CN103064009B  Artificial circuit fault diagnosis method based on wavelet analysis and limited gauss mixed model expectation maximization (EM) method  Google Patents
Artificial circuit fault diagnosis method based on wavelet analysis and limited gauss mixed model expectation maximization (EM) method Download PDFInfo
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 CN103064009B CN103064009B CN201210584648.9A CN201210584648A CN103064009B CN 103064009 B CN103064009 B CN 103064009B CN 201210584648 A CN201210584648 A CN 201210584648A CN 103064009 B CN103064009 B CN 103064009B
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Abstract
Description
Technical field
The present invention relates to a kind of analogcircuit fault diagnosis method based on wavelet analysis and limited gauss hybrid models EM method, belong to Analog Circuit Fault Diagnosis Technology field.
Background technology
Since the beginning of the sixties at the end of the fifties, people have carried out a series of exploration to the automation issues of fault diagnosis.At present, the fault diagnosis of digital circuit has achieved satisfied result, has occurred diagnosis and the Selfadaptive method of mass efficient.But the achievement in research of analog circuit fault diagnosing is unsatisfactory.According to document announcement, although proportion is more than 80% in the electronic device for digital circuit, more than 80% of equipment failure but occurs in mimic channel.Fault in mimic channel is distinguished by its character, can be divided into hard fault and soft fault.Hard fault is also known as large variation fault or bust, and be often referred to the short circuit of element, open circuit etc., it may cause system of serious failure, paralyses even completely, and the feature of this fault is that component value changes under two kinds of extreme cases, and it is a kind of structural damage.Soft fault is also known as departing from fault; refer to that the parameter value of fault element departs from the span of permission along with time or environmental baseline; namely the parameter shift of element exceeds range of tolerable variance; under most cases, they do not make equipment complete failure; but exception or the deterioration of system performance can be caused; the feature of this fault is the state that it may be formed is unlimited, and is easy to obscure with tolerance, and this is one of difficult point of analog circuit fault diagnosing.However, in order to have breakthrough in this respect, in these years establish based on fault dictionary, fuzzy theory, expert system, neural network, support vector machine, information fusion, wavelet analysis, the different faults diagnostic method of the various technology such as population, and good effect is achieved in the practice examining of mimic channel.But, how circuit, from normally there is intermediate state to fault, defines this intermediateness and what kind of it has affect on circuit, how this impact of accurate description, by By consulting literatures, a kind of reasonably method is not up to the present also had to address this problem.
Summary of the invention
In order to solve the technical matters of abovementioned existence, the invention provides one and utilize wavelet analysis, circuit alarm is carried out hierachical decomposition, obtain the signal content of different frequency range, get the composition of its energy faults signal characteristic as fault feature, and then adopt the EM method (maximum expected value method) based on limited gauss hybrid models to carry out the analogcircuit fault diagnosis method of fault category identification.This method solve the limitation of tolerance analog circuit fault diagnosing in the past, achieve good effect.
The object of the invention is to be achieved through the following technical solutions: based on the analogcircuit fault diagnosis method of wavelet analysis and limited gauss hybrid models EM method, its step is as follows:
(1) diagnostictype is defined:
If the set of circuitundertest component parameters is R={R _{1}, R _{2}..., R _{n}, R _{j}nominal value be tolerance is T _{j}, during circuit nonfault, the maximal increment of each component parameters is setting member parameter value height two threshold value: R _{jlow}and R _{jhigh}, then with regard to R _{j}, there are following five kinds of states:
A normal condition: component parameters changes in its tolerance allowed band, namely
The low malfunction of b: component parameters occurs negative increment and exceeds element Low threshold: R _{j}≤ R _{jlow};
The low subhealth state of c: component parameters is between normal condition and low malfunction:
D high malfunction: component parameters occurs negative increment and exceeds element high threshold: R _{j}>=R _{jhigh};
E height subhealth state: component parameters is between normal condition and high malfunction:
(2) selected proper vector:
1. simulate analog circuit.Several times Monte Carlo analysis is performed, image data for often kind of fault type in (1);
2. wavelet decomposition is performed to sampled data, under each wavelet function, calculate the highfrequency energy under each yardstick and the low frequency energy under out to out, generating feature vector;
Described wavelet function is: db2, db3, db5, db9, bior1.3, bior2.2, rbio1.3, rbio2.2, coif1, Haar, sym2;
3. by the step 2. middle proper vector generated, be input in undulatory property function, using formula (1) calculates undulatory property functional value respectively; Choose the wavelet function that undulatory property functional value is minimum;
S is same fault type number of samples, and N is wavelet decomposition scales, X _{i}for wavelet coefficient.
