CN103500267A - Method for judging assembling reliability degree of bolt connection device with state information - Google Patents

Abstract

The invention discloses a method for judging the assembling reliability degree of a bolt connection device with state information. According to the method, firstly, the state information of the device is acquired through a motivation test; then, the acquired state information is preprocessed through a feature extraction method to obtain a state feature matrix; the inherent mode of the feature matrix is analyzed through a mode recognition algorithm, and a state subspace corresponding to the state feature matrix is constructed; the similarity index of a normal state subspace and the current state subspace is calculated, and the index reflects the similarity of the two state subspaces, and can describe the closeness degree of the device performance at the current moment and a normal state; finally, the similarity index is used as a reliability index to quantitatively reflect the assembling reliability degree of the device. The method does not depend on a large number of failure samples, is simple and easy to implement, has the advantages of being reliable in result, strong in practicality and the like, is suitable for evaluating the assembling reliability degree of the bolt connection device in real time on site, and has engineering application value.

Description

A Method of Judging the Assembly Reliability of Bolted Connection Equipment Using State Information

technical field

The invention relates to a method for judging the assembly reliability of mechanical equipment, in particular to a method for judging the assembly reliability of bolt connection equipment by using state information.

Background technique

Bolted connection is a widely used connection form of mechanical components, which is used in key mechanical equipment such as aero-engines and gas turbines. This structural form uses bolts to connect independent mechanical parts to form a mechanical device with certain dynamic characteristics. Insufficient tightening force caused by loose bolts will change the assembly quality of the equipment, thereby affecting the equipment to complete its specified functions. Therefore, the assembly reliability judgment is of great significance to identify the assembly state and ensure the reliability and safety of equipment.

At present, the commonly used reliability analysis method is based on the assumption of large sample conditions, and the overall failure law is obtained according to the reliability statistics of batch equipment. There are two difficulties in using the traditional reliability analysis method to evaluate the reliability of mechanical equipment: 1) The traditional reliability analysis method is based on the large-sample theory, and it is difficult to effectively deal with small sample and single-sample failure data; 2) The traditional reliability analysis method does not Considering the individual characteristics of equipment degradation, it lacks the accuracy of evaluating the reliability of a single equipment.

Status information is the external manifestation of the internal health status of the equipment, which can reflect the reliability of the equipment and provide a basis for the evaluation of equipment reliability. When the assembly quality of bolted connection equipment degrades, the dynamic characteristics of the equipment, such as stiffness and damping, will change, which can be manifested as changes in the time-domain amplitude and frequency-domain structure of equipment state information under external excitation. Therefore, analyzing the difference between the normal assembly state and the current assembly state equipment state information, and then constructing the reliability index provides a way for the evaluation of the single equipment assembly reliability.

Contents of the invention

The purpose of the present invention is to provide a reasonable and effective method for judging the assembly reliability of bolted connection equipment, which can solve the problem of judging the assembly reliability of a single bolted connection equipment under the condition of insufficient failure samples.

To achieve the above object, the present invention is achieved by taking the following technical solutions:

A method for determining the assembly reliability of bolted connection equipment using state information, characterized in that it includes the following steps:

(1) Construct the state feature matrix

Carry out a bench knocking test on the bolted connection equipment, use the vibration acceleration sensor to collect the state information of the equipment under external excitation, calculate the time domain and frequency domain statistical characteristics of the state information, and use the extracted features to construct the state characteristic matrix;

(2) Construct the state subspace

Firstly, the feature matrix is mapped to the high-dimensional feature space by using the nonlinear mapping function, and the feature matrix is decomposed by the kernel local preserving projection method to obtain the projection matrix; secondly, the vectors in the projection matrix are orthogonalized by the orthogonalization method to obtain a A set of unit orthogonal vectors; finally, use the set of unit orthogonal vectors to form a state subspace;

(3) Calculate the state subspace similarity index

First, construct the reference state subspace and the current state subspace respectively; then, use the matrix norm to define the similarity index of the two types of state subspaces; the reference state subspace is:

in i=1,..., r ₁ represents the subspace basis vector, Represents the state feature matrix when it is well assembled, γ _i , i=1,..., r ₁ represents the weight vector, r ₁ represents the dimension of the subspace; the current state subspace is:

i=1，…，r₂表示子空间基向量，

表示当前时刻的状态特征矩阵，

i=1，…，r₂表示权值向量，r₂表示子空间维数；然后，利用矩阵范数定义两类状态子空间的相似度指标SI，表示为：in

i=1,...,r ₂ represents the subspace basis vector,

Represents the state feature matrix at the current moment,

i=1,..., r ₂ represents the weight vector, r ₂ represents the dimension of the subspace; then, the similarity index SI of the two types of state subspaces is defined by the matrix norm, expressed as:

