CN100386603C - State judging method, and state predicting method and device - Google Patents

Abstract

It is generally necessary that even if waveform data and feature parameter measured for monitoring the state of an object does not have normal distributions, the state diagnosis and state prediction of the object are conducted with high accuracy by a method such as a statistic testing, a specific component locally present in a measurement signal of the object is detected in real time when the signal is a pulsating one, and the state of the object is judged efficiently. The invention provides a method and device wherein measured waveform data or a feature parameter calculated from the waveform data is converted so as to have a know probability distribution (for example, a normal distribution), and thereafter the state judgment and state prediction of an object are conducted by a method such as a statistic testing. The invention also provides a method and device wherein if a measurement signal of an object is a pulsating one, a specific component of the signal is detected by determining the envelop waveform data of the signal from which noise is removed so as to conduct state judgment of the object.

Description

Feature decision method and signatures to predict method

Technical field

The present invention judges that about being used in fields such as Device Diagnostic, medical diagnosiss object has or not feature decision maker and the online signature monitoring and the diagnostic system of changing features.

Background technology

(1) supposition of the probability density function of the existing Wave data that records from the object of signature monitoring is carried out feature according to ' normal distribution ' and is judged that ([1] patent disclosure 2000-171291, the sharp husband of [2] Toyota, two protect and know also: ' only utilizing the abnormity diagnosis of the rotating machinery of vibrational waveform just often ', the meeting of Japanese equipment control Chi, Vol.11 when normal feature, No.1,1999, p.4-11.[3] the sharp husband of Liu Xinfang, Toyota, Chen Peng, Feng Fang, two protect and know also; ' utilizing the abnormity diagnosis of the rotating machinery of information discrete (Information Divergence) ', accurate engineering Hui Chi, Vol.66, No.1,2000, p.157-162)

(2) the supposition characteristic parameter that has no change to use for the feature of judging object is that the probability variable of normal distribution carries out statistical test (Jia Shu of [4] river portion, the sharp husband of Toyota, Jiangkou are saturating, Feitian and for a long time; ' utilize the deterioration tendency management (III) of the rotating machinery of nondimensional sign parameter, put down into the research in autumn of 7 years Japanese equipment control association and deliver conference collection of thesis, Vol.2, nineteen ninety-five, p.32.)

At the signal that the object from signature monitoring records is under the situation of fluctuating signal, utilizes characteristic parameter or probability density function etc. to be difficult to judge feature.In the past, as a kind of method that detects special component contained in the fluctuating signal (or unusual component),

(3) have a kind of detection method of utilizing the local anomaly of T/F analytic method (the Wei Bulai particular solution is analysed, Wigner distribution parsing, short time FFT etc.) ([5] Zhang Zhong, in rise abruptly intelligence it, cigarette ocean, river is clear; ' high speed Wei Bulaite conversion and the application on brain wave is resolved thereof ', Japanese mechanics can collections of thesis (C volume), Vol.65, No.632,1999, p.1915-1921.)

(4) according to the value of the predetermined distance sampling consistent with the peak value of fluctuating signal etc. smaller or equal to setting or and the difference of the value of sampling last time be judged to be during more than or equal to setting unusual.([6] spy opens flat 6-317215)

(5) be judged to be unusual ([7] spy opens flat 7-293311) during more than or equal to the threshold value of regulation according to the deviation (standard deviation) of the typical value of the each sampling of predetermined distance consistent with the peak value of fluctuating signal etc.

Summary of the invention

But above-mentioned existing method has following problem to exist.

With the 1st and the 2nd kind of method, though the value of supposition Wave data and characteristic parameter is according to normal distribution, but because even in fact normal feature also may not be according to normal distribution, so if the value of supposition Wave data and characteristic parameter is according to normal distribution, judge according to statistical test and the changing features of object then can cause erroneous judgement.

With the 3rd kind of method,, so detect distinguished point between being difficult at a time because it is long to handle required time.

With the 4th and the 5th kind of method, when gathering Wave data, because rotation speed change or load variations etc. are when causing variations in peak, although because sampled value is normal, still have quite big variation, so can cause erroneous judgement at interval according to the rules.In addition, when calculating the typical value deviation (standard deviation) of each sampling, be difficult to carry out real-time special detection.

For addressing the above problem, among the application, be transformed into the Wave data of known probability distribution (for example normal distribution) at the Wave data that will record after, or after will being transformed into the characteristic parameter of known probability distribution (for example normal distribution) according to the characteristic parameter that Wave data is calculated, the feature of utilizing statistical test or possibility theory or information theory etc. to carry out object is judged.

In addition, when the signal of the object that records is fluctuating signal, owing to be difficult to utilize the special component of extractions such as characteristic parameter or frequency spectrum and carry out the feature judgement, so obtain envelope Wave data except that the signal behind the denoising, utilize envelope Wave data and recurrent pulse after the normalized, special component in the detection signal carries out feature and judges.In addition, in above-mentioned, obtain peak value Wave data, and carry out the normalized of peak value Wave data, utilize normalized peak value Wave data and recurrent pulse Wave data except that the fluctuating signal behind the denoising, detect the special component in the fluctuating signal, carry out feature and judge.

Because for Wave data or characteristic parameter that the feature of monitored object thing is surveyed may not be according to normal distributions, so if according to above-mentioned Wave data or the characteristic parameter of normal distribution supposition, judge that according to statistical test object has or not changing features, perhaps, when carrying out signatures to predict, can bring sizable error.In this application, after the Wave data that records being transformed into the Wave data of known probability distribution (for example normal distribution), perhaps, after will being transformed into the characteristic parameter of known probability distribution (for example normal distribution) according to the characteristic parameter that Wave data is calculated, carry out the feature judgement of object according to statistical test or possibility theory or information theory etc.Therefore, the existing situation according to normal distribution of ratio of precision of its feature judgement of the application's method or signatures to predict wants high.

Under the situation of fluctuating signal, in the Wave data of the fluctuating signal that records, lack a part of peak value, or when having small special component, utilize existing decision method (characteristic parameter, frequency spectrum or probability density function etc.) to be difficult to detect in the part of Wave data.Among the application, obtain envelope Wave data and recurrent pulse after envelope Wave data except that the fluctuating signal behind the denoising utilizes normalization, detect the special component in the signal, carry out feature and judge.In addition, in above-mentioned, obtain peak value Wave data, the peak value Wave data is carried out normalized, utilize peak value Wave data and recurrent pulse Wave data after the normalized except that the fluctuating signal behind the denoising, detect the special component in the fluctuating signal, carry out feature and judge.With the application's method, main signal Processing can realize with hardware, because the burden of numerical value treating apparatus computing machine is light, so can detect unusual in real time.In addition and since be not Wave data with normal feature as benchmark, so even the pulsation period change, to detect and the influence of result of determination all less.

Description of drawings

Fig. 1 is divided into promptly big than the mean value data x of 4 classes for expression with the Wave data that records _I+, than the little data x of mean value _I-, by the absolute value data after formula (1) normalization | x _i| and all Wave data x _IAThe figure of example *.

Fig. 2 is the figure of the example of expressing possibility property distribution function

Fig. 3 does not overlap the figure of example of the vibrational waveform data of feature for expression normal feature and rotating shaft.

Fig. 4 is the figure of expression for the fundamental component analysis result of the vibrational waveform data of normal feature.

Fig. 5 does not overlap the figure of fundamental component analysis result of the vibrational waveform data of feature for rotating shaft for expression.

Fig. 6 is the figure of the example of the vibrational waveform data of normal feature of expression and uneven feature.

The figure that Fig. 7 uses for the representation feature Forecasting Methodology.

Fig. 8 is the figure of expression from the example of the vibrational waveform data of normal feature when the uneven changing features.

Fig. 9 is the figure of the characteristic ginseng value of each measured waveform of expression.

Figure 10 for expression utilize the envelope Wave data lack 1 peak value the time the figure of signal Processing example.

Figure 11 for expression utilize the peak value Wave data lack 1 peak value the time the figure of signal Processing example.

The figure of the signal Processing example when Figure 12 utilizes a plurality of peak values of envelope Wave data unusual for expression.

The figure of the signal Processing example when Figure 13 utilizes a plurality of peak values of peak value Wave data unusual for expression.

The figure that Figure 14 uses for the acquiring method of expression moving average Wave data.

