CN111879508A - Method and device for estimating instantaneous rotating speed of rotating machine based on time-frequency transformation and storage medium - Google Patents

Method and device for estimating instantaneous rotating speed of rotating machine based on time-frequency transformation and storage medium Download PDF

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CN111879508A
CN111879508A CN202010736076.6A CN202010736076A CN111879508A CN 111879508 A CN111879508 A CN 111879508A CN 202010736076 A CN202010736076 A CN 202010736076A CN 111879508 A CN111879508 A CN 111879508A
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李富才
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Wuxi Meisde Intelligent Measurement And Control Technology Co ltd
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
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    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention provides a rotating machine instantaneous rotating speed estimation method based on time-frequency transformation, which comprises the following steps: step S1, collecting a rotary mechanical vibration signal S (t); step S2, obtaining the time-frequency distribution of the vibration signal by time-frequency analysis; step S3, obtaining the estimation of the instantaneous frequency from the time-frequency distribution by using a ridge line extraction algorithm; step S4, according to the instantaneous frequency m, through the extracted ridge line, i.e. the instantaneous frequencyc(tn) The relationship with the rotation speed V is converted to obtain the instantaneous rotation speed of the rotating machine. The invention also provides a rotating machine instantaneous rotating speed estimation device based on time-frequency transformation and a storage medium. The invention has strong adaptability and good noise immunityHas the advantages of simple process and low cost.

Description

Method and device for estimating instantaneous rotating speed of rotating machine based on time-frequency transformation and storage medium
Technical Field
The invention relates to the field of rotary machine vibration analysis, in particular to a rotary machine instantaneous rotating speed estimation method based on time-frequency transformation.
Background
Rotary machines are widely used in our daily lives and productions. Due to the complexity and the variety of working environments, a plurality of machines often work at variable rotating speeds. Due to the rapid development of sensing and measuring techniques, physical quantities (e.g., vibration signals) related to the operating state of mechanical equipment can be easily obtained. Meanwhile, the vibration signal contains a large amount of abundant information related to the running state of the equipment. On the other hand, the instantaneous rotational speed of the rotating machine also plays an important role in the control of the equipment and the evaluation of the health of the components. It can be said that the rotational speed of the rotating machine is an important parameter reflecting the operating state of the equipment.
At present, the common method for measuring the rotating speed is to install an encoder, that is, to process a pulse signal generated by the encoder, so as to obtain the instantaneous rotating speed of the machine. The working principle is that the rotating speed is calculated by obtaining the rotating angular displacement within a certain time. However, in some special cases, limited by space or cost, for example, this can lead to difficulties in direct measurement of the rotational speed by the encoder. Therefore, such non-contact measurement is not suitable for most of the working situations. Therefore, some methods of extracting the rotation speed based on the vibration signal of the rotating machine are proposed. Among the methods, the rotation speed estimation based on the time-frequency analysis method can process non-stationary signals and has strong anti-noise capability, so that more researches and applications are obtained. For extracting the instantaneous frequency, a common algorithm is a direct maximum ridge extraction algorithm. The algorithm is simple in principle, and is easy to be interfered by noise because only the time-frequency distribution energy is considered. Typically, this approach fails in a strong noise background. Still other scholars propose ridge extraction algorithms based on penalty functions, which modify the direct maximum ridge extraction algorithm to some extent. Although the frequency continuity condition is increased, this method tends to fall into local optimality.
Therefore, some of the conventional ridge line extraction algorithms described above still cannot meet the requirements under strong noise conditions. Therefore, the existing algorithms still have a deficiency in the accuracy of the instantaneous frequency extraction.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a rotating machine instantaneous rotating speed estimation method based on time-frequency transformation and with strong adaptability and good anti-noise performance and a corresponding device.
In order to achieve the above purpose, the technical solution adopted in the embodiment of the present application is as follows:
in a first aspect, the application provides a method for estimating an instantaneous rotating speed of a rotating machine based on time-frequency transformation, which includes the following steps:
step S1, collecting a rotary mechanical vibration signal S (t);
step S2, obtaining the time-frequency distribution of the vibration signal by time-frequency analysis;
step S3, obtaining the estimation of the instantaneous frequency from the time-frequency distribution by using a ridge line extraction algorithm;
step S4, according to the instantaneous frequency m, through the extracted ridge line, i.e. the instantaneous frequencyc(tn) The relationship with the rotation speed V is converted to obtain the instantaneous rotation speed of the rotating machine.
