Online real-time identification method of vibration frequency based on dynamic response

Abstract

A method for online real-time identification of vibration frequency based on dynamic response, the method utilizes the mass, stiffness and damping of the measured system, measures the displacement, velocity or acceleration response of the system in real time, and uses the proposed frequency estimation expression to obtain the system's excitation frequency online in real time. This method utilizes the real-time response signal of the measured system, such as displacement, velocity or acceleration signal, to achieve real-time online identification of vibration frequency, so it can be used for online real-time monitoring of mechanical system excitation frequency and robustness design of vibration suppression controller; the algorithm of the present invention is simple, the calculation efficiency is high, the relative accuracy is high, and it is suitable for full-band identification. It solves the problems of slow identification speed, low accuracy, low efficiency, and narrow applicable frequency band in existing vibration frequency identification methods, and has rich application prospects and practical significance.

Description

Technical Field

[0001] The invention relates to an identification method, in particular to an online real-time identification method of vibration frequency based on dynamic response, which can be used for real-time monitoring of excitation frequency of a mechanical system. Background Art

[0002] Vibration is a common phenomenon in human production and life. In most cases, vibration is harmful and needs to be controlled. For example, mechanical structures subjected to vibration will suffer fatigue failure of materials due to alternating stress caused by vibration; vibration will increase the wear of mechanical parts and bring excessive noise; when cutting metal, vibration will cause the surface processing quality of the workpiece to deteriorate. In addition, if the natural frequency of the mechanical structure is close to or consistent with the frequency of external excitation, resonance will occur, causing large deformation or even failure of the mechanical structure. In order to reduce the harm of vibration and ensure the safe and reliable operation of mechanical equipment, it is very important to measure and monitor mechanical vibration in real time.

[0003] Vibration measurement is mainly divided into two categories, time domain vibration information measurement and frequency domain vibration information measurement. Time domain vibration information measurement includes displacement information measurement, velocity information measurement and acceleration information measurement. For the three different vibration signals of displacement, velocity and acceleration, there are corresponding mature sensor products, which include contact sensors and non-contact sensors. For frequency domain vibration information measurement, that is, for the acquisition of information on the vibration frequency of the measured system, there are currently two processing methods. The first is based on the time domain vibration signal of the measured system, using the Fourier transform method to obtain the vibration frequency of the system; the second is also based on the time domain signal of the measured system, and the zero point, peak and trough of the time domain signal are captured through signal conditioning, and then the vibration period and frequency are calculated and converted. In summary, in the field of vibration measurement, the time domain vibration information measurement method has developed very maturely and has been well applied in engineering, while the frequency domain vibration information measurement method still has some problems that need to be solved: the existing frequency identification methods are mostly based on vibration displacement, velocity or acceleration time domain signals, which are converted using signal processing methods such as Fourier transform. Frequency identification takes a long time, is inefficient, has a narrow applicable bandwidth, and cannot achieve online real-time frequency identification. Summary of the invention

[0004] The purpose of the present invention is to solve the problems of vibration frequency identification methods widely existing in current mechanical systems, such as long identification time, low efficiency, inability to achieve online real-time identification, narrow applicable bandwidth and low robustness of vibration suppression controllers. A method for online real-time identification of vibration frequency based on dynamic response is provided. The method utilizes the real-time response signal of the system under test, such as displacement, velocity or acceleration signal, to achieve real-time online identification of vibration frequency. Therefore, it can be used for online real-time monitoring of the excitation frequency of the mechanical system and robustness design of the vibration suppression controller.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] The online real-time identification method of vibration frequency based on dynamic response is as follows: Figure 1 As shown, by utilizing the mass, stiffness and damping of the system under test and measuring the displacement, velocity or acceleration response of the system in real time, the proposed frequency estimation expression is used to obtain the system's excitation frequency online in real time.

