CN111458122A - Rotary machine fault diagnosis method based on matching enhancement time-frequency representation - Google Patents
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Abstract
The invention provides a fault diagnosis method for a rotary machine with matching enhanced time-frequency representation, which belongs to the technical field of fault diagnosis for a variable-speed rotary machine and comprises the following steps: introducing a frequency modulation frequency to match the time-frequency characteristics of the signal with frequency change, and constraining the frequency modulation frequency selection range by utilizing a tangent function; extended linear transformation basis function e‑jωtObtaining a time-frequency representation capable of enhancing a plurality of time-frequency components simultaneously; calculating kurtosis values corresponding to different time-frequency graphs, selecting proper parameters in a self-adaptive mode by utilizing a kurtosis maximum criterion, and selecting time-frequency distribution corresponding to the maximum kurtosis for final time-frequency representation; searching the characteristic time-frequency ridge line of the rotary machine on the time-frequency graph obtained in the last step by using a local peak search algorithm; and diagnosing the fault type of the rotary machine according to the detected time-frequency ridge line. The invention enhances the time-frequency representation by matching the change characteristics of the frequency in the signal, can obtain more accurate time-frequency ridge line estimation and finally completes the fault diagnosis of the rotary machine.
Description
Technical Field
The invention belongs to the technical field of fault diagnosis of variable-speed rotating machinery, and particularly relates to a fault diagnosis method of rotating machinery, which is expressed by matching and enhancing time frequency.
Background
The time-frequency analysis of vibration signals can improve the readability of time-frequency representation so as to more accurately extract required fault-related features and is used for diagnosing the health state of corresponding parts in a system, the time-frequency analysis of vibration signals improves the trend of frequency change by adjusting the angle of a basis function of linear transformation, so that the energy aggregation of the time-frequency graph is improved, however, a single linear frequency modulation transformation can only enhance the time-frequency representation at a specific moment and cannot simultaneously enhance the whole moment, the generalized linear frequency modulation transformation (G L CT) is proposed by the people just before and after the like, the final result is obtained by superposing the maximum time-frequency graph amplitude at each time-frequency point, although the G L CT method can obtain better energy aggregation at the time-frequency ridge line, the cross term interference caused by improper frequency modulation of the time-frequency graph cannot be avoided due to the fact that all frequency modulation frequency demodulation transformation results are simultaneously reserved, and particularly when the frequency components are close and the analyzed signals contain larger noise.
Therefore, in order to solve the above technical problem, the present application provides a fault diagnosis method for a rotating machine based on matching enhancement time-frequency representation.
Disclosure of Invention
Considering that the fault diagnosis method of the variable-speed rotating machinery vibration signal has some defects, the problem that cross item interference in a time-frequency diagram is relieved while time-frequency representation is improved is solved, and in order to further enhance the obtained time-frequency representation, the invention establishes the enhanced time-frequency representation based on matched linear frequency modulation so as to realize more detailed and accurate instantaneous frequency estimation and final fault diagnosis. The method provided by the invention firstly divides the original signal into a plurality of sections, and then the frequency track of the truncated signal can be regarded as linear. Considering that the cross terms in the time-frequency diagram are caused by improper tuning frequency, a correct tuning frequency selection strategy guided by kurtosis in each time window is provided, and human intervention and dependence on a priori knowledge are avoided. The extension of the existing linear transformation basis functions enables the proposed method to enhance the time-frequency representation of multi-component signals simultaneously without the need for iteration. And then, analyzing the time-frequency graph through a local peak search algorithm to accurately extract an instantaneous frequency ridge line so as to make a diagnosis result.