Figure 15 is the process flow diagram of the special component detection and the flow process that abnormity diagnosis is handled of expression fluctuating signal.

Figure 16 is the process flow diagram of the treatment scheme of representation feature decision maker or online feature decision-making system.

Figure 17 is the circuit diagram of an example of the circuit of signal measurement and feature decision maker, and the label among the figure is as described below.

1 sensor, 2 amplifiers, 3 wave filters, 4 signal Processing and calculation element, 5 show output unit, 6 data RAM, 7AD transducer, 8DC passway, 9SCI (serial communication interface), 10CPU, 11 flash ROM, 12 outer computers

Figure 18 is the circuit diagram of an example of the circuit of fluctuating signal measurement and feature decision maker, and the label among the figure is as described below.

1 sensor, 2 amplifiers, 3 wave filters, 4 envelope handling parts, 5 recurrent pulse sensors, 6 show output unit, 7AD transducer, 8DC passway, 9SCI (serial communication interface), 10CPU, 11 flash ROM, 12 outer computers, 13 data RAM, 14 signal Processing and calculation element

Embodiment

1 about characteristic parameter

The characteristic parameter of usefulness has the characteristic parameter of time domain and frequency domain for feature judges.The characteristic parameter of frequency domain defines according to (list of references 1).([8] Chen Peng, the sharp husband of Toyota: utilize genetic programming to carry out the characteristic parameter of frequency domain from reorganization, Japanese mechanism collected works (C volume), Vol.65 No.633, pp.1946-1953,1998.) characteristic parameter to time domain here is elaborated.

In order to judge that object has or not the characteristic parameter of the time domain that changing features uses as described below.

1) nondimensional characteristic parameter

From the timing waveform data that record, utilize wave filter to extract the Wave data of basic, normal, high frequency domain out.With following formula the Wave data x (t) that extracts out is made normalized.

$x_i=\frac{{x^{\′}}_i-\mathrm{\μ}}{S}---\left(1\right)$

In the formula, x ' _iBe the discrete value of the x after the A/D conversion (t), μ and S are respectively x ' _iMean value and standard deviation.

Used in the past nondimensional characteristic parameter is shown in formula (2)～formula (13) ([9] Peng CHEN, ToshioTOYOTA, Yueton LIN, Feiyue Wang:FAILURE DIAGNOSIS OF MACHINERY BY SELF-REORGANIZATION OF SYMPTOM PARAMETERS IN TIME DOMAIN USING GENETICALGORITHMS, International Journal of Intelligent Control and System, Vol.3, No.4, pp.571-585,1999.)

The rate of change: p ₁=σ/μ _Abs(2)

In the formula

${\mathrm{\μ}}_{\mathrm{abs}}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left|x_i\right|/N---\left(3\right)$

Be absolute average, N is the sum of data.

$\mathrm{\σ}=\sqrt{\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(x_i-p)}^2}{N-1}}---\left(4\right)$

Be standard deviation.

Degree of distortion: ${\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">p</figure-callout>}}_2=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-\mathrm{\&mu;})}^3}{(N-1){\mathrm{\&sigma;}}^3}---\left(5\right)$

Kurtosis: ${\mathrm{<figure-callout\; id="3"\; label="p"\; filenames="C20048000592600271.png,C20048000592600292.png"\; state="\{\{state\}\}">p</figure-callout>}}_3=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(x_i-\mathrm{\&mu;})}^4}{(N-1){\mathrm{\&sigma;}}^4}---\left(6\right)$

p ₄＝μ _p/μ _abs (7)

μ in the formula _PMean value for the maximum value (peak value) of waveform.

p ₅＝|μ _max|/μ _p (8)

In the formula, | μ _Max| be 10 peaked mean values in the waveform.

p ₆＝μ _p/σ _p (9)

In the formula, σ _PStandard deviation value for maximum value.

p ₇＝μ _L/σ _L (10)

In the formula, μ _LAnd σ _LBe respectively the mean value and the standard deviation value of minimal value (trough value).

${\mathrm{<figure-callout\; id="8"\; label="p"\; filenames="C20048000592600351.png,C20048000592600352.png"\; state="\{\{state\}\}">p</figure-callout>}}_8=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\sqrt{\left|x_i\right|}}{N\sqrt{\mathrm{\&sigma;}}}---\left(11\right)$

$p_9=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i^2}{N{\mathrm{\&sigma;}}^2}---\left(12\right)$

${\mathrm{<figure-callout\; id="10"\; label="p"\; filenames="C20048000592600271.png"\; state="\{\{state\}\}">p</figure-callout>}}_{10}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\log \left|x_i\right|}{N\log \mathrm{\&sigma;}};(x_i\&NotEqual;0)---\left(13\right)$

Formula (2)～formula (13) is existing characteristic parameter, but for the ease of doing high-speed computation in the numerical evaluation, suc as formula the such new proposition of (14)～formula (21) ' interval characteristic parameter '.

$p_{11}=\frac{\underset{i=1}{\overset{N_{\mathrm{ki}}}{\mathrm{\&Sigma;}}}{x}_i^t}{N_{\mathrm{ki}}}---\left(14\right)$

${\mathrm{<figure-callout\; id="12"\; label="p"\; filenames="C20048000592600351.png,C20048000592600352.png"\; state="\{\{state\}\}">p</figure-callout>}}_{12}=\frac{\underset{i=1}{\overset{N_{\mathrm{ki}}}{\mathrm{\&Sigma;}}}{(x_i-{\mathrm{\&mu;}}_{\mathrm{ki}})}^t}{N_{\mathrm{ki}}}---\left(15\right)$

In the formula, x _i〉=k σ, k can set arbitrarily, for example k=0.5,1,2.μ _KiBe x _iMean value.T can set arbitrarily, for example t=0.5,1,2,3,4.

${\mathrm{<figure-callout\; id="13"\; label="p"\; filenames="C20048000592600352.png"\; state="\{\{state\}\}">p</figure-callout>}}_{13}=\frac{\underset{i=1}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N\; h"\; filenames="C20048000592600272.png,C20048000592600331.png"\; state="\{\{state\}\}">N</figure-callout>}}_h}{\mathrm{\&Sigma;}}}{\left|x_h\right|}^t}{N_{\mathrm{hi}}}---\left(16\right)$

${\mathrm{<figure-callout\; id="14"\; label="p"\; filenames="C20048000592600272.png,C20048000592600282.png"\; state="\{\{state\}\}">p</figure-callout>}}_{14}=\frac{\underset{i=1}{\overset{N_{\mathrm{hi}}}{\mathrm{\&Sigma;}}}{\left(\right|x_h|-{\mathrm{\&mu;}}_{\mathrm{hi}})}^t}{N_{\mathrm{hi}}}---\left(17\right)$

In the formula, x _h≤-h σ, h can set arbitrarily, for example h=0.5,1,2.μ _HiBe x _hMean value.T can set arbitrarily, for example t=0.5,1,2,3,4.

${\mathrm{<figure-callout\; id="15"\; label="p"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">p</figure-callout>}}_{15}=\frac{h_0}{h_p}---\left(18\right)$

In the formula, h _oFor timing waveform is crossed 0 frequency, h in the unit interval _pNumber of peaks for timing waveform in the unit interval.

$p_{16}=\frac{h_0}{h_v}---\left(19\right)$

$p_{17}=\frac{h_{\mathrm{n\&sigma;}}}{h_0}---\left(20\right)$

In the formula, h _{N σ}Cross the frequency that n σ is ordered for waveform in the unit interval, n can set arbitrarily, for example, and n=0.5,1,2.

$p_{18}=\frac{h_{-\mathrm{n\&sigma;}}}{h_0}---\left(21\right)$

In the formula, h _{-n σ}Be the waveform frequency that mistake-n σ is ordered in the unit interval, n can set arbitrarily, for example, and n=0.5,1,2.

2) the dimension characteristic parameter is arranged

When calculating has the dimension characteristic parameter,, do not make the such normalized of formula (1) for the Wave data that records.