[0007] Furthermore, the method for online real-time identification of vibration frequency by real-time measurement of the displacement of the system is specifically as follows:

[0008] For a single degree of freedom mass-spring-damper system, such as Figure 2 As shown, its dynamic model is:

[0009]

[0010] Where m is mass, d is the differential symbol, t is time, x is the displacement of the system, c is the damping, k is the spring stiffness, and f(t) = F 0 sin(ωt+φ) is the external excitation acting on the system, F 0 is the excitation amplitude, ω is the frequency to be measured, and φ is the phase difference of the excitation.

[0011] Differentiating equation (1) twice with respect to time yields

[0012]

[0013] Multiply both sides of equation (1) by ω 2 get

[0014]

[0015] Adding equations (2) and (3) together we get

[0016]

[0017] Multiply both sides of formula (4) get

[0018]

[0019] In the formula, t 0 ≥0 indicates the start time of frequency estimation. Integrating equation (5) four times over time and performing partial integration can yield the following equation:

[0020]

[0021] Where r 4 ,p4 is an intermediate variable, and the expression is as follows

[0022]

[0023] In the formula, r 1 ,r 2 ,r 3 ,p 1 ,p 2 and p 3 All are intermediate parameters.

[0024] From equation (6), we can see that using only a small time interval [t 0 ,t 0 +ε], the external excitation frequency ω can be explicitly calculated, where ε is the time required for successful frequency identification.

[0025]

[0026] In the formula, Represents the estimated frequency obtained by this method, γ represents the filter gain, which is usually taken as 0.01, and e is the natural base.

[0027] Furthermore, the start time of frequency estimation is t 0 It can be adaptively readjusted according to the change of external excitation frequency. This strategy can effectively cope with the situation of external excitation frequency change. Figure 3 As shown, the frequency identification process can be divided into two parts, the transient stage and the steady-state stage. The duration of the transient stage is defined as t 1 , the difference value d is the difference between the frequency estimate of the current step and the frequency estimate of the previous step divided by the step length; D 1 It is a custom value. When the frequency estimate gradually converges, the difference value d gradually tends to 0. When d<D 1 , identifying the transition from transient stage to steady state stage; similarly, D 2 It is also a custom value. When the excitation frequency changes, the frequency estimate will change, and the differential value d will change from 0 or close to 0 to a larger value than D. 2 , at this time, t 0 Reselect the current time and identify the transition from the steady-state stage to the transient stage, t 1 , D 1 and D 2 It can be selected based on experience and system characteristics.

[0028] Furthermore, the method for online real-time identification of vibration frequency by real-time measurement of the speed or acceleration of the system is specifically as follows:

[0029] For a single degree of freedom mass-spring-damper system, such as Figure 2 As shown, its dynamic model is:

[0030]

[0031] Where m is mass, d is the differential symbol, t is time, x is the displacement of the system, c is the damping, k is the spring stiffness, and f(t) = F 0 sin(ωt+φ) is the external excitation acting on the system, F 0 is the excitation amplitude, ω is the frequency to be measured, and φ is the phase difference of the excitation.

[0032] Differentiate equation (1) once and twice with respect to time, and we get

[0033]

[0034]

[0035] In the formula

[0036] Formulas (9) and (10) are written in the following format:

[0037]

[0038] Where i = 1 or 2, y 1 express y 2 express Corresponding Indicates F 1 cos(ωt+φ), Indicates F 2 sin(ωt+φ).

[0039] The equation obtained by differentiating equation (11) twice with respect to time is multiplied by ω on both sides of equation (11) 2 Adding the obtained equations, we get

[0040]

[0041] Multiply both sides of formula (12) get

[0042]

[0043] In the formula, t 0 ≥0 indicates the start time of frequency estimation. Integrating equation (13) four times over time and performing partial integration can yield the following equation:

[0044]

[0045] In the formula is an intermediate variable, and the expression is as follows

[0046]

[0047] In the formula and is an intermediate parameter.

[0048] From equation (14), we can see that using only a small time interval [t 0 ,t 0 +ε], the external excitation frequency ω can be explicitly calculated, where ε is the time required for successful frequency identification.

[0049]

[0050] In the formula, Represents the estimated frequency obtained by this method, γ represents the filter gain, which is usually taken as 0.01, and e is the natural base.

