CN103792000A - Method and device for detecting transient components in signal based on sparse representation - Google Patents

Abstract

The invention discloses a method and device for detecting transient components in a signal based on sparse representation. The method and device are used for detecting and extracting the transient components in the signal. Results show that the method and device are simple and low in noise sensitivity. The method comprises the steps that analog-to-digital conversion is conducted on an input signal, so that a detected signal is obtained; the optimal wavelet basis of the detected signal is worked out; the optimal wavelet basis is expanded, and an optimal wavelet atom library is constructed; based on the optimal wavelet atom library, an optimization equation is solved through a split and augmentation Lagrange shrinkage algorithm, and the sparse representation coefficient of the detected signal on the optimal wavelet atom library is determined; a threshold value of the sparse representation coefficient is obtained, and the characteristic sparse representation coefficient is obtained; according to the characteristic sparse representation coefficient, the time of occurrence of the transient components in the detected signal is determined; according to the time of occurrence of the transient components in the detected signal, the period of the transient components in the detected signal is determined.

Description

Transient components detection method and device in a kind of signal based on rarefaction representation

Technical field

The present invention relates to the analyzing and testing field of signal, be specifically related to transient components detection method and device in a kind of signal based on rarefaction representation.

Background technology

At present, the detection of transient components in signal, has a wide range of applications in fields such as the fault diagnosis of plant equipment and status monitoring, biomedical signals measuring.Because the signal obtaining in gatherer process exists a large amount of noises, thereby the transient components of signal to be detected also can be by noise pollution, and detect for the transient state characteristic under strong noise background is a difficult problem for input always.

Wherein, the most general transient components detection method is exactly directly to judge in time-domain signal, whether there is transient components, but because the transient components in signal is often being mingled with much noise, the process accuracy directly transient components in signal being detected is lower, and efficiency is also lower; Empirical mode decomposition (Empirical Mode Decomposition is called for short EMD) is a kind of common method of ingredient in analytic signal.EMD becomes multiple intrinsic mode functions according to signal self time scale feature by signal decomposition, obtain the local feature under original signal different time yardstick, there is very strong adaptivity, but EMD decomposes the easily false component of generation and mode aliasing, affects the judgement of transient components in signal; And to the analytical effect of Low SNR signal a little less than.

In prior art, rarefaction representation is that a kind of adaptivity is good, the signal indication method being concise in expression, by the adaptive selection atom the most similar to signal in the complete storehouse of mistake, and make the atom number of selection few as much as possible, thereby original signal is expressed as to the linear expansion of one group of minimum basis function.It is good that sparse signal representation possesses adaptivity, and the feature such as be concise in expression, has been widely used in compression of images, the aspects such as compressed sensing.

Summary of the invention

The embodiment of the present invention provides transient components detection method and device in a kind of signal based on rarefaction representation, for detection of with extract transient components in signal, result represents succinct and little to noise sensitivity.

First aspect present invention provides transient components detection method in a kind of signal based on rarefaction representation, wherein, can comprise:

Input signal is carried out to mould/number conversion, obtain detection signal;

Calculate the optimal wavelet substrate of described detection signal;

Described optimal wavelet substrate is expanded to the former word bank of structure optimal wavelet;

According to the former word bank of described optimal wavelet, utilize division augmentation Lagrange contraction algorithm solving-optimizing equation, and determine the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet;

Described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient;

According to described feature rarefaction representation coefficient, determine the generation moment of transient components in described detection signal;

According to the generation moment of transient components in described detection signal, determine the cycle of transient components in described detection signal.

Preferably, the optimal wavelet substrate of the described detection signal of described calculating, comprising:

Set up wavelet library, described wavelet library is the set of one group of small echo atom;

Calculate the similarity of small echo atom in described detection signal and described wavelet library;

To be defined as optimal wavelet substrate with the highest small echo atom of detection signal similarity degree.

Preferably, described optimal wavelet substrate is wherein,

t represents respectively corresponding frequency, decay factor, delay parameter, time parameter;

Described described optimal wavelet substrate is expanded, the former word bank of structure optimal wavelet, comprising:

To described optimal wavelet substrate

to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

Preferably, described according to the former word bank of described optimal wavelet, utilize division augmentation Lagrange contraction algorithm solving-optimizing equation, and determine the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet, comprising:

According to described detection signal, the variable that obtains described detection signal separates expression formula;

Separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm;

Described in iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

Preferably, described described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, comprise: according to 3 σ criterions, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, wherein, described σ is the standard deviation of described rarefaction representation coefficient.

Second aspect present invention provides transient components pick-up unit in a kind of signal based on rarefaction representation, wherein, can comprise:

The first acquisition module, for input signal is carried out to mould/number conversion, obtains detection signal;

Computing module, for calculating the optimal wavelet substrate of described detection signal;

Constructing module, for described optimal wavelet substrate is expanded, the former word bank of structure optimal wavelet;

The first determination module, for according to the former word bank of described optimal wavelet, utilizes division augmentation Lagrange contraction algorithm solving-optimizing equation, and determines the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet;

The second acquisition module, for described rarefaction representation coefficient is got to threshold value, obtains feature rarefaction representation coefficient;

The second determination module, for according to described feature rarefaction representation coefficient, determines the generation moment of transient components in described detection signal;

The 3rd determination module, for according to the generation moment of described detection signal transient components, determines the cycle of transient components in described detection signal.

Preferably, described computing module specifically for: set up wavelet library, described wavelet library is the set of one group of small echo atom; Calculate the similarity of small echo atom in described detection signal and described wavelet library; To be defined as optimal wavelet substrate with the highest small echo atom of detection signal similarity degree.

Preferably, described optimal wavelet substrate is

wherein,

t represents respectively corresponding frequency, decay factor, delay parameter, time parameter;

Described constructing module specifically for: to described optimal wavelet substrate

to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

Preferably, described the first determination module, specifically for: according to described detection signal, the variable that obtains described detection signal separates expression formula; Separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm; Described in iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

Preferably, described the second acquisition module, specifically for: according to 3 σ criterions, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, wherein, described σ is the standard deviation of described rarefaction representation coefficient.

As can be seen from the above technical solutions, in a kind of signal based on rarefaction representation that the embodiment of the present invention provides, transient components detection method and device have the following advantages:

Model wavelet library in the inventive method, again detection signal is carried out to related operation, then expand and form the former word bank of small echo with different delayed time parameter, then in conjunction with division augmentation Lagrange contraction algorithm, can realize the rarefaction representation of signal to be detected on the former word bank of this small echo.The present invention changes into a sparse vector that only contains a small amount of numerical value by the transient components in original signal and shows, and has realized the succinct expression of transient components; Due to noise contribution in detection signal and the former word bank similarity degree of this small echo low, and the similarity of trouble unit and the former word bank of small echo is large, therefore the inventive method is little to noise sensitivity, can realize weak fault signature and detect; Can be used for the period transient state composition of mechanical equipment vibration signal to detect, can realize the detection to mechanical equipment fault feature.