In order to achieve the above purpose, the invention provides the following technical scheme:
the fault diagnosis method for the rotary machine represented by the matched enhanced time frequency comprises the following steps of:
step 3, calculating kurtosis values of the time-frequency graphs corresponding to different angles at each moment, selecting proper parameters in a self-adaptive mode by utilizing a kurtosis maximum criterion, and selecting time-frequency distribution corresponding to the maximum kurtosis for final time-frequency representation;
Preferably, the step 1 specifically includes:
step 1.1, analyzing and considering a time-frequency expression S (t, omega, c (t)) of frequency modulation;
defining a signal s (t), wherein the time-frequency expression is written as:
where s (u) represents the analysis signal, g (u) represents the window function, ω represents the frequency of the signal at time t, c (t) represents the selected tuning frequency, and when c (t) is 0, the time-frequency representation is a standard short-time fourier (STFT) representation, where the time-frequency representation amplitude considering the tuning frequency of the chirp transform (L CT) has the following relationship:
as can be seen from equation (2), when the set frequency modulation rate c (τ) is equal to the slope f' (τ) of the instantaneous frequency, there is the highest level of energy concentration in the time-frequency representation at that time;
step 1.2, calculating instantaneous frequency
Considering the frequency modulation effect, the instantaneous frequency is written as:
wherein the partial derivative of the time-frequency representation over time t can be calculated as:
in equation (4), c' (t) ═ 0, because c (t) is a constant at time t, Sg′(t, ω, c (t)) can be considered as a time-frequency representation obtained with a window function g' (t); then, by substituting equation (4) for equation (3), the instantaneous frequency of the signal can be obtained and written as:
instantaneous frequency
The corrected time-frequency distribution is shown to be along the frequency modulation direction in the time window taking the moment t as the center, namely when the frequency modulation is consistent with the real instantaneous frequency change, the obtained time-frequency graph can obtain the maximum time-frequency aggregation.
Preferably, the step 2 specifically includes:
step 2.1, expand existing linear transformation basis function e-jωt；
In a small time window, the original nonlinear frequency can be approximately regarded as a straight line, and is expanded by a Taylor polynomial and written as:
where f' (τ) represents the first derivative of the instantaneous frequency at time τ, i.e., the tuning frequency; this line can be further rewritten as:
in order to enable the proposed M L CT to process multi-component signals simultaneously, the transform basis functions (e) in the original time-frequency representation (1)-jω(t-τ)) Further extended, written as:
step 2.2, defining a tangent function to restrict the frequency modulation rate selection range (-pi/2, pi/2);
in order to determine the selectable range of the frequency modulation and to include the appropriate frequency modulation as much as possible, a tangent function is introduced to constrain the frequency modulation, since the tangent function reflects the inclination angle of the time-frequency ridge and also reflects the variation trend of the curve, and the tangent function itself has a determined range (-pi/2, pi/2) written as:
step 2.3, considering that the multi-component can be processed simultaneously to obtain a rewritten time-frequency expression S (t, omega, a (t));
the improved time-frequency expression can be finally written as:
where X (t) represents the analytic signal, w (t) represents the window function, ω represents the frequency of the signal at time τ, α (τ) represents the discretized angle, and X (τ, ω, α (τ)) represents the time-frequency representation obtained at time τ by angle α (τ).
Preferably, the step 3 specifically includes:
step 3.1, discretizing angle parameters and obtaining a series of transformation results;
where α (t) is also a function of time t, discretized angle α, written as:
in particular, when N is 1, the time-frequency expression of the formula (10) is equal to the standard STFT, and the operation time of the method is increased along with the increase of N;
step 3.2, introducing a kurtosis index to calculate a kurtosis value represented by a time frequency;
corresponding to different parameters α, different time-frequency representations can be obtained, in order to have a uniform standard to select appropriate variation parameters, the kurtosis corresponding to different results is calculated, and the kurtosis is written as:
step 3.3, selecting a proper parameter (angle) at each moment according to the kurtosis maximum criterion, and combining the time-frequency distributions at different moments to obtain a final result X (t, omega, α)*(t))；
At each instant, the optimal angle is determined by the maximum kurtosis, which can be written as:
α denotes the angle found by the maximum kurtosis, and accordingly, the time-frequency representation corresponding to the angle is the result and is denoted as X (τ, ω, α (τ)).
