CN103440527A - Method for improving ant colony algorithm optimization support vector machine parameters - Google Patents

Abstract

The invention relates to a method for improving ant colony algorithm optimization support vector machine parameters. The method includes the steps that the value range of n parameters is determined, and each parameter is equally divided into N parts to calculate the grid interval; ants select N grid points from the first row to the Nth row, the travel of the N grid points serves as one solution, and M ants find out M solutions; the M solutions are input into an objective function, and a largest objective function value and a smallest objective function value are found out; global information element updating is performed, Pt=Pt-1*rho, a certain number of information element values are added within a certain range near to the globally optimal solution according to the formula Pt=Pt-1-op, and the globally optimal solution is strengthened; a certain number of information element values are reduced within a certain range near to the globally worst solution according to the formula Pt=Pt-1-wp, and the globally worst solution is weakened; if the globally largest cycle index is not reached, the grids are redistricted again until the loop termination conditions are met and optimization of the parameters is completed. The method improves the speed and the accuracy rate for searching for the optimal combination. The principle of grids and high-probability random selection is fused in the method, and the sensitiveness of the ants on the optimal solution is increased.

Description

A kind of method of improving ant group algorithm Support Vector Machines Optimized parameter

Technical field

The present invention relates to a kind of method of improved Ant Colony System Support Vector Machines Optimized parameter of the fault diagnosis for mechanical bearing.

Background technology

In modern production, the fault diagnosis technology of plant equipment more and more comes into one's own, if certain equipment breaks down and fails find in time and get rid of, its result not only can cause equipment itself to damage, and even may cause fatal crass's serious consequence.Cause because certain equipment breaks down and go wrong product that whole production line is produced even to cause the loss that stopping production brings be huge.Therefore, the status of fault diagnosis in production line is very important.

Rolling bearing is widely used in plant equipment, and as critical component.Rolling bearing need to have higher reliability, and the generation of mechanical movement centre bearer fault may cause fatal mechanical fault.Therefore, the existence of accurate diagnosis and detection rolling bearing fault is extremely important,

Early stage rolling bearing diagnostic method can not reach industrial standard aspect diagnostic accuracy and efficiency.Along with the continuous progress of artificial intelligence technology, artificial intelligence approach is used in rolling bearing fault diagnosis.Such as expert system artificial neural network etc., the principle of these methods based on empirical risk minimization, have the shortcoming of some general character, such as easily be absorbed in locally optimal solution, speed of convergence slow, cross study etc., particularly at sample size, the too low generalization ability of prescribing a time limit is arranged.In most cases, in the fault diagnosis that artificial intelligence solves, lacking of fault sample is the bottleneck problem of diagnosis.The fault diagnosis result that too low generalization ability may lead to errors.

Summary of the invention

In order to solve the technical matters of above-mentioned existence, the invention provides a kind of method of improvement ant group algorithm Support Vector Machines Optimized parameter of the fault diagnosis for mechanical bearing.Use improved ant group algorithm to be optimized the parameter of support vector machine, find out best parameter combinations, complete the fault of rolling bearing is classified.

The objective of the invention is to be achieved through the following technical solutions: a kind of method of improving ant group algorithm Support Vector Machines Optimized parameter, its step is as follows:

(1) according to the problem of parameter optimization, determine the span of n parameter, and by each parameter being carried out to N etc. minute computing grid interval;

h _i=(x _m-x _l)/N

Formation n*(N+1) grid that individual point forms; Each net point pheromones value of initialization, maximum cycle and loop termination condition;

(2) every ant random net point of selecting some in each row, find out the selected element of these row the most of pheromones maximum, ant goes out N net point from first row to the N column selection, this N net point stroke is as a solution, and M ant found M solution;

(3) separate input objective function (support vector machine) by this M, find out maximum and minimum two objects functional value, these two values are globally optimal solution and the poorest solution of the overall situation;

(4) carry out the renewal of pheromones, at first carry out the global information element and upgrade, P _t=P _t-1ρ; Wherein ρ is the volatilization factor, means the volatilization process of pheromones;

According to formula P _t=P _t-1near the certain limit of-op globally optimal solution increases the value of a certain amount of pheromones, the strengthening globally optimal solution;

According to formula P _t=P _t-1near the certain limit of-wp the poorest solution of the overall situation carried out a certain amount of minimizing operation of pheromones, weakens the poorest solution of the overall situation;

(5) if do not reach Global maximum cycle index Nmax forward step (2) to, otherwise forward step (6) to, carry out repartitioning of grid;

(6) find out row corresponding to maximal value place in Pheromone Matrix after algorithm cycle index NC reaches Nmax, the span of dwindling variable in net point respective value near repartition grid; The initialization information prime matrix; Forward step (2) to and carry out circulation again, until reach loop stop conditions (grid interval h<ε), complete the optimizing of parameter.

