CN102721537B - Mechanical impact type fault diagnosis method based on variable space-scale frame - Google Patents

Abstract

The invention discloses a mechanical impact type fault diagnosis method based on a variable space-scale frame, which is characterized by comprising the following steps of: firstly, constructing frame functions with different space-scale characteristics on the basis of different control parameters; carrying out multiscale analysis on the dynamic response signal of electromechanical equipment by the constructed functions; calculating the global characteristic kurtosis of each time-scale frame function; selecting the optimal frame function of the dynamic signal by taking global characteristic kurtosis maximization as a target; analyzing the dynamic signal by the optimal frame function; calculating the time frequency joint kurtosis distribution map of each single reconstruction signal; and carrying out fault diagnosis by taking a sub-frequency band to which the maximum value of the time frequency joint kurtosis belongs in a picture as an optimal analysis sub-frequency band. With the method disclosed by the invention, an analysis parameter can be optimized, a key fault characteristic is self-adaptively extracted, the impact type fault diagnosis of the complex electromechanical equipment is realized, the phenomenon that the equipment operation quality is lowered is found as early as possible, and major machine accidents are avoided.

Description

Physical shock type method for diagnosing faults based on variable spaces-yardstick framework

Technical field

The present invention relates to a kind of mechanical failure diagnostic method, be specifically related to enhancing and the isolation technics of a kind of complicated electromechanical equipment (comprising rotating machinery and reciprocating machine) impingement feature.

Background technology

Large complicated electromechanical equipment is in all departments of national economy activity, as all played an important role in communications and transportation, energy supply for metallurgy, equipment manufacture and national defense industry.Under the severe operating condition of complexity, the key components and parts of important equipment, as the bearing of rotating machinery, gear and rotor, and the piston of reciprocating machine, air valve, crank and connecting rod etc., inevitable occur wear and tear, peel off, the local damage such as crackle causes performance degradation also to germinate gradually fault, causes the product facility running quality even fatal crass's serious accident that declines.Find early the incipient fault in these equipments, for ensureing carrying out in order and preventing major disaster incidents to there is remarkable economic worth and important social effect of activity in production.In country's medium-term and long-term plans (2006-2020), Eleventh Five-Year Plan and state natural sciences fund committee's scientific strategy research report (2006-2010), all classify the gordian techniquies such as great installation operational reliability, security, maintainability as important research direction.The development of the advanced theory and technology of equipment condition monitoring and the practical popularization in engineering practice thereof become the important subject of fault diagnosis field.

In the time of the kernel component generation local damage of complicated electromechanical equipment, due to the periodicity of himself or toward renaturation running, in dynamic response signal, produce faint fault shock characteristic.Often there is coupling and be submerged under powerful ground unrest in these fault signatures, conventional stationary signal disposal route is difficult to obtain satisfied feature extraction effect, has hindered effectively carrying out of fault diagnosis with other vibration modes.At present in complex apparatus status monitoring and fault diagnosis field, conventional fault diagnosis technology is mainly based upon on the dyadic wavelet analysis foundation that Daubechies discrete wavelet transformer is changed to representative.Wavelet transformation is a kind of Time-Frequency Analysis instrument for non-stationary signal, and its time-frequency atom is the oscillatory extinction function of local support.According to inner product matching principle, wavelet basis function can mate the shock characteristic of the early stage Weak fault of plant equipment preferably.

But the problem such as classical discrete small wave converting method, as Daubechies family etc., exists Wavelet time-frequency courtyard characteristic single, and basis function is fixing is unfavorable for mating complicated and diversified fault signature.On the other hand, wavelet basis function and analytical parameters thereof choose a large amount of supervision and the intervention that often need professional, for those skilled in the art, be difficult for understanding, thereby poor in the practicality of industry spot.

Summary of the invention

The object of the invention is to, a kind of complicated electromechanical equipment impingement method for diagnosing faults of variable spaces-yardstick framework time-frequency combination kurtosis distribution plan is provided.

For reaching above object, the present invention takes following technical scheme to be achieved:

A physical shock type method for diagnosing faults based on variable spaces-yardstick framework, is characterized in that: comprise the steps:

1) adopt variable spaces-yardstick framework function to decompose and single reconstruct the dynamic response signal gathering on complicated electromechanical equipment, described decomposition is that fault signature in this dynamic response signal and other vibration mode components are decomposed in different sub-bands, comprises the following steps:

A, control parameter sets γ ∈ of structure (p, q, s) | p, q, s ∈ Z ⁺to generate different variable spaces-yardstick framework function { B _{p, q, s}| (p, q, s) ∈ Γ }, wherein Z ⁺represent Positive Integer Set, the former subset of time-frequency of variable spaces-yardstick framework function is can refinement function wave filter h by one ₀(n) and one generating function wave filter g ₀(n) generate;

Control parameter p, q, s determines wave filter h jointly ₀and g (n) ₀(n) function space-dimensional properties of institute's generate, wherein p and q are for determining the yardstick contraction-expansion factor of variable spaces-yardstick framework function, and s determines the concentrated characteristic of the time domain energy of this framework function; Control parameter p, q, must meet structure permissive condition between s:

2≤p<q and p/q+1/s>1

Definition H ₀(ω) being can refinement function wave filter h ₀(n) frequency spectrum; G ₀(ω) be generating function wave filter g ₀(n) frequency spectrum, their analytic equation is defined as:

$H_0\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}\sqrt{\mathrm{pq}}& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;}),\\ \sqrt{\mathrm{pq}}{\mathrm{\&theta;}}_H\left(\frac{\mathrm{\&omega;}-a}{b}\right)& \mathrm{\&omega;}\&Element;[(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;},\mathrm{\&pi;}),\\ 0& \mathrm{\&omega;}\&Element;[\frac{1}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.$ And $G_0\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\mathrm{\&pi;}),\\ \sqrt{s}{\mathrm{\&theta;}}_G\left(\frac{\mathrm{\&omega;}-\mathrm{pa}}{\mathrm{pb}}\right)& \mathrm{\&omega;}\&Element;[\frac{s-1}{s}\mathrm{\&pi;},\frac{p}{q}\mathrm{\&pi;}),\\ \sqrt{s}& \mathrm{\&omega;}\&Element;[\frac{p}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.$

Wherein, a=(1-1/s) π/p, b=1/q-(1-1/s)/p,

${\mathrm{\&theta;}}_H\left(\mathrm{\&omega;}\right)=1/2(1+\cos \mathrm{\&omega;})\sqrt{2-\cos \mathrm{\&omega;}},$

