CN103487250A - Coal mining equipment predictive maintenance method based on two-dimensional projection - Google Patents

Abstract

The invention discloses a coal mining equipment predictive maintenance method through regression analysis combined with two-dimensional projection, and relates to a coal main fan and an elevator. The diagnosis method includes the steps of extracting a vibration signal from an equipment monitoring system to obtain 24 characteristic indexes used for describing equipment operating states through data analysis and calculation, respectively extracting a time sequence for each of the 24 characteristic indexes, carrying out regression analysis to obtain predictive factors corresponding to the 24 characteristic indexes respectively, projecting the predictive factors on a two-dimensional space by means of two-dimensional projection, building a fitting function of predictive factor projection values and corresponding characteristic index values, calculating future values of the 24 characteristic indexes, projecting the future values of the 24 characteristic indexes in a best projection image direction matrix, judging the trend of the equipment future operating state according to the distribution situation of the projection values, and accordingly achieving predictive maintenance of coal mine equipment.

Description

Coal mine equipment anticipatory maintenance method based on two-dimensional projections

Technical field

The invention belongs to coal mine equipment fault diagnosis technology field, be specifically related to a kind of vibration equipment data of utilizing and calculate 24 characteristic indexs, described 24 characteristic indexs are extracted respectively a time series and carried out separately auto-regressive analysis, obtain each self-corresponding predictor; Utilize two-dimensional projections that described predictor is projected to two-dimensional space, set up respectively the fitting function of predictor range and corresponding characteristic index value, extrapolate respectively the future value of 24 characteristic indexs; Projected under matrix in the best projection image space by the future value to described 24 characteristic indexs again, according to the trend of the following running status of distribution situation judgment device of range, thereby realized the anticipatory maintenance to coal mine equipment.

Background technology

Coal mine equipment breaks down and can have a strong impact on manufacturing schedule, even leads to catastrophic failure, and personnel and property have been caused to great harm.And existing equipment operation condition monitoring technology can not realize the prediction of the following operation conditions of equipment far away.

The anticipatory maintenance of coal mine equipment is a job with high content of technology, that difficulty is large, now domestic and international majority all adopts the modes of building real-time monitoring system at present, gather vibration signal, temperature signal, pressure signal and electric parameter signal etc., these monitoring meanss play positive role to the monitoring equipment fault.But, Monitoring Data being carried out to aspect the fault alarm processing, all by given threshold value, carry out fault alarm, there is serious drawback in Threshold Alerts: Fault Identification lags behind, and can not realize that fault hides the phase early warning, causes equipment maintenance and management work very passive.

Equipment failure is a deteriorated process gradually from there being extremely fault; to this process, the most responsive signal is frequency-region signal; at present also have by frequency-region signal and carry out equipment fault diagnosis; but be mainly to judge by the typical frequencies component; but the typical frequencies component often has fluctuation or deviation, and is difficult to determine with the corresponding relation of different faults type.Add coal mine working inclement condition, operating mode complexity simultaneously, therefore only depend on the typical frequencies component can't realize fast state judgement and accurate Fault Identification.Because typical frequencies component method can't accomplish the end in view, so still adopt above-mentioned more original passive Threshold Alerts method in colliery engineering at present.As can be seen here, to existing equipment running status anticipatory maintenance method, furtherd investigate significant.

Summary of the invention

The objective of the invention is can't realize for described coal mine equipment the present situation of anticipatory maintenance, propose a kind of real-time diagnosis method, a kind of forecast result is the anticipatory maintenance method comparatively accurately.The method combines the range distribution characteristics of 24 kinds of characteristic indexs, has invented and has had adaptive ability, the coal mine equipment running status anticipatory maintenance method that forecasting accuracy is higher.

Technical scheme of the present invention is:

(1) at the coal mine equipment key position---the acceleration vibration transducer is installed on the level of bearing, vertical, axial three directions, vibration data in the monitoring equipment operational process described vibration data is sent to rear end receives and disposal system incessantly, and deposit associated data files in;

(2) vibration data { a to extracting in the acceleration vibration transducer _i, i=1,2 ..., n} is processed, and concrete steps are:

1. to described vibration data { a _i, i=1,2 ..., n} carries out Fourier transform and obtains { x _i, i=1,2 ..., n};

2. calculate by following formula the 24 characteristic index vectors that can describe equipment running status

x ^*＝{x _av,x _p,x _rms,x _r,D _x,x _p-p,α,β,C _f,S _f,I _f,CL _f,K _v,f _avg,f _b,f _bb,f _v,f _rv,S,E _r1,E _r2,

，

E _r3,E _r4,E _r5}

Absolute mean: $x_{\mathrm{av}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\left|x_i\right|;$

Peak value: x _p=max|x _i|;

Effective value (root-mean-square value):

The root amplitude: $x_r={\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\sqrt{\left|x_i\right|}\right)}^2;$

Variance: $D_x=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-x_{\mathrm{av}})}^2;$

Peak-to-peak value: x _p-p=max (x _i)-min (x _i);

The skewness index: $\mathrm{\α}=\sqrt{\frac{1}{6n}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^3;$

The kurtosis index: $\mathrm{\β}=\sqrt{\frac{n}{24}}[\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^4-3];$

