CN102629243B - End effect suppression method based on neural network ensemble and B-spline empirical mode decomposition (BS-EMD) - Google Patents

Abstract

The invention discloses an endpoint effect suppression method based on neural network integration and BS-EMD, which comprises the following steps: A, using a speed sensor to measure and obtain a vibration signal; Continuation; C, using the B-spline mean function to obtain the mean value curve of the signal; D, performing empirical mode decomposition, discarding the data at both ends, and obtaining some IMF components corresponding to the original signal; E, analyzing each IMF component, extracting failure characteristics. The invention can effectively suppress the endpoint effect and solve the influence of the endpoint effect on the BS-EMD decomposition result.

Description

Endpoint Effect Suppression Method Based on Neural Network Ensemble and BS-EMD

technical field

The invention relates to the technical field of signal processing, in particular to an endpoint effect suppression method based on neural network integration and BS-EMD (B-spline empirical mode decomposition, B-spline empirical mode decomposition).

Background technique

Large rotating machinery is the key equipment of modern metallurgy, electric power, petroleum and other departments. Limited by the working environment and service life, some parts of the mechanical equipment are prone to some failures, which will affect the normal operation of the entire equipment, and even lead to machine crash and death, resulting in major economic losses. When the rotating machinery breaks down or is abnormal, the vibration signals are mostly nonlinear and non-stationary, and these non-stationary signals often contain a large amount of fault characteristic information. Therefore, fault diagnosis and monitoring of rotating machinery is of great significance to avoid major mechanical accidents and promote economic development. At present, scholars at home and abroad have made some achievements, but the rotating machinery still needs to be further researched and perfected.

EMD (Empirical Mode Decomposition, Empirical Mode Decomposition) method is a new time series signal analysis method developed in recent years, which decomposes complex signals into a series of IMF (Intrinsic Mode Function, Intrinsic Mode Function) sum of components. Since EMD is adaptive, this method is suitable for the analysis of nonlinear and non-stationary signals.

However, when the inventor realizes the present invention, he finds that there is a problem of endpoint effect in the prior art, that is, in the EMD process, when the extreme point is used as the node for spline interpolation to construct the envelope, it cannot ensure that the left and right sides of the data sequence The end point is exactly the extreme point, so that the interpolation accuracy of the spline curve at the end point is very poor, and the phenomenon of "overshoot" or "undershoot" is prone to occur, and this adverse effect will gradually "pollute" the entire data sequence through loop iterations , which eventually leads to serious distortion of the decomposition results of EMD.

Contents of the invention

(1) Technical problems to be solved

The problem to be solved by the present invention is to provide an endpoint effect suppression method based on neural network integration and BS-EMD, so as to overcome the defect of the endpoint effect in the EMD process in the prior art.

(2) Technical solutions

To achieve the above object, the present invention provides a method for suppressing endpoint effects based on neural network integration and BS-EMD, said method comprising the following steps:

A. Use the speed sensor to measure and obtain the vibration signal;

B. Using neural network integration to carry out left extension and right extension of the signal;

C, utilize B-spline mean value function to obtain the mean value curve of described signal;

D. Decompose the empirical mode, discard the data at both ends, and obtain some IMF components corresponding to the original signal;

E. Analyze each IMF component and extract fault features.

Preferably, said step B specifically includes:

B1. When there is only one layer of neural network, learn the neural network to obtain the determined values of weight and threshold;

B2. According to the formula Get the output of the single-layer neural network; where, is the output of a single neuron, is the weight, is the threshold, is the input sample.

B3, using weighted average for integration, using An ensemble pair of neural networks For approximation, the weight of the network satisfies the following formula

;

in, Represents a mapping from n- dimensional space to one-dimensional space.

B4. According to the distribution Randomly selected to get the training set; among them, in the network Next, when the input is , the output is ;

According to the formula Get the output of the neural network ensemble;

According to the formula Get the generalization error of the neural network;

According to the formula Get the generalization error of the neural network ensemble;

According to the formula Obtain the weighted average of the generalization errors of each network;

According to the formula Obtain the difference degree of the neural network;

According to the formula Obtain the integrated difference degree;

From this, the generalization error of the neural network ensemble can be obtained .

Preferably, said step C specifically includes:

C1. Assuming a finite interval [ ], given the division: , Represents the node value, according to the formula calculate sub-B-spline basis functions, where, . Specifies that when the denominator in the formula is 0, the value of the function is 0. No. The local support of a B-spline function is

;

C2, using B-spline, according to the formula Get the mean curve of the signal. is the control point of the B-spline, which can be obtained from the moving average of the extreme points of the signal, is the local support of the jth B-spline function.