[0051] Furthermore, the start time of frequency estimation is t 0 It can be adaptively readjusted according to the change of external excitation frequency. This strategy can effectively cope with the situation of external excitation frequency change. Figure 3 As shown, the frequency identification process can be divided into two parts, the transient stage and the steady-state stage. The duration of the transient stage is defined as t 1 , the difference value d is the difference between the frequency estimate of the current step and the frequency estimate of the previous step divided by the step length; D 1 It is a custom value. When the frequency estimate gradually converges, the difference value d gradually tends to 0. When d<D 1 , identifying the transition from transient stage to steady state stage; similarly, D 2 It is also a custom value. When the excitation frequency changes, the frequency estimate will change, and the differential value d will change from 0 or close to 0 to a larger value than D. 2 , at this time, t 0 Reselect the current time and identify the transition from the steady-state stage to the transient stage, t 1 , D 1 and D 2 It can be selected based on experience and system characteristics.

[0052] The beneficial effects of the present invention compared with the prior art are as follows: the algorithm of the present invention is simple, the calculation efficiency is high, the relative accuracy is high, and it is applicable to full-band identification. Through a single real-time response signal (displacement, velocity or acceleration), the real-time online frequency identification of simple harmonic external excitation can be realized, which solves the problems of slow identification speed, low accuracy, low efficiency, and narrow applicable frequency band in the existing vibration frequency identification method, and has rich application prospects and practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the principle of the present invention;

[0054] Figure 2 It is a schematic diagram of a single degree of freedom mass-stiffness-damping system;

[0055] Figure 3 is the frequency identification flow chart and t 0 Adjustment strategy diagram;

[0056] Figure 4 is the displacement response diagram of the system under external excitation shown in formula (19);

[0057] Figure 5 is an identification result diagram under external excitation shown in formula (19);

[0058] Figure 6 is the displacement response diagram of the system under external excitation shown in formula (9);

[0059] Figure 7 is an identification result diagram under external excitation shown in formula (9);

[0060] Figure 8 is the system speed response diagram under external excitation shown in formula (19) in implementation 2;

[0061] Fig. 9 is the identification result diagram under the external excitation shown in formula (19) in implementation 2;

[0062] Fig.10 is the system speed response diagram under external excitation shown in formula (9) in implementation 2;

[0063] Fig.11 is the identification result diagram under the external excitation shown in formula (9) in implementation 2;

[0064] Fig.12 It is the acceleration response diagram of the system under external excitation shown in formula (19) in the implementation of three;

[0065] Fig.13 It is the identification result diagram under the external excitation shown in formula (19) of the third embodiment;

[0066] Fig.14 It is the acceleration response diagram of the system under external excitation shown in formula (9) in the implementation of three;

[0067] Fig.15 It is the identification result diagram under the external excitation shown in formula (9) in the implementation of the third one. DETAILED DESCRIPTION

[0068] The following will be combined with the attached Figure 1 To Attachment Fig.15 Specific implementation cases of the present invention are described in more detail. It should be noted that the present invention can be implemented in various forms and should not be limited by the implementation cases described here. In fact, these implementation cases are provided to enable a more thorough understanding of the present invention and to fully convey the scope of application of the present invention to those skilled in the art. Specific implementation method one:

[0070] The online real-time frequency identification method proposed in the present invention is used to identify the system vibration frequency based on the displacement response signal through numerical simulation. In the implementation case, the mass m is selected as 2kg, the spring stiffness k is 8000N / m, and the damping c is 10N / m. 2 , the filter gain γ is selected as 0.01.

[0071] For a single degree of freedom mass-spring-damper system, as shown in the following Figure 2 As shown, its dynamic model is:

[0072]

[0073] In the formula, d is the differential symbol, m is the mass, k is the stiffness, c is the damping, x is the displacement of the system, t is the time, f(t) = F 0 sin(ωt+φ) is the external excitation acting on the system, with the unit of N.