Peak index: $C_f=\frac{x_p}{x_{\mathrm{rms}}};$

The waveform index: $S_f=\frac{x_{\mathrm{rms}}}{x_{\mathrm{av}}};$

The pulse index: $I_f=\frac{x_p}{x_{\mathrm{rms}}};$

The nargin index: ${\mathrm{CL}}_f=\frac{x_p}{x_r};$

The coefficient of variation: $K_v=\frac{\sqrt{D_x}}{x_{\mathrm{av}}};$

Gravity frequency (average frequency):

Equal square frequencies: $f_b=\frac{{\∫}_0^{\∞}{f}^{2}p\left(f\right)\mathrm{df}}{{\∫}_0^{\∞}p\left(f\right)\mathrm{df}};$

The root mean square frequency: $f_{\mathrm{bb}}={\left(\frac{{\∫}_0^{\∞}{f}^{2}p\left(f\right)\mathrm{df}}{{\∫}_0^{\∞}p\left(f\right)\mathrm{df}}\right)}^{1/2};$

The frequency variance: $f_v=\frac{{\∫}_0^{\∞}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\∫}_0^{\∞}p\left(f\right)\mathrm{df}};$

Frequency standard is poor: $f_{\mathrm{rv}}={\left[\frac{{\∫}_0^{\∞}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\∫}_0^{\∞}p\left(f\right)\mathrm{df}}\right]}^2;$

Spectrum peak index of stability: $S=\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\Σ}}}\{{f_i}^2\·P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\Σ}}}P\left(f_i\right)}}/\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\Σ}}}\{{f_i}^4\·P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\Σ}}}{f_i}^2\·P\left(f_i\right)}};$

The first frequency band relative energy: ${\mathrm{<figure-callout\; id="1"\; label="E\; r"\; filenames="131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_0^{B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The second frequency band relative energy: ${\mathrm{<figure-callout\; id="2"\; label="E\; r"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{B_f}^{2B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 3rd frequency band relative energy: $E_{r3}={\&Integral;}_{2B_f}^{3B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 4th frequency band relative energy: ${\mathrm{<figure-callout\; id="4"\; label="E\; r"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{3B_f}^{4B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 5th frequency band relative energy: ${\mathrm{<figure-callout\; id="5"\; label="E\; r"\; filenames="131008161942.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{4B_f}^{5B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df},$

In described 24 characteristic index computing formula, f means the frequency of signal, and p (f) means the power spectrum of signal, B _fmean 1/5 frequency range value, F _smean highest frequency value;

(3) to 24 characteristic index vector X ^*process and set up assessment indicator system, concrete steps are:

1. 24 characteristic indexs vectors X ^*the pre-service of training sample:

The a certain duty of equipment, described state can be normal condition or a certain typical fault state, with { q _i, i=1,2 ..., s} means, 24 characteristic index vector X under described a certain state ^*the composing training sample space can be used the matrix X of p * n ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., n} means, wherein, and x ^*i the characteristic index that (i, j) is j state sample, p means the dimension of sample space, i.e. the quantity of characteristic index, n means the number of training sample;

For the impact of eliminating each characteristic index dimension the fluctuation range of unifying its value, need to carry out normalized to sample data:

wherein, x _max(j), x _min(j) mean respectively raw data x ^*maximal value and the minimum value of (i, j) i index, X={x (i, j) | i=1,2 ..., p; J=1,2 ..., n} means X ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., the sequence after the n} normalized;

2. 24 characteristic index vectors are projected, are analyzed its range characteristic distributions:

Described projection be exactly the p dimension data x (i, j) | i=1,2 ..., p; J=1,2 ..., n} is converted into matrix a={a (1), a (2), and a (3) ..., a (p) } be the one dimension range z (j) of projecting direction:

$z\left(j\right)=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}a\left(i\right)x(i,j),j=\mathrm{1,2},...,n,$

A representation unit length vector wherein, then according to range z (j) | j=1,2 ..., the characteristic distributions of n} is sorted out;

3. for by described step (3) 2. in range zone under each exemplary apparatus state separate, structure projection objective function is to seek best projecting direction matrix A=[a ₁, a ₂..., a _m],

Projection objective function index can be expressed as: Q (a)=S _zd _z,

Wherein, S _zfor range z (i) standard deviation is used for describing between class distance; D _zfor range z (i) local density is used for describing density in class,

$S_z=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(z\left(i\right)-E\left(z\right))}^2}{n-1}},$

$D_z=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(R-r(i,j))\&CenterDot;u(R-r(i,j)),$

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; The windows radius that R is local density, its span is generally:

the quantity that p is characteristic index; R (i, j) means the distance between sample, r (i, j)=| z (i)-z (j) |; Unit-step function $u\left(t\right)=\left\{\begin{array}{c}1,t\&GreaterEqual;0\\ 0,t<0\end{array}\right.,$

Maximize objective function: Max:Q (a)=S _zd _z,

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

At best projecting direction matrix A=[a ₁, a ₂..., a _m] under, 24 characteristic index vector projection value w under described each exemplary apparatus state _i(i=1,2 ..., the s) distribution that becomes band, described zonal arrangement system has formed equipment state assessment indicator system W;

(4) foundation of the coal mine equipment state anticipatory maintenance model based on two-dimensional projections

1. determine predictor

{ x* (the i) } expression for wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs, the coefficient of autocorrelation R (k) that { x* (i) } postpones the k step is:

$R\left(k\right)=\frac{\underset{i=k+1}{\overset{n}{\mathrm{\&Sigma;}}}(x*\left(i\right)-\mathrm{Ex}*)(x*(i-k)-\mathrm{Ex}*)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2},$