Preferably, said step D specifically includes:

D1. Assuming the original signal is infinitely long, according to the formula Get the mean of the signal , and according to the formula Get the interpolation function;

D2. According to the IMF criterion, if is not an IMF, the as Into the formula Repeat the above process until is an eigenmode function;

Repeat the above process to get each IMF component and residual function, according to the formula gets broken down into A signal of eigenmode functions and a trend term ,in is the i -th eigenmode function, r is the trend item;

D3. Process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal.

Preferably, the step D1 specifically includes:

D11. Find out the rotor fault vibration speed signal For all local extreme points, connect all local maximum points with B-spline curves to form an upper envelope, and use B-spline curves to connect all local minimum points to form a lower envelope;

D12, the average value of the upper envelope and the lower envelope is denoted as , find .

Preferably, the step D2 specifically includes:

D21. Judgment Is the condition of the IMF met, and if so, then for the signal The first component of satisfying the IMF condition;

If not, the As the original data, repeat steps D11 and D12, and then use the B-spline function to obtain the average value of the upper and lower envelopes ,judge Whether the IMF condition is met, repeat the above process until the IMF condition is met ;remember ,but for the signal The first component of satisfying the IMF condition;

D22. Will from the speed signal separated from the ;

Will Repeat steps D11, D12 and D21 as raw data to get The second one that satisfies the IMF component condition ;repeat loop times, get the speed signal of A component that satisfies the IMF condition ;

when When it becomes a monotonic function, the loop ends and the speed signal is obtained .

(3) Beneficial effects

1. The present invention adopts the combination of neural network integration and BS-EMD method, and proposes a new method to solve the endpoint effect;

2. The B-spline interpolation method is used to obtain the upper and lower envelopes of the signal, which solves the overshoot and undershoot problems caused by the cubic spline envelope curve method;

3 Using neural network integration to synthesize the conclusions of multiple neural networks through training, which significantly improves the generalization ability of the learning system;

4. Solved the influence of endpoint effect on BS-EMD decomposition results.

Description of drawings

Fig. 1 is a flow chart of an endpoint effect suppression method based on neural network integration and BS-EMD according to an embodiment of the present invention;

Fig. 2 is the flow chart that utilizes BS-EMD method to decompose vibration signal in the embodiment of the present invention;

Fig. 3 is the schematic diagram of the EMD decomposition result of prior art;

Fig. 4 is a schematic diagram of decomposition results of an embodiment of the present invention.

Detailed ways

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

An endpoint effect suppression method based on neural network integration and BS-EMD in an embodiment of the present invention is shown in Figure 1, including the following steps:

Step s101, using a speed sensor to measure and acquire a vibration signal.

Step s102, performing left extension and right extension on the signal by neural network integration. Extending the signal using neural network ensembles involves the following steps:

(1) When there is only one layer of neural network, the data sequence extension using neural network is mainly divided into two steps: learning and extension. The purpose of the neural network learning process is to obtain certain values of weights and thresholds.

(2) The output of a single-layer neural network can be expressed as

(1)

in, is the output of a single neuron, is the weight, is the threshold, is the input sample.

(3) Integration adopts weighted average, using set of neural networks Approximating in pairs, the weight of the network satisfies the following formula

(2)

(3)

in, Represents a mapping from n- dimensional space to one-dimensional space.

(4) The training set is distributed according to randomly selected from the network When the input is , the output is , the output of the neural network integration at this time is

(4)

Generalization Error of Neural Networks and the generalization error of the ensemble respectively

(5)

(6)

The weighted average of the generalization errors of each network is

(7)

The degree of variance of the neural network and integrated difference respectively

(8)

(9)

The generalization error of the neural network ensemble is

(10)

In formula (10) It shows the correlation degree of each network integrated by the neural network. Therefore, only by making the errors of each network in the integration uncorrelated as much as possible can the generalization ability of the neural network be enhanced.

Step s103, using the B-spline mean function to obtain the mean value curve of the signal:

(1) calculation The sub-B-spline basis functions are:

(11)

in,

(12)

It is stipulated that when the denominator in formula (11) is 0, it will appear In the case of , define its value as 0 at this time. No. The local support of a B-spline function is

(13)

(2) B-spline basis functions have the properties of recursion, local support and linear independence. Using B-spline to calculate the mean curve of the signal is

(14)

Step s104, perform empirical mode decomposition, discard the data at both ends, and obtain several IMF components corresponding to the original signal. The specific decomposition process is as follows:

s1041, assuming the original signal is infinitely long, according to formula (14) to find the mean value of the signal , then the interpolation function is

(15)

s1042, according to the IMF criterion, if is not an IMF, the as Substitute into formula (15) and repeat the above process until is an eigenmode function until each IMF component and residual function are obtained. signal at this time is broken down into eigenmode functions and a trend term, namely

(16)

S1043, process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal.