${\mathrm{\&theta;}}_G\left(\mathrm{\&omega;}\right)=1/2(1-\cos \mathrm{\&omega;})\sqrt{2+\cos \mathrm{\&omega;}},$ Frequencies omega ∈ [0, π];

B, to the dynamic response signal x (n) gathering on complicated electromechanical equipment carry out J layer variable spaces-yardstick framework function decompose, obtain coefficient in transform domain:

W={w ₁(n),w ₂(n),…,w _J+1(n)|n∈Z ⁺∪{0}}，

W wherein _j(n) be transform domain subsequence;

It is that the crucial transient state characteristic relevant to potential mechanical fault strengthened that described list props up reconstruct; To a certain variable spaces-yardstick framework function B _{p, q, s}signal coefficient in transform domain W carry out single and select and obtain weighted transformation domain coefficient

$\tilde{W}\left\{j\right\}=\{{\tilde{w}}_{j,1}\left(n\right),{\tilde{w}}_{j,2}\left(n\right),...,{\tilde{w}}_{j,J+1}\left(n\right)|,j=1,...,J+1,n\&Element;Z^{+}\&cup;\left\{0\right\}\},$

To weighted transformation domain coefficient inverse process according to variable spaces-yardstick framework decomposition algorithm carries out single reconstruct, and the list that obtains j yardstick props up reconstruction signal r _j(n)

Variable spaces-yardstick framework function B _{p, q, s}input dynamic response signal x (n) is analyzed to the each list obtaining and prop up reconstruct dynamic response signal set R _{p, q, s}be expressed as:

R _p，q,s={r ₁(n),r ₂(n),…,r _J+1(n)|n∈Z ⁺∪{0}}

For weighted transformation domain coefficient in sequence computing formula as follows:

${\tilde{w}}_{j,k}\left(n\right)=w_k\left(n\right)\&CenterDot;\mathrm{\&delta;}(j-k)$

K=0 in formula, 1 ..., J, Kronecker function δ (j-k) is defined as:

2) " the global characteristics kurtosis " of definition variable spaces-yardstick framework function, and definition can quantitative response list be propped up " the time-frequency combination kurtosis " of impact degree in reconstruct dynamic response signal;

3) turn to optimum variable spaces-yardstick framework function of the adaptively selected dynamic response signal analysis of optimization aim with " global characteristics kurtosis " maximum; Adopt this optimum variable spaces-yardstick framework function to decompose and single reconstruct dynamic response signal; Calculate time-frequency combination kurtosis value that each list props up reconstruct dynamic response signal to generate corresponding time-frequency combination kurtosis distribution plan; Using sub-band under time-frequency combination kurtosis maximal value in scheming as optimum analysis sub-band; This optimum sub-band signal is carried out to Hilbert envelope demodulation with the transient state characteristic relevant to potential mechanical fault in identification Dynamic Signal, then carry out fault diagnosis.

In said method, the transform domain subsequence w described in step 1) sub-step b _j(n) obtain by following computing:

1. initialization Decomposition iteration number of times j=1, adopts wave filter h ₀and g (n) ₀(n) Dynamic Signal of complicated electromechanical equipment is carried out to multiple dimensioned decomposition, the process of decomposition completes on frequency domain, wherein can refinement function branch before decomposing, must carry out p and increase sampling, must carry out lower q down-sampled after decomposing; And that generating function branch only need to carry out lower s after filtering is down-sampled.Obtaining ground floor can refinement sequence of function c ₁and generating function sequence w (n) ₁(n);

2. adopt wave filter h _jand g (n) _j(n) what to last layer, decomposition obtained can refinement sequence of function c _j-1(n) decompose again, obtain new generating function sequence w _j(n) and new can refinement sequence of function c _j(n), decomposition algorithm is identical with the first Scale Decomposition, wave filter h _jand g (n) _j(n) frequency spectrum function H _j(ω) and G _j(ω) defined by following formula

$H_j\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}{\mathrm{\&Pi;}}_{k=0}^{j-1}H\left(q^{j-1-k}{p}^k\mathrm{\&omega;}\right)& \mathrm{\&omega;}\&Element;[0,\mathrm{\&pi;}/q^j),\\ 0& \mathrm{\&omega;}\&Element;(\mathrm{\&pi;}/q^j,\mathrm{\&pi;}],\end{array}\right.$

G _j(ω)=H _j(ω)G ₀(q ^jω)，

Wave filter h _jand g (n) _j(n) coefficient is respectively by H _j(ω) and G _j(ω) inverse Fourier transform obtains;

3. judge whether iterations j is greater than predetermined maximum decomposition level and counts J, if it is finishes decomposable process, and makes w _j+1(n)=c _j(n); Otherwise to j add 1 and repeating step 2..

Step 2) described in the definition of " global characteristics kurtosis " and " time-frequency combination kurtosis ", comprise the following steps:

A, calculating R _{p, q, s}in each list prop up the improvement kurtosis value of reconstruct dynamic response signal, improve kurtosis value Kurt[x (n)] computing formula is as follows:

Kurt[x(n)]=E[(C[x,λ ₁,λ ₂]-μ) ⁴]/σ ⁴

Operator E[in formula] expression mathematical expectation, operator C[x (n), λ ₁, λ ₂] effect be list entries x (n) to be carried out to head and the tail block, in the time that the length of list entries x is L, retain in x index at interval [λ ₁l, λ ₂l] within coefficient; Mean value and the standard deviation of rear sequence blocked in μ and σ representative.Function B _{p, q, s}signal x (n) is analyzed to the improvement kurtosis value that the list obtaining props up reconstruct dynamic response signal is

K _p，q,s={Kurt[r ₁(n)],Kurt[r ₂(n)],…,Kurt[r _J+1(n)]}；

B, calculating variable spaces-yardstick framework function B _{p, q, s}global characteristics kurtosis value CK[B _{p, q, s}], be defined as follows

CK[B _p，q,s]=max?K _p，q，s；

C, variable spaces-yardstick framework function B _{p, q, s}signal x (n) is analyzed to the list obtaining and prop up reconstruct dynamic response signal r _j(n) time-frequency combination kurtosis TFK[r _j(n)], be defined as

TFK[r _j(n)]=Thres (Kurt[C[|R _j(f) |, f _min, f _max]]) Kurt[C[r _j(n), 0.05,0.95]] wherein: Thres (t) represents threshold function table, is defined as

$\mathrm{Thres}\left(t\right)=\left\{\begin{array}{cc}0& 0\&le;t<6\\ 1& 6\&le;t\end{array}\right.;$

R _j(f) represent r _i,j(n) Fourier transform spectral series number, [f _min, f _max] expression variable spaces-chi framework function j yardstick generating function wave filter G _j(ω) normalization passband.

