Method for diagnosing rotor rub-impact in rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement

Abstract

A method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement, including: converting, based on two-stage integration transformation and high-pass filtering, vibratory acceleration signals from a rotating machinery device into vibratory displacement signals; performing targeted extraction on a rotating frequency component therein based on an improved variational mode decomposition method; calculating and estimating instantaneous fluctuation characteristics of a fundamental frequency of the extracted rotating frequency component using a quadrature-derivative-based normalized Hilbert transform to obtain an instantaneous frequency; inputting a calculated instantaneous frequency sequence into an optimum stochastic resonance system for anti-noise enhancement of intrawave frequency modulation characteristics; and processing FFT on an instantaneous frequency of intrawave frequency modulation characteristics after anti-noise enhancement, and diagnosing and identifying a rotor rub-impact fault of the rotating machinery based on a distribution characteristic of harmonic amplitudes related to a rotor rotating frequency.

Description

TECHNICAL FIELD

The present disclosure belongs to the field of condition monitoring and fault diagnosis of rotating machineries, and particularly relates to a method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement.

BACKGROUND

The structural rotor is one of the most pivotal components of rotor-system-based rotating machineries, such as wind turbines, rotary compressors, centrifugal pumps, and generator sets, which have occupied a crucial place in numerous modern applications, including mining, metallurgy, energy production, and transportation. Due to the extreme and harsh operating conditions, structural rotors can be subjected to a variety of potential malfunctions, for instance, imbalance, cracking, misalignment, looseness, oil whirl, cocked, and so on. As a frequently occurring failure exhibiting nonlinearities, a rub-impact fault happens when the rotor cyclically strikes the rotor system's stator, the cause of which usually can be the initial subtle imbalance and faint misalignment of the rotor, especially when the shaft is at a tremendously high rotational speed and the radial clearance between the stator and the rotor is considerably faint, the rub-impact fault of the rotor is very likely to occur. As a matter of fact, with the higher requirements and more stringent specifications of assembly precision, today's machine structure of most power equipment has become relatively more sophisticated and more compact, parts of which operates under extremely diminutive clearance, making the occurring probability of rub-impact in the rotor system increase more impressively. Once the rub-impact fault occurs, it can induce the rotor system dynamic instability and attenuate the operating accuracy of a machine to a large extent, and provoke prejudicial impacts on the concerned power equipment's structural attributes and performance as well as bring about extra defects to the parts associated with it, like bearings and impellers, which will eventually result in system-wide catastrophic failures. Therefore, it is of extremely important practical engineering significance to perform condition monitoring and fault diagnosis on rotor systems for detecting the initial occurrence of incipient rub-impact faults, which can effectively promote the equipment prognosis and health management level and guarantee the safe and stable production of industries.

At present, there are generally the following methods for monitoring and diagnostic analysis of the rotor rub-impact fault of the rotating machinery:

(1) Based on a conventional spectrum analysis technology, a rotating frequency, a half frequency, a high-order harmonic frequency and the like corresponding to fault characteristics that may exist in a Fourier spectrum of a collected vibration signal and include synchronous vibration, subsynchronous vibration as well as supersynchronous vibration. However, these frequency characteristic symptoms may also occur when other types of faults occur in the machine, for example, rotor shaft cracking and mechanical looseness, and these characteristic representations are not significant at an early stage of the generation of the rotor rub-impact fault in the rotating machinery, and are difficult to detect in time.

(2) An impact generated by a quasi-periodic contact and separation process between the rotor and the stator in a time-domain signal is observed, methods such as signal deconstruction is generally required to effectively separate and extract the component, which mainly includes empirical mode decomposition, blind source separation, empirical wavelet transform, etc. However, when other parts of the rotating machinery fail, similar fault symptoms may also be generated, such as gear defects and partial damage of the rolling bearing, and different noise distribution forms and noise degrees also tend to affect the effectiveness and availability of a signal deconstruction result.

(3) An intelligent method based on data driving mainly includes a set of end-to-end flow as “data pre-processing-characteristic extraction-characteristic selection/dimension reduction-characteristic learning-diagnosis output”, and the mainstream methods involved include a support vector machine, a random forest, a deep belief network, a convolutional neural network, etc. However, on the one hand, these methods usually require training and learning through a large number of identically-distributed high-quality data samples with labels, and are difficult to meet in a practical condition; and on the other hand, opacity and unexplainability of those deep intelligent diagnosis models make them “black boxes”, and the diagnosis conclusion output thereby is difficult to be fully trusted in practical applications.

(4) A rotor rub-impact fault diagnosis technology of the rotating machinery based on nonlinear random kinetic behaviour analysis mainly includes a Volterra series identification and nonlinear output frequency response function estimation method, and the like. However, such method is generally relatively complex in calculation, and a certain amount of calculation and analysis time is required to obtain a reliable diagnosis result of the rotor rub-impact fault, which is generally difficult to satisfy the timeliness of implementing on-line monitoring and diagnosis in practical engineering applications.

(5) A method such as a rotor rub-impact diagnosis technology based on vibration signal amplitude modulation and frequency modulation characteristic extraction usually involves time-frequency domain analysis of the signal, and mainly includes short-time Fourier transform (STFT), continuous wavelet transform (CWT), Hilbert-Huang transform (HHT), and adaptive chirp mode decomposition (ACMD) and the like. However, such method is generally less robust in the case of noise interference, and tends to face failure when analyzing and processing vibration data with a low signal-to-noise ratio, which greatly limits the practical application of these methods.

