CN104156585A - Double-dictionary matching pursuit bearing fault degree evaluation method based on multiple index properties - Google Patents

Abstract

Provided is a double-dictionary matching pursuit bearing fault degree evaluation method based on multiple index properties, and belongs to the technical field of bearing fault diagnosis. The index properties include an LZC index, a kurtosis index and a pulse index. According to bearing vibration signal features, a modulation dictionary and an impact time frequency dictionary are selected to form a double dictionary, matched atoms are selected in each sub-dictionary of the double dictionary in each iteration, and coefficients of various orders are compared to obtain the most matched atom. An analysis signal is projected on an iteration atom of each time, and the signal is subtracted by the projection to form a residual signal for next decomposition. The decomposition process is finished after iteration ending conditions are met, the matched atoms and the matching coefficients are extracted, signals are reconstructed, an LZC index, a kurtosis index and a pulse index of the reconstructed signal are calculated, and fault degree evaluation is achieved through the change tendency of the three indexes.

Description

A kind of doubledictionary match tracing bearing fault degree evaluation method based on many index feature

Technical field

The present invention relates to a kind of bearing fault degree evaluation method, be particularly related to a kind of doubledictionary match tracing bearing fault degree evaluation method of many index feature, its many index is characterized as LZC index, kurtosis index and pulse index, belongs to bearing failure diagnosis technical field.

Background technology

Bearing is the important composition parts of rotation class plant equipment, and failure rate is higher.At present, bearing failure diagnosis research mainly concentrates on judgement that fault has or not and the etiologic diagnosis aspects such as pattern-recognition of fault type, yet need to realize the breakthrough to quantitative examination by qualitative examination to mechanical fault diagnosis, disclose generation, development and the Evolution of equipment failure state, thereby accomplish the maintenance of real effectively coaching device, save production cost.

In Chinese scholars aspect the quantitative Diagnosis of bearing fault, carried out useful exploration and obtained certain achievement.The current assessment for the fault order of severity is the angle based on energy and evaluation index angle mainly, comprise and set up the empirical model of estimating tooth root crackle size according to local energy, according to the proportional hazards model of introducing degeneration index, realize the equipment operational reliability assessment of Injured level vibration signal, by the methods such as relation between time domain index root mean square, kurtosis index and peak index research and lesion size.Normalized Lempel-Ziv complexity index is a kind of upgrade kit of weighing finite time sequence complexity, is also introduced into fault diagnosis, studies the relation between itself and fault degree.Visible, by realizing evaluation and the prediction of fault degree to the index analysis of signal, or be called " sxemiquantitative " diagnosis.But the signal collecting from production scene contains a large amount of Noise and Interference compositions, will greatly have a strong impact on the effect that index is evaluated.Therefore, adopt effective fault signature extraction and noise reduction means to become the important preprocessing method of follow-up judgement.

Matching pursuit algorithm (the MatchingPursuit that Mallat and Zhang propose, MP) there is basis function flexibly, can realize the extraction of individual features signal with separated, therefore construct suitable former word bank, the bearing fault quantitative Diagnosis of application based on MP algorithm is a kind of new exploration and trial.And being combined with index, reconstruction signal becomes a kind of new approaches of bearing fault degree evaluation.

Summary of the invention

In order to solve the above-mentioned technical matters in bearing fault quantitative Diagnosis, the invention provides a kind of doubledictionary match tracing bearing fault degree evaluation method of many index feature.The vibration signal of bearing fault shows as the modulation that the recurrent pulses that caused by resonance and non-homogeneous load cause, and follows a large amount of ground unrests.Fault occur and evolution in, on the one hand, along with the vibration severe degree of the increase vibration signal of fault is in increase; On the other hand, the process of Collection is mainly that sensor is fixed on casing, and therefore for outer ring fault, the load distribution of injury region is not more big changes.When fault, due to the existence of damaged area, rolling body streaks moment and outer ring raceway face real contact area reduces, and causes the quick increase of footprint pressure to fall after rise again, and the footprint pressure constantly changing can cause strong frequency modulation (PFM) effect.And along with fault worsens, damaged area constantly expands, pressure change increases gradually, and modulation phenomenon will be obvious all the more, be reflected in frequency spectrum to there will be increasing spectrum peak and harmonic wave thereof, that is to say that the composition in signal is more and more mixed and disorderly.And complexity index is just in time a kind of instrument of weighing finite time sequence complexity, can be used for this to weigh.Yet for the signal that contains a large amount of ground unrests and interference component, directly time domain index is analyzed often effect, therefore, in order to realize the evaluation of fault degree, first signal is carried out to fault signature extraction and noise reduction, then calculate LZC index, kurtosis index and the pulse index time domain index of reconstruction signal, thereby realize the evaluation for bearing fault degree.