The concrete grammar of described step 3) comprises following sub-step:

A, turn to optimization aim and select optimum variable spaces-yardstick framework function of fault signature in matched signal with global characteristics kurtosis maximum

${\mathrm{\&gamma;}}_{\mathrm{opt}}=(p^{*},q^{*},s^{*})=\underset{\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}}{\arg \max }\mathrm{CK}\left[B_{p,q,s}\right]$

The parameter space of γ is elected as

{(p,q,s)|p,q,s∈Z ⁺,2≤p≤9,q=p+1,1≤s≤3}

By γ _opt=(p ^*, q ^*, s ^*) variable spaces-yardstick framework function of determining for the Optimal Signals analytic function of selecting.

B, adopt optimum variable spaces-yardstick framework function signal is successively decomposed and single reconstruct, obtain reconstruction signal

R _opt={r _i,j(n)|i,j∈Z ⁺,n∈Z ⁺∪{0},j≤i};

C, calculating R _optin respectively signal x (n) analyzed to the list obtaining prop up reconstruct dynamic response signal r _i,j(n) time-frequency combination kurtosis value; the time-frequency combination kurtosis value calculating is drawn on the two dimensional surface about " frequency-yardstick "; " the time-frequency combination kurtosis distribution plan " being improved, the numerical values recited of time-frequency combination kurtosis is corresponding with color depth degree in figure;

D, choose in improved " time-frequency combination kurtosis distribution plan " sub-band under time-frequency combination kurtosis maximal value and analyze, make its Hilbert envelope and envelope spectrum with identification shock characteristic wherein, carry out fault diagnosis.

Variable spaces-yardstick framework function of the inventive method has advantages of that structure is flexible and " space-yardstick " characteristic is adjustable, for fault transient state characteristic coupling provides the abundant former word bank of time-frequency.Utilize variable spaces-yardstick framework function to decompose also fill order to Dynamic Signal and prop up reconstruct, can, by original dynamic response signal map on meticulous " space-yardstick " plane, be conducive to the key feature relevant to mechanical fault from multiple angle extraction signals.

Kurtosis index is a kind of dimensionless higher order statistical index in statistics, particularly responsive to the early stage Weak fault feature of equipment component.Original definition based on kurtosis has proposed two kinds and has improved index: " the global characteristics kurtosis " of variable spaces-yardstick framework function and " the time-frequency combination kurtosis " of single reconstruction signal thereof.The former is for selecting adaptively variable spaces-yardstick framework function of energy Optimum Matching dynamic response signal fault shock characteristic; The interference that after latter can effectively suppress variable spaces-yardstick framework function and decomposes, the boundary effect of single reconstruction signal is calculated index, is especially showing premium properties aspect the inhibition of the sudden impulse disturbances of Gaussian noise and dereferenced.Adopt preferred framework function signal successively to be decomposed to and draw the time-frequency combination kurtosis distribution plan of single reconstruction signal in " frequency-yardstick " plane.In figure, sub-band corresponding to time-frequency combination kurtosis maximal value can disclose the feature by complicated electromechanical equipment impingement failure induction of hiding in signal effectively.

The present invention has the following significant advantage that is different from classic method:

1) conversion of variable spaces-yardstick framework function is a kind of tight frame conversion with fractional order yardstick contraction-expansion factor, and its function waveform number of oscillation is adjustable.Variable spaces-yardstick framework function is transformed to complicated electromechanical equipment dynamic measuring signal a kind of more comprehensive and meticulous analysis tool is provided, and can effectively disclose and be hidden in the non-stationary and the transient state characteristic component that in signal, are brought out by mechanical fault;

2) a kind of improved " global characteristics kurtosis " index has been proposed, it is corresponding one by one with variable spaces-yardstick framework function, and utilizing global characteristics kurtosis index maximum to turn to optimization aim, to have realized optimum variable spaces-yardstick framework function of fault signature leaching process adaptively selected.

3) a kind of " time-frequency combination kurtosis " index has been proposed, this index can be decomposed the Gaussian noise in rear sub-band to variable spaces-yardstick framework function, the sudden impact composition of unlinkability is effectively distinguished and suppresses, thereby accurately extracting the crucial non-stationary and the transient state characteristic composition that in sub-band, are caused by mechanical fault.

4) a kind of improvement being associated with variable spaces-yardstick framework function " time-frequency combination kurtosis distribution plan " has been proposed.Utilize optimum framework function to carry out multiple dimensioned decomposition to complicated electromechanical equipment dynamic response signal and fill order props up reconstruct, calculate the time-frequency combination kurtosis that each list props up reconstruction signal, be drawn on the optimum analysis sub-band of " frequency-yardstick " two dimensional surface to select to comprise critical failure information.

5) algorithm of the present invention is simple, and counting yield is high, has good engineering application prospect.

Brief description of the drawings

The dynamic response signal waveforms that Fig. 1 gathers for rolling bearing experiment table for the inventive method.Wherein: (a) time domain waveform; (b) be Hilbert envelope spectrum.

Fig. 2 is the bearing signal global characteristics kurtosis value that adopts the inventive method variable spaces-yardstick framework function to calculate from Fig. 1 oscillogram.Wherein, (a) global characteristics kurtosis value while being s=1; (b) the global characteristics kurtosis value while being s=2; (c) the global characteristics kurtosis value while being s=3.

Fig. 3 adopts optimum variable spaces-yardstick framework function to decompose dynamic response signal in Fig. 1 in the inventive method; Calculate the time-frequency combination kurtosis that each list props up reconstruct dynamic response signal and obtain corresponding time-frequency combination kurtosis distribution plan.

Fig. 4 is time domain waveform (a figure) and the Hilbert envelope demodulation spectrogram (b figure) thereof of optimum analysis sub-band in Fig. 3 of the present invention.

The dynamic response signal waveforms that Fig. 5 gathers for finishing stand reducer casing experiment table for the inventive method.Wherein: (a) time domain waveform; (b) be Hilbert envelope spectrum.

Fig. 6 is the finishing stand reducer casing signal global characteristics kurtosis value that adopts the inventive method variable spaces-yardstick framework function to calculate from Fig. 5 oscillogram.Wherein, (a) global characteristics kurtosis value while being s=1; (b) the global characteristics kurtosis value while being s=2; (c) the global characteristics kurtosis value while being s=3.

Fig. 7 adopts optimum variable spaces-yardstick framework function to decompose dynamic response signal in Fig. 5 in the inventive method; Calculate the time-frequency combination kurtosis that each list props up reconstruct dynamic response signal and obtain corresponding time-frequency combination kurtosis distribution plan.