It can be seen that the existing various methods for monitoring and diagnosing analysis of the rotor rub-impact fault of the rotating machinery all have their respective defects and deficiencies. Therefore, there is a need to develop an efficient method for the rotor rub-impact diagnosis of the rotating machinery, which can detect the early rotor rub-impact fault of the rotating machinery in a timely manner in a complex environment, can effectively improve the prognosis and health management level of the device, and has extremely important practical engineering significance. In addition, since a displacement signal usually has a high signal-to-noise ratio and can accurately reflect a vibration condition of the rotor, the above method mostly performs diagnosing analysis of a rotor system based on the vibratory displacement signal. However, it should be noted that although a displacement sensor has advantages such as a large linear range, a zero frequency response, a strong anti-interference capability, and easy calibration, its practical application is not as extensive as an acceleration sensor, and is generally and only applicable to monitoring of the rotor system of a large rotating machinery, and is mainly limited by complex installation requirements, economic considerations, and other factors. Therefore, in some cases, the method for diagnosing rotor rub-impact in the rotating machinery based on the vibratory displacement signal analysis may be difficult to meet practices and cannot be implemented, and thus it is necessary to study and apply more general and universal advanced diagnosis strategies, because the rotor rub-impact fault may occur in various rotating machineries based on the rotor system.

SUMMARY

In order to solve the above problems of the prior art, the present disclosure provides a method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement, which may diagnose and discriminate a rotor rub-impact fault of a rotating machinery of power equipment under intricate noise interferences based on vibratory acceleration signal analysis.

The objective of the present disclosure is achieved by the following technical solutions:

A method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement includes:

Step 1: collecting, by a vibration acceleration sensor, a signal sequence from a rotating machinery device.

Step 2: converting, based on two-stage integration transformation and high-pass filtering, a collected vibratory acceleration signal into a vibratory displacement signal.

Step 3: performing targeted extraction on a rotating frequency component in the vibratory displacement signal based on an improved variational mode decomposition method.

Step 4: calculating and estimating instantaneous fluctuation characteristics of a fundamental frequency of the extracted rotating frequency component using a quadrature-derivative-based normalized Hilbert transform to obtain an instantaneous frequency.

Step 5: inputting a calculated instantaneous frequency sequence into an optimum stochastic resonance system for anti-noise enhancement of intrawave frequency modulation characteristics, wherein potential energy parameters of a stochastic resonance system and a step length of a Runge-Kutta calculation process are optimized by a particle swarm optimization algorithm to obtain the optimum stochastic resonance system.

Step 6: processing fast Fourier transform on the instantaneous frequency of the intrawave frequency modulation characteristics after anti-noise enhancement, and diagnosing and identifying a rotor rub-impact fault of the rotating machinery based on a distribution characteristic of harmonic amplitudes related to a rotor rotating frequency.

Compared with the prior art, the present disclosure has the following beneficial effects:

Aiming at defects and deficiencies of the existing rotor rub-impact fault diagnosis and analysis technology of the rotating machinery of the power equipment, the present disclosure provides to take vibratory acceleration signal analysis processing as a main manner, convert the vibratory acceleration signal into the vibratory displacement signal through two-stage integration transformation, perform targeted extraction on the rotating frequency component therein based on a signal deconstruction method, then calculate and estimate an instantaneous frequency of the rotating frequency component, then input the obtained instantaneous frequency sequence into the optimum stochastic resonance system for intrawave modulation characteristic anti-noise enhancement, then process fast Fourier transform on the outputted instantaneous frequency subjected to frequency modulation characteristic enhancement, and finally diagnose and identify the rotor rub-impact fault of the rotating machinery based on the distribution characteristics of the harmonic amplitudes related to the rotor rotating frequency. This method is based on a vibratory acceleration signal processing technology used more widely and commonly, and has excellent robustness to the inevitable intricate noise interferences in the signal collection and signal transformation processing process in industrial environments, making it of significant importance for practical engineering applications.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic flow diagram of a method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement of the present disclosure.

FIG. 2 is a time-domain waveform diagram of a vibratory acceleration signal sequence collected from a centrifugal pump via a vibration acceleration sensor in an embodiment of the present disclosure.

FIG. 3 is a time-domain waveform diagram of a vibratory displacement signal converted from a vibratory acceleration signal via two-stage integration transformation and high-pass filtering in an embodiment of the present disclosure.

FIG. 4 is a spectrum diagram of a vibratory displacement signal converted from a vibratory acceleration signal via two-stage integration transformation and high-pass filtering in an embodiment of the present disclosure.

FIG. 5 is a time-frequency diagram of a rotating frequency component in a vibratory displacement signal extracted via an improved variational mode decomposition method in an embodiment of the present disclosure.

FIG. 6 is a spectrum diagram of an instantaneous frequency of a rotating frequency component estimated using a quadrature-derivative-based normalized Hilbert transform in an embodiment of the present disclosure.

FIG. 7 is a spectrum diagram of an instantaneous frequency with frequency modulation characteristic enhancement outputted by an optimum stochastic resonance system in an embodiment of the present disclosure.

FIGS. 8(a)-8(c) show the analysis results of HHT and ACMD, where FIG. 8(a) shows time-frequency representation (TFR) of HHT, FIG. 8(b) shows TFR of ACMD, and FIG. 8(c) shows Fourier spectrum of the instantaneous frequency (IF) extracted by ACMD.

DESCRIPTION OF EMBODIMENTS

The present disclosure will be described below in detail with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present disclosure will become more apparent. It should be understood that the specific embodiments described here are only intended to explain the present disclosure, but not to limit the present disclosure.

