CN115495924A - MOSFET service life prediction method based on ARIMA model - Google Patents
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Abstract
The invention relates to the field of power electronic circuits, in particular to an ARIMA model-based MOSFET service life prediction method, which comprises the following specific steps: s1, a time sequence to be analyzed; s2, checking stability; s3, automatically selecting model parameters; s4, residual error detection; s5, testing and evaluating a prediction model; s6, a MOSFET service life prediction model; the invention collects characteristic parameter on-resistance R closely related to the service life of the power MOSFET through the MOSFET power cycle test platform ds(on) Inspection by using ADFDifferential method for MOSFET characteristic parameter on-resistance R ds(on) And carrying out stabilization processing on the original data, carrying out parameter estimation by combining an autocorrelation function ACF and a partial autocorrelation function PACF, and finally constructing an ARIMA model to realize the prediction of the residual service life of the MOSFET.
Description
Technical Field
The invention relates to the field of power electronic circuits, in particular to a MOSFET service life prediction method based on an ARIMA model.
Background
The power electronic circuit is widely applied to the fields of industrial control, aerospace, military and the like, and the reliability of the MOSFET serving as a core power electronic device for bearing power conversion and control influences the safety of the whole power electronic system. If the health state of the MOSFET can be evaluated, the residual service life of the MOSFET is predicted, and the MOSFET is timely repaired or replaced, the reliability of a power electronic system is greatly improved. Therefore, power electronic device life prediction techniques are increasingly gaining attention.
The residual service life prediction of the power MOSFET is influenced by a plurality of external factors, mainly including environmental factors and device operating condition factors, and the influence of the factors is not negligible for the residual service life prediction of the MOSFET.
For example, in the method for predicting the inflow of industrial sewage based on the ARIMA model, which is disclosed by Chinese patent application No. 108564229A, the autocorrelation coefficient and the partial autocorrelation coefficient of the calculated stationary data are adopted to initially select the p and q values, then the AIC information criterion is adopted to optimize the p and q values, the initial determination of the model parameters according to the calculated autocorrelation coefficient and the partial autocorrelation coefficient is obtained through 'truncation' and 'tailing' in a correlation diagram, and the judgment is subjective. Generally, the p and q values determined by this method are large. The akage information criterion AIC is to find a model that can best interpret data but contains the least free parameters, so the complexity of the model can be reduced by the akage information criterion, which helps to reduce overfitting. If the initial p, q are too small, the model optimized by the akage information criterion AIC may not be optimal.
Disclosure of Invention
In order to solve the problems, the invention provides a MOSFET service life prediction method based on an ARIMA model.
The MOSFET service life prediction method based on the ARIMA model comprises the following specific steps:
s1, time series to be analyzed: characteristic parameter on-resistance R extracted through MOSFET reliability experiment platform and used for representing service life of device ds（on) Before model prediction, the original data is detected to eliminate obvious abnormalityAnd obtaining a null value to obtain a time sequence to be analyzed;
s2, stability test: on the basis of predicting the residual service life of the MOSFET by using an ARIMA model, if the time sequence of the acquired data is a stable sequence, the next step can be carried out, and otherwise, the sequence data is subjected to differential processing;
s3, automatic selection of model parameters: the model parameters comprise three parameters, namely a d value, a p value and a q value, the d value can be obtained through the step S2, the p value and the q value are obtained through the information quantity criterion AIC and the Bayesian information criterion BIC based on the Chichi pool, and the optimal p value and q value can be obtained through the maximum p value and the maximum q value of the input signal and the difference order d, namely p =5 and q =0;
s4, residual error detection: checking the first-order autocorrelation of the residual error by Durbin-Watson;
s5, testing and evaluating a prediction model:
a. single step prediction: testing the model by taking the on-resistance as a health index in a single-step prediction mode;
b. multi-step prediction: setting a threshold value according to the relevant standards of electronic devices and expert experience by taking the on-resistance as a health index, and recording the real residual service life as RealRUL;
s6, a MOSFET service life prediction model: the remaining life of the MOSFET is known and can be evaluated, and if only the historical data of the stage exists, the time required for reaching the threshold can be predicted according to the size of the threshold, as described in step S5 b.
