CN109902339A - A kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM - Google Patents
A kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM Download PDFInfo
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Abstract
The present invention relates to a kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM, belong to mechanical engineering field of automation technology.The present invention uses the method for Wavelet transformation to carry out feature extraction to the fault data of rolling bearing first, and is normalized to form training sample and train to it and obtains SVM model；Then processing is optimized using penalty factor and kernel functional parameter of the improved self-adapted genetic algorithm to SVM model, the SVM model after being optimized i.e. SVM fault diagnosis model finally carries out fault diagnosis to rolling bearing using SVM fault diagnosis model.The invention enables failure diagnostic process expression it is clear and accurate, fault diagnosis model is rationally effective, improve its classify prediction effect.
Description
Technical field
The present invention relates to a kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM, belong to mechanical engineering automation skill
Art field.
Background technique
With the raising of automatization level, the performance requirement of mechanical equipment is also increased accordingly.Rolling bearing is whirler
The chief component of tool equipment, since its long-term work is under harsh natural environment, by the shadow of various uncertain factors
It rings, it is caused the result is that the reliability of rolling bearing is worst in entire rail engineering machinery equipment.Once it breaks down,
The duration will be caused to delay and economic loss to a certain extent, casualties is very likely to cause when serious.So mechanical equipment
Fault diagnosis technology receive more and more attention and study.If can judge in time and feed back to relevant work
Personnel are handled, that can reduce loss to the full extent.
Rotating machinery is widely used in the industries such as metallurgy, electric power, railway in actual production and life, operation conditions with
National economy is closely bound up.In view of rolling bearing key position locating in entire rotating machinery operation process, institute
There is huge practical value so that its all kinds of failure are carried out with the classification prediction of high-efficiency high-precision.
The method of the artificial intelligence such as expert system, neural network, fuzzy theory has been widely used in rotation in recent years
Turn the fault diagnosis field of mechanical equipment, but still remains inefficiency, the problems such as nicety of grading is not high.Therefore, of the invention
It designs a kind of based on IAGA-SVM (improved self-adapted genetic algorithm Support Vector Machines Optimized, Improved Adaptive
Genetic Algorithm optimizes Support Vector Machine) method for diagnosing faults, it be based on knot
Structure principle of minimization risk, the problem of efficiently avoiding overfitting, have very strong generalization ability, and it is one convex excellent
Change problem, so his locally optimal solution is centainly also globally optimal solution.
Summary of the invention
The technical problem to be solved by the present invention is to obtain the failure modes of high-accuracy with speed as fast as possible, provide
A kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM.
The technical solution adopted by the present invention is that: a kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM is adopted first
Feature extraction is carried out with fault data of the method for Wavelet transformation to rolling bearing, and it is normalized to form training
Sample and training obtain SVM model；Then using improved self-adapted genetic algorithm to the penalty factor and core letter of SVM model
Number parameter γ parameter optimizes processing, and the SVM model after being optimized i.e. SVM fault diagnosis model finally utilizes SVM failure
Diagnostic model carries out fault diagnosis to rolling bearing.
Because the process of data acquisition often contains inevitable noise and invalid information, if carried out to initial data
Untreated use, result always will not be satisfactory.Therefore, better experimental result, the present invention utilize in order to obtain
Wavelet transformation carries out feature extraction to the original signal after denoising, to obtain the effective information in data.
Specific step is as follows for the method:
Step1, initialization relevant parameter, are arranged the number of iterations k=0, parameter mainly includes population at individual quantity N, individual
Crossover probability PcWith individual variation probability Pm, algorithm maximum number of iterations etc..
Step2, the fitness value for calculating each individual in group.