The present disclosure is based on vibratory acceleration signal analysis to first convert a vibratory acceleration signal into a vibratory displacement signal through two-stage integration transformation, then perform targeted extraction on a rotating frequency component therein via a signal deconstruction method, then calculate and estimate an instantaneous frequency of the rotating frequency component, then input an obtained instantaneous frequency sequence into an optimum stochastic resonance system for intrawave modulation characteristic anti-noise enhancement, finally perform fast Fourier transform processing on the instantaneous frequency subjected to frequency modulation characteristic enhancement outputted by optimum stochastic resonance, and diagnose and identify a rotor rub-impact fault of a rotating machinery based on distribution characteristics of harmonic amplitudes related to the rotor rotating frequency, thereby providing important technical support for timely monitoring, control, safe and efficient operation and maintenance of the operation condition of the rotor system of the rotating machinery of the power equipment.

As shown in FIG. 1, a method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement includes the following steps: step 1: collecting, by a vibration acceleration sensor, a signal sequence from a rotating machinery device.

In an example, the vibration acceleration sensor is rigidly connected to the target rotating machinery device to collect a vibration signal sequence for a certain time. The collected vibration signal sequence is transmitted to a data acquisition unit based on wireless communication or wired transmission that complies with the ISO standard protocol. The data acquisition unit converts the vibration signal sequence from an analog signal type to a digital signal type, and then transmits the vibration signal sequence after conversion to the digital signal type to a memory where the main control unit is located through the wireless communication or wired transmission that complies with the ISO standard protocol, thereby completing the data collection process of the vibration acceleration signal sequence.

In step 1, the signal sequence collected from the rotating machinery device through the vibration acceleration sensor is recorded as S_ao(i), i=1, 2, 3, . . . , N, where N is the number of total sampling points, and a sampling frequency is recorded as f_s. In a signal collecting process, a frequency response parameter of the used vibration acceleration sensor should be not less than 2 kHz, a sampling frequency of a vibration signal sequence should be not less than 5.12 kHz and not greater than 100 kHz, and a sampling duration should be not less than 1 s.

Step 2: converting, based on two-stage integration transformation and high-pass filtering, a collected vibratory acceleration signal into a vibratory displacement signal:

(2-1) one integration is performed first to convert the vibratory acceleration signal S_ao into a vibratory velocity signal, as follows:S_vo(1)=0,S_vo(i)=S_vo(i−1)+S_a(i−1)×ΔT,i=2,3, . . . ,N+1,where ΔT=1/f_s, S_a is obtained by filtering a signal S_ao through a high-pass filter. In order to avoid the adverse effect of an extremely low-frequency component in an original vibration signal on a final integral result, a cut-off frequency W_BG1 of the high-pass filter is generally taken from 10 Hz to 25 Hz so as to obtain a better signal integral result.

(2-2) Then, an extremely low-frequency component of the obtained vibratory velocity signal S_a, is also removed through a high-pass filter, and a cut-off frequency W_BG2 of the filter is taken from 10 Hz to 25 Hz so as to obtain a filtered signal S_v. Then an integration operation is performed on S_v to obtain a final vibratory displacement signal S_x:S_x(i)=(S_v(1)+S_v(2))/2×ΔT, S_x(i)=S_x(i−1)+(S_v(i)+S_v(i+1))/2×ΔT,i=2,3, . . . ,N.

In the step 2, a high-pass filter with a stopband attenuation of 60 dB is used to perform zero-phase filtering on the vibratory acceleration signal and the vibratory velocity signal, respectively, and the high-pass filter attenuates a frequency lower than a specified passband frequency, which is able to compensate for a delay introduced by a digital filter.

Step 3: performing targeted extraction on a rotating frequency component in the vibratory displacement signal based on an improved variational mode decomposition. Step 3 includes the following sub-steps:

(3-1) First, a series of intrinsic mode functions u_k(t), k∈(1, 2, . . . , K), with K being the total number of modes, with respect to the signal S_x are defined as a series of amplitude modulation-frequency modulation signals, which may be expressed as:u_k(t)=A_k(t)cos(φ_k(t)),where A_k(t) and φ_k(t) represent an instantaneous amplitude and an instantaneous phase, respectively, and φ_k (t) is a nondecreasing function, that is, the instantaneous frequency always satisfies ω_k(t)=d[φ_k(t)]/dt≥0. Compared with φ_k(t), rates of change of A_k(t) and ω_k(t) are almost extremely slow, so these intrinsic mode functions may be regarded as a series of bandwidth-limited signals, which may be expressed by a calculus of variations as:

${\mathrm{BW}}_k={{\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)*u_k\left(t\right)\right]e^{-j{\omega }_{k}t}}_2,$ where δ(⋅) is a Dirac function, and * is a convolution manipulator; and BW_k is a norm of a bandwidth of u_k(t) in a frequency domain. So far, a constrained variational problem may be remodeled as:

$\underset{\left\{u_k\right\},\left\{{\omega }_k\right\}}{\min }\left\{{\sum }_{k=1}^K{{\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)*u_k\left(t\right)\right]e^{-j{\omega }_{k}t}}_2^2\right\}\mathrm{subject}\mathrm{to}{\sum }_{k=1}^K{u}_k\left(t\right)=S_x\left(t\right),$ where ω_k represents a center frequency of K intrinsic mode functions, k∈(1, 2, . . . , K).

(3-2) A quadratic penalty term and a Lagrangian multiplier term are introduced to address a minimization problem, as follows:

$L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \right)=\alpha {\sum }_{k=1}^K{{\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)*u_k\left(t\right)\right]e^{-j{\omega }_{k}t}}_2^2+{S_x\left(t\right)-{\sum }_{k=1}^K{u}_k\left(t\right)}_2^2+\langle \lambda \left(t\right),S_x\left(t\right)-{\sum }_{k=1}^K{u}_k\left(t\right)\rangle ,$ where α represents a bandwidth balance parameter, and λ(t) is a Lagrangian multiplier coefficient. The equation is resolved via an alternate direction Lagrangian multiplier method, so as to obtain K intrinsic mode functions u_k(t), k∈(1, 2, . . . , K) with respect to the vibratory displacement signal S_x(t).