Beneficial effect of the present invention: this method adopts such scheme, by improving the mode of ant lastest imformation element in ant group algorithm, selects fast best of breed and avoids subtractive combination, thereby improved speed and the accuracy rate of seeking the parameters optimal combination.And merged the random principle of selecting of grid and high probability in improved ant group algorithm, increased ant to the susceptibility of optimum solution and avoided being absorbed in local extremum, increased the searching ability to globally optimal solution.The inventive method has solved the difficult problem of the parameter selection of support vector machine, and the inventive method is applied to bearing failure diagnosis, realizes good failure modes effect.

The accompanying drawing explanation

Fig. 1 is based on the process flow diagram that improves the ant group algorithm Support Vector Machines Optimized.

Fig. 2 is the parameter space grid chart.

Fig. 3 is the peak-to-peak value curve map of data.

Fig. 4 is the draw value curve map of data.

Fig. 5 is the absolute average curve map of data.

Fig. 6 is the mean square value curve map of data.

Fig. 7 is the curve map of taking root in of data.

Fig. 8 is the variance curve figure of data.

Fig. 9 is the standard deviation curves figure of data.

Figure 10 is the degree of bias curve map of data.

Figure 11 is the peak curve figure of data.

Figure 12 (A) is the accuracy rate curve map that load is 0hp and the fault diameter data set that is 14mil.

Figure 12 (B) is the time plot that load is 0hp and the fault diameter data set that is 14mil.

Figure 13 (A) is the accuracy rate curve map that load is 2hp and the fault diameter data set that is 14mil.

Figure 13 (B) is the time plot that load is 2hp and the fault diameter data set that is 14mil.

Embodiment

One, theoretical foundation of the present invention:

1, ant group algorithm is to be learned the people such as Dorigo M at first to propose by Italy the inspiration that [13] are subject to the cluster behavior of nature ant.Between ant, by the pheromones exchange message, every ant determines factum according to the size of pheromones, also produces a certain amount of pheromones simultaneously environment is on every side exerted an influence.Single ant is made corresponding selection according to own residing environment, is singly random behavior, but integral body is to exchange the orderly group behavior of height of formation.Ant group algorithm is not strong to the dependence of initial solution, and constantly carries out information interchange and transmission between individuality, and its positive feedback mechanism more is conducive to find to separate preferably, and the characteristics of global optimization and heuristic search are arranged.The random selection of high probability and grid are combined with ant group algorithm, change lastest imformation element update mode and the mode of selecting net point in ant group algorithm.The selected probability of the value that in net point, pheromones is large is relatively large, and corresponding pheromones constantly increases, and will make ant of future generation be easy to select this solution, and stagnation behavior easily occurs.Certain net point by random selection, of selecting pheromones maximum wherein, prevent from being absorbed in local globally optimal solution.Upgrade near the poorest solution of the overall situation near lastest imformation element globally optimal solution, make ant choose the probability of globally optimal solution to reduce and can not break away from certain limit again simultaneously.Thereby ant selects the probability of other elements to increase, and the diversity of solution is guaranteed, and has reduced the possibility that is absorbed in stagnation behavior.Near the corresponding pheromones that the reduces the poorest solution of the overall situation, the speed of having accelerated the exclusive segment solution has namely accelerated to think the hunting speed of optimum solution, improves convergence of algorithm speed.

2, ant group algorithm Support Vector Machines Optimized parameter: support vector machine is a kind of machine learning method based on structural risk minimization, its objective is solving classification problem, by the back gauge between two relative classes, maximizes.Support vector machine is the machine learning techniques proposed according to statistical theory, SVM utilizes the structural risk minimization in statistical theory to replace traditional empirical risk minimization principle, improved generalization ability and the learning ability of support vector machine, and solved to a great extent Model Selection and crossed problem concerning study, non-linear and dimension disaster problem, local smallest point problem.

3, support vector machine considerable advantage is introduced kernel function exactly, and this makes SVM have the ability to process high-dimensional feature space and nonlinear characteristic space.Kernel function is mapped to nonlinear sample space the feature space of higher-dimension, the nonlinear problem of sample space is transformed into to the linear problem of feature space.Research is found, selects different kernel functions little to the performance impact of support vector machine, and in the different IPs function, the selection of parameter is huge to the performance impact of support vector machine.The same empiric risk as balance study machine and the penalty factor of fiducial range ratio are also the key factors that determines the study machine performance.

