Fault diagnosis method under convergence trend of center frequency

Abstract

The present invention discloses a fault diagnosis method under a convergence trend of a center frequency, including: (1) acquiring a dynamic signal x(t) of a rotary machine equipment; (2) setting initial decomposition parameters of a variational model; (3) decomposing the dynamic signal x(t) by using the variational model with the set initial decomposition parameters, and traversing a signal analysis band and performing iterative decomposition on the dynamic signal x(t) under the guidance of a convergence trend of a center frequency, to obtain optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N} and corresponding center frequencies {ω.sub.1 . . . ω.sub.n . . . ω.sub.N}; (4) searching a fault related modal m.sub.I, guiding parameter optimization by using a center frequency ω.sub.I of the fault related modal m.sub.I, and retrieving an optimal target component m.sub.I including fault information; and (5) performing envelopment analysis on the optimal target component m.sub.I, and diagnosing the rotary machine equipment according to an envelope spectrum.

Claims

1. A fault diagnosis method under a convergence trend of a center frequency, comprising steps of, (1) acquiring a dynamic signal x(t) of a diagnosis target by using a sampling frequency f.sub.s, wherein t is a time; (2) setting initial decomposition parameters of a variational model: an initial center frequency ω.sub.0 is 0, an increase step size Δω of the initial center frequency is 100 Hz, an initial step count z is 1, a balance parameter α is [1000,4000], and a quantity K of modal components is 1, wherein K is a positive integer; (3) performing primary decomposition on the dynamic signal x(t) by using the variational model with the set initial decomposition parameters, determining a convergence trend of a center frequency, and traversing a signal analysis band and performing iterative decomposition on the dynamic signal x(t) under the guidance of the convergence trend of the center frequency, to obtain optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N} and corresponding center frequencies {ω.sub.1 . . . ω.sub.n . . . ω.sub.N}, wherein N is a positive integer and n is a positive integer between 1 and N; (4) searching the obtained optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N} for a fault related modal m.sub.I, guiding parameter optimization by using the center frequency ω.sub.I of the fault related modal m.sub.I, and retrieving an optimal target component m.sub.I including fault information, wherein I is a positive integer; and (5) performing envelopment analysis on the retrieved optimal target component m.sub.I, and diagnosing a rotary machine equipment according to an envelope spectrum of the target component.

2. The fault diagnosis method under a convergence trend of a center frequency according to claim 1, wherein in step (3), a constraint model in the variational model is calculated by using an alternating direction method of multipliers: $L\left(m_k,{\omega }_k\right)=\alpha \underset{k=1}{\overset{K}{.Math.}}{.Math.{\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)*m_k\right]e^{-j{\omega }_{k}t}.Math.}_2^2+{.Math.x\left(t\right)-\underset{k=1}{\overset{K}{.Math.}}{m}_k.Math.}_2^2,$ where in the formula, x(t) is the dynamic signal, * represents a convolution operator, ∂.sub.t represents calculating a partial derivative of time t, δ(t) is a Dirichlet distribution function, and an exponential regulation item e.sup.−jω.sup.k.sup.t is used for translating the frequency spectrum of each component; and the signal x(t) is decomposed into K modal components m.sub.k(k=1, 2, 3 . . . K), wherein each modal component m.sub.k surrounds its center frequency ω.sub.k.

3. The fault diagnosis method under a convergence trend of a center frequency according to claim 1, wherein performing iterative decomposition on the dynamic signal x(t) under the guidance of the convergence trend of the center frequency comprises: (S31) performing primary decomposition on the dynamic signal x(t) by using the variational model with the set initial decomposition parameters, to obtain the updated center frequency ω.sub.1; (S32) determining a convergence trend e=ω.sub.1-ω.sub.0 of the center frequency: if the convergence trend e=ω.sub.1-ω.sub.0 is an upward trend, outputting a corresponding modal component as the optimized modal m.sub.n, wherein the corresponding center frequency ω.sub.n is a retrieved optimal center frequency; or if the convergence trend e=ω.sub.1-ω.sub.0 is a downward trend, making ω.sub.0=ω.sub.0+zΔω, and simultaneously determining whether to traverse the entire band, and if ω.sub.0=(ω.sub.0+zΔω)<f.sub.s/2, returning to step (S31), or otherwise, stopping the iterative decomposition; and (S33) updating the initial center frequency ω.sub.0 with the retrieved optimal center frequency ω.sub.n, and if the new center frequency ω.sub.0<f.sub.s/2, returning to step (S31), or otherwise, stopping the iterative decomposition.

