Patent Publication Number: US-11644391-B2

Title: Fault diagnosis method under convergence trend of center frequency

Description:
This application is the National Stage Application of PCT/CN2020/105689, filed on Jul. 30, 2020, which claims priority to Chinese Patent Application No. 201910750064.6, filed on Aug. 14, 2019, which is incorporated by reference for all purposes as if fully set forth herein. 
     FIELD OF THE INVENTION 
     The present invention relates to the technical field of diagnosing weak faults in machines, and more particularly to a fault diagnosis method under a convergence trend of a center frequency. 
     DESCRIPTION OF THE RELATED ART 
     Rotary machine equipment has been widely applied in industrial production. The status of machine parts directly affects the operating status and the safety status of the machine equipment. When a fault occurs in machine parts, a periodic instantaneous impulse response is generated. How to effectively retrieve and accurately evaluate such periodic instantaneous impulse response is the key to bearing fault diagnosis. However, due to the complexity of an actual operating environment, a dynamic signal acquired on site from equipment includes a large amount of noise. A weak fault feature in the signal is usually overwhelmed in the noise, leading to severe impact on the recognition of a fault feature signal. Therefore, it is of practical significance to retrieve and determine an instantaneous feature of a weak fault in a machine. 
     At present, many fault diagnosis methods for machines, for example, conventional weak fault diagnosis methods such as a time-frequency domain analysis method, empirical modal decomposition, and local mean decomposition, have been developed. However, these conventional methods have respective limitations, for example, problems such as the difficulty in selecting a stopping criterion and relatively poor anti-noise performance, which results in the limited application ranges. A variational modal decomposition method is an adaptive signal decomposition method based on a variational model and has relatively high noise immunity, and a non-filtering decomposition manner is used to decompose a signal to reduce transfer errors. In recent years, scholars have gradually introduced the variational modal decomposition method in the field of machine signal processing, and have developed a bearing fault diagnosis method based on a combination of variational modal decomposition and a classification model; have utilized the application of the variational modal decomposition method in the fault diagnosis of a rolling bearing in a multistage centrifugal pump; and have extended the applicability of variational modal decomposition in system recognition of structures. However, at present, when the variational modal decomposition method is used to process a machine signal, it is very difficult to predict an actual center frequency and a quantity of modal components in an original dynamic signal of equipment and it is very difficult to completely retrieve an optimal balance parameter of a corresponding target component. 
     SUMMARY OF THE INVENTION 
     The present invention provides a fault diagnosis method under a convergence trend of a center frequency. Based on a variational modal decomposition method, a decomposition manner under the guidance of a convergence trend of a center frequency is used to implement intelligent decomposition for diagnosing an original dynamic signal of target equipment, to overcome the difficulty of setting initial parameters in a conventional variational modal decomposition method, so that an acquired dynamic signal of the equipment can be adaptively analyzed, and it becomes less difficult for a technician to perform fault diagnosis on a machine by using a variational modal decomposition method. 
     To resolve the foregoing technical problem, the present invention provides a fault diagnosis method under a convergence trend of a center frequency, including the following steps: 
     (1) acquiring a dynamic signal x(t) of a diagnosis target by using a sampling frequency f s ; 
     (2) setting initial decomposition parameters of a variational model: an initial center frequency ω 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; 
     (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 1  . . . m n  . . . m N } and corresponding center frequencies {ω 1  . . . ω n  . . . ω N }; 
     (4) searching the obtained optimized modals {m 1  . . . m n  . . . m N } for a fault related modal m I , guiding parameter optimization by using the center frequency ω I  of the fault related modal m I , and retrieving an optimal target component  m I     including fault information; and 
     (5) performing envelopment analysis on the retrieved optimal target component  m I   , and diagnosing a rotary machine equipment according to an envelope spectrum of the target component. 
     In a preferred embodiment of the present invention, in step (3), a constraint model in the variational model is calculated by using an alternating direction method of multipliers: 
     
       
         
           
             