Fig. 8 is time domain waveform (a figure) and the Hilbert envelope demodulation spectrogram (b figure) thereof of optimum analysis sub-band in Fig. 7 of the present invention.

Embodiment

Below in conjunction with accompanying drawing, content of the present invention is described in further detail:

1, complicated electromechanical equipment is carried out to vibration-testing, utilize the dynamic response signal of vibration transducer collecting device operational process, comprise the following steps

A, on complicated electromechanical equipment, arrange vibration transducer, the position that sensor is arranged comprises bearing seat and casing surface.The sensor type adopting comprises eddy current displacement sensor, electromagnetic type speed pickup and piezoelectric acceleration transducer.

B, utilize dynamic signal testing instrument to nurse one's health and discrete sampling the signal of vibration transducer collection.The described signal to vibration transducer collection is nursed one's health and is referred to signal is carried out anti-aliasing filter and adds rectangular window and block.When signal is carried out to discrete sampling, should guarantee sample frequency f _sand between sampling length N, meet following relation

N/f _s≥0.8

The dynamic response signal gathering from complicated electromechanical equipment is as shown in accompanying drawing 1 and accompanying drawing 5.

2, the structure of variable spaces-yardstick framework function

Construct one control parameter sets γ ∈ (p, q, s) | p, q, s ∈ Z ⁺to generate different variable spaces-yardstick framework function { B _{p, q, s}| (p, q, s) ∈ Γ }, wherein Z ⁺represent Positive Integer Set.Control parameter p, q, s determines wave filter h jointly ₀and g (n) ₀(n) function space-dimensional properties of institute's generate, wherein p and q are for determining the yardstick contraction-expansion factor of variable spaces-yardstick framework function, and s determines the concentrated characteristic of the time domain energy of this framework function; Control parameter p, q, must meet structure permissive condition between s:

2≤p<q and p/q+1/s>1;

The former subset of time-frequency of variable spaces-yardstick framework function is can refinement function wave filter h by one ₀(n) and one generating function wave filter g ₀(n) generate, in a certain variable spaces-yardstick framework function any one time-frequency atom be all by this framework function corresponding can refinement function wave filter h ₀and generating function wave filter g (n) ₀(n) flexible, the spatial translation of yardstick separately and mutual convolution algorithm obtain.When controlling parameter p, after the numerical value of q and s is determined, corresponding variable space-yardstick framework function B _{p, q, s}the former subset Ψ of time-frequency in fact formed a square summable function space l ²(Z) a super complete substrate, wherein Z represents integer set.

Definition H ₀(ω) being can refinement function wave filter h ₀(n) frequency spectrum; G ₀(ω) be generating function wave filter g ₀(n) frequency spectrum, their analytic equation is defined as:

$H_0\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}\sqrt{\mathrm{pq}}& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;}),\\ \sqrt{\mathrm{pq}}{\mathrm{\&theta;}}_H\left(\frac{\mathrm{\&omega;}-a}{b}\right)& \mathrm{\&omega;}\&Element;[(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;},\mathrm{\&pi;}),\\ 0& \mathrm{\&omega;}\&Element;[\frac{1}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.$ And $G_0\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\mathrm{\&pi;}),\\ \sqrt{s}{\mathrm{\&theta;}}_G\left(\frac{\mathrm{\&omega;}-\mathrm{pa}}{\mathrm{pb}}\right)& \mathrm{\&omega;}\&Element;[\frac{s-1}{s}\mathrm{\&pi;},\frac{p}{q}\mathrm{\&pi;}),\\ \sqrt{s}& \mathrm{\&omega;}\&Element;[\frac{p}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.$

Wherein, a=(1-1/s) π/p, b=1/q-(1-1/s)/p,

${\mathrm{\&theta;}}_H\left(\mathrm{\&omega;}\right)=1/2(1+\cos \mathrm{\&omega;})\sqrt{2-\cos \mathrm{\&omega;}},$

${\mathrm{\&theta;}}_G\left(\mathrm{\&omega;}\right)=1/2(1-\cos \mathrm{\&omega;})\sqrt{2+\cos \mathrm{\&omega;}},$ Frequencies omega ∈ [0, π];

Variable p in formula, q and s are the control parameter of variable spaces-yardstick framework function.

On definition time-frequency former subset Ψ mesoscale j can refinement function wave filter h _jand generating function wave filter g (n) _j(n) frequency spectrum function is H _j(ω) and G _j(ω).Function H _j(ω) and G _j(ω) analytic equation is defined as

$H_j\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}{\mathrm{\&Pi;}}_{k=0}^{j-1}H\left(q^{j-1-k}{p}^k\mathrm{\&omega;}\right)& \mathrm{\&omega;}\&Element;[0,\mathrm{\&pi;}/q^j),\\ 0& \mathrm{\&omega;}\&Element;(\mathrm{\&pi;}/q^j,\mathrm{\&pi;}],\end{array}\right.$

G _j(ω)=H _j(ω)G ₀(q ^jω)。

Correspondingly, can refinement function wave filter h _jand generating function wave filter g (n) _j(n) coefficient is respectively by H _j(ω) and G _j(ω) inverse Fourier transform obtains.

3, adopt variable spaces-yardstick framework function to decompose dynamic response signal

Make time series x (n) represent the dynamic response signal gathering from complicated electromechanical equipment, B _{p, q, s}represent by controlling parameter p q, and the common variable spaces-yardstick framework function determining of s.This framework function B _{p, q, s}to the multiscale analysis of time series x (n), to signal carry out the decomposition of J layer after obtain J+1 coefficient in transform domain sequence

W={w ₁(n),w ₂(n),…,w _J+1(n)|n∈Z ⁺∪{0}}，

The wherein coefficient in transform domain sequence w on j yardstick _j(n) calculation process comprises the following steps:

A, initialization decompose number of plies j=1, the frequency response function H that employing can refinement function wave filter ₀(ω) and the frequency response function G of generating function wave filter ₀(ω) time series x (n) is carried out to filtering, filtering completes on frequency domain.The algorithm of two filtering branch is respectively

1) can refinement function filter branch

1. make L _xrepresent the original length of sequence x input time (n).Time series x (n) is carried out to upper p and increase sampling, increase the sequence x obtaining after sampling _l(n) mathematic(al) representation is

2. make L _hrepresent wave filter h ₀(n) original length, to h ₀(n) carry out zero padding continuation, the sequences h after continuation _extend(n) mathematic(al) representation is

$h_{\mathrm{extend}}\left(n\right)=\left\{\begin{array}{cc}{h}_0\left(n\right)& 0\&le;n\&le;L_h-1,\\ 0& L_h\&le;n\&le;(L-1)p\end{array}\right.$

3. respectively to sequence x _land h (n) _extend(n) carry out Fourier transform and obtain frequency spectrum function X _l(ω) and H _extend(ω), two frequency spectrum functions that obtain are multiplied each other, multiplied result is carried out to inverse Fourier transform (IFFT[]) and obtain filtered time series

x _h(n)=IFFT[X _l(ω)·H _extend(ω)]

Wherein IFFT[] represent inverse Fourier transform operator.