Two, according to above-mentioned theory, the present invention proposes a kind of method of improving ant group algorithm Support Vector Machines Optimized parameter, and the whole process of the method as shown in Figure 1.Its step is as follows:

According to the problem of parameter optimization, determine the span of n parameter, and by each parameter being carried out to N etc. minute computing grid interval.

h _i=(x _m-x _l)/N

Formation n*(N+1) grid that individual point forms.Each net point pheromones value of initialization, maximum cycle and loop termination condition.

Every ant is selected at random the net point of some in each row, finds out the selected element of these row the most of pheromones maximum, and ant goes out N net point from first row to the N column selection, solution of this N net point stroke, and M ant found M solution, as Fig. 2.

This M is separated and input objective function, find out minimum and maximum two objects functional value, these two values are globally optimal solution and the poorest solution of the overall situation.

Carry out the renewal of pheromones, at first carry out the global information element and upgrade, P _t=P _t-1ρ; Wherein ρ is the volatilization factor, means the volatilization process of pheromones.

According to formula P _t=P _t-1-op, near certain limit globally optimal solution increases the value of a certain amount of pheromones, the strengthening globally optimal solution.According to formula P _t=P _t-1-wp, near the certain limit the poorest solution of the overall situation is carried out a certain amount of minimizing operation of pheromones, weakens the poorest solution of the overall situation.

If do not reach the Global maximum cycle index forward step (2) to, otherwise forward step (6) to, carry out repartitioning of grid;

Find out row corresponding to maximal value place in Pheromone Matrix after algorithm circulation Nmax, the span of dwindling variable in net point respective value near repartition grid.The initialization information prime matrix.Forward step 2 to and carry out circulation again, know and reach loop stop conditions.Complete the optimizing of parameter.

Three, by a kind of fault diagnosis of the method for ant group algorithm Support Vector Machines Optimized parameter for mechanical bearing of improving of the present invention, concrete steps are as follows:

1, gather original signal: during the rolling bearing data from U.S.'s Case Western Reserve University electrical engineering laboratory.Different loads (0,1,2,3hp) and the different faults degree of depth (7,14, four kinds of states are arranged under 21mil), be respectively normal, inner ring fault, outer ring fault, rolling body fault.The sample frequency of data is 12K and 48K.Each state has 50 groups of samples, comes to 200 groups.Wherein 120 groups of data are as training sample, and 80 groups of data are as test sample book.In order better to verify that this method is applicable to small sample, select 80 groups of data as training sample, 120 groups of data are as test sample book simultaneously.

2, original signal is carried out to feature extraction:

(1) signal is carried out to pre-service, extract feature, the vibration signal eigenwert must have been calculated a variety of methods, selects peak-to-peak value, average, absolute average, mean square value, root-mean-square value, variance, standard deviation, the degree of bias, peak value this in 9 eigenwert process original signal.

1. peak-to-peak value refers to the variation range of signal.Formula is:

max(x _i)-min(x _i) （1）

2. mean value is the mean value of signal

${\mathrm{\&mu;}}_x=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sum;}}}{x}_i---\left(2\right)$

3. absolute average is the arithmetic mean of signal amplitude absolute value

${\mathrm{\&mu;}}_{\left|x\right|}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sum;}}}\left|x_i\right|---\left(3\right)$

4. not only mean value also fluctuation and the dispersion degree of reaction signal of reaction signal of mean square value

${\mathrm{\&psi;}}_x^2=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sum;}}}{x}_i^2---\left(4\right)$

5. the size of r. m. s. value reaction signal oscillation intensity and energy.

${\mathrm{\&psi;}}_x=\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sum;}}}}{x}_i^2---\left(5\right)$

6. variance is described the cymomotive force that signal departs from central tendency, and formula is

${\mathrm{\&sigma;}}_x^2=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sum;}}}{(x_i-{\mathrm{\&mu;}}_x)}^2---\left(6\right)$

7. standard deviation formula; Standard deviation is a kind of standard of degree of scatter of metric data distribution.

$s=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sum;}}}{(x_i-\mathrm{\&mu;})}^2}{n-1}}---\left(7\right)$

μ is average

8. the degree of bias refers to that the skewness of vibration signal refers to skew direction and degree that data distribute.

