CN102222151A - Analog circuit fault prediction method based on ARMA (Autoregressive Moving Average) - Google Patents

Abstract

The invention discloses an analog circuit fault prediction method based on ARMA (Autoregressive Moving Average), which comprises the following steps: extracting a plurality of characteristic quantities of a plurality of measuring points of an analog circuit to form a characteristic vector which can characterize fault information; utilizing an ARMA model to predict the characteristic vector to obtain a predicted characteristic vector; using the weighting Mahalanobis distance to calculate the distance between the obtained characteristic vector and a characteristic vector set in a circuit fault-free tolerance range; comparing the calculated distance and the maximum value of the Mahalanobis distance in the fault-free tolerance range, and converting the deviation degree of the calculated distance and the maximum value of the Mahalanobis distance to a fault occurring rate; and more intuitively monitoring the healthy state of the analog circuit. By experiment verification, the method can be used for better predicting the health state of the analog circuit, has a high fault detection rate, and can be used for the early monitoring of the analog circuit fault well.

Description

A kind of analog circuit fault Forecasting Methodology based on autoregressive moving average

Technical field

The invention belongs to the electric signal processing technology field, more specifically say, relate to a kind of analog circuit fault Forecasting Methodology based on autoregressive moving average.

Background technology

At present, mimic channel has been widely used in various aspects such as automatic control, measurement instrument, military project, and along with development of electronic technology, mimic channel constitutes electronic system and also becomes increasingly complex, correction maintenance and periodic maintenance will be paid the upkeep cost of great number, and be no longer suitable.Event is necessary carries out failure prediction to mimic channel, thereby looks the feelings maintenance.

Also very abundant about the research of analog circuit fault Forecasting Methodology both at home and abroad at present, wherein autoregressive moving average (ARMA) model is the classical way of System Discrimination and prediction, its model is more flexible, and precision of prediction is higher, existing application widely aspect the analog circuit fault prediction.

As on 03 23rd, 2011 Granted publications, notification number be CN101329697B, name to be called " a kind of method for predicting analog circuit state based on immingle algorithm " Chinese invention patent be exactly a kind of analog circuit fault Forecasting Methodology based on autoregressive moving average, what its prediction obtained is the analog circuit state value.

Yet the just numerical value of characteristic quantity that just utilizes arma modeling to dope separately, and fail intuitively the health status of these numerical value and mimic channel to be interrelated, so whether the characteristic quantity numerical value that need predict is converted to and can intuitively reflects the amount of mimic channel health status, thereby be easy to exist fault to judge to mimic channel.

Summary of the invention

The objective of the invention is to overcome the defective that prior art utilizes the numerical value of ARMA forecast model prediction can not be intuitively to interrelate with the health status of mimic channel separately, a kind of analog circuit fault Forecasting Methodology based on autoregressive moving average is provided, to monitor the health status of mimic channel more intuitively, well analog circuit fault is carried out early monitoring.

For achieving the above object, the present invention is based on the analog circuit fault Forecasting Methodology of autoregressive moving average, it is characterized in that, may further comprise the steps:

(1), at the physical simulation circuit, select a plurality of measuring points, each measuring point is selected one or more characteristic quantities, these characteristic quantities constitute the proper vector that characterizes failure messages;

Mimic channel is carried out repeatedly the Monte Carlo analyze, obtain the many eigenvectors of mimic channel in the non-fault range of tolerable variance, these proper vector constitutive characteristic vector sets; Calculate mimic channel in the non-fault range of tolerable variance each eigenvectors and the mahalanobis distance between the set of eigenvectors, and obtain mahalanobis distance maximal value in the non-fault range of tolerable variance;

(2), the proper vector on each time point in mimic channel actual motion a period of time is extracted, and, utilize autoregressive moving average (ARMA) model that it is predicted, obtain the predicted characteristics vector as raw data;

(3), calculate the weight of each characteristic quantity;

(4), according to the weight of each characteristic quantity of obtaining, utilize weighting mahalanobis distance method to calculate the predicted characteristics vector of acquisition and the weighting mahalanobis distance between the set of eigenvectors of mimic channel in the non-fault range of tolerable variance;

(5), the value of the weighting mahalanobis distance that obtains and the mahalanobis distance maximal value in the non-fault range of tolerable variance are compared, the irrelevance with both is converted to the health status that rate of breakdown is monitored mimic channel.