$\mathrm{<span\; class="notranslate">\; Si</span>}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">T</figure-callout></span><figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">S</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

(4) Define the reliability index

Since the variation range of the similarity index SI is [0, 1], and it can reflect the similarity between the state of the bolted connection equipment and its normal state at the current moment, this index is used as the reliability index R to quantitatively reflect the assembly reliability of the bolted connection equipment, so The reliability index is defined as:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Si</span>}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">T</figure-callout></span><figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">S</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$

(5) Reliability judgment

The reliability index R can be used to determine the assembly reliability of the bolted connection equipment: R close to 1 means that the equipment assembly quality is close to the reference state at the moment; conversely, R close to 0 means that the equipment assembly quality deviates from the reference state at the moment.

Compared with the traditional method based on the assumption of large sample conditions and the statistical information of batch equipment reliability, the method of the present invention obtains the state information of the equipment through the stimulus test; uses the feature extraction method to preprocess the obtained state information to obtain the state feature matrix; The pattern recognition algorithm analyzes the inherent mode of the feature matrix, and constructs the state subspace corresponding to the state feature matrix; then calculates the similarity index between the reference state subspace and the current state subspace, which reflects the similarity between the two types of state subspaces , which can describe the closeness between the equipment performance and the normal state at the current moment; the similarity index can be used as a reliability index to quantitatively reflect the equipment assembly reliability level. A large number of failure samples, simple and easy to implement, has the characteristics of reliable results and strong real-time performance. It is suitable for on-site real-time evaluation of the assembly reliability of bolted connection equipment, which is conducive to improving the safety and reliability of equipment operation, and has engineering application value.

Description of drawings

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Fig. 1 is the time-domain waveform of the state information of a bolted connection equipment under different assembly states. Among them, Fig. 1(a) is the time-domain waveform diagram of the state information in the normal assembly state; Fig. 1(b) is the time-domain waveform diagram of the state information when the three tie rod bolts are loosened for half a turn; Fig. 1(c) is The time-domain waveform diagram of state information when 12 tie rod bolts are loosened half a turn; Figure 1(d) is the time-domain waveform diagram of state information when 24 tie rod bolts are loosened by half a turn; Figure 1(e) is the time domain waveform diagram of 24 tie rods The time-domain waveform diagram of the state information when the bolts are loosened for one circle; Fig. 1(f) is the time-domain waveform diagram of the state information when the 24 tie rod bolts are loosened for one and a half circles. The abscissa in the figure represents time in seconds; the ordinate represents the vibration signal amplitude in g.

Fig. 2 is a state information spectrum diagram of a bolted connection equipment under different assembly states. Among them, Fig. 2(a) is the spectrum diagram of the state information in the normal assembly state; Fig. 2(b) is the state information spectrum diagram when the bolts of the three tie rods are loosened for half a circle; Spectrum diagram of state information when the bolts are loosened half a turn; Fig. 2(d) is the state information spectrum diagram when 24 tie bolts are loosened for half a turn; Fig. 2(e) is the state information when 24 tie bolts are loosened for one turn Spectrum diagram; Figure 2(f) is a spectrum diagram of state information when 24 tie rod bolts are loosened for one and a half circles. In the figure, the abscissa indicates the frequency component, and the unit is Hz; the ordinate indicates the frequency amplitude, and the unit is g.

Figure 3 is a typical time-domain feature change trend diagram of the state information of a bolted connection equipment. The abscissa in the figure represents the sample number; the ordinate represents the characteristic amplitude; S1-S6 represent six assembly states.

Fig. 4 is a trend diagram of typical frequency domain characteristics of the status information of a bolted connection equipment. The abscissa in the figure represents the sample number; the ordinate represents the characteristic amplitude; S1-S6 represent six assembly states.

Figure 5 is a diagram of the judgment results of the assembly reliability of a certain bolted connection equipment. The abscissa in the figure represents six assembly states, and the ordinate represents the equipment assembly reliability R corresponding to each assembly state.

Its specific implementation

Referring to Figure 5, when the assembly state is good, the reliability judgment result of the equipment is 1, and as the assembly quality changes from good to bad, the assembly reliability index R gradually decreases. The change trend of the reliability index R well reflects the process of equipment assembly quality changing from good to bad.