Preferably, the step 4 specifically includes:
step 4.1, extracting time-frequency ridge lines of the time-frequency representation X (tau, omega, α (tau)) obtained in the step 3.3 by using a local peak search algorithm;
the local peak search algorithm selects the time frequency point with the maximum time frequency graph amplitude value, can define the frequency variable range searched at two adjacent moments, and the ridge line of the searched instantaneous frequency can be expressed as
If (t) represents the searched time-frequency ridge line, and since the frequency of the signal is changed, the frequency is recorded as a function of time change;
step 4.2, diagnosing the fault type of the rotary machine;
and (4) calculating a corresponding ratio by using the changed instantaneous frequency ridge line obtained in the step (4.1), and comparing the corresponding ratio with the real fault characteristic frequency to obtain a final diagnosis result. .
The rotary machine fault diagnosis method based on the matching enhancement time-frequency representation comprehensively analyzes the time-frequency variation trend of the rotary machine, improves the time-frequency aggregation so as to enhance the time-frequency representation, enables the obtained final result not to be interfered by fuzzy and cross terms, further carries out peak value search on the improved time-frequency representation so as to obtain more accurate time-frequency ridge lines and completes fault diagnosis of the rotary machine. The method can better reflect the time-frequency change characteristics, obtain clearer time-frequency representation and be successfully applied to fault diagnosis of the rotary machine.
Drawings
Fig. 1 is a flowchart of a fault diagnosis method for a rotating machine represented by a matching enhanced time frequency according to embodiment 1 of the present invention;
FIG. 2 is a schematic flow chart of the enhanced time-frequency representation algorithm obtained by the present invention;
FIGS. 3a and 3b are time-frequency representations of simulated multi-component signals without noise for example 1 and STFT, respectively, of the present invention; FIGS. 3c and 3d are ridge extraction for example 1 and STFT, respectively, of the present invention;
FIGS. 4a and 4b are time-frequency representations (signal-to-noise ratio 6dB) of simulated multi-component signals of embodiment 1 and STFT, respectively, of the present invention; FIGS. 4c and 4d are ridge extraction for example 1 and STFT, respectively, of the present invention;
FIG. 5 is a schematic structural diagram of an inner ring fault bearing test bed;
FIG. 6 is a time-frequency representation of the collected bearing vibration signal;
FIG. 7 is a graph of instantaneous frequency ridges extracted from a time-frequency representation.
Detailed Description
In order that those skilled in the art will better understand the technical solutions of the present invention and can practice the same, the present invention will be described in detail with reference to the accompanying drawings and specific examples. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
The invention provides a fault diagnosis method for a rotary machine represented by matching enhanced time frequency, which comprises the following steps of:
s1, introducing frequency modulation to match the time-frequency characteristics of the signals with frequency changes, and analyzing the influence of the set frequency modulation on a time-frequency graph; the method specifically comprises the following steps:
s1.1, analyzing and considering a time-frequency expression S (t, omega, c (t)) of frequency modulation;
defining a signal s (t), wherein the time-frequency expression is written as:
where s (u) represents the analysis signal, g (u) represents the window function, ω represents the frequency of the signal at time t, c (t) represents the selected tuning frequency, and when c (t) is 0, the time-frequency representation is a standard STFT representation, where the time-frequency representation amplitude considering the tuning frequency of L CT has the following relationship:
as can be seen from equation (2), when the set frequency modulation rate c (τ) is equal to the slope f' (τ) of the instantaneous frequency, there is the highest level of energy concentration in the time-frequency representation at that time;
s1.2, calculating instantaneous frequency
Considering the influence of the set frequency modulation rate on time-frequency representation;
considering the frequency modulation effect, the instantaneous frequency can be written as:
wherein the partial derivative of the time-frequency representation over time t can be calculated as:
in equation (4), c' (t) ═ 0, because c (t) is a constant at time t, Sg′(t, ω, c (t)) can be considered as a time-frequency representation obtained with a window function g' (t); then, by substituting equation (4) for equation (3), the instantaneous frequency of the signal can be obtained and written as:
instantaneous frequency
The corrected time-frequency distribution is shown to be along the frequency modulation direction in the time window taking the moment t as the center, namely when the frequency modulation is consistent with the real instantaneous frequency change, the obtained time-frequency graph can obtain the maximum time-frequency aggregation.