In step S1, the specific extraction method of the MOSFET reliability test platform is as follows: the experiment platform is positioned in the thermostat and can simulate the actual working environment condition of the device; simulating the actual working condition through power circulation, and extracting the on-resistance R on the basis ds（on) And establishing a reliable ARIMA model as life prediction data.
In step S2, the ARIMA model is a model that is created by converting the non-stationary time series into the stationary time series and then regressing the dependent variable only for its lag value and the current value and the lag value of the random error term, and the expression is:
wherein phi is an AR coefficient, and theta is an MA coefficient;
the time series model, namely ARIMA, requires three main parameters, namely, the order p of an autoregressive model, the order q of a moving average model and the differential time d when the time series presents stable autocorrelation;
ARIMA model:
the autoregressive process, denoted as AR (p), can be expressed as:
x t ＝φ 1 x t-1 +φ 2 x t-2 +…+φ p x t-p +u t (2)
wherein phi i Is a regression parameter, u t Is a white noise process, and the autoregressive process can be interpreted as being composed of x t P previous weights of and u t Adding the components together to obtain a product;
the carry-over hysteresis operator can be expressed as:
(1-φ 1 L-φ 2 L 2 -…-φ p L p )x t ＝Φ(L)x t ＝u t (3)
in the formula, L is only a symbol instead of operation, and has no practical significance, and it should be stationary when connected with the regression model, and when the absolute values of all roots of the characteristic equation Φ (L) =0 are greater than 1, the process is a stationary process, and the mathematical expression is as follows:
Φ(L)＝1-φ 1 L-…-φ p L p ＝(1-G 1 L)(1-G 2 L)…(1-G p L) (4)
in the formula (I), the compound is shown in the specification,
for roots of phi (L) =0, replace x t And u t The expression mode of the relationship includes:
thus, x t Condition of stationarity phi (L) -1 Must converge, i.e. | G i If 1, if phi (L) -1 Divergence, calculated x t Will change over time, does not meet the smooth basic idea,
moving average model:
MA is a moving average process, denoted as MA (q), and the q-order average moving process can be expressed as:
x t ＝u t +θ 1 u t-1 +θ 2 u t-2 +…+θ q u t-q (6)
wherein, theta i Is a regression parameter, u t Is a white noise process, x t Is u t And u t Q lagged terms, the substitution lagged operator can be written as:
x t ＝(1+θ 1 L+θ 2 L 2 +…+θ q L q )u t (7)
the abbreviation is:
x t ＝Θ(L)u t (8)
the moving average process and the autoregressive process have different emphasis, and the moving regression process mainly focuses on the reversibility of the process:
θ(L)＝(1+θ 1 L+θ 2 L 2 +…+θ a L q )＝0 (9)
in the definition, the moving average process has the reversibility condition that the absolute value of all roots of formula (9) is greater than 1, the conversion form is:
Θ(L) -1 x t ＝u t (10)
is provided with
For the solution of the eigen equation, Θ (L) can be expressed as:
Θ(L)＝(1-H 1 L)(1-H 2 L)…(1-H q L) (11)
namely:
to ensure that the MA (q) process can be converted into an infinite order autoregressive process, i.e., the condition that MA (q) has reversibility is θ (L) -1 Convergence, if theta (L) -1 Divergence, x t Will also diverge, lose stationarity, Θ (L) -1 Convergence must have | H j I < 1 because the solution to zero for equation (11) is L j ＝1/H j To make L j Outside the unit circle, |1/H j | H is greater than 1, so j |＜1，
Autoregressive moving average model:
a random process contains d unit roots, and then it can be transformed into a stable autoregressive moving average process after d differences, considering the model:
Φ(L)D d y t ＝Θ(L)u t (13)
wherein D is d y t Denotes y t D times of score checking to obtain a stable process, wherein phi (L) and theta (L) are respectively an autoregressive operator of the stable process and a moving average operator of the stable process, and x is taken t ＝D d y t Then the model can be expressed as:
Φ(L)x t ＝θ(L)u t (14)
in the step S2, the stability of data is checked by adopting the ADF single piece, and when the ADF check is not 0, the data passes the check; if the ADF inspection result is 0, carrying out differential processing on the ADF inspection result until the ADF inspection result is not 0; the first order difference of the raw data is a smooth sequence, i.e. d =1, analyzed by matlab program.
