD. Background Technology

[0002] Rotating machinery (such as steam turbines and compressors) widely uses sliding bearings for support, resulting in extremely small clearances between the rotor and stator, making them highly susceptible to dynamic-static rubbing failures during operation. Rubbing failures can cause severe vibrations, and in serious cases, lead to equipment damage or even production shutdowns. Therefore, accurately extracting the characteristics of rubbing failures is of great significance for equipment condition monitoring and early warning.

[0003] When rotating machinery experiences rubbing failures, vibration signals in mutually perpendicular directions (X and Y directions) on the same cross section of the rotor often exhibit different characteristics. Analyzing solely based on a single-channel vibration signal can easily lead to incomplete or misjudged results due to limited information. Full-vector spectral technology can fuse vibration signals from two orthogonal directions on the same cross section, using the major semi-axis of the elliptical trajectory (principal vector) to comprehensively characterize the rotor's eddy current intensity at various frequencies, effectively compensating for the deficiencies of single-source information.

[0004] On the other hand, vibration signals generated by rubbing faults exhibit typical nonlinear and non-stationary characteristics. Empirical Mode Decomposition (EMD), as an adaptive signal processing method, can decompose complex signals into several Intrinsic Mode Functions (IMFs) and has been widely used in mechanical fault diagnosis. However, traditional EMD methods typically decompose the X and Y directions separately when processing dual-channel signals. Due to differences in the energy distribution and extreme point distribution of the signals in the two directions, the orders of the resulting IMFs are often inconsistent, making it difficult to fuse information from the same source and complicating subsequent feature extraction. Complex Empirical Mode Decomposition constructs the dual-channel signals into complex signals for overall decomposition, ensuring uniform decomposition scale in both directions. However, it still lacks effective means of fusing information from the same source to highlight the typical frequency components (such as fundamental frequency, harmonics, and sub-frequency divisions) of rubbing faults.

[0005] Therefore, there is an urgent need for a method that can decompose dual-channel vibration signals in a unified manner and effectively fuse their characteristic information in order to achieve comprehensive and accurate extraction of dynamic and static collision fault characteristics. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a method for extracting dynamic and static collision fault features based on full vector spectrum and complex EMD, thereby improving the diagnostic accuracy of dynamic and static collision faults.

[0007] This invention adopts the following technical solution: a method for extracting dynamic and static collision fault features based on full vector spectrum and complex EMD, comprising the following steps:

[0008] Step 1: On the rotor of the rotating machinery to be monitored, select a key section (such as the sliding bearing support, gear meshing point, or shaft segment experiencing abnormal vibration). At this section, install two identical eddy current displacement sensors in two mutually perpendicular directions (usually defined as horizontal direction X and vertical direction Y) to synchronously acquire the dual-channel vibration signal of the rotor at this section. Synchronous integer-cycle sampling is used, with the sampling frequency set to 6–10 times the highest analysis frequency of the rotor (usually not lower than 1600Hz), and the number of sampling points N being an integer power of 2 (e.g., 1024, 2048).

[0009] Step 2: Construct a complex signal z(t) from the two mutually perpendicular vibration displacement signals x(t) and y(t) of the same cross section obtained in Step 1:

[0010]

[0011] Where j is the imaginary unit t=0,1,…,N-1, and N is the number of sampling points.

[0012] Complex Empirical Mode Decomposition (EMD) is employed, specifically using Bivariate Empirical Mode Decomposition (BEMD) to adaptively decompose the complex signal z(t). EMD projects the complex signal onto multiple directions (typically K=4 or 8 uniformly distributed directions), calculates the envelope mean in each direction, and through multiple iterations, decomposes z(t) into the sum of several complex intrinsic mode functions and a residual component.

[0013]

[0014] Where M represents the total order of the CIMF obtained from the decomposition, and r(t) represents the residual components. The CIMFs of each order are arranged in descending order of rotational frequency, i.e., CIMF1 has the highest frequency, and CIMF... M Lowest frequency.