$\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n,$

Wherein, the sample size that n is described arbitrary characteristic index sequential { x* (i) }, k=1,2 ..., m, m<[n/4]; The variance of R (k) reduces along with reducing of k, but the estimated accuracy of R (k) increases along with reducing of k, so the value of m should be less; According to the theory of sampling process of R (k), in the situation that confidence level 1-α, when the value of R (k) does not belong to following interval range,

$R\left(k\right)\&NotElement;[\frac{-1-{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k},\frac{-1+{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k}],$

Illustrate that sequential { x* (i) } and the dependence that postpones the x* (i-k) after the k step are significant, so x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } postpones k, to walk dependence not remarkable; In the situation that known confidence level, minute position μ of described interval range _α/2can from the standardized normal distribution table, check in;

2. predictor two-dimensional projections

At first, described arbitrary characteristic index time series { x* (i) } is carried out to standardization:

$x\left(i\right)=\frac{x*\left(i\right)-\mathrm{Ex}*}{\mathrm{\&sigma;x}*},$

Wherein, mean value $\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n,$ Variance $\mathrm{\&sigma;x}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2};$

Described through standardized arbitrary characteristic index sample with x (i) | i=1,2 ..., n} means, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} means, n wherein, and p is respectively sample size and predictor quantity;

By the p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} is in projecting direction a={a (1), a (2), a (3) ..., a (p) on projected,

i=p+1, p+2 ..., n, wherein, a is the unit length vector; Thereby set up x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} with x (i) | i=1,2 ..., the mathematical relation between n};

3. described predictor range is carried out to the orthogonal Hermite fitting of a polynomial

This patent utilizes classical Hermite Polynomial Families, and its expression formula is:

-∞<z<∞, meet ${\&Integral;}_{-\&infin;}^{\&infin;}{h}_i\left(z\right)h_j\left(z\right)\mathrm{dz}={\mathrm{\&delta;}}_{\mathrm{ij}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1,i=\mathrm{<figure-callout\; id="0"\; label="j"\; filenames="131008161928.png,131008161932.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 0,i\&NotEqual;j\end{array}\right.,$ Wherein, r! Represent the factorial of r, z=a ^tx, for the standard Gauss equation;

The expression formula that obtains so the coal mine equipment anticipatory maintenance model based on two-dimensional projections is:

$\hat{x}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{R}{\mathrm{\&Sigma;}}}{c}_{\mathrm{ij}}{h}_{\mathrm{ij}}\left(a_i^{T}X\right),$

i＝1,2,...,m，j＝1,2,...,r，

Wherein,

mean a certain characteristic index in described 24 characteristic indexs, the exponent number of R representative polynomial, c means the Hermite multinomial coefficient, h means the orthogonal Hermite polynomial expression, $H=\left[\begin{array}{c}{h}_1\left(z_l\right)\\ h_2\left(z_l\right)\\ ...\\ h_R\left(z_l\right)\end{array}\right],$ l＝1,2,...,n。

4. optimize the projection objective function and seek best projecting direction matrix a ' and optimum polynomial coefficient c

Structure projection target function, solve by minimizing objective function,

Minimize objective function: $\min Q(a,c)=\frac{1}{n-p}\underset{i=p+1}{\overset{n}{\mathrm{\&Sigma;}}}{(x\left(i\right)-\hat{x}\left(i\right))}^2,$

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

Obtain best projecting direction matrix a and optimum polynomial coefficient c, finally determined the coal mine equipment anticipatory maintenance model based on two-dimensional projections in substitution (4) 3.;

(5) realization of anticipatory maintenance

1. calculate the future value of 24 characteristic indexs

According to the coal mine equipment anticipatory maintenance model based on two-dimensional projections obtained in step (4), can calculate the future value of 24 characteristic indexs:

X ^*′＝{x _av′,x _p′,x _rms′,x _r′,D _x′,x _p-p′,α′,β′,C _f′,S _f′,I _f′,CL _f′,K _v′,f _avg′,f _b′,f _bb′,f _v′,f _rv′,

；

S′,E _r1′,E _r2′,E _r3′,E _r4′,E _r5′}

2. the future value of 24 characteristic indexs is carried out to two-dimensional projections

The best projecting direction matrix A that 3. future value of 24 characteristic indexs that step (5) is tried to achieve in 1. tries to achieve in step (3)=[a ₁, a ₂..., a _m] under carry out two-dimensional projections, obtain range w ', just can judge the equipment state recognition result according to the distributing position of described range w ' is q ', whether dope coal mine equipment will exist extremely future, and identify described which kind of fault type that extremely belongs to simultaneously, according to described state recognition result, the staff takes corresponding rational anticipatory maintenance measure so.

With respect to prior art, the present invention has following remarkable advantage:

1, in this method to the selection of 24 characteristic indexs and objective function, to be based upon laboratory practical experience for many years screens to the research conclusion of equipment failure vibration signal characteristics and in conjunction with the professional, selected various features index is with strong points, susceptibility is strong, Clustering Effect is obvious, can accurately reflect the subtle change of equipment running status, and its judged result and actual conditions are very identical;

2, in this method, diagnose 24 adopted characteristic indexs all through normalized, to be converted into dimensionless index, thereby in the equipment running status identifying, different environment and equipment are had to same adaptive ability, all can use various types of collieries;

3, this method proposes to adopt the orthogonal Hermite fitting of a polynomial one dimension ridge function wherein of variable-order, has avoided in the two-dimensional projections using huge function table, and can guarantee the precision of approaching.