In a second aspect, the present application provides a device for estimating an instantaneous rotational speed of a rotating machine based on time-frequency transformation, including:
a memory storing a computer program;
a processor for executing the computer program to implement the steps of the time-frequency transform-based method for estimating an instantaneous rotational speed of a rotating machine according to any one of the above.
In a third aspect, the present application is directed to a storage medium,
the storage medium has a computer program stored therein, and the computer program is used for implementing the steps of the time-frequency transform-based rotating machine instantaneous rotation speed estimation method described in any one of the above.
After adopting above technical scheme, this application has following advantage:
1. the method is strong in adaptability, and based on time-frequency distribution, the method can be suitable for most of current time-frequency analysis algorithms, such as short-time Fourier transform, synchronous compression transform and the like, and has certain universality;
2. the anti-noise performance is good, and because the preprocessing adopts a time-frequency analysis algorithm, some non-stable signals can be processed; on the other hand, the loss function considers the continuity and the smoothness of the ridge line at the same time, so that the method can be applied to a noise environment;
3. the method is economical and portable, and can realize the estimation of the instantaneous rotating speed of the rotating machine by collecting the vibration signal without an additional encoder and the like.
Drawings
FIG. 1 is a flow chart of a method in an embodiment of the invention.
Fig. 2 is a schematic time-domain waveform of a vibration signal of a rotor test bed in an embodiment of the invention.
Fig. 3 is a schematic frequency spectrum diagram of a vibration signal of the rotor test bed in the embodiment of the invention.
FIG. 4 is a time-frequency distribution diagram of a vibration signal according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a three-dimensional matrix for ridge line extraction and mapping in the embodiment of the present invention.
FIG. 6 is a schematic diagram illustrating ridge line extraction in an embodiment of the invention
FIG. 7 is a schematic diagram of extracted instantaneous frequencies in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a rotating machine instantaneous rotating speed estimation method based on time-frequency transformation, which comprises the following steps:
step S1, collecting a rotary mechanical vibration signal S (t);
in the embodiment, a rotor test bed is used as a rotating machine, and the time domain waveform of the vibration signal of the rotor test bed is collected and is shown in fig. 2; also its frequency spectrum is shown in fig. 3;
because the rotor test bed works at a variable rotating speed, the frequency spectrum of the rotor test bed is subjected to aliasing, and the vibration characteristics of the rotor cannot be extracted; in order to analyze the non-stationary signal, the application selects a time-frequency analysis method (short-time Fourier transform) to analyze the data;
step S2, obtaining the time-frequency distribution of the vibration signal by time-frequency analysis; FIG. 4 is a time-frequency distribution diagram of vibration signals of a rotor test stand according to an embodiment;
in the step, the time-frequency analysis is carried out on the collected vibration signals s (t) to obtain the time-frequency distribution of the vibration signals s (t);
in a specific embodiment, a time-frequency distribution result is obtained by performing time-frequency analysis by using short-time Fourier transform; the short-time fourier transform uses a sliding window function g (t), and is defined as follows:
Figure BDA0002605107240000031
η represents frequency; in the formula (1), the first and second groups,
Figure BDA0002605107240000032
the time frequency distribution result obtained by short-time Fourier transform;
in practical numerical simulations, g (t) is usually chosen as a gaussian window function, defined as follows:
Figure BDA0002605107240000033
wherein σ is a parameter for adjusting time and frequency resolution;
Figure BDA0002605107240000034
defined as the result of a fourier transform of a window function g (t);
