CN102967452B - Method for determining assembly reliability of detachable disc-drum rotor - Google Patents

Abstract

The invention discloses a method for determining the assembly reliability of a detachable disc-drum rotor. The method comprises subjecting the detachable disc-drum rotor to bench knock test, collecting dynamic response signals, extracting characteristics, and constructing characteristic matrixes of various assembly states; creating orthogonal subspaces of the characteristic matrixes of all the states; and calculating a main included angle of orthogonal subspace base vectors of reference states and unknown states, and defining an indicator-a main included angle cosine which is used for determining the assembly quality of the detachable disc-drum rotor and serves as a reliability degree of the assembly quality of the detachable disc-drum rotor. The method is simple and convenient to operate, reliable in result and high in real-time performance; applicable to production fields for determining reliability degrees of detachable disc-drum rotors and helpful for improving assembly qualities and operation reliabilities of detachable disc-drum rotors in aero-engines and gas turbine engines, and has engineering application values.

Description

A kind of method of judging removable disk drum type rotor assembling fiduciary level

Technical field

The present invention relates to mechanized equipment assembly quality and detect (reliability decision), be specifically related to a kind of decision method of the assembling of the removable disk drum type rotor for aeromotor or gas turbine fiduciary level.

Background technology

In, complex rotation mechanized equipment large-scale at aeromotor and gas turbine etc., removable disk drum type rotor is a kind of rotor structure form of extensive employing.It mainly compresses separate wheel discs at different levels by stay-bolt, thereby forms a complete rotor structure.In this rotor structure, the size of stay-bolt pretightning force and the dynamics of the whole rotor structure of differentia influence between each stay-bolt pretightning force, and then exert an influence to equipping whole serviceability.In order to guarantee good assembly quality, in practical set process, there is strict assembly technology requirement.In process of production, by the RELIABILITY INDEX of judging that the similarity of unknown confined state and normal condition (good confined state) obtains, can determine the assembly quality of removable disk drum type rotor; In process, due to the impact of complex working condition, removable disk drum type rotor often occurs, due to the loosening assembly quality degradation phenomena producing of stay-bolt, affecting equipment reliability of operation under arms.So, in real time, effectively determine that removable disk drum type rotor assembly quality is significant to reliability and the security of raising equipment.Existing removable disk drum type rotor assembling fiduciary level judges how based on large sample, to suppose, yet, removable disk drum type rotor has the advantages that reliability is high, the life-span is long, lacks inefficacy sample in reality, uses existing assembling fiduciary level decision method can not effectively determine assembly quality.Therefore, how under the condition of inefficacy sample deficiency, to judge that removable disk drum type rotor assembling fiduciary level is one of key problem to be solved by this invention.

When the assembly quality of removable disk drum type rotor occurs to degenerate, the dynamicss such as the rigidity of rotor structure and damping will change, and the statistical informations such as Time Domain Amplitude, frequency content and frequency domain energy distribution that show as structure dynamic response signal change.The status flag matrix consisting of temporal signatures, frequency domain character and the wavelet field feature of dynamic response signal can characterize these variations.Analysis result shows, when assembling is loosening, statistical nature amplitude is by the change occurring in various degree; But the variation tendency of single feature does not have monotonicity, inconsistent with aeration level change procedure, can not be as the judgement index of removable disk drum type rotor assembling fiduciary level.How to merge the statistical information of primitive character, constructing the RELIABILITY INDEX consistent with the actual degenerative process of assembly quality is also one of key issue to be solved by this invention.

Summary of the invention

The object of the invention is under the condition of inefficacy sample deficiency, a kind of statistical information that merges primitive character is provided, construct the method that the RELIABILITY INDEX consistent with the actual degenerative process of assembly quality judged removable disk drum type rotor assembling fiduciary level.