The accompanying drawing explanation

Fig. 1 is bear vibration installation of sensors mode;

Fig. 2 is the state evaluation index system under roller normal condition and four kinds of different lesion size;

Fig. 3 is that the roller lesion size is respectively the assessment indicator system under 0.014 inch and 0.021 inch;

The frequency variance f of Fig. 4 for obtaining through better fitting _vthe anticipatory maintenance model curve;

The projection distribution situation that Fig. 5 is 24 characteristic index forecasted future values;

Fig. 6 is coal mine equipment anticipatory maintenance workflow diagram.

Embodiment

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

(1) bearing is as the key components and parts of large rotating machinery equipment, its fault type is divided into rolling body fault, inner ring fault, outer ring fault, the large class of retainer fault four, in addition the different degree of injury of described four large class fault simulations again Further Division be different groups, can be divided as the case may be.Acceleration vibration transducer (as shown in Figure 1) is installed on the level of bearing to be assessed, vertical, axial three directions, the vibration data of monitoring equipment operational process centre bearer incessantly, and described vibration data is sent to rear end receives and disposal system, and deposits in associated data files and use for back-end analysis.

(2) vibration data { a to extracting in the acceleration vibration transducer _i, i=1,2 ..., n} is processed, and concrete steps are:

1. to vibration data { a _i, i=1,2 ..., n} carries out Fourier transform and obtains { x _i, i=1,2 ..., n};

2. calculate by following formula the 24 characteristic index vector x that can describe the bearing running status ^*={ x _av, x _p, x _rms, x _r, D _x, x _p-p, α, β, C _f, S _f, I _f, CL _f, K _v, f _avg, f _b, f _bb, f _v, f _rv, S, E _r1, E _r2,

，

E _r3,E _r4,E _r5}

Absolute mean: $x_{\mathrm{av}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|x_i\right|;$

Peak value: x _p=max|x _i|;

Effective value (root-mean-square value):

The root amplitude: $x_r={\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\sqrt{\left|x_i\right|}\right)}^2;$

Variance: $D_x=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x_i-x_{\mathrm{av}})}^2;$

Peak-to-peak value: x _p-p=max (x _i)-min (x _i);

The skewness index: $\mathrm{\&alpha;}=\sqrt{\frac{1}{6n}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^3;$

The kurtosis index: $\mathrm{\&beta;}=\sqrt{\frac{n}{24}}[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^4-3];$

Peak index: $C_f=\frac{x_p}{x_{\mathrm{rms}}};$

The waveform index: $S_f=\frac{x_{\mathrm{rms}}}{x_{\mathrm{av}}};$

The pulse index: $I_f=\frac{x_p}{x_{\mathrm{rms}}};$

The nargin index: ${\mathrm{CL}}_f=\frac{x_p}{x_r};$

The coefficient of variation: $K_v=\frac{\sqrt{D_x}}{x_{\mathrm{av}}};$

Gravity frequency (average frequency):

Equal square frequencies: $f_b=\frac{{\&Integral;}_0^{\&infin;}{f}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}};$

The root mean square frequency: $f_{\mathrm{bb}}={\left(\frac{{\&Integral;}_0^{\&infin;}{f}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}}\right)}^{1/2};$

The frequency variance: $f_v=\frac{{\&Integral;}_0^{\&infin;}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}};$

Frequency standard is poor: $f_{\mathrm{rv}}={\left[\frac{{\&Integral;}_0^{\&infin;}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}}\right]}^2;$

Spectrum peak index of stability: $S=\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}\{{{\mathrm{<figure-callout\; id="2"\; label="f\; i"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">f</figure-callout>}}_i}^2\&CenterDot;P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}P\left(f_i\right)}}/\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}\{{{\mathrm{<figure-callout\; id="4"\; label="f\; i"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">f</figure-callout>}}_i}^4\&CenterDot;P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}{{\mathrm{<figure-callout\; id="2"\; label="f\; i"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">f</figure-callout>}}_i}^2\&CenterDot;P\left(f_i\right)}};$

The first frequency band relative energy: ${\mathrm{<figure-callout\; id="1"\; label="E\; r"\; filenames="131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_0^{B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The second frequency band relative energy: ${\mathrm{<figure-callout\; id="2"\; label="E\; r"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{B_f}^{2B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 3rd frequency band relative energy: $E_{r3}={\&Integral;}_{2B_f}^{3B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 4th frequency band relative energy: ${\mathrm{<figure-callout\; id="4"\; label="E\; r"\; filenames="131008161928.png,131008161937.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{3B_f}^{4B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 5th frequency band relative energy: ${\mathrm{<figure-callout\; id="5"\; label="E\; r"\; filenames="131008161942.png"\; state="\{\{state\}\}">E</figure-callout>}}_r={\&Integral;}_{4B_f}^{5B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df},$

In described 24 characteristic index computing formula, f means the frequency of signal, and p (f) means the power spectrum of signal, B _fmean 1/5 frequency range value, F _smean highest frequency value.