$g=\frac{n}{(n-1)(n-2)s^3}\underset{i=1}{\overset{n}{\mathrm{\&Sum;}}}{(x_i-\mathrm{\&mu;})}^3---\left(8\right)$

S is that standard deviation μ is average

9. peak value refers to that index is according to the vibration signal high and steep degree of point or the protruding degree in peak that distribute

$h=\frac{n(n-1)}{(n-1)(n-2)(n-3){\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="130729143043.png"\; state="\{\{state\}\}">s</figure-callout>}}^4}\underset{i=1}{\overset{n}{\mathrm{\&Sum;}}}{(x_i-\mathrm{\&mu;})}^4-3\frac{{(n-1)}^2}{(n-2)(n-3)}---\left(9\right)$

(2) vibration signal of time domain is converted into the Second Characteristic signal to Fault-Sensitive by above calculating.But these Second Characteristics are different to the susceptibility of fault.Fig. 3-11 shows the distribution situation of the sample point of different characteristic function, is contrasting respectively the susceptibility of nine kinds of feature extracting methods to failure modes, peak-to-peak value, and absolute average, r. m. s. value, the classification feature of standard deviation is more obvious, higher to the susceptibility of fault.Therefore, select this nine kinds of features input of support vector machine the most.

3, the number of ant: for the impact of ant number on classification results is described intuitively, in the situation that experimental data is identical, we,, in the situation that the ant number is different, are tested.From table 1, we can find out, different ant numbers have a great impact nicety of grading.The ant number reaches at 4 o'clock, and accuracy rate and the stability of classification peak, and the training time is also within the acceptable range.

Table 1

4, pheromones is upgraded op and wp: near globally optimal solution and the poorest solution of the overall situation, pheromones is upgraded.If the excessive globally optimal solution of op and wp may be filtered, if the too small meeting of op and wp causes speed of convergence excessively slow, cause the training time longer.The purpose of op and wp is an appropriate training time to select globally optimal solution.Table 2 has shown different op and the wp impact on training time and nicety of grading.We can find out that training time and classification accuracy reach best when op and wp are 0.4 and 0.2.

Table 2

5, generalization ability and contrast test: generalization ability is the key factor of test sample book performance.Generalization ability refers to the ability of the model explanation delta data of setting up based on available data.Say that this method and cross-validation method, genetic algorithm are contrasted.Table 3 shown in the situation that the identical this method of training sample on training time and accuracy rate higher than cross-validation method and genetic algorithm.And go rate in the situation that minimizing training sample increase test sample book this method still has higher standard, verified that this method has generalization ability preferably.

Table 3

The accuracy rate that Figure 12 and Figure 13 are the different pieces of information collection and time contrast (fault diameter is 14 Mills, and load is 0hp, 2hp).As shown in Figure 12 (A) and Figure 13 (A), with the star line, with triangle line, to compare, rectangular lines is more stable.Improved ant group algorithm is optimized the SVM algorithm and is had higher accuracy rate than the method for cross validation and genetic algorithm.In Figure 12 (B) and Figure 13 (B), blue line and red line are with reference to left axle, and green line is with reference to right axle.By observing Figure 12 (B) and Figure 13 (B), improved ant group algorithm optimization SVM algorithm than the method for cross validation and genetic algorithm spended time still less.It is more excellent than the method for cross validation and performance of genetic algorithms that the improved ant group algorithm of presentation of results is optimized the SVM algorithm.

Claims (1)

1. a method of improving ant group algorithm Support Vector Machines Optimized parameter, its step is as follows:

(1) according to the problem of parameter optimization, determine the span of n parameter, and by each parameter being carried out to N etc. minute computing grid interval;

h _i=(x _m-x _l)/N

Formation n*(N+1) grid that individual point forms; Each net point pheromones value of initialization, maximum cycle and loop termination condition;

(2) every ant random net point of selecting some in each row, find out the selected element of these row the most of pheromones maximum, ant goes out N net point from first row to the N column selection, this N net point stroke is as a solution, and M ant found M solution;

(3) separate the input objective function by this M: support vector machine, find out maximum and minimum two objects functional value, these two values are globally optimal solution and the poorest solution of the overall situation;

(4) carry out the renewal of pheromones, at first carry out the global information element and upgrade, P _t=P _t-1ρ; Wherein ρ is the volatilization factor, means the volatilization process of pheromones;

According to formula P _t=P _t-1near the certain limit of-op globally optimal solution increases the value of a certain amount of pheromones, the strengthening globally optimal solution;

According to formula P _t=P _t-1near the certain limit of-wp the poorest solution of the overall situation carried out a certain amount of minimizing operation of pheromones, weakens the poorest solution of the overall situation;

(5) if do not reach Global maximum cycle index Nmax forward step (2) to, otherwise forward step (6) to, carry out repartitioning of grid;

(6) find out row corresponding to maximal value place in Pheromone Matrix after algorithm cycle index NC reaches Nmax, the span of dwindling variable in net point respective value near repartition grid; The initialization information prime matrix; Forward step (2) to and carry out circulation again, until reach loop stop conditions (grid interval h<ε), complete the optimizing of parameter.

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