4. The fault diagnosis method under a convergence trend of a center frequency according to claim 1, wherein in step (4), during the searching the obtained optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N} for the fault related modal m.sub.I, the fault related modal is determined by calculating Gini index values of the optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N}.

5. The fault diagnosis method under a convergence trend of a center frequency according to claim 4, wherein in step (4), guiding parameter optimization by using the center frequency ω.sub.I of the fault related modal m.sub.I, and retrieving an optimal target component m.sub.I comprising fault information comprises: (S51) setting two groups of initial decomposition parameters: a balance parameter is α=α.sub.0+Δα, a quantity of modal components is K=1, and an initial center frequency is ω.sub.I; and a balance parameter α=α.sub.0−Δα, a quantity of modal components is K=1, and an initial center frequency is ω.sub.I, wherein Δα is the step size of the change in the balance parameter α; (S52) respectively decomposing the original dynamic signal x(t) by using the two groups of initial decomposition parameters set in step (S51), to obtain two groups of modal components Ur.sub.1 and Ul.sub.1; (S53) respectively calculating Gini index values Gnir.sub.1 and Gnil.sub.1 of the modal components Ur.sub.1 and Ul.sub.1; and (S54) determining the values of Gnir.sub.1 and Gnil.sub.1, and if Gnir.sub.1>Gnil.sub.1, performing an optimization solution of incrementing a balance parameter; or otherwise, performing an optimization solution of decrementing a balance parameter.

6. The fault diagnosis method under a convergence trend of a center frequency according to claim 5, wherein the optimization solution of incrementing a balance parameter comprises: (S61) setting decomposition parameters: a balance parameter is α=α.sub.0+iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω.sub.I; (S62) decomposing the original dynamic signal x(t) by using the decomposition parameters set in the step (S61), to obtain the modal component Ur.sub.i, and calculating a Gini index value Gnir.sub.i of the modal component Ur.sub.i; and (S63) determining the values of Gnir.sub.i and Gnir.sub.i-1, and if Gnir.sub.i>Gnir.sub.i-1, making i=i+1, and returning to step (S61); or otherwise, making m.sub.I=Ur.sub.i-1.

7. The fault diagnosis method under a convergence trend of a center frequency according to claim 5, wherein the optimization solution of decrementing a balance parameter comprises: (S71) setting decomposition parameters: a balance parameter is α=α.sub.0−iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω.sub.I; (S72) decomposing the original dynamic signal x(t) by using the decomposition parameters set in step (S71), to obtain the modal component Ul.sub.i, and calculating a Gini index value Gnil.sub.i of the modal component Ul.sub.i; and (S73) determining the values of Gnil.sub.i and Gnil.sub.i-1, and if Gnil.sub.i>Gnil.sub.i-1, making i=i+1, and returning to step (S71); or otherwise, making m.sub.I=Ul.sub.i-1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flowchart of a fault diagnosis method according to an embodiment of the present invention;

(2) FIG. 2 is a flowchart of a process of decomposing a dynamic signal under the guidance of a convergence trend of a center frequency according to an embodiment of the present invention;

(3) FIG. 3 is a flowchart of retrieving an optimal target component including fault information with guidance of parameter optimization by a center frequency according to an embodiment of the present invention;

(4) FIG. 4 is a waveform diagram of a group of acquired dynamic signals of damage of a gearbox;

(5) FIG. 5 is a waveform diagram of four components of the dynamic signal in FIG. 4 obtained through intelligent decomposition by using a fault diagnosis method according to an embodiment of the present invention;

(6) FIG. 6 is a histogram of determining a fault related component by using a Gini index; and

(7) FIG. 7 is an envelope spectrum of an optimal target component including fault information retrieved with guidance of parameter optimization by a center frequency.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) The present invention is further described below with reference to the accompanying drawings and specific embodiments, to enable a person skilled in the art to better understand and implement the present invention. However, the embodiments are not intended to limit the present invention.