Step3, pass through selection, intersection, variation, generation population of new generation, self-adapted genetic algorithm (Adaptive
Genetic Algorithm, AGA) superiority to be that the crossover probability that will be fixed in genetic algorithm and mutation probability carry out linear
Adaptive adjustment.Crossover probability determines the ability of searching optimum of genetic algorithm, and mutation probability determines the office of genetic algorithm
Portion's search capability.But the algorithm is easily trapped into the predicament of local optimum, in order to solve the feelings of group's stagnation as far as possible
Condition, the present invention improve self-adapted genetic algorithm:
In formula: fmaxIndicate maximum fitness value in group, fbiggerIt indicates to participate in two individuals of crossing operation
Biggish fitness value, favgIndicate the average fitness value of group, f indicates the fitness value of current variation individual.Pmax1With
Pmin1Respectively indicate the upper and lower bound of crossover probability, Pmax2And Pmin2The upper and lower bound of mutation probability is respectively indicated, α is one
A constant.It is such to be arranged so that PcAnd PmFitness value in fmaxAnd favgBetween carry out nonlinear adjustment, largely
On the drawbacks of having evaded local convergence.
Step4, step Step2-Step3 is repeated, until reaching maximum number of iterations.
Step5, optimizing terminate, and determine the penalty factor of SVM and the best parameter group of kernel functional parameter γ.
Step6, fault diagnosis will be carried out in the feature vector mentioned input SVM fault diagnosis identifier.
Svm classifier model is used only to solve two classification problems when initial, but commonly more in practice
Classification problem.In order to make svm classifier model that polytypic function may be implemented, need successively to construct the classifier of n two classification,
To achieve the effect that n classifies.The method is theoretically simple and easy, but in practical applications since it needs the circulation that solves
Number is more, and model efficiency is caused to be had a greatly reduced quality, so be not suitable for promoting and applying.The present invention uses the branch based on binary tree structure
Hold the more classification methods of vector machine (DT-SVM).
Assuming that the sample set of n training sample is expressed asxi∈Rn, RnIndicate sample space.yi∈{-
1,1}.When sample set D is linear separability, then (1) formula is a certain hyperplane equation of sample:
ω·xi+ b=0 (1)
In formula: ω is the normal vector of hyperplane, and b is displacement.
Its optimal separating hyper plane must satisfy equation (2):
yi(ωxi+ b) >=1, i=1,2 ..., n (2)
Formula (3) can be used at this time to classify to training sample data:
In formula: ωTFor the transposed vector of ω, ω2Indicate to after ω modulus again square.
The above problem is solved using Lagrangian:
In formula: αi>=0, i=1,2 ..., n, αiFor Lagrange multiplier.
?And αiUnder the constraint condition of >=0, i=1,2 ..., n, the dual form of Lagrange function is utilized
To Lagrange multiplier αiMaximizing:
Equation (5) due to constraint condition presence, therefore its solution only one.Assuming that its optimal solution isIt can then be found out
Optimal classification function are as follows:
In formula:b*It can be byIt is calculated.
When training sample is linearly inseparable, then it is non-linear to data progress to need to seek a suitable mapping function
Mapping.It is expressed as with letterWherein H is high-dimensional feature space,For high dimensional feature input
Vector.By Mercer condition it is found that if kernel function K (xi,xj) can be write asSo problem
It translates into constraint conditionAnd αiUnder >=0, i=1,2 ..., n, dual-quadratic programming problem is solved:
(8) formula is to solve resulting optimal classification functional expression:
The selection that can be seen that kernel function from above-mentioned expression formula plays a crucial role to the superiority and inferiority of SVM performance.Present invention selection
Radial basis kernel function RBF, that is, K (xi,xj=exp (- γ*(xi,xj)2), γ > 0, γ are the sphere of actions for describing kernel function, are determined
The complexity of model.Introduce slack variable ξi>=0, then constraint condition at this time is by yi(ωxi+ b) >=1, i=1,2 ...,
N becomes:
yi(ω·xi+b)≥1-ξi, i=1,2 ..., n (9)
Corresponding quadratic convex programming problem becomes at this time:
In formula: C is the penalty factor greater than zero, and effect is for weighing the punishment dynamics to wrong sample.