4. the proper vector that the proper vector under the minimum wavelet function of undulatory property functional value is selected as final fault diagnosis is chosen;
(3) carry out EM computing based on limited gauss hybrid models for proper vector, obtain fault diagnosis result.Concrete steps are as follows:
1. according to formula (2), the Gaussian distribution that often kind of fault type is obeyed is calculated;
Wherein, X=[x _{1}, x _{2}..., x _{m}] ^{t}it is m dimensional vector;
U _{j}=[u _{j1}, u _{j2}..., u _{jm}] ^{t}that jth class m ties up average column vector;
2. the previous accumulated probability of often kind of fault type is calculated according to formula (3);
ρ _{j}·G(X;u _{j},∑ _{j}),j=1,2,...,k（3）
3. the probability of arbitrary proper vector is calculated according to formula (4);
4. objective matrix Z is calculated according to formula (5) _{ij}expectation value (Estep in EM method), and calculate maximal possibility estimation (Mstep in EM method) with it.
E(Z _{ij}X _{i};θ _{j})=ρ _{j}·G(X _{i};u _{j},∑ _{j})/p(X _{i})（5）
Wherein,
At calculating u _{j}, ∑ _{j}time, still use formula (5), only the E produced need be replaced Z _{ij}, iterate, until convergence.
5. press formula (6) after method convergence and calculate Z _{ij}.
At Z _{ij}in, i is sample number, and j is fault category numbering;
6. according to Z _{ij}failure judgement classification, works as Z _{ij}when=1, represent that certain element exists certain fault, Z _{ij}=0 represents that this element does not exist this kind of fault.
Beneficial effect of the present invention: 1, the present invention carrys out rendering circuit from the normal intermediate state to existing fault by introducing " inferior health " concept, be defined as subhealth state, and increase inferior health diagnostictype in an experiment, solve the limitation of tolerance analog circuit soft fault diagnosis in the past.2, Soft Fault Diagnosis of Analog Circuit problem and tolerance problem are the bottleneck problems of restriction analog circuit fault diagnosing always, the present invention proposes to select wavelet energy as proper vector, gauss hybrid models and EM algorithm (greatest hope valuebased algorithm) are combined and carries out failure modes, because gauss hybrid models can approach any population distribution function preferably, and the proper vector that mimic channel often plants fault has respective feature, the present invention does diagnosis modeling by gauss hybrid models better can describe often kind of fault signature distribution situation, preferably resolve fault model projection overlap problem, EM algorithm is adopted to carry out failure modes, for the soft fault diagnosis of mimic channel provides new approaches.Wherein, E step: the expectation value of estimating target classification results, provides current parameter estimation; M walks: reappraise distribution parameter, to make the likelihood of data maximum, provide the expectation estimation of target classification result.The estimates of parameters that M step finds is used to next E and walks in calculating, and this process constantly hockets, thus reaches the object of fault diagnosis.
Accompanying drawing explanation
Centered by Fig. 1, frequency is the circuit diagram of 23kHz SallenKey second order voltage controlled voltage source bandpass filter.
Fig. 2 is that the low transactional analysis of C1 exports response diagram.
Fig. 3 is the BP graph of errors of first CUT.
Fig. 4 is the Feedback BP graph of errors of first CUT.
Fig. 5 is for a CUT distinct methods diagnosis comparison diagram.
Fig. 6 is biquad filter circuit diagram.
Fig. 7 is the BP graph of errors of second CUT.
Fig. 8 is the Feedback BP graph of errors of second CUT.
Fig. 9 is for two CUT distinct methods diagnosis comparison diagrams.