it can be found on the time-frequency distribution map that although the time-frequency distribution shows the time-varying characteristics of the rotating machine, the signal is much disturbed by noise. Near the first-order frequency conversion, the interference of a plurality of noise signals brings difficulty to the accurate extraction of the ridge line of the time-frequency diagram;
step S3, next, obtaining the estimation of the instantaneous frequency from the time-frequency distribution by using a ridge line extraction algorithm;
because the proposed method is based on the result of signal time-frequency distribution, some important parameters need to be defined in advance; the link can eliminate the influence of some noise points and reduce the calculation time of the whole ridge line extraction algorithm;
νm(t) and Qm(t) respectively representing the positions of energy maximum points on the time-frequency distribution and the corresponding energy sizes:
Figure BDA0002605107240000035
Figure BDA0002605107240000036
wherein the content of the first and second substances,
Figure BDA0002605107240000037
about eta pairs
Figure BDA0002605107240000038
Operator of partial derivation, Np(t) represents the number of energy maximum points at each instant; the time-frequency ridge line can be expressed as
Figure BDA0002605107240000039
Where m isc(t) represents the position of the maximum point of the loss function at each instant t;
the application provides a more general extraction scheme of the ridge line of the loss function; meanwhile, in order to reduce the computational complexity, a dynamic algorithm is adopted to solve the optimization problem of the loss function;
in the present application, the loss function is expressed as follows:
Figure BDA00026051072400000310
wherein v ism(tn) Represents tnPosition of energy maximum point on time-frequency distribution, vk(tn-1) Watch (A)Show tn-1Position of energy maximum point in time-frequency distribution, vl(tn-2) Represents tn-2The position of an energy maximum value on time-frequency distribution; alpha and beta respectively represent a ridge continuity adjustment factor and a ridge smoothness adjustment factor; ω () and ρ () are as shown in equation (6):
Figure BDA0002605107240000041
then, a dynamic algorithm is used to find the coordinates m of the loss function maximum point of the ridgec(tn) The objective function is optimized in all time series, and the objective function is as follows:
Figure BDA0002605107240000042
thus, the ridge line may be represented as
Figure BDA0002605107240000043
As a result of analysis, at each time tnUpper time frequency point vm(tn) There is a history loss function maximum point { m }c(m,t1),…,mc(m,tn-1) At this point, the dynamic algorithm is expressed as follows:
Figure BDA0002605107240000044
loss function F [ Q ]m(tn),vm(tn),vk(tn-1),vl(tn-2)]Dependent only on the current time tnMagnitude of energy Q of time-frequency distributionm(tn) Magnitude of frequency value vm(tn) And the frequency v of the first two instantsm(tn-1) And vm(tn-2) (ii) a Thus, the following relationship can be obtained:
U(m,tn)＝F[Qm(tn),vm(tn),vm(tn-1),vm(tn-2)]+U(m,tn-1) (9)
it should be noted that the peak point of the energy at each time is not the same, i.e., Np(tn) Not equal to a constant; to solve this problem, Qm(tn),νm(tn),vm(tn-1),νm(tn-2) And Um(tn-1) Is mapped to a three-dimensional matrix
Figure BDA0002605107240000045
The method comprises the following steps:
Figure BDA0002605107240000046
Figure BDA0002605107240000047
three-dimensional matrix
Figure BDA0002605107240000048
Is of size Np(tn)×Np(tn-1)×Np(tn-2) (ii) a This matrix is a parameter for storing temporary variables, which are stored at each time tnWill be updated; at time tnAt the moment of time, the time of day,
Figure BDA0002605107240000049
is first selected and determined to be located at jth(ii) a Therefore, make
Figure BDA00026051072400000410
Frequency point i of maximum valuethCan also be determined, another variable q (m, t) can be definedn) I, storing connection information of the ridge line; so that the dynamic algorithm function, equation (9), accumulates to point vm(tn) Has a value of
Figure BDA00026051072400000411
Finally, q (m, t)n) And U (m, t)n) Updating in sequence at each time point;
from the three-dimensional matrix, q (m, t) can be determinedn) And U (m, t)n) Finally, a two-dimensional matrix shown in fig. 6 is formed;
after the above process is completed, the matrix q (m, t)n) All connection information of the lifting line ridge is contained; the optimal result can be in U (m, t)N) Obtaining; v ism(tN) By the formula: m isc(tN)＝arg maxmU(m,tN) Obtaining; for the same reason, all ridge position points that promote the optimal path may be from mc(tN) To mc(t1) Are obtained in turn.