The absolute average of Wave data: ${\mathrm{<figure-callout\; id="1"\; label="p\; d"\; filenames="C20048000592600272.png,C20048000592600331.png"\; state="\{\{state\}\}">p</figure-callout>}}_d=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\left|x_i\right|}{N-1}---\left(22\right)$

The effective value of Wave data: ${\mathrm{<figure-callout\; id="2"\; label="p\; d"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">p</figure-callout>}}_d=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_i^2}{N-1}---\left(23\right)$

The peak averaging value of Wave data absolute value: ${\mathrm{<figure-callout\; id="3"\; label="p\; d"\; filenames="C20048000592600271.png,C20048000592600292.png"\; state="\{\{state\}\}">p</figure-callout>}}_d=\frac{\underset{i=1}{\overset{N_P}{\mathrm{\&Sigma;}}}{\left|x_i\right|}_p}{N_P}---\left(24\right)$

In the formula, | x _i| _pPeak value (maximum value), N for the Wave data absolute value _pSum for peak value.

The peak value effective value of Wave data absolute value: $p_{d4}=\frac{\underset{i=1}{\overset{N_P}{\mathrm{\&Sigma;}}}{{\left|x_i\right|}_p}^2}{N_P}---\left(25\right)$

Also have, except that above-mentioned characteristic parameter, go back definable various features parameter, but when use this method, at first try by above-mentioned characteristic parameter, not good enough as if the effect of feature identification, then also can append the characteristic parameter that defines other.

2. Wave data and characteristic parameter are transformed into the probability distribution of appointment

Use x _i ^*The Wave data that expression records is used p _i ^*The characteristic parameter that expression is calculated according to Wave data.Using x _i ^*Or p _i ^*When carrying out feature judgement and signatures to predict, must know x in advance according to statistical theory _i ^*Or p _i ^*According to what kind of probability distribution.But most situation is not know x in advance _i ^*Or p _i ^*What kind of distribute according to probability.Therefore, as the known probability distribution function of establishing appointment is ∑, then can utilize following formula with x _i ^*Or p _i ^*Be transformed into probability variable x according to ∑ _iOr p _i

$x_i={\mathrm{\&Sigma;}}^{-1}\left(F_{\mathrm{xi}}\left(x_i^{*}\right)\right)---\left(26\right)$

$p_i={\mathrm{\&Sigma;}}^{-1}\left(F_{\mathrm{pi}}\left(p_i^{*}\right)\right)---\left(27\right)$

In the formula, F _Xi(x _i ^*) or F _Pi(p _i ^*) be respectively x _i ^*And p _i ^*Cumulative probability distribute (or cumulative frequency distribution) ∑ ^-1It is the inverse function of ∑.For example: ∑ is normal distribution, Weibull distribution, exponential distribution, Gamma distribution etc.With x _i ^*Or p _i ^*Be transformed into x _iOr p _iAfter, utilize statistical test etc. to carry out feature and judge or signatures to predict.

Also has original Wave data x _i ^*Can be divided into four kinds as shown in Figure 1.Promptly big data x than mean value _I+, than the little data x of mean value _I-, according to the absolute value data after formula (1) normalization | x _i| and all Wave data x _IA ^*, F is used in cumulative probability distribution (or cumulative frequency distribution) separately _Xi+(x _I+), F _Xi-(x _I-), F _{| xi|}(| x _i|), and F _XiA(x ^* _IA) expression, below, specify as nothing, then unified with F _Xi(x ^* _i) expression.Characteristic parameter p in addition _i ^*Can be with the x after the normalization _I+And x _I-, | x _i|, x ^* _IAIn any calculating.

Here, as an example, being described in detail in and specifying ∑ is under the situation of normal distribution, to x _i ^*Or p _i ^*Carry out conversion and make its method according to normal distribution.

The probability density function f (t) of normal distribution can be represented by the formula.

$f\left(t\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{l}^{-\frac{{(1-\mathrm{\&mu;})}^2}{{2\mathrm{\&sigma;}}^2}}---\left(28\right)$

In the formula, μ is the mean value of probability variable t, and σ is a standard deviation.

(1) situation of basis of reference feature

The reference characteristic of decision determination object, the feature when for example measuring for the 1st time is established the Wave data x of this moment _Io ^*Or characteristic parameter p _Io ^*Probability density function and cumulative distribution function be respectively f _Xo(x ^* _Io) and F _Xo(x ^* _Io) or f _Po(p ^* _Io) and F _Po(p ^* _Io).If the probability density function that average value mu is 0, standard deviation is 1 standardized normal distribution is φ (x _i), the probability distribution function of standardized normal distribution is Φ (x _i).Also have, though can be the x of discrete data also with ' frequency distribution function ' or ' histogram ' replacement ^* _IoOr p ^* _IoProbability density function, below, utilize ' probability density function ' to describe.

1) is transformed into method according to the mean value of normal distribution

Can be with the x of following formula with feature k ^* _IkAnd p ^* _IkBe transformed into separately μ according to normal distribution _XikoAnd μ _PikoAlso have, feature k is feature arbitrarily, also comprises reference characteristic.

${\mathrm{\&mu;}}_{\mathrm{xik}0}=x_{\mathrm{ik}}^{*}-{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="xi"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">xi</figure-callout>}0}\&times;{\mathrm{\&Phi;}}^{-1}\left(F_{x0}\left(x_{\mathrm{ik}}^{*}\right)\right)---\left(29\right)$

${\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="0"\; label="pik"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">pik</figure-callout>}0}=p_{\mathrm{ik}}^{*}-{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="pi"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">pi</figure-callout>}0}\&times;{\mathrm{\&Phi;}}^{-1}\left(F_{p0}\left(p_{\mathrm{ik}}^{*}\right)\right)---\left(30\right)$

In the formula, Φ ^-1Be the inverse function of Φ, σ _XioAnd σ _PioFor being transformed into the x of normal distribution separately ^* _IkAnd p ^* _IkStandard deviation, can try to achieve with following formula.

${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="xi"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">xi</figure-callout>}0}=\frac{1}{f_0\left({x^{*}}_{\mathrm{ik}}\right)}\mathrm{\&Phi;}\left({\mathrm{\&Phi;}}^{-1}\left(F_0\left(x_{\mathrm{ik}}^{*}\right)\right)\right)---\left(31\right)$

${\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="pi"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">pi</figure-callout>}0}=\frac{1}{f_0\left({p^{*}}_{\mathrm{ik}}\right)}\mathrm{\&Phi;}\left({\mathrm{\&Phi;}}^{-1}\left(F_0\left(p_{\mathrm{ik}}^{*}\right)\right)\right)---\left(32\right)$

Use average value mu _XikoAnd μ _PikoCarrying out feature judges and signatures to predict.

2) Direct Transform method

With the x of following formula with feature k ^* _IkAnd p ^* _IkBe transformed into the probability variable of normal distribution.

${x^{\&prime;}}_{\mathrm{ik}0}=s_{\mathrm{xk}}{\mathrm{\&Phi;}}^{-1}\left(F_{x0}\left(x_{\mathrm{ik}}^{*}\right)\right)+{\mathrm{\&mu;}}_{\mathrm{xk}}---\left(33\right)$

${p^{\&prime;}}_{\mathrm{ik}0}=s_{\mathrm{pk}}{\mathrm{\&Phi;}}^{-1}\left(F_{p0}\left(p_{\mathrm{ik}}^{*}\right)\right)+{\mathrm{\&mu;}}_{\mathrm{pk}}---\left(34\right)$

In the formula, S _XkAnd S _PkBe respectively x ^* _IkAnd p ^* _IkStandard deviation, μ _XkAnd μ _PkBe respectively x ^* _IkAnd p ^* _IkMean value.Utilize x ' _IkoOr p ' _IkoCarrying out feature judges and signatures to predict.

(2) situation of basis of reference feature not

At first, establish the Wave data x of feature k ^* _IkWith characteristic parameter p ^* _IkProbability density function (or frequency distribution) be respectively f _Xk(x ^* _Ik) and f _Pk(p ^* _Ik), establishing probability distribution function (or cumulative frequency distribution) is F _Xk(x ^* _Ik) and F _Pk(p ^* _Ik).

1) direct change of variable method

With following formula with Wave data x ^* _IkWith characteristic parameter p ^* _IkBe transformed into the probability variable of normal distribution.