In the step S4, a judgment is made according to the value of the test statistic d, since d is approximately equal to 2 (1- ρ), the closer the statistic d is to 2, the better the value is, no problem exists between 1 and 3, and less than 1 indicates that the residual error has autocorrelation, if the DW test is not passed, the model needs to be modified or the data needs to be processed, and the DW0 test result in matlab is 1.51.
In step S5, in step a, 201 data are predicted by using the first 200 data of the data, and 202 data are predicted by using the first 201 data until the end, and the prediction performance of the model is evaluated by using the relative error and the absolute error.
In step S5, performing multi-step prediction by a data interception method, that is, performing prediction by using different ratios of historical data, to obtain a predicted residual life as estRUL, where an absolute Error is calculated as Error = rerul-estRUL, and a relative Error RA = I rerul-estRUL I/rerul 100%.
The beneficial effects of the invention are: the invention collects the characteristic parameter on-resistance R closely related to the service life of the power MOSFET through the MOSFET power cycle test platform ds（on) The characteristic parameter on-resistance R of the MOSFET is detected and differentiated by adopting an ADF single-element method ds（on) And carrying out stabilization processing on the original data, carrying out parameter estimation by combining an autocorrelation function ACF and a partial autocorrelation function ACF, and finally constructing an ARIMA model to realize the prediction of the residual service life of the MOSFET.
Drawings
The invention is further illustrated by the following examples in conjunction with the drawings.
FIG. 1 is a flow chart of ARIMA model-based prediction according to the present invention;
FIG. 2 is a diagram of normalized residuals for the ARIMA model residual test of the present invention;
FIG. 3 is a histogram of normalized residuals for the ARIMA model residual test of the present invention;
FIG. 4 is a schematic diagram of the autocorrelation of the residuals of the ARIMA model residual test of the present invention;
FIG. 5 is a schematic diagram of the partial autocorrelation of the residuals of the ARIMA model residual test of the present invention;
FIG. 6 is a sample data-normal diagram for ARIMA model residual test of the present invention;
FIG. 7 is a diagram illustrating the single-step prediction results of the ARIMA model of the present invention;
FIG. 8 is a first schematic diagram of the single step prediction error of the ARIMA model of the present invention;
FIG. 9 is a diagram illustrating a single step prediction error of the ARIMA model of the present invention;
FIG. 10 is a schematic of the lifetime prediction of the ARIMA model of the present invention.
Detailed Description
The present invention will be further described in order to make the technical means, the creation characteristics, the achievement purposes and the effects of the present invention easy to understand.
As shown in fig. 1 to 10, the method for predicting the lifetime of a MOSFET based on an ARIMA model includes the following steps:
s1, time series to be analyzed: characteristic parameter on-resistance R extracted through MOSFET reliability experiment platform and used for representing service life of device ds（on) Before model prediction is carried out, original data are detected, obvious abnormity and null values are removed, and a time sequence to be analyzed is obtained;
s2, stability testing: on the basis of predicting the residual service life of the MOSFET by using an ARIMA model, if the time sequence of the acquired data is a stable sequence, the next step can be carried out, and otherwise, the sequence data is subjected to differential processing;
s3, automatic selection of model parameters: the model parameters comprise three parameters, namely a d value, a p value and a q value, the d value can be obtained through the step S2, the p value and the q value are obtained through the Chichi information content criterion AIC and the Bayesian information criterion BIC, and the optimal p value and q value can be obtained through the maximum p value and the maximum q value of the input signal and the difference order d, namely p =5 and q =0;
s4, residual error detection: checking the first-order autocorrelation of the residual error by Durbin-Watson;
s5, testing and evaluating a prediction model:
a. single step prediction: testing the model by taking the on-resistance as a health index in a single-step prediction mode;
b. multi-step prediction: setting a threshold value according to the relevant standards of electronic devices and expert experience by taking the on-resistance as a health index, and recording the real residual service life as RealRUL;
s6, a MOSFET service life prediction model: the remaining life of the MOSFET is known and can be evaluated, and if only the historical data of the stage exists, the time required for reaching the threshold can be predicted according to the size of the threshold, as described in step S5 b.