Embodiment

(9) This embodiment provides a fault diagnosis method under a convergence trend of a center frequency (under the guidance of a convergence trend of a center frequency). Referring to FIG. 1, the method includes the following steps:

(10) (1) acquiring a group of dynamic signals x(t) of damage of a gearbox by using a sampling frequency f.sub.s with a dynamic signal sensor, wherein for a waveform diagram of the group of dynamic signals, reference may be made to FIG. 4.

(11) (2) setting initial decomposition parameters of a variational model: it is set that an initial center frequency ω.sub.0 is 0, an increase step size Δω of the initial center frequency is 100 Hz, an initial step count z is 1, a balance parameter α is [1000, 4000], and a quantity K of modal components is 1.

(12) (3) performing primary decomposition on the dynamic signal x(t) by using the variational model with the set initial decomposition parameters, determining a convergence trend of a center frequency, and traversing a signal analysis band and performing iterative decomposition on the dynamic signal x(t) under the guidance of the convergence trend of the center frequency, to obtain optimized modals {(m.sub.1 . . . m.sub.n . . . m.sub.N} and corresponding center frequencies {ω.sub.1 . . . ω.sub.n . . . ω.sub.N}, wherein the signal analysis band is half the sampling frequency f.sub.s.

(13) Specifically, a constraint model in the variational model is calculated by using an alternating direction method of multipliers:

(14) $L\left(m_k,{\omega }_k\right)=\alpha \underset{k=1}{\overset{K}{.Math.}}{.Math.{\partial }_t\left[\left(\delta \left(t\right)+\frac{j}{\pi t}\right)*m_k\right]e^{-j{\omega }_{k}t}.Math.}_2^2+{.Math.x\left(t\right)-\underset{k=1}{\overset{K}{.Math.}}{m}_k.Math.}_2^2,$

(15) where in the formula, x(t) is the dynamic signal, * represents a convolution operator, ∂.sub.t represents calculating a partial derivative of time t, δ(t) is a Dirichlet distribution function, and an exponential regulation item e.sup.−jω.sup.k.sup.t is used for translating the frequency spectrum of each component; and

(16) the signal x(t) is decomposed into K modal components m.sub.k(k=1, 2, 3 . . . K), where each modal component m.sub.k surrounds its center frequency ω.sub.k.

(17) Referring to FIG. 2, a process of performing iterative decomposition on the dynamic signal x(t) under the guidance of the convergence trend of the center frequency includes:

(18) (S31) performing primary decomposition on the dynamic signal x(t) by using the variational model with the initial decomposition parameters set in step (2), to obtain the updated center frequency ω.sub.1;

(19) (S32) determining a convergence trend e=ω.sub.1-ω.sub.0 of the center frequency:

(20) if the convergence trend e=ω.sub.1-ω.sub.0 is an upward trend, outputting a corresponding modal component as the optimized modal m.sub.n, where the corresponding center frequency ω.sub.n is a retrieved optimal center frequency; or

(21) if the convergence trend e=ω.sub.1-ω.sub.0 is a downward trend, making ω.sub.0=ω.sub.0+zΔω, and simultaneously determining whether to traverse the entire band, and if ω.sub.0=(ω.sub.0+zΔω)<f.sub.s/2, returning to step (S31), or otherwise, stopping the iterative decomposition; and

(22) (S33) updating the initial center frequency ω.sub.0 with the retrieved optimal center frequency ω.sub.n, and if the new center frequency ω.sub.0<f.sub.s/2, returning to step (S31), or otherwise, stopping the iterative decomposition.