${x^{\&prime;}}_{\mathrm{ik}}=s_{\mathrm{xk}}{\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{xk}}\left(x_{\mathrm{ik}}^{*}\right)\right)+{\mathrm{\&mu;}}_{\mathrm{xk}}---\left(35\right)$

${p^{\&prime;}}_{\mathrm{ik}}=s_{\mathrm{pk}}{\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{pk}}\left(p_{\mathrm{ik}}^{*}\right)\right)+{\mathrm{\&mu;}}_{\mathrm{pk}}---\left(36\right)$

In the formula, S _XkAnd S _PkBe respectively x ^* _IkAnd p ^* _IkStandard deviation, μ _XkAnd μ _PkBe respectively x ^* _IkAnd p ^* _IkMean value.Utilize x ' _IkOr p ' _IkCarrying out feature judges and signatures to predict.

2) be transformed into method according to the mean value of normal distribution

Mean value according to normal distribution can be obtained with following formula.

${\mathrm{\&mu;}}_{\mathrm{xik}}=x_{\mathrm{ik}}^{*}-{\mathrm{\&sigma;}}_{\mathrm{xik}}\&times;{\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{xk}}\left(x_{\mathrm{ik}}^{*}\right)\right)---\left(37\right)$

${\mathrm{\&mu;}}_{\mathrm{pik}}=p_{\mathrm{ik}}^{*}-{\mathrm{\&sigma;}}_{\mathrm{pik}}\&times;{\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{pk}}\left(p_{\mathrm{ik}}^{*}\right)\right)---\left(38\right)$

In the formula, σ _XikAnd σ _PikCan obtain with following formula.

${\mathrm{\&sigma;}}_{\mathrm{xik}}=\frac{1}{f_{\mathrm{xk}}\left({x^{*}}_{\mathrm{ik}}\right)}\mathrm{\&Phi;}\left({\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{xk}}\left(x_{\mathrm{ik}}^{*}\right)\right)\right)---\left(39\right)$

${\mathrm{\&sigma;}}_{\mathrm{pik}}=\frac{1}{f_{\mathrm{pk}}\left({p^{*}}_{\mathrm{ik}}\right)}\mathrm{\&Phi;}\left({\mathrm{\&Phi;}}^{-1}\left(F_{\mathrm{pk}}\left(p_{\mathrm{ik}}^{*}\right)\right)\right)---\left(40\right)$

Because μ _XikAnd μ _PikAccording to normal distribution, so utilize μ _XikOr μ _PikCarrying out feature judges and signatures to predict.

3) indirect conversion method

If M characteristic parameter p _Ik ^*Minimum value and maximal value be respectively (p ^* _Ik) _Min(p ^* _Ik) _MaxFrom (p ^* _Ik) _MinTo (p ^* _Ik) _MaxBe divided into N equally spaced interval.If each interval typical value (for example intermediate value) is p ^* _IkjHere, j=1～N.If use p ^* _IkjReplace p ^* _Ik, substitution formula (36) or (38) then can obtain N p " _IkOr μ ' _PikUtilize p " _IkOr μ ' _PikCarrying out feature judges and signatures to predict.

Equally, establish M waveform parameter x _Ik ^*Minimum value and maximal value be respectively (x ^* _Ik) _Min(x ^* _Ik) _MaxFrom (x ^* _Ik) _MinTo (x ^* _Ik) _MaxBe divided into N equally spaced interval.If each interval typical value (for example intermediate value) is x ^* _IkjHere, j=1～K.If use x ^* _IkjReplace x ^* _Ik, substitution formula (35) or (34) then can obtain K x " _IkOr μ ' _XikUtilize x " _IkOr μ ' _XikCarrying out feature judges and signatures to predict.

4) ask characteristic parameter p ^* _IkThe method of average value in interval

Obtain N characteristic parameter p ^* _IkAfterwards, be divided into the M group, the mean value of j group can followingly be tried to achieve like that.

${{\mathrm{\&mu;}}_k}^{\left(j\right)}=\underset{i=1}{\overset{N_J}{\mathrm{\&Sigma;}}}{p}_{\mathrm{ik}}/N_j---\left(41\right)$

In the formula, N _jFor being positioned at the p of j group ^* _IkQuantity.Because μ _k ^(j)Approx according to normal distribution, so, μ used _k ^(j)Carrying out feature judges and signatures to predict.

With formula (29), formula (33), formula (35), formula (37) with Wave data x ^* _IkBe transformed into the μ of the Wave data of normal probability paper distribution _Xiko, x ' _Iko, x ' _Ik, μ _Xik, x " _Ik, μ ' _XikBe called ' Wave data of normal distribution '.In addition, use formula (30), formula (34), formula (36), formula (38) with characteristic parameter p ^* _iBe transformed into the μ of normal probability paper variable _Piko, p ' _Iko, p ' _Ik, μ _Pik, p " _Ik, μ ' _Pik, μ _k ^(j)Be called ' characteristic parameter of normal distribution '.

3 utilize the feature method of discrimination of the characteristic parameter of normal distribution

Below, narration utilizes the characteristic parameter of normal distribution to differentiate the method for object feature.

(1) utilize statistical theory to differentiate

1) mean value of the characteristic parameter of check normal distribution

The characteristic parameter that is located at the normal distribution of trying to achieve under feature k and the feature y is respectively p _IkAnd p _IyHere, i=1～M, M represent the sum of the characteristic parameter of the normal distribution used.If p _IkAnd p _IyMean value be respectively μ _IkAnd μ _Iy, with p _IkAnd p _IyStandard deviation be respectively S _IkAnd S _IyUsually calculate J p with following formula _jAverage value mu and standard deviation S.

$\mathrm{\&mu;}=\frac{\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{p}_j}{J}---\left(42\right)$

${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\frac{\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}{(p_j-\stackrel{\&OverBar;}{p})}^2}{J-1}---\left(43\right)$

μ _IkAnd μ _Iy(with reference to list of references 3) carried out in the check that whether equates as described below.

(list of references 3) K.A.Brownlee.Statistical Theory and Methodology inScience and Engineering, Second Edition, The University Chicago, 1965

If

$|{\mathrm{\&mu;}}_{\mathrm{ik}}-{\mathrm{\&mu;}}_{\mathrm{iy}}|>\frac{S_{\mathrm{iy}}}{\sqrt{J}}{t}_{\mathrm{\&alpha;}/2}(J-1)---\left(44\right)$

Set up, then judge ' μ according to level of signifiance α _IkAnd μ _Iy, not etc. '.In the formula, t _α/2(J-1) be the percentage point of the probability density function that distributes of the t of its degree of freedom J-1 for downside probability α/2.

2) characteristic parameter of check normal distribution is discrete

S _IkAnd S _Iy(with reference to list of references 4) carried out in the check that whether equates as described below

(list of references 4) K.A.Brownlee.Statistical Theory and Methodology inScience and Engineering, Second Edition, The University Chicago, 1965

If

$\frac{{S_{\mathrm{ik}}}^2}{{{\mathrm{<figure-callout\; id="2"\; label="S\; iy"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{iy}}}^2}>F_{\mathrm{\&alpha;}/2}(J-1,J-1)\mathrm{or}\frac{{S_{\mathrm{iy}}}^2}{{{\mathrm{<figure-callout\; id="2"\; label="S\; ik"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{ik}}}^2}>F_{\mathrm{\&alpha;}/2}(J-1,J-1)---\left(45\right)$

Set up, then judge ' S according to level of signifiance α _IkAnd S _Iy, not etc. '.In the formula, F _α/2(J-1 J-1) is the percentage point of the probability density function that distributes of the F of its degree of freedom J-1 for downside probability α/2.

When changing level of signifiance α, whether satisfy formula (44) or formula (45), and decision feature y is to the degree of the changing features of feature k by affirmation.Utilize the example of level of signifiance α decision changing features degree to be shown in table 1.Also having, under the situation of Device Diagnostic, if establishing feature k is normal feature, is normal feature, attention characteristics, or dangerous feature for differentiating feature y, can be as shown in table 1, set ' normally ' (α for ₁), ' attention ' (α ₂), and ' danger ' (α ₃) test.That is, formula (44) or formula (45) are at α ₁Shi Ruo is false, and then is judged to be ' normally '.In addition, formula (44) or formula (45) are at α ₂The time if set up, then be judged to be ' attention ', at α ₃The time if set up, then be judged to be ' danger '.Also have, the numerical range of the α in the table 1 is an example, can be decided by the importance of equipment etc.