S2, expanding the existing linear transformation basis function e-jωtObtaining a time-frequency representation capable of enhancing a plurality of time-frequency components simultaneously, and constraining the frequency modulation selection range by utilizing a tangent function; the method specifically comprises the following steps:
s2.1, expanding the existing linear transformation basis function e-jωt；
In a small time window, the original nonlinear frequency can be approximately regarded as a straight line, and is expanded by a Taylor polynomial and written as:
where f' (τ) represents the first derivative of the instantaneous frequency at time τ, i.e., the tuning frequency; this line can be further rewritten as:
in order to enable the proposed M L CT to process multi-component signals simultaneously, the transform basis functions (e) in the original time-frequency representation (1)-jω(t-τ)) Further extended, written as:
s2.2, defining a tangent function to restrict the frequency modulation selection range (-pi/2, pi/2);
in order to determine the selectable range of the frequency modulation and to include the appropriate frequency modulation as much as possible, a tangent function is introduced to constrain the frequency modulation, since the tangent function reflects the inclination angle of the time-frequency ridge and also reflects the variation trend of the curve, and the tangent function itself has a determined range (-pi/2, pi/2) written as:
s2.3, considering that the multi-component can be processed simultaneously to obtain a rewritten time-frequency expression S (t, omega, a (t));
the improved time-frequency expression can be finally written as:
where X (t) represents the analytic signal, w (t) represents the window function, ω represents the frequency of the signal at time τ, α (τ) represents the discretized angle, and X (τ, ω, α (τ)) represents the time-frequency representation obtained at time τ by angle α (τ).
S3, calculating the kurtosis value of the time-frequency graph corresponding to different angles at each moment, selecting proper parameters in a self-adaptive mode by utilizing the kurtosis maximum criterion, and selecting the time-frequency distribution corresponding to the maximum kurtosis for the final time-frequency representation; the method specifically comprises the following steps:
s3.1, discretizing angle parameters and obtaining a series of transformation results;
where α (t) is also a function of time t, discretized angle α, written as:
in particular, when N is 1, the time-frequency expression of the formula (10) is equal to the standard STFT, and the operation time of the method is increased along with the increase of N;
s3.2, introducing a kurtosis index to calculate a kurtosis value represented by a time frequency;
corresponding to different parameters α, different time-frequency representations can be obtained, in order to have a uniform standard to select appropriate variation parameters, the kurtosis corresponding to different results is calculated, and the kurtosis is written as:
s3.3, selecting proper parameters (angles) at each moment according to the kurtosis maximum criterion, and combining the time-frequency distribution at different moments to obtain a final result X (tau, omega, α)*(τ))；
At each instant, the optimal angle is determined by the maximum kurtosis, which can be written as:
α denotes an angle found by the maximum kurtosis, and accordingly, the time-frequency representation corresponding to the angle is the result and is marked as X (τ, ω, α (τ));
s4, searching the characteristic time-frequency ridge line of the rotary machine on the time-frequency graph obtained in the step 3 by using a local peak search algorithm; diagnosing the fault type of the rotary machine according to the detected time-frequency ridge line; the method specifically comprises the following steps:
s4.1, extracting time-frequency ridge lines of the time-frequency representation X (tau, omega, α (tau)) obtained in the step 3.3 by using a local peak search algorithm;
the local peak search algorithm selects the time frequency point with the maximum time frequency graph amplitude value, can define the frequency variable range searched at two adjacent moments, and the ridge line of the searched instantaneous frequency can be expressed as
If (t) represents the searched time-frequency ridge line, and since the frequency of the signal is changed, the frequency is recorded as a function of time change;
s4.2, diagnosing the fault type of the rotary machine;
and (4) calculating a corresponding ratio by using the changed instantaneous frequency ridge line obtained in the step (4.1), and comparing the corresponding ratio with the real fault characteristic frequency to obtain a final diagnosis result.
