CN103487250B - Based on the coal mine equipment anticipatory maintenance method of two-dimensional projections - Google Patents

Abstract

The invention discloses a kind of auto-regressive analysis merging two-dimensional projections and realize coal mine equipment anticipatory maintenance, relate to Coal Mine Main Fan and hoister.Diagnostic method of the present invention extracts vibration signal from monitoring of equipment supervisory system, through data analysis with calculate 24 characteristic indexs in order to describe equipment running status; A time series extracted respectively to described 24 characteristic indexs and carries out auto-regressive analysis separately, obtaining each self-corresponding predictor; Utilize two-dimensional projections that described predictor is projected two-dimensional space, set up predictor range and the fitting function of corresponding characteristic index value respectively, extrapolate the future value of 24 characteristic indexs respectively; Again by projecting as under direction matrix in the best projection the future value of described 24 characteristic indexs, according to the trend of the following running status of the distribution situation judgment device of range, thus realize the anticipatory maintenance to coal mine equipment.

Description

Based on the coal mine equipment anticipatory maintenance method of two-dimensional projections

Technical field

The invention belongs to coal mine equipment fault diagnosis technology field, being specifically related to one utilizes vibration equipment data to calculate 24 characteristic indexs, a time series extracted respectively to described 24 characteristic indexs and carries out auto-regressive analysis separately, obtaining each self-corresponding predictor; Utilize two-dimensional projections that described predictor is projected two-dimensional space, set up predictor range and the fitting function of corresponding characteristic index value respectively, extrapolate the future value of 24 characteristic indexs respectively; Again by projecting as under direction matrix in the best projection the future value of described 24 characteristic indexs, according to the trend of the following running status of the distribution situation judgment device of range, thus realize 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, all causes great harm to personnel and property.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 the work that with high content of technology, difficulty is large, now majority all adopts the mode of building real-time monitoring system both at home and abroad at present, gather vibration signal, temperature signal, pressure signal and electric parameter signal etc., these monitoring meanss play positive role to monitoring equipment fault.But carrying out in fault alarm process to Monitoring Data, all carrying out fault alarm by given threshold value, there is serious shortcomings in Threshold Alerts: Fault Identification is delayed, can not realize fault and hide phase early warning, causes equipment maintenance and management work very passive.

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

Summary of the invention

The object of the invention is the present situation that cannot realize anticipatory maintenance for described coal mine equipment, propose a kind of real-time diagnosis method, a kind of forecast result is 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 coal mine equipment key position---the level of bearing, vertical, axial three directions install acceleration vibration transducer, described vibration data is also sent to rear end reception and disposal system by the vibration data incessantly in monitoring equipment operational process, and stored in associated data files;

(2) to the vibration data { a extracted in acceleration vibration transducer _i, i=1,2 ..., n} process, 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. go out to describe 24 characteristic index vectors of equipment running status by following formulae discovery

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):

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);

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

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

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

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

Margin 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):

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

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

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

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

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

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

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

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

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

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

1. 24 characteristic index vector 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} represents, 24 characteristic index vector X under described a certain state ^*composing training sample space can use the matrix X of p × n ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., n} represents, wherein, and x ^*i-th characteristic index that (i, j) is a jth state sample, p represents the dimension of sample space, i.e. the quantity of characteristic index, and n represents the number of training sample;

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

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

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

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

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

3. in order to by described step (3) 2. in range region 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, namely

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

$D_z=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}(R-r(i,j))\·u(R-r(i,j)),$

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; R is the windows radius of local density, and its span is generally: p is the quantity of characteristic index; R (i, j) represents 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 ..., s) become band distribution, and namely described zonal arrangement system defines equipment state assessment indicator system W;

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

1. predictor is determined

Wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs represents with { x* (i) }, and coefficient of autocorrelation R (k) that { x* (i) } postpones 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, n is the sample size of described arbitrary characteristic index sequential { x* (i) }, k=1,2 ..., m, m < [n/4]; The variance of R (k) reduces along with the reduction of k, but the estimated accuracy of R (k) increases along with the reduction of k, and therefore the value of m should be less; According to the theory of sampling process of R (k), when 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 sequential { x* (i) } with postpone k walk after the dependence of x* (i-k) be significant, therefore x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } delay k step dependence is not remarkable; When known confidence level, point position μ of described interval range _α/2can check in from standardized normal distribution table;