[0015] The specific screening process for the decomposition of complex EMD is as follows:

[0016] (1) Project the complex signal z(t) onto K uniformly distributed direction angles k = 2πk / K (k = 1, 2, ..., K) to obtain the projected signals in each direction. ;

[0017] (2) For each projection signal Local maxima are extracted, and cubic spline interpolation is used to fit the envelope curve in that direction. ;

[0018] (3) After transforming the envelope curves in all directions to the recovery domain, calculate the average value to obtain the local mean function m(t);

[0019] (4) Subtract the local mean function from the original complex signal to obtain h(t) = z(t) - m(t);

[0020] (5) Determine whether h(t) satisfies the stopping criterion of CIMF (usually the standard deviation SD is between 0.2 and 0.3 as the criterion); if it is satisfied, then CIMF1 = h(t); if it is not satisfied, then h(t) is used as the new z(t) and the above steps are repeated until the condition is satisfied.

[0021] (6) After separating CIMF1 from the original signal, the remaining signal r1(t) = z(t) - CIMF1(t) is obtained. The above process is repeated for r1(t) to extract CIMF2, CIMF3, ..., CIMF1 in sequence. M This continues until the remaining signal r(t) no longer contains any rotational components.

[0022] The CIMFs obtained by decomposition retain the amplitude and phase information of the original dual-channel signal. Furthermore, due to the use of global decomposition in the complex domain, the decomposition scales of x(t) and y(t) are completely consistent in each CIMF, thus avoiding the problem of order mismatch after decomposition by traditional channel-specific EMD.

[0023] Step 3: For the complex intrinsic mode functions (CIMFs) obtained from the decomposition in Step 2... i (t) (i=1,2,…,M), which is considered as a complex signal, with its real part corresponding to the horizontal vibration component and its imaginary part corresponding to the vertical vibration component. For each order CIMF i (t) is subjected to Fast Fourier Transform (FFT) to obtain its spectral sequence Z. i (k), where k=0,1,…,N-1, and N is the number of sampling points.

[0024] According to the full vector spectrum theory, the whirl trajectory of the rotor at a certain frequency is an ellipse, and the length of the major semi-axis of the ellipse is defined as the principal vibration vector, which characterizes the vibration intensity at that frequency. For the i-th order CIMF, the principal vibration vector R at its u-th frequency point (u=1,2,…,N / 2-1) is... ai (u) Calculate using the following formula:

[0025]

[0026] In the formula, |Z i(u)| represents the amplitude at the u-th frequency point in the first half of the spectrum sequence, and |Zi(Nu)| represents the amplitude at the corresponding conjugate point in the second half of the spectrum sequence. N is the number of sampling points.

[0027] After calculating the principal amplitude vectors at all frequency points, the principal amplitude vector spectrum R of the i-th order CIMF is obtained. ai (f), where f is the frequency (in Hz). The principal oscillation vector spectrum comprehensively reflects the eddy current intensity of this order CIMF at different frequencies, and integrates the amplitude and phase information of the two channels.

[0028] Repeat the above calculations for the first P orders (usually P=4~6) of CIMF to obtain the principal vibration vector spectra R of each order. a1 (f),R a2 (f),…,R aP (f). Since the CIMFs of each order are arranged from high to low rotation frequency, the energy distribution of their principal oscillation vector spectrum also concentrates towards lower frequencies as the order increases.

[0029] The principal vibration vector spectrum output in this step will serve as the basis for subsequent sensitive CIMF screening and rubbing fault feature extraction.

[0030] Step 4: Analyze the principal vibration vector spectra obtained in Step 3. As input, calculate the passband energy E of each principal oscillation vector spectrum. i

[0031]

[0032] In the formula, f s The sampling frequency is used. The first Q-order CIMF (usually Q=3~5) with the largest passband energy proportion is selected as the sensitive CIMF, denoted as CIMF. s1 CIMF s2 CIMF sQ These sensitive CIMFs concentrate the main eddy energy of the rotor at this cross-section, giving them the strongest response to rubbing faults.