To achieve these goals, the technical solution used in the present invention is a kind of doubledictionary match tracing bearing fault degree evaluation method of many index feature, its many index is characterized as LZC index, kurtosis index and pulse index, and the method comprises the following steps, and S1 gathers bearing vibration signal; S2 carries out the decomposition based on doubledictionary matching pursuit algorithm to bearing vibration signal; S3 is reconstructed signal, and to reconstruct calculated signals LZC index, kurtosis index and pulse index, according to the variation tendency of index, bearing fault degree is evaluated.

S1 gathers bearing vibration signal

The vibration signal of bearing fault shows as the modulation that the recurrent pulses that caused by resonance and non-homogeneous load cause, and follows a large amount of ground unrests.The collection of described vibration signal gathers gear case by acceleration transducer; Therefore to meet the characteristic atomic storehouse of fault signature be dictionary to structure---modulation dictionary and impact the doubledictionary of time-frequency dictionary:

The primitive function of modulating former word bank is which amplitude modulation function, and function model is:

g _mod(f ₁,f ₂)＝K _mod(1+cos2πf ₁t)cos2πf ₂t

Wherein, f ₁for low frequency modulations frequency, f ₂for high frequent carrier frequency, K _modfor normalized parameter, for guaranteeing that each atom has unit energy, || K _mod(f ₁, f ₂) || ₂=1;

The primitive function that impacts time-frequency dictionary is decaying exponential function, and its function model is:

$g_{\mathrm{imp}}(p,u,f_{\mathrm{imp}},\mathrm{\&Phi;})=\left\{\begin{array}{c}{K}_{\mathrm{imp}}{e}^{-p(t-u)}\sin 2\mathrm{\&pi;}{f}_{\mathrm{imp}}(t-\mathrm{\&Phi;}),t\&GreaterEqual;u\\ 0,t<u\end{array}\right.$

Wherein, the damping vibration attenuation feature that p is shock response, u is the moment that shock response occurs, f _impfor the damped natural frequency corresponding to system, Φ is phase deviation, K _impfor normalization coefficient.

The structure of dictionary is that the parameters in dictionary basis function model is carried out to discretize assignment in setting span; And adopt doubledictionary can better meet fault signature, and in match tracing atom selection course, from above two dictionaries, choose atom simultaneously, then compare the matching factor of two atoms, choosing the atom that matching factor is large is optimum atom, i.e. described doubledictionary;

S2 carries out the doubledictionary match tracing Its Sparse Decomposition based on LZC index, kurtosis index and pulse index to bearing vibration signal.Wherein, doubledictionary match tracing Its Sparse Decomposition algorithm comprises the following steps:

2.1 vibration signals collecting.Utilize acceleration transducer to measure gear case, obtain vibration acceleration signal as signal x to be analyzed;

2.2 initialization process.Signal x to be analyzed is assigned to residual signals, obtains initial residual signals R ₀=x;

2.3 choose matched atoms.Respectively from two words of doubledictionary with in, carry out matched atoms g _1kand g _2kchoose, matched atoms choose as shown in the formula,

|<R ₀,g _jk>|＝sup|<R ₀,g _ji>|,(j＝1,2)