2. predictor two-dimensional projections

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

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

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} represents, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} represents, wherein n, p are respectively sample size and predictor quantity;

By p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} in projecting direction a={a (1), a (2), a (3) ..., a (p) on project, i=p+1, p+2 ..., n, wherein, a is unit length vector; Thus establish 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. orthogonal Hermite fitting of a polynomial is carried out to described predictor range

This patent utilizes classical Hermite Polynomial Families, and its expression formula is: -∞ < z < ∞, meets ${\&Integral;}_{-\&infin;}^{\&infin;}{h}_i\left(z\right)h_j\left(z\right)\mathrm{dz}={\mathrm{\&delta;}}_{\mathrm{ij}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1,i=j\\ 0,i\&NotEqual;j\end{array}\right.,$ Wherein, r! Represent the factorial of r, z=a ^tx, for standard gaussian equation;

The expression formula so obtained based on the coal mine equipment anticipatory maintenance model of 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, represent a certain characteristic index in described 24 characteristic indexs, the exponent number of R representative polynomial, c represents Hermite multinomial coefficient, and h represents 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 projection objective function and seek best projecting direction matrix a ' and optimum polynomial coefficient c

Structure projection target function, solves by minimizing objective function, namely

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, in substitution (4) 3., finally determine the coal mine equipment anticipatory maintenance model based on two-dimensional projections;

(5) realization of anticipatory maintenance

1. the future value of 24 characteristic indexs is calculated

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

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

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

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

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

2,24 adopted characteristic indexs are diagnosed all to be converted into dimensionless index through normalized in this method, thus in equipment running status identifying, to different environment and equipment, there is same adaptive ability, all can use various types of colliery;

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

Accompanying drawing explanation

Fig. 1 is bear vibration sensor mounting means;

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

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

Fig. 4 is the frequency variance f obtained through better fitting _vanticipatory maintenance model curve;

Fig. 5 is the projection distribution situation of 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 the large class of rolling body fault, inner ring fault, outer ring fault, retainer fault four, in addition described four large class faults according to different degree of injury again Further Division be different groups, can divide as the case may be.The level, vertical, axial three directions of bearing to be assessed install acceleration vibration transducer (as shown in Figure 1), the vibration data of monitoring equipment operational process centre bearer incessantly, and described vibration data is sent to rear end reception and disposal system, and use for back-end analysis stored in associated data files.

(2) to the vibration data { a extracted in acceleration vibration transducer _i, i=1,2 ..., n} process, 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. go out to describe 24 characteristic index vector x of bearing running status by following formulae discovery ^*={ 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):

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);

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

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

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

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

Margin 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):

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

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

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

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

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

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

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

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 represents the frequency of signal, and p (f) represents the power spectrum of signal, B _frepresent 1/5 frequency range value, F _srepresent highest frequency value.

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

1. 24 characteristic index vector 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} represents, 24 characteristic index vector X under described a certain state ^*composing training sample space can use the matrix X of p × n ^*={ x ^*(i, j) | i=1,2 ..., p; J=1,2 ..., n} represents, wherein, and x ^*i-th characteristic index that (i, j) is a jth state sample, p represents the dimension of sample space, i.e. the quantity of characteristic index, and n represents the number of training sample;

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

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

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

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

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

3. in order to by described step (3) 2. in range region 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, namely