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

A method of judging removable disk drum type rotor assembling fiduciary level, is characterized in that, comprises the steps:

(1) the dynamic response signal of the good confined state of Real-time Collection removable disk drum type rotor and unknown confined state, Time-domain Statistics feature, frequency domain statistical nature and the Wavelet domain statistical feature of calculating dynamic response signal;

(2) to the vibration response signal segmentation collecting, extract temporal signatures, frequency domain character and the Wavelet domain statistical feature of each segment signal, form status flag matrix X:

$X=[x_1,...,x_i,...,x_s]=\left[\begin{array}{ccccc}{T}_1^1& ...& T_1^i& ...& T_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ T_{16}^1& ...& T_{16}^i& ...& T_{16}^s\\ F_1^1& ...& F_1^i& ...& F_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ F_{13}^1& ...& F_{13}^i& ...& F_{13}^s\\ D_{\mathrm{WPE}}^1& ...& D_{\mathrm{WPE}}^i& ...& D_{\mathrm{WPE}}^s\end{array}\right]$

Wherein, t ₁, T ₂..., T ₁₆represent 16 Time-domain Statistics features; F ₁, F ₂..., F ₁₃represent 13 frequency domain statistical natures; D _wPErepresent Wavelet domain statistical feature; I=1,2 ..., s represents institute's statistical signal hop count; Utilize core principle component analysis method to decompose this status flag matrix, set up the orthogonal subspaces of status flag matrix;

V=[v ₁,v ₂,…,v _r]

Wherein, v ₁, v ₂..., v _rthe base vector that represents status flag matrix subspace V, r is space dimensionality;

(3) calculate subspace base vector main folder angle cosine value:

The normal condition orthogonal subspaces that assembly quality is good is: the orthogonal subspaces of assembly quality unknown state is: wherein i=1,2 ..., r ₁with =1,2 ..., r ₂be respectively V ₁and V ₂base vector; Base vector with element number all equal the number of time domain, frequency domain and Wavelet domain statistical feature;

Definition matrix S is: matrix S is carried out to svd, obtains the feature value vector of matrix S:

$\mathrm{\Λ}=[{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,...,{\mathrm{\λ}}_{\min (r_1,r_2)}]$

Wherein, λ _i, i=1,2 ..., min (r ₁, r ₂) be eigenwert; According to feature value vector Λ, the main angle theta of calculating between subspace base vector is:

$\mathrm{\θ}=[{\mathrm{\θ}}_1,{\mathrm{\θ}}_2,...,{\mathrm{\θ}}_{\min (r_1,r_2)}],$

Wherein: θ _i=arccos (λ _i); I=1,2 ..., min (r ₁, r ₂);

Main angle theta has reflected matrix V ₁and V ₂similarity degree;

(4) utilize main angle theta, definition RELIABILITY INDEX is:

$R=\cos \left(\frac{1}{\sqrt{\min (r_1,r_2)}}{\left|\right|\mathrm{\θ}\left|\right|}_2\right)$

Wherein, from the definition at main folder angle, θ _imeet hence one can see that $0\≤\frac{1}{\sqrt{\min (r_1,r_2)}}{\left|\right|\mathrm{\θ}\left|\right|}_2\≤\frac{\mathrm{\π}}{2},$ 0≤R≤1；

(5) with RELIABILITY INDEX R can judge removable disk drum type rotor assembly quality: R more approach 1 show removable disk drum type rotor assembly quality and normal condition more approaching; Otherwise R more approaches 0 and shows that removable disk drum type rotor assembly quality more departs from normal condition.

In such scheme, the described Wavelet domain statistical feature of step (2) is to adopt second generation wavelet packet energy spread method to calculate, and comprises the steps:

A, utilize second generation wavelet packet transform method to decompose original signal, obtain the signal w in different frequency bands _ii=1,2 ..., 2 ^m, m is positive integer;

B, calculate the energy value E of each band signal _i:

$E_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left(w_i\left(j\right)\right)}^2/N;$

Wherein, i represents band number; N represents i the data point number of inband signaling frequently; w _i(j) represent i j data point of inband signaling frequently; E _irepresent i band signal energy;

C, each frequency band energy is normalized, obtains normalized energy

${\tilde{E}}_i=\frac{E_i}{\underset{i=1}{\overset{2^m}{\mathrm{\Σ}}}{E}_i}$

Wherein, represent each frequency band energy sum;

D, obvious, normalized energy meets will be equal to probability, second generation wavelet packet energy spread is:

$D_{\mathrm{WPE}}=\underset{i}{\overset{2^m}{\mathrm{\Σ}}}{\tilde{E}}_i^1\ln \frac{{\tilde{E}}_i^1}{{\tilde{E}}_i^2};$

Wherein, i=1,2 ..., 2m; the normalized energy that represents vibration response signal i frequency band when rotor assembly quality is good; the normalized energy that represents vibration response signal i frequency band when rotor confined state is unknown.Energy spread D _wPEthe similarity that has reflected rotor response signal energy distribution when assembling good and confined state the unknown.