[0033] The fundamental frequency f0 = n / 60 is calculated based on the rotor's rated speed n (unit: r / min). The amplitude characteristics of the following key frequency points are extracted from the principal oscillation vector spectrum of each order sensitive CIMF:

[0034] (1) Fundamental frequency amplitude A 1X =R a (f0);

[0035] (2) 2nd harmonic amplitude A 2X =R a (2f0);

[0036] (3) 3rd harmonic amplitude A 3X =R a(3f0);

[0037] (4) 4th harmonic amplitude A 4X =R a (4f0);

[0038] (5) 1 / 2 times the frequency division amplitude A 0.5X =R a (0.5f0).

[0039] Simultaneously, the secondary oscillation vector R of each order of sensitive CIMF is calculated. bi Its ratio to the principal oscillation vector (reflecting the flatness of the axis trajectory):

[0040]

[0041] In the formula, R bi Calculated using the secondary vibrational vector formula in the full vector spectrum theory:

[0042]

[0043] Arrange all the above feature parameters in order of order and normalize them to form a multidimensional collision-fault feature vector F:

[0044]

[0045] In the formula, the superscripts (1), (2), ..., (Q) represent the corresponding sensitive CIMF order. This feature vector contains the typical frequency components (fundamental frequency, harmonics, and sub-frequencys) of the rubbing fault as well as the trajectory shape information, which can effectively distinguish dynamic and static rubbing faults from other common faults (such as imbalance, misalignment, etc.).

[0046] Step 5: Use the multidimensional feature vector F constructed in Step 4 as the feature output of the dynamic-static collision fault, which is then used for subsequent fault identification and status assessment. This feature vector can be directly input into a classifier (such as a support vector machine, random forest, or threshold-based expert system) for automatic identification of collision fault types, or it can be used for historical trend analysis of equipment operating status.

[0047] In practical engineering applications, dual-channel vibration displacement signals at the same cross-section of rotating machinery under unknown conditions are acquired. Steps 1 to 4 are executed sequentially to extract the feature vector F of the measured state. test Using an offline-trained classification model or a pre-set fault threshold rule, the F... test Perform the identification and output the type of rubbing fault:

[0048] (1) If F test Mid-frequency amplitude A 1x Dominated by the passband energy (usually A) 1xIf / ΣA≥0.8), and the amplitudes of both the multiplication and division frequencies are below the threshold, then it is determined to be a state of no contact or normal operation.

[0049] (2) If F test It simultaneously contains significant fundamental, second, third, and fourth harmonic components, and ρ i If the value is greater than 0.3, it is determined that a dynamic-static contact fault has occurred;

[0050] (3) If F test The amplitude of the 1 / 2 frequency division is significant (A) 0.5x / A 1x If the value is greater than 0.2 and accompanied by high-order harmonic components, it is judged as a severe or localized rubbing fault.

[0051] The feature vector F can also be saved to a historical database for plotting feature trend curves, enabling early warning and severity assessment of collision-related faults. The feature vectors extracted in this invention have clear physical meaning, do not rely on large amounts of labeled data or complex deep learning networks, and are easy to deploy in engineering and apply in the field.

[0052] This invention addresses the shortcomings of existing techniques for extracting features of dynamic and static rubbing faults in rotating machinery by proposing a method based on full vector spectrum and complex EMD for fault feature extraction. Existing single-channel spectral analysis provides limited information, easily leading to missed or incorrect diagnoses. While traditional full vector spectrum can fuse orthogonal direction information, it relies on Fourier transform, which is insufficient for processing nonlinear and non-stationary signals. Furthermore, conventional empirical mode decomposition, when processing the X and Y directions separately, suffers from inconsistent orders of intrinsic mode functions due to differences in energy and extremum distribution between the two directions, preventing effective fusion of information from the same source. This invention constructs a complex signal from two mutually perpendicular dual-channel vibration signals at the same cross-section and uses complex empirical mode decomposition for overall processing, ensuring uniform decomposition scale in both directions and natural alignment of complex intrinsic mode components. It then introduces full vector spectrum technology, using the major semi-axis (principal vector) of the elliptical trajectory to comprehensively characterize the rotor's eddy current intensity at various frequencies, effectively compensating for the deficiencies of single-source information and overcoming the bottleneck of traditional full vector spectrum being limited to stationary signals. This method forms a complete technical chain of "unified decomposition - homogeneous correspondence - information fusion", which can adaptively extract typical nonlinear and nonstationary features such as fundamental frequency, harmonic frequency and frequency division contained in the collision and rubbing faults. It significantly improves the accuracy and comprehensiveness of fault identification, and provides more reliable technical support for early warning and condition monitoring of dynamic and static collision and rubbing faults of rotating machinery. It has important engineering application value. Attached Figure Description