Matching factor is respectively c _1kand c _2ksee following formula, relatively c _1kand c _2k, choosing the atom that matching factor is large is matched atoms g _jk, and return to its parameters information f ₁, f ₂or p, u, f _imppreserve;

c _jk＝|<R ₀,g _jk>|

2.4 upgrade residual signals.Matched atoms g by residual signals in each iteration _jkupper projection, the residual signals after the k time iteration is R _k+1, wherein K is maximum iteration time;

$R_{k+1}=R_k-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

Whether 2.5 checks meet stopping criterion for iteration; End condition can arrange maximum iteration time K, residual signals energy Ratios; If satisfied finishing iteration enters step S3, otherwise repeated execution of steps S2.3～S2.4;

S3 signal reconstruction;

Reconstruction signal can approximate representation be

$x=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

S4 calculates reconstruction signal LZC index, kurtosis index and pulse index; Calculate LZC index, kurtosis index and the pulse index of reconstruction signal, according to the situation of change of three indexs, the order of severity of judgement bearing fault; For bearing outer ring signal, along with the increase of fault degree, three indexs all show as the trend of increase, accordingly, just can realize the evaluation to fault degree.

Described LZC index, kurtosis index and pulse index, wherein kurtosis index and pulse index are common time domain index, and kurtosis index and pulse index are for the Fault-Sensitive of impact-type, particularly early stage in fault, and their value has obvious increase;

Kurtosis index

In formula, x _ifor signal value, N is signal length, for standard deviation

Pulse index

$I=\frac{X_{\max }}{\stackrel{\&OverBar;}{\left|X\right|}}$

In formula, X _maxfor signal peak swing, for signal averaging amplitude.

LZC index is a kind of upgrade kit of weighing finite time sequence complexity, the basic thought of complexity is: the complexity of sequence is larger, periodic component in sequence is fewer, sequence is more irregular, level off to random state, the frequency content that sequence comprises is abundanter, and the complicacy of illustrative system is also larger; The complexity of sequence is less, and in sequence, periodic component is more obvious, is more tending towards cycle status, and the frequency content that sequence comprises is less, and the complicacy of illustrative system is lower.

The basic process of complexity is: convert signal to binary sequence; If i.e. X (i)>=mean (X (n)) (i=1,2,3 ... n), define S (i)=1 (i=1,2,3 ... otherwise S (i)=0 n); Thereby obtain one at sequence S _n; Defined nucleotide sequence S _n={ S ₁, S ₂, S ₃... S _n, the complexity of definition signal is C _n(r), through N circulation, obtain final complexity;

(1) when r=0, definition S _{v, 0}={ }, Q ₀={ }, C _n(0)=0; When r=1, make Q ₁={ Q ₀s ₁, due to Q ₁do not belong to S _{v, 0}, C _n(1)=C _n(0)+1=1, Q ₁={ }, r=r+1;

(2) make Q _r={ Q _r-1s _r, S _{v, r-1}={ S _{v, r-2}s _r-1, judgement Q _rwhether belong to S _{v, r-1}; If so, C _n(r)=C _n(r-1), r=r+1.If not, C _n(r)=C _n(r)+1, Q _r={ }, r=r+1; Repeating step (2), altogether n circulation;

Above-mentioned C _n(r) it is obvious that value is subject to the length n impact of sequence S (n), and in order to obtain relatively independent index, Lempel and Ziv further propose following normalization formula, by normalization, calculate Lempel-Ziv complexity C _{ul, n}:

$0\&le;C_n=\frac{C_n\left(n\right)}{C_{\mathrm{ul},n}}\&le;1$

$C_{\mathrm{ul},n}=\underset{n\&RightArrow;\&infin;}{\lim }{C}_n\left(n\right)=\frac{n}{{\log }_{2}n}$

Compared with prior art, the present invention has following beneficial effect.