(3-3) A rotating frequency component in the vibratory displacement signal S_x is extracted based on an improved variational mode decomposition method, that is, before performing the variational mode decomposition and the intrinsic mode function extraction on the signal S_x, the mode number K is set to be 1, an initial bandwidth balance parameter α is set to be 5000, an initial central frequency of a mode is set to be a rotating frequency f_roc, and a target frequency index MTFI is used to evaluate a spectrum definition of a signal deconstruction result, wherein an optimal parameter of a deconstruction algorithm is obtained by performing optimization via forward and reverse alternate iterations.

A calculation formula of the target frequency index MTFI is as follows:

$\begin{array}{c}\mathrm{MTFI}=\frac{F^{*}\left(f_{\mathrm{roc}}\right)}{{\sum }_{f_j}F\left(f_j\right)},\\ F^{*}\left(f_{\mathrm{roc}}\right)=\max \left[F\left(f_{\mathrm{roc}}-0.02f_{\mathrm{roc}},f_{\mathrm{roc}}+0.02f_{\mathrm{roc}}\right)\right],\end{array}$ where F(f_j) represents a Fourier spectrum amplitude corresponding to an output signal at a frequency f_j; and F*(f_roc) represents a maximum frequency amplitude within a range of 22% values around the rotating frequency f_roc.

Finally, an intrinsic mode function u_target corresponding to the maximum MTFI value is the extracted rotating frequency component.

Sub-step (3-3) includes the following sub-sub-steps:

(3-3-1) A vibratory displacement signal S_x is input, an iteration count Iter=0 is initialized, the maximum iteration number MaxIter=500 is set, and a searching step of the bandwidth balance parameter is set to be Δα=500.

(3-3-2) A primary deconstruction is performed on the vibratory displacement signal S_x by using the variational mode decomposition to obtain an intrinsic mode function u₀ and a target frequency index MTFI₀.

(3-3-3) Loop is started, Iter=Iter+1 is made, and the bandwidth balance parameter is changed into α₁=α₀+Δα and α₂=α₀−Δα, respectively; then, two obtained values α₁ and α₂ of the bandwidth balance parameter are substituted into a variational mode decomposition algorithm, respectively, to perform a deconstruction on the vibratory displacement signal S_x, so as to obtain u_1,Iter and u_2,Iter as well as a corresponding MTFI_1,Iter and MTFI_2,Iter, respectively.

(3-3-4) If MTFI₀>MTFI_1,Iter and MTFI₀>MTFI_2,Iter, the loop is broken and a final target rotating frequency-related component u_target=u₀ is outputted; and if MTFI₀ does not satisfy the above condition, MTFI₀=max(MTFI_1,Iter,MTFI_2,Iter) and

${\alpha }_0=\underset{{\alpha }_i,i=1,2}{\arg \max }\left({\mathrm{MTFI}}_{i,\mathrm{Iter}}\right)$

(3-3-5) If Iter>MaxIter, the loop is broken, a result u_target obtained by using a variational mode decomposition method to deconstruct the vibratory displacement signal S_x under the action of the latest bandwidth balance parameter α₀ is outputted; else, sub-sub-step (3-3-3) is performed.

(3-3-6) The loop is ended and a final target rotating frequency component u_target is outputted.

In the sub-sub-steps (3-3-2), (3-3-3) and (3-3-5), using the variational mode decomposition method to deconstruct the vibratory displacement signal S_x includes the following sub-steps:

(i) The Fourier transform of u_k (t), f(t) and λ(t) are set as û_k(ω), {circumflex over (f)}(ω) and {circumflex over (λ)}(ω), respectively. {û_k¹}, {ω_k¹} and {circumflex over (λ)}¹ are initialized, and iteratively counting n=0 is performed.

(ii) Iteratively counting n=n+1 is performed.

(iii) For k=1, 2, . . . , K, all α_k are updated one by one, expressed as follows:

${\hat{u}}_k^{n+1}\left(\omega \right)\leftarrow \frac{\hat{f}\left(\omega \right)-{\sum }_{i<k}{\hat{u}}_i^{n+1}\left(\omega \right)-{\sum }_{i>k}{\hat{u}}_i^n\left(\omega \right)+{\hat{\lambda }}^n\left(\omega \right)/2}{1+2{\alpha \left(\omega -{\omega }_k^n\right)}^2}.$

ω_k is updated simultaneously:

${\omega }_k^{n+1}\leftarrow \frac{{\int }_0^{\infty }\omega {❘{\hat{u}}_k^{n+1}\left(\omega \right)❘}^{2}d\omega }{{\int }_0^{\infty }{❘{\hat{u}}_k^{n+1}\left(\omega \right)❘}^{2}d\omega }.$

(iv) {circumflex over (λ)}(ω) is updated:{circumflex over (λ)}ⁿ⁺¹(ω)←{circumflex over (λ)}ⁿ(ω)+τ({circumflex over (f)}(ω)−Σ_kû_kⁿ⁺¹(ω)),where τ is a noise tolerance coefficient, in order to avoid the influence of strong noise on a signal deconstruction result, and completely reconstructing a signal is not the final objective of the present disclosure, and therefore the noise tolerance coefficient is taken as τ=0 to regulate and control the influence of the noise on a reconstruction process.