[0074] Differentiating equation (1) twice with respect to time yields

[0075]

[0076] Multiply both sides of equation (1) by ω 2 get

[0077]

[0078] Adding equations (2) and (3) together we get

[0079]

[0080] Multiply both sides of formula (4) get

[0081]

[0082] In the formula, t 0 ≥0 indicates the start time of frequency estimation. Its adjustment strategy is as shown in the attached Figure 3 As shown. Integrate equation (5) four times with respect to time and perform partial integration to obtain the following equation:

[0083]

[0084] Where r 4 ,p 4 is an intermediate variable, and the expression is as follows

[0085]

[0086] In the formula, r 1 ,r 2 ,r 3 ,p 1 ,p 2 and p 3 All are intermediate parameters.

[0087] From formula (6), we can see that only a small time interval [t 0 ,t 0 +ε] can be used to explicitly calculate the simple harmonic vibration frequency ω. To avoid singularity in the frequency estimation process, filter processing is used on equation (6) to obtain

[0088]

[0089] In the formula, Represents the estimated frequency obtained by this method, γ represents the filter gain, which is usually taken as 0.01, and e is the natural base.

[0090] Example 1: Design simple harmonic excitation as

[0091] F(t)=0.2sin(3×2π×t) (17)

[0092] The displacement response of the system is shown in the attached figure. Figure 4 The frequency identification result is calculated by using formula (8) as shown in the attached figure. Figure 5 It can be seen that the excitation frequency is identified as 3 Hz at t = 0.05 s, and the signal time length used for identification is less than 1 / 6 of the vibration signal period.

[0093] Example 2: Design simple harmonic excitation as

[0094] F(t)=F 0 (t)sin(2πωt) (18)

[0095] In the formula,

[0096]

[0097] The displacement response of the system is shown in the attached figure. Figure 6 The frequency identification result calculated by formula (8) is shown in the attached figure. Figure 7It can be seen that at each frequency stage, the algorithm can quickly identify the real frequency using the system displacement, which shows that the present invention can accurately and quickly identify multiple simple harmonic excitation signals. Specific implementation method 2:

[0099] The parameters and their values ​​in the first specific implementation mode are adopted, and the online real-time frequency identification method proposed in the present invention is utilized to identify the system vibration frequency based on the speed response information through numerical simulation.

[0100] Differentiating equation (1) with respect to time once yields

[0101]

[0102] In the formula

[0103] It can be seen that formula (9) has the same structure as formula (1). By performing the same processing and derivation on formula (9) as in the first embodiment, the explicit expression of vibration frequency based on speed response can be obtained:

[0104]

[0105] In the formula The expression is as follows,

[0106]

[0107] In the formula and is an intermediate parameter.

[0108] Example 3: Using the simple harmonic excitation (17) in the first embodiment, the speed response of the system is as shown in the attached figure. Figure 8 As shown in the figure, the frequency identification result is calculated by using formula (20) as shown in the attached figure. Fig. 9 It can be seen that the excitation frequency is identified as 3 Hz at t = 0.05 s, and the signal time length used for identification is less than 1 / 6 of the vibration signal period.

[0109] Example 4: Using the simple harmonic excitation (18) in the first embodiment, the speed response of the system is as shown in the attached figure. Fig.10 As shown in the figure, the frequency identification result calculated by formula (20) is shown in the attached figure. Fig.11 It can be seen that at each frequency stage, the algorithm can identify the real frequency very quickly, which shows that the present invention can accurately and quickly identify multiple simple harmonic excitation signals. Specific implementation method three:

[0111] The parameters and their values ​​in the first specific implementation mode are adopted, and the online real-time frequency identification method proposed in the present invention is utilized to identify the system vibration frequency based on the acceleration response information through numerical simulation.

[0112] Differentiating equation (1) twice with respect to time yields

[0113]

[0114] In the formula

[0115] It can be seen that formula (10) has the same structure as formula (1). By performing the same processing and derivation on formula (10) as in the first embodiment, the explicit expression of vibration frequency based on speed response can be obtained:

[0116]

[0117] In the formula The expression is as follows,

[0118]

[0119] In the formula and is an intermediate parameter.