The linear combination of the m item atom based on doubledictionary is resolved into bearing vibration signal successive iteration in the present invention.Signal doubledictionary forms by modulating dictionary and impacting two sub-characteristics dictionaries of time-frequency dictionary, and the different structure composition characteristic of subcharacter dictionary basis signal, by carrying out the acquisition of discretize assignment to parameters in its basis function.In each iteration decomposable process of signal, in each subcharacter dictionary, search a matched atoms and matching factor thereof, by coefficient of comparisons, draw matched atoms and matching factor value, projection in the matched atoms that signal is chosen in all previous iteration, signal deducts projection and forms residual signals for decomposing next time.Reconstruction signal, obtain after noise reduction can analytic signal, calculate LZC index, kurtosis index and the pulse index of signal, by checking that the variation tendency of three indexs evaluates fault degree.

Accompanying drawing explanation

Fig. 1 is the signal Its Sparse Decomposition process flow diagram based on doubledictionary match tracing of the present invention.

Fig. 2 is the bearing fault degree evaluation method overall flow figure of the doubledictionary match tracing based on LZC index, kurtosis index and pulse index of the present invention.

Fig. 3 is time domain waveform and the spectrogram of the 0.1778mm bearing fault experimental signal that adopts in the present invention.

Fig. 4 is time domain waveform and the spectrogram of the 0.5334mm bearing fault experimental signal that adopts in the present invention.

Fig. 5 is reconfiguration waveform and the spectrogram to 0.1778mm bearing fault experimental signal in the present invention.

Fig. 6 is reconfiguration waveform and the spectrogram to 0.5334mm bearing fault experimental signal in the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

Fig. 1 is the signal Its Sparse Decomposition process flow diagram based on doubledictionary match tracing of the present invention.Below in conjunction with process flow diagram, the doubledictionary match tracing bearing fault degree evaluation Method And Principle based on LZC index, kurtosis index and pulse index is elaborated.

(1) utilize acceleration transducer to measure gear case, obtain vibration acceleration signal as signal x to be analyzed, sampling length is decided to be 2 integer power, according to bearing rotating speed and the gear number of teeth, sets sample frequency;

(2) bearing vibration signal shows as the modulation that the recurrent pulses that caused by resonance and non-homogeneous load cause; For the design feature of signal, structure modulation subcharacter dictionary and impact time-frequency subcharacter dictionary, both form doubledictionary;

The primitive function of modulating former word bank is which amplitude modulation function, and function model is:

g _mod(f ₁,f ₂)＝K _mod(1+cos2πf ₁t)cos2πf ₂t

Wherein, f ₁for low frequency modulations frequency, f ₂for high frequent carrier frequency, K _modfor normalized parameter, for guaranteeing that each atom has unit energy, || K _mod(f ₁, f ₂) || ₂=1;

The primitive function that impacts time-frequency dictionary is decaying exponential function, and its function model is:

$g_{\mathrm{imp}}(p,u,f_{\mathrm{imp}},\mathrm{\&Phi;})=\left\{\begin{array}{c}{K}_{\mathrm{imp}}{e}^{-p(t-u)}\sin 2\mathrm{\&pi;}{f}_{\mathrm{imp}}(t-\mathrm{\&Phi;}),t\&GreaterEqual;u\\ 0,t<u\end{array}\right.$

Wherein, the damping vibration attenuation feature that p is shock response, u is the moment that shock response occurs, f _impfor the damped natural frequency corresponding to system, Φ is phase deviation, K _impfor normalization coefficient;

Above-mentioned primitive function is carried out to parametrization, the corresponding atom of each group parameter, the set of atom forms dictionary;

(3) signal to be analyzed is assigned to initial residual signals R ₀=x;

(4) residual signals R _k, k=0 wherein, 1,2 ..., K-1, K is iterations; At subcharacter dictionary $G_{\mathrm{imp}}=\{g_{1_i},i=\mathrm{1,2,3},...,m,...\}$ With $G_{\mathrm{mod}}=\{g_{2_i},i=\mathrm{1,2,3},...,m,...\}$ In seek matched atoms g _1kand g _2kmeet | <R ₀, g _jk>|=sup|<R ₀, g _ji>|, (j=1,2);