[0053] Figure 1 This is a flowchart of the present invention.

[0054] Figure 2 This is a schematic diagram of the installation of the rotor dual-channel sensor according to the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. This embodiment takes a 3000kW TRT generator set from a steel company as an example. Both the turbine rotor and generator rotor of this unit are supported by sliding bearings, with a rated speed of 3000 r / min and a critical speed range of 1400–1700 r / min. Abnormal vibration occurs during unit operation, requiring dynamic and static rubbing fault feature extraction.

[0056] The sliding bearing housing near the turbine rotor end of the generator (the section with the most significant vibration) is designated as the critical monitoring section. At this section, two identical eddy current displacement sensors (frequency response range 0–10 kHz, sensitivity 8 V / mm) are installed along the horizontal (X-direction) and vertical (Y-direction) directions, respectively. The two sensors are perpendicular to each other, with an included angle of 90° ± 1°. The sensor probes are perpendicular to the shaft surface, and the installation gap is controlled within the range of 1.0–1.5 mm to ensure the sensors operate in the linear segment.

[0057] A synchronous full-cycle sampling method is adopted, using the unit's key phase signal (one pulse per revolution) to trigger data acquisition, ensuring the same number of sampling points per revolution. The unit's rated rotational frequency f0 = 3000 / 60 = 50Hz. Based on the spectral characteristics of rubbing faults (including fundamental frequency, second harmonic, third harmonic, fourth harmonic, and other higher harmonics), the highest analysis frequency is set to 20 times the rotor rotational frequency, i.e., f0 = 3000 / 60 = 50Hz. max =1000Hz. The sampling frequency is taken as 8 times the highest analysis frequency, i.e., f s =8 × 1000 = 8000 Hz. The number of sampling points N is 2048 (an integer power of 2). The vibration displacement signals of two channels are synchronously acquired through a data acquisition card, denoted as x(t) and y(t), where t = 0, 1, ..., 2047. The acquired raw time-domain signals are not subjected to any filtering or noise reduction preprocessing to preserve complete fault information.

[0058] The acquired dual-channel vibration displacement signals are constructed as complex signals:

[0059]

[0060] Where j is the imaginary unit.

[0061] The complex empirical mode decomposition (specifically the binary empirical mode decomposition BEMD algorithm) is used to decompose z(t), with the number of projection directions K=8. The decomposition process is as follows:

[0062] (1) Project z(t) onto K uniformly distributed direction angles =2πk / K (k=1,2, …, K), thus obtaining the projection signals in each direction:

[0063]

[0064] (2) Extract each projection signal p ϕk The local maxima of (t) are obtained by fitting the envelope curve e in this direction using cubic spline interpolation. ϕk (t);

[0065] (3) After transforming the envelope curves in all directions to the recovery domain, calculate the average value to obtain the local mean function:

[0066]

[0067] (4) Subtract the local mean function from the original complex signal:

[0068]

[0069] (5) Determine whether h(t) meets the CIMF stopping criterion, using the standard deviation SD as the criterion:

[0070]

[0071] Usually, 0.2 ≤ SD ≤ 0.3 is taken. If it is satisfied, then CIMF1 = h(t); if it is not satisfied, then h(t) is used as the new z(t) and steps (1) to (4) are repeated until the condition is satisfied.