(v) The sub-steps (ii)-(iv) are repeated until an ending condition is satisfied:Σ_k∥û_kⁿ⁺¹−û_kⁿ∥₂²/∥û_kⁿ∥₂²<εwhere ϵ represents a convergence coefficient, and ε=1×10⁻⁶.

Step 4: calculating and estimating instantaneous fluctuation characteristics of a fundamental frequency of the extracted rotating frequency component using a quadrature-derivative-based normalized Hilbert transform to obtain an instantaneous frequency. Step 4 includes the following sub-steps:

(4-1) For a monocomponent amplitude modulation-frequency modulation signal g(t), all maximum extreme values in an absolute form are searched if the amplitude of the signal is not normalized, and then cubic spline function fitting is performed on these extreme values to obtain an empirical envelope function B₀(t).

(4-2) Amplitude normalization is performed on the signal g(t), namely:g₁(t)=g(t)/B₀(t).

Sub-step (4-1) is performed if the amplitude of g₁(t) is still not completely normalized, until difference between the amplitude of the L empirical envelope function and 1 is smaller than 10⁻⁵, and the obtained output signal g_L+1(t) at this time is regarded as a pure frequency modulation signal.

(4-3) An instantaneous amplitude signal B(t)=B₀(t)·B₁(t)· . . . ·B_L(t) of the signal g(t) is calculated, and a frequency modulation signal F(t) of g(t) is recalculated:F(t)=g(t)/B(t).

(4-4) Q(t)=±√{square root over (1−F²(t))} is set, so that an instantaneous phase ϕ(t) is estimated as:ϕ(t)=arctan[Q(t)/F(t)]

Based on the instantaneous phase ϕ(t), an instantaneous frequency ω(t) is then calculated and estimated as:

$\omega \left(t\right)=\frac{\left[d\varphi \left(t\right)/\mathrm{dt}\right]}{2\pi }.$ where ω(t)>0 is always satisfied.

Step 5: inputting a calculated instantaneous frequency sequence into an optimum stochastic resonance system for anti-noise enhancement of intrawave frequency modulation characteristics, wherein potential energy parameters of a stochastic resonance system and a step length of a Runge-Kutta calculation process are optimized by a particle swarm optimization algorithm to obtain the optimum stochastic resonance system.

Step 5 includes the following sub-steps:

(5-1) A stochastic resonance system is constructed as follows:

$\frac{\mathrm{dx}}{\mathrm{dt}}=-\frac{\mathrm{dU}\left(x\right)}{\mathrm{dx}}+S\left(t\right)+N\left(t\right),$ where x represents a motion trajectory of a particle, S(t) represents a tenuous periodic signal, N(t) represents Gaussian white noise, and U(x) represents a potential function.

(5-2) A reflection-symmetric quartic potential function is used as U(x):

$U\left(x\right)=-\frac{1}{2}{\mathrm{ax}}^2+\frac{1}{4}{\mathrm{bx}}^4,$ where a and b represent positive parameters controlling a potential barrier and a potential well of the reflection-symmetric quartic potential function U(x), respectively.

The stochastic resonance system is derived as:

$\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{ax}-{\mathrm{bx}}^3+S\left(t\right)+N\left(t\right).$

(5-3) The stochastic resonance system is resolved based on a fourth-order Runge-Kutta approach to obtain:k₁=ax(i)−bx(i)³+S(i)+N(i)k₂=a(x(i)+hk₁/2)−b(x(i)+hk₁/2)³+S(i)+N(i)k₃=a(x(i)+hk₂/2)−b(x(i)+hk₂/2)³+S(i+1)+N(i+1)k₄=a(x(i)+hk₃)−b(x(i)+hk₃)³+S(i+1)+N(i+1)x(i+1)=x(i)+(k₁+2k₂+2k₃+k₄)h/6where x(i), S(i) and N(i) represent discrete forms of the signals x(t), S(t) and N(t), respectively, and h represents a calculation step.

(5-4) An output x(i) of the stochastic resonance system is evaluated by using a signal-to-noise ratio index SNR as follows:

$\mathrm{SNR}=10{\log }_{10}\frac{P_{\mathrm{signal}}}{P_{\mathrm{noise}}}=10{\log }_{10}\frac{P\left(\mathrm{round}\left(\frac{f_m}{\Delta f}\right)+1\right)}{{\sum }_{j=1}^{\mathrm{Num}}P\left(j\right)-P\left(\mathrm{round}\left(\frac{f_m}{\Delta f}\right)+1\right)},$ where P(⋅) represents a power spectrum of the signal x(i), Δf=f/N is a spectrum resolution, f_m is a target frequency component, namely, a rotating frequency, and thus f_m=f_roc; and round(·) represents a rounding operator.

(5-5) The determined instantaneous frequency ω(t) of an input instantaneous frequency signal covers components S(t) and N(t). Therefore, magnitudes of a, b and h needs to be appropriately adjusted to achieve an optimum stochastic resonance effect, as follows:

$\left(a^{*},b^{*},h^{*}\right)=\underset{a\in \left(0,+\infty \right),b\in \left(0,+\infty \right),h\in \left(0,+\infty \right)}{\arg \max }\mathrm{SNR}\left(a,b,h\right).$

The present disclosure uses a particle swarm optimization algorithm to search for an optimum (a*, b*, h*) combination in a parameter space, performs intrawave modulation characteristic anti-noise enhancement on an input instantaneous frequency ω(t) via the optimum stochastic resonance system under the parameter combination, and outputs to obtain ω₀*(t).