The beneficial effects of the present invention are:
1, the fault diagnosis model and optimization method of rolling bearing are proposed, so that failure diagnostic process expression is clear quasi-
Really, fault diagnosis model is rationally effective；
2, traditional self-adapted genetic algorithm is improved, the upper and lower bound of crossover probability and mutation probability, pole are introduced
The earth improves the local optimal searching ability and global optimizing ability of self-adapted genetic algorithm；
3, using the penalty factor and kernel functional parameter γ of improved self-adapted genetic algorithm Support Vector Machines Optimized, make
The classification prediction effect for obtaining model is optimal.
Detailed description of the invention
Overall flow figure Fig. 1 of the invention
The energy profile of tetra- kinds of states of Fig. 2
The reconstruction signal figure of Fig. 3 bearing outer-ring fault-signal
The fault diagnosis accuracy rate of Fig. 4 GA-SVM, AGA-SVM and tri- kinds of models of IAGA-SVM.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings and specific examples.
Embodiment 1: as shown in Figure 1, a kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM, uses small echo first
The method of variation carries out feature extraction to the fault data of rolling bearing, and is normalized to form training sample simultaneously to it
Training obtains SVM model；Then using improved self-adapted genetic algorithm to the penalty factor and kernel functional parameter of SVM model
γ parameter optimizes processing, the SVM model after being optimized i.e. SVM fault diagnosis model, finally utilizes SVM fault diagnosis mould
Type carries out fault diagnosis to rolling bearing.
Because the process of data acquisition often contains inevitable noise and invalid information, if carried out to initial data
Untreated use, result always will not be satisfactory.Therefore, better experimental result, the present invention utilize in order to obtain
Wavelet transformation carries out feature extraction to the original signal after denoising, to obtain the effective information in data.
Specific step is as follows for the method:
Step1, initialization relevant parameter, are arranged the number of iterations k=0, parameter mainly includes population at individual quantity N, individual
Crossover probability PcWith individual variation probability Pm, algorithm maximum number of iterations etc..
Step2, the fitness value for calculating each individual in group.
Step3, pass through selection, intersection, variation, generation population of new generation, self-adapted genetic algorithm (Adaptive
Genetic Algorithm, AGA) superiority to be that the crossover probability that will be fixed in genetic algorithm and mutation probability carry out linear
Adaptive adjustment.Crossover probability determines the ability of searching optimum of genetic algorithm, and mutation probability determines the office of genetic algorithm
Portion's search capability.But the algorithm is easily trapped into the predicament of local optimum, in order to solve the feelings of group's stagnation as far as possible
Condition, the present invention improve self-adapted genetic algorithm:
In formula: fmaxIndicate maximum fitness value in group, fbiggerIt indicates to participate in two individuals of crossing operation
Biggish fitness value, favgIndicate the average fitness value of group, f indicates the fitness value of current variation individual.Pmax1With
Pmin1Respectively indicate the upper and lower bound of crossover probability, Pmax2And Pmin2The upper and lower bound of mutation probability is respectively indicated, α is one
A constant.It is such to be arranged so that PcAnd PmFitness value in fmaxAnd favgBetween carry out nonlinear adjustment, largely
On the drawbacks of having evaded local convergence.
Step4, step Step2-Step3 is repeated, until reaching maximum number of iterations.
Step5, optimizing terminate, and determine the penalty factor of SVM and the best parameter group of kernel functional parameter γ.
Step6, fault diagnosis will be carried out in the feature vector mentioned input SVM fault diagnosis identifier.
Svm classifier model is used only to solve two classification problems when initial, but commonly more in practice
Classification problem.In order to make svm classifier model that polytypic function may be implemented, need successively to construct the classifier of n two classification,
To achieve the effect that n classifies.The method is theoretically simple and easy, but in practical applications since it needs the circulation that solves
Number is more, and model efficiency is caused to be had a greatly reduced quality, so be not suitable for promoting and applying.The present invention uses the branch based on binary tree structure
Hold the more classification methods of vector machine (DT-SVM).