Goal of the invention of the present invention is achieved in that

A plurality of characteristic quantities that the present invention extracts a plurality of measuring points of mimic channel constitute the proper vector that can characterize failure message, utilize arma modeling that it is predicted and obtain the predicted characteristics vector, utilize the weighting mahalanobis distance to calculate the proper vector of prediction acquisition and the distance between the interior set of eigenvectors of circuit non-fault range of tolerable variance again, by with the non-fault range of tolerable variance in the maximal value of mahalanobis distance compare, both irrelevances are converted to rate of breakdown, monitor the health status of mimic channel more intuitively.Checking by experiment, the present invention can well predict the health status of mimic channel, fault recall rate height, and can well be used for the early monitoring of analog circuit fault.

The mahalanobis distance method of discrimination is the sample that newly records is discerned and to be judged that it also is being widely used aspect pattern recognition classifier and the fault diagnosis according to the characteristic quantity of the sample that observes.When yet complicated mimic channel electronic system breaks down, the information that characterizes malfunction has a lot of signals, extract single measuring point or single voltage signal indication circuit fault signature to greatest extent sometimes, each characteristic quantity susceptibility difference when mimic channel breaks down in addition, when utilizing traditional mahalanobis distance, do not consider the difference of each characteristic quantity importance, its importance all is considered as unanimity, but in actual applications, the importance difference of each characteristic quantity.Therefore, in the present invention, extract a plurality of characteristic quantities of a plurality of measuring points of mimic channel, and take weight by the calculated characteristics amount, give bigger weight to the characteristic quantity of mimic channel sensitivity, improve the recall rate of analog circuit fault, thereby better the health status of mimic channel is predicted in conjunction with arma modeling more on this basis.

Description of drawings

Fig. 1 is the process flow diagram that the present invention is based on the analog circuit fault Forecasting Methodology of autoregressive moving average;

Fig. 2 is physical simulation circuit theory diagrams of checking analog circuit fault Forecasting Methodology of the present invention;

Fig. 3 is a predicted value and the measured value comparison diagram that utilizes arma modeling to predict.

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described, so that those skilled in the art understands the present invention better.What need point out especially is that in the following description, when perhaps the detailed description of known function and design can desalinate main contents of the present invention, these were described in here and will be left in the basket.

Embodiment

Fig. 1 is the process flow diagram that the present invention is based on the analog circuit fault Forecasting Methodology of autoregressive moving average.

Step shown in Figure 1 does not repeat them here with the content unanimity in the summary of the invention.

1, the mahalanobis distance maximal value of calculating in the non-fault range of tolerable variance

Mahalanobis distance is proposed by India statistician Mahalanobis (P.C.Mahalanobis), the covariance distance of expression data.It is the minimum distance of a sample of a kind of effective calculating and a sample set " center of gravity ", perhaps calculates the method for two unknown sample collection similarities.Mahalanobis distance can be measured the distance between observation sample and known sample easily.

In this enforcement, establish a plurality of measuring points of selecting mimic channel, each measuring point is selected one or more characteristic quantities, altogether m characteristic quantity.

Mimic channel is carried out n Monte Carlo analyze, obtain the n eigenvectors of mimic channel in the non-fault range of tolerable variance, this n eigenvectors constitutive characteristic vector set is n * m matrix X.