The present invention utilizes state information to determine the assembly reliability of bolted connection equipment according to the following specific steps:

1) State feature matrix construction:

The bench knocking test is carried out on the bolted connection equipment, and the vibration acceleration sensor is used to collect the state information of the equipment under external excitation. Calculate the time-domain statistical features and frequency-domain statistical features of state information, and use the extracted features to construct a state feature matrix.

2) State subspace construction:

Firstly, the feature matrix is mapped to the high-dimensional feature space by using the nonlinear mapping function, and the feature matrix is decomposed by the kernel local preserving projection method to obtain the projection matrix; secondly, the vectors in the projection matrix are orthogonalized by the orthogonalization method to obtain a A set of unit orthogonal vectors; finally, the state subspace is constructed using the set of unit orthogonal vectors.

3) Subspace similarity index calculation:

First, construct the state subspace S ¹ when the bolted connection equipment is well assembled, expressed as:

i=1，…，r₁表示子空间基向量，

表示装配良好时的状态特征矩阵，γ_i，i=1，…，r₁表示权值向量，r₁表示子空间维数。构造当前时刻的状态子空间S²，表示为：Call it the base state subspace, where

i=1,..., r ₁ represents the subspace basis vector,

Represents the state feature matrix when it is well assembled, γ _i , i=1,..., r ₁ represents the weight vector, and r ₁ represents the dimension of the subspace. Construct the state subspace S ² at the current moment, expressed as:

i=1，…，r₂表示子空间基向量，

表示当前时刻的状态特征矩阵，

i=1，…，r₂表示权值向量，r₂表示子空间维数。然后，利用矩阵范数定义两类状态子空间的相似度指标SI，表示为：Call it the current state subspace, where

i=1,...,r ₂ represents the subspace basis vector,

Represents the state feature matrix at the current moment,

i=1,..., r ₂ represents the weight vector, and r ₂ represents the dimension of the subspace. Then, the matrix norm is used to define the similarity index SI of the two types of state subspaces, expressed as:

$\mathrm{<span\; class="notranslate">\; Si</span>}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">T</figure-callout></span><figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">S</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; .</span>$

4) Definition of reliability index:

According to the properties of matrix norm, ||(S ¹ ) ^T S ² || ₂ , ||(S ¹ ) ^T || ₂ , ||S ² || ₂ are not less than 0, and ||(S ¹ ) ^T S ² || ₂ ≤||(S ¹ ) ^T || ₂ ||S ² || ₂ , therefore, the variation range of the similarity index is [0, 1], namely:

0≤SI≤1

The similarity index reflects the similarity between the two types of state subspaces, and the variation range is [0, 1]. It can be used as the reliability index R to quantitatively reflect the reliability of the equipment state. Therefore, the reliability index is defined as:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Si</span>}<span\; class="notranslate">\; =</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">T</figure-callout></span><figure-callout\; id="2"\; label="T\; S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="S"\; filenames="HDA0000378338530000011.png,HDA0000378338530000031.png"\; state="\{\{state\}\}">S</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; .</span>$

5) Judgment of assembly reliability:

The reliability index R can be used to determine the assembly reliability of the bolted connection equipment: R close to 1 means that the assembly quality of the equipment is close to the reference state at the moment, and the assembly reliability is close to 1; otherwise, R close to 0 means that the assembly quality of the equipment deviates from the reference state at the moment, and the assembly quality is close to 1. Reliability is close to 0.

A specific application example process is given below, and the effectiveness of the present invention in engineering applications is verified at the same time.

The assembly reliability of a detachable disc-drum type aero-engine rotor is judged. The rotor mainly includes discs, drums and tie rod bolts. Six rotor assembly states are simulated by loosening tie rod bolts, and the definition and representation of each assembly state are shown in Table 1.

Table 1 defines the representation method of each assembly state, the number of loose bolts and the degree of looseness. It can be seen that state S1 means that no bolts are loose, which is the normal (reference) state; in state S2, there are 3 tie rod bolts loose, and the degree of looseness of each bolt is 0.5 turns; and so on for states S3-S6. From state S1 to S6, the degree of assembly looseness of the rotor increases sequentially.

Table 1 Assembly state definition and representation method

In the six assembly states of the rotor, the rotor is excited by the vibrator, and the vibration acceleration response of the rotor structure is collected and stored by the vibration acceleration sensor and data acquisition equipment, that is, the state information.