(3) to 24 characteristic index vector X ^*process and set up assessment indicator system, concrete steps are:

1. 24 characteristic indexs vectors X ^*the pre-service of training sample:

The a certain duty of equipment, described state can be normal condition or a certain typical fault state, with { q _i, i=1,2 ..., s} means, 24 characteristic index vector X under described a certain state ^*the composing training sample space can be used the matrix X of p * n ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., n} means, wherein, and x ^*i the characteristic index that (i, j) is j state sample, p means the dimension of sample space, i.e. the quantity of characteristic index, n means the number of training sample;

For the impact of eliminating each characteristic index dimension the fluctuation range of unifying its value, need to carry out normalized to sample data:

wherein, x _max(j), x _min(j) mean respectively raw data x ^*maximal value and the minimum value of (i, j) i index, X={x (i, j) | i=1,2 ..., p; J=1,2 ..., n} means X ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., the sequence after the n} normalized;

2. 24 characteristic index vectors are projected, are analyzed its range characteristic distributions:

Described projection be exactly the p dimension data x (i, j) | i=1,2 ..., p; J=1,2 ..., n} is converted into matrix a={a (1), a (2), and a (3) ..., a (p) } be the one dimension range z (j) of projecting direction:

$z\left(j\right)=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}a\left(i\right)x(i,j),j=\mathrm{1,2},...,n,$

A representation unit length vector wherein, then according to range z (j) | j=1,2 ..., the characteristic distributions of n} is sorted out;

3. for by described step (3) 2. in range zone under each exemplary apparatus state separate, structure projection objective function is to seek best projecting direction matrix A=[a ₁, a ₂..., a _m],

Projection objective function index can be expressed as: Q (a)=S _zd _z,

Wherein, S _zfor range z (i) standard deviation is used for describing between class distance; D _zfor range z (i) local density is used for describing density in class,

$S_z=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(z\left(i\right)-E\left(z\right))}^2}{n-1}},$

$D_z=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(R-r(i,j))\&CenterDot;u(R-r(i,j)),$

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; The windows radius that R is local density, its span is generally:

the quantity that p is characteristic index; R (i, j) means the distance between sample, r (i, j)=| z (i)-z (j) |; Unit-step function $u\left(t\right)=\left\{\begin{array}{c}1,t\&GreaterEqual;0\\ 0,t<0\end{array}\right.,$

Maximize objective function: Max:Q (a)=S _zd _z,

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

At best projecting direction matrix A=[a ₁, a ₂..., a _m] under, 24 characteristic index vector projection value w under described each exemplary apparatus state _i(i=1,2 ..., the s) distribution that becomes band, described zonal arrangement system has formed equipment state assessment indicator system W; Be that the bearing roller set up according to step (3) normally reaches lesion size and is respectively 0.007 inch, 0.014 inch, 0.021 inch, the 0.028 inch assessment indicator system under five kinds of states as shown in Figure 2 as shown in the figure: under normal condition, projection value is distributed near main axis=0.5 (shown in ☆); When the rolling body lesion size is 0.007 inch, projection value is distributed near main axis=-8 (shown in △); During 0.028 inch of rolling body damage, projection value is distributed near main axis=-13 (* shown in); During rolling body damage 0.014 inch (shown in) and 0.021 inch (shown in *), projection value overlaps, be distributed near main axis=-11, in order to distinguish two states, it is carried out to independent projection so, projection value distributes as shown in Figure 3: when rolling body damages 0.014 inch, projection value is distributed near main axis=-14 (shown in), and during rolling body damage 0.021 inch (shown in *), projection value is distributed near main axis=8 (shown in *).Fig. 2 and Fig. 3 have formed complete assessment indicator system under these five kinds of states.

(4) foundation of the coal mine equipment state anticipatory maintenance model based on two-dimensional projections

1. determine predictor

{ x* (the i) } expression for wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs, the coefficient of autocorrelation R (k) that { x* (i) } postpones the k step is:

$R\left(k\right)=\frac{\underset{i=k+1}{\overset{n}{\mathrm{\&Sigma;}}}(x*\left(i\right)-\mathrm{Ex}*)(x*(i-k)-\mathrm{Ex}*)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2},$

$\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n,$

Wherein, the sample size that n is described arbitrary characteristic index sequential { x* (i) }, k=1,2 ..., m, m<[n/4]; The variance of R (k) reduces along with reducing of k, but the estimated accuracy of R (k) increases along with reducing of k, so the value of m should be less; According to the theory of sampling process of R (k), in the situation that confidence level 1-α, when the value of R (k) does not belong to following interval range,

$R\left(k\right)\&NotElement;[\frac{-1-{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k},\frac{-1+{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k}],$

Illustrate that sequential { x* (i) } and the dependence that postpones the x* (i-k) after the k step are significant, so x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } postpones k, to walk dependence not remarkable; In the situation that known confidence level, minute position μ of described interval range _α/2can from the standardized normal distribution table, check in;

2. predictor two-dimensional projections

At first, described arbitrary characteristic index time series { x* (i) } is carried out to standardization:

$x\left(i\right)=\frac{x*\left(i\right)-\mathrm{Ex}*}{\mathrm{\&sigma;x}*},$

Wherein, mean value $\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n,$ Variance $\mathrm{\&sigma;x}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2};$

Described through standardized arbitrary characteristic index sample with x (i) | i=1,2 ..., n} means, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} means, n wherein, and p is respectively sample size and predictor quantity;

By the p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} is in projecting direction a={a (1), a (2), a (3) ..., a (p) on projected,

i=p+1, p+2 ..., n, wherein, a is the unit length vector; Thereby set up x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} with x (i) | i=1,2 ..., the mathematical relation between n};