(5) ask residual signals at each subcharacter dictionary with the projection coefficient c of upper the k time iteration _1kand c _2k, projection coefficient is realized by calculating the inner product of residual signals and matched atoms, that is: c _jk=| <R ₀, g _jk>|, relatively c _1kand c _2k, numerical value the greater is matched atoms g _jk;

(5) residual signals deducts projection and obtains new residual signals:

(6) check whether meet stopping criterion for iteration; If meet, forward step (7) to, otherwise return to step (4);

(7) decompose and finish, reconstruction signal:

$x=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

(8) calculate LZC index, kurtosis index and the peak index of reconstruct reconstruction signal, according to the trend of these three indexs, change bearing fault degree is evaluated.Fig. 2 is the bearing fault degree evaluation method overall flow figure based on doubledictionary match tracing of the present invention.

Fig. 3 is time domain waveform and the spectrogram of the 0.1778mm bearing fault experimental signal that adopts in the present invention, and Fig. 4 is time domain waveform and the spectrogram of the 0.5334mm bearing fault experimental signal that adopts in the present invention.Bearing fault degree evaluation method decomposed signal, the reconstruction signal of the doubledictionary match tracing of employing based on LZC index, kurtosis index and pulse index also calculates LZC index, kurtosis index and the pulse index of reconstruction signal.

Fig. 5 is reconfiguration waveform and the spectrogram to 0.1778mm bearing fault experimental signal in the present invention, and Fig. 6 is reconfiguration waveform and the spectrogram to 0.5334mm bearing fault experimental signal in the present invention.Can find out, in reconstruction signal, fault signature is obvious.

Following table is in the present invention, to calculate LZC index, kurtosis index and the pulse index of the reconstruction signal of 0.1778mm and 0.5334mm bearing fault experimental signal.Can find out that three indexs all show the trend of increase, can failure judgement degree deepen again.

Fault size (mm)	LZC index	Kurtosis index	Pulse index
				0.1778	0.2686	9.2649	8.2799
0.5334	0.3276	21.6523	19.6471

Claims (2)

1. the doubledictionary match tracing bearing fault degree evaluation method based on many index feature, is characterized in that: described many index is characterized as LZC index, kurtosis index and pulse index, and the method comprises the following steps, and S1 gathers bearing vibration signal; S2 carries out the decomposition based on doubledictionary matching pursuit algorithm to bearing vibration signal; S3 is reconstructed signal, and to reconstruct calculated signals LZC index, kurtosis index and pulse index, according to the variation tendency of index, bearing fault degree is evaluated;

S1 gathers bearing vibration signal

The vibration signal of bearing fault shows as the modulation that the recurrent pulses that caused by resonance and non-homogeneous load cause, and follows a large amount of ground unrests; The collection of described vibration signal gathers gear case by acceleration transducer; Therefore to meet the characteristic atomic storehouse of fault signature be dictionary to structure---modulation dictionary and impact the doubledictionary of time-frequency dictionary:

The primitive function of modulating former word bank is which amplitude modulation function, and function model is:

g _mod(f ₁,f ₂)＝K _mod(1+cos2πf ₁t)cos2πf ₂t

Wherein, f ₁for low frequency modulations frequency, f ₂for high frequent carrier frequency, K _modfor normalized parameter, for guaranteeing that each atom has unit energy, || K _mod(f ₁, f ₂) || ₂=1;

The primitive function that impacts time-frequency dictionary is decaying exponential function, and its function model is:

$g_{\mathrm{imp}}(p,u,f_{\mathrm{imp}},\mathrm{\&Phi;})=\left\{\begin{array}{c}{K}_{\mathrm{imp}}{e}^{-p(t-u)}\sin 2\mathrm{\&pi;}{f}_{\mathrm{imp}}(t-\mathrm{\&Phi;}),t\&GreaterEqual;u\\ 0,t<u\end{array}\right.$

Wherein, the damping vibration attenuation feature that p is shock response, u is the moment that shock response occurs, f _impfor the damped natural frequency corresponding to system, Φ is phase deviation, K _impfor normalization coefficient;