[0120] Example 5: Using the simple harmonic excitation (17) in the first embodiment, the acceleration response of the system is as shown in the attached figure. Fig.12 As shown in the figure, the frequency identification result is calculated by using formula (22) as shown in the attached figure. Fig.13 It can be seen that the excitation frequency is identified as 3 Hz at t = 0.08 s, and the signal time length used for identification is less than 1 / 4 of the vibration signal period.

[0121] Example 6: Using the simple harmonic excitation (18) in the first embodiment, the speed response of the system is as shown in the attached figure. Fig.14 As shown in the figure, the frequency identification result calculated by formula (22) is shown in the attached figure. Fig.15 It can be seen that at each frequency stage, the algorithm can identify the real frequency very quickly, which shows that the present invention can accurately and quickly identify multiple simple harmonic excitation signals.

[0122] The above three implementation modes and six examples thereof can provide a more thorough understanding of the present invention and its implementation, and more intuitively demonstrate the excellent frequency identification performance and huge engineering application potential of the present invention.

[0123] For the identification method using displacement or velocity response, the frequency value can be accurately calculated within 0.05s, and for the identification method using acceleration response, the frequency value can be accurately calculated within 0.08s. As in implementations 1, 2, and 3, whether it is fixed frequency simple harmonic excitation or variable frequency simple harmonic excitation, the frequency identification method based on displacement, velocity, and acceleration response in the present invention can accurately and quickly identify the vibration frequency.

Claims

1. A method for online real-time identification of vibration frequency based on dynamic response, characterized in that: Based on the mass, stiffness and damping of the measured system, the proposed frequency estimation expression is used to obtain the system's excitation frequency online in real time by measuring the system's displacement response in real time. The vibration frequency is identified online in real time by measuring the system's displacement in real time. The principle is as follows: For a single degree of freedom mass-spring-damper system, its dynamic model is: Where m is mass, d is the differential symbol, t is time, x is the displacement of the system, c is the damping, k is the spring stiffness, f(t) = F0 sin(ωt+φ) is the external excitation acting on the system, F0 is the excitation amplitude, ω is the frequency to be measured, and φ is the phase difference of the excitation; Differentiating equation (1) twice with respect to time yields Multiply both sides of equation (1) by ω 2 get Adding equations (2) and (3) together we get Multiply both sides of formula (4) get In the formula, t0≥0 represents the start time of frequency estimation. By integrating the time four times in formula (5) and performing partial integration, the following equation can be obtained: In the formula, r4 and p4 are intermediate variables, and the expression is as follows: In the formula, r1, r2, r3, p1, p2 and p3 are all intermediate parameters; From equation (6), it can be seen that the external excitation frequency ω can be explicitly calculated using only the displacement signal within a small time interval [t0, t0+ε], where ε is the time required for successful frequency identification, In the formula, represents the estimated frequency, γ represents the filter gain, and e is the natural base; The start time of frequency estimation can be adaptively readjusted according to the change of external excitation frequency. This strategy can be used to effectively cope with the change of external excitation frequency. The frequency identification process can be divided into two parts, the transient stage and the steady-state stage. The frequency difference value is defined as the difference between the frequency estimation value of the current step and the frequency estimation value of the previous step divided by the step size. The initial process of frequency identification is a transient process. In this stage, when the frequency difference value converges, the frequency estimation value also approaches the true value, and the identification process enters the steady-state stage. In this stage, if the frequency difference value changes suddenly, it means that the excitation frequency has changed. At this time, the start time of the frequency estimation is updated to the current moment. The above is the adjustment strategy for the start time of frequency estimation in response to the change of external excitation frequency.