When utilizing a plurality of characteristic parameters to carry out the feature judgement, the result of judgement changes the result of determination of maximum characteristic parameter according to representation feature.For example use three characteristic parameter p ₁, p ₂, p ₃When judging, at p ₁Result of determination be ' attention ', p ₂Result of determination be ' normally ', p ₃Result of determination when being ' danger ', final result of determination is ' danger '.

Table 1

	Feature no change (normally)	In the changing features (attention)	Changing features big (danger)
				The level of signifiance (example)	α 1 (0.3～0.7)	α 2 (0.1～0.4)	α 3 (0.1～0.3)

(3) utilize fiducial interval to judge

If establishing the mean value of the characteristic parameter of the normal distribution that the Wave data that records constantly from benchmark obtains is μ _Io, the mean value of the characteristic parameter of the normal distribution that the Wave data that records from other moment is obtained is μ _Ik, μ then _IoFiducial interval can represent by following formula.

${\mathrm{\&mu;}}_{i0}\&PlusMinus;t_{\mathrm{\&sigma;}/2}(J-1){\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">S</figure-callout>}}_i/\sqrt{J}---\left(46\right)$

In the formula, t _α/2(J-1) be the percentage point of the probability density function that distributes of the t of its degree of freedom J-1 for downside probability α/2.S _I0Be the p that obtains from Wave data _I0Standard deviation.If μ _IkIn the interval that formula (46) illustrates, then we can say probability and μ with 1-α _IoBetween indifference exist.μ _I099% fiducial interval in J＞10 o'clock, approximate become following.

${\mathrm{\&mu;}}_{i0}\&PlusMinus;3{\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">S</figure-callout>}}_i/\sqrt{J}---\left(47\right)$

Thereby, μ _IkAs exceed the scope of formula (47), then judge and μ with 99% probability _IoDifferent.The μ that obtains according to the Wave data that records is arranged again _IkFiducial interval can try to achieve by following formula.

${\mathrm{\&mu;}}_{\mathrm{ik}}\&PlusMinus;3S_{\mathrm{ik}}/\sqrt{J}---\left(48\right)$

In the formula, S _IkBe the p that obtains from Wave data _IkStandard deviation.

α substitution formula (46) with table 1 can get following fiducial interval.

The interval (normally) that does not have changing features: ${\mathrm{\&mu;}}_{i0}\&PlusMinus;t_{{\mathrm{\&sigma;}}_1/2}(J-1){\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">S</figure-callout>}}_i/\sqrt{J}---\left(49\right)$

Interval in the changing features (attention): ${\mathrm{\&mu;}}_{i0}\&PlusMinus;t_{{\mathrm{\&sigma;}}_2/2}(J-1){\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">S</figure-callout>}}_i/\sqrt{J}---\left(50\right)$

The interval that changing features is big (danger): ${\mathrm{\&mu;}}_{i0}\&PlusMinus;t_{{\mathrm{\&sigma;}}_3/2}(J-1){\mathrm{<figure-callout\; id="0"\; label="S\; i"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">S</figure-callout>}}_i/\sqrt{J}---\left(51\right)$

According to μ _IkWhether be positioned at these intervals and carry out the feature judgement.

Utilizing a plurality of characteristic parameters to carry out under the situation that feature judges, final result of determination and formula (49), (50), (51) described content are identical.

(2) differentiate according to possibility theory

1) generates probability distribution function

Calculate the characteristic parameter p of normal distribution with the Wave data of feature k _iValue after, with formula (52) from p _iProbability density function f _k(p _i) obtain probability distribution function P _k(p _i).According to possibility theory, no matter p _iAccording to what probability distribution, can both try to achieve its probability distribution function.At p _iUnder the situation according to normal distribution, the probability distribution function P of N section _k(p _i) can followingly obtain (with reference to list of references 5).

$P_k\left(p_{\mathrm{ix}}\right)=\underset{y=1}{\overset{Y}{\mathrm{\&Sigma;}}}\min \{{\mathrm{\&lambda;}}_x,{\mathrm{\&lambda;}}_y\}---\left(52\right)$

In the formula

${\mathrm{\&lambda;}}_x={\&Integral;}_{p_{\mathrm{ix}-1}}^{p_{\mathrm{ix}}}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="S\; i"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">S</figure-callout>}}_i\sqrt{2\mathrm{\&pi;}}}\exp \{-\frac{{(p-{\mathrm{\&mu;}}_i)}^2}{2{S_i}^2}\}\mathrm{dp}---\left(53\right)$

${\mathrm{\&lambda;}}_y={\&Integral;}_{p_{\mathrm{iy}-1}}^{p_{\mathrm{iy}}}\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="S\; i"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">S</figure-callout>}}_i\sqrt{2\mathrm{\&pi;}}}\exp \{-\frac{{(p-{\mathrm{\&mu;}}_i)}^2}{2{S_i}^2}\}\mathrm{dp}---\left(54\right)$

But, in the following formula, p _Ix=min{p _i}+x * (max{p _i}-min{p _i)/N, x=1～N, S _iBe p _iStandard deviation, μ _iBe p _iMean value.

(list of references 5) L.Davis:HANDBOOK OF GENETIC ALGORITHMS, Van NostrandReinhold, A Division of wadsworth, Inc (1990)

2) acquiring method of possibility

As shown in Figure 2, be located at the characteristic parameter p of the normal distribution of trying to achieve under feature k and the feature y _iProbability distribution function be respectively P _k(p _i) and P _y(p _i), the value of establishing the characteristic parameter of the normal distribution of trying to achieve under the feature y is p ' _i, then the possibility w of ' feature y is identical with feature k ' can try to achieve as follows.

A) a) according to p ' _iMean value p ' _iMean and P _k(p _i) between coupling decision w,

B) b) according to P _y(p _i) and P _k(p _i) between coupling decision w,

Also have, according to P _y(p _i) and P _k(p _i) between cooperation ask the formula of w to be expressed as follows.

$w=\underset{x=-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{P}_k\left(p_{\mathrm{ix}}\right)\&CenterDot;P_y\left(p_{\mathrm{ix}}\right)---\left(55\right)$

3) differentiate changing features

Characteristic parameter p in the normal distribution that obtains obtaining under the feature k _iProbability distribution function pk (p _i) after, the probability distribution function (p of ' changing features is little ' of the left and right sides _C1(p _i) and p _C2(p _i)), and the probability distribution function (p of ' changing features is big ' _D1(p _i) and p _D2(p _i)) decision as illustrated in fig. 2.Boundary value

μ _i±iS _i，μ _i±jS _i (56)

I, j decide by user's input, be made as i=3, j=6 as standard value.

Under the situation of Device Diagnostic, the probability distribution function of establishing normal feature is pk (p _i), the probability distribution function of attention characteristics is p _C1(p _i) and p _C2(p _i), the probability distribution function of dangerous feature is p _D1(p _i) and p _D2(p _i).' normally ', ' attention ' that Fig. 2 obtains when actual identification is shown, the possibility of ' danger '.In addition, when judging ' danger ', also can give the alarm.

(3) the feature diagnostic method of carrying out according to information theory

If the probability density function of the characteristic parameter of the normal distribution under the reference characteristic of object is f _Po(p _i), the probability density function of the characteristic parameter of the normal distribution beyond the reference characteristic is f _Pk(p _i).The feature in the moment beyond the reference characteristic is called ' test feature '.Can judge with ' Information Divergence (information discrete, ID) ' method whether test feature is the feature identical with reference characteristic according to following ' Kullback-Leibler Information (Ku Erbake quantity of information, KI) '.