Figure 10 is based on the Troubleshooting Flowchart of gauss hybrid models EM algorithm
Embodiment
1. technical solution of the present invention introduces " inferior health " concept for mimic channel from the normal phenomenon to there is intermediate state fault: subhealth state is a kind of free band " disease " state between health status and morbid state, the diagnosis of its state is difficult to define, and system band " disease " to run the loss brought may be fatal.Therefore, the subhealth state concern that people should be caused enough.For tolerance analog circuit, component diagnostics type definition is as follows:
If the set of circuitundertest component parameters is R={R _{1}, R _{2}..., R _{n}, R _{j}nominal value be tolerance is T _{j}, during circuit nonfault, the maximal increment of each component parameters is setting member parameter value height two threshold value: R _{jlow}(be generally 0.5R _{j}) and R _{jhigh}(be generally 1.5R _{j}), then with regard to R _{j}, there are following five kinds of states:
1) normal condition: component parameters changes in its tolerance allowed band, namely
2) low malfunction: component parameters occurs negative increment and exceeds element Low threshold: R _{j}≤ R _{jlow};
3) low subhealth state: component parameters is between normal condition and low malfunction:
4) high malfunction: component parameters occurs negative increment and exceeds element high threshold: R _{j}>=R _{jhigh};
5) high subhealth state: component parameters is between normal condition and high malfunction:
The low inferior health of circuit component and high subhealth state are referred to as the inferior health of circuit component.
2. wavelet transformation extracts fault feature
The selection of 2.1 proper vectors
Because increasing mimic channel adopts closed or integrated form design encapsulation, therefore adopt output voltage signal as feature extraction source, by obtaining time domain and the frequency domain information of this moment output voltage to the wavelet decomposition of voltage data.First emulate circuit, the magnitude of voltage chosen in output voltage signal under the different frequency that can describe various fault status information is sampled.During due to circuit malfunctions, energy in each frequency band can change, sampled data is after multiscale wavelet function decomposition, the low frequency coefficient under the high frequency coefficient of each yardstick and out to out can be obtained, with the squared absolute value of each multiscale wavelet coefficient of dissociation sequence with for element (being called corresponding energy here) constitutive characteristic vector.Comprise the highfrequency energy E under each Scale Decomposition _{k}(k=1,2 ...) and out to out under low frequency energy E _{0}if out to out is n, then the highfrequency energy E under k yardstick _{k}be expressed as:
E _{k}=∑(E _{k}) ^{2},(k=1,2,...,n)
Low frequency energy E under out to out _{0}be expressed as:
E _{0}=∑(d _{0})2
Wherein, d _{0}for the low frequency coefficient under out to out, d _{k}for the high frequency coefficient under k Scale Decomposition.Because the energy in frequency band each during circuit malfunctions can change, therefore using the proper vector of the energy aggregation l of each yardstick as fault diagnosis.Fault feature vector can be expressed as:
l＝E _{0},E _{1},E _{2},...,E _{n})
Choosing of 2.2 wavelet functions
Wavelet technique extracts in the compression of higherdimension fault signature data and sensitive signal and is widely used, but wavelet function choose the unified standard of neither one.At present existing scholar calculated by the wavelet decomposition of actual samples signal data, proper vector, undulatory property function ratio comparatively etc. technology choosing of wavelet function is studied.Result shows, the correct recognition rata of different wavelet function to fault diagnosis also exists difference, according to the quality of decomposing the stability obtaining proper vector and can differentiate wavelet function.Whether stability is determined by undulatory property functional value, and functional value is less shows that proper vector is more stable.
Undulatory property function formula is as follows:
S is the number of times of same fault sampling, and N is wavelet decomposition scales, X _{i}for wavelet coefficient.
Adopt different wavelet function to carry out wavelet decomposition to sampled data, obtain proper vector, specific implementation step is as follows:
1) emulate mimic channel, often kind of fault type performs repeatedly Monte Carlo analysis, image data.
2) sampled data is performed to the wavelet decomposition of different wavelet function, under each wavelet function, calculate the low frequency energy under the little high frequency of each yardstick and out to out, generating feature vector.
3) according to proper vector and undulatory property function, calculate the undulatory property functional value under different wavelet function, choose undulatory property functional value minimum for optimal wavelet function.
4) using the proper vector of the proper vector under the most applicable wavelet function as final fault diagnosis.