4. to sequence x _h(n) carry out lower q down-sampled, obtain Approximate Sequence c ₁(n).C ₁(n) mathematic(al) representation is

C ₁(n)=x _up(nq-n), wherein

representative is no more than the maximum integer of real number ξ.

2) generating function filter branch

1. make L _xrepresent the original length of sequence x input time (n).Make L _grepresent wave filter g ₀(n) original length, to g ₀(n) carry out zero padding continuation, the sequence g after continuation _extend(n) mathematic(al) representation is

$g_{\mathrm{extend}}\left(n\right)=\left\{\begin{array}{cc}{g}_0\left(n\right)& 0\&le;n\&le;L_g-1,\\ 0& L_g\&le;n\&le;L_x\end{array}\right.$

2. respectively to sequence x (n) and g _extend(n) carry out Fourier transform and obtain frequency spectrum function X (ω) and G _extend(ω), two frequency spectrum functions that obtain are multiplied each other, multiplied result is carried out to inverse Fourier transform (IFFT[]) and obtain filtered time series x _g(n).X _g(n) can describe by following formula:

x _g(n)=IFFT[X(ω)·G _extend(ω)]；

3. to sequence x _g(n) carry out lower s down-sampled, obtain ground floor change of scale domain coefficient sequence w ₁(n).W ₁(n) mathematic(al) representation is

W ₁(n)=x _g(ns-n), wherein

By above step, finally obtaining the first yardstick can refinement sequence of function c ₁(n) and the first change of scale domain coefficient sequence w ₁(n).

B, employing j scaling filter h _jand g (n) _j(n) what j-1 Scale Decomposition is obtained can refinement sequence of function c _j-1(n) decompose, decomposable process is as described in step a again, and obtaining j yardstick can refinement sequence of function c _jand j change of scale domain coefficient sequence w (n) _j(n);

C, judge whether iterations j is greater than predetermined maximum decomposition level and counts J, if it is finishes decomposable process, and makes w _j+1(n)=c _j(n); Otherwise j is added to 1 and repeating step b.

4, variable spaces-yardstick framework function decomposition transform domain coefficient of dynamic response signal is carried out to single reconstruct

In the time of key components and parts generation local damage in complicated electromechanical equipment, will in dynamic measuring signal, produce corresponding periodic shock component.These periodic shock components are exactly the crucial transient state characteristic relevant to potential mechanical fault.Decompose and can realize separating of these crucial transient state characteristics and other irrelevant vibration mode components by dynamic measuring signal being carried out to variable spaces-yardstick framework function, but down-sampling operation causes spatial domain resolution to decline, and need to these features be strengthened and be recovered by single reconstruct.The algorithm that j change of scale domain coefficient is carried out to single reconstruct comprises the following steps:

A, coefficient in transform domain W is selected to weighting, obtain weighted transformation domain coefficient

$\tilde{W}\left\{j\right\}=\{{\tilde{w}}_{j,1}\left(n\right),{\tilde{w}}_{j,2}\left(n\right),...,{\tilde{w}}_{j,J+1}\left(n\right)|n\&Element;Z^{+}\&cup;\left\{0\right\}\}$

Wherein weighted transformation territory subsequence computing formula as follows

${\tilde{w}}_{j,k}\left(n\right)=w_k\left(n\right)\&CenterDot;\mathrm{\&delta;}(j-k)$

Kronecker function δ (j-k) is defined as follows

B, to weighted transformation domain coefficient inverse process according to variable spaces-yardstick framework decomposition algorithm (as shown in step 3) is processed, and the list that obtains j yardstick props up reproducing sequence r _j(n).

C, subsequences all in transform domain sequence W is carried out respectively to single reconstruct, obtain the set of single reconstruct dynamic response signal on each yardstick

R _p，q，s={r ₁(n),r ₂(n),…,r _J+1(n)|n∈Z ⁺∪{0}}

5, " the global characteristics kurtosis " of definition variable spaces-yardstick framework function, and definition can quantitative response list be propped up " the time-frequency combination kurtosis " of impact degree in reconstruct dynamic response signal, comprises the following steps:

A, adopt a certain variable spaces-yardstick framework function B _{p, q, s}input dynamic response signal x (n) is carried out to J layer decomposes and single reconstruct obtains the set R of single reconstruct dynamic response signal on each yardstick _{p, q, s}

B, calculate R respectively _{p, q, s}middle list props up reconstruct dynamic response signal r _j(n) improvement kurtosis value Kurt[r _j(n)], computing formula is as follows:

Kurt[x(n)]=E[(C[x,λ ₁,λ ₂]-μ) ⁴]/σ ⁴，

Operator E[in formula] expression mathematical expectation, operator C[r _j(n), λ ₁, λ ₂] effect be to list entries r _jcarry out head and the tail and block, in the time that the length of list entries x (n) is L, in reservation x, index is at interval [λ ₁l, λ ₂l] within coefficient, wherein 0≤λ ₁< λ ₂≤ 1; Mean value and the standard deviation of rear sequence blocked in μ and σ representative.Here λ, ₁=0.05, and λ ₂=0.95.Variable spaces-yardstick framework function B _{p, q, s}the improvement kurtosis of each yardstick list of input dynamic response signal being propped up to reconstruct dynamic response signal is

K _p，q,s={Kurt[r ₁(n)],Kurt[r ₂(n)]，...,Kurt[r _J+1(n)]}；

C, choose set K _{p, q, s}in maximal value as variable spaces-yardstick framework function B _{p, q, s}global characteristics kurtosis CK[B _{p, q, s}], be defined as follows

CK[B _p，q,s]＝max?K _p，q，s；

D, variable spaces-yardstick framework function B _{p, q, s}to inputting, dynamic response signal x (n) carries out the decomposition of J layer and single reconstruct obtains single reconstruct dynamic response signal r on each yardstick _j(n) time-frequency combination kurtosis TFK[r _j], be defined as

TFK[r _j(n)]=Thres (Kurt[C[|R _j(f) |, f _min, f _max]]) Kurt[C[r _j(n), 0.05,0.95]] wherein Thres (t) represents threshold function table, is defined as

$\mathrm{Thres}\left(t\right)=\left\{\begin{array}{cc}0& 0\&le;t<6\\ 1& 6\&le;t\end{array}\right.;$

R _j(f) represent r _j(n) Fourier transform spectral series number, [f _min, f _max] expression variable spaces-chi framework function B _{p, q, s}j yardstick generating function wave filter G _j(ω) normalization passband.