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

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

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; R is the windows radius of local density, and its span is generally: p is the quantity of characteristic index; R (i, j) represents 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 ..., s) become band distribution, and namely described zonal arrangement system defines equipment state assessment indicator system W; Namely be that the normal and lesion size of the bearing roller set up according to step (3) is respectively assessment indicator system under 0.007 inch, 0.014 inch, 0.021 inch, 0.028 inch five kinds of states as shown in Figure 2 as shown in the figure: under normal condition, projection value is distributed in (shown in ☆) near main axis=0.5; When rolling body lesion size is 0.007 inch, projection value is distributed in (shown in △) near main axis=-8; When rolling body damages 0.028 inch, projection value to be distributed near main axis=-13 (× shown); When rolling body damages 0.014 inch (shown in) and 0.021 inch (* is shown), projection value overlaps, be distributed near main axis=-11, so in order to distinguish two states, it is projected separately, projection value distribution is as shown in Figure 3: when rolling body damages 0.014 inch, projection value is distributed in (shown in) near main axis=-14, and when rolling body damages 0.021 inch (shown in *), projection value is distributed in (shown in *) near main axis=8.The assessment indicator system that Fig. 2 and Fig. 3 is complete under namely defining these five kinds of states.

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

1. predictor is determined

Wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs represents with { x* (i) }, and coefficient of autocorrelation R (k) that { x* (i) } postpones 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, n is the sample size of described arbitrary characteristic index sequential { x* (i) }, k=1,2 ..., m, m < [n/4]; The variance of R (k) reduces along with the reduction of k, but the estimated accuracy of R (k) increases along with the reduction of k, and therefore the value of m should be less; According to the theory of sampling process of R (k), when 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 sequential { x* (i) } with postpone k walk after the dependence of x* (i-k) be significant, therefore x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } delay k step dependence is not remarkable; When known confidence level, point position μ of described interval range _α/2can check in from standardized normal distribution table;

2. predictor two-dimensional projections

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

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

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} represents, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} represents, wherein n, p are respectively sample size and predictor quantity;

By p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} in projecting direction a={a (1), a (2), a (3) ..., a (p) on project, i=p+1, p+2 ..., n, wherein, a is unit length vector; Thus establish 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. orthogonal Hermite fitting of a polynomial is carried out to described predictor range

This patent utilizes classical Hermite Polynomial Families, and its expression formula is: -∞ < z < ∞, meets ${\&Integral;}_{-\&infin;}^{\&infin;}{h}_i\left(z\right)h_j\left(z\right)\mathrm{dz}={\mathrm{\&delta;}}_{\mathrm{ij}},$ ${\mathrm{\&delta;}}_{\mathrm{ij}}=\left\{\begin{array}{c}1,i=j\\ 0,i\&NotEqual;j\end{array}\right.,$ Wherein, r! Represent the factorial of r, z=a ^tx, for standard gaussian equation;

The expression formula so obtained based on the coal mine equipment anticipatory maintenance model of 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, represent a certain characteristic index in described 24 characteristic indexs, the exponent number of R representative polynomial, c represents Hermite multinomial coefficient, and h represents 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 projection objective function and seek best projecting direction matrix a ' and optimum polynomial coefficient c

Structure projection target function, solves by minimizing objective function, namely

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, in substitution (4) 3., finally determine the coal mine equipment anticipatory maintenance model based on two-dimensional projections;

(5) realization of anticipatory maintenance

1. the future value of 24 characteristic indexs is calculated

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

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, in figure, curve is the frequency variance f obtained through better fitting according to step (4) _vanticipatory 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; The forecasted future value of other 23 characteristic indexs can be obtained after the same method.

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

By step (5) 1. in best projecting direction matrix A=[a of 3. trying to achieve in step (3) of the future value of 24 characteristic indexs of trying to achieve ₁, a ₂..., a _m] under carry out two-dimensional projections, obtain range w ', just can judge that equipment state recognition result is q ' according to the distributing position of described range w ', namely dope coal mine equipment and whether there is exception future, and identify described exception simultaneously and belong to which kind of fault type, so according to described state recognition result, staff takes corresponding rational anticipatory maintenance measure.As shown in Figure 5, the distribution of the projection value of sample to be tested under above-mentioned optimal projection direction matrix (shown in zero), can find out that projection value when its basic and rolling body damages 0.028 inch overlaps, therefore can judge that the state of now rolling body is: rolling body damages 0.028 inch.Then this state recognition result is submitted to staff supply its reference and take 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 coal mine equipment key position---the level of bearing, vertical, axial three directions install acceleration vibration transducer, described vibration data is also sent to rear end reception and disposal system by the vibration data incessantly in monitoring equipment operational process, and stored in associated data files;