3. based on the EM method of limited gauss hybrid models
Data set is D={X _{i} i=1,2 ..., n}, wherein n is data amount check, and the dimension of each data is m, i.e. X _{i}=[x _{i1}, x _{i2}..., x _{im}] ^{t}.Tentation data is divided into k class, Z={z _{ij} i=1,2 ..., n; J=1,2 ..., k}, if z _{ij}=1 represents data X _{i}data belong to jth class; Otherwise, z _{ij}=0 represents data X _{i}data do not belong to jth class.
Each class defines a Gaussian distribution:
Wherein, X=[x _{1}, x _{2}..., x _{m}] ^{t}it is m dimensional vector;
U _{j}=[u _{j1}, u _{j2}..., u _{jm}] ^{t}that jth class m ties up average column vector;
Prior probability is accumulated as:
ρ _{j}·G(X;u _{j},∑ _{j}),j=1,2,...,k
Any one X _{i}probability be:
Calculate Z _{ij}expectation value (Estep), and calculate maximal possibility estimation (Mstep) with it.
E(Z _{ij}X _{i};θ _{j})=ρ _{j}·G(X _{i};u _{j},∑ _{j})/p(X _{i})；
Wherein,
At calculating u _{j}, ∑ _{j}time, still use formula above, only the E produced need be replaced Z _{ij}, iterate, until convergence.Z is calculated as follows after method convergence _{ij}, the object of Fault Identification can be reached.
Z
_{ij}=1 and if only if
Z
_{ij}=0 and if only if
At Z _{ij}in, i is sample number, and j is fault category numbering;
According to Z _{ij}failure judgement classification, Z _{ij}=1 represents that certain element exists certain fault, Z _{ij}=0 represents that this element does not exist this kind of fault.Concrete judgement flow process is as shown in Figure 10:
(1) assumed fault type k=4, error ε=0.0001, Offered target classification matrix Z _{ij};
(2) compute classes mean vector u _{jl}, covariance matrix ∑ _{j};
(3) primary iteration number of times t=0 is set, and initialization u _{j}(t), ∑ _{j}(t), ρ _{j}(t), p (X _{i}(t));
(4) E (Z is calculated _{ij}(t)  X _{i}; θ _{j});
(5) u is calculated _{j}(t+1), ∑ _{j}(t+1), ρ _{j}(t+1), p (X _{i}(t+1));
(6) 6, E (Z is calculated _{ij}(t+1)  X _{i}; θ _{j}), Result=Sum ( E (Z _{ij}(t+1)  X _{i}; θ _{j})E (Z _{ij}(t)  X _{i}; θ _{j}) )≤ε
(7) if Result=1 time, terminate;
(8) if Result ≠ 1 time, E (t)=E (t+1), returns step (5).
4. performing step
4.1 first CUT
1) circuit simulation.Adopt centre frequency to be that 23kHz SallenKey second order voltage controlled voltage source bandpass filter carries out emulation experiment, as shown in Figure 1, wherein the nominal value of each element marks circuit all in the drawings, and in circuit, each resistance value tolerance gets 5%, and capacitance tolerance gets 10%.Because the change of some component parameters is little on the impact of output signal frequency, so advanced line sensitivity analysis before the diagnosis, can is C1, C2, R2, R3 by the components and parts diagnosed in accompanying drawing 1.C1 is low, C1 is high, C2 is low, C2 is high, R2 is low, R2 is high, R3 is low, R3 is high and inferior health nine kinds of fault modes and normal totally ten kinds of diagnostic modes describe as shown in table 1.
Table 1 first CUT fault diagnosis type specification
2) data sampling.Adopting Pspice10.5 simulation software to add an amplitude to circuit is the pulse excitation signal of 5V, low to C1 by PSpice, C1 is high, C2 is low, C2 is high, R2 is low, R2 is high, R3 is low, R3 is high and normal totally nine kinds of diagnostic modes are simulated, in order to image data is convenient, be that the Circuits System subhealth state that 5V sports under the pulse excitation signal of 10V is simulated by supply voltage by amplitude, low for C1, by smallsignal transactional analysis, circuit can be obtained and export response diagram, as shown in Figure 2, wherein horizontal ordinate is frequency, and ordinate is test point voltage.