The invention collects characteristic parameter on-resistance R closely related to the service life of the power MOSFET through the MOSFET power cycle test platform ds(on) The characteristic parameter on-resistance R of the MOSFET is detected by adopting an ADF single element and a difference method ds(on) And (3) carrying out stabilization processing on the original data, carrying out parameter estimation by combining an autocorrelation function ACF and a partial autocorrelation function PACF, and finally constructing an ARIMA model to realize the prediction of the residual service life of the MOSFET.
The specific description related to the technical terms in the text is as follows:
MOSFET: metal-oxide semiconductor field effect transistor
AR: autoregressive model
MA: a moving average model.
ARIMA: difference integration moving average autoregressive model
ACF: auto-correlation function
PACF: partial autocorrelation function
Durbin-Watson test: dubin Watson test
ADF: and (4) unit root testing.
Fig. 2 is a visualization of a residual signal, the value of which fluctuates around the value 0, and fig. 3 is a normal distribution thereof, which substantially conforms to the normal distribution.
Fig. 4 and 5 are an autocorrelation graph and a partial autocorrelation graph of a residual signal, where if the residual signal is ideal white noise, except that the autocorrelation coefficient of the 0 th order is 1, the autocorrelation coefficients of the k-order samples of other delays are all 0, and actually, due to the existence of random disturbance, the autocorrelation coefficients are not strictly equal to 0, and the values fluctuate at the 0 value, and the best effect is that the point mean value is inside the shadow except the 0 th order.
Fig. 6 is a qq diagram commonly used for verifying whether data obeys normal distribution, and if the residual signal is a white noise sequence, the normal distribution is a straight line, i.e., as shown by a dotted line in fig. 6, and it can be known from fig. 6 that the result approximately conforms to white noise.
The single step prediction result shown in fig. 7 is obtained by taking the on-resistance as the health indicator, calculating the average value at intervals of one minute, and predicting 201 data by the first 200 data, predicting 202 data by the first 201 data, and going to the end.
The figure 8 results show that the single step prediction absolute error is less than 0.2 ohm.
The figure 9 results show that the relative error of the single step prediction is 0.0041 ohm.
In the figure 10, an early warning value of 0.27 is set based on the life prediction curve of the amama, and the model is verified by adopting a data interception method corresponding to the residual life of 669 minutes.
In step S1, the specific extraction method of the MOSFET reliability test platform is as follows: the experiment platform is positioned in the thermostat and can simulate the actual working environment condition of the device; simulating the actual working condition through power circulation, and extracting the on-resistance R on the basis ds（on) And establishing a reliable ARIMA model as life prediction data.
In step S2, the ARIMA model is a model that is created by converting the non-stationary time series into the stationary time series and then regressing the dependent variable only for its lag value and the current value and the lag value of the random error term, and the expression is:
wherein phi is an AR coefficient, and theta is an MA coefficient;
the time series model, namely ARIMA, requires three main parameters, namely, the order p of an autoregressive model, the order q of a moving average model and the differential time d when the time series presents stable autocorrelation;
an autoregressive model:
the autoregressive process, denoted as AR (p), can be expressed as:
x t ＝φ 1 x t-1 +φ 2 x t-2 +…+φ p x t-p +u t (2)
wherein phi i Is a regression parameter, u t Is a white noise process, and the autoregressive process can be interpreted as being composed of x t P previous weights of and u t Adding the two components together;
the carry-over hysteresis operator can be expressed as:
(1-φ 1 L-φ 2 L 2 -…-φ p L p )x t ＝Φ(L)x t ＝u t (3)
in the formula, L is only a symbol instead of operation, and has no practical significance, and it should be stationary when connected with the regression model, and when the absolute values of all roots of the characteristic equation Φ (L) =0 are greater than 1, the process is a stationary process, and the mathematical expression is as follows:
Φ(L)＝1-φ 1 L-…-φ p L p ＝((1-G 1 L)(1-G ２ L)…(1-G p L) (4)
in the formula (I), the compound is shown in the specification,
for the root of phi (L) =0, replace x t And u t The expression mode of the relationship includes:
thus, x t Condition of stationarity phi (L) -1 Must converge, i.e. | G i If 1, if phi (L) -1 Divergence, calculated x t Will change over time, does not meet the smooth basic idea,
moving average model:
MA is a moving average process, denoted as MA (q), and the q-th order average moving process can be expressed as:
x t ＝u t +θ 1 u t-1 +θ 2 u t-2 +…+θ q u t-q (6)
wherein, theta i Is a regression parameter, u t Is a white noise process, x t Is u t And u t The weighted sum of q lag terms of (a), the substitution of the lag operator can be written as:
x t ＝(1+θ 1 L+θ 2 L 2 +…+θ q L q )u t (7)
the abbreviation is:
x t ＝Θ(L)u t (8)
the moving average process and the autoregressive process are different in emphasis, and the moving regression process mainly focuses on the reversibility of the process:
Θ(L)＝(1+θ 1 L+θ 2 L 2 +…+θ a L q )＝0 (9)
in the definition, the moving average process has the reversibility condition that the absolute value of all roots of formula (9) is greater than 1, the conversion form is:
θ(L) -1 x t ＝u t (10)
is provided with
For the solution of the characteristic equation, θ (L) can be expressed as:
θ(L)＝(1-H 1 L)(1-H 2 L)...(1-H q L) (11)
namely:
to ensure that the MA (q) process can be converted into an infinite order autoregressive process, i.e., the condition that MA (q) has reversibility is Θ (L) -1 Convergence, if Θ (L) -1 Divergence, x t Will also diverge, lose stationarity, Θ (L) -1 Convergence must have | H j I < 1 because the solution to zero for equation (11) is L j ＝1/H j To make L i Outside the unit circle, |1/H j | H is greater than 1, so j |＜1，
ARIMA model:
a random process contains d unit roots, and then it can be transformed into a stable autoregressive moving average process after d differences, considering the model:
Φ(L)D d y t ＝θ(L)u t (13)
wherein D is d y t Denotes y t D times of score checking and stabilizing process, wherein phi (L) and theta (L) are respectively an autoregressive operator of the stabilizing process and a moving average operator of the stabilizing process, and x is taken t ＝D d y t Then the model can be expressed as:
Φ(L)x t ＝θ(L)u t (14)
in step S2, the on-resistance R ds（on) The method is a random variable depending on time t, the random variable is related to the residual service life of the MOSFET, the stability of data is checked by adopting the ADF (automatic frequency planning) singly, and when the ADF is not checked to be 0, the verification is passed; if the ADF inspection result is 0, carrying out differential processing on the ADF inspection result until the ADF inspection result is not 0; the first order difference of the raw data is a smooth sequence, i.e. d =1, analyzed by matlab program.
In step S4, a residual error check is also required to ensure that the determined order is appropriate. The residual error is the residual signal obtained by subtracting the signal fitted by the model from the original signal, if the residual error is in random normal distribution and is not autocorrelation, the residual error is a section of white noise signal, namely useful signals are extracted into the ARMA model, judgment is carried out according to a test statistic d value, as d is approximately equal to 2 (1-rho), the closer the statistic value is, the better the statistic value is, no problem exists between 1 and 3, if the statistic value is less than 1, the autocorrelation exists in the residual error, if the DW test is not passed, the model needs to be modified or data needs to be processed, and the test result of DWO in mat lab is 1.51.
In step S5, in step a, 201 data are predicted from the first 200 data of the data, and 202 data are predicted from the first 201 data until the end, and the prediction performance of the model is evaluated by using the relative error and the absolute error.
In step S5, performing multi-step prediction by a data interception method, that is, performing prediction by using different ratios of historical data, to obtain a predicted residual life as estRUL, where an absolute Error is calculated as Error = rerul-estRUL, and a relative Error RA = I rerul-estRUL I/rerul 100%.
As shown in fig. 10, the normalized residuals are obtained by checking whether the residuals are approximately normally distributed, and the ideal residuals are approximately normally distributed; the ideal result of the autocorrelation and partial autocorrelation of the residual should be that there are no points in the graph beyond the blue line; the graph is checked to see if the residuals are close to being too positive distributed, and ideally the midpoint should be close to the line.
The correlation was checked by Durbin-Watson. The Durbin-Watson test, also known as DW test, is used to test the first order autocorrelation of the residual in regression analysis, especially for time series data, assuming the residual is e t Correlation equation of each residual using e t ＝ρe t-1 +v t And the original hypothesis of the test is as follows: ρ =0, alternative assumptions: ρ ≠ 0, test statistics:
since d is approximately equal to 2 (1- ρ), the closer the statistical value is to 2, the better, generally between 1 and 3, indicating no problem, and less than 1 indicating that the residual has autocorrelation. If the DW check is not passed, the model needs to be modified or the data needs to be processed. The test by DWO in matlab results in 1.51.