Accompanying drawing explanation

In order to be illustrated more clearly in the technical scheme of the embodiment of the present invention, below the accompanying drawing of embodiment being described to required use is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

The process flow diagram of transient components detection method in a kind of signal based on rarefaction representation that Fig. 1 provides for the embodiment of the present invention;

Another schematic flow sheet of transient components detection method in the signal based on rarefaction representation that Fig. 2 a provides for the embodiment of the present invention;

Another schematic flow sheet of transient components detection method in the signal based on rarefaction representation that Fig. 2 b provides for the embodiment of the present invention;

Another schematic flow sheet of transient components detection method in the signal based on rarefaction representation that Fig. 2 c provides for the embodiment of the present invention;

Fig. 3 is the inner drive mechanism schematic diagram of the embodiment of the present invention one middle gear case;

Time domain waveform when Fig. 4 is the embodiment of the present invention one middle gear case third gear broken conditions and small echo rarefaction representation testing result schematic diagram;

Fig. 5 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of the embodiment of the present invention two centre bearer outer ring local faults;

Fig. 6 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of the embodiment of the present invention two centre bearer inner ring local faults;

Fig. 7 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of the embodiment of the present invention two centre bearer rolling body local faults;

The structural representation of transient components pick-up unit in a kind of signal based on rarefaction representation that Fig. 8 provides for the embodiment of the present invention.

Embodiment

The embodiment of the present invention provides transient components detection method and device in a kind of signal based on rarefaction representation, for detection of with extract transient components in signal, result represents succinct and little to noise sensitivity.

For making goal of the invention of the present invention, feature, advantage can be more obvious and understandable, below in conjunction with the accompanying drawing in the embodiment of the present invention, technical scheme in the embodiment of the present invention is clearly and completely described, obviously, the embodiments described below are only the present invention's part embodiment, but not whole embodiment.Based on the embodiment in the present invention, those of ordinary skills, not making all other embodiment that obtain under creative work prerequisite, belong to the scope of protection of the invention.

Term " first " in instructions of the present invention and claims and above-mentioned accompanying drawing, " second ", " the 3rd " " 4th " etc. (if existence) are for distinguishing similar object, and needn't be used for describing specific order or precedence.The data that should be appreciated that such use suitably can exchanged in situation, so as embodiments of the invention described herein can with except diagram here or describe those order enforcement.In addition, term " comprises " and " having " and their any distortion, intention is to cover not exclusive comprising, for example, those steps or unit that process, method, system, product or the equipment that has comprised series of steps or unit is not necessarily limited to clearly list, but can comprise clearly do not list or for these processes, method, product or equipment intrinsic other step or unit.

Below by specific embodiment, be described in detail respectively.

Please refer to Fig. 1, the process flow diagram of transient components detection method in a kind of signal based on rarefaction representation that Fig. 1 provides for the embodiment of the present invention, wherein, described detection method comprises:

Step S101, input signal is carried out to mould/number conversion, obtain detection signal;

Wherein, can utilize sensing device to input and carry out mould/number conversion, obtaining detection signal, being designated as _y(t); Be that detection signal y (t) is the signal that uses in actual applications sensor device measuring to collect.

Step S102, the optimal wavelet substrate of calculating described detection signal y (t);

Be understandable that, in the embodiment of the present invention, the criterion of described optimal wavelet substrate is weighed with the maximum similarity of original signal (being y (t)) at the bottom of conventionally using wavelet basis, and wherein, maximum similarity can carry out quantificational expression with maximum correlation coefficient.

For example: at the bottom of wavelet basis, the related coefficient of ψ and signal y can be expressed as: wherein, < ψ, y> represents the inner product of ψ and signal y at the bottom of wavelet basis; || ψ || ₂, || ψ || ₂represent respectively the mould of ψ and signal y at the bottom of wavelet basis.When at the bottom of wavelet basis in the time constantly changing, can produce different related coefficients, choosing at the bottom of the wavelet basis that maximum correlation coefficient is corresponding is optimal wavelet substrate.

Step S103, described optimal wavelet substrate is expanded the former word bank of structure optimal wavelet;

Wherein, regard the optimal wavelet substrate in step S102 as a small echo atom, this small echo atom is carried out to a series of time delays and construct the small echo atom having without delay parameter, then the small echo atom that these are had to different delayed time is combined the former word bank of formation optimal wavelet.

Step S104, according to the former word bank of described optimal wavelet, utilize division augmentation Lagrange contraction algorithm solving-optimizing equation, and determine the rarefaction representation coefficient of described detection signal y (t) on the former word bank of described optimal wavelet;

Step S105, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient;

Step S106, according to described feature rarefaction representation coefficient, determine the generation moment of transient components in described detection signal y (t);

Step S107, according to the generation moment of transient components in described detection signal y (t), determine the cycle of transient components in described detection signal y (t).

Transient components detection method in a kind of signal based on rarefaction representation provided by the invention, its principle is: under wavelet basis, pass through the rarefaction representation to original signal, transient components in original signal is expressed as to a sparse vector, transient components in non-zero Parametric Representation original signal in sparse vector, thereby can detect the transient components in original signal by the non-zero parameter in sparse vector.Containing the signal of period transient state composition, it is essentially in original signal and contains a series of transient components, and this signal also shows as periodically simultaneously.Due to the transient components in the non-zero Parametric Representation original signal in sparse vector, and transient components presents periodically, and the non-zero parameter in sparse vector is also rendered as periodically.Therefore, the transient components in the non-zero Parametric Representation original periodic signal in sparse vector, and the mean value in time interval between non-zero parameter can be used as the cycle of original periodic signal.At some specific areas: as rotary machinery fault diagnosis, need to extract transient components and periodic component in signal in biomedical signals measuring.That is to say, the present invention changes into a sparse vector that only contains a small amount of numerical value by the transient components in original signal and shows, and can realize the succinct expression of transient components, and little to noise sensitivity.

For the embodiment of each step, transient components detection method in the signal based on rarefaction representation is carried out to analytic explanation below:

Preferably, in some embodiments of the invention, can be with reference to figure 2a, Fig. 2 a is the schematic flow sheet of a step S102 preferred implementation; Described step S102 can specifically comprise the following steps:

Step S1021, set up wavelet library Ψ;

Described wavelet library Ψ is carried out to parametrization and represent, be designated as Ψ={ ψ (f, ζ, τ, t) };

Wherein, wavelet library Ψ is defined as the set of one group of small echo atom, and described small echo atomic parameter is represented, is designated as ψ (f, ζ, τ, t); Parameter f represents frequency, and ζ represents decay factor, and τ represents delay time, and t represents time parameter; Wherein, parameter f, the value that ζ and τ can be discrete in the scope presetting, this scope presetting can be determined according to priori.

Be understandable that, in the embodiment of the present invention, if detect for the fault-signal of rotating machinery gear and bearing, can select wavelet library and be respectively Morlet small echo and Laplace small echo, expression formula is respectively:

Morlet small echo: $\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},t)=e^{\frac{-\mathrm{\&zeta;}}{\sqrt{1-{\mathrm{\&zeta;}}^2}}{\left[2\mathrm{\&pi;f}(t-\mathrm{\&tau;})\right]}^2}\cos \left(2\mathrm{\&pi;f}(t-\mathrm{\&tau;})\right);$

Laplace small echo: $\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},f)=\left\{\begin{array}{cc}{e}^{\frac{-\mathrm{\&zeta;}}{\sqrt{1-{\mathrm{\&zeta;}}^2}}2\mathrm{\&pi;f}(t-\mathrm{\&tau;})}& t\&GreaterEqual;\mathrm{\&tau;}\\ 0& t<\mathrm{\&tau;}\end{array}\right.;$

Wherein, Morlet small echo is a kind of small echo with bilateral symmetry attenuation characteristic; Laplace small echo is a kind of small echo with monolateral attenuation characteristic.These two kinds of small echos, in the widespread use of mechanical fault diagnosis field, are not made specific explanations herein to this.