Sub-step (5-5) includes the following sub-sub-steps:

(5-5-1) The estimated instantaneous frequency ω(t) is input into the stochastic resonance system, S(t)+N(t)=ω(t) is made, the particle swarm size N_p=50 is initialized, the number of dimensions of a parameter search space is set to be 3, a higher bound and a lower bound of searching with respect to the parameters (a, b, h) are set to be LB=[0,0,0] and HB=[0.05, 5000, 0.05], respectively, an inertia weight of a particle is set to be w=0.6, acceleration constants are set to be γ₁=γ₂=1.5, and an absolute value of a maximum particle motion velocity is less than 0.8; and an iteration count IterPSO=0 is initialized, a maximum iteration number MaxIterPSO=500 is set, and a precision coefficient for controlling an iteration process is set to be ε_P=0.001.

(5-5-2) The particles are randomly initialized, and parameters of these particles are substituted into the stochastic resonance system to calculate a corresponding output, respectively; and the current global best output ω₀*(t) and its SNR₀ are found.

(5-5-3) Loop is started, IterPSO=IterPSO+1 is set, a position and velocity of each particle are updated and adjusted, and parameters of these particles are re-substituted into the stochastic resonance system to calculate the corresponding output, respectively; and the current global best output ω_IterPSO*(t) and its SNR_IterPSO are found.

(5-5-4) A signal-to-noise ratio variation degree ΔSNR=|SNR₀−SNR_IterPSO is calculated, and SNR₀=max(SNR₀,SNR_IterPSO) and

${\omega }_0^{*}\left(t\right)=\underset{{\omega }_i^{*}\left(t\right),i=1,2}{\arg \max }\left({\mathrm{SNR}}_0,{\mathrm{SNR}}_{\mathrm{IterPSO}}\right)$ are updated.

(5-5-5) If IterPSO>MaxIterPSO or ΔSNR<ε_P, the loop is broken and ω₀*(t) is outputted; else, sub-sub-step (5-5-3) is performed.

(5-5-6) The loop is ended, and a final output result ω₀*(t) for performing the anti-noise enhancement of the intrawave frequency modulation characteristics on the input instantaneous frequency ω(t) based on the optimum stochastic resonance system under the optimal (a*, b*, h*) combination is outputted.

Step 6: processing fast Fourier transform on the instantaneous frequency of the intrawave frequency modulation characteristics after anti-noise enhancement, and diagnosing and identifying a rotor rub-impact fault of the rotating machinery based on a distribution characteristic of harmonic amplitudes related to a rotor rotating frequency.

In step 6, when the distribution characteristic of the harmonic amplitudes related to the rotor rotating frequency f_roc on the Fourier spectrum of the instantaneous frequency ω₀*(t) satisfies the following two conditions, it is able to be determined that a rotor of the rotating machinery has a rub-impact fault: (1) sharp rotor rotating frequency f_roc and its harmonics that can be clearly distinguished from noise and other mechanical vibration components exist; and (2) an amplitude of the fundamental rotating frequency f_roc is the maximum.

When the distribution characteristic of the harmonic amplitudes related to the rotor rotation frequency f_roc on the Fourier spectrum of the instantaneous frequency ω₀*(t) are determined based on judgment logic, preset values, symbol relationships and other conditions to satisfy the two conditions for the existence of the rotor rub-impact fault, the main control unit issues a warning to an operator, indicating that the rotor system of the target rotating machinery may have a rub-impact fault. The operator promptly conducts a shutdown inspection of the target rotating machinery based on the warning, and can effectively manage and rectify the rotor rubbing fault by adjusting the air gap between the stator and rotor, replacing the rotor, and adjusting the operational conditions of the rotating machinery, etc., thereby obtaining a rotating machinery without rotor rub-impact faults, ensuring the safe, stable and efficient operation of the engineering machinery system.

The effects of the method of the present disclosure will be demonstrated below by a specific embodiment.

S01, a signal sequence is collected from a centrifugal pump which may have a potential rotor rub-impact fault via a vibration acceleration sensor, and a time-domain waveform of a vibratory acceleration signal is as shown in FIG. 2. The centrifugal pump is operated at a rotational speed of 1500 rpm, so that a rotor rotating frequency f_roc thereof can be calculated as 25 Hz, a sampling frequency of the vibration acceleration sensor is 5120 Hz, and a sampling duration is 2 s. From the time-domain waveform of the vibration acceleration signal of FIG. 2, it is difficult to observe the characteristic symptoms associated with the rotor rub-impact fault of the centrifugal pump.

S02, based on two-stage integration transformation and high-pass filtering, the collected vibratory acceleration signal is converted into a vibratory displacement signal, wherein cut-off frequencies W_BG1 and W_BG2 of a high-pass filter are set to be 24 Hz in the two high-pass filtering processes, and an obtained time-domain waveform diagram of the converted vibratory displacement signal is as shown in FIG. 3, and a frequency spectrum diagram thereof is as shown in FIG. 4. It can be seen from FIG. 4 that there are other frequency components in addition to the most significant rotating frequency f_roc (represented by ∘).

S03, targeted extraction is performed on the rotating frequency component in the vibratory displacement signal based on the improved variational mode decomposition method, and instantaneous fluctuation characteristics (i.e. frequency modulation characteristics) of its fundamental frequency are calculated and estimated by using a quadrature-derivative-based normalized Hilbert transform, so as to obtain a time-frequency diagram of the rotating frequency component as shown in FIG. 5. It may be observed that there is an intrawave modulation phenomenon in the rotating frequency of the vibration signal, indicating a potential fault in the rotor of the centrifugal pump, but further clarification is needed on the specific type of fault.

S04, a spectrum diagram of an instantaneous frequency of the rotating frequency component estimated using the quadrature-derivative-based normalized Hilbert transform is drawn, as shown in FIG. 6. It can be seen that due to the interference of noise and other complex factors, distribution characteristics of harmonic amplitudes related to the rotor rotating frequency f_roc on a Fourier spectrum of the instantaneous frequency cannot meet the criteria for determining the rotor rub-impact fault. Therefore, it is still difficult to determine whether the centrifugal pump has experienced the rotor rub-impact fault.