From accompanying drawing 2, the change of circuit test point voltage when C1 is low is the most obvious for affecting between 1K ~ 10MHz frequency, therefore choose the frequency that 1KHz, 10kHz, 20kHz, peak(crest voltage is corresponding), 30kHz, 40kHz, 50kHz, 60kHz, 70kHz, 80kHz, 90kHz, 100kHz, 1MHz, 10MHZ corresponding numerical value composition 14 dimension original data vector.Consider resistance and capacitance tolerance, 30 MC (Monte Carlo) are carried out respectively to often kind of state and analyzes, and extract fault signature, as training sample, remain 10 times as test sample book 20 times.Partial fault primary data is as shown in table 2.
Table 2 first CUT partial fault primary data
3) fault signature extracts.Common wavelet basis function has: Haar, Db, Coif1, sym, bior, Rbio etc., Matlab7.0 is adopted to carry out to raw data the decomposition that yardstick is the multiple wavelet function of 3 respectively herein, obtain proper vector, and then calculate undulatory property functional value, in fault set out of order undulatory property functional value with as shown in table 3.
Table 3 first CUT undulatory property functional value table
As can be seen from Table 3, the extraction of the most applicable fault characteristic signals of Haar wavelet basis function, obtains the proper vector of fault diagnosis according to this.Partial fault feature samples value is as shown in table 4.
Table 4 first CUT partial fault feature samples value
4) based on the fault diagnosis of limited gauss hybrid models EM method.According to the proper vector initiation parameter of fault diagnosis, wherein intrinsic dimensionality m=4, fault category k=10, tolerance is 1e4, Z is objective matrix, i.e. Z={Z _{ij} i=1,2 ..., n; J=1,2 ..., k}, if data X _{i}data belong to jth class, z _{ij}=1; Otherwise, z _{ij}=0.Iterated by Estep and Mstep in EM method, the difference gradually between outstanding data, until convergence.After iteration convergence, Data classification completes, thus reaches the object of fault diagnosis.The basis for estimation of first CUT fault type is as shown in table 5:
The basis for estimation table of table 5 first CUT fault type
5) contrast experiment.The technology that analog circuit fault diagnosing is conventional has BP neural network, RBF neural, support vector machine etc., in order to verify the validity of method when diagnosing and the speed of speed of convergence in literary composition, are respectively used to Feedback BP neural network and RBF neural training by identical proper vector sample.All experiments are all carried out in the computing machine of 3GHzCPU, 2GB internal memory, and each experiment software and hardware condition is all identical.
Basic BP Neural Network Structure Design: 41110 trilayers of BP neural network that this experimental selection is basic, is normalized to each input quantity [1,1], and data transformation is as follows to the formula of [1,1]:
Wherein: x _{mid}=0.5 (x _{max}+ x _{min}), x _{i}for sample set, x _{min}for the minimum value of sample changed, x _{max}for the maximal value of sample changed.Graph of errors as shown in Figure 3.
Feedback BP Neural Network Structure Design: Feedback BP Neural Network Structure Design: this experimental selection output layer band
Feedback three layers of BP neural network, each input quantity is normalized to [1,1], with formula (9) by data transformation to [1,1].
Proper vector is 4 dimension data, and diagnostictype number is 10, and therefore the output layer neuron of network is 10,
Input layer is 14 (comprising 4 characteristic vector data nodes, 10 output layer Error Feedback nodes), and through many experiments, when result shows that neural network structure is 141210, the training time is short, fast convergence rate.Graph of errors as shown in Figure 4.
This method and contrast experiment's diagnostic result as shown in table 6, diagnosis comparison diagram is as shown in Figure 5.
Table 6 first CUT contrast experiment diagnostic result
4.2 second CUT
1) circuit simulation.Below with biquadratic filtering circuit for diagnosis example, verify the superiority of proposed analogcircuit fault diagnosis method.Biquadratic filter circuit construction as shown in Figure 6.
In circuit, the nominal value of each element is as shown in table 7, according to sensitivity analysis, R1, C2 change time the frequency response of circuit is had the greatest impact, component value depart from its nominal value ± 50%, fault type is as shown in table 7.All circuit analysis emulation all uses OrCAD10.5 circuit simulating software.