[0072] (6) After separating CIMF1 from the original signal, the remaining signal is obtained:

[0073]

[0074] Repeat the above process for r1(t), extracting CIMF2 and CIMF3 sequentially, until the remaining signal r(t) no longer contains rotational components. The final decomposition result is:

[0075]

[0076] In this embodiment, a total of 6 CIMFs were obtained by decomposition, and each order was arranged from high to low rotation frequency.

[0077] Perform Fast Fourier Transform on the decomposed CIMF1 to CIMF6 respectively to obtain the spectral sequence Z. i (k) (i=1,…,6, k=0,…,2047). For the i-th order CIMF, the principal vector at the u-th frequency point (u=1,2,…,N / 2-1) is calculated by the following formula:

[0078]

[0079] The secondary vibration vector is calculated using the following formula:

[0080]

[0081] Where N=2048. After calculating the principal vibration vectors at all frequency points, the principal vibration vector spectra of each order are obtained. The results showed: The principal oscillation vector energy is concentrated in the high-frequency range (200~400 Hz). Concentrated in (150~250 Hz), Concentrated in (50~120 Hz), to The energy is mainly concentrated below 50 Hz.

[0082] Calculate the passband energy of each principal oscillation vector spectrum:

[0083]

[0084] Energy percentage of each order This embodiment yields... to The percentages are 5.2%, 12.8%, 45.6%, 28.3%, 6.1%, and 2.0%, respectively. The top three orders with the highest energy percentages are selected. , , ( ) as a sensitive CIMF.

[0085] Calculate the fundamental frequency based on the rotor's rated speed of 3000 r / min. In the principal amplitude spectrum of each order sensitive CIMF, the amplitudes at key frequency points are extracted: fundamental frequency amplitude. 2nd harmonic amplitude 3rd harmonic amplitude 4th harmonic amplitude 1 / 2 times the frequency division amplitude Simultaneously calculate the axial trajectory flattening for each order of sensitive CIMF:

[0086]

[0087] The extracted feature values ​​are shown in the table below:

[0088]

[0089] The above feature parameters are arranged in order of order and then subjected to min-max normalization. The normalization formula is as follows:

[0090]

[0091] Constructing the multidimensional collision and rubbing fault feature vector F:

[0092]

[0093] In this embodiment, all components are within the [0,1] interval after normalization.

[0094] The constructed feature vector F is input into a support vector machine-based classifier (trained offline). The classifier identifies faults based on the following discrimination rules:

[0095] (1) If A 1X If / ∑A≥0.8 and the amplitudes of both the harmonic and the frequency division are below the threshold, it is determined that there is no friction or normal operation.

[0096] (2) If significant fundamental, second, third, and fourth harmonic components exist simultaneously, and ρ i >0.3 indicates a dynamic-static friction fault.

[0097] (3) If A 0.5X / A 1X If the friction value is ≥0.2 and accompanied by higher harmonics, it is judged as severe friction or local friction.

[0098] In this embodiment: CIMF3's A 1X It accounts for 68% of the energy of this order (less than 0.8, but combined with other characteristics), CIMF2, CIMF3, and CIMF4 all contain significant 2nd, 3rd, and 4th harmonic components, and ρ3 = 0.45 > 0.3. Based on the above rules, the fault was determined to be a severe localized rubbing failure. After disassembling the sliding bearing near the turbine rotor end of the generator on-site, obvious friction and rubbing marks were observed on the bearing surface, consistent with the diagnostic results, thus verifying the effectiveness of this method.

[0099] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for extracting dynamic and static collision fault features based on full vector spectrum and complex EMD, characterized in that, Includes the following steps: Vibration signals along two mutually perpendicular directions at the same cross section of the rotor of a rotating machine are collected and denoted as x(t) and y(t), respectively. The x(t) and y(t) are constructed as complex signals. , where j is the imaginary unit; Complex empirical mode decomposition is performed on the complex signal z(t) to obtain several complex intrinsic mode functions (CIMFs) arranged in descending order of frequency; The principal vibration vector spectra of each CIMF of each order obtained by decomposition are calculated. Based on the principal vibration vector spectra of each order, feature parameters reflecting the collision and rubbing fault are extracted, and a collision and rubbing fault feature vector is constructed. The complex EMD decomposition of the complex signal z(t) includes: The complex signal z(t) is projected onto multiple uniformly distributed directions to obtain the projected signals in each direction; Local maxima of the projection signals in each direction are extracted, and envelope curves in each direction are obtained by interpolation fitting. After transforming the envelope curves in each direction into the recovery domain, the average is obtained to obtain the local mean function; The complex signal is subtracted from the local mean function, and iterative sieving is performed until the stopping criterion is met to obtain the first-order CIMF. After separating the obtained CIMF, repeat the above operation on the remaining signal until all CIMF and residual components are decomposed.