Step S1022, calculate the similarity of small echo atom ψ (f, ζ, τ, t) in described detection signal y (t) and described wavelet library;

Wherein, can use related coefficient k for detection signal y (t) with the similarity of small echo atom ψ (f, ζ, τ, t) _γrepresent, using as evaluation index;

Described related coefficient k _γfor:

$k_{\mathrm{\&gamma;}}=\frac{|<\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},t),y\left(t\right)>|}{{\left|\right|\mathrm{\&psi;}\left|\right|}_2{\left|\right|y\left|\right|}_2}---\left(1\right)$

According to the principle of related coefficient maximum, in wavelet library Ψ, choose the base small echo the highest with detection signal y (t) similarity degree, this criterion of choosing is: in wavelet library Ψ, find the small echo atom with signal to be analyzed (being detection signal y (t)) related coefficient maximum, using this small echo atom as the base small echo the highest with signal similar degree,,, determine the parameter that it is corresponding thereafter.

Step S1023, small echo atom the highest to described and signal similar degree is defined as to optimal wavelet substrate;

That is to say, base small echo described and that signal similar degree is the highest is defined as to optimal wavelet substrate;

In this embodiment, described optimal wavelet substrate is designated as

wherein,

t represents respectively corresponding frequency, decay factor, delay parameter, time parameter.

Further preferably, in some embodiments of the invention, according to abovementioned steps S1021, step S1022 and step S1023, step S103 can be specially:

To described optimal wavelet substrate

to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

As a further improvement on the present invention, can be with reference to figure 2b, Fig. 2 b is the schematic flow sheet of a step S104 preferred implementation, described step S104 can specifically comprise:

Step S1041, according to described detection signal y (t), obtain described detection signal y (t) variable separate expression formula;

Step S1042, separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm;

Described in step S1043, iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

Be understandable that, described step S1041, step S1042 and step S1043 can specifically realize in the following manner:

In this embodiment, described detection signal y (t) can be expressed as:

y(t)=x(t)+n(t)=Ac+n (2)

Wherein, y (t) is detection signal, x (t) is actual signal, n (t) represents the noise contribution in detection signal, A represents the former word bank A of described optimal wavelet (t, τ) (also can be referred to as over-complete dictionary of atoms), c represents described rarefaction representation coefficient, and n represents described noise contribution n (t)

Be understandable that, for convenience of understanding, in embodiments of the present invention the unified italic that adopts of variable represented, matrix or the positive runic of the unified employing of vector are represented; Y (t) in formula (2), the letter occurring in x (t) and n (t) all represents variable, therefore represents by italic; And A represents the former word bank of optimal wavelet in formula (2), be a matrix, c represents rarefaction representation coefficient, is a vector, n represents noise contribution n (t), is also a vector, therefore represents with positive runic.

In addition, because detection signal y (t) is the signal that uses in actual applications sensor device measuring to collect, consider that the signal of measurement contains much noise conventionally, therefore need just can obtain Useful Information by this signal of analyzing and testing.

Further, the rarefaction representation of signal x (t) on over-complete dictionary of atoms A can be described as:

$\begin{array}{ccc}\underset{c}{\min }{\left|\right|c\left|\right|}_0& s.t.& {\left|\right|\mathrm{Ac}-y\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}---\left(3\right)$

Wherein, in formula (3), " s.t. " is the abbreviation of " subject to ", represents the meaning of " meeting ".Formula (3) also can be write as "

and meet

", formula (3) represents, is meeting prerequisite under, make || c|| ₀the solution that minimum vectorial c is this equation.

In formula (3), || c|| ₀for the 0-norm of c, be the number of non-zero in coefficient vector c, be also the degree of rarefication of vectorial c; Y represents described detection signal y (t); ε represents an enough little value.Formula (3) be one about owing surely polynomial problem; Based on this, this is owed to determine polynomial expression problem and can change into conventionally:

$\begin{array}{ccc}\underset{c}{\min }{\left|\right|c\left|\right|}_1& s.t.& {\left|\right|\mathrm{Ac}-y\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}---\left(4\right)$

In formula (4), || c|| ₁for the 1-norm of c, be defined as

n represents the number of element in rarefaction representation coefficient vector c.Wherein,

represent the absolute value summation to the each element in vectorial c, total N the element of vectorial c mono-, c (n) represents n element in N element in vectorial c.

Based on this, the rarefaction representation Solve problems of formula (4) can utilize base to follow the trail of denoising method and change into linear programming problem:

$J\left(c\right)\underset{c}{\arg \mathrm{<figure-callout\; id="1"\; label="min"\; filenames="HDA0000467967090000051.png"\; state="\{\{state\}\}">min</figure-callout>}\frac{1}{2}}{\left|\right|y-\mathrm{Ac}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|c\left|\right|}_1---\left(5\right)$

Wherein in formula (5), λ is Lagrange multiplier.

Be understandable that, formula (5) is carried out in the process of variable separation, the Part I of formula (5) equal sign right-hand member

be a function about uncertain vectorial c, can be used function f ₁(c) represent.The Part II λ of formula (5) right-hand member || c|| ₁also be a function about vectorial c, used function f ₂(c) represent.

That is to say, can get f ₂(c)=λ || c|| ₁, the variable that obtains described detection signal y (t) separates expression formula:

$\begin{array}{cc}\underset{c}{\min }& f_1\left(c\right)+f_2\left(v\right)\\ s.t.& c=v\end{array}---\left(6\right)$

Further, get E (z)=f ₁(c)+f ₂(v) $z=\left[\begin{array}{c}c\\ v\end{array}\right],$ B=0, H=[I-I], obtain the augmentation Lagrangian formulation of described variable separation problem (being formula (6)):

$\begin{array}{c}\underset{z}{\min }E\left(z\right)\\ \begin{array}{cc}s.t.& \mathrm{Hz}-b=0\end{array}\end{array}---\left(7\right)$

Wherein, f in formula (6) ₁(c)+f ₂(v) be a binary function about uncertain vectorial c and v, get $z=\left[\begin{array}{c}c\\ v\end{array}\right],$ F in formula (6) ₁(c)+f ₂(v) just convert a function about vectorial z to, therefore can be by f ₁(c)+f ₂(v) be denoted as a function E (z) about vectorial z.

Matrix I representation unit matrix, the element on the principal diagonal of unit matrix is all 1, all the other elements are 0.Matrix-I represents all elements in unit matrix I to get opposite number.The matrix [I-I] being made up of matrix I and matrix-I represents by matrix H.

Obtain, after formula (7), can solving it by iterative algorithm, this iterative algorithm is:

$z_{k+1}=\underset{z}{\arg \min }E\left(z\right)+(\mathrm{\&mu;}/2){\left|\right|\mathrm{Hz}-d_k\left|\right|}_2^2$

d _k+1=d _k-(Hz _k+1-b)

Wherein, μ represents to punish parameter.

Owing to considering E (z) in formula (7), z, b, the concrete form of H, and getting matrix A is the former word bank of optimal wavelet in described step S103, obtain new iterative algorithm---the subbasal division augmentation Lagrange of small echo contraction algorithm, this iterative algorithm specifically comprises the following steps:

Step 1: given initial parameter k=0, μ >0, v ₀, d ₀, iterations M.