6, the optimum framework function of dynamic response signal is selected

The global characteristics kurtosis value of dynamic response signal has reflected framework function B _{p, q, s}to the analysis result R of dynamic response signal x (n) _{q, q, s}middle list props up the energy size of impacting composition in reconstruct dynamic response signal.Global characteristics kurtosis is larger, shows framework function B _{p, q, s}better to being hidden in crucial transient state characteristic matching effect in dynamic measuring signal.In the Γ of selection of control parameter space, framework function corresponding to global characteristics kurtosis maximal value is the optimum framework function of dynamic response signal.

Turn to optimum variable spaces-yardstick framework function of fault signature in optimization aim selection matched signal with global characteristics kurtosis maximum

${\mathrm{\&gamma;}}_{\mathrm{opt}}=(p^{*},q^{*},s^{*})=\underset{\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}}{\arg \max }\mathrm{CK}\left[B_{p,q,s}\right]$

The parameter space of γ is elected as

Γ={(p,q,s)|p,q,s∈Z ⁺,2≤p≤9,q=p+1，1≤s≤3}

By γ _opt=(p ^*, q ^*, s ^*) variable spaces-yardstick framework function of determining for the optimum framework function of selecting, as shown in accompanying drawing 2 and accompanying drawing 5.

7, adopt optimum variable spaces-yardstick framework function of selecting in step 6 to decompose and single reconstruct dynamic response signal; Calculate time-frequency combination kurtosis that each list props up reconstruct dynamic response signal to generate corresponding time-frequency combination kurtosis distribution plan; Using sub-band under time-frequency combination kurtosis maximal value in scheming as optimum analysis sub-band, this optimum analysis sub-band signal is carried out to Hilbert envelope demodulation with the crucial transient state characteristic relevant to potential mechanical fault in identification Dynamic Signal.Comprise the following steps:

A, adopt optimum variable spaces-yardstick framework function signal is successively decomposed and single reconstruct, obtain single reconstruct dynamic response signal set

R _opt={r _i,j(n)|i,j∈Z ⁺,n∈Z ⁺∪{0},j≤i}

B, calculating R _optin each list prop up reconstruct subsignal r _i,j(n) time-frequency combination kurtosis value T _opt:

T _opt={TFK[r _i,j(n)]|i,j∈Z ⁺,n∈Z∪{0},j≤i}

C, by the time-frequency combination kurtosis T calculating _optbe drawn on the two dimensional surface about " frequency-yardstick ", " the time-frequency combination kurtosis distribution plan " being improved, the numerical values recited of time-frequency combination kurtosis is corresponding with color depth degree in figure, as shown in accompanying drawing 3 and accompanying drawing 7.

D, choose in improved " time-frequency combination kurtosis distribution plan " sub-band under time-frequency combination kurtosis maximal value and analyze, make its Hilbert envelope and envelope spectrum with identification shock characteristic wherein, carry out fault diagnosis, as shown in accompanying drawing 4 and accompanying drawing 8.

Embodiment 1

The present embodiment is mainly verified validity and the accuracy of the inventive method.The acceleration signal that adopts vibration acceleration sensor to gather from locomotive running gear rolling bearing experiment table, rolling bearing model is 552732QT, its structural parameters are as shown in table 1.The rotating speed of axle is 653r/min, and sample frequency is 12.8KHz, and sampling length is 16384.According to housing washer fault characteristic frequency computing formula

f _o=0.5n(1-d/D _p?cosθ)f _r

The outer ring fault characteristic frequency that obtains test bearing is 78.52Hz.

Table 1 is tested rolling bearing parameter

Fig. 1 is vibration signal and the frequency spectrum gathering on testing table.Order is controlled parameter γ in space

Γ={(p,q,s)|p,q,s∈Z ⁺,2≤p≤9,q=p+1,1≤s≤3}

Middle value is also calculated variable spaces-yardstick framework function to test bearing global characteristics kurtosis value after treatment.During due to γ=(2,3,3), do not meet the admissible condition of structure, therefore this group parameter is removed.

Table 2 is gathered the global characteristics kurtosis that the variable spaces-yardstick framework function in Γ calculates

When controlling parameter s=1, global characteristics kurtosis value histogram when s=2 and s=3 is as shown in Fig. 2 (a) ~ (c), and corresponding global characteristics kurtosis index value is listed in table 2.As shown in Table 2, the variable spaces-yardstick framework function signal after treatment in the time that control parameter γ elects (2,3,1) as has the highest global characteristics kurtosis value 5.351.

The variable time-frequency frame of the optimum function B that utilization is selected _2,3,1the vibration signal of test bearing is decomposed and is drawn its improvement time-frequency combination kurtosis distribution plan, as shown in Figure 3.Wherein signal is carried out to 3 layers of low frequency approximation signal after decomposition and there is maximum improvement time-frequency combination kurtosis value 5.788.The time domain waveform figure of this sub-band signal and Hilbert envelope demodulation frequency spectrum are as shown in Fig. 4 (a) and 4 (b).In Fig. 4 (a), show to have the monolateral oscillatory extinction pulse of regularity taking 0.0127s (78.74Hz) as interval in signal, in Fig. 4 (b), occurred 1 ~ 5 frequency multiplication harmonic wave of outer ring fault characteristic frequency.The theoretical value of the outer ring fault characteristic frequency of this and test bearing is identical, and shows correctness and the validity of institute's put forward the methods fault diagnosis result.

Embodiment 2

This embodiment has provided the specific implementation process of the present invention in engineering practice.

In operational process, there is abnormal vibration in the mm finishing mill unit frame of certain steelmaker.This finishing stand is driven by alternating current generator, after spiral gear deceleration case increases square, roll-force is distributed to execution roll.Vibrating speed sensors is installed on the bearing (ball) cover of reducer casing to gather vibration signal, sample frequency is 5120Hz, and sampling length is 4096.Structural parameters and the characteristic frequency of reducer casing are as shown in table 3.

Table 3 finishing stand gearbox structure parameter and characteristic frequency

Reducer casing input end apart from the time domain waveform of the vertical measuring point collection signal of a motor side far away and envelope demodulation frequency spectrum thereof as shown in Fig. 5 (a) and 5 (b).Order is controlled parameter γ at parameter space

Γ={(p,q,s)|p,q,s∈Z ⁺,2≤p≤9,q=p+1,1≤s≤3}

Middle value, calculates each control parameter γ corresponding variable space-yardstick framework function the signal gathering in speed reduction box shaft bearing is carried out to global characteristics kurtosis index after treatment.When controlling parameter s=1, the global characteristics kurtosis histogram calculating when s=2 and s=3 is as shown in accompanying drawing 6 (a) ~ (c), and corresponding global characteristics kurtosis index value is listed in table 4.