Example 2
The method described in example 1 is described in detail below with reference to simulation and experimental signals, respectively:
the structure of the simulation signal model is shown below
Wherein, c k1,1.5,2, f (t) denotes instantaneous frequency, and n (t) denotes white gaussian noise added. The instantaneous frequency can be written as:
the sampling frequency was set to 100Hz and the signal lasted 6 seconds. This multi-component signal is first analyzed without adding noise.
According to the S, in order to introduce proper parameters to match the signals to be analyzed, the signals are respectively analyzed through a series of discretized points, and then the most proper result is selected.
Define angle α, with ranges defined as (- π/2, π/2.) then each α may represent a specific angle, defined as:
where N is the number of angles, here set to 30.
After the angle α is determined, the new linear transformation basis function can be determined and written as:
multiplying the obtained basis function by a windowing signal to obtain time-frequency representation:
through the S, 30 different time-frequency representations are obtained, wherein a result which is most matched with a target time-frequency ridge line can be found, the correct selection of the angle is realized through the index with the maximum kurtosis, the dependence and the human intervention of priori knowledge are avoided, and finally the time-frequency representation obtained at the time when t is tau is marked as X (tau, omega, α)*(τ))。
FIG. 2 is a schematic flow chart of the enhanced time-frequency representation algorithm obtained by the present invention, which specifically includes the following steps:
step 1: input signal x (t);
step 2: defining a window function g (t) and the number N of discretization angles;
and step 3: when i is 1, judging whether i is largeAt N; if yes, entering step 4; otherwise, calculating corresponding time-frequency representation X (tau, omega, a)*(τ)), when i is i +1, continuing to determine whether i is greater than N;
and 4, step 4: calculating the steepness Ki；
And 5: i.e. i*,a*←argmax(ki)；
Step 6: output time-frequency representation X (tau, omega, a)*(τ))。
The time-frequency representation results are shown in fig. 3 (a). To illustrate the improvement of the proposed invention on the time-frequency diagram by the new linear transformation basis function, the time-frequency representation obtained by using the existing linear transformation basis function is shown in fig. 3 (b).
After the noise added in the multi-component simulation signal is 6dB, the signal is analyzed, and the obtained time-frequency representation is shown in figure 4 (a); also, a time-frequency diagram not involving the matching basis function (STFT) is shown in FIG. 4 (b).
According to the four obtained time-frequency graphs, time-frequency ridge lines are extracted by using a peak maximum search algorithm, and the obtained results are shown in fig. 3(c) - (d) and fig. 4(c) - (d). Their errors were calculated separately: when the signal is free of noise, the average relative error of the proposed invention is 0.33%, and the STFT result is 0.47%; after noise is added, the average relative error of the proposed invention is 0.54%, and the STFT result is 4.95%, which illustrates the effectiveness of the proposed invention in enhancing time-frequency representation and improving time-frequency ridge line estimation.
And analyzing the experimental signal, wherein the bearing to be analyzed contains inner ring faults. The simulation experiment table for the bearing inner ring fault is shown in figure 5. The experiments were performed on a SpectraQuest mechanical Fault simulator (MFS-PK 5M). The motor drives a shaft with two ER16K ball bearings. The left bearing is healthy and the right bearing has a local defect on the inner race. The speed of the rotating shaft was controlled by a dc drive and an accelerometer mounted to record bearing vibration data, and also verified using an encoder (EPC model 775) to measure the instantaneous rotational frequency of the shaft. The bearing specification parameters including inner ring failure are shown in table 1. The calculated fault signature coefficient (FCC) was 5.43.