Step 2: calculate c by following formula _k+1;

$c_{k+1}=\underset{c}{\arg \min }{\left|\right|A\&CenterDot;c-y\left|\right|}_2^2+(\mathrm{\&mu;}/2)\left|\right|c-v_k-d_k{\left|\right|}_2^2---\left(8\right)$

Step 3: calculate v by following formula _k+1;

$v_{k+1}=\underset{v}{\arg \min }\mathrm{\&lambda;}{\left|\right|v\left|\right|}_1+(\mathrm{\&mu;}/2){\left|\right|c_{k+1}-v-d_k\left|\right|}_2^2---\left(9\right)$

Step 4: calculate d by following formula _k+1;

d _k+1=d _k-(c _k+1-v _k+1) (10)

Step 5: k=k+1;

Step 6: if k>M, finishing iteration; Otherwise go to step two.

So far,, by iterative algorithm described in iteration, obtain described rarefaction representation coefficient c.

As a further improvement on the present invention, described step S105 can be specially:

According to 3 σ criterions, described rarefaction representation coefficient c is got to threshold value, obtain feature rarefaction representation coefficient

wherein σ is the standard deviation of described rarefaction representation coefficient.

Be understandable that, 3 σ criterions, are generally used for the processing of measuring error, and major function is the gross error of choosing in measuring error; Wherein, coefficient absolute value is less than the zero setting of 3 σ, and the coefficient that is greater than 3 σ retains.

Can be with reference to figure 2c, Fig. 2 c is the schematic flow sheet of a step S105 preferred implementation, described step S105 can specifically comprise:

Step S1051, compute sparse represent the standard deviation sigma of coefficient vector c;

$\mathrm{\&sigma;}=\sqrt{\left(\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i^2\right)}---\left(11\right)$

Wherein, c _irepresent the element in sparse coefficient c.Initialization, gets i=1.

Step S1052, judge c _iif, c _i<3 σ, c _i=0, i=i+1, if i>N stops calculating; Otherwise, repeated execution of steps S1052.

The feature rarefaction representation coefficient of step S1053, acquisition is denoted as

Can be denoted as according to described feature rarefaction representation coefficient

determine the generation moment of transient components in described detection signal y (t), thereby determine the cycle of transient components in described detection signal y (t).

From the above, in a kind of signal based on rarefaction representation that the embodiment of the present invention provides in transient components detection method, model wavelet library, again detection signal is carried out to related operation, then expand and form the former word bank of small echo with different delayed time parameter, in conjunction with division augmentation Lagrange contraction algorithm, can realize the rarefaction representation of signal to be detected on the former word bank of this small echo again.The present invention changes into a sparse vector that only contains a small amount of numerical value by the transient components in original signal and shows, and has realized the succinct expression of transient components; Due to noise contribution in detection signal and the former word bank similarity degree of this small echo low, and the similarity of trouble unit and the former word bank of small echo is large, therefore the inventive method is little to noise sensitivity, can realize weak fault signature and detect; Can be used for the period transient state composition of mechanical equipment vibration signal to detect, can realize the detection to mechanical equipment fault feature.

In the signal based on rarefaction representation that the embodiment of the present invention provides, transient components detection method can be applicable in equipment failure detection, first, need to be on the appropriate location of equipment to be detected sensor installation, using the vibration signal of equipment to be detected as detection signal y (t), the detection method that adopts the embodiment of the present invention to provide detects signal y (t), if the cycle of detecting and the fault signature cycle of this equipment part coincide, in determining apparatus, the part position corresponding with this cycle has fault.

Can cause when breaking down under rotating machinery constant rotational speed periodic feature to occur, use above-mentioned signal transient composition small echo rarefaction representation detection method, on the housing of equipment to be detected, acceleration transducer is installed, the vibration acceleration signal of checkout equipment, as detection signal y (t), adopt above-mentioned signal small echo rarefaction representation detection method to detect signal y (t), in the time there is period transient state composition in signals and associated noises y (t), the method can detect the generation moment of each transient components; For Periodic Rotating machinery, the mean value in each time interval can be regarded the cycle as.Utilize this to judge in plant equipment in cycle possible breakdown position that should the cycle is existed to fault.

In order to understand better numerical procedure of the present invention, below so that fault signature a little less than gear tooth breakage fault detect and bearing part is detected as example, the application of transient components detection method in the described signal based on rarefaction representation is told about in detail:

Embodiment mono-: a kind of gear tooth breakage fault detect

If after the fracture of certain tooth of gear, can make to exist in vibration signal transient impact composition, and this transient impact composition is carried in the meshing frequency of noise and gear, input need to be carried out and fault signature could be expressed clearly.

Subjects is the detection of the third gear meshing gear fault of certain automotive transmission, can be in the lump with reference to figure 3, and Fig. 3 is the inner drive mechanism schematic diagram of embodiment mono-middle gear case.Be understandable that, piezoelectricity be installed in process of the test on the housing of variator and accelerated dynamic sensor, for picking up vibration acceleration signal.Vibration acceleration signal is also stored by computer acquisition after piezoelectric acceleration sensor, charge amplifier.

Can reference table 1, the parameter of the third gear that table 1 is this gear case:

Table 1

Vibration signal under third gear engagement is carried out to the detection of period transient state composition characteristics, and the vibration signal under gear tooth breakage state shows as the signal of the bilateral decay of series of periodic, and therefore, getting small echo atom is the Morlet small echo of bilateral decay.

Please refer to Fig. 4, time domain waveform when Fig. 4 is embodiment mono-middle gear case third gear broken conditions and small echo rarefaction representation testing result schematic diagram; Wherein, vibration signal y (t) waveform that Fig. 4 (a) records while there is broken teeth fault for third gear, having the cycle is the transient impact composition of 50ms, but in time-domain diagram, cannot observe out this cycle.Fig. 4 (b) is the spectrogram of gear distress vibration signal, and the meshing frequency that can obtain this gear vibration in spectrogram is 500Hz, but can not obtain its failure-frequency.Fig. 4 (c) is the Morlet small echo atom mating most with signal y (t), at the bottom of this wavelet basis, can be expressed as: and A (t, 0.2210)=ψ (f, ζ, 0.2210, t), wherein f=268Hz, ζ=0.0057.Using one of atom in the former word bank of small echo at the bottom of this wavelet basis, expanding the former word bank of small echo is A (t, τ), and frequency f and dampingratioζ are constant, and τ is by the inverse (1/f of default sample frequency _s) equally spaced value, the former word bank of this small echo can be expressed as A (t, τ)=ψ (268,0.0057, τ, t).

Gear distress signal is carried out to the subbasal rarefaction representation of Morlet small echo, obtain rarefaction representation coefficient vector as shown in Fig. 4 (d).Adopt 3 σ criterions to obtain feature rarefaction representation coefficient to the sparse coefficient c in Fig. 4 (d)

as shown in Fig. 4 (e).From Fig. 4 (e), the shock response moment can intuitively obtain gear distress time.Please also refer to table 2, in table 2, provide the transient impact moment shown in sparse table in gear distress situation, because the rotating speed of gear is not strict constant rotational speed, therefore the spacing between the shock response moment does not strictly equate as can be seen from Table 2, get the mean value of spacing as the cycle of this vibration signal,

basically identical with theoretical inaction interval.Fig. 4 (f) is the gear distress signal of reconstruct, can obviously find out the validity of the transient impact composition detection that the method causes at gearbox fault from Fig. 4 (f).