S05, intrawave modulation characteristic anti-noise enhancement is performed by inputting an instantaneous frequency sequence obtained through calculation into an optimum stochastic resonance system, wherein potential energy parameters of the stochastic resonance system and a step length of a Runge-Kutta calculation process are optimized by a particle swarm optimization algorithm, and an optimal (a*, b*, h*) parameter combination obtained through algorithm optimization is (2.9×10⁻⁴, 4.4×10³, 0.0015). The spectrum of the instantaneous frequency ω₀*(t) subjected to the frequency modulation characteristic enhancement and outputted by the optimum stochastic resonance system is as shown in FIG. 7, sharp rotor rotating frequency f_roc and its harmonics that can be clearly distinguished from noise and other mechanical vibration components exist, and an amplitude of first rotating frequency f_roc is the largest. From this, it can be determined that the centrifugal pump experienced the rotor rub-impact fault during operation. The main control unit issued a warning to the operator, indicating potential rub-impact faults in the rotor system of the centrifugal pump. Based on this warning, the operator conducts a shutdown inspection of the centrifugal pump, and can take measures such as adjusting the stator-rotor gap, replacing the rotor, and adjusting the operating conditions of the rotating machinery to address the rub-impact faults. As a result, the centrifugal pump is restored to a condition without rotor rub-impact issues.

FIGS. 8(a)-8(c) show the analysis results of HHT and ACMD, which are the prior art. For HHT, due to its inherent deficiencies of mode mixing, recursive sifting, and misclassification caused by fixed band allocation, it is still unable to seize the rapid fluctuating intermediate frequency modal of the target frequency component in this case, and the restricted frequency range time-frequency representation (TFR) of HHT severely suffers from energy diffusion that can smear the manifestation. For ACMD, the weighting coefficient is selected as 1×10⁻⁶ and the smooth parameter is selected as 1×10⁴, and the revealed target IF pattern demonstrated in FIG. 8(b) registers as excessive amplitude of intrawave frequency modulation and a certain degree of energy diffusion. Even so, in FIG. 8(c), the rotating frequency and its harmonics can be observed and the rotor rubbing failure can be diagnosed through this result. Here, the harmonic components in the ACMD result are very damaged by the interference component, which is visually inferior to the result obtained by the proposed method. As a consequence, the overall performance of the method of the present disclosure in intrawave frequency modulation characteristic detection for structural rotor rub-impact detection and diagnostics is generally more robust and superior to the HHT and ACMD methods.

Those ordinarily skilled in the art may understand that the above is only the preferred embodiments of the present disclosure and is not configured to limit the present disclosure. Although the present disclosure is illustrated in detail referring to the aforementioned embodiments, those skilled in the art may still modify the technical solutions recorded in all the aforementioned embodiments, or perform equivalent replacement on part of technical features therein. Modifications, equivalent replacements, improvements and the like made within the spirit and scope of the present disclosure shall all be contained in the scope of protection of the present disclosure.

Claims

1. A method for diagnosing rotor rub-impact in a rotating machinery based on vibration signal deconstruction and frequency modulation characteristic anti-noise enhancement comprising the following steps: step 1: collecting, by a vibration acceleration sensor, a signal sequence from a rotating machinery device;step 2: converting, based on two-stage integration transformation and high-pass filtering, a collected vibratory acceleration signal into a vibratory displacement signal;step 3: performing targeted extraction on a rotating frequency component in the vibratory displacement signal based on an improved variational mode decomposition method;step 4: calculating and estimating instantaneous fluctuation characteristics of a fundamental frequency of the extracted rotating frequency component using a quadrature-derivative-based normalized Hilbert transform to obtain an instantaneous frequency;step 5: inputting a calculated instantaneous frequency sequence into an optimum stochastic resonance system for anti-noise enhancement of intrawave frequency modulation characteristics, wherein potential energy parameters of a stochastic resonance system and a step length of a Runge-Kutta calculation process are optimized by a particle swarm optimization algorithm to obtain the optimum stochastic resonance system; andstep 6: processing fast Fourier transform on the instantaneous frequency of the intrawave frequency modulation characteristics after anti-noise enhancement, diagnosing and identifying a rotor rub-impact fault of the rotating machinery based on a distribution characteristic of harmonic amplitudes related to a rotor rotating frequency, issuing, by a main control unit, a warning to an operator, and promptly conducting, by the operator, a shutdown inspection and a maintenance of the target rotating machinery, to obtain the rotating machinery without the rotor rub-impact fault.

2. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein in the step 1, the signal sequence collected from the rotating machinery device by the vibration acceleration sensor is recorded as Sao(i), i=1, 2, 3, . . . , N, where N represent a number of total sampling points, and a sampling frequency is recorded as fs; and in a signal collecting process, a frequency response parameter of the used vibration acceleration sensor is not less than 2 kHz, a sampling frequency of a vibration signal sequence is not less than 5.12 kHz and not greater than 100 kHz, and a sampling duration is not less than 1 s.

3. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein the step 2 comprises the following sub-steps: sub-step (2-1), performing one integration to convert the vibratory acceleration signal Sao into a vibratory velocity signal as follows: Svo(1)=0,Svo(i)=Svo(i−1)+Sa(i−1)×ΔT,i=2,3, . . . ,N+1,

4. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein the step 3 comprises the following sub-steps: sub-step (3-1), defining a series of intrinsic mode functions uk(t), k∈(1, 2, . . . , K), with K being the total number of modes, with respect to the signal Sx as a series of amplitude modulation-frequency modulation signals with a limited bandwidth, expressed as: uk(t)=Ak(t)cos(φk(t)

5. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 4, wherein the sub-step (3-3) comprises the following sub-sub-steps: sub-sub-step (3-3-1), inputting a vibratory displacement signal Sx, initializing an iteration count Iter=0, setting the maximum iteration number MaxIter=500, and setting a searching step of the bandwidth balance parameter to be Δα=500;sub-sub-step (3-3-2), performing a primary deconstruction on the vibratory displacement signal Sx using the variational mode decomposition to obtain an intrinsic mode function u0 and a target frequency index MTFI0;sub-sub-step (3-3-3), starting loop, setting Iter=Iter+1, and changing the bandwidth balance parameter into α1=α0+Δα and α2=α0−Δα, respectively; and substituting two obtained values α1 and α2 of the bandwidth balance parameter into a variational mode decomposition algorithm, respectively, to perform a deconstruction on the vibratory displacement signal Sx, to obtain u1,Iter and u2,Iter as well as a corresponding MTFI1,Iter and MTFI2,Iter, respectively;sub-sub-step (3-3-4), breaking the loop and outputting a final target rotating frequency-related component utarget=u0 when MTFI0>MTFI1,Iter and MTFI0>MTFI2,Iter; and updating MTFI0=max(MTFI1,Iter, MTFI2,Iter) and

6. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 5, wherein in the sub-sub-steps (3-3-2), (3-3-3) and (3-3-5), said using the improved variational mode decomposition method to deconstruct the vibratory displacement signal Sx comprises the following sub-steps: sub-step (i), setting the Fourier transform of uk(t), f(t) and λ(t) as ûk(ω), {circumflex over (f)}(ω) and {circumflex over (λ)}(ω), respectively; and initializing {ûk1}, {ω1k} and {circumflex over (λ)}1, iteratively counting n=0;sub-step (ii), iteratively counting n=n+1;sub-step (iii), updating, for k=1, 2, . . . , K, all ûk one by one, expressed as follows:

7. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein the step 4 comprises the following sub-steps: sub-step (4-1), seeking out, for a monocomponent amplitude modulation-frequency modulation signal g(t), all maximum extreme values in an absolute form when am amplitude of the signal g(t) is not normalized, and performing cubic spline function fitting on these extreme values to obtain an empirical envelope function B0(t);sub-step (4-2), performing amplitude normalization on the signal g(t), namely: g1(t)=g(t)/B0(t),repeating the sub-step (4-1) when the amplitude of the signal g1(t) is still not completely normalized, until difference between the amplitude of Lth empirical envelope function and 1 is smaller than 105, and considering the obtained output signal gL+1(t) as a pure frequency modulation signal;sub-step (4-3), calculating an instantaneous amplitude signal B(t)=B0(t)·B1(t)· . . . ·BL(t) of the signal g(t), and recalculating a frequency modulation signal F(t) of the signal g(t): F(t)=g(t)/B(t), andsub-step (4-4), letting Q(t)=±√{square root over (1−F2(t))}, so that an instantaneous phase ϕ(t) is defined as: ϕ(t)=arctan[Q(t)/F(t)],calculating and estimating an instantaneous frequency ω(t) as:

8. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein the step 5 comprises the following sub-steps: sub-step (5-1), constructing a stochastic resonance system as follows:

9. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 8, wherein the sub-step (5-5) comprises the following sub-sub-steps: sub-sub-step (5-5-1), inputting the estimated instantaneous frequency ω(t) into the stochastic resonance system, letting S(t)+N(t)=ω(t), initializing a particle swarm size Np=50, setting dimensions of a parameter search space to be 3, setting a higher bound and a lower bound of searching with respect to the parameters (a, b, h) to be LB=[0,0,0] and HB=[0.05, 5000, 0.05], respectively, setting an inertia weight of a particles to be w=0.6, setting acceleration constants to be γ1=γ2=1.5, and an absolute value of a maximum particle motion velocity being less than 0.8; and initializing an iteration number IterPSO=0, setting a maximum iteration number MaxIterPSO=500, and setting a precision coefficient for controlling an iteration process to be εP=0.001;sub-sub-step (5-5-2), randomly initializing the particles, and substituting parameters of these particles into the stochastic resonance system to calculate a corresponding output; and finding a current global best output ω0*(t) and SNR0;sub-sub-step (5-5-3), starting loop, setting IterPSO=IterPSO+1, updating and modifying a position and velocity of each particle, and re-substituting parameters of the particles into the stochastic resonance system to calculate the corresponding output, respectively; and finding a current global best output ωIterPSO*(t) and SNRIterPSO;sub-sub-step (5-5-4), calculating a signal-to-noise ratio variation degree ΔSNR=|SNR0−SNRIterPSO|, and updating SNR0=max(SNR0,SNRIterPSO) and

10. The method for diagnosing rotor rub-impact in the rotating machinery based on the vibration signal deconstruction and the frequency modulation characteristic anti-noise enhancement according to claim 1, wherein in the step 6, determining that the rotor rub-impact fault of the rotating machinery exists when the distribution characteristic of the harmonic amplitudes related to the rotor rotating frequency froc on the Fourier spectrum of the instantaneous frequency ω0*(t) satisfies following two conditions: a sharp rotor rotating frequency froc and harmonics of the sharp rotor rotating frequency froc exist, wherein the sharp rotor rotating frequency froc and the harmonics of the sharp rotor rotating frequency froc are capable of being clearly distinguished from noise and other mechanical vibration components; andan amplitude of the fundamental rotating frequency froc is the maximum.