(2) to the vibration data { a extracted in acceleration vibration transducer _i, i=1,2 ..., n} process, 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. go out to describe 24 characteristic index vectors of equipment running status by following formulae discovery

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: $x_{\mathrm{rms}}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i^2};$

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);

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

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

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

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

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

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

Gravity frequency: $f_{\mathrm{avg}}=\frac{{\&Integral;}_0^{\&infin;}\mathrm{fp}\left(f\right)\mathrm{df}}{{\&Integral;}_0^{\&infin;}p\left(f\right)\mathrm{df}};$

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

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

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

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

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

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

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

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 represents the frequency of signal, and p (f) represents the power spectrum of signal, B _frepresent 1/5 frequency range value, F _srepresent highest frequency value;

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

1. 24 characteristic index vector 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} represents, 24 characteristic index vector X under described a certain state ^*composing training sample space can use the matrix X of p × n ^*={ x ^*(i, j) i=1,2 ..., p; J=1,2 ..., n} represents, wherein, and x ^*i-th characteristic index that (i, j) is a jth state sample, p represents the dimension of sample space, i.e. the quantity of characteristic index, and n represents the number of training sample;

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

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

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

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

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

3. in order to by described step (3) 2. in range region 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, namely

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

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

Wherein, E (z) is sequence z={z (i) | i=1, and 2 ..., the mean value of n}; R is the windows radius of local density, and its span is generally: p is the quantity of characteristic index; R (i, j) represents the distance between sample, r (i, j)=| z (i)-z (j) |; Unit-step function $u\left(t\right)=\left\{\begin{array}{cc}1,& t\&GreaterEqual;0\\ 0,& t>0\end{array}\right.,$

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 ..., s) become band distribution, and namely described zonal arrangement system defines equipment state assessment indicator system W;

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

1. predictor is determined

Wherein arbitrary characteristic index time series of described 24 kinds of characteristic indexs represents with { x* (i) }, and coefficient of autocorrelation R (k) that { x* (i) } postpones k step is:

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

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

Illustrate sequential { x* (i) } with postpone k walk after the dependence of x* (i-k) be significant, therefore x* (i-k) can be used as the predictor of x* (i), otherwise sequential { x* (i) } delay k step dependence is not remarkable; When known confidence level, point position μ of described interval range _α/2can check in from standardized normal distribution table;

2. predictor two-dimensional projections

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

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

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} represents, so standardized predictor with x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} represents, wherein n, p are respectively sample size and predictor quantity;

By p dimension data x (i-k) | k=1,2 ..., p; I=k+1, k+2 ..., n} in projecting direction a={a (1), a (2), a (3) ..., a (p) on project, i=p+1, p+2 ..., n, wherein, a is unit length vector; Thus establish 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. orthogonal Hermite fitting of a polynomial is carried out to described predictor range

This patent utilizes classical Hermite Polynomial Families, and its expression formula is: 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 standard gaussian equation;

The expression formula so obtained based on the coal mine equipment anticipatory maintenance model of 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, represent a certain characteristic index in described 24 characteristic indexs, the exponent number of r representative polynomial, c represents Hermite multinomial coefficient, and h represents orthogonal Hermite polynomial expression, $H=\left[\begin{array}{c}{h}_1\left(z_l\right)\\ h_2\left(z_l\right)\\ ...\\ h_R\left(z_l\right)\end{array}\right],l=\mathrm{1,2},...,n.$

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

Structure projection target function, solves by minimizing objective function, namely

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, in substitution (4) 3., finally determine the coal mine equipment anticipatory maintenance model based on two-dimensional projections;

(5) realization of anticipatory maintenance

1. the future value of 24 characteristic indexs is calculated

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

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

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