Table 2

Embodiment bis-: the detection of the weak fault signature in a kind of bearing part

Outer ring, inner ring and the rolling body of bearing is the main happening part of bearing fault, and the slight local fault (as the peeling off of part, corrosion etc.) that occurs in these positions tends to cause occur in bear vibration transient impact.When bearing under constant rotational speed breaks down, its vibration signal shows as periodic transient impact response component.But the duration of the vibration causing due to local fault is short, this transient impact is mixed in powerful ground unrest often simultaneously, and when minor failure, the energy increase of time-domain signal is not remarkable, and the frequency band in frequency domain is wider, is difficult for detecting.

Subjects is NJ208 (TMB) type cylinder roller bearing, utilizes line cutting on bearing outer ring, inner ring and rolling body, to be all provided with 0.2mm and connects slight crack fault, simulates respectively the minor failure at the each position of bearing.In this embodiment, the axle that testing table is connected with motor by motor, by shaft coupling, bearing and the charger of stationary shaft form, and vibration signal is recorded by data collecting instrument, and sample frequency is 51.2KHz.When test, bearing rotating speed is 1496rpm.As calculated, the theoretical fault characteristic frequency that bearing outer ring, inner ring and rolling body are corresponding is respectively 142.8Hz, 206.3Hz and 132.6Hz, and the corresponding cycle is respectively 7.00ms, 4.85ms and 7.54ms.

The vibration signal that gathers the local minor failure of bearing outer ring, inner ring and rolling body, utilizes respectively small echo rarefaction representation detection method to its analyzing and processing, calculates the corresponding fault signature cycle.Vibration signal under bearing fault state shows as the signal of the monolateral decay of series of periodic, and therefore, getting small echo atom is the Laplace small echo of monolateral decay.

Please also refer to Fig. 5, Fig. 5 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of these embodiment bis-centre bearer outer ring local faults, and wherein, Fig. 5 (a) is the time domain waveform that outer ring minor failure is corresponding.From Fig. 5 (a), can not find out the existence of many shock responses of loop cycle composition, can not identify the generation moment of transient impact composition, thereby can not judge fault type.Fig. 5 (b) is the spectrogram that this vibration signal is corresponding, and spectrogram can not show inaction interval.

First obtain according to correlation filtering method the Laplace small echo basis function mating most with original signal, at the bottom of this wavelet basis, can be expressed as, A (t, 0.0159)=ψ (f, ζ, 0.0159, t), wherein f=3024Hz, ζ=0.0890, this small echo basis function is as shown in Fig. 5 (c).Using one of atom in the former word bank of small echo at the bottom of this wavelet basis, expanding the former word bank of small echo is A (t, τ), and frequency f and dampingratioζ are constant, and τ is by the inverse (1/f of default sample frequency _s) equally spaced value, the former word bank of this small echo can be expressed as A (t, τ)=ψ (3024,0.0890, τ, t).

Bearing outer ring minor failure signal is carried out to the subbasal rarefaction representation of Laplace small echo, obtain rarefaction representation coefficient vector as shown in Fig. 5 (d), adopt 3 σ criterions to obtain feature rarefaction representation coefficient to the sparse coefficient c in Fig. 5 (d) as shown in Fig. 5 (e), the shock response moment can intuitively obtain bearing outer ring fault from Fig. 5 (e) time.The bearing outer ring minor failure signal that Fig. 5 (f) is reconstruct, can find out that from Fig. 5 (f) the method can identify moment point and the inaction interval of transient impact effectively.Please refer to table 3, in table 3, provide the transient impact moment shown in sparse table in housing washer minor failure situation, because the rotating speed of bearing is not strict constant rotational speed, therefore the spacing between the shock response moment does not strictly equate as can be seen from Table 3, get the mean value of spacing as the cycle of this vibration signal, basically identical with theoretical inaction interval.

Table 3

Please also refer to Fig. 6, Fig. 6 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of these embodiment bis-centre bearer inner ring local faults; Wherein, Fig. 6 (a) is the time domain waveform that inner ring minor failure is corresponding, as can be seen from the figure has many shock responses pulse, but can not obtain its cycle, can not identify the generation moment of shock response composition.Fig. 6 (b) is the spectrogram that this vibration signal is corresponding, and spectrogram can not show inaction interval.

Obtained the Laplace small echo basis function mating most with original signal by correlation filtering method, at the bottom of this wavelet basis, can be expressed as, A (t, 0.0467)=ψ (f, ζ, 0.0467, t), wherein f=6402Hz, ζ=0.1400, this small echo basis function is as shown in Fig. 6 (c).Be A (t, τ) by the former word bank of small echo expanding at the bottom of this wavelet basis, frequency f and dampingratioζ are constant, and τ is still by the inverse (1/f of default sample frequency _s) equidistant value, obtaining ψ (f, ζ, τ, t)=ψ (6402,0.1400, τ, t) is the former word bank of this small echo.Fig. 6 (d) is the coefficient vector after rarefaction representation, adopts 3 σ criterions to obtain feature rarefaction representation coefficient to the sparse coefficient c in Fig. 6 (d)

as shown in Fig. 6 (e).The shock response moment can intuitively obtain bearing inner race fault in Fig. 6 (e) time.The bearing inner race minor failure signal that Fig. 6 (f) is reconstruct, Fig. 6 (f) shows that the method can effectively identify shock response moment point and inaction interval.Please refer to Fig. 4, table 4 has provided the shock response moment that in rolling bearing inner ring minor failure situation, rarefaction representation obtains, and gets the mean value of spacing as the cycle of this vibration signal,

consistent with theoretical inaction interval.

Table 4

Please refer to Fig. 7, Fig. 7 is time domain waveform and the small echo rarefaction representation testing result schematic diagram of embodiment bis-centre bearer rolling body local faults; Wherein, bearing roller minor failure time domain waveform is as shown in Fig. 7 (a).Fig. 7 (b) is the spectrogram that this vibration signal is corresponding, and spectrogram can not show inaction interval.Can be as shown in Fig. 7 (c) at the bottom of the wavelet basis that is obtained mating most with original signal by correlation filtering method.The former word bank that A (t, τ)=ψ (5712,0.2350, τ, t) obtains for construction of function at the bottom of wavelet basis.Rarefaction representation coefficient vector is as shown in Fig. 7 (d).Adopt 3 σ criterions to obtain feature rarefaction representation coefficient to the sparse coefficient c in Fig. 7 (d)

as shown in Fig. 7 (e).Shock response moment and inaction interval can intuitively obtain bearing roller fault from Fig. 7 (e) time.The bearing roller minor failure signal that Fig. 7 (f) is reconstruct.Reference table 5 in the lump, table 5 has provided the shock response moment that in bearing roller minor failure situation, rarefaction representation obtains, and gets the mean value of spacing as the cycle of this vibration signal,

basically identical with theoretical inaction interval.

Table 5

Can find out from analytic process and application example, transient components detection method in signal based on rarefaction representation provided by the invention, can effectively detect the generation moment of the transient state characteristic composition in signal, find corresponding inaction interval, thereby efficient diagnosis is out of order, its feature has determined that the method can effectively be applied to rotary machinery fault diagnosis.