TABLE 1 bearing parameters
The number of angles was also set to 30 in the same manner as in the above analysis. The analysis result is shown in fig. 6, the peak search algorithm is used again, the obtained time-frequency ridge line is shown in fig. 7, and the effectiveness of the method is illustrated by the more accurate ridge line.
TABLE 2 ratio and relative error between frequency ridges
The ratio between the ridges of the instantaneous frequencies is shown in table 2. From Table 2, it can be found that the ratios of the lowest instantaneous frequency to the upper three are R15.29,10.55 and 15.80. Corresponding to the instantaneous rotation frequency of the shaft and the characteristic frequency of the first three-order fault. Calculated, R22.70,5.38 and 8.05, corresponding to 2 times the instantaneous shaft rotation frequency and the first three order fault signature frequency. And the error of all calculated ratios and corresponding fault characteristic coefficients is less than 3%. Therefore, it can be concluded that the bearing contains an inner ring failure. During the analysis of this signal, a window length of 1 second was set. The above results show that the method provided by the invention can be successfully used for bearing fault type diagnosis.
According to the analysis process and the application example, the rotary machine fault diagnosis method based on the matching enhancement time-frequency representation can effectively improve the readability of the time-frequency representation, remove the fuzzy problem in the time-frequency graph, provide more concentrated time-frequency aggregation, and show that the algorithm can obtain a clearer video graph and is more accurate in result through the accuracy of the ridge line extracted by the local peak value search algorithm, and finally, the method is successfully used for fault diagnosis of the bearing.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any simple modifications or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Claims (5)
1. The fault diagnosis method for the rotary machine represented by the matching enhanced time frequency is characterized by comprising the following steps of:
step 1, introducing frequency modulation to match time-frequency characteristics of signals with frequency changes, and analyzing the influence of the set frequency modulation on a time-frequency graph;
step 2, expanding the existing linear transformation basis function e-jωtObtaining a time-frequency representation capable of enhancing a plurality of time-frequency components simultaneously, and constraining the frequency modulation selection range by utilizing a tangent function;
step 3, calculating kurtosis values of the time-frequency graphs corresponding to different angles at each moment, selecting proper parameters in a self-adaptive mode by utilizing a kurtosis maximum criterion, and selecting time-frequency distribution corresponding to the maximum kurtosis for final time-frequency representation;
step 4, searching the characteristic time-frequency ridge line of the rotary machine by using a local peak search algorithm on the time-frequency graph obtained in the step 3; and diagnosing the fault type of the rotary machine according to the detected time-frequency ridge line.
2. The method for fault diagnosis of a rotating machine represented by matching enhanced time-frequency according to claim 1, wherein the step 1 specifically comprises:
step 1.1, analyzing and considering a time-frequency expression S (t, omega, c (t)) of frequency modulation;
defining a signal s (t), wherein the time-frequency expression is written as:
where s (u) represents the analysis signal, g (u) represents the window function, ω represents the frequency of the signal at time t, c (t) represents the selected tuning frequency, and when c (t) is 0, the time-frequency representation is a standard STFT representation, where the time-frequency representation amplitude considering the tuning frequency of L CT has the following relationship:
as can be seen from equation (2), when the set frequency modulation rate c (τ) is equal to the slope f' (τ) of the instantaneous frequency, there is the highest level of energy concentration in the time-frequency representation at that time;
step 1.2, calculating instantaneous frequency
Considering the frequency modulation effect, the instantaneous frequency is written as:
wherein the partial derivative of the time-frequency representation over time t can be calculated as:
in equation (4), c' (t) ═ 0, because c (t) is a constant at time t, Sg′(t, ω, c (t)) can be considered as a time-frequency representation obtained with a window function g' (t); then, by substituting equation (4) for equation (3), the instantaneous frequency of the signal can be obtained and written as:
instantaneous frequency
The corrected time-frequency distribution is shown to be along the frequency modulation direction in the time window taking the moment t as the center, namely when the frequency modulation is consistent with the real instantaneous frequency change, the obtained time-frequency graph can obtain the maximum time-frequency aggregation.