Calculate mimic channel each eigenvectors x in the non-fault range of tolerable variance _i, i=1,2 ..., n and set of eigenvectors, i.e. mahalanobis distance d between n * m matrix X _i:

$d_i^2=\frac{1}{m^2}[x_i-\stackrel{\‾}{x}]C_X^{-1}{[x_i-\stackrel{\‾}{x}]}^{\′}---\left(1\right)$

Wherein, x _iBe the concentrated i eigenvectors of proper vector,

Be the center of gravity of matrix X,

Inverse matrix for the covariance matrix of matrix X.The center of gravity of matrix X For:

$\stackrel{\‾}{x}=\frac{1}{m}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i$

Covariance matrix C _XFor:

$C_X=\frac{1}{m-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[x_i-\stackrel{\‾}{x}]{[x_i-\stackrel{\‾}{x}]}^{\′}$

At n mahalanobis distance d _iIn find out maximal value, promptly obtain the mahalanobis distance maximal value d in the non-fault range of tolerable variance _Max

2, obtain the predicted characteristics vector

Proper vector on each time point in mimic channel actual motion a period of time is extracted, and, utilized autoregressive moving average (ARMA) model that it is predicted, obtain predicted characteristics vector y as raw data.

3, calculate the weight of each characteristic quantity

Because in the mimic channel of reality, proper vector is to each element, and is all different as the susceptibility of electric capacity, resistance, inductance etc., certainly the susceptibility of characteristic quantity to each element all calculated, and calculates mean value again as the susceptibility to entire circuit.But in real work, electronic product becomes increasingly complex.Element is very many in the circuit, and such method is less feasible.

Given this, in the present embodiment, will be in the mimic channel operational process, when the value of the actual proper vector of measuring and circuit non-fault the departure degree of the value of proper vector as this moment characteristic quantity to the susceptibility of circuit, a kind of changeable weight analytical approach based on susceptibility has been proposed, though do not know which element of circuit is out of order this moment, but the susceptibility that calculates is exactly the susceptibility at the element that breaks down this moment, the weight of utilizing method of weighted mean to calculate again just makes has given bigger weight to the characteristic quantity of the element sensitivity that breaks down this moment, makes that the fault recall rate is higher.

If the proper vector of extracting during the mimic channel non-fault is t=(t ₁, t ₂..., t _m), after mimic channel actual motion a period of time, utilize autoregressive moving average (ARMA) model that it is predicted, obtain predicted characteristics vector y=(y ₁, y ₂, y _m), the susceptibility of i characteristic quantity is defined as:

s _i＝|y _i-t _i|/t _i

Utilize calculated with weighted average method to go out the weight of i characteristic quantity again:

w _i＝s _i/(s ₁+s ₂+…+s _m)

By following formula as can be known essence will give bigger weight to the characteristic quantity of circuit sensitive, make that the fault recall rate of system is higher.

4, the weighting mahalanobis distance between calculating predicted characteristics vector and the set of eigenvectors

The weight matrix W that the weight of characteristic quantity constitutes is:

$W=\left[\begin{array}{cccc}{w}_1,& 0,& ...& 0\\ 0,& w_2& ...& 0\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ 0,& 0& ...& w_m\end{array}\right]$

Obtain predicted characteristics vector y and the set of eigenvectors of mimic channel in the non-fault range of tolerable variance, i.e. weighting mahalanobis distance between n * m matrix X;

$d_{\mathrm{forecast}}^2=[y-\stackrel{\‾}{x}]{\mathrm{WC}}_X^{-1}W{[y-\stackrel{\‾}{x}]}^{\′}---\left(2\right)$

5, calculate rate of breakdown

In mimic channel, extract a plurality of characteristic quantities of its a plurality of measuring points, after with arma modeling it being predicted, utilize set of eigenvectors in proper vector that prediction that the weighting mahalanobis distance calculates obtains and the non-fault range of tolerable variance, promptly between n * m matrix X apart from d _Forecast, can't whether break down with mimic channel intuitively interrelates, so weighting mahalanobis distance d _ForecastBe converted into the rate of breakdown of mimic channel, express the health status of mimic channel more intuitively.