${\mathrm{KI}}_p={\&Integral;}_{-\&infin;}^{\&infin;}{f}_{p0}\left(p_i\right)\frac{f_{p0}\left(p_i\right)}{f_{\mathrm{pk}}\left(p_i\right)}{\mathrm{dp}}_i$

$=\frac{1}{2}\{\log \frac{{\mathrm{\&sigma;}}_{\mathrm{ipk}}}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ip"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ip</figure-callout>}0}}+\frac{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ip"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ip</figure-callout>}0}}^2+{({\mathrm{\&mu;}}_{\mathrm{ip}0}-{\mathrm{\&mu;}}_{\mathrm{ipk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{ipk}}}^2}-1\}---\left(57\right)$

${\mathrm{ID}}_p={\&Integral;}_{-\&infin;}^{\&infin;}\{f_{p0}\left(p_i\right)-f_{\mathrm{pk}}\left(p_i\right)\}\frac{f_{p0}\left(p_i\right)}{f_{\mathrm{pk}}\left(p_i\right)}{\mathrm{dp}}_i$

$=\frac{1}{2}\{\frac{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ip"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ip</figure-callout>}0}}^2+{({\mathrm{\&mu;}}_{\mathrm{ip}0}-{\mathrm{\&mu;}}_{\mathrm{ipk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{ipk}}}^2}+\frac{{{\mathrm{\&sigma;}}_{\mathrm{ipk}}}^2+{({\mathrm{\&mu;}}_{\mathrm{ip}0}-{\mathrm{\&mu;}}_{\mathrm{ipk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ip"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ip</figure-callout>}0}}^2}-2\}---\left(58\right)$

According to KI _pAnd ID _pThe feature diagnostic method in [10], have a detailed description, so just repeat no more here.(the sharp husband of [10] Liu Jinfang, Toyota, Chen Peng, Feng Fang, two protect and know also: ' utilizing the discrete abnormity diagnosis that is rotated machinery of information ', accurate engineering can Chi, Vol.66, No.1,2000, p.157-162.)

(4) by the feature diagnostic method that a plurality of characteristic parameters are comprehensive

Also can a plurality of characteristic parameters are comprehensive, judge to have or not changing features or carry out signatures to predict.The integrated approach of characteristic parameter has the fundamental component analytic approach or the KL method of development etc., and the new characteristic parameter that utilizes the overall approach of characteristic parameter to try to achieve is called ' comprehensive characteristics parameter '.The example of fundamental component analytic approach is shown here.([11] Da Jin, chestnut field, Guan Tianzhu: pattern-recognition, towards storehouse bookstore, 1996.)

For example: during Device Diagnostic, for the nondimensional characteristic parameter (p that tries to achieve under the normal feature of equipment ₁, p ₂... p _m), m fundamental component can be expressed as follows.

z ₁＝a ₁₁p ₁+a ₁₂p ₂+…+a _1mp _m

z ₂＝a ₂₁p ₁+a ₂₂p ₂+…+a _2mp _m (59)

.

.

.

z _m＝a _m1p ₁+a _m2p ₂+…+a _mmp _m

Each fundamental component z ₁～z _mBe also referred to as ' comprehensive characteristics parameter '.

Relevant matrix can be obtained as follows.

$R=\left[\begin{array}{cccc}{r}_{11}& {\mathrm{<figure-callout\; id="12"\; label="r"\; filenames="C20048000592600351.png,C20048000592600352.png"\; state="\{\{state\}\}">r</figure-callout>}}_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{1m}\\ r_{21}& r_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{2m}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ r_{m1}& {\mathrm{<figure-callout\; id="2"\; label="r\; m"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">r</figure-callout>}}_m& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{mm}}\end{array}\right]---\left(60\right)$

In the formula, be { p if establish the n group data of including under the normal feature _1k, p _2k..., p _Mk, k=1,2 ..., n, then

$r_{\mathrm{ij}}=\frac{s_{\mathrm{ij}}}{\sqrt{s_{\mathrm{ii}}{s}_{\mathrm{jj}}}},$ $s_{\mathrm{ij}}=\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{ik}}{P}_{\mathrm{jk}}/(n-1)---\left(61\right)$

If inherent vector λ=(λ of relevant matrix R ₁, λ ₂..., λ _m), λ ₁〉=λ ₂〉=... 〉=λ _m, then

$\left[\begin{array}{cccc}{r}_{11}& {\mathrm{<figure-callout\; id="12"\; label="r"\; filenames="C20048000592600351.png,C20048000592600352.png"\; state="\{\{state\}\}">r</figure-callout>}}_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{1m}\\ r_{21}& r_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& r_{2m}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ r_{m1}& {\mathrm{<figure-callout\; id="2"\; label="r\; m"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">r</figure-callout>}}_m& \&CenterDot;\&CenterDot;\&CenterDot;& r_{\mathrm{mm}}\end{array}\right]\left[\begin{array}{c}{a}_{i1}\\ a_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">i</figure-callout>}2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ a_{\mathrm{im}}\end{array}\right]={\mathrm{\&lambda;}}_i\left[\begin{array}{c}{a}_{i1}\\ a_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="C20048000592600261.png,C20048000592600271.png"\; state="\{\{state\}\}">i</figure-callout>}2}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ a_{\mathrm{im}}\end{array}\right]---\left(62\right)$

Ask and eigenvalue λ _iThe coefficient of corresponding formula (59), i fundamental component can be tried to achieve as described below.

z _i＝a _i1p ₁+a _i2p ₂+…+a _imp _m (63)

Utilize fundamental component to judge as shown in the formula carrying out feature like that.

$\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left[\frac{z_i-{\stackrel{\&OverBar;}{z}}_i}{\sqrt{{\mathrm{\&lambda;}}_i}}\right]}^2\&le;{\mathrm{\&chi;}}^2(K,\mathrm{\&alpha;})---\left(64\right)$

In the formula, K is the number of the fundamental component of use, and α is the level of signifiance, χ ²(K α) is the χ of degree of freedom K ²The probability density function that distributes is for the percentage point of upside probability α.The determining method of α is with table 1.Also have, for K=3, α=0.05 o'clock, χ ²(3,0.05)=7.815.

Also have, except the decision method shown in the formula (64), also the comprehensive characteristics parameter that the integrated approach that utilizes characteristic parameter can be tried to achieve is after for example the fundamental component shown in the formula (63) is transformed into the probability variable of normal distribution, carries out feature according to statistical test or possibility theory and judges.

Here, represent a real example, Fig. 3 vibration acceleration Wave data that (Fig. 3 (b)) records when (Fig. 3 (a)) and rotating shaft do not overlap feature during for the normal feature of certain rotating machinery.Fig. 4 (a) and Fig. 5 (a) try to achieve 14 nondimensional characteristic parameters shown in formula (2)～formula (13) and formula (the 18)～formula (21) 60 times, before the normal distribution conversion, and the value (60) on formula (64) the right of obtaining during expression K=3.Fig. 4 (b) and Fig. 5 (b) expression is according to the value (9) on formula (64) the right of obtaining after formula (31) the normal distribution conversion, during K=3.According to these figure, can know that the result before result after the normal distribution conversion is than normal distribution conversion is good.Also have, the value that said ' good ' is meant formula (64) left side is little when normal feature, and is big when off-note.

4 utilize the feature diagnostic method of the Wave data of normal distribution

(1) utilizes the feature diagnostic method of characteristic parameter

Utilize formula (33) will to object measure Wave data x _i ^*(for example Fig. 6 (a), (c) are transformed into the Wave data x of normal distribution _Iko' after (for example Fig. 6 (b), (d)), can utilize the Wave data x of normal distribution _Iko' carry out feature according to the feature method of discrimination of the characteristic parameter of aforesaid normal distribution and judge.Also have, this method is applicable to the Wave data μ of normal distribution _XikoAnd x _Iko'.

(2) according to the feature diagnostic method of information theory

If the probability density function of the Wave data of the normal distribution of reference characteristic is f _Ko(x _i), the probability density function of the Wave data of the normal distribution in the moment beyond the reference characteristic is f _Xk(x _i).Also have, claim be characterized as ' test feature ' in the reference characteristic moment in addition.Can judge with ' Information Divergence (information discrete, ID) ' method whether test feature is the feature identical with reference characteristic with following ' Kullback-LeiblerInformation (Ku Erbake quantity of information, KI) '.