3. described predictor range is carried out to the orthogonal Hermite fitting of a polynomial

This patent utilizes classical Hermite Polynomial Families, and its expression formula is:

-∞<z<∞, meet ${\&Integral;}_{-\&infin;}^{\&infin;}{h}_i\left(z\right)h_j\left(z\right)\mathrm{dz}={\mathrm{\&delta;}}_{\mathrm{ij}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1,i=\mathrm{<figure-callout\; id="0"\; label="j"\; filenames="131008161928.png,131008161932.png"\; state="\{\{state\}\}">j</figure-callout>}\\ 0,i\&NotEqual;j\end{array}\right.,$ Wherein, r! Represent the factorial of r, z=a ^tx,

for the standard Gauss equation;

The expression formula that obtains so the coal mine equipment anticipatory maintenance model based on two-dimensional projections is:

$\hat{x}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{R}{\mathrm{\&Sigma;}}}{c}_{\mathrm{ij}}{h}_{\mathrm{ij}}\left(a_i^{T}X\right),$

i＝1,2,...,m，j＝1,2,...,r，

Wherein, mean a certain characteristic index in described 24 characteristic indexs, the exponent number of R representative polynomial, c means the Hermite multinomial coefficient, h means the orthogonal Hermite polynomial expression, $H=\left[\begin{array}{c}{h}_1\left(z_l\right)\\ h_2\left(z_l\right)\\ ...\\ h_R\left(z_l\right)\end{array}\right],$ l＝1,2,...,n。

4. optimize the projection objective function and seek best projecting direction matrix a ' and optimum polynomial coefficient c

Structure projection target function, solve by minimizing objective function,

Minimize objective function: $\min Q(a,c)=\frac{1}{n-p}\underset{i=p+1}{\overset{n}{\mathrm{\&Sigma;}}}{(x\left(i\right)-\hat{x}\left(i\right))}^2,$

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

Obtain best projecting direction matrix a and optimum polynomial coefficient c, finally determined the coal mine equipment anticipatory maintenance model based on two-dimensional projections in substitution (4) 3.;

(5) realization of anticipatory maintenance

1. calculate the future value of 24 characteristic indexs

According to the coal mine equipment anticipatory maintenance model based on two-dimensional projections obtained in step (4), can calculate the future value of 24 characteristic indexs:

X ^*′＝{x _av′,x _p′,x _rms′,x _r′,D _x′,x _p-p′,α′,β′,C _f′,S _f′,I _f′,CL _f′,K _v′,f _avg′,f _b′,f _bb′,f _v′,f _rv′,

；

S′,E _r1′,E _r2′,E _r3′,E _r4′,E _r5′}

As shown in Figure 4, the frequency variance f of curve for obtaining through better fitting according to step (4) in figure _vthe anticipatory maintenance model curve, * is depicted as the predicted value of characteristic index training sample, the measured value of zero representation feature index training sample, the following measured value of representation feature index, the forecasted future value of △ representation feature index; Can obtain the forecasted future value of other 23 characteristic indexs after the same method.

2. the future value of 24 characteristic indexs is carried out to two-dimensional projections

The best projecting direction matrix A that 3. future value of 24 characteristic indexs that step (5) is tried to achieve in 1. tries to achieve in step (3)=[a ₁, a ₂..., a _m] under carry out two-dimensional projections, obtain range w ', just can judge the equipment state recognition result according to the distributing position of described range w ' is q ', whether dope coal mine equipment will exist extremely future, and identify described which kind of fault type that extremely belongs to simultaneously, according to described state recognition result, the staff takes corresponding rational anticipatory maintenance measure so.As shown in Figure 5, the distribution of the projection value (zero shown in) of sample to be tested under above-mentioned optimal projection direction matrix, projection value overlaid in the time of can finding out 0.028 inch of its basic and rolling body damage, therefore can judge the now state of rolling body and be: rolling body damages 0.028 inch.Then this state recognition result submitted to the staff for its reference and taked corresponding counter-measure.

Claims (1)

1. a coal mine equipment anticipatory maintenance method, is characterized in that, the method comprises the following steps:

(1) at the coal mine equipment key position---the acceleration vibration transducer is installed on the level of bearing, vertical, axial three directions, vibration data in the monitoring equipment operational process described vibration data is sent to rear end receives and disposal system incessantly, and deposit associated data files in;

(2) vibration data { a to extracting in the acceleration vibration transducer _i, i=1,2 ..., n} is processed, and concrete steps are:

1. to described vibration data { a _i, i=1,2 ..., n} carries out Fourier transform and obtains { x _i, i=1,2 ..., n};

2. calculate by following formula the 24 characteristic index vectors that can describe equipment running status

X ^*＝{x _av,x _p,x _rms,x _r,D _x,x _p-p,α,β,C _f,S _f,I _f,CL _f,K _v,f _avg,f _b,f _bb,f _v,f _rv,S,E _r1,E _r2,

，

E _r3,E _r4,E _r5}

Absolute mean: $x_{\mathrm{av}}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left|x_i\right|;$

Peak value: x _p=max|x _i|;

Effective value (root-mean-square value):

The root amplitude: $x_r={\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\sqrt{\left|x_i\right|}\right)}^2;$

Variance: $D_x=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x_i-x_{\mathrm{av}})}^2;$