Value d with the weighting mahalanobis distance that obtains _ForecastWith the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxCompare, both irrelevance is converted to the health status that rate of breakdown is monitored mimic channel.In the present embodiment, the rate of breakdown p of mimic channel is defined as:

From (3) formula as can be seen, the value d of the weighting mahalanobis distance that obtains _ForecastLess than the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxThe time, think that mimic channel is normal at this moment, rate of breakdown is 0; Value d when the weighting mahalanobis distance that obtains _ForecastGreater than the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxThe time, the value d of weighting mahalanobis distance _ForecastWith the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxBetween the degree that departs from the major break down incidence is also big more more, conform to actual conditions, and think and surpassed mahalanobis distance maximal value d in the non-fault range of tolerable variance when irrelevance _MaxThe time, it just is 1 that fault is sent out rate.

It is just far away more to show that when rate of breakdown is big more mimic channel departs from normal state, when being 0～0.1, rate of breakdown shows that circuit state is good, can normally move, rate of breakdown is that 0.1～0.5 o'clock circuit departs from normal condition, should strengthen the monitoring of every operating index, rate of breakdown is for surpassing at 0.5 o'clock, and we just should give the attention of height, in time take appropriate measures and the analysis circuit failure cause, prevent the further expansion of fault harm.

Case verification

Fig. 2 is physical simulation circuit theory diagrams of checking Forecasting Methodology of the present invention.Among Fig. 2, this mimic channel comprises that 6 operational amplifiers and resistance R 1～12, capacitor C 1～4 form.Test point t1～12 are arranged, and according to the characteristic of this mimic channel, selecting resistance R 9 is fault element, it is 0～20% that its parameter variation range is set, and fault type is that parameter increases gradually, electric capacity and resistance tolerance all be taken as ± and 10%, the selection amplitude is 2v, and frequency is the sinusoidal signal input of 1k.

Step 1: the peak I 2 of selecting electric current between the peak I 1 of electric current between peak value V1, the V2 of measuring point t8, t12 two point voltages and wavelet character amount E1, E2 and measuring point t7, t8 and measuring point t11, t12 is as characteristic quantity, these characteristic quantities constitute the proper vector [V1 that characterizes failure message, V2, I1, I2, E1, E2].Wherein, wavelet character amount E1, E2 chooses ' db5 ' small echo carries out the energy of the low frequency coefficient that extracts behind 3 layers of wavelet analysis to the magnitude of voltage of 2 of t8, t12.

This mimic channel is carried out 30 Monte Carlos analyze, obtain 30 eigenvectors of mimic channel in the non-fault range of tolerable variance, this 30 eigenvectors constitutive characteristic vector set is 30 * 6 matrix X.

By formula (1) obtains the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxBe 0.5502.

Step 2: the value of extracting circuit R9 each characteristic quantity on 50 time points in the increase process gradually in 0～20%, each characteristic quantity on former respectively 40 time points is imported as raw data, utilize arma modeling to carry out the prediction of 10 steps, each characteristic quantity that obtains predicting, and predicted composition proper vector.In this example, be example with the characteristic quantity E2 of measuring point t12, the characteristic quantity E2 on preceding 40 time points is imported as raw data, back 10 points verify, its predicted value and measured value more as shown in Figure 2.As can be seen from Figure 2, predicted value and measured value error are very little, and simultaneously, the prediction step number is many more, and error increases gradually.

Step 3: the value of the proper vector that obtains according to step 2 actual prediction, utilize in the present embodiment changeable weight analytic approach based on susceptibility to obtain the weight of the characteristic quantity that extracted, as shown in table 1.

Table 1

Step 4:, obtain predicted characteristics vector y and the set of eigenvectors of mimic channel in the non-fault range of tolerable variance, i.e. weighting mahalanobis distance d between 30 * 6 matrix X according to the weight of each characteristic quantity that obtains _Forecast

Table 2

Step 5: utilize formula (3), failure rate conversion method promptly of the present invention is with the value d of the weighting mahalanobis distance that obtains _ForecastWith the mahalanobis distance maximal value d in the non-fault range of tolerable variance _MaxIrrelevance be converted to the reflection malfunction rate of breakdown, as shown in table 3.