Assuming that the sample set of n training sample is expressed asxi∈Rn, RnIndicate sample space.yi∈{-
1,1}.When sample set D is linear separability, then (1) formula is a certain hyperplane equation of sample:
ω·xi+ b=0 (1)
In formula: ω is the normal vector of hyperplane, and b is displacement.
Its optimal separating hyper plane must satisfy equation (2):
yi(ωxi+ b) >=1, i=1,2 ..., n (2)
Formula (3) can be used at this time to classify to training sample data:
In formula: ωTFor the transposed vector of ω, | | ω | |2Indicate to after ω modulus again square.
The above problem is solved using Lagrangian:
In formula: αi>=0, i=1,2 ..., n, αiFor Lagrange multiplier.
?And αiUnder the constraint condition of >=0, i=1,2 ..., n, the dual form of Lagrange function is utilized
To Lagrange multiplier αiMaximizing:
Equation (5) due to constraint condition presence, therefore its solution only one.Assuming that its optimal solution isIt can then be found out
Optimal classification function are as follows:
In formula:b*It can be byIt is calculated.
When training sample is linearly inseparable, then it is non-linear to data progress to need to seek a suitable mapping function
Mapping.It is expressed as with letterWherein H is high-dimensional feature space,For high dimensional feature input to
Amount.By Mercer condition it is found that if kernel function K (xi,xj) can be write asSo problem is just
It is converted into constraint conditionAnd αiUnder >=0, i=1,2 ..., n, dual-quadratic programming problem is solved:
(8) formula is to solve resulting optimal classification functional expression:
The selection that can be seen that kernel function from above-mentioned expression formula plays a crucial role to the superiority and inferiority of SVM performance.Present invention selection
Radial basis kernel function RBF, that is, K (xi,xj=exp (- γ*(xi,xj)2), γ > 0, γ are the sphere of actions for describing kernel function, are determined
The complexity of model.Introduce slack variable ξi>=0, then constraint condition at this time is by yi(ωxi+ b) >=1, i=1,2 ...,
N becomes:
yi(ω·xi+b)≥1-ξi, i=1,2 ..., n (9)
Corresponding quadratic convex programming problem becomes at this time:
In formula: C is the penalty factor greater than zero, and effect is for weighing the punishment dynamics to wrong sample.
Embodiment 2: extracting specific rolling bearing fault signal in the present embodiment, specially selection wavelet packet pair
Signal after denoising carries out feature extraction.3 layers of decomposition of wavelet packet will acquire to 8 frequency ranges, then carry out signal reconstruction to it,
Energy value after each frequency range normalized forms a feature vector.The energy of four kinds of each frequency ranges of state is as shown in table 1:
Each band energy table of 1 four kinds of states of table
After normalized, Fig. 2 intuitively describes the Energy distribution situation of four kinds of each frequency ranges of state.
Energy profile corresponding to four kinds of states of rolling bearing has biggish difference, this energy as can be seen from Figure 2
The difference of amount distribution is very helpful to the identification of fault type.
The reconstruction signal of 8 frequency ranges after wherein outer ring fault-signal is decomposed is as shown in Figure 3.
In order to prove the superiority of this paper institute climbing form type, ad hoc meter is tested such as next group of contrast model.Pass through ratio
Compared with the accuracy rate of GA-SVM, AGA-SVM and IAGA-SVM tri- models, ten independent sorting bearing faults, obtained classification is accurate
Rate such as Fig. 4 shows.
By Fig. 4 it can be seen that seeking the SVM failure modes after ginseng using IAGA, Average Accuracy is up to 97.5%, and AGA pairs
The failure modes model and GA that SVM is sought after joining seek the failure modes model after ginseng to SVM, and Average Accuracy is 95% respectively,
And 93.5%, it is much high not as good as the accurate rate of IAGA-SVM disaggregated model.In summary: IAGA-SVM model is with higher
Nicety of grading, and can accurately predict the fault type of rolling bearing.
Above in conjunction with attached drawing, the embodiment of the present invention is explained in detail, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
Put that various changes can be made.