${\mathrm{KI}}_x={\&Integral;}_{-\&infin;}^{\&infin;}{f}_{x0}\left(x_i\right)\frac{f_{x0}\left(x_i\right)}{f_{\mathrm{xk}}\left(x_i\right)}d{x}_i$

$=\frac{1}{2}\{\log \frac{{\mathrm{\&sigma;}}_{\mathrm{ixk}}}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ix"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ix</figure-callout>}0}}+\frac{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ix"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ix</figure-callout>}0}}^2+{({\mathrm{\&mu;}}_{\mathrm{ix}0}-{\mathrm{\&mu;}}_{\mathrm{ixk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{ixk}}}^2}-1\}---\left(65\right)$

${\mathrm{ID}}_x={\&Integral;}_{-\&infin;}^{\&infin;}\{f_{x0}\left(x_i\right)-f_{\mathrm{xk}}\left(x_i\right)\}\frac{f_{x0}\left(x_i\right)}{f_{\mathrm{xk}}\left(x_i\right)}d{x}_i$

$=\frac{1}{2}\{\frac{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ix"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ix</figure-callout>}0}}^2+{({\mathrm{\&mu;}}_{\mathrm{ix}0}-{\mathrm{\&mu;}}_{\mathrm{ixk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{ixk}}}^2}+\frac{{{\mathrm{\&sigma;}}_{\mathrm{ixk}}}^2+{({\mathrm{\&mu;}}_{\mathrm{ix}0}-{\mathrm{\&mu;}}_{\mathrm{ixk}})}^2}{{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="0"\; label="ix"\; filenames="C20048000592600331.png,C20048000592600351.png"\; state="\{\{state\}\}">ix</figure-callout>}0}}^2}-2\}---\left(66\right)$

Because to utilizing KI _XAnd ID _XThe feature diagnostic method be described in detail, so repeat no more here.([12] Liu Xinfang, the sharp husband of Toyota, Chen Peng, Feng Fang, two protect and know also; ' utilizing the abnormity diagnosis of information discrete (Information Divergence) diagnosis rotating machinery ', accurate engineering Hui Chi, Vol.66, No.1,2000, p.157-162)

Here, represent a concrete instance, Fig. 6 (a) is the Wave data of the vibration acceleration that records when the normal feature of certain rotating machinery.The Wave data of Fig. 6 (c) for recording when same rotating machinery uneven.

Will be more than or equal to the Wave data x of mean value _I+, smaller or equal to the Wave data x of mean value _I-, and absolute value data | x _i| after being transformed into the Wave data of normal distribution, use x ' respectively _I+, x ' _I-, | x _i| ' expression.X ' _I+, x ' _I-, | x _i| ' mean value and standard deviation as follows.

X ' _I+: mean value=1.96 when mean value just often=0.69, imbalance

Standard deviation=2.37 when standard deviation just often=1.03, imbalance

X ' _I-: mean value=-0.66 when mean value just often=-0.37, imbalance

Standard deviation=0.69 when standard deviation just often=0.47, imbalance

| x _i| ': mean value=3.29 when mean value just often=1.45, imbalance

Standard deviation=3.53 when standard deviation just often=1.52, imbalance

According to (list of references 8), established verification and measurement ratio α=0.15, loss β=0.15, if ' test feature is different from reference characteristic ' then judged according to the probability of 85%n in KI＞1.21 or ID＞2.43.Above-mentioned x ' _I+, x ' _I-, | x _i| ' KI and ID be as described below.

x’ _i+：KI＝0.519、ID＝2.24

x’ _i-：KI＝0.53、ID＝0.40

|x _i |’：KI＝0.57、ID＝2.67

According to | x _i| ' ID＞2.43, can judge ' feature of Fig. 6 (a) is different from the feature of Fig. 6 (c) ' according to the probability of 85%n.

In addition, utilizing mean value shown in formula (44) and the formula (45) and discrete check to carry out feature judges.

Have again, also can utilize above-mentioned x ' _I+, x ' _I-, | x _i| ', ask characteristic parameter with formula (2)～formula (25), carry out feature according to the integrated approach of statistical test or possibility theory and characteristic parameter and judge.

5. signatures to predict

Obtain the characteristic parameter p of normal distribution _iAfter, utilize existing signatures to predict method, can predict determination object feature (very clear, the military rattan Bo Dao of [13] Ishikawa: Forecasting Methodology, measurement and control, 1982.3.[14] Ogawa, M.; Time series analysis and stochastic prediction, Bull.Math.Stat., 8,8-72,1958.[15] B. pick up Ni Aoer work, little village Yin two, Chai Shan palace favour translate: the statistics of prediction usefulness, the foreign Books of rolling shop, 1987.)

Fig. 7 representation feature Forecasting Methodology.Each is being measured (x constantly ₁～x ₇) characteristic ginseng value that records or fundamental component value according to the normal probability paper distribution transformation after, ask prediction curve and fiducial interval thereof according to regretional analysis, ask ' short life ', ' mean lifetime ', and ' MaLS ' at intersection point place with ' lifetime limitation '.

Fig. 8 is that certain rotating machinery is from the normal feature waveform example that 8 times record during uneven changing features.Measuring 1 is normal feature, and measuring 8 is the most severe uneven feature of uneven degree.The mean value of the characteristic parameter in each measurement that Fig. 9 represents to obtain with formula (2)～formula (13).From this example as can be known: characteristic parameter is along with the degree of off-note increases the weight of, and the dull characteristic parameter that increases of numerical value (p is for example arranged ₄, p ₅), the dull characteristic parameter that reduces of numerical value is also arranged (for example: p ₂, p ₈, p ₉, p ₁₀).In addition, the characteristic parameter that numerical value is almost constant even also there is the degree of off-note to increase the weight of (p for example ₁, p ₇).Thereby, must select the numerical value dullness to increase the characteristic parameter of (or dull minimizing), carry out life prediction.In addition, when utilizing the fundamental component bimetry, should only select the dull characteristic parameter that increases of numerical value (or the dull characteristic parameter that reduces of numerical value), obtain fundamental component, carry out life prediction.

Figure 16 (a) expression realizes above-mentioned Wave data and characteristic parameter are transformed into method, feature decision method, and the measurement used of signatures to predict method and the flow process of processing of the probability variable of normal distribution.In addition, Figure 17 represents to realize the Wave data measurement of Figure 16 (a) usefulness and the circuit of feature decision maker.

6. according to the detection method and the feature criterion of the special component of fluctuating signal

Here, utilize the example of the flame-out diagnosis of gas engine to describe.

Cylinder pressure Wave data when Figure 10 (a), Figure 11 (a), Figure 12 (a), Figure 13 (a) produce flame-out (the peak value exception among the figure) for gas engine.Also has the example that a plurality of anomaly peaks of Figure 12 (a), Figure 13 (a) expression produce continuously.For the local anomaly that produces in such fluctuating signal (special component), online flow process of carrying out distinguished point detection and feature judgement is shown in Figure 15.Its step below is described.

1) preparation (Figure 15 (a)) of diagnosis usefulness

(1) measures the fluctuating signal and the rotational pulse signal of diagnosis object simultaneously.Have, rotational pulse signal is also referred to as periodic pulse signal again, uses when the moment of each peak value of decision fluctuating signal.

(2) in order to remove denoising, carry out low-pass filtering.The cutoff frequency fL of low-pass filtering is determined by following formula.

$f_L=\frac{n}{60}z+f_0---\left(67\right)$

In the formula, n is the rotating speed (rpm) of axle, and z is the peak value (change peak value/1) of revolution, and f0 is unnecessary frequency (＞n/60 is decided by the noise effects of removing behind the observation filter).

(3) ask envelope Wave data or peak value Wave data or moving average Wave data after the low-pass filtering.

(4) as shown in the formula like that above-mentioned envelope Wave data or peak value Wave data or moving average Wave data being carried out normalized.

$x\left(t\right)=\frac{x^{\&prime;}\left(t\right)-{\mathrm{\&mu;}}^{\&prime;}\left(t\right)}{s}---\left(68\right)$

In the formula, x (t) is an x ' standard deviation (t) for x ' mean value, s (t) (t) for original Wave data, μ ' (t) for the Wave data after the normalization, x '.Also have, asking μ ' (t) and during s, the Wave data of normal feature preferably, but be not that the Wave data of normal feature also can.In addition, asking μ ' (t) and during s, operating condition (rotating speed or load) is being set for when judging identical as far as possible.Even but operating condition has some variations, result of determination also there are not much influences.

(5) investigate relative position relation between the peak value of the peak value of rotational pulse signal and fluctuating signal in advance, the threshold value of the unusual usefulness of decision identification.Setting about threshold value is now considered as follows. exists

|x(t)|＞kσ (69)

During establishment, judge and take place unusually.In the formula, k (=2～4) depends on the diagnosis object thing.

At | x (t) | than k σ big during, judge that the peak value place of the fluctuating signal corresponding with rotational pulse signal has unusually.

2) inline diagnosis (Figure 15 (b))

(1) measures fluctuating signal and the rotational pulse signal of judging object simultaneously.