Wherein the specific process of step s1041 and step s1042 is as follows:

1) Find out the rotor fault vibration speed signal All the local extreme points are connected with B-spline curves to form the upper envelope. Then use the B-spline curve to connect all the local minimum points to form the lower envelope, and the upper and lower envelopes should include all the data points.

2) The average value of the upper and lower envelopes is recorded as , find

(17)

Ideally, if satisfies the conditions of the IMF, then that is The first IMF component of .

3) if does not meet the conditions of the IMF, the As the original data, repeat steps 1)~2), and then use the B-spline function to get the average value of the upper and lower envelopes , and then judge Whether to meet the IMF conditions. remember ,but for the signal The first component of is that satisfies the IMF condition.

4) Will from the speed signal separated from the

(18)

Will Repeat steps 1)~3) as the original data to get The second one that satisfies the IMF component condition , repeating the loop times to get the vibration acceleration signal of Each component that satisfies the IMF condition, namely

(19)

When the termination condition is met (i.e. becomes a monotonic function from which IMF components can no longer be extracted), the loop ends. At this time, the speed signal can be expressed as

. (20)

In the formula, Represents the average trend of the signal and is the residual component of the signal. Each IMF component contains components of different frequency bands from high to low of the signal, and each frequency band contains different frequency components. Moreover, each IMF component changes with the change of the vibration signal itself.

Step s105, analyzing each IMF component and extracting fault features.

The BS-EMD of the present invention obtains the upper and lower envelope curves of the signal through the B-spline interpolation function, avoiding the undershoot and overshoot problems of the signal, and the B-spline interpolation has good local properties, and is widely used in function interpolation and pseudo Together and so on. Use the neural network integration to extend the rotor test data left and right, and use the B-spline interpolation curve to interpolate the data to obtain the mean value curve of the signal, then decompose the empirical mode, and finally discard the extended data at both ends, that is, get the same as the original signal The corresponding eigenmode function.

The invention aims at solving the problem of the endpoint effect by utilizing the neural network integration to extend the endpoint of the signal, and analyzes the unbalanced fault signal of the rotor of the rotary machine through theoretical research and test analysis. Firstly, the signal is extended by neural network integration, and then decomposed to obtain the characteristic components of the signal, and the frequency characteristics of the signal are obtained by analyzing each component, so as to extract the information of the fault. The process of decomposing the vibration signal by using the BS-EMD method in the embodiment of the present invention is shown in FIG. 2 . The present invention demonstrates that the method can effectively suppress the problem of endpoint effect through test signals.

In this embodiment, the rotor misalignment fault is simulated on the rotating machinery fault simulation platform, and its fault characteristic frequency has a double frequency in addition to the power frequency. The vibration signal in the vertical direction is extracted by the speed sensor. The rotational speed of the shaft is 924r/min, the sampling frequency is 500Hz, and the number of collection points is 512 points. The signal is decomposed and the characteristic value of the signal is extracted.

Under the above circumstances, the schematic diagram of the EMD decomposition result in the prior art is shown in FIG. 3 , and the schematic diagram of the decomposition result in the embodiment of the present invention is shown in FIG. 4 .

Referring to Figure 3, the waveform of the original signal is "signal", which is directly decomposed by EMD. It can be seen from the figure that IMF2 and IMF3 have endpoint effects at the endpoints.

Referring to Fig. 4, it can be seen from IMF2 and IMF3 in the figure that the endpoint effect of the signal is obviously suppressed. In the figure, IMF1 represents the double frequency component, and IMF2 represents the power frequency component. Comparing the IMF3 of the two, it is found that the IMF3 obtained by the original method fluctuates at the endpoints, especially at the left endpoint. However, the values at the endpoints obtained by the embodiment of the present invention are relatively flat, the frequency components are relatively concentrated, and the energy leakage is relatively small. By comparing these two decomposition methods, it can be seen that both methods can successfully reveal the misalignment fault of the signal, but the signal decomposition in the embodiment of the present invention has a better performance at the end point, which can effectively suppress the end point effect, Make fault features easier to accurately identify. By comparing Fig. 3 and Fig. 4, it can be seen that the method proposed by the present invention is a very effective method for suppressing the endpoint effect.

The endpoint effect suppression method based on neural network integration and BS-EMD in the embodiment of the present invention has the following beneficial effects:

1. The present invention adopts the combination of neural network integration and BS-EMD method, and proposes a new method to solve the endpoint effect;

2. The B-spline interpolation method is used to obtain the upper and lower envelopes of the signal, which solves the overshoot and undershoot problems caused by the cubic spline envelope curve method;

3 Using neural network integration to synthesize the conclusions of multiple neural networks through training, which significantly improves the generalization ability of the learning system;

4. Solved the influence of endpoint effect on BS-EMD decomposition results.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and replacements can also be made, these improvements and replacements It should also be regarded as the protection scope of the present invention.