Claims (3)
1. a kind of Fault Diagnosis of Roller Bearings based on IAGA-SVM, it is characterised in that: use the side of Wavelet transformation first
Method carries out feature extraction to the fault data of rolling bearing, and is normalized to form training sample and train to it and obtain
SVM model；Then using improved self-adapted genetic algorithm to the penalty factor of SVM model and kernel functional parameter γ parameter into
Row optimization processing, the SVM model i.e. SVM fault diagnosis model after being optimized, finally using SVM fault diagnosis model to rolling
Bearing carries out fault diagnosis.
2. the Fault Diagnosis of Roller Bearings according to claim 1 based on IAGA-SVM, it is characterised in that: using changing
Into self-adapted genetic algorithm the detailed process of processing is optimized such as to the penalty factor and kernel functional parameter γ of SVM model
Under:
Step1, initialization relevant parameter, are arranged the number of iterations k=0, parameter includes population at individual quantity N, individual intersection probability Pc
With individual variation probability PmAnd maximum number of iterations；
Step2, the fitness value for calculating each individual in group；
Step3, pass through selection, intersect, variation, generating a new generation population:
In formula: fmaxIndicate maximum fitness value in group, fbiggerIt indicates to participate in larger in two individuals of crossing operation
Fitness value, favgIndicate the average fitness value of group, f indicates the fitness value of current variation individual, Pmax1And Pmin1Point
Not Biao Shi crossover probability upper and lower bound, Pmax2And Pmin2The upper and lower bound of mutation probability is respectively indicated, α is a constant；
Step4, step Step2-Step3 is repeated, until reaching maximum number of iterations；
Step5, optimizing terminate, and determine the penalty factor of SVM and the best parameter group of kernel functional parameter γ.
3. the Fault Diagnosis of Roller Bearings according to claim 1 based on IAGA-SVM, it is characterised in that: utilize instruction
Using the more classification methods of support vector machines based on binary tree structure, detailed process when practicing sample training SVM model are as follows:
If the sample set of n training sample is expressed asxi∈Rn, RnIndicate sample space, yi∈ { -1,1 },
When sample set D is linear separability, a certain hyperplane equation of sample are as follows:
ω·xi+ b=0
In formula: ω is the normal vector of hyperplane, and b is displacement, and optimal separating hyper plane must satisfy following formula:
yi(ωxi+ b) >=1, i=1,2 ..., n
Classify at this time to training sample data:
Wherein, ωTFor the transposed vector of ω, | | ω | |2Indicate to after ω modulus again square；
The above problem is solved using Lagrangian:
Wherein, αi>=0, i=1,2 ..., n, αiFor Lagrange multiplier；
?And αiUnder the constraint condition of >=0, i=1,2 ..., n, to Lagrange multiplier αiMaximizing:
Wherein, j=1,2 ..., n；
If its optimal solution isIts optimal classification function can then be found out are as follows:
Wherein,b*It can be byIt is calculated；
When training sample is linearly inseparable, then needs to seek a suitable mapping function and non-linear reflect is carried out to data
It penetrates, is expressed with letter are as follows:Rn→H；Wherein H is high-dimensional feature space,For high dimensional feature input vector,
By Mercer condition it is found that kernel function K (xi,xj) write asProblem is converted into constraint item
PartAnd αiUnder >=0, i=1,2 ..., n, quadratic programming problem is solved:
Solve resulting optimal classification functional expression:
Introduce slack variable ξi>=0, then constraint condition at this time is by yi(ωxi+ b) >=1, i=1,2 ..., n becomes:
yi(ω·xi+b)≥1-ξi, i=1,2 ..., n
Corresponding quadratic convex programming problem becomes at this time:
Wherein, C is the penalty factor greater than zero, for weighing the punishment dynamics to wrong sample.
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| CN112132191A (en) * | 2020-09-01 | 2020-12-25 | 兰州理工大学 | Intelligent evaluation and identification method for early damage state of rolling bearing |
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