The structure of dictionary is that the parameters in dictionary basis function model is carried out to discretize assignment in setting span; And adopt doubledictionary can better meet fault signature, and in match tracing atom selection course, from above two dictionaries, choose atom simultaneously, then compare the matching factor of two atoms, choosing the atom that matching factor is large is optimum atom, i.e. described doubledictionary;

S2 carries out the doubledictionary match tracing Its Sparse Decomposition based on LZC index, kurtosis index and pulse index to bearing vibration signal; Wherein, doubledictionary match tracing Its Sparse Decomposition algorithm comprises the following steps:

2.1 vibration signals collecting; Utilize acceleration transducer to measure gear case, obtain vibration acceleration signal as signal x to be analyzed;

2.2 initialization process; Signal x to be analyzed is assigned to residual signals, obtains initial residual signals R ₀=x;

2.3 choose matched atoms; Respectively from two words of doubledictionary with in, carry out matched atoms g _1kand g _2kchoose, matched atoms choose as shown in the formula,

|<R ₀,g _jk>|＝sup|<R ₀,g _ji>|,(j＝1,2)

Matching factor is respectively c _1kand c _2ksee following formula, relatively c _1kand c _2k, choosing the atom that matching factor is large is matched atoms g _jk, and return to its parameters information f ₁, f ₂or p, u, f _imppreserve;

c _jk＝|<R ₀,g _jk>|

2.4 upgrade residual signals; Matched atoms g by residual signals in each iteration _jkupper projection, the residual signals after the k time iteration is R _k+1, wherein K is maximum iteration time;

$R_{k+1}=R_k-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

Whether 2.5 checks meet stopping criterion for iteration; End condition can arrange maximum iteration time K, residual signals energy Ratios; If satisfied finishing iteration enters step S3, otherwise repeated execution of steps S2.3～S2.4;

S3 signal reconstruction;

Reconstruction signal can approximate representation be

$x=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

S4 calculates reconstruction signal LZC index, kurtosis index and pulse index; Calculate LZC index, kurtosis index and the pulse index of reconstruction signal, according to the situation of change of three indexs, the order of severity of judgement bearing fault; For bearing outer ring signal, along with the increase of fault degree, three indexs all show as the trend of increase, accordingly, just can realize the evaluation to fault degree;

Described LZC index, kurtosis index and pulse index, wherein kurtosis index and pulse index are common time domain index, and kurtosis index and pulse index are for the Fault-Sensitive of impact-type, particularly early stage in fault, and their value has obvious increase;

Kurtosis index

In formula, x _ifor signal value, N is signal length, for standard deviation

Pulse index

$I=\frac{X_{\max }}{\stackrel{\&OverBar;}{\left|X\right|}}$

In formula, X _maxfor signal peak swing, for signal averaging amplitude;

LZC index is a kind of upgrade kit of weighing finite time sequence complexity, the basic thought of complexity is: the complexity of sequence is larger, periodic component in sequence is fewer, sequence is more irregular, level off to random state, the frequency content that sequence comprises is abundanter, and the complicacy of illustrative system is also larger; The complexity of sequence is less, and in sequence, periodic component is more obvious, is more tending towards cycle status, and the frequency content that sequence comprises is less, and the complicacy of illustrative system is lower;

The basic process of complexity is: convert signal to binary sequence; If i.e. X (i)>=mean (X (n)) (i=1,2,3 ... n), define S (i)=1 (i=1,2,3 ... otherwise S (i)=0 n); Thereby obtain one at sequence S _n; Defined nucleotide sequence S _n={ S ₁, S ₂, S ₃... S _n, the complexity of definition signal is C _n(r), through N circulation, obtain final complexity;

(1) when r=0, definition S _{v, 0}={ }, Q ₀={ }, C _n(0)=0; When r=1, make Q ₁={ Q ₀s ₁, due to Q ₁do not belong to S _{v, 0}, C _n(1)=C _n(0)+1=1, Q ₁={ }, r=r+1;