Peak-to-peak value: x _p-p=max (x _i)-min (x _i);

The skewness index: $\mathrm{\&alpha;}=\sqrt{\frac{1}{6n}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^3;$

The kurtosis index: $\mathrm{\&beta;}=\sqrt{\frac{n}{24}}[\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{x_i-x_{\mathrm{av}}}{\sqrt{D_x}}\right)}^4-3];$

Peak index: $C_f=\frac{x_p}{x_{\mathrm{rms}}};$

The waveform index: $S_f=\frac{x_{\mathrm{rms}}}{x_{\mathrm{av}}};$

The pulse index: $I_f=\frac{x_p}{x_{\mathrm{rms}}};$

The nargin index: ${\mathrm{CL}}_f=\frac{x_p}{x_r};$

The coefficient of variation: $K_v=\frac{\sqrt{D_x}}{x_{\mathrm{av}}};$

Gravity frequency (average frequency):

Equal square frequencies: $f_b=\frac{{\&Integral;}_0^{\&infin;}{f}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}};$

The root mean square frequency: $f_{\mathrm{bb}}={\left(\frac{{\&Integral;}_0^{\&infin;}{f}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}}\right)}^{1/2};$

The frequency variance: $f_v=\frac{{\&Integral;}_0^{\&infin;}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}};$

Frequency standard is poor: $f_{\mathrm{rv}}={\left[\frac{{\&Integral;}_0^{\&infin;}{(f-f_{\mathrm{avg}})}^{2}p\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}}\right]}^2;$

Spectrum peak index of stability: $S=\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}\{{f_i}^2\&CenterDot;P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}P\left(f_i\right)}}/\sqrt{\frac{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}\{{f_i}^4\&CenterDot;P\left(f_i\right)\}}{\underset{i=1}{\overset{n/2}{\mathrm{\&Sigma;}}}{f_i}^2\&CenterDot;P\left(f_i\right)}};$

The first frequency band relative energy: $E_{r1}={\&Integral;}_0^{B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The second frequency band relative energy: $E_{r2}={\&Integral;}_{B_f}^{2B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 3rd frequency band relative energy: $E_{r3}={\&Integral;}_{2B_f}^{3B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 4th frequency band relative energy: $E_{r4}={\&Integral;}_{3B_f}^{4B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

The 5th frequency band relative energy: $E_{r5}={\&Integral;}_{4B_f}^{5B_f}p\left(f\right)\mathrm{df}/{\&Integral;}_0^{F_s}p\left(f\right)\mathrm{df};$

In described 24 characteristic index computing formula, f means the frequency of signal, and p (f) means the power spectrum of signal, B _fmean 1/5 frequency range value, F _smean highest frequency value;

(3) to 24 characteristic index vector X ^*process and set up assessment indicator system, concrete steps are:

1. 24 characteristic indexs vectors X ^*the pre-service of training sample:

The a certain duty of equipment, described state can be normal condition or a certain typical fault state, with { q _i, i=1,2 ..., s} means, 24 characteristic index vector X under described a certain state ^*the composing training sample space can be used the matrix X of p * n ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., n} means, wherein, and x ^*i the characteristic index that (i, j) is j state sample, p means the dimension of sample space, i.e. the quantity of characteristic index, n means the number of training sample;

For the impact of eliminating each characteristic index dimension the fluctuation range of unifying its value, need to carry out normalized to sample data: wherein, x _max(j), x _min(j) mean respectively raw data x ^*maximal value and the minimum value of (i, j) i index, X={x (i, j) | i=1,2 ..., p; J=1,2 ..., n} means X ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., the sequence after the n} normalized;

2. 24 characteristic index vectors are carried out to two-dimensional projections, analyze its range characteristic distributions:

Described two-dimensional projections be exactly the p dimension data x (i, j) | i=1,2 ..., p; J=1,2 ..., n} is converted into matrix a={a (1), a (2), and a (3) ..., a (p) } be the range z (j) of projecting direction:

$z\left(j\right)=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}a\left(i\right)x(i,j),j=\mathrm{1,2},...,n,$

A representation unit length vector wherein, then according to range z (j) | j=1,2 ..., the characteristic distributions of n} is sorted out;

3. for by described step (3) 2. in range zone under each exemplary apparatus state separate, structure projection objective function is to seek best projecting direction matrix A=[a ₁, a ₂..., a _m],

Projection objective function index can be expressed as: Q (a)=S _zd _z,

Wherein, S _zfor range z (i) standard deviation is used for describing between class distance; D _zfor range z (i) local density is used for describing density in class,

$S_z=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(z\left(i\right)-E\left(z\right))}^2}{n-1}},$

$D_z=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}(R-r(i,j))\&CenterDot;u(R-r(i,j)),$

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; The windows radius that R is local density, its span is generally:

the quantity that p is characteristic index; R (i, j) means the distance between sample, r (i, j)=| z (i)-z (j) |; Unit-step function $u\left(t\right)=\left\{\begin{array}{c}1,t\&GreaterEqual;0\\ 0,t<0\end{array}\right.,$

Maximize objective function: Max:Q (a)=S _zd _z,

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

At best projecting direction matrix A=[a ₁, a ₂..., a _m] under, 24 characteristic index vector projection value w under described each exemplary apparatus state _i(i=1,2 ..., the s) distribution that becomes band, described zonal arrangement system has formed equipment state assessment indicator system W;