Refer to Figure 1, Figure 2, Figure 3 and Figure 4 for the time domain waveform, frequency domain waveform, time domain typical characteristics and frequency domain typical characteristics of the rotor state information in the six assembly states. It can be seen from Figure 1 that the state information has the characteristics of shock attenuation, and the attenuation is relatively fast. There is no obvious difference in the time-domain waveforms of the state information under the six assembly states, and the looseness of the rotor cannot be directly judged according to the time-domain waveforms. It can be seen from Figure 2 that the spectrum energy is concentrated in the high frequency band, that is, the 1600Hz-3200Hz frequency band. Similar to the time-domain waveform, the difference in the spectrogram is not obvious, and the loose state of the rotor cannot be directly judged from the frequency-domain waveform. It can be seen from Figure 3 and Figure 4 that although the typical characteristic T ₂ (rms value) in the time domain and the typical characteristic F ₃ in the frequency domain can better distinguish the states S1, S2 and S6, they cannot distinguish the state S3 well , S4 and S5, and there is no obvious trend of change in the characteristics, which is inconsistent with the change trend of the degree of looseness.

The state information measured under the normal assembly state is divided into two parts, one part is used as the reference state information, and the other part is the current state information measured under the loose assembly state. The method of the invention is used to calculate the similarity between the reference state and the current state, and then obtain the assembly reliability of the rotor in each state. The results of reliability judgment are shown in Table 2 and Figure 5. It can be seen that the reliability index R is equal to 1 when the assembly state is good; as the looseness of tie rod bolts gradually deepens, the assembly quality changes from good to bad, and the reliability index R also decreases. The downward trend of reliability is related to the degree of bolt looseness The deepening process is consistent. The reliability judgment result is consistent with the actual assembly state of the aero-engine rotor, which verifies the validity of the method of the invention.

Table 2 The assembly reliability evaluation results of a detachable disc-drum aeroengine rotor

Claims (1)

1. a method of utilizing status information to judge bolt connection device assembling fiduciary level, is characterized in that, comprises following steps:

(1) structural regime eigenmatrix

The bolt connection device is carried out to the stand Knock test, utilize the status information of vibration acceleration sensor collecting device under externally encouraging, the time domain of computing mode information and frequency domain statistical nature, utilize the latent structure status flag matrix extracted;

(2) structural regime subspace

At first, utilize the Nonlinear Mapping function that eigenmatrix is mapped to high-dimensional feature space, and utilize core locality preserving projections method characteristics of decomposition matrix to obtain projection matrix; Secondly, utilize orthogonalization method to the vectorial orthogonalization in projection matrix, obtain one group of unit orthogonal vector; Finally, utilize these group unit's orthogonal vector to form subspace method;

(3) computing mode subspace index of similarity

At first, construct respectively normal condition subspace and current state subspace; Then, utilize matrix norm to define the index of similarity of two class subspace methods; Described normal condition subspace is:

Wherein

i=1 ..., r ₁mean subspace base vector, mean status flag matrix when assembling is good, γ _i, i=1 ..., r ₁mean weight vector, r ₁mean the subspace dimension; Described current state subspace is:

Wherein

i=1 ..., r ₂mean subspace base vector,

the status flag matrix that means current time,

i=1 ..., r ₂mean weight vector, r ₂mean the subspace dimension; Then, utilize matrix norm to define the index of similarity SI of two class subspace methods, be expressed as:

$\mathrm{SI}=\frac{{\left|\right|{\left(S^1\right)}^T{S}^2\left|\right|}_2}{{\left|\right|{\left(S^1\right)}^T\left|\right|}_2{\left|\right|S^2\left|\right|}_2};$

(4) definition RELIABILITY INDEX

Because the variation range of index of similarity SI is [0,1], and the similarity degree that can reflect current time bolt connection device state and its normal condition, therefore the assembling fiduciary level using this index as RELIABILITY INDEX R quantitative response bolt connection device is defined as RELIABILITY INDEX:

$R=\mathrm{SI}=\frac{{\left|\right|{\left(S^1\right)}^T{S}^2\left|\right|}_2}{{\left|\right|{\left(S^1\right)}^T\left|\right|}_2{\left|\right|S^2\left|\right|}_2};$

(5) fiduciary level is judged

Can judge that with RELIABILITY INDEX R the assembling fiduciary level of bolt connection device: R approaches 1 and means that equipment assembly quality and normal condition approach this moment; Otherwise R approaches 0 and means that the equipment assembly quality departs from normal condition this moment.

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