               
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     where in the formula, x(t) is the dynamic signal, * represents a convolution operator, ∂ t  represents calculating a partial derivative of time t, δ(t) is a Dirichlet distribution function, and an exponential regulation item e −jω     k     t  is used for translating the frequency spectrum of each component; and 
     the signal x(t) is decomposed into K modal components m k (k=1, 2, 3 . . . K), where each modal component m k  surrounds its center frequency ω k . 
     In a preferred embodiment of the present invention, performing iterative decomposition on the dynamic signal x(t) under the guidance of the convergence trend of the center frequency includes: 
     (S 31 ) 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 1 ; 
     (S 32 ) determining a convergence trend e=ω 1 -ω 0  of the center frequency: if the convergence trend e=ω 1 -ω 0  is an upward trend, outputting a corresponding modal component as the optimized modal m n , where the corresponding center frequency ω n  is a retrieved optimal center frequency; or 
     if the convergence trend e=ω 1 -ω 0  is a downward trend, making ω 0 =ω 0 +zΔω, and simultaneously determining whether to traverse the entire band, and if ω 0 =(ω 0 +zΔω)&lt;f s /2, returning to step (S 31 ), or otherwise, stopping the iterative decomposition; and 
     (S 33 ) updating the initial center frequency ω 0  with the retrieved optimal center frequency ω n , and if the new center frequency ω 0 &lt;f s /2, returning to step (S 31 ), or otherwise, stopping the iterative decomposition. 
     In a preferred embodiment of the present invention, in step (4), during the searching the obtained optimized modals {m 1  . . . m n  . . . m N } for the fault related modal m I , the fault related modal is determined by calculating Gini index values of the optimized modals {m 1  . . . m n  . . . m N }. 
     In a preferred embodiment of the present invention, in step (4), guiding parameter optimization by using the center frequency ω I  of the fault related modal m I , and retrieving an optimal target component  m I     including fault information includes: 
     (S 51 ) setting two groups of initial decomposition parameters: a balance parameter is α=α 0 +Δα, a quantity of modal components is K=1, and an initial center frequency is ω I ; and a balance parameter α=α 0 −Δα, a quantity of modal components is K=1, and an initial center frequency is ω I , 
     where Δα is the step size of the change in the balance parameter α; 
     (S 52 ) respectively decomposing the original dynamic signal x(t) by using the two groups of initial decomposition parameters set in step (S 51 ), to obtain two groups of modal components Ur 1  and Ul 1 ; 
     (S 53 ) respectively calculating Gini index values Gnir 1  and Gni 1  of the modal components Ur 1  and Ul 1 ; and 
     (S 54 ) determining the values of Gnir 1  and Gnil 1 : 
     if Gnir 1 &gt;Gnil 1 , performing an optimization solution of incrementing a balance parameter; or 
     otherwise, performing an optimization solution of decrementing a balance parameter. 
     In a preferred embodiment of the present invention, the optimization solution of incrementing a balance parameter includes: 
     (S 61 ) setting decomposition parameters: a balance parameter is α=α 0 +iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω I ; 
     (S 62 ) decomposing the original dynamic signal x(t) by using the decomposition parameters set in the step (S 61 ), to obtain the modal component Ur i , and calculating a Gini index value Gnir i , of the modal component Ur i ; and 
     (S 63 ) determining the values of Gnir i  and Gnir i=1 , and 
     if Gnir i &gt;Gnir i=1 , making i=i+1 and returning to step (S 61 ); or otherwise, making  m I   =Ur i-1 . 
     In a preferred embodiment of the present invention, the optimization solution of decrementing a balance parameter includes: 
     (S 71 ) setting decomposition parameters: a balance parameter is α=α 0 −iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω I ; 
     (S 72 ) decomposing the original dynamic signal x(t) by using the decomposition parameters set in step (S 71 ), to obtain the modal component Ul i , and calculating a Gini index value Gnil i  of the modal component Ul i ; and 
     (S 73 ) determining the values of Gnil i  and Gnil i-1 , and 
     if Gnil i &gt;Gnil i-1 , making i=i+1, and returning to step (S 71 ); or 
     otherwise, making  m I   =Ul i-1 . 
     The beneficial effects of the present invention are as follows: 
     First, in the fault diagnosis method under a convergence trend of a center frequency in this embodiment of the present invention, based on a variational modal decomposition method, a decomposition manner under the guidance of a convergence trend of a center frequency is used to implement intelligent decomposition for diagnosing an original dynamic signal of target equipment, to overcome the difficulty of setting initial parameters in a conventional variational modal decomposition method, so that an acquired dynamic signal of the equipment can be adaptively analyzed, and it becomes less difficult for a technician to perform fault diagnosis on a machine by using a variational modal decomposition method. 
     Next, in the fault diagnosis method under a convergence trend of a center frequency in this embodiment of the present invention, based on the variational modal decomposition method, a decomposition manner under the guidance of a convergence trend of a center frequency is used, so that a convergence process of a decomposition algorithm can be accelerated, and at the same time the problems of modal aliasing and false components caused by a preset inappropriate quantity of modal components in decomposition in existing decomposition methods are avoided. 
     Third, in the fault diagnosis method under a convergence trend of a center frequency in this embodiment of the present invention, a center frequency is used to guide the adaptive optimization of a balance parameter, so that the bandwidth of an eventually obtained component can match the bandwidth of an actual faulty component to the greatest extent and the amount of calculation is reduced. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a flowchart of a fault diagnosis method according to an embodiment of the present invention; 
         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; 
         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; 
         FIG.  4    is a waveform diagram of a group of acquired dynamic signals of damage of a gearbox; 
         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; 
         FIG.  6    is a histogram of determining a fault related component by using a Gini index; and 
         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 
     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 
     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: 
     (1) acquiring a group of dynamic signals x(t) of damage of a gearbox by using a sampling frequency f s  with a dynamic signal sensor, wherein for a waveform diagram of the group of dynamic signals, reference may be made to  FIG.  4   . 
     (2) setting initial decomposition parameters of a variational model: it is set that an initial center frequency ω 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. 
     (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 1  . . . m n  . . . m N } and corresponding center frequencies {ω 1  . . . ω n  . . . ω N }, wherein the signal analysis band is half the sampling frequency f s . 
     Specifically, a constraint model in the variational model is calculated by using an alternating direction method of multipliers: 
     