The present invention is based on status flag matrix subspace base vector structure RELIABILITY INDEX---base vector main folder cosine of an angle value can reflect the similarity degree of two state matrixs, and has monotonicity and nonnegativity; The variation tendency of this RELIABILITY INDEX is consistent with assembly quality degenerative process, so can in real time, effectively judge the degree of reliability of removable disk drum type rotor assembly quality.

The present invention compares with traditional fiduciary level decision method, and its advantage is:

1, by judging that the similarity of unknown confined state and normal condition (good confined state) obtains RELIABILITY INDEX, do not rely on large sample experimental data, can the in the situation that of no-failure sample, judge the fiduciary level of detachable rotor assembly quality.

2, the fiduciary level of utilizing the detachable rotor assembling of dynamic response signal determining, has the advantages such as real-time is good, workable, is applicable to the assembly quality of on-the-spot real-time judgment removable disk drum type rotor, improves the operational reliability of removable disk drum type rotor.

The RELIABILITY INDEX of 3, constructing has monotonicity, and variation tendency is consistent with assembly quality degenerative process.Than original temporal signatures, frequency domain character and wavelet field feature, the RELIABILITY INDEX of constructing can reflect the degree of degeneration of assembly quality preferably.

Accompanying drawing explanation

Below in conjunction with the drawings and the specific embodiments, content of the present invention is described in further detail.

Fig. 1 is the dynamic response time domain plethysmographic signal figure of six kinds of confined states of a kind of aeromotor removable disk drum type rotor.Wherein: (a) be the dynamic response time domain plethysmographic signal figure of removable disk drum type rotor when assembling is good; (b) be removable disk drum type rotor dynamic response time domain plethysmographic signal figure when the loosening half-turn of three stay-bolts; (c) be removable disk drum type rotor dynamic response time domain plethysmographic signal figure when the loosening half-turn of 12 stay-bolts; (d) be removable disk drum type rotor dynamic response time domain plethysmographic signal figure when the loosening half-turn of 24 stay-bolts; (e) be removable disk drum type rotor dynamic response time domain plethysmographic signal figure when the loosening circle of 24 stay-bolts; (f) be that removable disk drum type rotor is at the loosening circle half dynamic response time domain plethysmographic signal figure of 24 stay-bolts.In figure, horizontal ordinate represents the time, and unit is s (second); Ordinate represents vibration amplitude, and unit is g (acceleration).

Fig. 2 is Fig. 1 aeromotor removable disk drum type rotor dynamic response signal characteristic feature variation diagram when six kinds of confined states.Wherein: (a) be removable disk drum type rotor dynamic response signal time domain characteristic feature variation diagram when six kinds of confined states; (b) be removable disk drum type rotor dynamic response signal frequency domain characteristic feature variation diagram when six kinds of confined states; (c) be removable disk drum type rotor dynamic response signal second generation wavelet packet energy spread variation diagram when six kinds of confined states.In figure, be characterized as the dimensionless feature after normalization, horizontal ordinate represents the time, and unit is s (second).

Fig. 3 is the result of determination figure of Fig. 1 aeromotor removable disk drum type rotor assembly quality (fiduciary level).Horizontal ordinate represents six kinds of confined states, and ordinate represents the fiduciary level R of removable disk drum type rotor assembling under every kind of confined state.

Fig. 4 is the time domain waveform figure of the dynamic response signal after Fig. 1 aeromotor removable disk drum type rotor is on active service 446 hours.

Embodiment

The inventive method obtains its dynamic response signal by removable disk drum type rotor stand Knock test, extracts dynamic response signal temporal signatures, frequency domain character and wavelet field feature and forms status flag matrix; Then set up the orthogonal subspaces of status flag matrix; Finally calculate the main folder angle of subspace base vector, and define a RELIABILITY INDEX---main folder angle cosine value, judge the degree of reliability that rotor assembles.