And (3) life prediction:
the average value of the on-resistance is calculated at intervals of one minute, and the first 200 data of the data are used for predicting 201 data, the first 201 data are used for predicting 202 data, and the average value is calculated till the end. Absolute error is less than 0.02 Ω, total error Terror =2.3080, average error Merror =0.0041.
For each experiment, the predicted time (tP) and the percentage of this predicted time in the experiment, the true remaining life RealRUL, the estimated remaining life is noted estRUL, and the absolute error is calculated as:
Error＝ReaRUL-estRUL (16)
relative error:
RA＝I RealRUL-estRUL I/RealRUL*100％ (17)
and setting an early warning value of 0.27, corresponding to the service life of 669 minutes, and verifying the model by adopting a data interception method.
Based on the service life prediction of the ARIMA model, the data can be found to have good head-to-tail prediction effect; the middle part leads to poorer life prediction results because the device degradation trend is faster, and in general, the ARIMA model is used for predicting the short-term residual service life of the MOSFET with higher accuracy.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. The MOSFET service life prediction method based on the ARIMA model is characterized in that: the method comprises the following specific steps:
s1, time sequence to be analyzed: characteristic parameter on-resistance R extracted through MOSFET reliability experiment platform and used for representing service life of device ds(on) Before model prediction is carried out, original data are detected, obvious abnormity and null values are removed, and a time sequence to be analyzed is obtained;
s2, stability testing: on the basis of predicting the residual service life of the MOSFET by using an ARIMA model, if the time sequence of the acquired data is a stable sequence, the next step can be carried out, and otherwise, the sequence data is subjected to differential processing;
s3, automatic selection of model parameters: the model parameters comprise three parameters, namely a d value, a p value and a q value, the d value can be obtained through the step S2, the p value and the q value are obtained through the Chichi information content criterion AIC and the Bayesian information criterion BIC, and the optimal p value and q value can be obtained through the maximum p value and the maximum q value of the input signal and the difference order d, namely p =5 and q =0;
s4, residual error detection: checking the first-order autocorrelation of the residual error by Durbin-Watson;
s5, testing and evaluating a prediction model:
a. single step prediction: testing the model by adopting a single-step prediction mode by taking the on-resistance as a health index;
b. multi-step prediction: setting a threshold value according to the relevant standards of electronic devices and expert experience by taking the on-resistance as a health index, and recording the real residual service life as RealRUL;
s6, a MOSFET service life prediction model: the remaining life of the MOSFET is known, the remaining life can be evaluated, and if only the historical data of the stage exists, the time required for reaching the threshold can be predicted according to the size of the threshold, as described in step S5 b.
2. A MOSFET lifetime prediction method based on an ARIMA model according to claim 1, characterized in that: in the step S1, a specific extraction method of the MOSFET reliability experiment platform is as follows: the experiment platform is positioned in the thermostat and can simulate the actual working environment condition of the device; simulating the actual working condition through power circulation, and extracting the on-resistance R on the basis ds(on) As life prediction data, a reliable ARIMA model is established.