2. The method according to claim 1, characterized in that, The stopping criterion is as follows: calculate the standard deviation SD during the screening process, and stop the screening iteration of the current CIMF when the standard deviation satisfies 0.2≤SD≤0.

3.

3. The method according to claim 1, characterized in that, The process of performing full vector spectrum calculations on each order of CIMF obtained from the decomposition includes: Performing a Fast Fourier Transform on each order of CIMF yields the spectral sequence Z. i (k), where i is the order of CIMF and k is the frequency index; Calculate the principal oscillation vector R of each order CIMF using the following formula. ai : ， Where N is the number of sampling points, |Z i (u)| represents the amplitude of the u-th frequency point in the first half of the spectrum sequence, and |Zi(Nu)| represents the amplitude of the corresponding conjugate point in the second half of the spectrum sequence.

4. The method according to claim 3, characterized in that, After obtaining the principal vibration vector spectra of each order, a screening step for sensitive CIMFs is also included: Calculate the passband energy of each principal amplitude vector spectrum. ， In the formula, f s The sampling frequency is denoted as ; the first Q-order CIMF with the largest passband energy ratio is selected as the sensitive CIMF; where the value of Q ranges from 3 to 5.

5. The method according to claim 4, characterized in that, The feature parameters reflecting the rubbing fault extracted based on the principal vibration vector spectra of each order include: Calculate the fundamental frequency f0 based on the rotor's rated speed; In the master vector spectrum of each order of sensitive CIMF, the amplitudes at the fundamental frequency f0, second harmonic 2f0, third harmonic 3f0, fourth harmonic 4f0, and half harmonic 0.5f0 are extracted.

6. The method according to claim 5, characterized in that, The characteristic parameters also include the axis trajectory flattening feature, specifically: calculating the secondary vibration vector R of each order of sensitive CIMF. bi R bi Calculated using the secondary vibrational vector formula in the full vector spectrum theory: ， Calculate the ratio of principal to secondary vibrational vectors for each order of sensitive CIMF. The ρ i Elliptic flatness used to reflect the rotor shaft trajectory.

7. The method according to claim 6, characterized in that, After constructing the rubbing fault feature vector, the method further includes: combining the fundamental frequency, harmonics, and frequency division amplitudes of each order of sensitive CIMFs, as well as the shaft trajectory flatness ρ. i Arranged in order of order and normalized, the resulting multidimensional feature vector F is used for classification and recognition.

8. The method according to claim 7, characterized in that, After constructing the feature vector, the method further includes: inputting the feature vector F into an offline trained fault classifier for automatic identification, wherein the fault classifier includes a support vector machine, a random forest, or a threshold-based expert judgment system.

9. The method according to claim 8, characterized in that, The fault classifier identifies the current device status based on the following discrimination rules: If the fundamental frequency amplitude dominates the feature vector, and the amplitudes of the harmonics and sub-harmonics are both below the preset threshold, then it is determined to be in a state of no contact or normal operation. If the eigenvector simultaneously contains significant fundamental, second, third, and fourth harmonic components, and the axial trajectory flatness ρ i If the value is greater than 0.3, it is determined that a dynamic-static contact fault has occurred; If the amplitude of the 1 / 2 frequency division in the eigenvector is significant and accompanied by higher harmonic components, the condition for significance is A. 0.5f0 / A f0 If the value is ≥0.2, it is determined to be a severe or partial friction failure.

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