In the matrix of FIG. 6, it needs to be in U (m, t)N) Find the maximum value in since q (m, t)n) The connection information of the ridge lines is included, so that all the optimal points on the ridge lines can be sequentially traced forwards; finally, the ridge line on the time-frequency diagram can be extracted, as shown in fig. 7. By comparing the real frequency conversion, the fact that the instantaneous frequency conversion obtained by the ridge line extraction algorithm is basically consistent with the real frequency conversion can be found, and the engineering requirements can be met.
Step S4, according to the instantaneous frequency m, through the extracted ridge line, i.e. the instantaneous frequencyc(tn) Converting the relation with the rotating speed V to obtain the instantaneous rotating speed of the rotating machine;
V＝60*mc(tn) (12)
by comparing the real frequency conversion, it can be found that the instantaneous frequency conversion obtained by the ridge line extraction algorithm is basically consistent with the real frequency conversion, as shown in fig. 7, and the engineering requirements can be met.
The embodiment of the present application further provides a device for estimating an instantaneous rotational speed of a rotating machine based on time-frequency transformation, including:
a memory storing a computer program;
a processor for executing the computer program to implement the steps of the time-frequency transform-based method for estimating an instantaneous rotational speed of a rotating machine according to any one of the above.
Embodiments of the present application provide a storage medium,
the storage medium has a computer program stored therein, and the computer program is used for implementing the steps of the time-frequency transform-based rotating machine instantaneous rotation speed estimation method described in any one of the above.
Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to examples, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (7)

1. A rotating machinery instantaneous speed estimation method based on time-frequency transformation is characterized by comprising the following steps:
step S1, collecting a rotary mechanical vibration signal S (t);
step S2, obtaining the time-frequency distribution of the vibration signal by time-frequency analysis;
step S3, obtaining the estimation of the instantaneous frequency from the time-frequency distribution by using a ridge line extraction algorithm;
step S4, according to the instantaneous frequency m, through the extracted ridge line, i.e. the instantaneous frequencyc(tn) The relationship with the rotation speed V is converted to obtain the instantaneous rotation speed of the rotating machine.
2. The time-frequency transform-based method for estimating the instantaneous rotational speed of a rotating machine according to claim 1, wherein in step S2,
performing time-frequency analysis by adopting short-time Fourier transform to obtain a time-frequency distribution result; the short-time fourier transform uses a sliding window function g (t), and is defined as follows:
Figure FDA0002605107230000011
η represents frequency; in the formula (1), the first and second groups,
Figure FDA0002605107230000012
the time frequency distribution result obtained by short-time Fourier transform.
3. The time-frequency transform-based method of estimating instantaneous rotational speed of a rotating machine according to claim 2,
g (t) is chosen as a gaussian window function, defined as follows:
Figure FDA0002605107230000013
wherein σ is a parameter for adjusting time and frequency resolution;
Figure FDA0002605107230000014
defined as the result of a fourier transform of the window function g (t).
4. The time-frequency transform-based method for estimating instantaneous rotational speed of a rotating machine according to claim 2 or 3,
in the step S3, in the step S,
vm(t) and Qm(t) respectively representing the positions of energy maximum points on the time-frequency distribution and the corresponding energy sizes:
Figure FDA0002605107230000015
Qm(t)≡|Vs g(vm(t)，t)|，m＝1，...，Np(t) (4)
wherein the content of the first and second substances,
Figure FDA0002605107230000016
representing with respect to η pair | Vs gOperator for (eta, t) | derivation, Np(t) represents the number of energy maximum points at each instant; time-frequency ridgeThe lines are shown as
Figure FDA0002605107230000017
Where m isc(t) represents the position of the maximum point of the loss function at each instant t;
solving the optimization problem of the loss function by adopting a dynamic algorithm;
the loss function is expressed as follows:
Figure FDA0002605107230000018
Figure FDA0002605107230000021
wherein v ism(tn) Represents tnPosition of energy maximum point on time-frequency distribution, vk(tn-1) Represents tn-1Position of energy maximum point on time-frequency distribution, vl(tn-2) Represents tn-2The position of an energy maximum value on time-frequency distribution; alpha and beta respectively represent a ridge continuity adjustment factor and a ridge smoothness adjustment factor; ω () and ρ () are as shown in equation (6):
Figure FDA0002605107230000022
then, a dynamic algorithm is used to find the coordinates m of the loss function maximum point of the ridgec(tn) The objective function is optimized in all time series, and the objective function is as follows:
Figure FDA0002605107230000023
the ridge line is represented as
Figure FDA0002605107230000024
Can be obtained by analysisAt each time tnUpper time frequency point vm(tn) There is a history loss function maximum point { m }c(m，t1)，...，mc(m，tn-1) At this point, the dynamic algorithm is expressed as follows:
Figure FDA0002605107230000025
loss function F [ Q ]m(tn)，vm(tn)，vk(tn-1)，vl(tn-2)]Dependent only on the current time tnMagnitude of energy Q of time-frequency distributionm(tn) Magnitude of frequency value vm(tn) And the frequency v of the first two instantsm(tn-1) And vm(tn-2) (ii) a The following relationship is obtained:
U(m，tn)＝F[Qm(tn)，vm(tn)，vm(tn-1)，vm(tn-2)]+U(m，tn-1) (9)
Qm(tn)，vm(tn)，vm(tn-1)，vm(tn-2) And Um(tn-1) Is mapped to a three-dimensional matrix
Figure FDA00026051072300000212
Middle (as shown in fig. 5):
Figure FDA0002605107230000026
Figure FDA0002605107230000027
three-dimensional matrix
Figure FDA0002605107230000028
Is of size Np(tn)×Np(tn-1)×Np(tn-2) (ii) a This matrix is a parameter for storing temporary variables, which are stored at each time tnWill be updated; at time tnAt the moment of time, the time of day,
Figure FDA0002605107230000029
is first selected and determined to be located at jth(ii) a Therefore, make
Figure FDA00026051072300000210
Frequency point i of maximum valuethCan also be determined, defining another variable q (m, t)n) I, storing connection information of the ridge line; so that the dynamic algorithm function, equation (9), accumulates to point vm(tn) Has a value of
Figure FDA00026051072300000211
Finally, q (m, t)n) And U (m, t)n) Updating in sequence at each time point;
after the above process is completed, the matrix q (m, t)n) All connection information of the lifting line ridge is contained; the optimal result can be in U (m, t)N) Obtaining; v. ofm(tN) By the formula: m isc(tN)＝arg maxmU(m，tN) Obtaining; for the same reason, all ridge position points that promote the optimal path may be from mc(tN) To mc(t1) Are obtained in turn.
5. The time-frequency transform-based method for estimating the instantaneous rotational speed of a rotating machine according to claim 1 or 2, wherein in step S4,
instantaneous frequency mc(tn) The relationship with the rotation speed V is expressed as follows:
V＝60*mc(tn) (12)。
6. a rotating machinery instantaneous speed estimation device based on time-frequency transformation is characterized by comprising the following components:
a memory storing a computer program;
a processor for executing the computer program for implementing the steps of the time-frequency transform based method for estimating an instantaneous rotational speed of a rotating machine according to any of claims 1 to 5.
7. A storage medium characterized in that,
the storage medium has stored therein a computer program which, when being executed by a processor, is adapted to carry out the steps of the method for estimating an instantaneous rotational speed of a rotating machine based on time-frequency transformation according to any one of claims 1 to 5.
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CN113565584A (en) * 2021-08-10 2021-10-29 西安交通大学 Time-frequency filtering method for leaf-end timing signals
CN113565584B (en) * 2021-08-10 2022-08-09 西安交通大学 Time-frequency filtering method for leaf-end timing signals
CN114062708A (en) * 2021-11-23 2022-02-18 中国航发哈尔滨轴承有限公司 Rotating speed non-contact measuring system and measuring method for rotating machinery
CN114492539A (en) * 2022-02-21 2022-05-13 西南交通大学 Bearing fault detection method and device, electronic equipment and storage medium
CN116010806A (en) * 2023-03-28 2023-04-25 湖北工业大学 Time-frequency analysis method for rotary mechanical time-varying multi-component signal
CN116010806B (en) * 2023-03-28 2023-09-01 湖北工业大学 Time-frequency analysis method for rotary mechanical time-varying multi-component signal

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