3. The ARIMA model based MOSFET life prediction method of claim 1 further comprising: in step S2, the ARIMA model is a model that is created by converting the non-stationary time series into the stationary time series and then regressing the dependent variable only for its lag value and the current value and the lag value of the random error term, and the expression is:
wherein phi is an AR coefficient, and theta is an MA coefficient;
the time sequence model, namely ARIMA, needs three main parameters, namely the order p of an autoregressive model, the order q of a moving average MA model and the differential time d when the time sequence presents stable autocorrelation;
autoregressive model AR:
the autoregressive process, denoted as AR (p), can be expressed as:
x t ＝φ 1 x t-1 +φ 2 x t-2 +…+φ p x t-p +u t (2)
wherein phi i Is a regression parameter, u t Is a white noise process, and the autoregressive process can be interpreted as being composed of x t P previous weights of and u t Adding the components together to obtain a product;
the carry-over hysteresis operator can be expressed as:
(1-φ 1 L-φ 2 L 2 -…-φ p L p )x t ＝Φ(L)x t ＝u t (3)
in the formula, L is only a symbol instead of operation, and has no practical significance, and it should be stationary when connected with the regression model, and when the absolute values of all roots of the characteristic equation Φ (L) =0 are greater than 1, the process is a stationary process, and the mathematical expression is as follows:
Φ(L)＝1-φ 1 L-…-φ p L p ＝(1-G 1 L)(1-G 2 L)...(1-G p L) (4)
in the formula (I), the compound is shown in the specification,
for roots of phi (L) =0, replace x t And u t The expression mode of the relationship includes:
thus, x t With stability phi (L) -1 Must converge, i.e. | G i If 1, if phi (L) -1 Divergence, calculated x t Will change over time, will not meet the smooth basic idea,
moving average model:
MA is a moving average process, denoted as MA (q), and the q-order average moving process can be expressed as:
x t ＝u t +θ 1 u t-1 +θ 2 u t-2 +…+θ q u t-q (6)
wherein, theta i Is a regression parameter, u t Is a white noise process, x t Is u t And u t The weighted sum of q lag terms of (a), the substitution of the lag operator can be written as:
x t ＝(1+θ 1 L+θ 2 L 2 +…+θ q L q )u t (7)
the abbreviation is:
x t ＝Θ(L)u t (8)
the moving average process and the autoregressive process have different emphasis, and the moving regression process mainly focuses on the reversibility of the process:
Θ(L)＝(1+θ 1 L+θ 2 L 2 +…+θ a L q )＝0 (9)
in the definition, the moving average process has the reversibility condition that the absolute value of all roots of formula (9) is greater than 1, the conversion form is:
θ(L) -1 x t ＝u t (10)
is provided with
For the solution of the characteristic equation, θ (L) can be expressed as:
θ(L)＝(1-H 1 L)(1-H 2 L)...(1-H q L) (11)
namely:
to ensure that the MA (q) process can be converted into an infinite order autoregressive process, i.e., the condition that MA (q) has reversibility is Θ (L) -1 Convergence, if theta (L) -1 Divergence, x t Will also diverge, lose stationarity, Θ (L) -1 Convergence must have | H j I < 1 because the solution to zero for equation (11) is L j ＝1/H j To make L i Outside the unit circle, |1/H j | H is greater than 1, so | H is required j |＜1，
ARIMA model:
a random process contains d unit roots, and then it can be transformed into a stable autoregressive moving average process after d differences, considering the model:
Φ(L)D d y t ＝θ(L)u t (13)
wherein D is d y t Denotes y t D times of score checking and stabilizing process, phi (L) and theta (L) are respectively an autoregressive operator of the stabilizing process and a moving average operator of the stabilizing process, and x is taken t ＝D d y t Then the model can be expressed as:
Φ(L)x t ＝Θ(L)u t (14)。
4. a MOSFET lifetime prediction method based on ARIMA model according to claim 3, characterized in that: in the step S2, the stability of data is checked by adopting an ADF single piece, and when the ADF check is not 0, the data passes the check; if the ADF inspection result is 0, carrying out differential processing on the ADF inspection result until the ADF inspection result is not 0; the first order difference of the raw data is a smooth sequence, i.e. d =1, analyzed by matlab program.
5. A MOSFET lifetime prediction method based on an ARIMA model according to claim 1, characterized in that: in the step S4, a judgment is made according to the value of the test statistic d, since d is approximately equal to 2 (1- ρ), the closer the statistic value is to 2, the better the statistic value is, no problem exists between 1 and 3, and the smaller the statistic value is, the residual error has autocorrelation, if DW test is not passed, the model needs to be modified or data needs to be processed, and the test result of DW in matlab is 1.51.
6. The ARIMA model based MOSFET life prediction method of claim 1 further comprising: in step S5, in step a, 201 data are predicted from the first 200 data of the data, and 202 data are predicted from the first 201 data until the end, and the prediction performance of the model is evaluated by using the relative error and the absolute error.
7. The ARIMA model based MOSFET life prediction method of claim 1 further comprising: in the step S5 b, multi-step prediction is performed by a data interception method, that is, prediction is performed by using different ratios of historical data, and a predicted residual life is recorded as estRUL, an absolute Error is calculated as Error = rerul-estRUL, and a relative Error RA = i rerul-estRUL i/rerul is 100%.
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