(23) (4) searching the obtained optimized modals {m.sub.1 . . . m.sub.n . . . m.sub.N} for a fault related modal m.sub.I, guiding parameter optimization by using the center frequency ω.sub.I of the fault related modal m.sub.I, and retrieving an optimal target component m.sub.I including fault information.

(24) Specifically, referring to FIG. 3, a process of guiding parameter optimization by using the center frequency ω.sub.I of the fault related modal m.sub.I, and retrieving an optimal target component m.sub.I including fault information includes:

(25) (S51) setting two groups of initial decomposition parameters: a balance parameter is α=α.sub.0+Δα, a quantity of modal components is K=1, and an initial center frequency is ω.sub.I; and a balance parameter α=α.sub.0−Δα, a quantity of modal components is K=1, and an initial center frequency is ω.sub.I,

(26) where Δα is the step size of the change in the balance parameter α;

(27) (S52) respectively decomposing the original dynamic signal x(t) by using the two groups of initial decomposition parameters set in step (S51), to obtain two groups of modal components Ur.sub.1 and Ul.sub.1;

(28) (S53) respectively calculating Gini index values Gnir.sub.1 and Gnil.sub.1 of the modal components Ur.sub.1 and Ul.sub.1; and

(29) (S54) determining the values of Gnir.sub.1 and Gnil.sub.1:

(30) if Gnir.sub.1>Gnil.sub.1, performing an optimization solution of incrementing a balance parameter; or

(31) otherwise, performing an optimization solution of decrementing a balance parameter.

(32) The optimization solution of incrementing a balance parameter includes:

(33) (S61) setting decomposition parameters: a balance parameter is α=α.sub.0+iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω.sub.1;

(34) (S62) decomposing the original dynamic signal x(t) by using the decomposition parameters set in the step (S61), to obtain the modal component Ur.sub.i, and calculating a Gini index value Gnir.sub.i of the modal component Ur.sub.i; and

(35) (S63) determining the values of Gnir.sub.i and Gnir.sub.i-1, and

(36) if Gnir.sub.i>Gnir.sub.i-1, making i=i+1, and returning to step (S61); or otherwise, making m.sub.I=Ur.sub.i-1.

(37) The optimization solution of decrementing a balance parameter includes:

(38) (S71) setting decomposition parameters: a balance parameter is α=α.sub.0−iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω.sub.I;

(39) (S72) decomposing the original dynamic signal x(t) by using the decomposition parameters set in step (S71), to obtain the modal component Ul.sub.i, and calculating a Gini index value Gnil.sub.i of the modal component Ul.sub.i; and

(40) (S73) determining the values of Gnil.sub.i and Gnil.sub.i-1, and

(41) if Gnil.sub.i>Gnil.sub.i-1, making i=i+1, and returning to step (S71); or otherwise, making m.sub.I=Ul.sub.i-1;

(42) (5) performing envelopment analysis on the retrieved optimal target component m.sub.I, and diagnosing a health status of a rotary machine equipment according to an envelope spectrum of the target component.

(43) In the technical solution in this embodiment, a fault diagnosis method is used to diagnose the dynamic signal x(t) of damage of the gearbox shown in FIG. 4. x(t) is decomposed to obtain four modal components shown in FIG. 5. The modal components are then indicated by Gini indices to obtain a fault related component as shown in FIG. 6. It may be obtained that the second component is a faulty component.

(44) A center frequency is further used to guide parameter optimization to retrieve an optimal target component including fault information. An envelope spectrum of the optimal target component is shown in FIG. 7. It may be clearly observed that a feature frequency of a fault in a gear is f.sub.g.

(45) The fault diagnosis method in the technical solution in this embodiment has a capability of processing a weak fault signal in a machine, a retrieval result has high precision, the anti-interference capability is high, and the robustness is adequate.

(46) The foregoing embodiments are merely preferred embodiments used to fully describe the present invention, and the protection scope of the present invention is not limited thereto. Equivalent replacements or variations made by a person skilled in the art to the present invention all fall within the protection scope of the present invention. The protection scope of the present invention is as defined in the claims.