3. The method for fault diagnosis of a rotating machine represented by matching enhanced time-frequency according to claim 2, wherein the step 2 specifically comprises:
step 2.1, expand existing linear transformation basis function e-jωt；
In a small time window, the original nonlinear frequency can be approximately regarded as a straight line, and is expanded by a Taylor polynomial and written as:
where f' (τ) represents the first derivative of the instantaneous frequency at time τ, i.e., the tuning frequency; this line can be further rewritten as:
in order to enable the proposed M L CT to process multi-component signals simultaneously, the transform basis functions (e) in the original time-frequency representation (1)-jω(t-τ)) Further extended, written as:
step 2.2, defining a tangent function to restrict the frequency modulation rate selection range (-pi/2, pi/2);
in order to determine the selectable range of the frequency modulation and to include the appropriate frequency modulation as much as possible, a tangent function is introduced to constrain the frequency modulation, since the tangent function reflects the inclination angle of the time-frequency ridge and also reflects the variation trend of the curve, and the tangent function itself has a determined range (-pi/2, pi/2) written as:
step 2.3, considering that the multi-component can be processed simultaneously to obtain a rewritten time-frequency expression S (t, omega, a (t));
the improved time-frequency expression can be finally written as:
where X (t) represents the analytic signal, w (t) represents the window function, ω represents the frequency of the signal at time τ, α (τ) represents the discretized angle, and X (τ, ω, α (τ)) represents the time-frequency representation obtained at time τ by angle α (τ).
4. The method for fault diagnosis of a rotating machine represented by matching enhanced time-frequency according to claim 3, wherein the step 3 specifically comprises:
step 3.1, discretizing angle parameters and obtaining a series of transformation results;
where α (t) is also a function of time t, discretized angle α, written as:
in particular, when N is 1, the time-frequency expression of the formula (10) is equal to the standard STFT, and the operation time of the method is increased along with the increase of N;
step 3.2, introducing a kurtosis index to calculate a kurtosis value represented by a time frequency;
corresponding to different parameters α, different time-frequency representations can be obtained, in order to have a uniform standard to select appropriate variation parameters, the kurtosis corresponding to different results is calculated, and the kurtosis is written as:
step 3.3, selecting a proper parameter (angle) at each moment according to the kurtosis maximum criterion, and combining the time-frequency distributions at different moments to obtain a final result X (t, omega, α)*(t))；
At each instant, the optimal angle is determined by the maximum kurtosis, which can be written as:
α denotes the angle found by the maximum kurtosis, and accordingly, the time-frequency representation corresponding to the angle is the result and is denoted as X (τ, ω, α (τ)).
5. The method for fault diagnosis of a rotating machine represented by matching enhanced time-frequency according to claim 4, wherein the step 4 specifically comprises:
step 4.1, extracting time-frequency ridge lines of the time-frequency representation X (tau, omega, α (tau)) obtained in the step 3.3 by using a local peak search algorithm;
the local peak search algorithm selects the time frequency point with the maximum time frequency graph amplitude value, can define the frequency variable range searched at two adjacent moments, and the ridge line of the searched instantaneous frequency can be expressed as
If (t) represents the searched time-frequency ridge line, and since the frequency of the signal is changed, the frequency is recorded as a function of time change;
step 4.2, diagnosing the fault type of the rotary machine;
and (4) calculating a corresponding ratio by using the changed instantaneous frequency ridge line obtained in the step (4.1), and comparing the corresponding ratio with the real fault characteristic frequency to obtain a final diagnosis result.
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| CN113639999A (en) * | 2021-08-16 | 2021-11-12 | 北京信息科技大学 | Fault diagnosis method, system, medium and equipment for rolling bearing under variable rotating speed |
| CN117232841A (en) * | 2022-12-27 | 2023-12-15 | 西安交通大学 | Nonlinear sparse-based aviation intermediate bearing instantaneous dynamic frequency fault diagnosis method |
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