Table 7 second CUT fault diagnosis type specification
2) data sampling.Adopting Pspice10.5 simulation software, to add an amplitude to circuit be the pulse excitation signal of 5V, in order to image data is convenient, is that the Circuits System subhealth state that 5V sports under the pulse excitation signal of 3V is simulated by supply voltage by amplitude.The output node contact potential series under each diagnostictype is gathered according to table 7.Consider resistance and capacitance tolerance, 30 MC (Monte Carlo) are carried out respectively to often kind of state and analyzes, and extract fault signature, as training sample, remain 10 times as test sample book 20 times.Partial fault primary data is as shown in table 8.
Table 8 second CUT partial fault primary data
3) fault signature extracts.According to the undulatory property of formula (4) counting circuit.Undulatory property functional value under different wavelet basis is as shown in table 9.
Table 9 second CUT undulatory property functional value table
As can be seen from Table 8, the extraction of the most applicable fault characteristic signals of db2 wavelet basis function, obtains the proper vector of fault diagnosis according to this.Partial fault feature samples value is as shown in table 10.
Table 10 second CUT partial fault feature samples value
4) based on the fault diagnosis of limited gauss hybrid models EM method.Obtain fault diagnosis data according to mentioned above, initiation parameter, wherein intrinsic dimensionality m=4, fault category k=6, error is 1e4, Z is objective matrix, i.e. Z={z _{ij} i=1,2 ..., n; J=1,2 ..., k}, if data X _{i}data belong to jth class, z _{ij}=1; Otherwise, z _{ij}=0.Iterated by Estep and Mstep in EM method, until convergence, the difference between data is highlighted.After iteration convergence, Data classification completes, thus reaches the object of fault diagnosis.The basis for estimation of second CUT fault type is as shown in table 11:
The basis for estimation table of table 11 second CUT fault type
5) contrast experiment.By the experimental data of second CUT according to 5 under 4.1 joints) be contrast experiment, wherein BP network structure is 466, and the BP network structure of band feedback is 1086.The BP graph of errors that BP and band feed back is respectively as shown in accompanying drawing 7,8.This method and contrast experiment's diagnostic result as shown in table 12, diagnosis comparison diagram is as shown in Figure 9.
Table 12 second CUT contrast experiment diagnostic result
5. experimental analysis
1) as can be seen from table 6 and table 12, in first CUT, low and the low two kinds of faults of R3 of C1, in second CUT, the normal and low two kinds of faults of R1, three laboratory diagnosis rates are not high herein, its reason is that mimic channel allows tolerance to exist, there is data overlap phenomenon between different faults categorical data, fluctuate between fault type data of the same race still very large, this is also one of reason of Soft Fault Diagnosis of Analog Circuit difficulty.Make a concrete analysis of as follows:
Feedback BP Neural Network Diagnosis rate is have employed output layer band feedback arrangement higher than BP neural network reason, the difference of output layer nodal value and expectation value is fed back to input layer, and then obtain the optimization of weights and threshold, exactly because also have employed feedback arrangement to result in the complicated of network structure, add Diagnostic Time.
It is that diagnostic data exists overlapping phenomenon that this method is obviously better than other two kinds of method causes, because gauss hybrid models can approach any population distribution function preferably, and the proper vector that mimic channel often plants fault has respective feature, therefore, do diagnosis modeling with gauss hybrid models and better can describe often kind of fault signature distribution situation, and then reach good diagnosis effect.
2) according to testing above, as can be seen from Fig. 3 to Fig. 5 with table 6 and Fig. 7 to Fig. 9 and table 12, for first each fault type of CUT and second CUT, BP is not high with the fault diagnosis rate of band Feedback BP, and iteration reaches target error value 4000 times not yet, and Diagnostic Time is longer.By two CUT experimental verifications, method diagnostic result in this paper is obviously better than BP and band Feedback BP.
3) because the weights of BP and band Feedback BP are generated by random function initialization, therefore BP and band Feedback BP diagnostic result have randomness, and this method has stability while having higher diagnosis, repeatedly diagnoses, and comes to the same thing.
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