       
         
           
             
               
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     where in the formula, x(t) is the dynamic signal, * represents a convolution operator, ∂ t  represents calculating a partial derivative of time t, δ( t ) is a Dirichlet distribution function, and an exponential regulation item e −jω     k     t  is used for translating the frequency spectrum of each component; and 
     the signal x(t) is decomposed into K modal components m k (k=1, 2, 3 . . . K), where each modal component m k  surrounds its center frequency ω k . 
     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: 
     (S 31 ) 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 1 ; 
     (S 32 ) determining a convergence trend e=ω 1 -ω 0  of the center frequency: 
     if the convergence trend e=ω 1 -ω 0  is an upward trend, outputting a corresponding modal component as the optimized modal m n , where the corresponding center frequency ω n  is a retrieved optimal center frequency; or 
     if the convergence trend e=ω 1 -ω 0  is a downward trend, making ω 0 =ω 0 +zΔω, and simultaneously determining whether to traverse the entire band, and if ω 0 =(ω 0 +zΔω)&lt;f s /2, returning to step (S 31 ), or otherwise, stopping the iterative decomposition; and 
     (S 33 ) updating the initial center frequency ω 0  with the retrieved optimal center frequency ω n , and if the new center frequency ω 0 &lt;f s /2, returning to step (S 31 ), or otherwise, stopping the iterative decomposition. 
     (4) searching the obtained optimized modals {m 1  . . . m n  . . . m N } for a fault related modal m I , guiding parameter optimization by using the center frequency ω I  of the fault related modal m I , and retrieving an optimal target component  m I     including fault information. 
     Specifically, referring to  FIG.  3   , a process of guiding parameter optimization by using the center frequency ω I  of the fault related modal m I , and retrieving an optimal target component  m I     including fault information includes: 
     (S 51 ) setting two groups of initial decomposition parameters: a balance parameter is α=α 0 +Δα, a quantity of modal components is K=1, and an initial center frequency is ω I ; and a balance parameter α=α 0 −Δα, a quantity of modal components is K=1, and an initial center frequency is ω I , 
     where Δα is the step size of the change in the balance parameter α; 
     (S 52 ) respectively decomposing the original dynamic signal x(t) by using the two groups of initial decomposition parameters set in step (S 51 ), to obtain two groups of modal components Ur 1  and Ul 1 ; 
     (S 53 ) respectively calculating Gini index values Gnir 1  and Gnil 1  of the modal components Ur 1  and Ul 1 ; and 
     (S 54 ) determining the values of Gnir 1  and Gnil 1 : 
     if Gnir 1 &gt;Gnil 1 , performing an optimization solution of incrementing a balance parameter; or 
     otherwise, performing an optimization solution of decrementing a balance parameter. 
     The optimization solution of incrementing a balance parameter includes: 
     (S 61 ) setting decomposition parameters: a balance parameter is α=α 0 +iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω 1 ; 
     (S 62 ) decomposing the original dynamic signal x(t) by using the decomposition parameters set in the step (S 61 ), to obtain the modal component Ur i , and calculating a Gini index value Gnir i  of the modal component Ur i ; and 
     (S 63 ) determining the values of Gnir i  and Gnir i-1 , and 
     if Gnir i &gt;Gnir i-1 , making i=i+1, and returning to step (S 61 ); or otherwise, making  m I   =Ur i-1 . 
     The optimization solution of decrementing a balance parameter includes: 
     (S 71 ) setting decomposition parameters: a balance parameter is α=α 0 −iΔα(i=2), a quantity of modal components is K=1, and an initial center frequency is ω I ; 
     (S 72 ) decomposing the original dynamic signal x(t) by using the decomposition parameters set in step (S 71 ), to obtain the modal component Ul i , and calculating a Gini index value Gnil i  of the modal component Ul i ; and 
     (S 73 ) determining the values of Gnil i  and Gnil i-1 , and 
     if Gnil i &gt;Gnil i-1 , making i=i+1, and returning to step (S 71 ); or otherwise, making  m I   =Ul i-1 ; 
     (5) performing envelopment analysis on the retrieved optimal target component  m I   , and diagnosing a health status of a rotary machine equipment according to an envelope spectrum of the target component. 
     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. 
     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 g . 
     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. 
     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.