Claims (5)

1. an endpoint effect suppression method based on neural network integration and BS-EMD, is characterized in that, described method comprises the following steps: A. Use the speed sensor to measure and obtain the vibration signal; B. Using neural network integration to carry out left extension and right extension of the signal; C, utilize B-spline mean value function to obtain the mean value curve of described signal; D. Decompose the empirical mode, discard the data at both ends, and obtain some IMF components corresponding to the original signal; E. Analyze each IMF component and extract fault features; Described step B specifically comprises: B1. When there is only one layer of neural network, learn the neural network to obtain the determined values of weight and threshold; B2. Obtain the output of the single-layer neural network according to the formula a _i = f(ω _i × p _{m, i} + b _i ); wherein, a _i is the output of a single neuron, ω _i is the weight, b _i is the threshold, p _{m, i} is the input sample; B3. Use the weighted average to integrate, and use the integration composed of N neural networks to approximate f:R ⁿ → R, and the network weight ω _α satisfies the following formula $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \underset{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; ;</span>$ Among them, f:R ⁿ → R represents the mapping from n-dimensional space to one-dimensional space; B4. Randomly extract according to the distribution p(x) to obtain the training set; wherein, under the network α, when the input is X, the output is V ^α (X); According to the formula Get the output of the neural network ensemble; Obtain the generalization error of the neural network according to the formula E ^α =∫dxp(x)(f(x)-V ^α (x)) ² ; According to the formula Get the generalization error of the neural network ensemble; According to the formula Obtain the weighted average of the generalization errors of each network; According to the formula Obtain the difference degree of the neural network; According to the formula Obtain the integrated difference degree; From this, the generalization error of the neural network ensemble can be obtained 2. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 1, is characterized in that, described step C specifically comprises: C1. Assuming a finite interval [a,b], given the division: Δa=t ₀ <t ₁ <...<t _N-1 <t _N ＝b, t _j represents the node value, according to the formula $B_{j,k}\left(t\right)=\frac{t-t_j}{t_{j+k-1}-t_j}{B}_{j,k-1}\left(t\right)+\frac{t_{j+k}-t}{t_{j+k}-t_{j+1}}{B}_{j+1,k-1}\left(t\right)$ Compute k-th B-spline basis functions, where, It is stipulated that when the denominator in the formula is 0, the value of the function is 0; the local support of the jth B-spline function is C2, using B-spline, according to the formula Obtain the mean value curve of the signal; ω _j is the control point of the B-spline, which can be obtained from the moving average of the extreme points of the signal, and B _j,k (t) is the local support of the jth B-spline function. 3. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 2, is characterized in that, described step D specifically comprises: D1. Assuming that the original signal x(t) is infinitely long, according to the formula Obtain the mean value m of the signal, and obtain the interpolation function according to the formula x(t)-m=h; D2, according to the IMF criterion, if h is not an IMF, then use h as x (t) to substitute into formula x (t)-m=h and repeat the above-mentioned process, until h is an eigenmode function; Repeat the above process to get each IMF component and residual function, according to the formula Obtain the signal x(t) decomposed into n eigenmode functions and a trend item, where c _i (t) is the i-th eigenmode function, and r is the trend item; D3. Process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal. 4. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 3, is characterized in that, described step D1 specifically comprises: D11. Find out all the local extreme points of the rotor fault vibration speed signal x(t), connect all local maximum points with B-spline curves to form an upper envelope, and use B-spline curves to connect all local extreme points The minimum points are connected to form the lower envelope; D12. The average value of the upper envelope and the lower envelope is denoted as m ₁ , and x(t)-m ₁ =h ₁ is obtained. 5. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 4, is characterized in that, described step D2 specifically comprises: D21, judge whether h ₁ satisfies the condition of IMF, if yes, then h ₁ is the first component that satisfies the IMF condition of signal x(t); If not, take h ₁ as the original data, repeat steps D11 and D12, and then use the B-spline function to obtain the average value m ₁₁ of the upper and lower envelopes, judge whether h ₁₁ = h ₁ -m ₁₁ satisfies the IMF condition, and repeat the above process , until h _1k satisfying the IMF condition is obtained; record c ₁ =h _1k , then c ₁ is the first component of the signal x(t) satisfying the IMF condition; D22. Separate c ₁ from the speed signal x(t), and obtain r ₁ =x(t)-c ₁ ; Repeat steps D11, D12 and D21 using r ₁ as the original data to obtain the second c ₂ of x(t) that meets the IMF component condition; repeat the cycle n times to obtain n components of the velocity signal x(t) that meet the IMF condition weight $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right.<span\; class="notranslate">\; ;</span>$ When r _n is a monotone function, the loop ends and the speed signal is obtained