2. The online real-time identification method of vibration frequency based on dynamic response is characterized by: Based on the mass, stiffness and damping of the system under test, the system's velocity response is measured in real time, and the proposed frequency estimation expression is used to obtain the system's excitation frequency online in real time. The vibration frequency is identified online in real time by measuring the system's velocity in real time. The principle is as follows: For a single degree of freedom mass-spring-damper system, its dynamic model is: Where m is mass, d is the differential symbol, t is time, x is the displacement of the system, c is the damping, k is the spring stiffness, f(t) = F0 sin(ωt+φ) is the external excitation acting on the system, F0 is the excitation amplitude, ω is the frequency to be measured, and φ is the phase difference of the excitation; Differentiate equation (1) with respect to time, and we get In the formula Formula (9) can be written as follows: In the formula, i=1, y1 represents The corresponding fy1(t) represents F1cos(ωt+φ); The equation obtained by differentiating equation (11) twice with respect to time is multiplied by ω on both sides of equation (11) 2 Adding the obtained equations, we get Multiply both sides of formula (12) get In the formula, t0≥0 represents the start time of frequency estimation. By integrating the time four times in formula (13) and performing partial integration, the following equation can be obtained: In the formula is an intermediate variable, and the expression is as follows In the formula and is the intermediate parameter; From equation (14), it can be seen that the external excitation frequency ω can be explicitly calculated using only the displacement signal within a small time interval [t0, t0+ε], where ε is the time required for successful frequency identification, In the formula, represents the estimated frequency, γ represents the filter gain, and e is the natural base; The start time of frequency estimation can be adaptively readjusted according to the change of external excitation frequency. This strategy can be used to effectively cope with the change of external excitation frequency. The frequency identification process can be divided into two parts, the transient stage and the steady-state stage. The frequency difference value is defined as the difference between the frequency estimation value of the current step and the frequency estimation value of the previous step divided by the step size. The initial process of frequency identification is a transient process. In this stage, when the frequency difference value converges, the frequency estimation value also approaches the true value, and the identification process enters the steady-state stage. In this stage, if the frequency difference value changes suddenly, it means that the excitation frequency has changed. At this time, the start time of the frequency estimation is updated to the current moment. The above is the adjustment strategy for the start time of frequency estimation in response to the change of external excitation frequency.

3. The online real-time identification method of vibration frequency based on dynamic response is characterized by: Based on the mass, stiffness and damping of the system under test, the proposed frequency estimation expression is used to obtain the system's excitation frequency online in real time by measuring the acceleration response of the system in real time. The vibration frequency is identified online in real time by measuring the acceleration of the system in real time. The principle is as follows: For a single degree of freedom mass-spring-damper system, its dynamic model is: Where m is mass, d is the differential symbol, t is time, x is the displacement of the system, c is the damping, k is the spring stiffness, f(t) = F0 sin(ωt+φ) is the external excitation acting on the system, F0 is the excitation amplitude, ω is the frequency to be measured, and φ is the phase difference of the excitation; Differentiate equation (1) twice with respect to time, and we get In the formula Formula (10) can be written as follows: In the formula, i=2, y2 represents Corresponding represents F2sin(ωt+φ); The equation obtained by differentiating equation (11) twice with respect to time is multiplied by ω on both sides of equation (11) 2 Adding the obtained equations, we get Multiply both sides of formula (12) get In the formula, t0≥0 represents the start time of frequency estimation. By integrating the time four times in formula (13) and performing partial integration, the following equation can be obtained: In the formula is an intermediate variable, and the expression is as follows In the formula and is the intermediate parameter; From equation (14), it can be seen that the external excitation frequency ω can be explicitly calculated using only the displacement signal within a small time interval [t0, t0+ε], where ε is the time required for successful frequency identification, In the formula, represents the estimated frequency, γ represents the filter gain, and e is the natural base; The start time of frequency estimation can be adaptively readjusted according to the change of external excitation frequency. This strategy can be used to effectively cope with the change of external excitation frequency. The frequency identification process can be divided into two parts, the transient stage and the steady-state stage. The frequency difference value is defined as the difference between the frequency estimation value of the current step and the frequency estimation value of the previous step divided by the step size. The initial process of frequency identification is a transient process. In this stage, when the frequency difference value converges, the frequency estimation value also approaches the true value, and the identification process enters the steady-state stage. In this stage, if the frequency difference value changes suddenly, it means that the excitation frequency has changed. At this time, the start time of the frequency estimation is updated to the current moment. The above is the adjustment strategy for the start time of frequency estimation in response to the change of external excitation frequency.

Images