From above-described embodiment, transient components detection method in signal based on rarefaction representation provided by the invention, utilize sensing device to input and carry out mould/number conversion, obtain detection signal y (t), detect in described signal y (t) and whether have period transient state composition, comprise the steps: to set up wavelet library, and parametrization represents; According to the principle of related coefficient maximum, choose the base small echo the highest with signal similar degree, and determine its corresponding parameter, be designated as

structure has the former word bank A of small echo (t, τ) of different delay parameter; Former this small echo word bank substrate is replaced to the substrate in augmentation Lagrangian Arithmetic, obtain rarefaction representation coefficient by iterative algorithm; According to 3 σ criterions, rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient; From rarefaction representation coefficient, read the generation moment of each transient impact composition.The transient components in original signal is expressed as the numerical value in sparse vector by the present invention, realized easily the rarefaction representation of transient components feature.By the numerical value in sparse vector, the transient components in signal is effectively detected, realized the detection in rotating machinery fault cycle, to being concise in expression of signal, little to the sensitivity of noise, be specially adapted to the automatic identification of the fault to plant equipment.

For ease of transient components detection method in the signal based on rarefaction representation that better the enforcement embodiment of the present invention provides, the embodiment of the present invention also provides a kind of device based on transient components detection method in above-mentioned signal.Wherein the implication of noun is identical with said method, the explanation of specific implementation details in can reference method embodiment.

Please refer to Fig. 8, the structural representation of transient components pick-up unit in a kind of signal based on rarefaction representation that Fig. 8 provides for the embodiment of the present invention, wherein, described device comprises:

The first acquisition module 801, for input signal is carried out to mould/number conversion, obtains detection signal y (t);

Computing module 802, for calculating the optimal wavelet substrate of described detection signal y (t);

Be understandable that, in the embodiment of the present invention, the criterion of described optimal wavelet substrate is weighed with the maximum similarity of original signal (being y (t)) at the bottom of conventionally using wavelet basis, and wherein, maximum similarity can carry out quantificational expression with maximum correlation coefficient.

For example: at the bottom of wavelet basis, the related coefficient of ψ and signal y can be expressed as: wherein, < ψ, y> represents the inner product of ψ and signal y at the bottom of wavelet basis; || ψ || ₂, || ψ || ₂represent respectively the mould of ψ and signal y at the bottom of wavelet basis.When at the bottom of wavelet basis in the time constantly changing, can produce different related coefficients, choosing at the bottom of the wavelet basis that maximum correlation coefficient is corresponding is optimal wavelet substrate.

Constructing module 803, for described optimal wavelet substrate is expanded, the former word bank of structure optimal wavelet;

Wherein, regard the optimal wavelet substrate in step S102 as a small echo atom, this small echo atom is carried out to a series of time delays and construct the small echo atom having without delay parameter, then the small echo atom that these are had to different delayed time is combined the former word bank of formation optimal wavelet.

The first determination module 804, for according to the former word bank of described optimal wavelet, utilizes division augmentation Lagrange contraction algorithm solving-optimizing equation, and determines the rarefaction representation coefficient of described detection signal y (t) on the former word bank of described optimal wavelet;

The second acquisition module 805, for described rarefaction representation coefficient is got to threshold value, obtains feature rarefaction representation coefficient;

The second determination module 806, for according to described feature rarefaction representation coefficient, determines the generation moment of transient components in described detection signal y (t);

The 3rd determination module 807, for according to the generation moment of described detection signal y (t) transient components, determines the cycle of transient components in described detection signal y (t).

For the embodiment of each functional module, transient components pick-up unit in the signal based on rarefaction representation is carried out to analytic explanation below:

Described computing module 802 can be specifically for: set up wavelet library, described wavelet library is the set of one group of small echo atom; Calculate the similarity of small echo atom in described detection signal y (t) and described wavelet library; To be defined as optimal wavelet substrate with the highest small echo atom of detection signal y (t) similarity degree.

Be understandable that, described wavelet library can be designated as Ψ, ripple storehouse Ψ is carried out to parametrization and represent, is designated as Ψ={ ψ (f, ζ, τ, t) };

Wherein, wavelet library Ψ is defined as the set of one group of small echo atom, and described small echo atomic parameter is represented, is designated as ψ (f, ζ, τ, t); Parameter f represents frequency, and ζ represents decay factor, and τ represents delay time, and t represents time parameter; Wherein, parameter f, the value that ζ and τ can be discrete in the scope presetting, this scope presetting can be determined according to priori.

Be understandable that, in the embodiment of the present invention, if detect for the fault-signal of rotating machinery gear and bearing, can select wavelet library and be respectively Morlet small echo and Laplace small echo, expression formula is respectively:

Morlet small echo: $\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},t)=e^{\frac{-\mathrm{\&zeta;}}{\sqrt{1-{\mathrm{\&zeta;}}^2}}{\left[2\mathrm{\&pi;f}(t-\mathrm{\&tau;})\right]}^2}\cos \left(2\mathrm{\&pi;f}(t-\mathrm{\&tau;})\right);$

Laplace small echo: $\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},f)=\left\{\begin{array}{cc}{e}^{\frac{-\mathrm{\&zeta;}}{\sqrt{1-{\mathrm{\&zeta;}}^2}}2\mathrm{\&pi;f}(t-\mathrm{\&tau;})}& t\&GreaterEqual;\mathrm{\&tau;}\\ 0& t<\mathrm{\&tau;}\end{array}\right.;$

Wherein, Morlet small echo is a kind of small echo with bilateral symmetry attenuation characteristic; Laplace small echo is a kind of small echo with monolateral attenuation characteristic.These two kinds of small echos, in the widespread use of mechanical fault diagnosis field, are not made specific explanations herein to this.

Wherein, can use related coefficient k for detection signal y (t) with the similarity of small echo atom ψ (f, ζ, τ, t) _γrepresent, using as evaluation index;

Described related coefficient k _γfor:

$k_{\mathrm{\&gamma;}}=\frac{|<\mathrm{\&psi;}(f,\mathrm{\&zeta;},\mathrm{\&tau;},t),y\left(t\right)>|}{{\left|\right|\mathrm{\&psi;}\left|\right|}_2{\left|\right|y\left|\right|}_2}---\left(1\right)$

According to the principle of related coefficient maximum, in wavelet library Ψ, choose the base small echo the highest with detection signal y (t) similarity degree, this criterion of choosing is: in wavelet library Ψ, find the small echo atom with signal to be analyzed (being detection signal y (t)) related coefficient maximum, using this small echo atom as the base small echo the highest with signal similar degree,,, determine the parameter that it is corresponding thereafter.

Base small echo described and that signal similar degree is the highest is defined as to optimal wavelet substrate;

In this embodiment, described optimal wavelet substrate is designated as wherein, t represents respectively corresponding frequency, decay factor, delay parameter, time parameter.