(4) foundation of the coal mine equipment anticipatory maintenance model based on two-dimensional projections

1. determine predictor

{ x* (the i) } expression for wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs, the coefficient of autocorrelation R (k) that { x* (i) } postpones the k step is:

$R\left(k\right)=\frac{\underset{i=k+1}{\overset{n}{\mathrm{\&Sigma;}}}(x*\left(i\right)-\mathrm{Ex}*)(x*(i-k)-\mathrm{Ex}*)}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2}$

$\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n$

Wherein, the sample size that n is described arbitrary characteristic index sequential { x* (i) }, k=1,2 ..., m, m<[n/4]; The variance of R (k) reduces along with reducing of k, but the estimated accuracy of R (k) increases along with reducing of k, so the value of m should be less; According to the theory of sampling process of R (k), in the situation that confidence level 1-α, when the value of R (k) does not belong to following interval range,

$R\left(k\right)\&NotElement;[\frac{-1-{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k},\frac{-1+{\mathrm{\&mu;}}_{\mathrm{\&alpha;}/2}\&CenterDot;{(n-k-1)}^{0.5}}{n-k}],$

Illustrate that sequential { x* (i) } and the dependence that postpones the x* (i-k) after the k step are significant, so x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } postpones k, to walk dependence not remarkable; In the situation that known confidence level, minute position μ of described interval range _α/2can from the standardized normal distribution table, check in;

2. predictor two-dimensional projections

At first, described arbitrary characteristic index time series { x* (i) } is carried out to standardization:

$x\left(i\right)=\frac{x*\left(i\right)-\mathrm{Ex}*}{\mathrm{\&sigma;x}*},$

Wherein, mean value $\mathrm{Ex}*=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}x*\left(i\right)/n,$ Variance $\mathrm{\&sigma;x}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(x*\left(i\right)-\mathrm{Ex}*)}^2};$

Described through standardized arbitrary characteristic index sample with x (i) | i=1,2 ..., n} means, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} means, n wherein, and p is respectively sample size and predictor quantity;

By the p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} is in projecting direction a={a (1), a (2), a (3) ..., a (p) on projected,

i=p+1, p+2 ..., n, wherein, a is the unit length vector; Thereby set up x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} with x (i) | i=1,2 ..., the mathematical relation between n};

3. described predictor range is carried out to the orthogonal Hermite fitting of a polynomial

This patent utilizes classical Hermite Polynomial Families, and its expression formula is:

-∞<z<∞, meet ${\&Integral;}_{-\&infin;}^{\&infin;}{h}_i\left(z\right)h_j\left(z\right)\mathrm{dz}={\mathrm{\&delta;}}_{\mathrm{ij}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1,i=j\\ 0,i\&NotEqual;j\end{array}\right.,$ Wherein, r! Represent the factorial of r, z=a ^tx,

for the standard Gauss equation;

The expression formula that obtains so the coal mine equipment anticipatory maintenance model based on two-dimensional projections is:

$\hat{x}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{R}{\mathrm{\&Sigma;}}}{c}_{\mathrm{ij}}{h}_{\mathrm{ij}}\left(a_i^{T}X\right),$

i＝1,2,...,m，j＝1,2,...,r，

Wherein,

mean a certain characteristic index in described 24 characteristic indexs, the exponent number of R representative polynomial, c means the Hermite multinomial coefficient, h means the orthogonal Hermite polynomial expression, $H=\left[\begin{array}{c}{h}_1\left(z_l\right)\\ h_2\left(z_l\right)\\ ...\\ h_R\left(z_l\right)\end{array}\right],$ l＝1,2,...,n。

4. optimize the projection objective function and seek best projecting direction matrix a and optimum polynomial coefficient c

Structure projection target function, solve by minimizing objective function,

Minimize objective function: $\min Q(a,c)=\frac{1}{n-p}\underset{i=p+1}{\overset{n}{\mathrm{\&Sigma;}}}{(x\left(i\right)-\hat{x}\left(i\right))}^2,$

Constraint condition: $\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{a}^2\left(j\right)=1,$

Obtain best projecting direction matrix a and optimum polynomial coefficient c, finally determined the coal mine equipment anticipatory maintenance model based on two-dimensional projections in substitution (4) 3.;

(5) realization of anticipatory maintenance

1. calculate the future value of 24 characteristic indexs

According to the coal mine equipment anticipatory maintenance model based on two-dimensional projections obtained in step (4), can calculate the future value of 24 characteristic indexs:

X ^*′＝{x _av′,x _p′,x _rms′,x _r′,D _x′,x _p-p′,α′,β′,C _f′,S _f′,I _f′,CL _f′,K _v′,f _avg′,f _b′,f _bb′,f _v′,f _rv′,

；

S′,E _r1′,E _r2′,E _r3′,E _r4′,E _r5′}

2. the future value of 24 characteristic indexs is carried out to two-dimensional projections

The best projecting direction matrix A that 3. future value of 24 characteristic indexs that step (5) is tried to achieve in 1. tries to achieve in step (3)=[a ₁, a ₂..., a _m] under carry out two-dimensional projections, obtain range w ', just can judge the equipment state recognition result according to the distributing position of described range w ' is q ', whether dope coal mine equipment will exist extremely future, and identify described which kind of fault type that extremely belongs to simultaneously, according to described state recognition result, the staff takes corresponding rational anticipatory maintenance measure so.

Images