The present invention implements by following concrete steps:

1) structural regime eigenmatrix set up status flag matrix subspace

Removable disk drum type rotor is carried out to stand Knock test, and adopt vibration acceleration sensor and data acquisition equipment to gather the dynamic response signal (good confined state and unknown confined state) of removable disk drum type rotor.

The Time-domain Statistics feature of calculating dynamic response signal, computing formula is in Table 1

Table 1 Time-domain Statistics feature representation formula

T wherein _i, i=1,2 ..., 16, represent Time-domain Statistics feature; z _lrepresent time-domain signal amplitude; N represents sampled point number.

The frequency domain statistical nature that calculates dynamic response signal, feature calculation formula is in Table 2:

Table 2 frequency domain statistical nature expression formula

F wherein _i, i=1,2 ..., 13, represent frequency domain statistical nature; y _lthe spectrum value that represents signal; N represents frequency spectrum point number; f _lthe spectral magnitude that represents signal.

Calculate the Wavelet domain statistical feature of dynamic response signal, adopt second generation wavelet packet energy spread computing method, its concrete steps are:

Utilize second generation wavelet packet transform method to decompose original signal, obtain the signal w in different frequency bands _i(i=1,2 ..., 2 ^m, m is positive integer), and calculate the energy value E of each band signal _ifor:

$E_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left(w_i\left(j\right)\right)}^2/N$

Wherein, i represents band number; N represents i the data point number of inband signaling frequently; w _i(j) represent i j data point of inband signaling frequently; E _irepresent i band signal energy.Each frequency band energy is normalized, obtains normalized energy for:

${\tilde{E}}_i=\frac{E_i}{\underset{i=1}{\overset{2^m}{\mathrm{\Σ}}}{E}_i}$

Wherein, represent each frequency band energy sum.

Obviously, normalized energy meets will be equal to probability, second generation wavelet packet energy spread is:

$D_{\mathrm{WPE}}=\underset{i}{\overset{2^m}{\mathrm{\Σ}}}{\tilde{E}}_i^1\ln \frac{{\tilde{E}}_i^1}{{\tilde{E}}_i^2}$

Wherein, i=1,2 ..., 2 ^m; D _wPErepresent second generation wavelet packet energy spread; vibration response signal i frequency band normalized energy when expression rotor assembly quality is good; vibration response signal i frequency band normalized energy while representing the unknown of rotor confined state.Energy spread D _wPEthe similarity that has reflected rotor response signal energy distribution when assembling good and confined state the unknown.

Utilize above three kinds of latent structure status flag matrixes that extract, status flag matrix can be expressed as:

$X=[x_1,...,x_i,...,x_s]=\left[\begin{array}{ccccc}{T}_1^1& ...& T_1^i& ...& T_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ T_{16}^1& ...& T_{16}^i& ...& T_{16}^s\\ F_1^1& ...& F_1^i& ...& F_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ F_{13}^1& ...& F_{13}^i& ...& F_{13}^s\\ D_{\mathrm{WPE}}^1& ...& D_{\mathrm{WPE}}^i& ...& D_{\mathrm{WPE}}^s\end{array}\right]$

Wherein, X represents status flag matrix; t ₁, T ₂..., T ₁₆represent 16 Time-domain Statistics features; F ₁, F ₂..., F ₁₃represent 13 frequency domain statistical natures; I=1,2 ..., s represents institute's statistical signal hop count.Utilize core principle component analysis method characteristics of decomposition matrix, set up the orthogonal subspaces of eigenmatrix.Key step is, utilizes Nonlinear Mapping virgin state eigenmatrix X is mapped in high-dimensional feature space F, x wherein ₁, x ₂..., x _sfor the column vector of matrix X, s is column vector number.In feature space, covariance matrix can be expressed as:

The eigenwert of covariance matrix C and proper vector can obtain by solving following equation, that is:

λv=Cv

Wherein, λ representation feature value; V represents corresponding proper vector.Proper vector can be by linear expression, that is:

Through a series of abbreviations, eigenvalue equation is reduced to:

mλα＝Kα

Wherein, expression nuclear matrix is nuclear matrix.By solving proper vector α, and then the orthogonal subspaces that can obtain status flag matrix is:

V=[v ₁,v ₂,…,v _r]

Wherein, v ₁, v ₂..., v _rthe base vector that represents status flag matrix subspace V.