Further preferably, in some embodiments of the invention, described constructing module 803 can be specifically for: to described optimal wavelet substrate to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

As a further improvement on the present invention, described the first determination module 804, can be specifically for: according to described detection signal y (t), the variable that obtains described detection signal y (t) separates expression formula; Separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm; Described in iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

Particularly, described detection signal y (t) can be expressed as:

y(t)=x(t)+n(t)=Ac+n (2)

Wherein, y (t) is detection signal, x (t) is actual signal, n (t) represents the noise contribution in detection signal, A represents the former word bank A of described optimal wavelet (t, τ) (also can be referred to as over-complete dictionary of atoms), c represents described rarefaction representation coefficient, and n represents described noise contribution n (t)

Be understandable that, for convenience of understanding, in embodiments of the present invention the unified italic that adopts of variable represented, matrix or the positive runic of the unified employing of vector are represented; Y (t) in formula (2), the letter occurring in x (t) and n (t) all represents variable, therefore represents by italic; And A represents the former word bank of optimal wavelet in formula (2), be a matrix, c represents rarefaction representation coefficient, is a vector, n represents noise contribution n (t), is also a vector, therefore represents with positive runic.

In addition, because detection signal y (t) is the signal that uses in actual applications sensor device measuring to collect, consider that the signal of measurement contains much noise conventionally, therefore need just can obtain Useful Information by this signal of analyzing and testing.

Further, the rarefaction representation of signal x (t) on over-complete dictionary of atoms A can be described as:

$\begin{array}{ccc}\underset{c}{\min }{\left|\right|c\left|\right|}_0& s.t.& {\left|\right|\mathrm{Ac}-y\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}---\left(3\right)$

Wherein, in formula (3), " s.t. " is the abbreviation of " subject to ", represents the meaning of " meeting ".Formula (3) also can be write as "

and meet

", formula (3) represents, is meeting

prerequisite under, make || c|| ₀the solution that minimum vectorial c is this equation.

In formula (3), || c|| ₀for the 0-norm of c, be the number of non-zero in coefficient vector c, be also the degree of rarefication of vectorial c; Y represents described detection signal y (t); ε represents an enough little value.Formula (3) be one about owing surely polynomial problem; Based on this, this is owed to determine polynomial expression problem and can change into conventionally:

$\begin{array}{ccc}\underset{c}{\min }{\left|\right|c\left|\right|}_1& s.t.& {\left|\right|\mathrm{Ac}-y\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}---\left(4\right)$

In formula (4), || c|| ₁for the 1-norm of c, be defined as

n represents the number of element in rarefaction representation coefficient vector c.Wherein,

represent the absolute value summation to the each element in vectorial c, total N the element of vectorial c mono-, c (n) represents n element in N element in vectorial c.

Based on this, the rarefaction representation Solve problems of formula (4) can utilize base to follow the trail of denoising method and change into linear programming problem:

$J\left(c\right)\underset{c}{\arg \mathrm{<figure-callout\; id="1"\; label="min"\; filenames="HDA0000467967090000051.png"\; state="\{\{state\}\}">min</figure-callout>}\frac{1}{2}}{\left|\right|y-\mathrm{Ac}\left|\right|}_2^2+\mathrm{\&lambda;}{\left|\right|c\left|\right|}_1---\left(5\right)$

Wherein in formula (5), λ is Lagrange multiplier.

Be understandable that, formula (5) is carried out in the process of variable separation, the Part I of formula (5) equal sign right-hand member be a function about uncertain vectorial c, can be used function f ₁(c) represent.The Part II λ of formula (5) right-hand member || c|| ₁also be a function about vectorial c, used function f ₂(c) represent.

That is to say, can get

f ₂(c)=λ || c|| ₁, the variable that obtains described detection signal y (t) separates expression formula:

$\begin{array}{cc}\underset{c}{\min }& f_1\left(c\right)+f_2\left(v\right)\\ s.t.& c=v\end{array}---\left(6\right)$

Further, get E (z)=f ₁(c)+f ₂(v), $z=\left[\begin{array}{c}c\\ v\end{array}\right],$ B=0, H=[I-I], obtain the augmentation Lagrangian formulation of described variable separation problem (being formula (6)):

$\begin{array}{c}\underset{z}{\min }E\left(z\right)\\ \begin{array}{cc}s.t.& \mathrm{Hz}-b=0\end{array}\end{array}---\left(7\right)$

Wherein, f in formula (6) ₁(c)+f ₂(v) be a binary function about uncertain vectorial c and v, get $z=\left[\begin{array}{c}c\\ v\end{array}\right],$ F in formula (6) ₁(c)+f ₂(v) just convert a function about vectorial z to, therefore can be by f ₁(c)+f ₂(v) be denoted as a function E (z) about vectorial z.

Matrix I representation unit matrix, the element on the principal diagonal of unit matrix is all 1, all the other elements are 0.Matrix-I represents all elements in unit matrix I to get opposite number.The matrix [I-I] being made up of matrix I and matrix-I represents by matrix H.

Obtain, after formula (7), can solving it by iterative algorithm, this iterative algorithm is:

$z_{k+1}=\underset{z}{\arg \min }E\left(z\right)+(\mathrm{\&mu;}/2){\left|\right|\mathrm{Hz}-d_k\left|\right|}_2^2$

d _k+1=d _k-(Hz _k+1-b)

Wherein, μ represents to punish parameter.

Owing to considering E (z) in formula (7), z, b, the concrete form of H, and getting matrix A is the former word bank of described optimal wavelet, obtains new iterative algorithm---the subbasal division augmentation Lagrange of small echo contraction algorithm, and this iterative algorithm specifically comprises the following steps:

Step 1: given initial parameter k=0, μ >0, v ₀, d ₀, iterations M.

Step 2: calculate c by following formula _k+1;

$c_{k+1}=\underset{c}{\arg \min }{\left|\right|A\&CenterDot;c-y\left|\right|}_2^2+(\mathrm{\&mu;}/2)\left|\right|c-v_k-d_k{\left|\right|}_2^2---\left(8\right)$

Step 3: calculate v by following formula _k+1;

$v_{k+1}=\underset{v}{\arg \min }\mathrm{\&lambda;}{\left|\right|v\left|\right|}_1+(\mathrm{\&mu;}/2){\left|\right|c_{k+1}-v-d_k\left|\right|}_2^2---\left(9\right)$

Step 4: calculate d by following formula _k+1;

d _k+1=d _k-(c _k+1-v _k+1) (10)

Step 5: k=k+1;

Step 6: if k>M, finishing iteration; Otherwise go to step two.

So far,, by iterative algorithm described in iteration, obtain described rarefaction representation coefficient c.

As a further improvement on the present invention, described the second acquisition module 805, can be specifically for: according to 3 σ criterions, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, wherein, described σ is the standard deviation of described rarefaction representation coefficient.

Be understandable that, 3 σ criterions, are generally used for the processing of measuring error, and major function is the gross error of choosing in measuring error; Wherein, coefficient absolute value is less than the zero setting of 3 σ, and the coefficient that is greater than 3 σ retains.

Particularly, represent the standard deviation sigma of coefficient vector c for compute sparse;

$\mathrm{\&sigma;}=\sqrt{\left(\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{c}_i^2\right)}---\left(11\right)$

Wherein, c _irepresent the element in sparse coefficient c.Initialization, gets i=1.

Judge c _iif, c _i<3 σ, c _i=0, i=i+1, if i>N stops calculating; Otherwise, repeated execution of steps S1052.

The feature rarefaction representation coefficient obtaining is denoted as

Can be denoted as according to described feature rarefaction representation coefficient

determine the generation moment of transient components in described detection signal y (t), thereby determine the cycle of transient components in described detection signal y (t).