Table 4 is gathered the global characteristics kurtosis that the variable spaces-yardstick framework function in Γ calculates

As shown in Table 4, the variable spaces-yardstick framework function signal after treatment in the time controlling parameter γ=(4,5,2) has the highest global characteristics kurtosis value-9.241.The variable time-frequency framework function of the optimum B that utilization is selected _4,5,2the vibration signal of test bearing is analyzed and is drawn its improvement time-frequency combination kurtosis distribution plan, as shown in Figure 7.The time-frequency combination kurtosis distribution plan of signal shows: the d of signal after 8 layers of decomposition ₂detail signal has maximum time-frequency combination kurtosis value, is therefore selected as optimum analysis sub-band.The time domain waveform figure of optimum analysis sub-band and Hilbert envelope demodulation frequency spectrum are as shown in Fig. 8 (a) and 8 (b).In Fig. 8 (a), show to have the monolateral oscillatory extinction pulse of periodicity taking 0.2216s as interval in signal, in Fig. 8 (b), occurred multiple frequency multiplication harmonic waves of pinion wheel frequency.Carry out really finding to exist tooth surface abrasion after shutdown inspection on pinion wheel.Show that put forward the methods of the present invention has accurately proposed the gear distress shock characteristic of actual deceleration case.

Claims (4)

1. the physical shock type method for diagnosing faults based on variable spaces-yardstick framework, is characterized in that: comprise the steps:

1) adopt variable spaces-yardstick framework function to decompose and single reconstruct the dynamic response signal gathering on complicated electromechanical equipment, described decomposition is that fault signature in this dynamic response signal and other vibration mode components are decomposed in different sub-bands, comprises the following steps:

A, control parameter sets γ ∈ of structure (p, q, s) | p, q, s ∈ Z ⁺to generate different variable spaces-yardstick framework function { B _{p, q, s}| (p, q, s) ∈ Γ }, wherein Z ⁺represent Positive Integer Set, the former subset of time-frequency of variable spaces-yardstick framework function is can refinement function wave filter h by one ₀(n) and one generating function wave filter g ₀(n) generate;

Control parameter p, q, s determines wave filter h jointly ₀and g (n) ₀(n) function space-dimensional properties of institute's generate, wherein p and q are for determining the yardstick contraction-expansion factor of variable spaces-yardstick framework function, and s determines the concentrated characteristic of the time domain energy of this framework function; Control parameter p, q, must meet structure permissive condition between s:

2≤p<q and p/q+1/s>1

Definition H ₀(ω) being can refinement function wave filter h ₀(n) frequency spectrum; G ₀(ω) be generating function wave filter g ₀(n) frequency spectrum, their analytic equation is defined as:

$H_0=\left(\mathrm{\&omega;}\right)=\begin{array}{c}\left\{\begin{array}{cc}\sqrt{\mathrm{pq}}& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;}),\\ \sqrt{\mathrm{pq}}{\mathrm{\&theta;}}_H\left(\frac{\mathrm{\&omega;}-a}{b}\right)& \mathrm{\&omega;}\&Element;[(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;},\mathrm{\&pi;}),\\ 0& \mathrm{\&omega;}\&Element;[\frac{1}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.\end{array}$ And $G_0=\left(\mathrm{\&omega;}\right)=\begin{array}{c}\left\{\begin{array}{cc}0& \mathrm{\&omega;}\&Element;[0,(1-\frac{1}{s})\frac{1}{p}\mathrm{\&pi;}),\\ \sqrt{\mathrm{pq}}{\mathrm{\&theta;}}_G\left(\frac{\mathrm{\&omega;}-\mathrm{pa}}{\mathrm{pb}}\right)& \mathrm{\&omega;}\&Element;[\frac{s-1}{s}\mathrm{\&pi;},\frac{p}{q}\mathrm{\&pi;}),\\ \sqrt{s}& \mathrm{\&omega;}\&Element;[\frac{p}{q}\mathrm{\&pi;},\mathrm{\&pi;}],\end{array}\right.\end{array}$ Wherein, a=(1-1/s) π/p, b=1/q-(1-1/s)/p,

${\mathrm{\&theta;}}_H\left(\mathrm{\&omega;}\right)=1/2(1+\cos )\sqrt{2-\cos \mathrm{\&omega;}},$

${\mathrm{\&theta;}}_G\left(\mathrm{\&omega;}\right)=1/2(1+\cos )\sqrt{2-\cos \mathrm{\&omega;}},$ Frequencies omega ∈ [0, π];

B, to the dynamic response signal x (n) gathering on complicated electromechanical equipment carry out J layer variable spaces-yardstick framework function decompose, obtain coefficient in transform domain:

W＝{w ₁(n),w ₂(n),…,w _J+1(n)|n∈Z ⁺∪{0}},

W wherein _j(n) be transform domain subsequence;

It is that the crucial transient state characteristic relevant to potential mechanical fault strengthened that described list props up reconstruct; To a certain variable spaces-yardstick framework function B _{p, q, s}signal coefficient in transform domain W carry out single and select and obtain weighted transformation domain coefficient

$\tilde{W}\left\{j\right\}=\{{\tilde{w}}_{j,1}\left(n\right),{\tilde{w}}_{j,2}\left(n\right),...,{\tilde{w}}_{j,J+1}\left(n\right)|,j=1,...,J+1,n\&Element;Z^{+}\&cup;\left\{0\right\}\},$

To weighted transformation domain coefficient inverse process according to variable spaces-yardstick framework decomposition algorithm carries out single reconstruct, and the list that obtains j yardstick props up reconstruction signal r _j(n)

Variable spaces-yardstick framework function B _{p, q, s}input dynamic response signal x (n) is analyzed to the each list obtaining and prop up reconstruct dynamic response signal set R _{p, q, s}be expressed as:

R _p,q,s＝{r ₁(n),r ₂(n),…,r _J+1(n)|n∈Z ⁺∪{0}}

For weighted transformation domain coefficient in sequence computing formula as follows:

${\tilde{w}}_{j,k}\left(n\right)=w_k\left(n\right)\&CenterDot;\mathrm{\&delta;}(j-k)$

K=1 in formula, 2 ..., J+1, Kronecker function δ (j-k) is defined as:

2) " the global characteristics kurtosis " of definition variable spaces-yardstick framework function, and definition can quantitative response list be propped up " the time-frequency combination kurtosis " of impact degree in reconstruct dynamic response signal;

3) turn to optimum variable spaces-yardstick framework function of the adaptively selected dynamic response signal analysis of optimization aim with " global characteristics kurtosis " maximum; Adopt this optimum variable spaces-yardstick framework function to decompose and single reconstruct dynamic response signal; Calculate time-frequency combination kurtosis value that each list props up reconstruct dynamic response signal to generate corresponding time-frequency combination kurtosis distribution plan; Using sub-band under time-frequency combination kurtosis maximal value in scheming as optimum analysis sub-band; This optimum sub-band signal is carried out to Hilbert envelope demodulation with the transient state characteristic relevant to potential mechanical fault in identification Dynamic Signal, then carry out fault diagnosis.