2) calculate subspace base vector main folder angle cosine value, the fiduciary level as the assembling of removable disk drum type rotor, comprises the following steps:

For the good normal condition orthogonal subspaces of assembly quality orthogonal subspaces with assembly quality unknown state wherein i=1,2 ..., r ₁with i=1,2 ..., r ₂be respectively V ₁and V ₂base vector; Base vector with element number all equal the number of time domain, frequency domain and Wavelet domain statistical feature.

Definition matrix S is:

$S=V_1^T{V}_2$

Matrix S is carried out to svd, obtain the feature value vector of matrix S, that is:

$\mathrm{\Λ}=[{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,...,{\mathrm{\λ}}_{\min (r_1,r_2)}]$

Wherein, λ _i, i=1,2 ..., for eigenwert; The main angle theta of calculating between subspace base vector according to feature value vector Λ is:

$\mathrm{\θ}=[{\mathrm{\θ}}_1,{\mathrm{\θ}}_2,...,{\mathrm{\θ}}_{\min (r_1,r_2)}],$

Wherein: θ _i=arccos (λ _i); I=1,2 ..., min (r ₁, r ₂).

Main angle theta has reflected matrix V ₁and V ₂similarity degree, utilize definition RELIABILITY INDEX in main folder angle to be:

$R=\cos \left(\frac{1}{\sqrt{\min (r_1,r_2)}}{\left|\right|\mathrm{\θ}\left|\right|}_2\right)$

Wherein, the known main angle theta of definition by main folder angle _imeet 0≤θ _i≤ (pi/2), can obtain thus 0≤R≤1.

R more approach 1 show removable disk drum type rotor assembly quality and normal condition more approaching; Otherwise R approaches 0 and shows that removable disk drum type rotor assembly quality departs from normal condition.The size of R is corresponding with the good degree of removable disk drum type rotor assembly quality, has reflected the degree of reliability of assembly quality.

In order to verify the feasibility of the method for the invention, the assembling fiduciary level of certain type aeromotor removable disk drum type rotor is judged.

Simulate six kinds of confined states of aeroengine rotor, by the test of aeroengine rotor vehicle frame, obtained its vibration acceleration signal, utilized method of the present invention to judge the fiduciary level of aeroengine rotor assembling under each confined state.

Six kinds of confined states of certain type aeromotor removable disk drum type rotor are:

(1) removable disk drum type rotor confined state is good;

(2) three stay-bolt pine half-turns of removable disk drum type rotor;

(3) 12 stay-bolt pine half-turns of removable disk drum type rotor;

(4) 24 stay-bolt pine half-turns of removable disk drum type rotor;

(5) 24 stay-bolt pine one circles of removable disk drum type rotor;

(6) 24 stay-bolt pines of removable disk drum type rotor, one circle half;

When confined state is good, record 20 groups of signals, under all the other every kind of states, record ten groups of signals.Using ten groups of signals that record under normal condition as normal reference data; the signal recording under other ten groups of signals and all the other five kinds of confined states is as test data; calculate the similarity of test data and normal reference data, and then obtain the fiduciary level of assembly quality under each state.

The fiduciary level result of determination that dynamic response time domain plethysmographic signal, the dynamic response signal characteristic feature of this removable disk drum type rotor under six kinds of confined states changes, assembles is respectively referring to Fig. 1, Fig. 2, Fig. 3.As can be seen from Figure 1, six kinds of not significantly differences of confined state in original time-domain signal; As can be seen from Figure 2, response signal characteristic feature can distinguish several confined states, but time, the variation tendency of frequency domain characteristic feature and the degenerative process of assembly quality inconsistent; Though the variation tendency of wavelet-packet energy divergence is obvious, fail confined state 3 and confined state 4 to distinguish completely; When as can be seen from Figure 3 confined state is good, the fiduciary level of rotor is 0.99, and along with assembly quality is backward, the fiduciary level of rotor declines gradually, and the variation tendency of fiduciary level is consistent with assembly quality degenerative process.Table 3 is the exact value of each confined state lower rotor part assembling fiduciary level in Fig. 3.