(2) make Q _r={ Q _r-1s _r, S _{v, r-1}={ S _{v, r-2}s _r-1, judgement Q _rwhether belong to S _{v, r-1}; If so, C _n(r)=C _n(r-1), r=r+1; If not, C _n(r)=C _n(r)+1, Q _r={ }, r=r+1; Repeating step (2), altogether n circulation;

Above-mentioned C _n(r) it is obvious that value is subject to the length n impact of sequence S (n), and in order to obtain relatively independent index, Lempel and Ziv further propose following normalization formula, by normalization, calculate Lempel-Ziv complexity C _{ul, n}:

$0\&le;C_n=\frac{C_n\left(n\right)}{C_{\mathrm{ul},n}}\&le;1$

$C_{\mathrm{ul},n}=\underset{n\&RightArrow;\&infin;}{\lim }{C}_n\left(n\right)=\frac{n}{{\log }_{2}n}$

2. a kind of doubledictionary match tracing bearing fault degree evaluation method based on many index feature according to claim 1, it is characterized in that: (1) utilizes acceleration transducer to measure gear case, obtain vibration acceleration signal as signal x to be analyzed, sampling length is decided to be 2 integer power, according to bearing rotating speed and the gear number of teeth, sets sample frequency;

(2) bearing vibration signal shows as the modulation that the recurrent pulses that caused by resonance and non-homogeneous load cause; For the design feature of signal, structure modulation subcharacter dictionary and impact time-frequency subcharacter dictionary, both form doubledictionary;

The primitive function of modulating former word bank is which amplitude modulation function, and function model is:

g _mod(f ₁,f ₂)＝K _mod(1+cos2πf ₁t)cos2πf ₂t

Wherein, f ₁for low frequency modulations frequency, f ₂for high frequent carrier frequency, K _modfor normalized parameter, for guaranteeing that each atom has unit energy, || K _mod(f ₁, f ₂) || ₂=1;

The primitive function that impacts time-frequency dictionary is decaying exponential function, and its function model is:

$g_{\mathrm{imp}}(p,u,f_{\mathrm{imp}},\mathrm{\&Phi;})=\left\{\begin{array}{c}{K}_{\mathrm{imp}}{e}^{-p(t-u)}\sin 2\mathrm{\&pi;}{f}_{\mathrm{imp}}(t-\mathrm{\&Phi;}),t\&GreaterEqual;u\\ 0,t<u\end{array}\right.$

Wherein, the damping vibration attenuation feature that p is shock response, u is the moment that shock response occurs, f _impfor the damped natural frequency corresponding to system, Φ is phase deviation, K _impfor normalization coefficient;

Above-mentioned primitive function is carried out to parametrization, the corresponding atom of each group parameter, the set of atom forms dictionary;

(3) signal to be analyzed is assigned to initial residual signals R ₀=x;

(4) residual signals R _k, k=0 wherein, 1,2 ..., K-1, K is iterations; At subcharacter dictionary $G_{\mathrm{imp}}=\{g_{1_i},i=\mathrm{1,2,3},...,m,...\}$ With $G_{\text{mod}}=\{g_{2_i},i=\mathrm{1,2,3},...,m,...\}$ In seek matched atoms g _1kand g _2kmeet | <R ₀, g _jk>|=sup|<R ₀, g _ji>|, (j=1,2);

(5) ask residual signals at each subcharacter dictionary with the projection coefficient c of upper the k time iteration _1kand c _2k, projection coefficient is realized by calculating the inner product of residual signals and matched atoms, that is: c _jk=| <R ₀, g _jk>|, relatively c _1kand c _2k, numerical value the greater is matched atoms g _jk;

(5) residual signals deducts projection and obtains new residual signals:

$R_{k+1}=R_k-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}};$

(6) check whether meet stopping criterion for iteration; If meet, forward step (7) to, otherwise return to step (4);

(7) decompose and finish, reconstruction signal:

$x=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}<R_k,g_{\mathrm{jk}}>g_{\mathrm{jk}}$

(8) calculate LZC index, kurtosis index and the peak index of reconstruct reconstruction signal, the variation of the trend of three indexs is evaluated bearing fault degree accordingly.