2. the physical shock type method for diagnosing faults based on variable spaces-yardstick framework as claimed in claim 1, is characterized in that step 1) the transform domain subsequence w described in sub-step b _j(n) obtain by following computing:

1. initialization Decomposition iteration number of times j=1, adopts wave filter h ₀and g (n) ₀(n) Dynamic Signal of complicated electromechanical equipment is carried out to multiple dimensioned decomposition, the process of decomposition completes on frequency domain, wherein can refinement function branch before decomposing, must carry out p and increase sampling, must carry out lower q down-sampled after decomposing; And that generating function branch only need to carry out lower s after filtering is down-sampled, obtaining ground floor can refinement sequence of function c ₁and transform domain subsequence w (n) ₁(n);

2. adopt wave filter h _jand g (n) _j(n) what to last layer, decomposition obtained can refinement sequence of function c _j-1(n) decompose again, obtain new transform domain subsequence w _j(n) and new can refinement sequence of function c _j(n), decomposition algorithm is identical with the first Scale Decomposition, wave filter h _jand g (n) _j(n) frequency spectrum function H _j(ω) and G _j(ω) defined by following formula

$H_j\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{cc}{\mathrm{\&Pi;}}_{k=0}^{j-1}H\left(q^{j-1-k}{p}^k\mathrm{\&omega;}\right)& \mathrm{\&omega;}\&Element;[0,\mathrm{\&pi;}/q^j),\\ 0& \mathrm{\&omega;}\&Element;\mathrm{\&pi;}/q^j,\mathrm{\&pi;}],\end{array}\right.$

G _j(ω)＝H _j(ω)G ₀(q ^jω)，

Wave filter h _jand g (n) _j(n) coefficient is respectively by H _j(ω) and G _j(ω) inverse Fourier transform obtains;

3. judge whether iterations j is greater than predetermined maximum decomposition level and counts J, if it is finishes decomposable process, and makes w _j+1(n)=c _j(n); Otherwise to j add 1 and repeating step 2..

3. the physical shock type method for diagnosing faults based on variable spaces-yardstick framework as claimed in claim 1, is characterized in that step 2) described in the definition of " global characteristics kurtosis " and " time-frequency combination kurtosis ", comprise the following steps:

A, calculating R _{p, q, s}in each list prop up the improvement kurtosis value of reconstruct dynamic response signal, improve kurtosis value Kurt[x (n)] computing formula is as follows:

Kurt[x(n)]＝E[(C[x,λ ₁,λ ₂]-μ) ⁴]/σ ⁴

Operator E[in formula] expression mathematical expectation, operator C[x (n), λ ₁, λ ₂] effect be list entries x (n) to be carried out to head and the tail block, in the time that the length of list entries x (n) is L, retain in x index at interval [λ ₁l, λ ₂l] within coefficient; Mean value and the standard deviation of rear sequence, framework function B are blocked in μ and σ representative _{p, q, s}to signal x (n) analyze the list obtaining prop up reconstruct dynamic response signal improve kurtosis value be

K _p,q,s＝{Kurt[r ₁(n)],Kurt[r ₂(n)],…,Kurt[r _J+1(n)]}；

B, calculating variable spaces-yardstick framework function B _{p, q, s}global characteristics kurtosis value CK[B _{p, q, s}], be defined as follows

CK[B _p,q,s]＝maxK _p,q,s；

C, by variable spaces-yardstick framework function B _{p, q, s}signal x (n) is analyzed and obtains single reconstruct dynamic response signal r _j(n) time-frequency combination kurtosis TFK[r _j(n)], be defined as

TFK[r _j(n)]＝Thres(Kurt[C[|R _j(f)|,f _min,f _max]])·Kurt[C[r _j(n),0.05,0.95]]，

Wherein: Thres (t) represents threshold function table, is defined as

$\mathrm{Thres}\left(t\right)=\left\{\begin{array}{cc}0& 0\&le;t<6\\ 1& 6\&le;t\end{array}\right.;$

R _j(f) represent r _j(n) Fourier transform spectral series number, [f _min, f _max] expression variable spaces-yardstick framework function B _{p, q, s}j yardstick generating function wave filter G _j(ω) normalization passband.

4. the physical shock type method for diagnosing faults based on variable spaces-yardstick framework as claimed in claim 1, is characterized in that described step 3) concrete grammar comprise following sub-step:

A, turn to optimization aim and select optimum variable spaces-yardstick framework function of fault signature in matched signal with global characteristics kurtosis maximum

${\mathrm{\&gamma;}}_{\mathrm{opt}}=(p^{*},q^{*},s^{*})=\underset{\mathrm{\&gamma;}\&Element;\mathrm{\&Gamma;}}{\arg \max }\mathrm{CK}\left[B_{p,q,s}\right]$

The parameter space of γ is elected as

{(p,q,s)|p,q,s∈Z ⁺,2≤p≤9,q＝p+1,1≤s≤3}

By γ _opt=(p ^*, q ^*, s ^*) variable spaces-yardstick framework function of determining for the Optimal Signals analytic function of selecting;

B, adopt optimum variable spaces-yardstick framework function signal is successively decomposed and single reconstruct, obtain reconstruction signal

R _opt＝{r _i,j(n)|i,j∈Z ⁺,n∈Z ⁺∪{0},j≤i}；

C, calculating R _optin each list prop up reconstruct dynamic response signal r _i,j(n) time-frequency combination kurtosis, the time-frequency combination kurtosis value calculating is drawn on the two dimensional surface about " frequency-yardstick ", " the time-frequency combination kurtosis distribution plan " being improved, the numerical values recited of time-frequency combination kurtosis is corresponding with color depth degree in figure;

D, choose in improved " time-frequency combination kurtosis distribution plan " sub-band under time-frequency combination kurtosis maximal value and analyze, make its Hilbert envelope and envelope spectrum with identification shock characteristic wherein, carry out fault diagnosis.