The fiduciary level of the different assembly qualities of certain type aeromotor removable disk drum type rotor of table 3

After the aeromotor removable disk drum type rotor of this embodiment is on active service 446 hours, it is carried out to the judgement of assembly quality fiduciary level.Referring to Fig. 4, the fiduciary level of utilizing the inventive method to calculate this aeromotor removable disk drum type rotor assembly quality is 0.57, much smaller than 1.The assembly quality that fiduciary level is less than this aeromotor removable disk drum type rotor of 1 explanation occurs degenerating in process under arms, and current assembly quality is in unhealthy condition.After dismounting, finding, there is crackle in the balancing orifice of nine grades of labyrinths of this aeromotor high-pressure compressor rotor, causes rotor assembling loosening.Fiduciary level result of determination and actual conditions are coincide, illustrate that removable disk drum type rotor proposed by the invention assembling fiduciary level decision method can determine the assembly quality of removable disk drum type rotor effectively, for fail-safe analysis and the health control of removable disk drum type rotor in industry spot provides a kind of new solution.

Claims (1)

1. a method of judging removable disk drum type rotor assembling fiduciary level, is characterized in that, comprises the steps:

(1) the dynamic response signal of the good confined state of Real-time Collection removable disk drum type rotor and unknown confined state, Time-domain Statistics feature, frequency domain statistical nature and the Wavelet domain statistical feature of calculating dynamic response signal; Wherein, Time-domain Statistics feature calculation formula is:

$\begin{array}{cccccc}{T}_1=\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}{z}_l& T_2=\sqrt{\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}{z}_l^2}& T_3={\left(\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}\sqrt{\left|z_l\right|}\right)}^2& T_4=\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}\left|z_l\right|& T_5=\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}{\left|z_l\right|}^3& T_6=\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}{z}_l^4\\ T_7=\frac{1}{M_1}\underset{l=1}{\overset{M_1}{\mathrm{\Σ}}}{z}_l^2& T_8=\max \left(z\right)& T_9=\min \left(z\right)& T_{10}=T_8-T_9& T_{11}=T_2/T_4& T_{12}=T_8/T_2\\ T_{13}=T_8/T_4& T_{14}=T_8/T_3& T_{15}=T_5/{\left(\sqrt{T_7}\right)}^3& T_{16}=T_6/{\left(T_7\right)}^2& & \end{array}$

Z wherein _lrepresent time-domain signal amplitude; M ₁represent sampled point number;

Frequency domain statistical nature computing formula is:

$\begin{array}{cccc}{F}_1=\frac{1}{M_2}\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{y}_l& F_2=\frac{1}{M_2-1}\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{(y_l-F_1)}^2& F_3=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{(y_l-F_1)}^3}{M_2\×\sqrt{F_2^3}}& F_4=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{(y_l-F_1)}^4}{M_2\×F_2^2}\\ F_5=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{f}_l{y}_l}{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{y}_l}& F_6=\sqrt{\frac{1}{M_2}\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}({(f_l-F_5)}^2\×y_l)}& F_7=\sqrt{\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(f_l^2\×y_l)}{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{y}_l}}& F_8=\sqrt{\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(f_l^4\×y_l)}{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(f_l^2\×y_l)}}\\ F_9=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(f_l^2\×y_l)}{\sqrt{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}{y}_l\×\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(f_l^4\×y_l)}}& F_{10}=\frac{F_6}{F_5}& F_{11}=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}({(f_l-F_5)}^3\×y_l)}{M_2\×F_6^3}& F_{12}=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}({(f_l-F_5)}^4\×y_l)}{M_2\×F_6^4}\\ F_{13}=\frac{\underset{l=1}{\overset{M_2}{\mathrm{\Σ}}}(\sqrt{f_l-F_5}\×y_l)}{M_2\×\sqrt{F_6}}& & & \end{array}$

Y wherein _lthe spectrum value that represents signal; M ₂represent frequency spectrum point number; f _lthe spectral magnitude that represents signal;

Wavelet domain statistical feature calculation step is:

A, utilize second generation wavelet packet transform method to decompose original signal, obtain the signal w in different frequency bands _i, i=1,2 ..., 2 ^m, m is positive integer;

B, calculate the energy value E of each band signal _i:

$E_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left(w_i\left(j\right)\right)}^2/N;$

Wherein, i represents band number; N represents i the data point number of inband signaling frequently; w _i(j) represent i j data point of inband signaling frequently; E _irepresent i band signal energy;