(2) carry out low-pass filtering.Determine the cutoff frequency fL of low-pass filter like that suc as formula (66).

(3) obtain envelope Wave data or peak value Wave data after the low-pass filtering.

(4) utilize formula (68) that above-mentioned envelope Wave data or peak value Wave data are made normalized.

(5) whether the absolute value of envelope Wave data after the supervision normalization or peak value Wave data is bigger than threshold value (k σ).As little, then be judged to be no abnormal.As greatly, then be judged to be take place unusual, at | x (t) | than k σ big during, utilize the relation between the peak value of surveying good rotational pulse signal and fluctuating signal in advance, judge unusual position.

Figure 10, Figure 11, Figure 12, Figure 13 represent the example according to the signal Processing of above-mentioned steps.Figure 10 (a) (b), Figure 11 (a) (b), Figure 12 (a) (b), Figure 13 (a) (b) the timing waveform data and the spectrogram of the cylinder pressure when representing that flame-out (the unusual position among the figure) takes place gas engine.

Figure 10 (c) (d), Figure 11 (c) (d), Figure 12 (c) (d), Figure 13 (c) is (d) for utilizing timing waveform data and spectrogram after low-pass filter removes denoising.

Figure 10 (e), Figure 11 (e), Figure 12 (e), Figure 13 (e) are rotary pulsed Wave data.

Figure 10 (f), Figure 12 (f) are the envelope Wave data.

Figure 11 (f), Figure 13 (f) are the peak value Wave data.

According to Figure 10,11,12,13 (f) as can be known: can judge when unusual (lack peak value or peak value diminishes) takes place its absolute value | x (t) | bigger than 2 σ.

In addition, can utilize absolute value | x (t) | big position and the corresponding relation between rotary pulsed Wave data than 2 σ, judge unusual position.

More than, the example of envelope Wave data and peak value Wave data is shown, but as shown in figure 14, as obtain moving average Wave data (u _i), then can utilize u (t) to replace x (t) and above-mentioned step similarly to detect the distinguished point of fluctuating signal.Also have, as utilize formula (67) to ask cutoff frequency (fc), then can obtain count (M) of moving average.

Figure 16 (b) expression realizes the special component detection of above-mentioned fluctuating signal and measurement and the treatment scheme that decision method is used.In addition, Figure 18 represents to realize the fluctuating signal measurement of Figure 16 (b) usefulness and the circuit of feature decision maker.

7. the treatment scheme of feature decision maker or online feature decision-making system

The treatment scheme of Figure 16 representation feature decision maker or online feature decision-making system.Shown in Figure 16 (a), from the measured waveform data, removing denoising, ask characteristic parameter, after this characteristic parameter is transformed into the probability variable of normal distribution, utilize the comprehensive of statistical test or possibility theory or characteristic parameter, judge to have or not changing features.These handle available computers or isolated plant is realized.In addition, shown in Figure 16 (b), in the special component detection and feature judgement according to fluctuating signal, its low-pass filter, envelope (or peak value) can be realized with hardware.Since numerical operation device (or computing machine) can carry out after the normalization x (t), | x (t)＞k σ | judgement, the detection at special position and the demonstration of judgement and result of determination, so can carry out in real time.

Claims (15)

1. one kind is carried out the feature judgement of object and the method for signatures to predict, it is characterized in that,

Described method is included in the step that a plurality of frequency domains are measured the Wave data of the object of supervision feature, remove the step of denoising from the described Wave data that records, utilize to remove the Wave data behind the denoising calculates the characteristic parameter of time domain and frequency domain as the primitive character parameter-definition step, described primitive character parameter transformation of calculating is become the step of the characteristic parameter of known distribution according to predetermined probability distribution, and the characteristic parameter that utilizes described known distribution carries out the feature judgement of object and the step of signatures to predict, thus, carrying out the feature of object judges and signatures to predict

Described method is in the step that the characteristic parameter with described time domain and frequency domain calculates as the primitive character parameter-definition, described primitive character parameter is if the dimensionless characteristic parameter, then after with described Wave data normalization after removing denoising, can calculate, in the step of the characteristic parameter that described primitive character parameter transformation is become known distribution, be divided into the reference object thing reference characteristic situation and not the situation of the reference characteristic of reference object thing carry out conversion.

2. the method for claim 1 is characterized in that,

Described normalized Wave data is divided into the Wave data bigger than mean value, than mean value little Wave data, absolute value Wave data and all Wave datas and be transformed into normal distribution after, calculate described primitive character parameter according to these Wave datas.

3. the method for claim 1 is characterized in that,

In the described primitive character parameter interval characteristic parameter is defined and calculates.

4. the method for claim 1 is characterized in that,

In the step of the characteristic parameter that described primitive character parameter transformation is become known distribution, comprise probability distribution, mean value and the discrete step of obtaining described primitive character parameter; Utilize the step of the value of the probability distribution, mean value of described primitive character parameter and the discrete characteristic parameter of obtaining known distribution.

5. the method for claim 1 is characterized in that,

Utilize the characteristic parameter of described known distribution, judge and signatures to predict according to the feature that the integrated approach and the information theory of statistical theory, possibility theory, characteristic parameter are carried out object.

6. the method for claim 1 is characterized in that,

The comprehensive characteristics parameter that the characteristic parameter that utilizes described known distribution is tried to achieve according to the integrated approach of characteristic parameter is according to predetermined probability distribution, be transformed into the comprehensive characteristics parameter of known distribution, utilize the comprehensive characteristics parameter of known distribution, carry out the feature of object according to statistical theory and possibility theory and judge and signatures to predict.

7. the method for claim 1 is characterized in that,

In described each method, only select the dull characteristic parameter that increases of numerical value or comprehensive characteristics parameter or dull characteristic parameter or the comprehensive characteristics parameter that reduces of numerical value along with changing features.

8. the method for claim 1 is characterized in that,

Carrying out the feature of described predetermined probability distribution when being normal distribution judges and signatures to predict.

9. one kind is carried out the feature judgement of object and the method for signatures to predict, it is characterized in that,

Described method be included in step that a plurality of frequency domains measure Wave data for the feature of monitored object thing, from the described Wave data that records remove the step of denoising, will be transformed into except that the Wave data behind the denoising according to predetermined probability distribution known distribution Wave data step and utilize the Wave data of described known distribution to carry out the feature judgement of object and the step of signatures to predict, thus, carrying out the feature of object judges and signatures to predict

Described method in the step of the Wave data that described Wave data after removing denoising is transformed into known distribution, Wave data normalization is divided into the reference object thing reference characteristic situation and not the situation of the reference characteristic of reference object thing carry out conversion.

10. method as claimed in claim 9 is characterized in that,

The described Wave data that removes behind the denoising is divided into the Wave data bigger than mean value, the Wave data littler than mean value, absolute value Wave data, and all Wave datas, carries out the Wave data conversion of known distribution according to predetermined probability distribution.

11. method as claimed in claim 9 is characterized in that,

Utilize the Wave data of described known distribution, carry out the feature of object according to characteristic parameter and information theory and judge and signatures to predict.

12. method as claimed in claim 9 is characterized in that,

When described predetermined probability distribution is normal distribution, Wave data is transformed into the Wave data of normal distribution.

13. a method of carrying out the feature judgement of object is characterized in that,

When described method is fluctuating signal at the signal with the object of sensor measurement, comprise from the fluctuating signal of described measurement remove denoising step, obtain describedly remove the step of the signature waveform data of the fluctuating signal behind the denoising, signature waveform Data Detection after described signature waveform data are carried out the step of normalized and utilized described normalization goes out special component and determines the step of the position of special component, thus, carrying out the feature of object judges

Described method is, it is the described situation of removing the envelope Wave data of the fluctuating signal behind the denoising that described signature waveform data are divided into, be the situation of the described peak value Wave data that removes the fluctuating signal behind the denoising and be that the described situation of removing the moving average Wave data of the fluctuating signal behind the denoising is obtained.

14. method as claimed in claim 13 is characterized in that,

Utilize low-pass filter to remove denoising from the described fluctuating signal that records.

15. method as claimed in claim 13 is characterized in that,

Utilize signature waveform data after the described normalization and the recurrent pulse Wave data that records simultaneously to detect special component, and determine the occurrence positions of special component.

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