From the above, in a kind of signal based on rarefaction representation that the embodiment of the present invention provides in transient components pick-up unit, model wavelet library, again detection signal is carried out to related operation, then expand and form the former word bank of small echo with different delayed time parameter, in conjunction with division augmentation Lagrange contraction algorithm, can realize the rarefaction representation of signal to be detected on the former word bank of this small echo again.The present invention changes into a sparse vector that only contains a small amount of numerical value by the transient components in original signal and shows, and has realized the succinct expression of transient components; Due to noise contribution in detection signal and the former word bank similarity degree of this small echo low, and the similarity of trouble unit and the former word bank of small echo is large, therefore little to noise sensitivity, can realize weak fault signature and detect; Can be used for the period transient state composition of mechanical equipment vibration signal to detect, can realize the detection to mechanical equipment fault feature.

In the above-described embodiments, the description of each embodiment is all emphasized particularly on different fields, in certain embodiment, there is no the part of detailed description, can be referring to the associated description of other embodiment.

Those skilled in the art can be well understood to, for convenience and simplicity of description, the system of foregoing description, the specific works process of device and unit, can, with reference to the corresponding process in preceding method embodiment, not repeat them here.

In the several embodiment that provide in the application, should be understood that, disclosed system, apparatus and method, can realize by another way.For example, device embodiment described above is only schematic, for example, the division of described unit, be only that a kind of logic function is divided, when actual realization, can have other dividing mode, for example multiple unit or assembly can in conjunction with or can be integrated into another system, or some features can ignore, or do not carry out.Another point, shown or discussed coupling each other or direct-coupling or communication connection can be by some interfaces, indirect coupling or the communication connection of device or unit can be electrically, machinery or other form.

The described unit as separating component explanation can or can not be also physically to separate, and the parts that show as unit can be or can not be also physical locations, can be positioned at a place, or also can be distributed in multiple network element.Can select according to the actual needs some or all of unit wherein to realize the object of the present embodiment scheme.

In addition, the each functional unit in each embodiment of the present invention can be integrated in a processing unit, can be also that the independent physics of unit exists, and also can be integrated in a unit two or more unit.Above-mentioned integrated unit both can adopt the form of hardware to realize, and also can adopt the form of SFU software functional unit to realize.

If described integrated unit is realized and during as production marketing independently or use, can be stored in a computer read/write memory medium using the form of SFU software functional unit.Based on such understanding, the all or part of of the part that technical scheme of the present invention contributes to prior art in essence in other words or this technical scheme can embody with the form of software product, this computer software product is stored in a storage medium, comprise that some instructions (can be personal computers in order to make a computer equipment, server, or the network equipment etc.) carry out all or part of step of method described in each embodiment of the present invention.And aforesaid storage medium comprises: various media that can be program code stored such as USB flash disk, portable hard drive, ROM (read-only memory) (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), magnetic disc or CDs.

Above transient components detection method and device in a kind of signal based on rarefaction representation provided by the present invention are described in detail, for one of ordinary skill in the art, according to the thought of the embodiment of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.

Claims (10)

1. a transient components detection method in the signal based on rarefaction representation, is characterized in that, comprising:

Input signal is carried out to mould/number conversion, obtain detection signal;

Calculate the optimal wavelet substrate of described detection signal;

Described optimal wavelet substrate is expanded to the former word bank of structure optimal wavelet;

According to the former word bank of described optimal wavelet, utilize division augmentation Lagrange contraction algorithm solving-optimizing equation, and determine the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet;

Described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient;

According to described feature rarefaction representation coefficient, determine the generation moment of transient components in described detection signal;

According to the generation moment of transient components in described detection signal, determine the cycle of transient components in described detection signal.

2. detection method according to claim 1, is characterized in that, the optimal wavelet substrate of the described detection signal of described calculating, comprising:

Set up wavelet library, described wavelet library is the set of one group of small echo atom;

Calculate the similarity of small echo atom in described detection signal and described wavelet library;

To be defined as optimal wavelet substrate with the highest small echo atom of detection signal similarity degree.

3. detection method according to claim 1 and 2, is characterized in that:

Described optimal wavelet substrate is

wherein,

t represents respectively corresponding frequency, decay factor, delay parameter, time parameter;

Described described optimal wavelet substrate is expanded, the former word bank of structure optimal wavelet, comprising:

To described optimal wavelet substrate

to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

4. detection method according to claim 3, it is characterized in that, described according to the former word bank of described optimal wavelet, utilize division augmentation Lagrange contraction algorithm solving-optimizing equation, and determine the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet, comprising:

According to described detection signal, the variable that obtains described detection signal separates expression formula;

Separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm;

Described in iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

5. detection method according to claim 3, is characterized in that, described described rarefaction representation coefficient is got to threshold value, obtains feature rarefaction representation coefficient, comprising:

According to 3 σ criterions, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, wherein, described σ is the standard deviation of described rarefaction representation coefficient.

6. a transient components pick-up unit in the signal based on rarefaction representation, is characterized in that, comprising:

The first acquisition module, for input signal is carried out to mould/number conversion, obtains detection signal;

Computing module, for calculating the optimal wavelet substrate of described detection signal;

Constructing module, for described optimal wavelet substrate is expanded, the former word bank of structure optimal wavelet;

The first determination module, for according to the former word bank of described optimal wavelet, utilizes division augmentation Lagrange contraction algorithm solving-optimizing equation, and determines the rarefaction representation coefficient of described detection signal on the former word bank of described optimal wavelet;

The second acquisition module, for described rarefaction representation coefficient is got to threshold value, obtains feature rarefaction representation coefficient;

The second determination module, for according to described feature rarefaction representation coefficient, determines the generation moment of transient components in described detection signal;

The 3rd determination module, for according to the generation moment of described detection signal transient components, determines the cycle of transient components in described detection signal.

7. pick-up unit according to claim 6, is characterized in that, described computing module specifically for: set up wavelet library, described wavelet library is the set of one group of small echo atom; Calculate the similarity of small echo atom in described detection signal and described wavelet library; To be defined as optimal wavelet substrate with the highest small echo atom of detection signal similarity degree.

8. according to the pick-up unit described in claim 6 or 7, it is characterized in that:

Described optimal wavelet substrate is

wherein,

t represents respectively corresponding frequency, decay factor, delay parameter, time parameter;

Described constructing module specifically for: to described optimal wavelet substrate

to preset sample frequency as time delay interval, expand by different time shifts, construct line display different time parameter, the former word bank A of the optimal wavelet of different delayed time parameter (t is shown in list, τ), wherein τ represents by the delay parameter of the even value of inverse of described default sample frequency.

9. pick-up unit according to claim 8, is characterized in that, described the first determination module, specifically for: according to described detection signal, the variable that obtains described detection signal separates expression formula; Separate expression formula according to the former word bank A of described optimal wavelet (t, τ) with described variable, obtain the subbasal division augmentation Lagrange of small echo contraction algorithm; Described in iteration, the subbasal division augmentation Lagrange of small echo contraction algorithm, obtains rarefaction representation coefficient.

10. pick-up unit according to claim 8, is characterized in that, described the second acquisition module, specifically for: according to 3 σ criterions, described rarefaction representation coefficient is got to threshold value, obtain feature rarefaction representation coefficient, wherein, described σ is the standard deviation of described rarefaction representation coefficient.

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