C, each frequency band energy is normalized, obtains normalized energy

${\tilde{E}}_i=\frac{E_i}{\underset{i=1}{\overset{2^m}{\mathrm{\Σ}}}{E}_i}$

Wherein, represent each frequency band energy sum;

D, obvious, normalized energy meets will be equal to probability, second generation wavelet packet energy spread is:

$E_{\mathrm{WPE}}=\underset{i}{\overset{2^m}{\mathrm{\Σ}}}{\tilde{E}}_i^1\ln \frac{{\tilde{E}}_i^1}{{\tilde{E}}_i^2};$

Wherein, i=1,2 ..., 2 ^m; the normalized energy that represents vibration response signal i frequency band when rotor assembly quality is good; the normalized energy that represents vibration response signal i frequency band when rotor confined state is unknown;

(2) to the vibration response signal segmentation collecting, extract temporal signatures, frequency domain character and the Wavelet domain statistical feature of each segment signal, form status flag matrix X:

$X=[x_1,\·\·\·,x_i,\·\·\·,x_s]=\left[\begin{array}{ccccc}{T}_1^1& \·\·\·& T_1^i& \·\·\·& T_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ T_{16}^1& \·\·\·& T_{16}^i& \·\·\·& T_{16}^s\\ F_1^1& \·\·\·& F_1^i& \·\·\·& F_1^s\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ F_{13}^1& \·\·\·& F_{13}^i& \·\·\·& F_{13}^s\\ D_{\mathrm{WPE}}^1& \·\·\·& D_{\mathrm{WPE}}^i& \·\·\·& D_{\mathrm{WPE}}^s\end{array}\right]$

Wherein, t ₁, T ₂..., T ₁₆represent 16 Time-domain Statistics features; F ₁, F ₂..., F ₁₃represent 13 step territory statistical natures; D _wPErepresent Wavelet domain statistical feature; I=1,2 ..., s represents institute's statistical signal hop count; Utilize core principle component analysis method to decompose this status flag matrix, set up the orthogonal subspaces of status flag matrix;

V＝[v ₁，v ₂，…，v _r]

Wherein, v ₁, v ₂..., v _rthe base vector that represents status flag matrix subspace V, r is space dimensionality;

(3) calculate subspace base vector main folder angle cosine value:

The normal condition orthogonal subspaces that assembly quality is good is: the orthogonal subspaces of assembly quality unknown state is: wherein i=1,2 ..., r ₁with be respectively V ₁and V ₂base vector; Base vector with element number all equal the number of time domain, frequency domain and Wavelet domain statistical feature;

Definition matrix S is: matrix S is carried out to svd, obtains the feature value vector of matrix S:

$\mathrm{\Λ}=[{\mathrm{\λ}}_1,{\mathrm{\λ}}_2,\·\·\·,{\mathrm{\λ}}_{\min (r_1,r_2)}]$

Wherein, λ _i, i=1,2 ..., min (r ₁, r ₂) be eigenwert; According to feature value vector Λ, the main angle theta of calculating between subspace base vector is:

$\mathrm{\θ}=[{\mathrm{\θ}}_1,{\mathrm{\θ}}_2,\·\·\·,{\mathrm{\θ}}_{\min (r_1,r_2)}],$

Wherein: θ _i=arccos (λ _i); I=1,2 ..., min (r ₁, r ₂);

Main angle theta has reflected matrix V ₁and V ₂similarity degree;

(4) utilize main angle theta, definition RELIABILITY INDEX is:

$R=\cos \left(\frac{1}{\sqrt{\min (r_1,r_2)}}{\left|\right|\mathrm{\θ}\left|\right|}_2\right)$

Wherein, from the definition at main folder angle, θ _imeet hence one can see that $0\≤\frac{1}{\sqrt{\min (r_1,r_2)}}{\left|\right|\mathrm{\θ}\left|\right|}_2\≤\frac{\mathrm{\π}}{2},$ 0≤R≤1：

(5) with RELIABILITY INDEX R can judge removable disk drum type rotor assembly quality: R more approach 1 show removable disk drum type rotor assembly quality and normal condition more approaching; Otherwise R more approaches 0 and shows that removable disk drum type rotor assembly quality more departs from normal condition.