Table 3

After table 3 was converted to rate of breakdown as can be seen, the rate of breakdown that the weighting mahalanobis distance obtains was all very high and surpassed 0.5, and just should take appropriate measures analyzing failure cause this moment.

From this example, we as can be seen the present invention can well predict fault recall rate height, and can well be used for the early monitoring of analog circuit fault to the health status of mimic channel.

Although above the illustrative embodiment of the present invention is described; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various variations appended claim limit and the spirit and scope of the present invention determined in, these variations are conspicuous, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (4)

1. the analog circuit fault Forecasting Methodology based on autoregressive moving average is characterized in that, may further comprise the steps:

(1), at the physical simulation circuit, select a plurality of measuring points, each measuring point is selected one or more characteristic quantities, these characteristic quantities constitute the proper vector that characterizes failure messages;

Mimic channel is carried out repeatedly the Monte Carlo analyze, obtain the many eigenvectors of mimic channel in the non-fault range of tolerable variance, these proper vector constitutive characteristic vector sets; Calculate mimic channel in the non-fault range of tolerable variance each eigenvectors and the mahalanobis distance between the set of eigenvectors, and obtain mahalanobis distance maximal value in the non-fault range of tolerable variance;

(2), the proper vector on each time point in mimic channel actual motion a period of time is extracted, and, utilize autoregressive moving average (ARMA) model that it is predicted, obtain the predicted characteristics vector as raw data;

(3), calculate the weight of each characteristic quantity;

(4), according to the weight of each characteristic quantity of obtaining, utilize weighting mahalanobis distance method to calculate the predicted characteristics vector of acquisition and the weighting mahalanobis distance between the set of eigenvectors of mimic channel in the non-fault range of tolerable variance;

(5), the value of the weighting mahalanobis distance that obtains and the mahalanobis distance maximal value in the non-fault range of tolerable variance are compared, the irrelevance with both is converted to the health status that rate of breakdown is monitored mimic channel.

2. the analog circuit fault Forecasting Methodology based on autoregressive moving average according to claim 1 is characterized in that, the weight of described each characteristic quantity of calculating of step (3) is:

The proper vector of extracting when the mimic channel non-fault is t=(t ₁, t ₂..., t _m), actual prediction gained proper vector is y=(y this moment ₁, y ₂, y _m), then the susceptibility of i characteristic quantity is:

s _i＝|y _i-t _i|/t _i；

Utilize calculated with weighted average method to go out the weight of i characteristic quantity:

w _i＝s _i/(s ₁+s ₂+…+s _m)。

3. the analog circuit fault Forecasting Methodology based on autoregressive moving average according to claim 2 is characterized in that, set of eigenvectors is n * m matrix X;

Weighting mahalanobis distance described in the step (4) is:

$d_{\mathrm{forecast}}^2=[y-\stackrel{\‾}{x}]{\mathrm{WC}}_X^{-1}W{[y-\stackrel{\‾}{x}]}^{\′},$

Wherein, x _iBe the concentrated i eigenvectors of proper vector,

Be the center of gravity of matrix X,

Inverse matrix for the covariance matrix of matrix X;

The center of gravity of matrix X

For:

$\stackrel{\‾}{x}=\frac{1}{m}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i;$

Covariance matrix C _XFor:

$C_X=\frac{1}{m-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[x_i-\stackrel{\‾}{x}]{[x_i-\stackrel{\‾}{x}]}^{\′};$

Weight matrix W is:

$W=\left[\begin{array}{cccc}{w}_1,& 0,& ...& 0\\ 0,& w_2& ...& 0\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ 0,& 0& ...& w_m\end{array}\right].$

4. the analog circuit fault Forecasting Methodology based on autoregressive moving average according to claim 3 is characterized in that, the irrelevance described in the step (5) is converted to rate of breakdown and is:

Rate of breakdown p is:

Wherein, d _MaxMahalanobis distance maximal value in the non-fault range of tolerable variance.

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